Packed Towers: In Processing and Environmental Technology

Reinhard Billet

Packed Towers

VCH Packed Towers in Processing and Environmental Technology. Reinhard Billet Copyright © 1995 VCH Verlagsgesellschaft mbH, Weinheim ISBN: 3-527-28616-0

© VCH Verlagsgesellschaft mbH, D-69451 Weinheim, (Federal Republic of Germany), 1995 Distribution: VCH, P.O. Box 1011 61, D-69451 Weinheim (Federal Republic of Germany) Switzerland: VCH, P.O. Box, CH-4020 Basel (Switzerland) United Kingdom and Ireland: VCH, 8 Wellington Court, Cambridge CBl 1HZ (United Kingdom) USA and Canada: VCH, 220 East 23rd Street, New York, NY 10010-4606 (USA) Japan: VCH, Eikow Building, 10-9 Hongo 1-chome, Bunkyo-ku, Tokyo 113 (Japan) ISBN 3-527-28616-0

Reinhard Billet

Packed Towers in Processing and Environmental Technology

Translated by James W. FuUarton

VCH

Weinheim • New York • Basel • Cambridge • Tokyo

Professor Dr.-Ing. Reinhard Billet Institut fur Thermo- und Fluiddynamik Fakultat fiir Maschinenbau Ruhr-Universitat Bochum UniversitatsstraBe 150 D-44801 Bochum

This book was carefully produced. Nevertheless, the author, translator and publisher do not warrant the information contained therein to be free of errors. Readers are advised to keep in mind that statements, data, illustrations, procedural details or other items may inadvertently be inaccurate.

Published jointly by VCH Verlagsgesellschaft mbH, Weinheim (Federal Republic of Germany) VCH Publishers, Inc., New York, NY (USA)

Editorial Directors: Louise Elsam, Karin Sora Production Manager: Peter Biel

Library of Congress Card No. applied for. British Library Cataloguing-in-Publication Data: A catalogue record for this book is available from the British Library. Die Deutsche Bibliothek - CIP-Einheitsaufnahme Billet, Reinhard: Packed towers in processing and environmental technology/ Reinhard Billet. Transl. by James W. Fullarton. - 1. ed. Weinheim ; New York ; Basel; Cambridge ; Tokyo : VCH, 1995 ISBN 3-527-28616-0

© VCH Verlagsgesellschaft mbH, D-69451 Weinheim (Federal Republic of Germany), 1995 Printed on acid-free and low-chlorine paper All rights reserved (including those of translation into other languages). No part of this book may be reproduced in any form - by photoprinting, microfilm, or any other means - nor transmitted or translated into a machine language without written permission from the publishers. Registered names, trademarks, etc. used in this book, even when not specifically marked as such, are not to be considered unprotected by law. Composition: Hagedornsatz GmbH, D-68519 Viernheim Printing: Betzdruck GmbH, D-64219 Darmstadt Bookbinding: Industrie- und Verlagsbuchbinderei Heppenheim GmbH, D-64646 Heppenheim Printed in the Federal Republic of Germany

Preface In the chemical and allied industries, there is a continuously rising trend towards separation processes that are operated in packed columns with systematically stacked or randomly dumped beds. It was initiated by the 1973 oil crisis and the associated demand for saving fuel by optimum design and operation of the processes. Another factor that has contributed towards the widespread adoption of packed beds in industry has been the increasing severity of ecological legislation. Since they can be operated under more moderate conditions, packed columns are superior to plate columns in coping with the demands of saving energy and protecting the environment. Thus packed columns can offer the following advantages: - They allow lower energy consumption in separation processes that entail a large number of theoretical stages. - They can more readily satisfy the requirements for the economic use of heat pumps. - They permit thermally instable mixtures to be separated at lower temperatures at the foot of the column and can thus minimize or even completely avoid products of decomposition or polymerization reactions that may be responsible for pollution. - In absorbers, particularly those for off-gas scrubbing, they require compressors of lower power ratings than those installed in plate columns. Beds of packing are also being used to an increasing extent for direct heat transfer between liquids and gases (or vapours) and for liquid-liquid extraction. The trend runs parallel to striking improvements in the design of traditional packing and has also led to the development of completely new packing geometries. However, the results obtained in process engineering studies did not always agree satisfactorily with the traditional relationships given in the literature. Consequently, research work had to be directed at devising new correlations and models for the efficiency and operating characteristics of packed columns with the aim of developing physically well-founded design methods that are applicable to all types of packing used in industry. The book "Packed Towers in Processing and Environmental Technology" is intended as a contribution towards this aim. The reliability of the methods presented here has been demonstrated by results gained in comprehensive experiments that embraced more than sixty types of metallic, ceramic, and plastics packing of various geometries and dimensions and were performed on systems that covered a wide range of physical properties in the liquid and the gas or vapour phases. These pilot-plant experiments were carried out over a period of more than 20 years in the course of the author's activities in research and industry. The results thus obtained provided a sound basis upon which a theoretical model could be developed to describe the hydrodynamics and mass transfer in packed columns. The experiments also served to verify the scientific accuracy of the models and thus to ensure close agreement between theory and practice. The author has presented papers on the subject at meetings held by various engineering institutions, including the VDI, EFCE and AIChE, and at the ACHEMA, CHISA and ACHEMASIA fairs. He has also held seminars on packed columns, e.g. in the Conicet Institute, Santa Fe and Bahia Blanca, Argentina; at the Glitsch Symposium in Dallas, Texas, USA; the Korean Institute of Energy Research in Taejon, South Korea; the Petrobras in Rio

VI

Preface

de Janeiro; the Belo Horizonte University in Brazil, and the Tientsin University in China. The book has been written in response to many requests for a review of the engineering aspects in packed columns. The author wishes to take this opportunity of expressing his most sincere thanks to all those who assisted him in the experimental work, to Dr. M. Schultes for his valuable cooperation in evaluating the examples, to M. Ernst for her commitment in typing the German manuscript, to Th. Cipa for his assistance in proof-reading, and - in particular - to J. W. Fullarton for translating the work into English. Bochum, January 1994

R. Billet

Biography Reinhard BILLET gained his Dipl.-Ing. (in 1953) and Dr.-Ing. (in 1957) degrees in Process and Chemical Engineering at the Technical University of Karlsruhe. From 1954-1960, he was a Scientific Assistant under Professor E. Kirschbaum at the Plant and Process Engineering Institute of Karlsruhe University. In 1960, he joined the staff of the BASF Chemical Engineering Research Department and was subsequently involved in plastics production, plant design, environmental protection, and industrial safety. In 1975, he was appointed Professor of Process Engineering and called to the Chair for Thermal Separation Processes; and 1992, to the Chair for Process and Environmental Engineering at the Ruhr-University of Bochum. During the period 1983/1984, he acted as the Dean of the Faculty of Mechanical Engineering. Professor Billet was awarded the Ring of Honour of the German Institute of Engineers (VDI) in 1964; and, in 1986, the Medal for Outstanding Merit, by the Technical University of Wroclaw. Most of his research work has been in the fields of evaporation, distillation, absorption, liquid-liquid extraction, and environmental engineering. He has written over 200 scientific articles, four university booklets, and three monographs in German. His book ,,Industrielle Destination" has been translated into English, Czechoslovakian, and Chinese; ,,Verdampfung und ihre technischen Anwendungen", into English and Chinese; and ,,Energieeinsparung bei thermischen Stofftrennverfahren", into Polish. The "Proceedings of the Packed Column Analysis and Design Seminar" is also available in Korean and Chinese. The results of his research work have been presented at national and international congresses and meetings. Professor Billet is a member of the VDI Panel of Experts on the thermal separation of gases and liquids and the European Federation of Chemical Engineering (EFCE) Working Party on Distillation, Absorption and Extraction. He is also a member of the New York Academy of Sciences.

Contents 1

Introduction

1

1.1 1.2 1.3 1.4

Fundamental operating characteristics of packed columns for gas-liquid systems Theoretical column efficiency 11 Energy consumption and number of theoretical stages 17 Height of bed determined from the HTU-NTU model 20

2

Types of packing

2.1 2.2 2.3

Packing dumped at random 24 Packing stacked in geometric patterns Geometric packing parameters 27

3

Experimental determination of packing performance

3.1 3.2 3.3 3.4

Pilot plants for testing gas-liquid systems Evaluation of measurements 31 Test systems 37 Experimental results 41

4

Fluid dynamics in countercurrent packed columns 73

4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10

Fluid-dynamics model 73 Resistance to flow 76 Loading conditions 82 Flooding conditions 84 Relationship between boundary loads 87 Pressure drop in packed columns 88 Liquid holdup in packed beds 96 Liquid entrainment at high loads 100 Phase inversion in packed beds 102 Relationship between loading and flood points

5

Mass transfer in countercurrent packed columns

5.1 5.2 5.3 5.4 5.5 5.6

Mass transfer in the liquid phase 119 Mass transfer in the vapour phase 121 Vapour-liquid phase boundary 124 Relationship between mass transfer and fluid dynamics 130 Mass transfer at high liquid loads 139 Mass transfer in absorbers accompanied by chemical reaction in the liquid phase

23 25

31

31

112

119

141

X

Contents

6

End effects in packed columns

147

6.1 6.2 6.3 6.4 6.5

Phenomenological description 147 Correlation of end effects 150 Experimental results 154 Column design and scale-up 157 Examples of scale-up 167

7

Liquid distribution at the inlets of packed columns

7.1 7.2 7.3 7.4 7.5 7.6

Theoretical considerations 171 Effect of inlet liquid distribution on the efficiency of packed columns Maximum packing efficiency in inlet zones 176 Effect of phase ratio on relative efficiency 183 Effect of height of packing on relative efficiency 185 Estimation of relative efficiency 185

8

Scale-up for end effects and phase distribution

8.1 8.2 8.3 8.4 8.5 8.6 8.7

Scale-up model 194 Inlet and end effects in industrial-scale plants identical to those in pilot plants 197 Inlet and end effects in industrial-scale plants different to those in pilot plants 198 Determination of the limiting number of liquid distributor outlets 199 Effect of phase maldistribution 206 Gas or vapour distribution 210 Effect of mass transfer coefficient on scale-up 212

9

Phase redistribution in columns

9.1 9.2 9.3

Estimation of optimum number of phase redistributors Costs relationships 219 Examples 225

10

Design of distributors

10.1 10.2

Fundamental design aspects and relationships Types of phase distributors 233

11

Overall evaluation of packing

11.1 11.2 11.3 11.4

Materials of construction 239 Capital investment 241 Evaluation for the separation of thermally unstable mixtures Evaluation in terms of minimum column volume 247

171 173

191

213 213

230 230

239

244

Contents

XI

11.5 11.6 11.7 11.8

Theoretical considerations in the design of column internals State of the art in the development of packing 255 Optimum area per unit volume in beds of packing 262 Limits to the further development of packing 270

12

Retrofitting columns by the installation of packing

12.1 12.2 12.3 12.4

Advantages of retrofitting 291 Potential for retrofitting with low-pressure-drop packing 296 Advantages of packing in steam rectification 302 Improvement in product purity caused by restricting the pressure drop in beds of packing 310

13

Applications for packing in liquid-liquid systems

13.1 13.2 13.3 13.4 13.5 13.6 13.7

General aspects 313 Experimental 314 Fluid dynamics of dispersed and continuous phases 318 Dispersed-phase holdup 318 Phase throughput 322 Mass transfer in the dispersed and continuous phases 324 Extraction efficiency, test results and derivation of model 327

14

Examples for the design of packed columns

14.1

Determination of the diameter of an off-gas absorption column with various types of packing 342 Design of a packed column for the rectification of an isobutane/n-butane mixture 344 Scaling up measurements performed in pilot plants 348 Design of an absorber for removing acetone from process air 350 Design of a desorber for removing carbon dioxide from process effluents 355 Determination of the difference between the theoretical and the real liquid holdup 360 Additional column height required to compensate maldistribution 361 Retrofitting a plate column with packing for steam distillation of crude oil 362 Reduction in height effected by redistributors 363 Advantages of geometrically arranged packing in fractionating fatty acids 364 Recovery of acetone from production effluents by liquid-liquid extraction 365

14.2 14.3 14.4 14.5 14.6 14.7 14.8 14.9 14.10 14.11

250

291

313

337

XII

Contents

15

Recent trends in packing technology

15.1 15.2 15.3

Fluidized beds of packing 369 Hydrodynamics of fluidized packed beds 370 Mass transfer in fluidized packed beds 370

References

Index

379

373

369

Key to symbols a a'

[m2/m3] [s/m]

ah aPh as

[m2/m3] [m2/m3] [m/s]

A Ah

[s/m] [m2] [m2] [m2] [s] [kmol/h];[kg/h] [kmol/m3] [DM/m3] [DM/m] [DM] [DM/m2] [DM]; [DM/m 3 [DM]

As B B c Cp CPs

Cr Cs

c Cc

ch cL CP

Cs Cv d dh dP ds D D D e E Ec Ev

fs fv fw

[m] [m] [m] [m] [DM/m] [m2/s] [kmol/h];[kg/h] [DM/m2]

[1/s]

total surface area per unit packed volume packing area per unit efficiency and per unit volumetric vapour flow rate hydraulic area of packing per unit volume of packed bed effective interfacial area per unit packed volume column shell area per unit efficiency and per unit volumetric vapour flow rate constant, specific for the packing cross-sectional area of an individual channel total area of packing free cross-sectional area constant, specific for the packing flow rate of bottom product concentration costs per unit volume of packing costs per unit height of column costs for one redistributor in a column of diameter ds costs per unit area of column shell costs; costs per unit volume of the packed column capital investment costs for a packed column packing constant to allow for liquid holdup packing constant to allow for mass transfer in liquid packing constant to allow for pressure drop costs of the packing to be evaluated in relation to those of a random bed of 50-mm Pall rings packing constant to allow for mass transfer in gas size of an element of packing hydraulic diameter particle diameter column diameter costs factor, specific for the material and method of production of the packing diffusion coefficient of transferring component flow rate of distillate (overhead product) relative efficiency, or energy parameter costs factor, specific for the material and method of construction of column shell column efficiency volumetric packing efficiency wall factor vapour load factor wetting factor

XIV

Key to symbols

[DM/m3]

costs factor, specific for the material and method of construction of column shell F [kmol/h];[kg/h] flow rate of feed [kg^m^V1] vapour capacity factor related to the free column cross-section Fv [m/s2] acceleration due to gravity g h [kJ/kmol] molar enthalpy Ah [kJ/kmol] molar condensation; evaporation enthalpy [m3/m3] liquid holdup hL H [m] effective height of fill of column packing [m] height of inlet zone in a bed of packing Ht [m] HTU height of a mass transfer unit [m] overall height of a mass transfer unit HTUO k [m/s] overall mass transfer coefficient K [DM s/m3] total costs, i.e. for the bed of packing and the column shell, per unit efficiency and per unit volumetric vapour flow rate Kp; Ks [DM s/m3] packing costs per unit efficiency and per unit volumetric vapour flow rate length of flow path for phase contact [m] L [kmol/h] flow rate of carrier liquid L [kmol/h] ;[kg/h] flow rate of liquid slope of equilibrium line myx;mYX - [kmol/kmol] M maldistribution nh number of flow channels number of theoretical stages corresponding a bed height H nt N number of separation units N packing density K3] NTU number of transfer units in a phase number of overall transfer units NTUO [bar];[mbar] pressure P Ap [mbar];[mmWG] pressure drop P [bar];[mbar] boiling pressure of a component liquid distribution coefficient [kJ/h] energy consumption Q film thickness s [m] s [m] thickness of the basic material, i.e. sheet, foil or fibre, of the packing elements S [kmol/h] flow rate of carrier steam t time [s] liquid phase residence time tL [s] T temperature [K] [m3m~2s~1] uL liquid load (also related to hour) uL [m/s] local liquid velocity Uy [m/s] superficial gas or vapour velocity Uy [m/s] average effective gas or vapour velocity v' volume of packing material per unit efficiency and volumetric gas [s] or vapour load

u

Key to symbols Vy

V V w w' X

X y Y Z

zh

[m3/(m3/s)] [kmol/h] [kmol/h];[kg/h] [kg/m3]

[kg nrV 1 ] [kmol/kmol] [kmol/kmol] [kmol/kmol] [kmol/kmol] [m~2]

[m-2]

specific column volume flow rate of carrier gas flow rate of gas or vapour specific gravity of packing packing weight per unit volumetric flow rate of gas or vapour and unit efficiency mole fraction in liquid phase molar load fraction of transfer component in liquid mole fraction in gas or vapour phase molar load fraction of transfer component in gas or vapour number of liquid distributor outlets number of flow channels per unit area of column cross-section

Greek symbols a CO.

8

[m/s] [m3/m3]

ri

[kg

V

Q

a T

Xy

[kg;kmol] [m2/s] [kg/m3] [kg/s2] [s] [N/m2]

relative volatility mass transfer coefficient void fraction of packing efficiency dynamic viscosity column efficiency stripping factor molecular mass; molar mass kinematic viscosity coefficient of resistance mass density surface tension duration of contact between the phases shear stress in gas flow diameter ratio flow parameter

Subscripts B C D e

F Fl L o P Ph

XV

bottom product continuous phase distillate (overhead product) effective feed flood point liquid surface pilot plant interface

ML

s S T V W

Key to symbols

film thickness; column shell loading point technical or industrial scale vapour or gas wetting

Dimensionless numbers Fo Fr Ma Re Sc We

Fourier number Froude number Marangoni number Reynolds number Schmidt number Weber number

1 Introduction The clamour for energy-saving techniques in almost all branches of industry has acted as a spur in the development of thermal separation equipment. The design and process engineering improvements that have ensued entail that feedstocks are subjected to less severe treatment and can thus be optimally exploited. They also entail production under ecologically favourable conditions (cf. Fig. 1.1). A typical example is provided by low-pressure-drop packing in the vacuum rectification of mixtures that are unstable to heat and that necessitate a large number of theoretical stages for their thermal separation. The attendant decrease in the total pressure drop and operation under vacuum ensure that the temperature at the bottom of the column is comparatively low. Hence, decomposition products that are detrimental to the environment can be largely avoided, i.e. atmospheric pollution is reduced and less residues have to be disposed of. Another advantage is that the reduction in the average column pressure brought about by vacuum operation increases the average relative volatility of the components in the mixture and thus reduces energy consumption. Low-pressure-drop, high-performance packing is an essential requirement in the economic design of an integrated separation plant, because it permits heat pumps to be installed and a number of columns to be linked together.

Fig. 1.1. Relationships established by separation techniques between energy consumption, processing and environmental protection Packed Towers in Processing and Environmental Technology. Reinhard Billet Copyright © 1995 VCH Verlagsgesellschaft mbH, Weinheim ISBN: 3-527-28616-0

2

1

Introduction

From this point of view, it is not surprising that packing designed to conserve energy has been the subject of many new developments on the part of equipment manufacturers. However, before any one particular type of packing can be selected for a given separation task, adequate knowledge must be available on the performance characteristics, e. g. the separation efficiency, the pressure drop, the liquid holdup, the capacity, and the costs. A physical model is required to describe the hydraulics and the mass transfer efficiency in a given separation column and thus to allow the main dimensions to be calculated and the process engineering performance to be predicted. The parameters that affect the design, the capacity, and the specific properties of the product and inlet streams must be known in order to devise the model, and the only means of acquiring these data is by experiment. Consequently, the aim of this book is to supplement the theoretical considerations by the results of relevant studies that were performed in the author's laboratories and pilot plants and were scaled up to meet practical requirements. It is known that packed columns, whether random or stacked, allow lower pressure drops per theoretical stage than plate columns and are thus better suited to meet demands on optimum energy consumption in thermal separation plants. The main applications for packed columns are the separation of vapour-liquid or gas-liquid systems, e.g. in rectification, absorption, and desorption. In many cases, they have also proved to be superior to conventional plate columns for liquid-liquid extraction processes. Greatest significance from the aspect of saving energy is attached to their use in rectification, a subject to which particular attention has been devoted in the course of this book. In future, these separation processes will not be confined to petroleum refineries and the chemical and allied industries. They will also be adopted on a wider scale in ecological engineering for purifying off-gas streams and for water treatment, and the demand for the necessary equipment, including packing, will grow accordingly. Rectification, absorption, desorption, and liquid-liquid extraction processes consist essentially of passing two countercurrent phases through a packed column (cf. Fig. 1.2). In rectification, the vapour produced in the distillation section of the column flows countercurrent to the liquid formed in a condenser. Contact between the two phases is thus established, with the result that the low-boiling component flows upwards and the high boiler accumulates at the bottom of the column. Physical absorption processes consist of mass transfer from the gas into the liquid phase, i. e. into a solvent that selectively absorbs the desired component from the gas stream. In desorption - often referred to as stripping - mass transfer proceeds in the opposite direction, i.e. from the liquid into the gas phase. In the extraction of a component from a mixture of liquids by means of a selective solvent, mass transfer takes place between two liquid phases. It is taken for granted here that the reader is already acquainted with these separation processes and their thermodynamic fundamentals together with the literature on the subject and the standard terminology. The scope of this book has therefore been restricted to a comprehensive treatment of packed-bed technology and its application to separation processes.

/. 1

Fundamental operating characteristics of packed columns for gas-liquid systems

Packed towers for continuous Rectification

Absorption Solvent I A (absorbent)J { b a s

Feed

Liquid = A Loaded feed : | gas

Extraction Feed j f Extract

*

Bottom product

Loaded solvent

- Feed Fig. 1.2.

Desorption

y

DesorbedTTcarrier liquid t t / 5 ™

-gas

— Auxiliary product

|f Raff mate ^ I Solvent

End product

Applications for packed columns in thermal separation processes

1.1 Fundamental operating characteristics of packed columns for gas-liquid systems The optimum choice of a packed column for a given separation task would be impossible without a sound knowledge of the characteristic parameters and physical quantities that permit process engineering evaluation and comparison. The gas or vapour load in a packed column is usually expressed by the capacity factor, which is given by Fy = Uy

(1-1)

where uv is the superficial velocity, o v is the density of the gas or vapour, and QL is the density of the liquid. At low or moderate pressures, QV is small compared to QL and can thus be neglected. Hence, the vapour capacity factor, which is often resorted to in practice as a measure of the dynamic load on the column, is the product of the superficial velocity uv and the square root of the vapour density, i.e. Fy = Uy \J~Qy~

(1-2)

1

Introduction

The maximum permissible value for the capacity factor also depends on a dimensionless flow parameter that allows for the ratio of the liquid to the vapour flow rate LIV and is given by (1-3) In practice, the capacity of packed columns is frequently described by the following function, which has to be determined by experiment: Fy

(1-4)

yfoL

A crucial factor in evaluating packed columns, especially those intended for vacuum rectification, is the resistance offered by the bed of packing to the flow of vapour. A major criterion in selecting packing for absorption processes in which gas is forced through the column by a compressor is the pressure drop Ap in the bed, because it largely governs the compressor rating. The pressure drop per unit height of bed Ap/H depends on the gas uv and liquid uL loads (cf. Fig. 1.3). It is usually expressed as a function of the capacity factor F v for a given liquid load uL or a given liquid-gas ratio, i.e. (1-5) Another factor of great importance in evaluating packed columns is the pressure drop per unit of separation efficiency, which is defined by the number of theoretical stages nt in rectification or by the number of transfer units NTU in absorption and desorption. A general term, i.e. the number of separation units N required for a given process, may be taken to cover both cases. Thus,

Gas or vapour

Liquid PT

Ap

Gas or vapour I

H=N T

? Liquid

Fig. 1.3.

Flowchart for a packed column

1.1

Fundamental operating characteristics of packed columns for gas-liquid systems

N = nt or N = NTU

5

(1-6)

The total pressure drop in the gas or vapour is given by

&P=PB-PT

where

(1-7)

pB is the pressure at the lower column inlet and pT is the pressure at the upper column outlet.

In analogy to Eqn (1-5), the total pressure drop per separation unit can be expressed as a function of the capacity factor for a given ratio LIV of the liquid to the vapour flow rate, i.e.

~ - = HFy)

(1-8)

The following relationship thus applies: ^

(1-9)

If the vapour pressure at the top of the column is kept constant during rectification, that at the bottom of the column - and thus the boiling point - become less as the pressure drop per unit efficiency for the specific bed of packing decreases. Low boiling points are an absolute necessity in the vacuum rectification of thermally instable mixtures. They also entail larger differences between the temperature of the heating medium and that of the mixture, i.e. more effective heat transfer. Moreover, if a large number of theoretical stages is required in a given vacuum rectification, a low pressure drop allows entire installations to be designed from the aspect of optimum energy consumption. The number of theoretical stages nt required to separate a binary feed with a molar flow rate F can be determined diagrammatically by the McCabe-Thiele method, which is based on the concept of an equilibrium stage, i.e. a stage in which the ascending vapour is in phase equilibrium with the descending liquid. An example of the corresponding diagram is shown in Fig. 1.4, in which x¥ is the mole fraction in the feed of the more volatile component that has to be concentrated to a mole fraction xD in the overhead product (distillate) with a molar flow rate D; and xB is the mole fraction of this volatile fraction that remains in the bottom product (molar flow rate B). The equilibrium curve is the locus of the points x, y. The two operating lines derived from material balance equations - BI for the stripping zone and DI for the enrichment zone - intersect at the point / on the g-line, which is the locus of all points of intersection of the two operating lines for any given feed stream. The number of theoretical stages nt is represented by the steps that link the equilibrium curve with the two operating lines between the points x B and xD. It is the sum of the number of stages in the enrichment zone ntez and the number in the stripping zone ntsz, i. e. nt = nt,ez + nt,sz

(1-10)

1

Introduction

Reflux condenser^

Number of theoretical stages n t Equilibrium curve Operating *i V

0

xB

xF xD Liquid mole fraction x

Fig. 1.4. Determination of the the number of theoretical stages in a continuous rectification column, taking a binary mixture as an example

If xF, xD and xB are given, nt depends on the phase equilibrium in the mixture, i. e. on the shape of the equilibrium curve for the binary system, and on the position of the two operating lines BI and DI. The position of the intersect / can be obtained from the material balance at the inlet cross-section of the column, i.e.

The factor / in this equation is a measure for the thermal state of the feed and is given by /=!-"

h'F-hF Ahv

(1-12)

where hF is the molar enthalpy of the feed at the inlet temperature, h'F is the molar enthalpy at the operating temperature in the inlet cross-section of the column, and Ahv is the molar condensation enthalpy of the vapour stream in the inlet cross-section. If the individual components of the mixture have roughly the same molar evaporation enthalpy, the molar flow rates of both the vapour and liquid will remain practically constant along the respective flow paths both above and below the inlet, i.e. in both the enrichment and stripping zones. In this case, the relationship between the vapour y and the liquid x mole fractions of the more volatile component in the enrichment zone is given by the following linear equation:

y = r + 1• x

+

r+ 1

(1-13)

1.1

Fundamental operating characteristics of packed columns for gas-liquid systems

7

where r is the ratio of the reflux flow rate L to the overhead product flow rate D, i.e. r=|-

d-14)

The corresponding equation for the stripping zone is

where b is the ratio of the flow rate of liquid L in the stripping zone to that of the bottom product B, i. e. b = -j

(1-16)

If the values for xF and / are given and those for xD and xB are specified, the operating lines for the enrichment and stripping zones in Fig. 1.4 can be easily plotted. Inserting x = 0 in Eqn (1-13) yields the value for y0 at the intercept with the axis of ordinates, i.e.

d-17) where xD is the mole fraction of the more volatile component in the overhead product. The reflux ratio r at the head of the column is a factor that greatly affects the economics of rectification. If the molar evaporation enthalpies for the low-boiling A/z, and the high-boiling Ahh components differ significantly, a linear relationship no longer exists between the mole fractions v and x of the more volatile component in the vapour and in the liquid respectively. In this case, allowance for the difference between Aht and Ahh is made by the expression K- —^— Ahh - Ahi

(1-18)

The equation for the enrichment zone is thus no longer linear, i.e.

r+1 y= r+1

^

r+1

#

The intercept >;0 with the axis of ordinates in this case is given by —

(1-20)

8

1

Introduction

Whether its position is higher or lower than the corresponding intercept formed by the linear relationship {cf. Eqn (1-17)} depends on which of the two components - the highboiler or the low-boiler - has the greater molar evaporation enthalpy. Likewise, the relationship for the stripping zone in the column is also nonlinear if the molar evaporation enthalpies of the components differ. In this case, the following equation applies: /

yA

*—r

(1 21)

"

where the parameter mI is given by xF-xB m, =

^

r,+f

^

(1-22)

the reflux ratio r7 at the inlet cross-section, by

=

and yt and xt are the coordinates of the intersect / (cf. Fig. 1.4). An alternative concept to the number of theoretical stages nt for the evaluation of separation efficiency is the number of transfer units NTU. If the molar flow rates for the liquid L and the vapour V are kept constant and there is no mixing in the axial direction, the NTU for steady-state operation can be expressed as follows in the terms of the concentration difference y* - y in the vapour (cf. Fig. 1.5): —£-

(1.24)

where y* is the phase equilibrium concentration of the more volatile component in the vapour in contact with the liquid of concentration x* at the phase boundary in any given horizontal cross-section of the column; and x and y are the fractions that correspond to the concentrations of the more volatile component in the bulk of the vapour and in the liquid respectively. It may often be assumed that the resistance to mass transfer in rectification is predominantly in the vapour phase, i. e. x —» x*. In this case, the surface mass transfer coefficient in the liquid phase is |3L —» °o and that in the vapour phase fV is identical to the overall mass transfer coefficient on the vapour side kov. Accordingly, NTUV = NTUOV. The height of a transfer unit is then defined by

1.1

Fundamental operating characteristics of packed columns for gas-liquid systems

HTUOV =

H NTUn

H

(1-25)

dy ye-y

If it is assumed that kov is constant over the height of the column in mass transfer controlled by the vapour phase, a mass balance yields HTUOV =

(1-26) ds kov aph

where aph is the phase contact area per unit column volume, ds is the column diameter, V is the molar flow rate of the vapour, and HTUOV is usually determined by experiment. Hence the following relationship exists between the number of theoretical stages per unit height nt/H and the height of a transfer unit HTUOV: V H

HTUn

(1-27)

\n[myxy-

(p v ) x * = x =k o v

"it y*dy x+dx

0&Z7/Z2 y

Liquid mole fraction x ^o

x0

J

a=-

Fig. 1.5. Determination of the number of transfer units by the two-film theory

10

1 Introduction

In other words, the number of transfer units in systems with a low relative volatility is given by (NTUov)a

= smal,

= n,

(1-28)

Likewise, the height of a transfer unit can be equated to the height equivalent of a theoretical stage, i.e. {HTUOy)

a

,

small

= HETS = —

(1-29)

The stripping factor X for a given section of the column is defined as the product of the mean slope myx of the equilibrium curve and the molar vapour/liquid ratio VIL, i. e. \ = myxj-

(1-30)

Once the height of a transfer unit HTUOV and the number of transfer units NTUOV are known, the height of the column required for the relevant separation process can be obtained from their product. Hence, cy

H = HTUQV

' NTUOV = HTUOV

^—

(1-31)

The figure thus derived is identical to that obtained from the number of theoretical stages nt and the separation efficiency ntIH for the packing concerned {cf. Eqn (1-27)}, i. e. H

=

An analogous analysis applies for mass transfer in the liquid phase. This procedure for the determination of column height is referred to in the literature as the HTU-NTU concept. It is applied in Chapters 3, 5 and 14. The efficiency, expressed as the number of separation units per unit height NIH, can be assessed graphically from its relationship to the column load or capacity factor, which can be written as NIH = i{Fv)

(1-33)

A knowledge of this function is essential in determining the load relationships for the pressure drop per unit height AplH {Eqn (1-5)} and the pressure drop per separation unit Ap/TV {Eqn (1-8)}. These relationships allow the column volume vv per unit of vapour flow rate and unit of separation efficiency to be determined in terms of the capacity factor /v{Eqn (1-34)} or the pressure drop per unit of separation efficiency ApIN {Eqn (1-35)}, i. e.

1.2

Theoretical column efficiency

11

vv=i(Fv)

(1-34)

vv=f(Ap/N)

(1-35)

The specific column volume vv is an important factor in determining the capital investment costs and is defined by

where H is the effective height of the column, N is the number of theoretical separation units, and uv is the superficial vapour velocity.

1.2 Theoretical column efficiency The relative volatility a, a term that was introduced in Eqns (1-28) and (1-29), is a measure for the ease with which a mixture can be separated. It expresses the relationship between the molar fraction y of the more volatile component in the vapour and that of the liquid x with which it is in phase equilibrium; and it is defined by

Its magnitude governs the shape of the equilibrium curve (cf. Fig. 1.4), which is defined by the following equation:

y =f

w

= i

a + (

/i)x

^-38)

If a is constant, the curve assumes the form of an equilateral hyperbola. The greater the value of a, the greater the value of y for a given value of x. As a rule, the relative volatility a of the two components of a mixture, and thus the ease with which they can be separated, decreases with a rise in pressure. Thus, if the value of a for a given mixture is comparatively small, the number of theoretical stages nt required for separation increases with the specific pressure drop Ap/nt within the packing, particularly during vacuum operation. If the pressure at the head of the column pT is kept constant, the pressure drop Ap governs the rise in pressure up to the value at the bottom of the column pB, i.e.

[^y

(1-39)

It follows that the reflux ratio required for separation in the enrichment zone of a rectification column rises. In other words, the energy consumption must increase. In view of the following relationship, the liquid-vapour ratio also increases:

12

1

Introduction

L_ V

(1-40)

r+ 1

Hence, the number of theoretical stages required for a given separation task, as defined by Eqn (1-41), is greater in beds of packing with high values of Ap/n, than in those with low values (cf. Fig. 1.6): Ap

Ap V\ n,

(1-41)

If this aspect is taken into consideration in the planning stages of a separation plant, it will be seen that the maximum feasible load entails not only the smallest column diameter but also the largest number of theoretical stages, and thus the greatest height. Hence, if separation is under vacuum with a large number of theoretical stages, the optimum load will be less than the maximum to an extent that depends on the pressure drop characteristic for the packing selected. Accordingly, the design load in separation tasks of this nature depends on the optimum pressure drop per separation stage and is associated with the minimum total costs. Particular attention must therefore be devoted to the pressure drop per theoretical stage Ap/nt in selecting packing for rectification processes involving a large number of theoretical stages. As Ap/nt increases, the relative volatility a of the mixture decreases in the direction from the top to the bottom of the column. Consequently, the theoretical number of separation

0

Liquid/Vapour ratio L/V

Reflux ratio r Fig. 1.6. Qualitative effect of the pressure drop per theoretical stage on the relationship between the number of theoretical stages and the reflux ratio

1.2

13

Theoretical column efficiency

stages nt ought to be higher than that in an isobaric column (ntiso), i.e. a column in which there is theoretically no pressure drop, and the ratio ntisolnt {Eqn (1-42)} can be regarded as the theoretical column efficiency r\c {Eqn (1-43)}: (nt)

Ap/nt = 0

(nt)

Ap/m > 0

=

nttiso

(1-42)

n

t

f [pT, a r Ap/nt> nt(L/V,

(1-43)

In other words, the theoretical column efficiency depends on the operating pressure pT and relative volatility aT at the top of the column, the pressure drop per separation stage Ap/nt, and the number of theoretical stages nt. The value of r\c thus varies from the one separation task to another. It is comparatively difficult to calculate x\c accurately from phase equilibrium relationships, and a graphicalmathematical method based on the qualitative method shown in Fig. 1.7 would therefore be more expedient for the evaluation of Eqn (1-41). This plot is analogous to that proposed by Gilliland for isobaric (theoretically Ap/nt = 0) columns. The ordinates in the diagram are referred to as stage-number parameters and are defined by Eqn (1-44) for isobaric and by Eqn (1-45) for nonisobaric columns, i. e. _ ft t, iso n

^t,min,iso , 1L

t,iso ~

ll

-

(1-44)

ll

t

S

_ -

t,min,iso

„

Fig. 1.7. Determination of the theoretical column efficiency

. 1

-

S

Wnt

(1-45)

> 0

o(v-D v rrmm,iso •

e=-

v

g rmin,iso+

Energy parameter

The abscissae are referred to as energy parameters and are defined by Eqn (1-46) for isobaric and Eqn (1-47) for nonisobaric columns, i. e.

14

1

Introduction riso-rmin.iso

(v-l)rminjso

=

e

^

=

o

( 1

j

^+1

.46)

7

vg rw/n^/50 + 1

According to Eqn (1-46), the reflux ratio riso in the isobaric column exceeds the minimum rminJso by a factor v, i. e.

Similarly, according to Eqn (1-47), the reflux ratio r in the real column exceeds the minimum in the isobaric column rminiso by a factor vg, i.e. f

=

V

g rmin,iso

(!- 49 )

If the factor v by which the actual reflux ratio exceeds the minimum rmin in the real column is the same as that for the isobaric column, as determined by Eqn (1-47), the following equation would apply: r = v rmin

(1-50)

In this case, the factor vg for the real column is given by Eqn (1-51), which is obtained by combining Eqns (1-49) and (1-50); and the reflux ratio r for the real column, by Eqn (1-52), which is obtained by combining Eqns (1-48) and (1-50), i. e.

(1-51)

r =ris0^shL-

(1-52)

'min, iso

This method allows the number of theoretical stages nt and the reflux ratio r for a real column to be determined from the corresponding values ntminiso and rminiso for an isobaric column. The theoretical column efficiency, as defined by Eqn (1-42), can then be obtained quite easily in the light of the qualitative diagram in Fig. 1.7. The following relationships apply and can be evaluated by alternative means: t, min. iso

iso

s-i co\

r] c = — —^—J v\c = nt,iso

(1-53) 1 - 5

n

t,min,iso

=

d-54) ' ^

_Lz±_ numinAso + siso *-

^iso

n

t,min,iso

'

3

1.2

15

Theoretical column efficiency

An example of a diagram that can thus be obtained is shown in Fig. 1.8. It allows the actual values for the reflux ratio and the number of theoretical stages to be obtained in both isobaric and real columns, i.e. for both Ap/nt = 0 and Aplnt > 0, from the corresponding minimum values for an isobaric column, i.e. a column with no pressure drop. In this case, the theoretical column efficiency r\c will also be known. It is evident from Fig. 1.9 that a low theoretical column efficiency, corresponding to a large number of theoretical stages, can be expected if the energy requirements are high in rectification columns with a moderate to comparatively high pressure drop per theoretical stage Ap/nt. This applies in this case particularly to columns that are operated with a lower reflux ratio, as defined by 1

(1-56)

Hence, an urgent requirement in separation processes of this nature is packing with a very small pressure drop per theoretical stage, e.g. 0 < Ap/nt < 3 mbar. The advantages of packing with small values of Ap/nt are demonstrated in Fig. 1.10. They apply particularly to operation under vacuum with a large number of theoretical stages nt.

0.7 0.6 0.5

V\ \ A V V\ \ \A \ \

\s s \

0.4

N

\

n s

t-ntmin.iso 1

r

s

s

0.3

X

2

0.2 nnin.iso 'Vg ~ ' ) Vg ^m i n. i s o "*"'

0.1

0.1

0.2

0.3

0.4

\ ^\

\

0.5

0.6

0.7

0.8

0.9

1.1

Energy parameter e Fig. 1.8. Diagram for the determination of the number of theoretical stages in nonisobaric vacuum rectification. Plotted for vacuum systems with relative volatilities between 1.1 and 3.6 and overhead pressures between 20 and 250 mbar

16

Introductior

eon column effi cien

1.0

Ap/n t = 6.5 fnbar

\

f

0.8

^. —' l , "C — ^-—

0.6

T" 7 r~~ k-7

i—•

"120 f)pm = 0 1 53 ] = 0.947 f =1

Ap/nt = 13mbar

I

0.2

• •

PT =15C mb(Jl

/

0.4

x B = 2 0 0 ppm »» —

•

90

100

110 120 Reflux ratio r

130

140

150

Fig. 1.9. Theoretical column efficiency as a function of the reflux ratio in the rectification of a mixture of thionyl chloride and ethylene chloride

too

=

,

=

=

:?-

•

/

0.96 \

0.92 0.88 0.84

/ /

0.80 g - 0.76

/ / /

0.72 0.68 10

7

/

A

I / /

\

V

j

/

/

/ *

7 /

/I

J

A 'J7 / / 20

1/ /

40 60

x D =0.9995, a T = \M ^tmin.Jso

100

=

^L

200

400 600 1000

Pressure at head of column pT [mbar] Fig. 1.10.

Theoretical column efficiency as a function of the overhead pressure

1.3

Energy consumption and number of theoretical stages

17

1.3 Energy consumption and number of theoretical stages One of the most important tasks in planning rectification plants is the exact determination of the relationship expressed by Eqn (1-41), i. e. between the number of theoretical stages nt and the reflux ratio r that corresponds to a constant pressure pT at the top of the column and that is required to separate a mixture with low-boiling mole fractions of xF, xD and xB in the feed, distillate and bottoms. This relationship forms the basis for all optimization calculations by fixing the mutual dependence of capital expenditure and the costs of utilities. This is demonstrated qualitatively in Fig. 1.11. The number of theoretical stages under otherwise identical conditions is theoretically higher in the separation of systems with a low relative volatility a than of systems with a high one. This relationship can be expressed in thermodynamic terms and, as has been demonstrated in Section 1.2, is of particular importance in planning rectification processes with a large number of theoretical stages designed to separate mixtures whose relative volatilities are comparatively small and, furthermore, become even less at higher pressures. The economics in cases of this nature dictate the use of packing with a low pressure drop per theoretical stage Ap/nt. This requirement is illustrated qualitatively in Fig. 1.6, which shows the number of theoretical stages nt as a function of the reflux ratio r for columns with low and high values of Ap/nt. A diagram of this nature is characteristic for the vacuum rectification of a mixture whose relative volatility a is comparatively small at a column overhead pressure pT and becomes progressively smaller as a result of the rise in pressure that occurs as the mixture descends through the column. Economic limits are imposed on the pressure drop per theoretical stage Ap/nt in separation tasks of this nature, because the minimum total costs CT>min, i.e. the sum of the capital investment C7 and the operating costs Co, shifts towards high reflux ratios r and towards large numbers of theoretical stages. The relationship is shown qualitatively in Fig. 1.12. The consequence of the shift is a pronounced rise in the minimum total costs CT>min, as is evident from the qualitative diagram presented in Fig. 1.13. The only economic solution for vacuum rectification in this case is to install low-pressure-drop, highly efficient packing, because it allows considerable savings in costs.

\ CO CD CO

x F , x D , xB = const

)

•

CO

1D3I

\

\

man! o

I ZD

Fig. 1.11. Qualitative relationship between the number of theoretical stages and the reflux ratio with the relative volatility as parameter

rmini

^ ^ " ^ ^

Reflux ratio r

18

1 Introduction

Theoretically, the curve that joins the minima M7, M2, in the set of total costs curves presented in Fig. 1.13 passes through a minimum itself. This case would arise in vacuum rectification with a large number of theoretical stages when the progressive increase in the pressure drop per theoretical stage Ap/nt is initially associated with a drop in capital investment costs; and subsequently, with a rise. The drop could be caused by the reduction in column diameter; and the rise, by the cumulative effect of the growing number of theoretical stages. Hence packing of this nature has an optimum value for the pressure drop per theoretical stage (Ap/nt)opt, at which the total costs CT pass through a minimum. The parameters that are given by the definition of the task are the molar flow rate F of the mixture fed with a molar fraction of xF of low-boiling components and the specified purities of the distillate and bottoms, which flow at rates of D and B and with molar fractions of xD and xB, respectively, of the low-boiling component. The rate of heat flow Q in a rectification plant operated along the lines of the flow chart shown in Fig. 1.4 is governed by the reflux ratio r, the characteristic molar liquid enthalpies hD' and hB of the distillate and bottoms at their respective boiling points, the molar liquid enthalpies hF and hF of the feed at its boiling point and its inlet temperature, respectively, and the molar evaporation enthalpy Ahvof the overhead product vapour, i.e. _ xD - xB

h

The parameter that decisively affects the rate of heat consumption is thus the reflux ratio r. It must always be higher than the minimum value rmin that is associated with an infinitely large number of theoretical stages and would therefore raise the costs to an infinite extent (cf. Fig. 1.11). In binary systems the minimum reflux ratio rmin is comparatively easy to determine (cf. Fig. 1.14). Thus, if flow is equimolar, min

~

x ° ymin

1-

x

° ~yi yl-x]

n ^sn (1 58) "

If the molar vaporization enthalpy A/i, of the low-boiling component differs from that of the high boiler Ahh, r r

"""

=

K yi

~

K-xD

XD X

~ '

- 1

yi-x,

(1-59)

(159)

where K is the factor given by Eqn (1-18) in Section 1.1. In Fig. 1.14, ymin is the point where the enrichment line, which passes through the common intersect / of the g-line and the equilibrium curve, intersects the axis of ordinates. The boundary case, in which hardly any overhead product is withdrawn arises if the reflux ratio r is infinitely large. The curves for the rectification and stripping zones then coincide with the diagonals in the ylx diagram. This case corresponds to a minimum number of theoretical stages ntmin, which can be calculated from the values of xD and xB for the lowboiling fractions in the overhead product and the bottoms by means of the Fenske equation, if it is assumed that the relative volatility is constant, i.e.

1.3

Energy consumption and number of theoretical stages

00


'

\

19

IV.

Fig. 1.12. Qualitative relationship between costs and the reflux ratio

Reflux ratio r x F . '
X

'I

cTmin 2

3

= const••

= const.

PT

jAp/nt) p(Ap/nt),

"1 1 m

1

Tmini

cTmin 1 Fig. 1.13. Effect of the pressure drop per theoretical stage on the total costs in vacuum rectification with a large number of theoretical stages

/

\

>/ x

\

(Ap/n t ),

\

M, /opii /opt 2

Reflux ratio r

Fig. 1.14. Graph for the determination of the minimum reflux ratio and the minimum number of theoretical stages. The example taken was a binary mixture

Liquid mole fraction x

^/

20

1 Introduction

ntmin = T1- In (-^±^AIn a \ 1 - xD xB I

1

(1-60)

In many cases, a rough estimation can be obtained from the following relationship, which is obtained by ignoring the enthalpy differences h'D - h'B and h'B - hF in Eqn (1-57):

4 ~^ t

^

(r + 1) A/V

(1-61)

xD - xB

It follows that, if the reflux ratio r is very high, it is almost directly proportional to the energy consumption Q in rectification processes.

1.4 Height of bed determined from the HTU-NTU model The HTU-NTU model for the determination of the requisite height of a bed of packing has previously been described by Eqn (1-31). The height of an overall transfer unit HTUO, i. e. for both the vapour HTUOV and liquid HTUOL phases, is related to the respective heights for the individual phases HTUV and HTUL by the stripping factor X, which is defined by Eqn (1-30). Thus Eqn (1-62) applies for the vapour phase; and Eqn (1-63), for the liquid phase: HTUOV = HTUV + X HTUL

(1-62)

HTUOL = HTUL + — HTUV

(1-63)

A,

Therefore, the height H required to realize NTUOV transfer units in the vapour phase is given by Eqn (1-64); and NTUOL in the liquid phase, by Eqn (1-65): H = HTUOV ' NTUOV

(1-64)

H = HTUOL • NTUOL

(1-65)

The procedure for the determination of the numerical values of NTUOV and NTUOL is illustrated qualitatively in Fig. 1.5. A knowledge of the slope myx of the equilibrium curve for the system is required for the determination of the stripping factor A, from Eqn (1-30). If the relative volatility is almost constant in the range of concentrations concerned, the slope can be obtained as a function of the mole fraction x of the liquid phase by differentiating Eqn (1-38), i. e.

(myx) a . cons, = - ^ =

[l+xla_1)f

d-66)

Thus the calculation of the effective height of bed consists essentially of determining the values for HTUV and HTUL as described in Chapter 5.

1.4

Height of bed determined from the HTU-NTU model

21

The equilibrium curve for absorption and desorption processes is often linear in the range of low transfer component loads Yin the gas and X in the liquid. In other words, the slope mYx of the Y = f(X) relationship can be regarded as constant, and the equilibrium curve can be defined by Y=mYXX The stripping factor in this case is then given by

where L/Vis the ratio of the liquid to the gas flow rate.

(1-67)

2 Types of packing Column packing for industrial separation processes is produced from various materials and is supplied in multifarious shapes and sizes. It may be dumped at random or stacked in regular geometric patterns, and it must ensure a large area of contact between the gas and the liquid phases and a uniform phase distribution. The current economic situation favours the adoption of packed columns in rectification, absorption, and liquid-liquid extraction processes. Consequently, the demand for packing in mass transfer equipment for the chemical and allied industries has greatly increased and has triggered off many new developments in the last few years. As has already been mentioned, packed columns have also become widely accepted in ecological engineering, e. g. in air and gas scrubbing processes and in water treatment. The main unit operation involved is mass transfer, but heat transfer by direct contact is also a significant factor. The only new high-performance packings to which consideration has been given in this book are those for which process engineering performance data are available. Hence, certain gaps may exist in the information presented. Nevertheless, the theoretical fundamentals and the fluid dynamics and mass transfer models that have been derived from the results obtained on all packings investigated are sufficiently accurate for application in industrial practice. The main applications dealt with here are systems in which the phases are in countercurrent flow. The analysis and design of packed columns for thermal separation processes can be difficult in many cases. This applies not only to the actual scale-up of laboratory and pilot plant results but also to the uncertainty involved in many cases by the procedures adopted. Most hydrodynamic calculations for packed columns are uncomplicated and lead to results that can be satisfactorily applied in practice. However, results obtained by mass transfer calculations, e. g. for the determination of column height, are often associated with a degree of uncertainty, and dubiety can thus arise. An example arises in applying the data derived from special absorption tests to solve rectification problems. Despite the valuable contributions made by some research workers, this task was still considered to be insoluble until a few years ago. Since the physical laws relating to mass transfer are fundamentally the same in all cases, it ought to be possible to describe thermal separation processes in terms that are valid for all systems. To this aim, the author has performed comprehensive experiments on numerous individual types of packing of various shapes and sizes. The results obtained with different systems and in columns of different dimensions have been systematically analyzed. They have been compared with those obtained in a previous model developed by the author about ten years ago for predicting the mass transfer efficiency of packed columns by means of a relationship of general validity. The model necessitates prior determination of the liquid holdup. It has been verified by measurements performed by the author or cited in the literature, and it allows all test results obtained with various rectification systems, including data from absorption studies, to be brought to a common denominator. A model for liquid-liquid systems in packed columns has also been checked against experimental results.

Packed Towers in Processing and Environmental Technology. Reinhard Billet Copyright © 1995 VCH Verlagsgesellschaft mbH, Weinheim ISBN: 3-527-28616-0

24

2

Types of packing

The trend in thermal separation techniques decidedly favours high-performance packing with the outstanding process engineering characteristics specified by the chemical and allied industries. The packing systems selected for consideration here can be regarded as representative of the progress made in this field. The scientific studies required to determine the packing characteristics and to derive data for industrial-scale columns were performed in the author's laboratories and external pilot plants.

2.1 Packing dumped at random Many conventional beds of random packing have caused difficulties and problems in large-diameter columns, and their shortcomings account for the reservations that are still held against them. A frequent difficulty has been to attain uniform distribution of the liquid over the entire cross-section at the feed inlet or the head of the column, i.e. to ensure that the packing is adequately wetted. The risk of maldistribution also exists in the layer of packing close to the column shell. Thus the likelihood of channelling in many beds of random packing introduces an uncontrollable and fortuitous element in the separation of mixtures with certain physical properties and poses the threat of poor efficiency in columns of large diameter. Consequently, special plates and, in some cases, geometrically arranged beds of packing were formerly given preference over random packing in an attempt to realize high capacities and efficiencies. However, great changes in the design of random packing have largely altered this situation in recent industrial practice. Modern types of random packing merit particular attention from the economic aspects of optimizing performance and minimizing materials consumption and production costs. They feature a low pressure drop per theoretical stage, which is an absolutely essential asset for saving energy and avoiding thermal decomposition of the product stream in separation processes. The examples presented in Fig. 2.1 have been restricted to types for which process engineering performance data were available from studies in the author's research facilities. The plastics Nor-Pac ring was the first modern type of high-performance packing to be introduced in industrial practice. It was followed by other latticework types, e.g. Hiflow rings and saddles and Hackette, Din-Pac, Envi-Pac, and VSP rings. They have one feature in common, viz. their latticework structure, but differ from one another in their basic geometry and the associated characteristic data, i.e. the effective void fraction, the surface area per unit volume, the packing density, and the bulk density. In the subsequent stages of widespread acceptance in practice, latticework packing set the pace. Systematic studies had shown that it represented an optimum, and it was accordingly recommended for a number of applications. Close runners-up were the plastics and metal cascade mini-rings, known under the tradename CMR. New designs of saddles include the Super-Torus. Characteristic examples of packing that were investigated in the author's laboratories are illustrated in Fig. 2.1 together with the relevant geometrical data, i.e. the nominal size d, the number N per unit volume, the surface area per unit volume a, and the void fraction e. The studies embraced a relatively wide range of metallic, ceramic and plastics packing of various geometries and dimensions, and the results allow the optimum packing to be selected for a given separation task.

2.2

Packing stacked in geometric patterns

25

Nominal packing size 50 mm

Fig. 2.1. Examples of packing for random beds including data on the number per unit volume, the area per unit volume, and the relative void fraction

2.2 Packing stacked in geometric patterns Packing stacked in a regular pattern permits the realization of a minimum pressure drop per theoretical stage, and is therefore most suitable for minimizing energy consumption in separation processes that necessitate many stages. It also permits the lowest possible column bottom temperature in the separation of heat-sensitive mixtures. The capital investment costs for geometrically arranged packing is normally higher than that for dumped. However, studies on separation process economics have shown that the greatest contribution towards the

26

2

Types of packing

total costs is made by energy, in which case preference would be given to arranged packing. In fact, the demand for energy-saving separation equipment has even diverted trends from mass-transfer trays towards columns with systematically arranged packing. The benefits offered by low-pressure-drop packing are by no means confined to rectification and are now widely recognized in absorption processes - for the removal of pollutants and recoverable products from off-gas streams - and in desorption. One of the factors that has initiated this trend has been the increased severity of the legislation imposed in industrial countries on the prevention of air and water pollution. The design aim of all new types of stacked packing has been to minimize the pressure drop per unit efficiency at high loads. The predecessors of most modern designs are Sulzer Chemtech gauze and sheet-metal packings. Various reports have confirmed the successful performance in practice of stacked packing, even in columns of comparatively large diameter. The provisos are that the beds have been carefully installed and that the liquid phase has been uniformly distributed. Maldistribution, which is often observed in conventional beds of packing and which greatly impairs the efficiency, can be largely avoided by devices for redistributing any liquid that may channel down the walls of the column. Normally, specialized knowledge on how best to distribute the liquid is part and parcel of manufacturing knowhow. The wide variety of thermal separation tasks in the process industries acts as an incentive for manufacturers of stacked packing to further modify existing designs (cf. Fig. 2.2). High-performance structured gauze packing has proved successful in many fields of the chemical and allied industries, e. g. the production of heavy water and the distillation of amines and glycols, higher fatty acids and alcohols, and methanol. A factor that restricts their widespread acceptance is their capital investment costs. For instance, they are uneconomical at pressure drops higher than 10 mm WG per theoretical stage. This costs factor entails a gap between the applications for stacked beds of packing and those for dumped beds. New and cheaper, yet more effective arranged packing had to be developed to close this gap. Again the first step towards meeting the requirements was made by Sulzer. The prototype that they introduced on the market was the Mellapak, which has since been succesfully used for many years in industrial columns with diameters of up to eight metres. Other companies followed suit with designs of outstanding merit, e.g. Glitsch structured sheet-metal packing, Montz Bl-type metal and Cl-type plastics packings, and Raschig Ralu Pak 250 VC metal packing. It is beyond the scope of this book to go into full details on all the developments that have been made in the last few years. The aim is more to outline the current state of the art and the direction of present trends and to illustrate these in the light of some examples of modern, high-performance, randomly dumped and systematically arranged beds of packing. Fig. 2.2 illustrates the geometry of some modern stacked packing and includes data on the geometry, e. g. the surface area per unit volume a and the void fraction 8. The corresponding process engineering data presented in Chapter 3 were derived from experiments in the author's pilot plants and were supplemented by manufacturers' data. Obviously, the list given in Fig. 2.2 is by no means complete; examples of packings with excellent process engineering characteristics that have not been included are the Rombopak and Norton types.

2.3

Geometric packing parameters

27

Nontz C 1^300

Mellapok 250 Y

a-250. e = 0.96 Nontz packing Bl - 300

a = 250

a^ 202 3

3

e=0,978 3

-7m ], £ [m /m ] Fig. 2.2. Examples of geometrically arranged packing including data on the area per unit volume and relative void fraction

2.3 Geometric packing parameters The examples shown in Figs. 2.1 and 2.2 represent a mere cross-section of the multifarious packings offered for process and ecological engineering. It can be seen that each packing has its own peculiar geometry and surface structure. Each must be subjected to comprehensive experiment in order to determine the performance characteristics upon which reliable fluid-dynamics and mass-transfer models can be based.

28

2

Types of packing

Column packing with a high volumetric efficiency obviously necessitates excellent hydrodynamic design and surfaces that greatly promote separation. A quantity to which the performance parameters are usually related is the ratio a of the surface area of the packing to the volume of the column, i.e. (2-1) The effective void fraction or porosity 8 in a bed of packing depends on the surface area Ap of the packing and the thickness s of the basic material, which is usually in the form of sheet metal, metal foil, or plastics film. The volume of material required for the bed is given by (2-2)

V < — sA

and the effective void fraction of the bed, by

vc-vP

(2-3)

Vr

A simple relationship between 8, a, and s can be obtained by combining Eqns (2-1) to (2-3). Thus (2-4)

8 > 1 - — as

20

60

100

140

180

220

260

300

340

380

420

460

500

Area per unit volume a [ m 2 /m 3 ] Fig. 2.3. The relationship between the relative void fraction, the area per unit volume, and the average wall thickness of packing

2.3

Geometric packing parameters

29

In principle, Eqns (2-1) to (2-4) are valid for all beds of packing, but the information that they yield on the efficiency, capacity, and pressure drop is purely qualitative. Other parameters are required to evaluate the performance, and they must allow for the geometry and texture of the packing. Together with 8 and a, they govern the phase distribution and the area of contact between phases. Eqn (2-4) reveals the limits within which the effective void fraction 8 for a desired surface area per unit volume a can be altered by appropriate selection of the practically realizable thickness s of the material. It can be seen from the nomogram presented in Fig. 2.3 that the effective void fraction increases as the thickness of the material decreases. The packing density TV and thus the area a per unit volume in random beds may be somewhat greater in large-diameter columns (subscript T) than in pilot columns (subscript P)

Fig. 2.4. Flue gas desulfurization plant in one of BASF AG's power stations. It consists of two absorption columns of 9.4 m diameter and 35 m total height. The beds of 50-mm plastic Hiflow rings are packed to an effective height of c. 8 m

30

2

Types of packing

of comparatively small diameter. The differences in the area per unit volume and the relative void fraction can be obtained from the following equations: (2-5) ET = 1 - (1 - EP) ^~

(2-6)

J\p

A photograph of a twin-line absorption plant is shown in Fig. 2.4. This example clearly demonstrates that columns with random beds of modern packing can also give good results in plants of large capacity.

3 Experimental determination of packing performance Accurate knowledge of the performance characteristics is a fundamental requirement for the optimum design of absorption, desorption and rectification columns from the aspects of fluid dynamics and mass transfer. Systematic experiments have led to new fundamental concepts and fresh knowledge in modern packing technology. They have allowed mathematical models to be derived from comprehensive physical relationships between the packing performance, the fluid dynamics, the loading conditions, the geometry of the packing, and the properties of the system to be separated. The results of the experiments have been evaluated in terms of the interrelationships between the separation efficiency, pressure drop, liquid and gas loads, liquid holdup, residence time, and pressure drop. Particular attention is attached to the load at which the liquid commences to hold up in the column and that at which flooding occurs. The studies have also yielded information on the operating zone of a packing, a knowledge of which is required for safe design and operation.

3.1 Pilot plants for testing gas-liquid systems The experimental results reported here were gained in a number of bench-scale and pilot plants. The flow chart for one of the pilot plants used for absorption/desorption experiments and hydraulic studies is reproduced in Fig. 3.1; and that of the layout for the rectification experiments, in Fig. 3.2. Various distributors with different numbers of perforations, five of which are shown in Figs. 3.3-3.7, were taken to determine the effect exerted by the number of liquid streams per unit of cross-sectional area. In the main tests, the number of liquid distribution points was varied between 15 and 2400 per square metre.

3.2 Evaluation of measurements The rectification efficiency, as expressed by the number of theoretical stages per unit height of packing nt/H, is a function of the vapour capacity factor Fv at a constant liquidvapour ratio LIV, i.e. nJH = f(Fv)

(if LIV = const.)

(3-1)

The same applies to the pressure drop per unit height, i.e. Ap/H = f(Fv)

(if LIV = const.)

(3-2)

The absorption efficiency, i.e. the height of a transfer unit HTUOV in the bed of packing, can also be expressed as a function of the capacity factor Fv if the liquid load uL is kept constant, i.e. HTUOV = f(Fv)

( if "L = const.)

Packed Towers in Processing and Environmental Technology. Reinhard Billet Copyright © 1995 VCH Verlagsgesellschaft mbH, Weinheim ISBN: 3-527-28616-0

(3-3)

32

3

Experimental determination of packing performance

I

s

ob"S

Alternatively, it can be expressed as a function of wL if Fv is constant, i. e. HTUOV = f ( M J (if / v = const.)

(3-4)

The pressure drop per unit height of bed Ap/H is also a function of Fv if uL is constant, i.e.

A/?/// = f (Fv) (if wL = const.)

(3-5)

3.2

33

Evaluation of measurements

a

c 'EH

o

u

If the resistance to mass transfer is entirely in the liquid phase, the desorption efficiency is given by $LaPh, the product of the mass transfer coefficient |3L and the interfacial area per unit volume aPh. In this form, it is referred to as the volumetric mass transfer coefficient and is expressed either as a function of the liquid load uL at a constant gas capacity factor Fv {Eqn (3-6)} or as a function of the gas capacity factor at a constant liquid load {Eqn (3-7)}: fiLaPh = t(uL)

(if Fv = const.)

(3-6)

fiLaPh = f(Fv)

(if uL = const.)

(3-7)

34

3

Experimental determination of packing performance I

&

-

I

'

^

$

l

d5 = 450 mm ds= 300 mm

& - •

l

Z = 730 1/m2 Z = 1350 1/m2

Fig. 3.3. Perforated-pipe distributor for pilot columns

d s =220 mm

Z = 2150 1/m2

Fig. 3.4.

Capillary distributor for pilot columns

Likewise, the liquid holdup hL can be expressed either as a function of the liquid load at a constant gas capacity factor {Eqn (3-8)} or as a function of the gas capacity factor at a constant liquid load {Eqn (3-9)}: hL = f(uL)

(if F v = const.)

(3-8)

hL = f(Fv)

(if uL = const.)

(3-9)

3.2

d s =450mm

Evaluation of measurements

1/m2

Z = 380 1/m2

Fig. 3.5. Profiled-slot distributor for pilot columns

d s =500 mm

Fig. 3.6. Nozzle distributor for pilot columns

.

Z = 610 1/mz

35

36

3

Experimental determination of packing performance

= 800 mm

Z = 490 1/m 2

Fig. 3.7. Funnel distributor for pilot columns

Normally, flooding represents the condition for the maximum capacity of a packed column. In other words, the dynamic load at the flood point Fv FJ/VQ^ is a measure for the upper capacity limit under operating conditions. It can be determined from its relationship to the dimensionless flow parameter \|), which is defined by Eqn (1-3). Hence, Qv VQL

\ V V 6L

(3-10)

The relationship expressed by Eqn (3-10) can be obtained by experiment. The height HTUOV of an overall mass transfer unit is related as follows to the heights of the transfer units in the gas HTUV and liquid HTUL phases: HTUQV

= HTUV + X HTUL

(3-11)

where X is the stripping factor and is given by (3-12) in which myx is the average slope of the equilibrium curve in the range of concentrations concerned.

3.3

Test systems

37

The height of a transfer unit in the liquid phase HTUL is obtained from the corresponding number of transfer units NTUL: HTUL = - J ^

(3-13)

The volumetric mass transfer coefficient $LaPh in the liquid phase is given by

The numerical value of HTUOV is obtained from the number of overall transfer units NTUOyin the gas phase for a given liquid load uL. i.e.

Once the values for HTUOV and $LaPh are known, the height of a gas transfer unit HTUV can be determined from HTUV = HTUOV - myx j . -J±±-

(3-16)

In absorption tests with an ammonia/air-water system, the resistance to mass transfer is located in both the gas and liquid phases. On the other hand, resistance to mass transfer is entirely in the liquid phase in desorption tests with a carbon dioxide-water/air system. These two systems have practically identical diffusion characteristics. Thus, data derived from tests on the one system may be applied to the other system. For instance, if HTU0V for the absorption system is known, the corresponding value of HTUV can be calculated by inserting the value of |3L
^

=

(317)

3.3 Test systems The hydrodynamic and mass-transfer parameters presented here for various gas-liquid systems were determined experimentally in the author's laboratories or taken from the literature. The physical properties of the systems selected for the determination of the gas-side pressure drop are listed in Table 3.2; those for the determination of liquid holdup, in Table 3.3; and those used together with the gas and liquid loads for the determination of the upper and lower loading points, in Table 3.4.

38

3

Experimental determination of packing performance

Table 3.1. General data on the investigated system, the pilot plant, and the process engineering magnitudes to be determined System

Column diameter

Packed height

Test function

Rectifcation 0.013-1 bar

0.22 m 0.5-0.8 m

0-15 m 0.5-4 m

n t /H, Ap/H, Ap/n t

Physical absorption 1 bar, 293 K

0.3-1.4 m

0-2 m

HTUQV, Ap/H,

Desorption 1 bar, 293 K

0.3 m

Chemical absorption 1 bar, 293 K

0.3 m

1.5 m

Air /Water 1 bar, 293 K

0.22-0.6 m

1.3-2 m

=

f(Fv)L/V = const. Ap/NTUov

H^V/u, = const.

0-2 m

HTU L , p L • a =

f

( u L ) F v = const.

HTUOV, Ap/H, Ap/NTUov = f(Fv)u,.= const. H L = f(F v ) U | = const . ^L tVULjpv = cons t.

Table 3.2. List of the densities and kinematic viscosities of the systems investigated in the studies on efficiency and pressure drop System

Air / water Air/methanol Air/turbine oil Air/machine oil 1 Air/machine oil 2 Air/ethylene glycol NH3-air/ water NH 3 -air/4% H 2 SO 4 in H 2 O SO2-air/1.78 mol. NaOH in H 2 O CO 2-air/water Methanol / ethanol Ethanol/water Chlorobenzene / ethylbenzene Chlorobenzene / ethylbenzene Chlorobenzene / ethylbenzene Chlorobenzene / ethylbenzene Chlorobenzene / ethylbenzene Chlorobenzene / ethylbenzene Toluene / n-octane Toluene / n-octane Toluene / n-octane trans-1 czs-Decahydronaphthalene 1,2 Dichloroethane / toluene Ethylbenzene / styrene

P mbar

Qv

1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 33 67 133 266 532 1000 100 133 266 13 1000 133

1.19 1.16 1.13 1.15 1.12 1.17 1.18 1.18 1.19 1.19 1.30 1.29 0.14 0.27 0.51 0.96 1.80 3.28 0.35 0.46 0.90 0.06 3.22 0.48

kg/m

3

v v • 106 m 2 /s

kg/m

15.1 15.6 16.1 15.8 15.2 15.4 15.1 15.2 15.1 15.1 8.5 8.4 46.0 28.9 15.9 8.8 4.9 2.9 20.8 16.4 8.5 105.8 2.9 15.9

999 791 870 885 890 1115 999 1033 1039 1000 738 791 963 949 926 905 886 866 839 833 763 844 924 833

QL

3

v L -10 6 m 2 /s 1.03 0.72 50.06 58.76 99.03 16.14 1.03 1.05 1.15 1.00 0.52 0.50 0.60 0.52 0.45 0.39 0.34 0.30 0.52 0.49 0.43 1.24 0.38 0.45

3.3

39

Test systems

Table 3.3. Some physical properties of the systems investigated in the studies on liquid holdup System

Air / water Air/methanol Air/benzene Air/ethylene glycol solution Air/4% H 2 SO 4 in water Air/1.78 M NaOH in water Air/sorbitol solution 1 Air/sorbitol solution 2 Air/sorbitol solution 3 Air/calcium chloride solution 1 Air/calcium chloride solution 2 Air/calcium chloride solution 3 Air/DuPont Petrowet solution 1 Air/DuPont Petrowet solution 2 Air/DuPont Petrowet solution 3 Nitrogen/heavy oil

kg/m 3

QL

riL-103 kg/ms

a L -10 3 kg/s 2

1000 800 878 1064 1033 1039 1299 1268 1215 1321 1225 1170 1000 1000 1000 1810

1.00 0.78 1.65 18.00 1.08 1.19 185.00 53.00 16.50 4.50 2.40 1.40 1.00 1.00 1.00 17.00

73.0 22.6 28.9 59.4 54.6 73.0 73.0 73.0 86.3 80.3 77.4 57.5 43.0 38.0 -

Table 3.4. Range of properties of the systems embraced by the studies on capacity [kg/m3] [kg/ms] [kg/m3] [kg/ms]

Gas density Gas viscosity Liquid density Liquid viscosity

QV T]v °L i]L

Gas velocity Liquid velocity

uVF1 [m/s] uLF1 [m3/m2 h]

0.30-1.37 7.14-10- 6 -18.19-10- 6 750-1026 0.36-10- 3 -92.60-10- 3 0.43-8.22 4.88-144

Table 3.5. Properties of the gas-liquid systems for which allowance had to be made in the evaluation of mass transfer Systems with liquid phase resistance

Carbon dioxide/water Carbon dioxide /methanol Carbon dioxide / buffer solution 1 Carbon dioxide / buffer solution 2 Carbon dioxide/1.78 M NaCl solution Carbon dioxide-water/air Carbon dioxide-air/water Oxygen-water / air Chlorine-air / water

T K

kg/m 3

QL

v L -10 6 m 2 /s

a L -10 3 kg/s 2

D L -10 9 m 2 /s

ScL

288 298 298 298 298 293 293 296 294

1003 788 1157 1237 1040 997 998 996 997

1.14 0.70 1.22 1.66 1.04 0.97 1.00 0.94 0.98

74.0 23.8 72.0 72.0 76.0 72.4 72.7 72.0 72.0

1.59 3.63 1.40 1.40 1.63 1.82 1.82 2.40 1.33

713 193 871 1186 641 535 '549 391 741

40

3

Experimental determination of packing performance

Table 3.6. Properties of the gas-liquid systems for which allowance had to be made in the evaluation of mass transfer Systems with gas phase resistance

Air / water Air/methanol Air/benzene Air/ethyl n-butyrate Helium / water Freon 12/water Ammonia-nitrogen / water Ammonia-oxygen / water Ammonia-air/4% H 2 SO 4 in water Sulfur dioxide-air/1.78 M NaOH in water Sulfur dioxide-Freon 12/3 M NaOH in water Chlorine-air/2 M NaOH in water Acetone-nitrogen / water

T K

kg/m 3

QV

vv • 106 m 2 /s

a L -10 3 kg/s 2

DylO6 m 2 /s

Scv

293 300 300 300 303 303 289 298 294

1.188 1.162 1.162 1.162 0.159 4.797 1.167 1.291 1.180

15.1 15.6 15.6 15.6 126.2 2.9 14.9 15.9 15.2

72.5 22.4 27.4 21.8 71.3 71.3 72.8 72.2 59.4

24.6 16.5 9.1 7.4 87.4 10.9 24.4 14.7 24.0

0.612 0.950 1.720 2.122 1.443 0.247 0.609 1.085 0.632

294

1.190

15.1

54.6

12.3

1.224

303 303 289

4.800 1.150 1.166

2.4 15.9 14.9

70.9 70.9 72.7

5.0 13.3 10.8

0.480 1.200 1.378

16 14

/

Rectification L/V= 1

12

/

/

10

-a a

>1

Ar

70

/

A~—0

0.4

0.8

Y

uvwn\ene

TTT 1.2

1.6

2.0

Vapour capacity factor F v [m'

1/Z

2.4 1

2.8 3.2 1/2

s" kg ]

Fig. 3.8. Liquid load as a function of the vapour capacity factor in systems operated at atmospheric pressure and under vacuum. Valid for total reflux

3.4

Experimental results

41

The physical properties of the gas-liquid systems selected for the mass transfer studies are reviewed in Tables 3.5 to 3.8. If the system's resistance to mass transfer is mainly in the liquid phase, Table 3.5 applies; if it is mainly in the gas phase, Table 3.6; and if it is in both the gas and liquid phases, Table 3.7. The physical properties relating to rectification, i.e. vapour-liquid, systems are entered in Table 3.8; and Fig. 3.8 indicates the wide range of liquid loads encompassed by the rectification tests performed under total reflux with these systems. The figures listed in Table 3.9 describe the range of capacities and the physical properties of all the mass transfer systems that were evaluated. Two systems listed in Table 3.10 were selected to study absorption processes in which mass transfer is accompanied by a fast chemical reaction in the liquid phase.

3.4 Experimental results Some of the results determined in experiments on fluid dynamic behaviour and mass transfer efficiency are presented in Figs. 3.9-3.50. They are representative for the comprehensive test program and were obtained by systematic evaluation of Eqns (3-1) - (3-10) and Eqn (3-17). Thus Figs. 3.9-3.17 show the efficiency and pressure drop chararacterics for random beds of metal packings in pilot columns of various diameters. They apply for rectification at atmospheric pressure and under vacuum with total reflux. Figs. 3.18 and 3.19 show the corresponding relationships for random beds of plastics and ceramic packings. It is evident from Figs. 3.20-3.22 that geometrically arranged metal packing has a low pressure drop per theoretical stage and a very high separation efficiency that depends very little on the load. The results represented in these diagrams were obtained in vacuum rectification. As opposed to this, the efficiency of metal gauze packing depends greatly on the load (Fig. 3.23). This can be ascribed to the fact that the surface of the gauze exerts a capillary action, which is particularly effective at low liquid loads, under which it spreads the small amounts of liquid uniformly over its surface and thus gives rise to a higher efficiency. Typical log-log pressure drop diagrams for random beds of packing produced from different materials are reproduced in Figs. 3.24-3.29. An increase in the slope of the pressure drop curves indicates that the loading point has been exceeded. Figs. 3.30 and 3.31 provide unmistakable evidence to the effect that, if the liquid load is kept constant below the loading point, the liquid holdup is practically independent of the gas load. On the other hand, it increases considerably in the loading range and attains a maximum at the flood point. The curves shown in Figs. 3.32-3.38 are characteristic for the relationship between the liquid holdup and the liquid load when the gas load is constant. Figs. 3.32 and 3.33 illustrate the effect exerted by the dimensions of the packing; Fig. 3.34, the effect of the material from which the packing was produced; Fig. 3.35, the effect of the shape of the packing; and Fig. 3.36, the effect of the system. Although geometrically arranged packing presents by far the greater area per unit volume, its liquid holdup is only slightly more than that of random packing (Figs. 4.36 and 4.37).

1.187

293

15.1

15.1 4.7 2.2 15.9 15.6 15.6 15.6 15.5

v v -10 6 m2 / s

15. 4

23.8 14.9 12.2 13.1 12.9 10.8 16.5 12.4

Dv-10 6 m2 / s

= negative system;

p

= positive system

33 67 133 267 533 1000 103 133 267 1000 133 13 1000 1000

Chlorobenzene / ethylbenzene" Chlorobenzene / ethylbenzene11 Chlorobenzene / ethylbenzene11 Chlorobenzene / ethylbenzene11 Chlorobenzene / ethylbenzene11 Chlorobenzene / ethylbenzene" Toluene / n-octane11 Toluene / n-octane11 Toluene / n-octane11 Ethanol / waterp Ethylbenzene / styrene" trans-1 cw-Decahydronaphthalene" Methanol / ethanol11 1,2-Dichloroethane / toluene"

n

Pr mbar

Rectification systems

314 329 345 364 385 407 321 327 345 352 350 336 343 365

Ts K 0.140 0.268 0.510 0.967 1.827 3.241 0.373 0.473 0.900 1.294 0.483 0.066 1.303 3.200

Qv

kg/m 3 52.4 28.7 15.8 8.8 4.9 2.9 19.1 15.3 8.5 8.2 15.9 105.8 8.4 3.2

Vv-10 6 m 2 /s

0.980

0.633 0.317 0.185 1.220 1.208 1.452 0.950 1.246

64.8 35.8 19.9 11.1 6.3 3.7 21.0 17.0 9.5 14.5 19.9 120.0 9.1 4.0

Dy-10 6 m 2 /s

Table 3.8. List of properties of the systems investigated in the rectification studies

1.188 1.763 4.929 1.150 1.297 1.162 1.162 1.168

293 301 295 303 297 300 300 298

Ammonia-air/water Ammonia-propane/water Ammonia-Freon 12/water Sulfur dioxide-air/water Sulfur dioxide-oxygen/water Acetone-air/water Methanol-air/water Ethanol-air/water Carbon dioxide-air/ 1 M NaOH in water

QV kg/m 3

T K

Systems with resistance in the gas and liquid phases

0.809 0.803 0.793 0.791 0.785 0.780 0.908 0.904 0.894 0.567 0.798 0.881 0.929 0.806

Scv

1043

999 996 998 989 998 997 997 997

QL

956 941 926 908 887 866 779 774 758 787 835 846 739 968

kg/m 3

QL

kg/m 3

0.59 0.52 0.45 0.39 0.34 0.30 0.53 0.50 0.43 0.53 0.45 1.24 0.54 0.35

6 v L •10 m2 /s

1.20

1.03 0.84 0.96 0.99 0.92 0.86 0.86 0.89

v L -10 6 m 2 /s

Table 3.7. Properties of the gas-liquid systems for which allowance had to be made in the evaluation of mass transfer

28.5 26.9 25.1 23.2 21.1 19.0 23.1 22.5 20.7 25.7 21.0 26.0 17.2 22.3

a L -10 3 kg/s 2

75.0

72.7 72.0 72.4 70.0 72.3 72.1 72.1 72.2

a L -10 3 kg/s 2

2.33 2.85 3.50 4.33 5.41 6.67 2.33 2.53 3.18 3.42 3.64 1.04 4.75 4.86

D L -10 9 m 2 /s

1.77

1.72 2.01 1.79 1.87 1.66 1.18 1.44 1.09

D L -10 9 m 2 /s

255 181 128 89 62 45 195 171 118 82 123 1019 113 70

ScL

678

597 418 536 530 556 728 600 819

ScL

jars'

B

3.4

Experimental results

43

Table 3.9. Loading ranges and properties of the systems investigated Gas capacity factor Liquid load

F v [m"1/2 kg1/2 s uL [m3/m2 h]

Liquid density Liquid viscosity Liquid-side diffusion coefficient Surface tension Gas density Gas viscosity Gas-side diffusion coefficient Schmidt number of liquid Schmidt number of gas

QL [kg/m3] vL [m 2 /s] D L [m 2 /s] aL [kg/s 2 ] Qv [kg/m 3 ] vv [m 2 /s] D v [m 2 /s] ScL

0.0029-2.773 0.2563-118.20 758-1237 0.30-1.66 1.04-6.50 17.2-74.0 0.066-4.929 2.2-126.2 3.7-87.4 45-1186 0.185-2.122

SCy

Number of packings investigated Number of absorption and desorption measurements Number of rectification measurements Absorption and desorption systems investigated Rectification systems investigated

67 2605 665 31 14

Table 3.10. Absorption systems embraced by the experiments System

NH3 - Air/H 2 O 3

QV [kg/m ] 3

QL[kg/m ] 2

r]v/Qv [m /s] 2

D v [m /s] Transfer component dissolved by Conditions

NH3 - Air/H 2 O + H2SO4 1.18

1.18

1.18

1032.7

998.2 15.2-10"

6

2.38-10"

15.2-10 5

Physical absorption in the solvent

SO2 - Air/H 2 O + NaOH

1039.4 15.2-lO"6

6

2.38-10-

5

Chemical absorption: 2NH 3 + H2SO4+ H2O = (NH4)2 SO4 + H2O

1.2-lO"5 Chemical absorption: SO2 + 2 NaOH = Na2SO3 + H2O

System operated at standard temperature and pressure

Fig. 3.39 gives an impression of the relationship between the flood load and the flow parameter for geometrically arranged metal packing of various sizes. As opposed to this, Fig. 3.40 clearly shows that the shape of packing exerts a not inconsiderable effect on the load at the flood point, even if the packings compared are of the same nominal size. Characteristic results of absorption experiments are presented in Figs. 3.41 and 3.42; and of desorption experiments, in Figs. 3.43-3.45. The effects of the packing dimensions are also revealed in the latter. It is evident from Fig. 3.46 that, in the range below the loading point, mass transfer in systems with resistance on the liquid side is independent of the gas load. Fig. 3.47 demonstrates that, if mass transfer in absorption systems is predominantly in the gas phase, it can be improved by increasing the gas or liquid load.

44

3

Experimental determination of packing performance

In the course of the studies, it was observed that when new, freshly installed beds of packing were first taken on stream the liquid holdup was slightly less than that of the packing a few days later. The same applies to the mass transfer, as is evident from Fig. 3.48, which is valid for a desorption system. In experiments with an absorption system (cf. Fig. 3.49), the differences in mass transfer were significantly greater, and the efficiency became stable after an operating period of a few days. Other studies were performed on plastics packing that had been given a surface finish, e.g. rendered hydrophilic. They led to the conclusion that the surface treatment did not increase the efficiency to a level higher than that attained by unfinished packing after an operating period of one week at the most (cf. Fig. 3.50):

Raschig rings, metal, ds=500mm, Z = 600 1/m2 Ethylbenzene/Styrene, 67 mbar, L/V = l. H = 2 m

cu .—.

£==

A.

2

D-

\

r\ \

—.—•-o—

O~

24

f

—o— —o—

20 O

^

—-A—

16

j

50 mm 25 mm 15 m m

9 /

/ /

12 CO '

•

y'

/

'

S5

S

A-

-o CO CO

a>

a E

Q.

c^

o cu

Q.

6 4 2

I

1 1

1 j

1

/

J

V

CDCO

0 0.4 0.6 0.8 1.0 12 1.4 16 1.8 2.0 2.2 2.4 Vapour capacity factor Fv [m' 1/z s"1 kg" 2 ] Fig. 3.9. Performance data for metal Raschig rings showing the effect of packing size

3.4

45

Experimental results

Raschig rings, metal, ds= 500 mm, Z = 600 1/m2 Ring size 50 mm, H = 2 m, ratio L/V=1

20 "Z 16 -a „

•••••• 1,2-Propylene/Ethylene glycol 6.7mbar - © - Ethylbenzene/Styrene 34 mbar - © - Ethylbenzene/Styrene 67 mbar Methanol/Ethanol 1 bar

a

JZ*

/

"a «_ . a CO

T

/

-Q

^— 0.4 0.6 0.8

1.0

1.2 1.4

1.6

1.8 2.0 2.2 2.4 2.6

Vapour capacity factor Fv [m" 1/2 s"1 kg 1/2 ] Fig. 3.10. Performance data for metal Raschig rings showing the effect of the system and the test conditions

46

3

Experimental determination of packing performance

Pall rings, metal, ds = 500 mm, Z = 600 1/m2 Ethylbenzene/Styrene, 67 mbor, L/V = 1, H = 2 m ^

--"

3

-cr-" o—••

CF—6-O-

—O"

-o-

A

12 10

a

/

>[3

- — u — bu mm — o — 25 mm —A— 15 mm

r

/

t .

^"'

/

•

y

, -—

-oS7 CD •

6

1

/ /

'

CD < ] QCO

0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 Vapour capacity factor Fv [m~ 1/2 s"1 kg 1/2 ]

Fig. 3.11. Performance data for metal Pall rings showing the effect of packing size

3.4

47

Experimental results

Pall rings, metal, ds = 500 mm, Z = 600 1/m2 Methanol/EthanolJ bar, L/V = 1. H = 2 m

"

_r—|

4

^

cz

—-^

o

.

i

'• •

•

o— —o- =

12 10

co CD

i A

vsb-

ZD CO

-D—^ ]

•

— o — 50 mm — a — 25 mm — A — 15 mm

' 3 -

yr

^

Q .

O

/ /

I d

V ./

^.

> > —O"

A-

u

!

i

CO CO CD

Ja D

E

(—>

o CD CDCO

cr

ID

<\

4

i

**—

2

n

>

M

M

0.4 0.6 0.8

—

1.0 1.2

—

1.4

1.6 1.8 2.0 2.2 2.4 2.6 2.'

Vapour capcity factor Fv tm" 1/z s"1 kg 1/2 ] Fig. 3.12.

Performance data for metal Pall rings showing the effect of packing size

48

3

Experimental determination of packing performance

Pall rings, metal, ds= 500 mm, Z = 600 1/mz Ring size 50 mm, H = 2 m, ratio L/V = 1

1,2-Propylene/Ethylene glycol -©-• Ethylbenzene/Styrene - © - Ethylbenzene/Styrene

_

6.7 mbar

6

/

a .

^

•

2 ••ir

0.8

1.0 1.2 1.4 1.6

1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2

Vapour capacity factor Fv [m" 1/z s"1 kg 1/z ] Fig. 3.13. Performance data for metal Pall rings showing the effect of the system and the test conditions

3.4

49

Experimental results

Metallic rings, ds=220 mm, Z=2036 1/m2 Chlorobenzene/Ethylbenzene, 67 mbar, L/V=1, H=15 m

38-mm Pall ring N=14301 irr3 — o — VSP ring 1 N = 30948 rrr3 —^— 50-mm Pall ring N=6000 m"3 — o - VSP ring 2 N = 7621 m"3 ••••A---

a Z3 CO

i 6 E

•te _ co CO

<±>

6

/

fcr .

•

*-

0 o CD CD.

0

0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 4.0 Vapour capacity factor Fv [m~1/2s~1 kg 1/z ]

Fig. 3.14. Performance data for various metal rings determined in tests on the same system and under the same conditions

50

3

Experimental determination of packing performance

50-mm rings, metal, ds=220 mm, Z=2036 1/m2 Chloro-/Ethylbenzene, 67 mbar, LAM. H=1.45 m 1.8 .a ^

/ A

1.4

—TT

VP

^ _ . \ / Or

\

3 &—• TOP-Pok. N = 6880 m-

Pall rings. N=6360 nr 3

> /

/


^

oo E cu •—• O

Q.

n0.4

0.8 1.2 1.6 2 2.4 2.8 3.2 Vapour capacity factor F v [m" l/2 s" 1 kg1/2]

Fig. 3.15. Performance data for metal Pall and Top-Pak rings determined in tests on the same system and under the same conditions

3.4

51

Experimental results

Metallic rings, d s = 220 mm, Z--2036 1/m2 Chlorobenzene/Ethylbenzene, 67 mbar, L/V=1, H = 1.5 m

V

10

•a CO

Ml

/

V

-CMR-Turbo No. 1.5, N=62430 m"3 Pall ring N=53200 m~3 P

O- - 2 5 - m m

t

/ V/

a __

A

¥--^—

Y

j

/

\A CD. O t_ CO

c5L <J

0.8 1.2 1.6 2.0 2.4 2.8 3.2 Vapour capacity factor F v [m" 1/2 s" 1 kg1/2]

3.6

Fig. 3.16. Performance data for metal Pall and CMR-Turbo rings determined in tests on the same system and under the same conditions

52

3

Experimental determination of packing performance

50-mm rings, metal, ds=220 mm , Z=2036 1/m2 Chlorobenzene/Ethy[benzene, 67mbar(L/V=1,H=15m

/

-a

.—.

I £•

J

/ 2

/

Y

rE <"

0.4

0.8 1.2 1.6 2.0 2.4 2.8 1/2 1 1/2 Vapour capacity factor Fv [ m s kg ]

3.2

Fig. 3.17. Performance data for metal Pall and Hiflow rings determined in tests on the same system and under the same conditions

3.4

53

Experimental results

Hiflow rings, plastic, ds=220mm , Z= 2036 1/m2 Chiorobenzene/EthyIbenzene, 67mbar, L/V = 1, H = 1.5m

CO '

'

> /

0.4

0.8

1.2 1.6 2.0 2.4 2.8 3.2 Vapour capacity factor Fv [m 1/2 s~ 1 kg 1 / 2 ]

Fig. 3.18. Performance data for plastic Hiflow rings showing the effect of packing size

3.6

54

3

Experimental determination of packing performance

50-mm rings, ceramic, ds=220 mm, Z=2036 1/m2 Chloro-/Ethylbenzene, 67 mbar, L/V--1, H--1.5 m 2.5 CD

1.5

o

0.5 12 10

•=

.-a— Pall ring N--6195 1/m3 - * - INTALOX saddle N = 8175 1/m3 o— Hiflow ring = 4684 1/m3

^

6

(ZL <

1

-o

CO CD

Q.

.

. _

CI

O

o cu Q. CO

0 0.6

1 1.4 1.8 2.2 2.6 3 3.4 Vapour capacity factor Fv [nr 1 / 2 s- 1 kg 1/z ]

Fig. 3.19. Performance data for various 50-mm ceramic packings determined in tests on the same system and under the same conditions

3.4

55

Experimental results

MONTZ-PAC Bl-300. metal, ds--220 mm. Z--2150 l/m 2 Chlorobenzene/Ethylbenzene, L/V=l H = 1.4 m

133 mbar 67 mbar 33 mbar

/

Qi • ' t _^..

9 L

Q. C=

—. 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 Vapour capacity factor Fv [m~1/2s~1 kg1/2 ] ^

-

*

0

—

•

—

—

—

Fig. 3.20. Performance data for metal Montz-Pac Bl-300 packing showing the effect of operating pressure

56

3

Experimental determination of packing performance

RALU-PAC 250 YC, metal, ds = 220 mm. Z=2150 1/m2 Chlorobenzene/Ethylbenzene, L/V=l H = 1.4 m

133 mbar

-—^— 67 mbar 33 mbar a. o "E 6

i

3 E 2 c=

CO

52CD GO

1 '

0 0.4

0.8 1.2 1.6 2 2.4 2.8 3.2 3.6 Vapour capacity factor F v lm~ l/2 s~ 1 kg 1/2 ]

Fig. 3.21. Performance data for metal Ralu-Pac 250 YC packing showing the effect of operating pressure

3.4

Experimental results

57

Gempak A 2T metal, ds=220mm. H=L5m. L/V=1, 67 mbar

10 8

— —o—

6I

Chlorobenzene/Ethylbenzene Z=215O 1/m2 — o ~ pQra-/meta-Xylene Z = 600 1/m2

1 /

11 /

4 2

r

0 1 1 / °-

cS-

c

/

2 s

0 0.4

0.8

1.2

^—

F—^

1.6

2.0

2.4

2.8

3.2 1

12

Vapour capacity tactor Fylm'^s" kg ' ] Fig. 3.22.

i

/

Performance data for metal Gempac A 2T packing for various test systems

3.6

4.0

58

3

Experimental determination of packing performance

Gauze packings, metal, ds=220 mm, Z=2036 1/m2 Chloro-/Ethylbenzene, 67 mbar, L/V = l. H=1.5 m

\ /

6

o CD

N

O

c> < ^

^ ^ --o— —•—

Sulzer packing BX Montz packing A1

o CD

rf

—on.

C_>

Q.

"•oE

<

r

———*"

CD

QL

CO

0.2

0.6

1.0

1.4

1.8

2.2

2.6

3.0 3.4

1

Vapour capacity factor Fv [ m ^ s " kg1'2] Fig. 3.23. Performance data for various types of metal gauze packing determined in tests on the same system and under the same conditions

3.4

59

Experimental results

25-mm Bialecki ring, metal N=55000 m"3, d s = 0.15m, H = 1.4m Air/Water, 1 bar, 293 K

50-mm NOR-PAC, plastic N=7320m 3 ,d s =0.3m.H=1.5m Air/Water. 1 bar,292 K 100 80

-A 3

2

u L [m /m h] a 0 ^60 20 #72.5

fl \l 1

W 40 •^ 30

•o CD

1r \ J, 3.V 'J / tf // /

HI

u L [m 3 /m 2 h] o 0, • 10 • 20. A 40 v 60. •

4

< 20

S 15 j

0.3 0.4

//i / / /

0.6 0.810

1.5 2

I'ftJ

3

/ Iff / IfI

Gas velocity u v [ m / s ] 0.3 0.4

/

10

3

0.6 0.8 1

1.5 2

3

4

Gas capacity factor Fv [m"l/2s~1kg1/2] Fig. 3.24. Pressure drop data for 25-mm metal Bialecki rings showing the effect of liquid load

0.6 0.8

n

T/

u

v

t /

if p /

f 1.5

2

3

1/z Gas capacity factor Fv [m""1/z s"1 kg g1/2]

Fig. 3.25. Pressure drop data for 50-mm plastic Nor-pac rings showing the effect of liquid load

60

3

Experimental determination of packing performance

45-mm Hackette, plastic N=12850 m-3ds=0-3m,H--L35m Air/Water, 1 bar, 291 K

50-mm Hiflow, plastic = 6280ni 3 ,d s --0.3m.H--Um Air/Water. I bar. 296 K 60

100

1 1 || 4

80

-i

60

40

—tf/ \

\ A

Y

m

/

D /

40 30 <

i i u L [m 3 /m 2 h] o 0 3 10 • 20, ^ 43

Ij' i

20

th u/

/'

15 CD

i/t

10 1

t /

d

r

/)

// p

< 3

•o

/m2h i

[m a 0 * 15 -&30.7 • 46.0 #61.4 ---70.6

f A%

/ w /A

10

/&

CD

j

/1111//Y/

/

I 20

Ihf

i l l

CO CO

i

t

7

f/ /

1

1.5 2

3

4

6

Gas capacity factor Fv [m"1/2 s"1 kg 1/2 ] Fig. 3.26. Pressure drop data for 50-mm plastic Hiflow rings showing the effect of the liquid load

2 06 1 2 3 4 Gas capacity factor Fv [m"l/2s"1 kg1/2l Fig. 3.27. Pressure drop data for 45-mm plastic Hackette packing showing the effect of the liquid load

3.4

Experimental results

61

50-mm packings, ceramic d s = 0.45 m, H =1.4 m Air/Water, 1 bar, 296 K

50-mm packing size, plastic d s --0.45m, H = U5m, Air/H 2 0, STP 100 IA

I /

4

9

i -/-

n

7 I

e (JD

20

i/ "A

D ^

/ -

r

1

/

/

0.5

J 20

CD CO CO

o>

Hiflow ring a , A N=5004m- 3

0 /

r „ -20

D

e

CD.

D

/

40

Q.

10

T

„

=1=

c

(

60

I

y 1//

60

INTALOX saddle o , v N-8882m" 3

U

2

n3/r n h

p 0.8 1

2 1.5

Gas capacity factor

0.6 Fv [rn l/2 s 1 kg l/2 ]

Fig. 3.28. Pressure drop in various beds of 50-mm plastic packing determined in tests on the same system and under the same conditions

1 1.5 2 3 Gas capacity factor F v lm- l / 2 s- 1 kg 1 / 2 ]

Fig. 3.29. Pressure drop data for 50-mm ceramic Hiflow rings and Intalox saddles showing the effect of liquid load

62

3

Experimental determination of packing performance

25-mm Bialecki ring, metal,ds=0.15m, H =1.5m,Air/H20.STP|

7 „

in

zl)

y/

pn

15

f

0u

60

e 10' T= 8<

-

r

° 6 —•

7

V

40

y-

• 20

z

H

1

/

^ n

7i

UL=10 m^/urr

"CD

]

—

-o

1" 2(

5 J

1.5

n1

1 0.1

0.15 0.2

0.3

0.4

0.6

0.8 1.0

1.5

2

3

Gas velocity u v [m/s] 0.1

0.15 0.2

0.3

0.4

0.6

0.8 1

1.5

2

3

Gas capacity factor Fv [m" l/2 s" 1 kg1/2 ]

Fig. 3.30. Liquid holdup data for 25-mm metal Bialecki rings showing the effect of load

25-mm NOR-PAC ring, ds= 0.15 m, H = 1.4 m, Air/H 2 0, STP 20 ^

plast i r e

15

/80 !! ^

t

io 8

n nr

M

/, 1Ci

I

/ ^

A

—-j — /ai Y 1A /

60'

6

ti

\ u -36 m3/m2h

I 4

j-

IB.

TD

A

'i- 3

/9 0.1

0.15 0.2

03

0.4

0.6 0.8

1

1.5

2

3

4

Gas velocity u v l m / s ]

Fig. 3.31. Liquid holdup data for 25-mm plastic Nor-Pac rings showing the effect of load

3.4

63

Experimental results

Pall rings,metal, Air/Water, 1 bar, 293 K, F v ^0.7 FVtFl

d=15mm,N=229225m d s =0.3m ( H=0.8mV d=25mm,N=52000m d s =0.22m,H=1m

d=35mm,N = 19520m ds= 0.22 m,H = 1.3 m 0.4

0.6 0.8 1 15 2 3 4 5 6 3 3 2 Liquid load u L -10 [m /m s]

Fig. 3.32. Liquid holdup data for metal Pall rings of three different sizes

Montz packing, metal, Air/Water 1 bar,291K, Fv < FvF| 10 - B1-300 ^ ds=0.22m

t31-200 \ J rl s =0.22m-

^

3

y

4

A

y

A y >

B1-IOC 1 1.5

0.6 0.6

-o.; y y ^y°

1

1.5 2 3 4 6 3 Liquid load uL-10 [m 3 /m 2 s

Fig. 3.33. Liquid holdup data for metal Montz packing of three different sizes

1.3'i-1.43r

10

n

15 20

64

3

Experimental determination of packing performance

50-mm Pall ring, d s = 0.3m, H = 1 -1.4 m Air/Water, 1 bar,293 K. F V <0.7-FV.FI A

/ y 3

y 4

—1~^

s^

y /

3

yd

2 1.5

y 1

1.5

r 2

3

4

6

3

8

3

10

Fig. 3.34. Liquid holdup data for ceramic, metal, and plastic Pall rings

15

2

Liquid load uL 10 [m /m s]

Plastic rings, Air/H 2 0,

d s = 0.3m,

H = 1.4m

FV =0.9 - U r n " 1 ' 2 s " 1 k g l / 2

STP.

• ^ ^

6

50-mm Hiflow, N = 6815 1/m 3 -

m

jE

N c

-^

y

3

a.

45-mmHackette

1 2

N--12000 1/m3

^ 5 0-mm JOR-F 1.5

2

3

4

N--7 i 6

8 o

Liquid load uL -10

710 1/m3 10 T

7

z

[rr/m s]

15

20

Fig. 3.35. Liquid holdup data for plastic Hiflow, Hackette, and

Nor-Pac packing

3.4

65

Experimental results

*-PAC rings, plastic, 1 bar, 273 K. Fv < 0.7 • R V.FI.

D

•=

0 Air/Water d s = 0.15m, H - - U m A Air/Solution of organic acid ds = 0.22m, H = 4.3m

3

r y

CZ)

/

^ 1.5

i

ds = 0.22m, H = 1m a Air/Water * Air/Methanol -B- Air/Water-Ethyleneglycol o Air/Water

••= 0.8

0.6 0.4 0.3 0.4

0.6 0.8 1

1.5 2

3 3

4 3

6

8 10

15

2

Liquid load uL-10 [m /m s] Fig. 3.36. Liquid holdup data for plastic Nor-Pac rings of two different sizes

Air/Water, 1 bar, 293K,

y°

— 10 —

Q

CD

D

Fv <0.7-F V F l

I I I

1

>> ;J

- M o n t z packing Bl-300, met al r<

1 4 i

o /

''y

r

1.5

y±Y

1

1.5 2

5()-mm Hi flow rina. plastic 3 = 6815 1/m 3

4

6

8 10

3

3

2

Liquid load uL-10 [m /m s] Fig. 3.37. Liquid holdup data for metal Montz packing and plastic Hiflow rings

15 20

66

3

Experimental determination of packing performance

Mellapak 250Y, metal, d 5 -- 0.22 m H--1.2m Air/Water, 1 bar, 295H,. F v <0.7 ' W . F l e 10 ^E

0

^f

Q

^

5

% •§

4

'

y

o

6b

o

i

3

'A

TD

f

c

?

Fig. 3.38.

OJ

1.5

2 3 4 6 8 10 3 Liquid load uL-10 [m 3 /m 2 s]

15 20

Liquid holdup data for metal Mellapak 250 Y packing

System

Packing p T lmbar] o Mellapak 250 Y 1000 A Ralupak 250 YC 1000

Air/Water 293 K

•&,•

Chloro-/Ethylbenze ne

2

3

21

B1300 B1200 Montz B1100 B1300

4

6

8 10

d s lm] 0.30 0.45

Him] 1.5 1.8 0.22,0.45 1.45,1.7 1.4 0.22 1.4 0.30 0.22 1.4

1000 1000 1000 67

20

30 40 60

L / Pv ? Flow parameter -7- -1/ — -10 Fig. 3.39.

Flood data for various types of structured sheet-metal packing

3.4

Si;

Plastics dumped packing

dtnim]

ds

H

N

m

m

1/m3

V

50

NOR-PAC ring

0.30

1.50

7320

D

50

Hiflow ring

0.30

1.40

6280

O

45

Hackette

030

135

12850

0 El

50

INTALOX saddle

0.30 0.45

1.45 1.20

9422

Flow parameter Fig. 3.40.

67

Experimental results

Flood data for various types of dumped plastic packing

4-

'-—

9875

3

68

Experimental determination of packing performance

|ds = 0.45 m, H^2 m, metol

50-mm rings , plastics, ds = 0.3m NH 3 -Air/Water, 1 bar, 295K

Hitlow ring,H=1.45m_ Ui=23m3/m2h 0.2

o Rolupak 250 YC

3

D 50-mm Hiflow Z = 2400 1/m2

u L =15m 3 /m 2 h,H435mii l l

2

_Q

2.0

§

N[1/m 3 ] A 9331 n 6425 o 6450 v 6660

1.0

1

0.8

<•

0.6

Q. <

Q. O

ZD CO CO CD

0.8 0.6 0.4

o

e

0.4

Z3 CO

n

ffl

0.3

3 -Air/H 2 0 1 bar. 295 K

CD
^

U L =10 m 3 /m 2 h CD

.0.2

0.1

I

0.15 0.4

0.6

0.8 1 1

1.5

2

3

4

1.5

2

3

4

Gas capacity factor

Gas capacity factor F v [m 1 / 2 s 1 kg 1/2 ] Fig. 3.41. Height of an overall transfer unit and specific pressure drop for various types of dumped plastic packing

Fig. 3.42. Height of an overall transfer unit and specific pressure drop for metal Ralupac 250 YC packing and 50-mm Hiflow rings

3.4

69

Experimental results

50-mm rings, metal, ds = 0.3 m, H=1.4m C0rAii7Water.l bar, 293 K. Fv=l nr 1/2 s- 1 kg1/2 20 r

15 / CO.

10

r-j

/

0.8 1

J

o H flow ring N=5000 1/ m 3 D Pall ring N= 6000 1/m 3

y

Fig. 3.43. Liquid-phase mass transfer coefficients for metal Hiflow and Pall rings

1.5 2

3

4

6

Liquid load u L l 0 3 [m 3 /m 2 s]

Plastic rings , ds=300mm , H = U m System: Air/C0 2 -H 2 0, 1 bar, 296 K

Fig. 3.44. Liquid-phase mass transfer coefficients for various types of dumped plastic packing

Vb o

2

3

4

6 3

8 10 3

Liquid load uL-10 [m /m2s]

8 10

70

3

Experimental determination of packing performance

Hiflow ring ceramic, d s = 0.3m, H = 1.3m C0 2 -Air/Water, 1 bar, 293 K 30

&

— 20-nim ring 3 20 N = 10740 l/21/m1 Fv-( 185 m- s" kg

<

y y

y

A\

y y

10 8

y

3 y yy

y ^

6

4

y

4

bU-rnm ring 5120 1/m3 1 1/2 n F v- 0.55 nr s- kg

\_J 1.5

2 3 4 6 8 10 Liquid load uL-103 [m 3 /m 2 s]

Fig. 3.45. Liquid-phase mass transfer coefficients for ceramic Hiflow rings showing the effect of the packing size

15

50-mm rings, plastic, ds=0.3 m, H =1.5 m CQ 2 -Air/H 2 0.1 bar. 294 K, uL=15 m 3 /m 2 h CO (—

. _ ~*pi

'

• CO

MITIOW

a

o

a

16 — Pall ring 14

f ° d 1 12 5 10

/ 0.4

•5-

1

lliiy

f

rT(—

/ /

^

A i

r

Q

0.6 0.8 1 1.5 2 Gas capacity factor Fv [m" 1/2 s" 1 kg 1/2 ] Fig. 3.46. Liquid-phase mass transfer coefficients for plastic Hiflow and Pall rings

3.4

71

Experimental results

50-mm rings - o - Hiflow N--6450m"3 - D - P a l l N = 6425m"3 NH 3 -Air/H 2 0, 1 bar. 288K. d s = 300mm, H = 1.35m Plastic u

1

O

.o o GO

o

15 m3/m2

• 0.4

0.6

1

1.5

2 V2

1/;i -1

v = 116 m

F

3 1

Gas capacity factor Fv [m s" kg

1.5 2

1/2

3

Liquid load

4

kg

5 3

1/2 • I

7 9 3

u L -10 [m /m 2 s]

Fig. 3.47. Gas-phase mass transfer coefficients for plastic Hiflow and Pall rings showing the effect of the gas and liquid loads

50-mm NOR-PAC ring, plastic d s --0.3m, H--1.4m, N--7710 1/m3 20 15 10

:=

J

L

Operation v start up A 2 days o 4 days • 12 days

6

C02-H20/Air, STP E

2

o CO

a

Fig. 3.48. Liquid-phase mass transfer coefficients and liquid holdup data for plastic Nor-Pac rings showing the effect of operating time

Liquid load

uL • 10

[m3/m3s]

72

3

Experimental determination of packing performance

25-mm NOR-PAC. plastic, ds=1m, H=1m NH 3 -Air/Water, 1 bar, 293 K

3

4

6 8 10 20 30 3 2 Liquid load uL [m /m h]

Fig. 3.49. Height of an overall transfer unit for 25-mm plastic Nor-Pac rings showing the effect of operating time

50-mm Hiflow ring, plastic, ds=0.3m, H=1.3m C0 2 -Air/Water, 1 bar, 293K. Fv = 0.55nTl/2s-1kg1/2 30 o

E

20

? I 15

A

unt rea ted N =68K3 1/m3 tre ateci N =6890 1;

i

X W

/ /

'£.

/ 1.5 2 3 4 6 8 10 3 3 Liquid load u r 1 0 [m /m 2 s]

15

Fig. 3.50. Liquid-phase mass transfer coefficients for treated and untreated surfaces of 50-mm plastic Hiflow rings

4 Fluid dynamics in countercurrent packed columns The flow patterns for the liquid and gas streams in packed separation columns depend on the geometry of the channels formed by the arrangement and size of the packing in the bed. Other relevant factors are the texture of the packing, the velocities of the countercurrent streams, and the physical properties of the two phases under operating conditions. The very complexity of these parameters and their interrelationships renders an accurate theoretical description of the flow patterns almost impossible. Consequently, simplifying assumptions must be made, and their validity must be confirmed by experiment.

4.1 Fluid-dynamics model It can be assumed that the liquid phase flows in the form of a film in channels of the same free volume as those in the bed of packing under consideration. The geometry of the channels can be described by the effective void fraction in the bed and by the ratio a of the surface of the packing to the volume of the bed. From the aspect of the hydrodynamics, the effective void fraction in a packed column is equivalent to the number of vertical flow channels in which a liquid of density QL and dynamic viscosity r\L flows in the form of a film of thickness so at an average velocity uL countercurrent to a stream of gas or vapour with an average velocity uv (cf. Fig. 4.1). Packing surface

Interfacial area

Frictional force

o

Force of gravity

1

Packing

Liquid holdup

Vapour or gas

Fig. 4.1. Equilibrium of forces during two-phase flow within a channel of a packed column Packed Towers in Processing and Environmental Technology. Reinhard Billet Copyright © 1995 VCH Verlagsgesellschaft mbH, Weinheim ISBN: 3-527-28616-0

74

4

Fluid dynamics in counter cur rent packed columns

If steady-state conditions exist and inertia forces are neglected, it can be assumed that the force of gravity is in equilibrium with the shear forces at any point in a given coaxial layer of thickness s within the liquid film and that the frictional force exerted by the vapour of density Qy acts at the surface of the film. Thus, in any given layer of thickness 5 in a liquid film of total thickness so, the equilibrium of forces can be described by duL>s

If the downward liquid velocity uLs is expressed as a function of the density QL and the dynamic viscosity r\L, Eqn (4-1) can be integrated to give uLtS = Ks-—

(4-2)

Differentiation then yields the velocity gradient in the film, i.e.

ds

S

° r\L

Multiplication by i}L yields the shear stress in the liquid at the gas interface. In steadystate operation, the shear stress in the liquid is in equilibrium with that in the vapour of density QV and velocity uv, i.e. T\LK - QLgso = - | ~Y~ Qv

(4-4)

The integration constant K can therefore be obtained. The equations thus derived are valid for vertical flow in both phases and laminar flow in the liquid film. Examples of departures from this model are oblique channels arising from the geometry of the packing, turbulent flow, and the texture of the packing. A practicable means of allowing for them is to introduce a function for the flow or resistance factor §. Experimental studies to verify the equations in the model have confirmed that this procedure is permissible. Rearranging Eqn (4-4) to give K and substituting this value in Eqn (4-2) yields the following equation for the local liquid velocity uLs at any point in a layer of thickness s in the liquid film: )s r\L

(4.5)

2 /

The theoretical average flow velocity uL for a liquid film of thickness so is defined by uL = — s

o

I

uLtS ds

(4-6)

4.1

Fluid-dynamics model

75

The solution to this equation is the mean local velocity uL of a liquid that descends countercurrent to an ascending stream of vapour flowing at a mean local velocity uv within a bed of packing, i. e. y g SOQL - ^ l u v

Qvj

(4-7)

If the liquid and vapour loads uL and uv are given, the mean velocities uL and uv depend on the packing geometry and the liquid holdup hL, which is defined by

where VL is the liquid volume and Vc is the column volume under operating conditions. Experience has shown that hL is influenced by the following factors: - the texture of the packing, - the ratio a of the surface area of the packing to the volume of the bed, and - the void fraction 8. The ratio a is defined by

where AP is the total area of the surface presented by the bed of packing and Vc is the column volume. The void fraction is given by 8-

Vc Vp

~

(4_io)

where VP is the volume occupied by the packing itself, i.e. without voids. The following relationship exists between a and e: s= l-a^AP

(4-11)

If the liquid holdup hL is known and the packing is uniformly wetted, the theoretical total film thickness So is given by so = — a

(4-12)

The following relationship exists between the mean liquid velocity uL and the volumetric flow rate, which is normally given in column design problems:

76

4

Fluid dynamics in countercurrent packed columns

(4-13)

so a

The corresponding relationship exists between the mean vapour velocity uv and the pg ume flow rate of vapour volume flow rate of vapour uuvv,, i.e. i.e

Substituting the terms on the right-hand sides of Eqns (4-12), (4-13), and (4-14) for so, uL, and Uy respectively in Eqn (4-7) gives

a\LuL = V (f

QL

-}

hL{;_htf

«}*,)

(4-15)

This equation describes flow in terms of the column load, the physical properties of the liquid-vapour system, and the packing characteristics. It is thus valid for all industrial packing. The exponent n is exactly n — V3 for laminar flow in vertical channels. The extensive experimental work required to verify the relationship is described in Chapter 3. The interrelationships between hL, uVy and uL, as described by Eqn (4-15), is shown qualitatively in Fig. 4.2, in which the subscript S refers to the loading point and the subscript Fl to the flood point. It can be seen from this diagram that, if the liquid load uL is kept constant, an increase in the gas velocity Uy does not significantly affect the liquid holdup hL until the loading point uv>s is reached at the surface of the film, i.e. at s = s0. In other words, if the liquid load uL is constant, the liquid holdup hL is practically equal to hLjS at loads uv < uvs. At the point s = s0, the flow velocity is theoretically zero, and the liquid commences to hold up in the bed of packing. Afterwards, in the Uy > uvs range, the liquid holdup hL increases with the gas velocity until it attains a maximum hL>m at the flood point, when the gas velocity is uV}F[. The experiments demonstrated that it does not undergo any further change once this point has been reached, even if uL > uLjF\ (cf. lower diagram in Fig. 4.2) and if uv > UyFl. They also revealed that the vapour velocity at the loading point uv>s is about 70 % of that at the flood point uFi. Theoretically, these relationships are valid between uVjS, uL;S and hL}S', and between uv>Fh uL>Fi and hL)Ft. They follow logically from the physical model, and the mathematical description applies to the entire loading range.

4.2 Resistance to flow The resistance factor § allows for the geometry of random packing or of the flow channels in systematically stacked beds. It also allows for the transition from laminar to turbulent liquid flow and thus depends on the vapour and liquid loads. The application of Eqn (4-15) to evaluate experimental results has revealed that § is analogous to the friction factor in pipe flow in that it is a function of Reynolds number Rey for the gas phase. This is evident from Fig. 4.3, which shows the correlation between gas and liquid flow in both circular pipes and packed beds. It can be seen that the slope is practically the same in all cases.

4.2

Res is tan ce to flo w

11

ZD TD

ID

Gos or vapour load u v

-o a o

Fig. 4.2. Qualitative relationship between the liquid holdup and the phase loads in a packed column

Liquid holdup hL

The resistance factor § also depends on the liquid holdup, which is defined as the volume of stationary liquid that exists in the form of a film on the surface of the packing or is present in voids, dead spots, and phase boundaries in the bed of packing within a two-phase countercurrent column during the period in which the liquid phase descends at a constant rate onto the surface of the bed. There are two components of liquid holdup: a static hLst and a dynamic hL>dyn. Thus hL>dyn

(4-16)

The dynamic component flows downwards, and the static remains within the bed. As the liquid load increases, the difference between the two components becomes progressively greater, until the stage is reached when the static can be regarded as nonexistent. In most industrial mass transfer processes, the dynamic component preponderates by several orders of magnitude. An expression for hL that is valid over the entire loading range can be obtained by rearranging Eqn (4-15). Thus

78

4

Fluid dynamics in countercurrent packed columns

Gas Reynolds number Re V(Packing

fe

&

o 3.

00 CD Cd

CO

oo CD

Gas Reynolds n u m b e r R e j Fig. 4.3. Qualitative log-log relationship between the resistance factor and the gas Reynolds number in the channels of a packed column with the liquid Reynolds number as parameter. The corresponding relationship for flow in tubes is presented as a comparison.

hL =

g 3

WiJ

(4-17)

a

„ 4

/IL) 2

The basic assumption in this case is that the flow of liquid over the packing is laminar. It differs from flow in the vertical channels of the model in that it continually changes direction and is interrupted at boundaries. Another point in which the theory departs from reality is that laminar flow in the film applies only at comparatively low liquid loads. The critical Reynolds number, above which flow becomes turbulent, has been derived from numerous measurements. According to definition, uL

ReL,cr = 10

(4-18)

For laminar liquid flow in the vertical channels of the model, the exponent n in Eqn (4-18) is exactly n = V3; and a figure of n = 2/3 has been determined for flow in systematically arranged beds of packing. The value changes at higher loads, and the following relationship for turbulent film flow was established by experiment on about 50 different types of packing dumped at random:

N\\ lh

n = \— ,a

(4-19)

where h is the height and d the outer diameter of an individual element of packing, N is the number of elements per cubic metre, and a is the surface area per unit volume in m2/m3.

4.2

79

Resistance to flow

Although Eqn (4-17) can be solved only by iteration, its great advantage is that it is analogous to the equation for two-phase countercurrent flow in vertical tubes. The curves presented in Fig. 4.4 convincingly verify this analogy. The first step in their compilation was to rearrange the equation to solve for §, i.e.

hL(z-hLf\

uL

1

(4-20)

UyQv

Values of | thus calculated for flow in a bed of metallic Bialecki ring packing were plotted against the corresponding Reynolds numbers with the liquid load uL as parameter. The values for the Reynolds numbers were derived from the following relationship:

Pipe flow

Bialecki rings

\

VV \ \ \V\ \^\ \ -A- V .^

100 70

\

V

\\

\\

50 40

V_

30

\ S

20

\

£

\\^ V\ \ \ \ \ \ \ \ \ \

S 5 4

\ \

\ \

10

\

\\

\ \^

3

\

2

L

41'

\

\ V

\V A

\ \ y_N\^\ _^.\

\ !^_ K\

w

ct:

10 Y 2.8

0.7 0.5 0.4

---

0.3

\

\N

\ ^ y.

\

\ \ \

\ \\ ^ \\ \\\

S

\ \

\

>

\\\ \\

0.2

01

30

= 80m 3 /m 2 h

\\v \\\ \\\ s V L 40 <\\\\V\ \ 1N A\ y vV 3^ s \ \> \ Nv v \ \ \ \ NVAS. \ A \ \\ v > v y \ \\

\ \ 0 " X \ \v

CO CD

ri ^g tQl N =78323 1/m3 a =331 m z /m 3 e =0.9381 - Syslem: Air/Water 1 bar ; 298 K

5-mni Biale :ki

\s

\ \ \-— A sy \ \\\> \\ \ yX

u = 80m /m h" V \

J

-2

50

100

300 500

1000

r-

r" --•2.8 3000 5000 10000

Gas Reynolds number Rev Fig. 4.4. Resistance factor as a function of the gas Reynolds number for a packed column and a tube with the liquid load as parameter. Valid for an air/water system at STP.

80

4

Fluid dynamics in counter cur rent packed columns Uyid-lSp)

Qy

(4-21)

Key —

The corresponding curves for two-phase pipe flow, calculated from the standard equations cited in the literature, have been included in the diagram. The fact that the two sets of curves are largely parallel in the range of laminar gas flow provides striking evidence of the analogy and confirms the validity of the model based on flow in vertical channels in packed columns. The relative positions of the two sets of curves show that the resistance factors are higher in the bed of packing. However, this is only to be expected, because the pressure drop for gas flow in beds of packing is considerably greater than that in vertical smooth pipes. Evaluation of the results obtained on all the packings investigated led to the following relationship: = C Rey2 ReL°

(4-22)

in which C is a constant that is characteristic for individual types of packing and must be determined experimentally. Numerical values for C at the loading and flood points for various types of packing are presented in Table 4.1. A relationship that is more useful in practice for the determination of § at the loading and flood points in specific separation tasks is (4-23) C2

rMlL

where r| L /ry is the viscosity ratio for the two phases and W is the well-known flow parameter described by Eqn (1-3), i.e.

Table 4.1. Data for determining the loading and flood points in random beds of packing Dumped Packing

Pall ring

Ralu ring

Material

Size mm

N 1/m3

Metal

50 35 25

6242 19517 53900

112.6 139.4 223.5

0.951 0.965 0.954

2.725 2.629 2.627

1.580 1.679 2.083

Plastic

50 35 25

6765 17000 52300

111.1 151.1 225.0

0.919 0.906 0.887

2.816 2.654 2.696

1.757 1.742 2.064

Ceramic

50

6215

116.5

0.783

2.846

1.913

Plastic

50 50 hydr.

5770 5720

95.2 95.2

0.938 0.939

2.843 2.843

1.812 1.812

CFI

8

m 3 /m 3

4.2

81

Resistance to flow

Table 4.1. (continued) Dumped Packing

Material

Size mm

N 1/m 3

a m 2 /m 3

m 3 /m 3

E

Cs

cFI

NOR PAC ring

Plastic

50 35 25 6 25 10

7330 17450 50000 48920

86.8 141.8 202.0 197.9

0.947 0.944 0.953 0.920

2.959 3.179 3.277 2.865

1.786 2.242 2.472 2.083.

Hiflow ring

Metal

50 25

5000 40790

92.3 202.9

0.977 0.962

2.702 2.918

1.626 2.177

Plastic

50 50 hydr. 50 S 25

6815 6890 6050 46100

117.1 118.4 82.0 194.5

0.925 0.925 0.942 0.918

2.894 2.894 2.866 2.841

1.871 1.871 1.702 1.98?

Ceramic

50 38 20

5120 13241 121314

89.7 111.8 286.2

0.809 0.788 0.758

2.819 2.840 2.875

1.694 1.930 2.410

Glitsch ring

Metal

30 PmK 30 P

29200 31100

180.5 164.0

0.975 0.959

2.694 2.564

1.900 1.760

Glitsch CMR ring

Metal

1.5" 1.5" T 1.0" 0.5"

60744 63547 158467 560811

174.9 188.0 232.5 356.0

0.974 0.972 0.971 0.952

2.697 2.790 2.703 2.644

1.841 1.870 1.996 2.178

TOP-Pak ring

Alu

50

6871

105.5

0.956

2.528

1.579

Raschig ring

Ceramic

50 25

5990 47700

95.0 190.0

0.830 0.680

2.482 2.454

1.574 1.899

VSP ring

Metal

50 25

7841 33434

104.6 199.6

0.980 0.975

2.806 2.755

1.689 1.970

ENVIPAC ring

Plastic

80 60 32

2000 6800 53000

60.0 98.4 138.9

0.955 0.961 0.936

2.846 2.987 2.944

1.522 1.864 2.012

Bialecki ring

Metal

50 35 25

6278 18200 48533

121.0 155.0 210.0

0.966 0.967 0.956

2.916 2.753 2.521

1.896 1.885 1.856

Tellerette

Plastic

25

37037

190.0

0.930

2.913

2.132

Hackette

Plastic

45

12000

139.5

0.928

2.832

1.966

Raflux ring

Plastic

15

193522

307.9

0.894

2.825

2.400

DINPAC

Plastic

70 47

9763 28168

110.7 131.2

0.938 0.923

2.970 2.929

1.912 1.991

hydr. = made hydrophilic

82

4

Fluid dynamics in countercurrent packed columns

(4 24)

-

The one and only constant C in Eqn (4-23) describes the shape and surface of the packing. The viscosity m and load nL exponents are practically independent of the type of packing, and the form of Eqn (4-23) has been confirmed for all the types of packing investigated.

4.3 Loading conditions If inertia forces are neglected and steady-state conditions exist in the main loading range, it is assumed for the purpose of drawing up the model that the shear forces and the force of gravity are in equilibrium in a layer of any given thickness between 5 = 0 and s = s0 within the liquid film. It is also assumed that the frictional force exerted by vapour of density QV and velocity uv acts at the surface of the liquid film (cf. Fig. 4.1). At a given liquid load wL, the liquid commences to hold up when its velocity at the interface with the vapour becomes zero, i.e. when ML,S — 0 at s = s0'. UL>S = 0

(ifs

= so)

(4-25)

The corresponding vapour velocity is the upper limit for the absolutely stable hydrodynamic range defined by

<426)

VtV^VIF

-

The practical application of Eqn (4-26) necessitates a knowledge of the liquid holdup hL = hLS at the loading point and the associated resistance factor (cf. Fig. 4.2). Substituting uv>s, as defined by Eqn (4-26), for uvin Eqn (4-15) yields the following theoretical relationship for the liquid holdup at the loading point: Solving for hL>s and inserting in Eqn (4-26) yields the following equation for the vapour velocity at the loading point:

—

i/12 8

12 rw UL QL

8

QL

LI nV/ Qv

As has already been mentioned, the resistance factor § 5 allows for the shape of the flow channels and is therefore dependent on the packing geometry and on the vapour and liquid loads; and it also allows for the transition from laminar flow in the liquid phase. It can be expressed as a function of the flow rate LIV, density QV/QL, and viscosity r\L/r\v ratios by combining Eqns (4-23) and (1-3). Thus,

4.3

Loading conditions

83

-

ci

(4-29)

Qv QL

In this equation, the load point constant C5, which is specific for the packing, and the exponent ns must be determined empirically. The equation has been confirmed by experiment and is presented graphically in Fig. 4.5. It can be seen from this diagram that a discontinuity, which correlates with the phase inversion, divides the function into two linear sections. The large majority of mass-transfer processes take place within the section represented by the lower values of flow parameter on the axis of abscissae. The values at the further end

Phase inversion

Continuous phase :gas ) Disperse phase : liquid S CO

on

0.4

Flow porameter I

ff

V I pL W Fig. 4.5. Qualitative log-log relationship between the resistance parameter and the modified flow parameter

of the axis correspond to very high liquid loads, and the high slope of the linear relationship in this range indicates an increase in the resistance factor 5s and a proportionally greater pressure drop in the gas phase. It can thus be concluded that the intersect of the two straight lines, i.e. the discontinuity, is the point at which phase inversion occurs. In other words, this is the point at which the gas becomes the disperse phase; and the liquid, the continuous. It is given by (4-30) The associated values for the liquid load correspond to phase inversion at 50-100 m3/m2h. Data on the higher loading range are not yet available for all the packings investigated. An example of a known relationship is presented in Fig. 4.6. Accordingly, the values for the constant Cs and the exponent ns in Eqn (4-29) depend on the loading range. It has been found that the following empirically determined numerical values of ns apply in common for all types of packing in the loading ranges concerned:

84

4

Fluid dynamics in counter cur rent packed columns

(4-31)

£ W i*-> 0.4-*„, =-0.723

(4-32)

35-mm Bialecki ring, metal, System: Air/Water, 1 bar, 293 K

*-*

*^

<s

0.1

0.2 0.3 0.4 0.50.6 0.8 1 Flow parameter | | / ^ ( A

2

3 4 56

N

Fig. 4.6. Resistance parameter for a bed of metal packing

Numerical values of the constant Cs for specific types of packing are listed in Table 4.1 (randomly dumped) and Table 4.2 (systematically stacked).

4.4 Flooding conditions The flood point in a bed of packing can be described physically by empirical curves in which the liquid holdup hL has been plotted against the gas load uv with the liquid load uL as parameter; or plotted against uL with the gas load uv as parameter. Curves of this nature are presented qualitatively in Fig. 4.2. In the upper diagram, the curves are vertical at the flood point, and can thus be described by the following equations: —— = 0;

uv^

uv>Fl

-JJ^- = 0; uL -* uLtFl

(tor uv = uv>Fl)

(for uL = uL>Fl)

(4-33) (4-34)

Applying these equations to Eqn (4-15) for n = % leads to the following theoretical flood point correlations:

4.4 Flooding conditions

85

Table 4.2. Data for determining the loading and flood points in geometrically arranged beds of packing Arranged packing

Material

Size mm

N 1/m3

a m2/m3

m3/m3

Pall ring

Ceramic

50

7502

155.2

0.754

Bialecki ring

Metal

35

20736

176.6

0.945

Ralu pack

Metal

YC-250

250.0

Mellapak

Metal

250 Y

Gempak

Metal

Impulse packing

Montz packing

Euroform

CFI

8

3.793

3.024

0.945

3.178

2.558

250.0

0.970

3.157

2.464

A2T-304

202.0

0.977

2.986

2.099

Metal

250

250.0

0.975

2.610

1.996

Ceramic

100

91.4

0.838

2.664

1.655

Metal

B1-200 Bl-300

200.0 300.0

0.979 0.930

3.116 3.098

2.339 2.464

Plastic

Cl-200 C2-200

200.0 200.0

0.954 0.900

2.653

1.973

PN-110

110.0

0.936

3.075

1.975

Plastic

for the gas load uV}Fi,

i / T T (e-hL>Fl)2 \lhLZL and for the liquid load, 1

QL

(4-36)

For a given liquid-gas mass flow ratio L/V, these equations are related as follows:

u

L,Fl —

Qv Qv QL

Tv

V

(4-37)

U

V,Fl

It follows that

I - 8) =

~y

g

V


UVtFi

(4-38)

QL

This is a purely theoretical relationship that shows how the liquid holdup at the flood point depends on the packing geometry, the physical properties of the system, and the gas or

86

4

Fluid dynamics in countercurrent packed columns

vapour load. Only one of the solutions of this fourth-order equation is of physical significance: in the first place, the liquid holdup cannot possibly exceed the effective void fraction; and, in the second place, the right-hand side of the equation must be positive. This implies that the liquid holdup at the flood point must not be less than e/3 and must therefore lie uniquely within the following limits: E/3 < hLtFl < e

(4-39)

The holdup at the flood point hLFh as defined by Eqn (4-38), is theoretical, and it remains to be seen whether its existence can be verified in practice. If Eqn (4-38) is written in the following simplified form, the values determined for hLF[ will be of the same order for water (subscript W) as the reference liquid: •SE]

hLtFl = 0.3741 8 - ^

r

\ QL

\W

(for 0.1
(4-40)

/ T I L > 1 - 1 0 " 4 kg/ms

Values determined by flood point measurements are usually lower, because the actual flood point is generally not attained owing to column instability and entrainment of packing elements in loose, dumped beds. The resistance factor §F/ at the flood point, as defined by Eqn (4-35), is given by (4-41) Qv QL

r\L \ r\v

Except that the exponent for the viscosity ratio is 0.2 instead of 0.4, the value at the loading point, the form of this equation is identical to that of Eqn (4-29). The constant CFi and the exponent nFh in common with Cs and ns in Eqn (4-9), must be determined empirically. The values thus obtained for nFt apply to all types of packing. In analogy to the numerical values quoted for ns in Eqns (4-31) and (4-32), they depend on whether the loading range is above or below the phase inversion, i.e.

•y L

y — < 0.4 -> nFl = -0.194

A

Ov

~77 \\ > °- 4 -> nFi = -0.708 V V QL

(4-42)

(4-43)

If the column load is higher than that at the phase inversion, the continuous gas phase becomes the dispersed phase and bubbles upwards through the downward stream of liquid, which then becomes the continuous phase. In analogy with Cs, Cm is a constant that depends on the shape and texture of the packing and must be determined empirically. Values thus obtained in numerous loading tests with air/water absorption and rectification systems are listed in Tables 4.1 and 4.2. It can be seen

4.5

Relationship between boundary loads

87

that they lie between CFl = 1.5 and CFt = 3.0 in the range of liquid loads between uL = 5 m3/m2h and uL = 80 m3/m2h. The theoretical limit is expressed by

(hL,Fi)th -> hLiFl = j e

(for uL^

0-^:^0)

(4-44)

This relationship can be derived from the preceding equations. Thus, at extremely low liquid loads, i.e. as uL or LIV tends to zero, the liquid holdup hLFi may account for about one-third of the effective void fraction 8 in the bed of packing. This fact leads to the following relationship for the theoretical maximum vapour load at the flood point uv>Fi,max'-

Uy,Fl,max = uVFl (for hLtFl = I-) = -J- \ -f- \ —\[\[^3

?

y

£>FI y

a

(4-45)

y Qv Qv

This equation contains the well-known packing factor ale3 formerly resorted to in the literature, e. g. by Sherwood, for flood point correlations. Theoretically, the maximum liquid holdup at the flood point hLFi corresponds to the void fraction e and would be reached at extremely high liquid velocities uL ^^> 0, in which case the gas velocity would be negligibly small, i. e. uv —> 0 or LIV'—» a>. Thus, (hL,Fi)th -» hL)Fi = e (for uL » 0; - y -> oo)

(4-46)

Inserting this boundary condition in Eqn (4-38) yields the theoretical maximum liquid load

uUmax\

UL,Fi,max = uL>Fi

(for hL}Fi = E) = —g — — 5 a r\L

(4-47)

4.5 Relationship between boundary loads According to the flow model, all the liquid in the bed of packing must be thrust upwards by the frictional force in the vapour if the following condition is satisfied {cf. Eqn (4-25)} uLtS = 0 (ifs = 0)

(4-48)

The associated vapour load at the flood point uv>Fi can be derived from Eqns (4-5), (4-12), (4-14), and (4-41), i.e. \ I 2g

A I hLFi * / QL

(A ^ X (4-49)

Values of uV;Fi obtained from this equation are higher than those calculated from Eqn (4-35) by a factor /, which is given by

4

Fluid dynamics in countercurrent packed columns

f = 1-

(4-50)

hr

The ratio of Eqn (4-26) to Eqn (4-49) is Uy,s

=

_1 1 [%Fi

e - /i L)5

(4-51);

and of Eqn (4-26) to Eqn (4-35), - h MV^W

^

\

§S

L}S

L,S

hL,Fl

(4-52)

These ratios lead to the conclusion that the loading point can be anticipated at about 70% of the flood point. Flooding can also be expected if the boundary condition for Eqn (4-36) is uL —> 0, in which case Eqn (4-35) becomes

W^F/

=

(4-53)

According to Eqn (4-44), the boundary condition uL —» 0 entails that hLFi = e/3. If this substitution is made in Eqn (4-53), Eqn (4-45) will again be obtained. Comprehensive experimental studies have verified that the flow model presented here can generally be applied to all kinds of packed columns with countercurrent gas-liquid systems. All the measurements agreed very well with the theoretically derived relationships for the loading and flood points. The liquid load in the tests was varied between uL>Fi = 4.88 and UL,FI = 144 m 3 /m 2 h; the gas density, between QV = 0.3 and QV = 1.37 kg/m3; the liquid density, between oL = 750 and QL = 1026 kg/m3; the dynamic viscosity of the gas, between r\v = 7.14 X 10~6 and r\v = 18.19 x 10~6 kg/ms; and the dynamic viscosity of the liquid, from T]L = 0.36 x 10"3 to y\L = 92.6 x 10"3 kg/ms.

4.6 Pressure drop in packed columns All equations found in the literature for the determination of gas-side pressure drop in packed absorption, desorption or rectification columns are empirical or semiempirical. They have largely been derived from studies on traditional packing and cannot be applied unreservedly to modern types. Therefore, the aim of this chapter is to devise a theoretical relationship that will allow the pressure drop to be calculated for both conventional and modern types of packing in two-phase countercurrent columns. It is to be based on the fluid-dynamics model described in Section 4.1, in the compilation of which it was assumed that the bed of packing is equivalent to a multiplicity of flow channels through which the liquid flows downwards in the form of a film. If inertia forces are neglected, gravity and shear are held

4.6

Pressure drop in packed colums

89

in equilibrium within the film by the frictional forces corresponding to the shear stress TV that acts in the gas or vapour at the surface of the film. xv is identical to the expression on the right-hand side of Eqn (4-4), i. e. TV= -^ - y - QV

(4-54)

in which QV is the gas density, uv the average gas velocity, and % the gas-side resistance factor. The pressure drop Ap in a bed of height H, effective area ae and effective void fraction ee = 8 - hL can be derived from Eqn (4-54). Thus, Qe

Ap = - — H xv = Ee

H xv

(4-55)

8 — h,L

The effective area ae is given by ae = fw a = au + aL

(4-56)

where fw is a factor that allows for the change in resistance caused by wetting the surface of packing with an area a, au is the area of the unwetted surface, and aL is the area of the surface of the liquid in the flow channels. In other words, the effective area ae is the sum of the unwetted area au and the area of the liquid surface aL in the flow channels. In an actual bed of packing, the hydraulic diameter of the flow channels differs from the theoretical value to an extent that depends on the column diameter ds. The difference can be allowed for by a wall factor fs, which can be obtained from the literature, i. e. —= 1+ —

(4-57)

Inserting the expressions given by Eqns (4-14), (4-54), (4-56), and (4-57) in Eqn (4-55) yields the following expression for the pressure drop per unit height: Ap

a

~W = %L (z-hLy

Uy

\

~QvJ 1

'

(4-58)

in which the § L is the resistance factor for the wetted bed of packing and is given by

| t = i/W = S ^ ^ -

(4-59)

90

4

Fluid dynamics in counter cur rent packed columns

The limiting case of hL = 0, i.e. fw = 1 and aL = 0, applies for the pressure drop per unit height Apo/H in a gas stream flowing through an unwetted bed of packing. Thus, inserting hL — 0 in Eqn (4-58) gives Apo

Qv

1T

fs

(4-60)

where %0 is the resistance factor for the dry bed of packing. The extent to which the pressure drop in the gas stream within the wetted bed exceeds that within the dry bed corresponds to the ratio Ap/Ap0, which is given by

Ap0

(4-61)

z-hL

This equation states that the increase in pressure drop caused by wetting can be described by the ratio of the resistance factors for two-phase and single-phase flow and a term that is a function of the liquid holdup, viz. (4-62)

e-hL

Eqn (4-27) allows Eqns (4-61) and (4-62) to be solved graphically in terms of the liquid load UL. This is demonstrated in Fig. 4.7, which applies to 50-mm plastics Hiflow rings. It can be seen that, as uL decreases, the function f(hL) approaches a limiting value of unity, because the liquid holdup tends towards zero and thus loses its effect. The higher the liquid load, the greater the effect on the function f(hL) and the higher the pressure drop. The diagram also shows empirically determined values for the pressure drop ratio AplAp0 plotted against the liquid load. It can be seen that the i{hL) function fairly closely fits the characteristic shape of the curve for the experimental values. Hence, the two axes of ordinates in the diagram can be equated, i.e.

50-mm Hiflow ring, PP. d s = 0.288 m, H = 1.37m Air/H2O. 1 bar, 293 K \

i

I

Theoretical curve

i

/

1

1

,d

—i

>>< » ii

H

? =99—^htoi—^^^ 0.8 0.8 ii i i i 1 0.6 0.8 1 1.5 2 3 4 5 6 8 10 15 20 Liquid load uL 103 [m 3 /m 2 s]

Fig. 4.7. Pressure drop ratio in a wetted and unwetted bed of packing as a function of the liquid load

4.6

Apo

"

Pressure drop in packed colums

91

(4-63)

\e-hL

where W is an expression for the degree of wetting. The resistance factor §# can be determined from the following equation, which has been taken from the literature: 64 Rev

1.

(4-64)

0.08

This relationship embraces the effect exerted on the gas stream by the gas Reynolds number Rev, which is defined by Uy dp Qy 6V

~

(1-8)%

Js

(4-65)

where dp is the particle diameter and is given by (4-66) The constant Cp characterizes the geometry and the surface of the unwetted packing and is therefore specific for any given type. It has to be determined experimentally. The relationship between the resistance factor %0 and the gas Reynolds number Rev is illustrated by the example given in Fig. 4.8, which is valid for an unwetted bed of 32-mm plastic Envipac rings. At low loads, the downward slope of the curve becomes more pronounced. In this range of Reynolds numbers (Rev ~ 2100 or less), flow is laminar, and the first summand in the expression on the right-hand side of Eqn (4-64) governs the shape of the curve. Above this, flow becomes turbulent, and the second summand becomes the more decisive.

32mm ENVIPAC,PP. d s =0.288m. H = 1.39m Air, 1 bar, 293 K

g ™ 0.8

• i s 0.6h u, Q 0.5

D —

-

i»

J % 0.4 Fig. 4.8. Resistance factor for a wetted bed of packing as a function of the gas Reynolds number

5

0.3 6

8 10J 2 3 4 5 6 8 104 Gas Reynolds number Rev

Equating Eqn (4-61) with Eqn (4-63) and substituting for §0 in Eqn (4-64) gives rise to the following relationship for the resistance factor ^L in two-phase flow:

92

4

Fluid dynamics in counter cur rent packed columns (3 -x)

(4-67) As the liquid trickles through the bed, static holdup occurs at the points of contact between the individual elements of packing and in the intervening spaces, and the liquid forms a film on the surface of the packing. Hence, the surface structure differs from that during gas flow through a dry bed, and this fact is expressed by the difference between Eqn (4-67) and Eqn (4-64), i.e. Eqn (4-67) contains an additional term. In Fig. 4.9, calculated values for the resistance factor § L have been plotted against the liquid load uL determined by measurements in a wetted bed of 32-mm plastic Envipac rings. Eqns (4-64) and (4-67) have been checked against the experimental results obtained on more than 50 types of packing. The check embraced the effects exerted by the various physical properties of 24 different systems (cf. Table 3.3) including some intended for purely hydraulic studies and mixtures intended for absorption, desorption, and rectification. Evaluation of the comprehensive data thus obtained revealed that the numerical value for the exponent x in Eqns (4-63) and (4-67) was x = 1.5 and that the expression for W can be replaced by a function, viz. W = exp

(4-68)

200/j \h

32-mm ENVIPAC. PP. d s = 0.288 m, H = 1.39m Air/H 2 O, 1 bar, 293 K CD O C

12 "co

1 0.8 0.6 0.5 0.4 0.81

—A-

A

.1

—

2 3 4 5 6 8 10 Liquid load u L -10 3 [m 3 /m 2 s]

20

Fig. 4.9. Resistance factor for a wetted bed of packing as a function of the liquid load

The Reynolds number ReL of the liquid in this case is given by ReL =

uL QL a r\L

(4-69)

The second term in Eqn (4-68) becomes unity in the range below the loading point. Mathematical prediction of the theoretical liquid holdup hL by means of Eqn (4-27) is restricted to the range below the loading point. The qualitative diagram presented in Fig. 4.10 is intended for the mathematical description of hL above this limit. It shows the theoretical relationship between the liquid holdup hL and the ratio of the gas velocity uy to the value at the flood point UV,FI- Up to the loading point, ht is practically independent of the gas velocity and assumes a constant value hLS- Above this point, the shear forces acting in

4.6

Fig. 4.10. Qualitative relationship between the liquid holdup and the relative gas load

Pressure drop in packed colums

0

93

Gas velocity ratio u v / u V F

the gas progressively support the liquid film, and the liquid holdup thus greatly increases until it attains a maximum hLyFl {cf. Eqn (4-40)} at the flood point. An empirical equation that satisfies this condition is = hL>s + (hLtFi - hLjS)

(4-70) uv,m

In this equation, hL>s is the liquid holdup as defined by Eqn (4-47), and hLjFi is that at the flood point, as defined by Eqn (4-40) and confirmed for 0 < uL < 200 m3/m2h and r| > 1 x 10=4 kg/ms. The empirically determined numerical value of the exponent n is n = 13. Hence, all that has now to be known for the determination of pressure drop is the one constant Cp, which is specific for any given type of packing, regardless of whether or not the bed is wetted. Numerical values of Cp determined by experiment on various conventional and modern types of packing are listed in Tables 4.3 (dumped at random) and 4.4 (stacked in regular arrangement). Precise measurement of the pressure drop by experiment is rendered difficult by the unsteady gas and liquid flow above the loading point, and the range of scattering of the values thus determined is correspondingly greater. Up to the loading point, the average deviation of the values calculated by means of Eqns (4-58), (4-67), (4-68), and (4-70) from the values determined by experiment amounts to about 9 %. It is higher in the loading range extending up to about 90 % of the flood point load uV;pi and attains the greatest value, viz. almost 11 %, in the actual vicinity of the flood point. At particularly high loads, the liquid flows so densely in the channels within the bed of packing that it coalesces in the narrow parts of the bed. As a result, extensive zones of the effective open cross-section become filled with liquid to form a continuous layer, through which the gas phase rises in the form of bubbles. If this limiting load, which is referred to as phase inversion, is exceeded, the liquid holdup and the resistance factor or pressure drop in the gas stream increase at disproportionately high rates. The points at which this stage is reached are defined by Eqns (4-42) and (4-43). At higher values of the parameters in these equations, Eqn (4-67) no longer applies. The pressure drop model derived here has been confirmed by measurements performed under the conditions listed in Table 4.5.

94

4

Fluid dynamics in countercurrent packed columns

Table 4.3. Data for determining the pressure drop in random beds of packing a m 2 /m 3

e m 3 /m 3

CP

6242 15772 19517 53900 229225

112.6 149.6 139.4 223.5 368.4

0.951 0.952 0.965 0.954 0.933

0.763 1.003 0.967 0.957 0.990

50 35 25

6765 17000 52300

111.1 151.1 225.0

0.919 0.906 0.887

0.698 0.927 0.865

Ceramic

50

6215

116.5

0.783

0.662

Ralu ring

Plastic

50 50, hydr.

5770 5720

95.2 94.3

0.938 0.939

0.468 0.439

Hilflow ring

Metal

50 25

5000 40790

92.3 202.9

0.977 0.962

0.421 0.689

Plastic

90 50 50, hydr. 25

1340 6815 6890 46100

69.7 117.1 118.4 194.5

0.968 0.925 0.925 0.918

0.276 0.327 0.311 0.741

Ceramic

75 50 35 20, 4 webs

1904 5120 16840 121314

54.1 89.7 108.3 286.2

0.868 0.809 0.833 0.758

0.435 0.538 0.621 0.628

Hiflow ring; Super

Plastic

50

6050

82.0

0.942

0.414

NOR-PAC ring

Plastic

50 35 25, TypeB 25, 10 webs 22 15

7330 17450 47837 44346 69274 193738

86.8 141.8 193.5 179.4 249.0 311.4

0.947 0.944 0.921 0.927 0.913 0.918

0.350 0.371 0.397 0.383 0.397 0.365

Raflux ring

Plastic

15

193522

307.9

0.894

0.595

VSP ring

Metal

50, No. 2 25, No. 1

7841 33434

104.6 199.6

0.980 0.975

0.773 0.782

ENVIPAC

Plastic

80, No. 3 60, No. 2 32, No. 1

2000 6800 53000

60.0 98.4 138.9

0.955 0.961 0.936

0.358 0.338 0.549

Top-pak

Aluminium

50

6947

106.6

0.956

0.604

Bialecki ring

Metal

50 35 25

6278 19303 55000

121.0 164.4 238.0

0.966 0.965 0.940

0.719 1.011 0.891

Arranged packing

Material

Size mm

Pall ring

Metal

50 38 35 25 15

Plastic

N 1/m3

4.6

95

Pressure drop in packed colums

Table 4.3. (continued) Arranged packing

Material

Size mm

Raschig ring

Ceramic

25

48175

INTALOX

Plastic

50

8656

Ceramic

50

8882

Hiflow saddle

Plastic

50

9939

Tellerette

Plastic

25

Hackette

Plastic

45

N 1/m3

a m 2 /m 3

e m 3 /m 3

CP

185.4

0.662

1.329

122.1

0.908

0.758

114.6

0.761

0.747

86.4

0.938

0.454

35365

182.0

0.900

0.538

12252

133.4

0.931

0.399

hydr. = made hydrophilic

Table 4.4. Data for determining the pressure drop in geometrically arranged beds of packing Arranged packing

Material

Size mm

N 1/m3

a m 2 /m 3

m 3 /m 3

CP

50

7502

155.2

0.754

0.233

7640 8150

131.3 140.1

0.916 0.911

0.172 0.172

250.0

0.945

0.191

96.7

0.828

0.417

E

Pall ring, stacked

Ceramic

Hilflow ring, stacked

Plastic

50 50, hydr.

Ralu pack

Metal

YC-250

Impulse packing

Ceramic

100

Metal

B1-200 B1-300

200.0 300.0

0.979 0.930

0.355 0.295

Plastic

Cl-200 C2-200

200.0 200.0

0.954 0.900

0.453 0.481

Plastic

PN-110

110.0

0.936

0.250

Euroform

hydr. = made hydrophilic

Table 4.5. Characteristic values required for fluid dynamic studies on random beds of packing Gas capacity factor Liquid load

Fv u L -10 3

Column diameter Packed height Interfacial area Void fraction

ds H a

Number of packings investigated Number of measurements

E

m -l/2

s -l

k g l/2

m 3 / m2 s

0.21-5.09 0.17-16.7 0.15-0.80 0.76-3.95 54-380 0.66-0.98

m m m 2 /m 3 m 3 /m 3 54 3296

96

4

Fluid dynamics in countercurrent packed columns

4.7 Liquid holdup in packed beds The relationships given in the literature for the liquid holdup in packed columns apply merely to a few conventional forms of packing and have often been derived solely from measurements on air/water systems. As was already mentioned in Chapter 3, the geometry of modern packing differs greatly in many respects from that of former types, with the result that the existing relationships can no longer yield reliable results for the liquid holdup. The model presented here for the prediction of liquid holdup has been based on the fundamental relationships enunciated in Sections 4.2-4.4. It is valid for both conventional and modern packing in two-phase countercurrrent columns and allows reliable results to be obtained for multifarious two-phase systems. An assumption made in deriving the model is that the effective void fraction in the bed of packing can be represented by a multiplicity of vertical flow channels, along the walls of which the liquid trickles downwards in counterflow with the ascending gas stream. The actual flow behaviour can be visualized by allowing for the fact that the surfaces of the packing are not completely wetted at the liquid loads normally encountered in practice. In this case, the thickness s0 of the descending liquid film can be described in terms of the liquid holdup hL and the hydraulic area ^ of the packing surface, i.e. so = — ah

(4-71)

This equation differs from Eqn (4-12), which is valid for uniform and complete wetting of the packed surfaces. Inserting the expressions for uL, uv, and So given by Eqns (4-13), (4-14), and (4-71) in Eqn (4-7) yields the liquid holdup for the entire loading range in twophase countercurrent flow, i.e.

hL =

a Vi

"

ah

-Qvuv

(4-72)

a

This equation is analogous to Eqn (4-17), but includes the term (ah/a)2/3 to embrace the effect of the hydraulic area ah. It allows for all the main parameters that affect hL up to the flood point in a two-phase countercurrent column: the phase densities QL and QV, the liquid viscosity \\L, the phase loads uL and uv, the acceleration due to gravity g, and the resistance factor § L . If the column is operated in the load range between the loading and flood points in twophase countercurrent flow, the downward stream of liquid is no longer independent of the gas load, because it is held up by the shear forces in the gas stream. The boundary condition that applies in this case is defined by Eqn (4-25), which states that the velocity uL)S tends to zero at the surface of the liquid. The results of the experiments described in Chapter 3 have shown that the liquid holdup in the uv < uv>s range is a function of uL only and that the gas stream exerts hardly any effect. Therefore, applying the boundary condition implied by Eqn (4-25) gives rise to the following relationship for the liquid holdup in the uv < uvs range:

4.7

Liquid holdup in packed beds

<*h i ,

QLg

97

( 4

_

7 3 )

I \ a

If this equation is compared with the theoretical relationship for the liquid holdup, as described by Eqn (4-27), it will be seen that allowance for the actual flow conditions in a packed bed has been made by the term (ayjd)/z', a power of the ratio of the hydraulic to the geometric area. The numerical value n 2/3 = for the index n has been generally confirmed by experiments on both random and stacked beds of packing. A relationship for the ratio aja has been determined in fluid dynamics studies on the liquid holdup and subsequently correlated to an empirical function. It was thus found that it depends on the liquid Reynolds number ReL, as defined by Eqn (4-69), and the Froude number FrL, which is related to the liquid holdup by Eqn (4-27). The following relationships for two ranges of Reynolds numbers were derived from the corresponding studies on the systems listed in Table 3.3: = ChRe£15Fr£1

(4-74)

= 0.85 Ch Rel25 FrlA

(4-75)

ReL<5

-^1 a

lReL>5

Numerical values for the constant Cy, are listed together with characteristic geometric data on the types of packing concerned in Tables 4.6 (dumped) and 4.7 (arranged). The data include the number N of packing elements per unit column volume and the void fraction e. On an average, the experimental results differ by only 6.7% from the figures for the liquid holdup calculated from Eqns (4-73), (4-74), and (4-75). A relationship between the holdup at the loading point hLiS, as determined from Eqn (4-73), and that at the flood point hLFh was also derived from the results of the experiments. It is presented graphically in Fig. 4.11, in which the holdup ratio hLlhLS has been plotted against the gas load ratio uv/uVjFi. The diagram confirms the theoretical considerations that were presented in Sect. 4.5 and led to the conclusion that the upper loading point is to be anticipated at about 70 % of the load at the flood point. It can also be seen that the liquid holdup near the flood point is about 2.2 times greater than that in the capacity range below the loading point, i.e. hLiPl = 2.2 hLtS

(4-76)

Inserting Eqn (4-76) in Eqn (4-70) leads to hL =

(4-77)

1 + 1.2 UVFI

This equation can be applied, together with Eqn (4-73), for the calculation of hL in the entire capacity range. The curve in Fig. 4.11 was plotted from these relationships. The conditions for the tests in which the data for the holdup evaluations were acquired are listed in Table 4.8.

98

4

Fluid dynamics in countercurrent packed columns

Table 4.6. Data for determining the liquid holdup in random beds of packing

ch

Size mm

N 1/m3

a m 2 /m 3

m 3 /m 3

Metal

50 35 25 15

6242 19517 47500 229225

112.6 139.4 215.0 368.4

0.951 0.965 0.942 0.933

0.784 0.644 0.719 0.590

Plastic

50 35 25

6664 16682 52300

102.0 148.3 225.0

0.926 0.907 0.887

0.593 0.718 0.528

Ceramic

50

6455

121.0

0.770

1.335

DINPAC ring

Plastic

70 45

9764 28518

110.7 182.9

0.938 0.922

0.991 1.173

Hiflow ring

Metal

50 25

5000 39917

92.3 197.5

0.977 0.962

0.876 0.799

Plastic

50

6997

120.2

0.924

1.038

Ceramic

20, 4 ribs 20, 6 ribs

101444 110688

239.3 265.8

0.797 0.776

1.167 0.958

Glitsch ring

Metal

1.5" CMR 1.5" CMR, T 1.0" CMR 0.5" CMR 30 P 30 PMK

60744 63547 158467 560811 32509 28445

174.9 188.0 232.5 356.0 168.9 180.2

0.974 0.972 0.971 0.955 0.958 0.975

0.935 0.870 1.040 1.338 0.851 0.930

NOR PAC ring

Plastic

50 35 25 15

7710 17147 44500 193738

95.1 139.0 180.0 319.7

0.949 0.930 0.927 0.918

0.651 0.587 0.601 0.343

Raflux ring

Plastic

15

193522

307.9

0.894

0.491

VSP ring

Metal

50, No. 2 25, No. 1

7841 33434

104.6 199.6

0.980 0.975

1.135 1.369

ENVIPAC ring

Plastic

80, No. 3 60, No. 2 32, No. 1

1962 6773 52681

58.8 100.0 138.0

0.959 0.961 0.937

0.641 0.794 1.039

Top-pak ring

Aluminium

50

6871

105.5

0.956

0.881

Bialecki ring

Metal

50 35 25

6278 18177 52000

121.0 154.8 225.0

0.966 0.965 0.945

0.798 0.787 0.692

Dumped packing

Pall ring

Material

8

4.7

99

Liquid holdup in packed beds

Table 4.6. (continued) Dumped packing

Material

ch

Size mm

N 1/m3

a m 2 /m 3

mVm3

Metal

15

260778

378.4

0.917

0.455

Ceramic

25 15 10 6

48381 220000 847552 3022936

191.9 310.2 492.1 771.9

0.726 0.690 0.570 0.620

0.577 0.648 0.791 1.094

Carbon

25

51913

205.7

0.700

0.623

Berl saddle

Ceramic

25 13

63920 529720

205.4 436.4

0.695 0.660

0.620 0.833

Tellerette

Plastic

25

35000

180.0

0.900

0.588

Hackette

Plastic

45

12000

139.5

0.928

0.643

Raschig ring

E

Table 4.7. Data for determining the liquid holdup in geometrically arranged beds of packing Arranged packing

Material

Size mm

N 1/m3

a m 2 /m 3

m 3 /m 3

£

ch

Pall ring

Ceramic

50

7510

138.7

0.670

1.066

Bialecki ring

Metal

35 25

20736 63700

176.6 275.0

0.960 0.930

0.690 0.395

Gempak

Metal

A2 T-304

202.0

0.977

0.678

Impulse packing

Metal

250

250.0

0.975

0.431

Ceramic

100

102.0

0.830

1.900

Montz packing

Metal

Bl-100 Bl-200 Bl-300

100.0 200.0 300.0

0.987 0.979 0.930

0.626 0.547 0.482

Mellapak

Plastic

250 Y

250.0

0.960

0.554

Euroform

Plastic

PN-110

110.0

0.936

0.511

100

4

Fluid dynamics in countercurrent packed columns

3

j

O

£

odel correlcitio n [ine / /

1

"TH

^

1i1 o

—&

W

0.8 0.2

0.3

\&

i-

0.4 0.5 0.6 0.8

Gas velocity ratio

1

U V /U V ( FI

Fig. 4.11. Values of liquid holdup calculated from the model compared with those determined by experiment Table 4.8. Characteristic values required for fluid dynamic studies on geometrically arranged beds of packing Gas velocity Liquid load

uv

ii L -10 3

m/s m 3 / m2 s

Column diameter Total area per unit volume Void fraction

ds a

m m 2 /m 3 m 3 /m 3

Liquid density Liquid viscosity Surface tension

8 QL

TlL-10 3 GL • 10 3

Number of systems investigated Number of packings investigated Number of measurements

kg/m 3 kg/ms kg/s 2

0.09-2.51 0.37-23.0 0.076-0.44 59-772 0.57-0.99 800-1810 0.78-185 22.6-86.3 16 56 822

4.8 Liquid entrainment at high loads If a bed of packing consists of large elements dumped at random or of elements stacked in a regular geometric pattern, the liquid flows through the channels largely in the form of a film or lamellae. However, if the basic pattern in a stacked bed is a latticework, the possibility exists that the liquid film may become partly detached from the lowermost edges of the packing surfaces, particularly at high liquid loads. The droplets thus formed would then fall through the void that lies between the tear-off edge and the underlying packing element. To an extent that depends on their size, the individual droplets may be held in suspension by a gas stream of the corresponding velocity. Alternatively, they may be entrained in the ascending gas and conveyed to the packing elements immediately above them, on which they would be deposited and thus mixed with the local descending liquid film. Hence, within this loading range, the flood point would not be reached; and, as has been demonstrated by experiment, the column efficiency could still be substantially improved (cf. Fig. 4.12).

4.8

101

Liquid entrainment at high loads

The onset of entrainment in cavities within beds of packing entails that the buoyancy forces acting on a liquid droplet of diameter d^r are in equilibrium with the force of gravity. In other words, the following condition must be satisfied: (4-78)

le ddr — MKe Qv = — dl — g(QL~ Qv) O

JO

Consequently, the capacity factor Fv>e, which governs entrainment, depends on the diameter d^ and stability of the droplets, i.e.

Fv,.= \/T

(4-79)

-tddr(QL-Qv)

Ethylbenzene/Styrene, L/V = 1 3 3

E

AL

=

inn

lUU /o

L

-—k>-

^ ^

— 2

i

-9 |

78°/.

x

e--23%

12%

1M

j

P

Pall ring 50 mm, metal

- d =500mm,Z=6001/m

2

s

I

8000

"7 - 3^

)ar|

/

/

Y

r /

/

r

AL

\I

1i

7000

! /> /

67 mbar

/ /

6000

y " • load at max.effy - • maximum load

5000 /

4000

4000 5000 6000

7000

—

8000 9000

Vapour load V [kg/m 2 h]

2.0

2.5 §5 35 Th

4^5

Fv [m- V2 s- l kg 1/2 ](34mbar) Fig. 4.12. Results of experiments on the entrainment of liquid droplets at the head of the column

1.5

2l Fv

E ^s" 1

10 ?.5

kg'/2](67mbar)

102

4

Fluid dynamics in counter cur rent packed columns

The lower diagram in Fig. 4.12 gives an idea of the amount of liquid AL that is entrained by the gas stream at the head of a Pall-ring column for the separation of an ethylbenzene/styrene system under vacuum and total reflux. It can be assumed that the volume of liquid that may be entrained within the voids of a packed bed does not exceed AL. This volume increases with the vapour capacity factor in the Fv > Fv>e range. Since the efficiency attains a maximum in this loading range (cf. upper diagram in Fig. 4.12), it can be assumed that the droplets are redeposited in the packing. As a result, the area of contact between the phases would be increased, and mass transfer would thus be intensified. Actual flooding does not commence until the liquid load becomes even greater and an increasing quantity of the liquid film or lamella is supported by the energy of the gas stream, as is expressed by a significant rise in the liquid holdup. The fluid dynamics model developed in Section 4.1 is thus confirmed, and it is physically unjustified to describe the onset of flooding in terms of descending liquid droplets when the equilibrium of forces has been attained. In actual fact, it can be deduced from Fig. 4.12 and the arguments presented above that packed columns are also eminently suitable for separating liquid droplets, and this fact has long since been exploited in industrial practice.

4.9 Phase inversion in packed beds Strictly speaking, the flow model presented in Section 4.1 is not valid unless the assumptions made in its development apply. Experimental studies have revealed that the relationships for the loading and flood points derived from the model can be applied in the loading range described by a load parameter of i|> < 4 without reservation and to within an accuracy that is adequate for practical purposes. However, if this value of load parameter is exceeded, phase inversion occurs, i. e. the original disperse phase - the liquid - becomes the continuous phase, and the previously continuous gas phase becomes the disperse phase. This stage sets in at the comparatively high liquid loads encountered in a number of absorption processes and, particularly, in high-pressure rectification. It ought to be possible to express phase inversion in physical terms by altering the exponent in the relationship for the resistance factor §, as is indicated by the example shown in Fig. 4.6. This assumption has, in fact, been confirmed experimentally in numerous studies, some results of which have been collated in Figs. 4.13 to 4.15. The associated diagrams apply to packing of various geometries and textures produced from various materials and with flow channels of various dimensions. It can be derived from them that the point at which phase inversion can be expected is at a flow parameter, as defined by Eqn (4-24), of ip = xps = 0.4

(4-80)

The physical interpretation of these relationships is as follows (cf. Fig. 4.16). If the transition point is reached at a given liquid load uL>i, the associated liquid holdup can be expressed as a fraction / of the relative void fraction, i.e. hL,i = {hLtS)t

= is

(4-81)

4.9

Phase inversion in packed beds

103

Nominal packing size 25 mm o Air/Water 1 bar 293 K; OToluene/n-Octane133mbar • Chlorobenzene/Ethylbenzene 67 mbar A Air/Ethylene glycol; v Air/Methanol.1 bar, 293 K

•c — * > ^ .

i i

Raschig ring, ceramic

s

«. 0.8 a > i < ^

n Pall ring, plastic

1 0.8 Z 6 =

r

3

-—.

2

s.

Bialecki ring, metal

0.8 Fig. 4.13. Resistance factor as a function of the modified flow parameter

0.06 0.1

0.2 0.3 0.4 0.6 0.8 1

2

k

3 4

>c

6 810

Modified flow parameter <\>s ( - p )

The corresponding vapour velocity at the loading point (uv?s)i can then be derived from Eqn (4-26). Thus

KS)/ = (i-QVn/ir-A/v\/ -

(4-82)

and the corresponding theoretical liquid load, from Eqn (4-27), i.e.

.i = («u)i

=

12

(4-83)

104

4

Fluid dynamics in countercurrent packed columns

Nominal packing size 50 mm oAir/Water 1 bar 293 K ; sEthanol/Wateri bar 0 Chlorobenzene/Ethylbenzene 67;133mbar b •

^

4

-^

3

i

i L

• Raschig ring , ceramic

1 a

-

I

I

i

!

pi i

k

i_

a a.

I

p

i

k

"GO

D

all

o

rin

ramie 1

a; S o

0.06 0.1

0.2 0.30.4 0.6 0.8 1

Fig. 4.14. Resistance factor as a function of the modified flow parameter

2 3 0.4

Modified flow parameter

^s(^p v T

lv>

Now, the following relationship exists between (uLS)i and (uv,s)i'L V

=

(uL>s)j

QL

(uv,s)i

Qv

(4-84)

Rearranging Eqn (4-24) gives (4-85) The relationship between §5>; and / then follows from Eqns (4-81) to (4-85), i. e. (4-86)

4.9

105

Phase inversion in packed beds

o Air/Water 1 bar 293 K D,mChlorobenzene/Ethylbenzene 67-133 mbar c

4 3 ? a <_ a

1

1

1 U - NOR-PAC ring, plastic, 15 mm - \— i i i i i i i

o 0

o

rTl

6

i

f. -)

i

i i

J

K

2

-Montz packing, metal, B1 - 300 1 i

11

1 Fig. 4.15. Resistance factor as a function of the modified flow parameter

0.06 0.1

02 0.30.4 0.60.8 1

i

2

3 4 v0.4

Modified flow parameter 4M YT

The experimentally verified relationship expressed by Eqn (4-29) must apply below the phase inversion, with the consequence that the equation valid immediately before the phase inversion is (4-87)

Combining Eqns (4-86) and (4-87) gives rise to a relationship that allows the phase inversion coefficient i for a bed of packing to be determined, i.e.

(i-0 2

(4-88) QLIUL

where qs is a characteristic constant that applies for the packing under the conditions at the loading point and is given by (4-89)

106

4

Fluid dynamics in countercurrent packed columns

Phases

/ V : disperse

ex

Gas load uv Fig. 4.16. Qualitative description of phase inversion

It is evident from Eqn (4-88) that i depends on the viscosity ratio of the two phases and on the density of the liquid. The relationship between the phase inversion coefficient / and the packing characteristic § 5 is shown graphically in Fig. 4.17 for the standard air/water system. An idea of the effect exerted by the physical properties of the various systems (cf. Table 3.3) can be obtained from Fig. 4.18. Measurements in packed columns have shown that the pressure drop curves Ap/H = t(uv)uL = const run parallel below the loading point. Above the loading point, the slope increases with the liquid load. In other words, the difference between the load at the loading point and that at the flood point becomes progressively smaller and tends towards zero, i.e. uvs = uVyFh when complete phase inversion occurs (cf. Fig. 4.19). Hence, if hL>m = hLiS — hLi, equating Eqn (4-26) with Eqn (4-35) would give (4-90) Equating the theoretical relationship derived from the model for the liquid holdup at the loading point {Eqn (4-27)} with that at the flood point {Eqn (4-38)} gives rise to

4.9

Phase inversion in packed beds

107

0.16 (hUs)-, e

0.14

*

\Q 0.12

^ ^

^

•

^ ^

o o

=

==—-=

.

/

0.

o CO

/ ^ System: Air/Water at STP

.£ 0. / 0.06 0.04

f 0

50

100 150 200 250 300 350 400 450 500 Packing characteristic qs-10"6[m^2S"2]

Fig. 4.17. Relationship between the phase inversion coefficient and the packing characteristics for an air/water system at STP

chloride solution 1 Air /Calcium chloride solution 1 Air/Methanol

150

200 250 300

350 400 450 500

Packing characteristic qs-10~6[rrr2 s~z] Fig. 4.18. Relationship between the phase inversion coefficient and the packing characteristics for various systems

108

4

Fluid dynamics

in countercurrent

packed

columns

-o a> ZD CO CO CD

Fig. 4.19. Qualitative pressure drop function

Gas or vapour load u v

(4-91) The theoretical boundary condition is defined by (4-92) In this case, the liquid holdup is given by (4-93) In other words, the liquid holdup accounts for one-half of the void fraction. It therefore follows that the resistance factors are all of the same magnitude, i. e. %m = h,t = &

(4-94)

As a consequence, Eqn (4-90) can be reduced to Eqn (4-93). Theoretically, the liquid holdup defined by Eqn (4-93) can be attained if the liquid load assumes the limiting value given by Eqn (4-83) (for i = 0.5), i. e.

"v.s-uKFI

%

a2

^

(4-95)

4.9

Phase inversion in packed beds

109

The corresponding vapour load is obtained from Eqn (4-82) (for / = 0.5), i. e.

The liquid holdup in the uL < uLi range is given by hL,m = m

(4-97)

where n < /2The corresponding vapour load follows from the general theoretical relationship to describe the liquid holdup at the flood point, i. e. Eqn (4-38). Thus,

Since UL>FI > 0 and, consequently, (3n - 1) > 0, it follows that %>n>

%

(4-99)

If Eqn (4-98) is applied to the conditions at the phase inversion, it can be equated to Eqn (4-83) to obtain the formal relationship between i and n, i. e. i = n 3V2(3n-l)

(4-100)

At the phase inversion, the relationship between them is given by (cf. Fig. 4.16) mt = nli

(4-101)

where m is the ratio of the liquid holdup at the flood point to that at the loading point, i.e. m = ^ L hus

(4-102)

Hence, if i is known from Eqn (4-88), n can be determined from Eqn (4-100); and m, from Eqn (4-101). The relationships n = f(qs) and mf = f(qs) for various systems at standard temperature and pressure are presented graphically in Fig. 4.20. Rearranging Eqn (4-89) gives rise to -Q-= (—)=— qs \a I a

\ a

(4-103)

110

4

Fluid dynamics in counter current packed columns

inversion

4.0

CD CO O

*•

3.5 3.0

-c:

i

/

\ \ \

2.5

^/ >^-

.

^ —

-—

= n 0.39 0.38

i

— Air/Calcium chloride solution 1

—

•^. A —»

——- ——

0.37 -——

——* —

—

-

^-—

-Air/Water

— « ,

—

• .

I 1.5 /

-i

,

V

2.0

i

A-r ...

^ +

\

-H \\

d.

itio rr

— Nitrogen/Heav / oil -

—

0.36

QJ O O

0.35

—I—I—J — — 0.34 ^n (I -

i

i/

i

i\

1.0

0.33 0

50

100 150 200 250 300 350 400 450 500 Packing characteristic q s 10" 6 [m~ 2 s " 2 ]

Fig. 4.20. Characterization of the phase inversion point in various systems Substituting for e3la2 in Eqn (4-83) then gives the liquid load at the phase inversion, i.e. uL.i = ^ T ^3 « —

—

(4-104)

This expression for the liquid load at the phase inversion is shown as a function of the area per unit volume a with the void fraction e as parameter in Fig. 4.21. Substituting ne for hL>m {Eqn (4-97)} and it for hL>s {Eqn (4-105)} in Eqn (4-102) gives 1

(4-105)

Since the liquid holdup at the flood point is very difficult to determine by experiment, the values of m derived from it are not very accurate. The average is m — 2.2 for lowviscosity systems (cf. Section 4.7). The following theoretical value of m is obtained by substituting hLyFllz for n in Eqn (4-105): (4-106) -1 In analogy to Eqn (4-40), the holdup at liquid loads of uL < uL>i can be estimated from (4-107) where ri = 0.349.

4.9

111

Phase inversion in packed beds

120

V

System: at

e = 0.98

Air/Water STP

•7

//

•

£ 80

Cs- 3.5 /£

a

=

'""\?

cr

e--0.9(]

40

• — — .

W.I'.r

Phase inversion 20 50

100

150

200

250

300

350 z

400

450

500

3

Area per unit volume a [m /m ] Fig. 4.21. Liquid load at the phase inversion point as a function of packing characteristics

If r\L = r\w, inserting values of hLjFilz thus obtained in Eqn (4-106) would again yield a value of about 2.2 for m. Solving Eqn (4-105) for n would then give rise to n = 0.349. The flow pattern is altered once the flow parameter exceeds the value i^- at which phase inversion commences (cf. Figs. 4.13 to 4.15). If the set of equations in the model is to be formally retained, this alteration would be expressed as a change in the exponents and constants in Eqns (4-29) and (4-41) for the resistance factors § 5 / and I=F/)I- respectively. Numerical values for the exponents can be obtained from Eqns (4-32) and (4-43). The following condition must be satisfied at the phase inversion: 55 -

(4-108)

55,i

Eqn (4-29) can therefore be converted into ("s - ns,i)

Cs,i = Cs

(4-109)

Inserting the numerical values then gives

CSi = 0.695 C 5 [ —

(4-110)

Another condition that must be satisfied at the phase inversion is (4-111)

112

4

Fluid dynamics in countercurrent packed columns

Eqn (4-41) can therefore be converted to yield the following relationship for the constant: (nFl-nFl,i)

\0.2

(4"112)

ZT) The simplified relationship in this case is thus

(

^

0.1028

—

(4-113)

Consequently, the vapour load at the loading and flood points can be formally determined by Eqns (4-28) and (4-35), even in the range above the phase inversion. The values of ^s and §F/ required for the calculations and corresponding to n$ = nSj, Cs = Cs,i, HFI = nFiti, and CFl = CFiA can be obtained from Eqns (4-29) and (4-41) respectively.

4.10 Relationship between loading and flood points The range between the loading and flood points is of utmost importance in the design and operation of packed columns. The liquid holdup and thus the pressure drop within this range increase at a higher rate than they do in the range below the loading point. The design load uVD, at which the column volume is a minimum, then lies between uV}s and uym, i- e. uv,s ^ uV}D < uVyF{

(4-114)

Substituting for uvs from Eqn (4-26), f$ from Eqn (4-57), ^L from Eqn (4-59), and fw>s for fw in Eqn (4-58) gives rise to the pressure drop per unit height (Ap/H)s in the uv = uV;S loading range, i.e.

Likewise, the pressure drop per unit height (Ap/H)Fi at the flood point uv = uVtn can be derived from Eqns (4-35), (4-57), (4-58), and (4-59) a n d / w = fWiFl. Thus,

The pressure drop ratio is therefore &PFI

„ fw,Fi = 2— fw,s

hLjm

e - hLjS

hLiS

e

Substituting m for hLiFilhL>s {cf. Eqn (4-102)} then gives

(4-117)

4.10

113

Relationship between loading and flood points

It follows from Eqns (4-97) and (4-102) that (4-119)

Hence, the pressure drop ratio can be expressed by the following simple relationship: ApFl n fw,Fl , x — = 2 ^-r— (m - n) Aps Jw,s

,. 1 o m (4-120)

Alternatively, it can be expressed as follows by substituting the right-hand side of Eqn (4-105) for m:

fw,s \ 3 V2(3n-l) - n

(4-121)

The factor n can be obtained by combining Eqns (4-97) and (4-107), i. e. /^ r

«-uL < ut =

0.349

\0.05

(4-122) r\wlQw

The factors fw>s and fw,Fi m Eqn (4-121) are defined by Eqn (4-56) as the ratios of the effective area ae to the area per unit volume a at the loading and flood points respectively. The effective area ae is that of the surface of the flow channels of hydraulic diameter dh in which the pressure drop would be the same as that encountered in the bed of packing under consideration. The hydraulic diameter dh is defined by (4-123)

fwa

The pressure drop per unit height at the loading and flood points can be derived from Eqn (4-58). Thus, Uy,S

.

H Ap

(4-124 a)

?5

is

-E

2

1 - hLyFi I

dhiFtfs

(4-124 b)

Substituting ne for hL>m {cf. Eqn (4-97)} and zn/m for hLfS {cf. Eqn (4-119)} in the ApFi/Aps ratio thus obtained gives rise to the following equation:

%Fl

fw

fw,S

1-

n

m 1- - n

(4-125) UV,S

114

4

Fluid dynamics in countercurrent packed columns

The ratio of the vapour load at the flood point to that at the loading point can be derived by equating Eqns (4-120) and (4-125). Thus, (4-126) uv,s

Substituting the right-hand side of Eqn (4-105) for m in this equation then gives (I-")2 uv,s

(4-127)

-«V2(3w-l)

where n is defined by Eqn (4-122) and the term h,s^Fi is the ratio of Eqn (4-29) to Eqn (4-41), i.e.

(nS -

Im

(4-128)

n

Fl)

This ratio can also be estimated by applying Eqn (4-59). Thus,

fw,Fl

(4-129)

fw.S

In this case, the ratio of this equation, i.e.

can be calculated from Eqn (4-67) or expressed in terms

64 lL,Fl

• +

hL,Fi \ ° ' 3 Rev,Fi

hL,s 1

64

- +

Re v,s

1.8 Reom 1.8 • Re v,s •

- hLtFl

\~

(4-130)

The expression within the square brackets in this equation can be equated to (uViS/uViFif-08 = 0.97. Applying Eqns (4-97) and (4-119) then gives rise to 0.97

1-n

| t ,,

(4-131)

t s

The fw,Filfw,s ratio is thus known from Eqn (4-59), and the pressure drop ratio can therefore be obtained from Eqn (4-121). Eqn (4-127) can also be derived by substituting Eqns (4-97) and (4-119) for hLiFt and hLS, respectively, in Eqn (4-52). The flood point exponent n depends fundamentally on the system and the flow parameter \p and can be calculated from the model. The liquid holdup hL>s accounts for only a fraction of the relative void fraction 8, i. e. it differs from e by a factor/. Thus hL.s = f e

(4-132)

4.10

115

Relationship between loading and flood points

Hence, in analogy to the derivation of Eqn (4-88) for the determination of the phase inversion coefficient /, the following relationship applies for the factor /:

f

144

d-f)2'

s2 *

(4-133) QL)\QL

Equating Eqns (4-97), (4-102) and (4-132) gives (4-134) Substituting f o r / o n the left-hand side of Eqn (4-105) then gives /5 _ (I-/) 2

n5[2(3n-l)f3 {l-n[2(3n-l)]V3}2

(4-135)

Three systems with different physical properties were taken as examples for evaluating the relationships discussed above: air/water, air/calcium chloride solution, and nitrogen/heavy oil, each at STP in the loading range below the phase inversion, i. e. \p < 0.4. Fig. 4.22 shows the relationship obtained from Eqn (4-131) between the flow parameter i|> and the modified resistance parameter ratio R, which is given by (4-136)

R =

«

2 8

i —

O

—

S 2.4 i_ CD

—-—— — .1

1 2.0

i

.

_

—

—

—

—

—

\\\0

«-—'

a

s

1

y / i

•55 1.2

1 0.8

/ / *

1 bar, 293 K

TZJ

04

1 1 0

0.04 0.08 0.12 0.16 0.2

0.24 0.28 0.32 0.36

Flow parameter i|) Fig. 4.22. Modified resistance parameter ratio as a function of the flow parameter

0.4

116

4

Fluid dynamics in counter current packed columns

Thus Fig. 4.23 would be obtained for packing with a CFilCs = 0.6 ratio. Fig. 4.24 was plotted from Eqns (4-133) and (4-135) and shows the coefficient n for the liquid holdup under flooding conditions as a function of the flow parameter I|J. It also shows the corresponding function for ra, which is the ratio of the liquid holdup at the flood point to that at the loading point and was determined from the relationship between m and n expressed by Eqn (4-105). Finally, if the functions n = f(i|j) and §5/^7 are known, the following can also be determined as functions of the flow parameter ip: the ratio of the resistance factors ^L,FI^L,S {Eqn (4-131)}; the vapour load ratio WV;F//"KS {Eqn (4-127)}; and the pressure drop ratio ApFl/Aps {Eqn (4-120)}. These relationships, as determined on some metal packings and an air/water system at STP, are shown as an example in Figs. 4.25-4.27.

_, 1

1

<-n

-—-

, — ^, —• •

O

0.8

—

"

— — — — — — ^——

r"

"a

0.6

\

-1 .

.. • ••

•

Air Water

/

0.4

A

0.2 r

If

^F 1

C5

i

=0.6

i

Dor, 293 K

CO CD

0

0.04 0.08 0.12

0.16

0.2

0.24

0.28 0.32 0.36 0.4

Flow parameter ty Fig. 4.23. Resistance parameter ratio as a function of the flow parameter

4.10

117

Relationship between loading and flood points

4.0

0.39

I

\

\ \

\

3.5

Air/Water \

\ \

3.0

\ \ \

8

(

- * •

ms

^-—-

—

——

~<—

r2

— — i

1.5

. . . .

Air/Calcium c:hloricle solution 1 — " V .... \ Nitrogen/Heavy oil \ * * — *——.

S-

N\ V

2.5 2.0 - q

1 bar, 2 9 3 K

n

•• —- —•

——— —

—

m.

—

— — .

.

mi

—

0.38 0.37 m - 0.36 —n

§

.

I

0.35 —

0.34

—— .• ••

1.0

0.33 0

0.04

0.08

0.12

0.16

0.20

0.24

Flow parameter

0.28

0.32

0.36

0.40

ty

Fig. 4.24. Ratio of the liquid holdup at the loading point to that at the flood point as a function of the flow parameter

Glitsch ring 30 P Air/Water, 1 bar, 293 K

™

0.9

-

0.8

———.

•

•

— — — ' ^

—

—

J.

_

— i — -

fw,Fl/fw,S

Fig. 4.25. Characteristics defining the loading range between the loading and flood points

0.1

0.2

0.3

Flow parameter ty

0.4

118

4

Fluid dynamics in countercurrent packed columns

Glitsch ring 30 Pmk Air/Water. 1 bar. 293 K 1.5

— -—

•

•

•

1.3

QJ CO

a

7

en

1

_,

—

5

—

1.1

H

0.9

_ 0.8

^ — -

«——

^—*• CO

*" a o

1

--4u ^

^— ™

•

•W F l ' 'W S

0.4

—

0.34

-

.—- ——

Fig. 4.26. Characteristics defining the loading range between the loading and flood points

—

0.33 0.1

0.2

0.3

0.4

Flow parameter ^

Glitsch ring 0.5 CMR 304 Air/Water. 1 bar. 293 K 1.5 s——•

—

—

1.3 6 <

V 0.8 1 a t_ a (—3

0.6

^ | — H — ^- — ^

fw.Fl/fw,S

^

0.345 ——— 0.335

Fig. 4.27. Characteristics defining the loading range between the loading and flood points

,

0.1 0.2 0.3 Flow parameter <\>

0.4

5 Mass transfer in countercurrent packed columns Effective mass transfer entails that the liquid must remain in intimate contact with the gas or vapour or that the two phases must flow countercurrent and be distributed as uniformly as possible over the entire cross-section of the packed column. The surface of the packing should be wetted to the utmost extent in order to ensure maximum area of contact at the interface with the countercurrent gas. Thus the shape and structure of the packing, the phase loads, and the physical properties of the system under consideration are of decisive importance for the intensity of mass transfer. It can be seen from the examples in Fig. 5.1 that the geometry and dimensions of the packing elements depend on the flow pattern of the phases and thus the mass transfer efficiency, which is also governed by the length of the flow path that has to be traversed before the surface of the liquid in contact with the gas is renewed. Since the liquid is continuously remixed at the points of contact with the packing, it can be assumed that mass transfer in both phases occurs by non-steady-state diffusion. In this case, the mass transfer coefficient |3 is described by the Higbie correlation, viz.

P ~ "Trif" V ~

(5-1)

where D is the diffusion coefficient for the component transferred and x is the duration of contact, i.e. the time required for the interfacial area to be renewed after each flow path of length lx has been traversed.

5.1 Mass transfer in the liquid phase If DL is the diffusion coefficient for the component transferred in the liquid phase, lT the length of the flow path in the free space between the elements of packing, and r L the corresponding duration of liquid contact along the path /T, the mass transfer coefficient |3L in the liquid phase is given by o

. / n (5-2)

The term xL is governed by the liquid holdup hL, the liquid load wL, and the length of lr of the flow path, i.e. xL = hL lT — uL

(5-3)

Combining Eqns (4-27), (5-2) and (5-3) gives rise to Eqn (5-4) for the volumetric mass transfer coefficient |3L<2Ph, i.e.

- c -*te)Mt)* •*"*?• Packed Towers in Processing and Environmental Technology. Reinhard Billet Copyright © 1995 VCH Verlagsgesellschaft mbH, Weinheim ISBN: 3-527-28616-0

(54>

-

120

5

Mass transfer in countercurrent packed columns

Standard ring

Pall ring

Saddle

Latticework

Shaped ring

Surface-treated

Stacked

Sheet

Grid

Spiral

Honeycomb

Gauze lamella

Fig. 5.1. Basic geometry of random and arranged packing Substituting this expression in Eqn (3-14) yields the following equation for the height of a transfer unit HTUL on the liquid side: 1

(5-5)

where CL is a constant that characterizes the shape and structure of the packing. Strictly speaking, Eqns (5-3) and (5-4) are valid for the capacity range up to the loading point, i. e. uv < uvs. If the gas or vapour load exceeds uvs, the liquid is held up so that hL > hLS- The liquid velocity uL decreases and can be estimated by an empirical equation of the form

5.2

Mass transfer in the vapour phase

121

(5-6) where, according to experiment, n = 2. The following equation applies for a given liquid load uL: uL = (uL)Uv>Uvs(hL)Uv>Uvs

(5-7)

The volumetric mass transfer coefficient in the capacity range between the loading and flood points can be derived from Eqns (5-2), (5-3), (5-7) and (4-27), i. e.

pL aPh = 12* CL a (uL)t > , s ( y ^ *f

(5-8)

where CL is the characteristic for the packing and is determined by mass transfer experiments. Numerical values are listed in Table 5.1 for dumped packing; and in Table 5.2 for regularly stacked packing. The method for the determination of the aPhla ratio is described in Section 5.3.

5.2 Mass transfer in the vapour phase The duration of contact x v with the gas phase is defined by the length of the path of contact between the phases /T, the superficial gas velocity uv, the void fraction e, and the liquid holdup hL, i. e. Tv=lT(e-hL)—

(5-9) Uy

In conventional beds of packing, xv is comparatively short, and mass transfer takes place within a very thin sublayer. It can therefore be assumed that mass transfer in the gas phase also follows the law of non-steady-state diffusion as described by Eqn (5-11), which embraces the diffusion coefficient D = Dv for the solute in the gas phase and the time iv, as described by Eqn (5-9), i.e.

The effect of the Reynolds Rev and Schmidt Scv numbers can be determined by expressing them in terms of the dynamic viscosity r\v and the density QV of the vapour phase. Thus ^ ^

(5-11)

a T] V

Scv = -^— QyDy

(5-12)

122

5

Mass transfer in countercurrent packed columns

Table 5.1. Calculation of liquid-side and gas-side volumetric mass transfer in random packing a m 2 /m 3

e m 3 /m 3

cL

Cv

6242 15772 19517 53900

112.6 149.6 139.4 223.5

0.951 0.952 0.965 0.954

1.192 1.227 1.012 1.440

0.410 0.341

50* 35* 25*

6765 17000 52300

111.1 151.1 225.0

0.919 0.906 0.887

1.239 0.856 0.905

0.368 0.380 0.446

Ceramic

50*

6215

116.5

0.783

1.227

0.415

Ralu ring

Plastic

50 50, hydr.

5770 5720

95.2 95.2

0.938 0.939

1.520 1.481

0.303 0.341

NOR PAC ring

Plastic

50 35* 25, type A 25, type B 25, typeC 25, 10 webs*

7330 17450 52356 50000 47619 48920

86.8 141.8 211.0 202.0 192.0 197.9

0.947 0.944 0.951 0.953 0.922 0.920

1.080 0.756 0.862 0.883 0.888 0.976

0.322 0.425

Metal

50 25*

5000 40790

92.3 202.9

0.977 0.962

1.168 1.641

0.408 0.402

Plastic

50* 50, hydr.* 25*

6815 6890 46100

117.1 118.4 194.5

0.925 0.925 0.918

1.487 1.553 1.577

0.345 0.369 0.390

Ceramic

50 38 20, 4 webs

5120 13241 110741

89.7 111.8 261.2

0.809 0.788 0.779

1.377 1.659 1.744

0.379 0.464 0.465

Hiflow ring; Super

Plastic

50

6050

82.0

0.942

1.219

0.342

TOP-Pac ring

Aluminium

50

6871

105.5

0.956

1.326

0.389

Raschig ring

Ceramic

50 38 25* 15* 13 10 8 6

5990 13275 47700 189091 378000 672000 1261000 3022936

95.0 118.0 190.0 312.0 370.0 440.0 550.0 771.9

0.830 0.680 0.680 0.690 0.640 0.650 0.650 0.620

1.416 1.536 1.361 1.276 1.367 1.303 1.210 1.130

0.210 0.230 0.412 0.401 0.265 0.272

Carbon

25 13

50599 378000

202.2 370.0

0.720 0.640

1.379 1.419

0.471

Metal

50, No. 2 25, No. 1

7841 33434

104.6 199.6

0.980 0.975

1.222 1.376

0.420 0.405

Dumped Packing

Material

Size mm

Pall ring

Metal

50* 38 35* 25*

Plastic

Hiflow ring

VSP ring

N 1/m3

0.336

0.366 0.410

5.2

123

Mass transfer in the vapour phase

Table 5.1. (continued) Dumped Packing

Material

Size mm

N 1/m3

cL

Cv

0.955 0.961 0.936

1.603 1.522 1.517

0.257 0.296 0.459

121.0 155.0 210.0 419.5

0.966 0.967 0.956 0.901

1.721 1.412 1.461 1.431

0.302 0.390 0.331 0.288

a m 2 /m 3

m 3 /m 3

2000 6800 53000

60.0 98.4 138.9

6278 18200 48533 436096

E

Envi Pac ring

Plastic

80, No. 3 60, No. 2 32, No. 1

Bialecki ring

Metal

50* 35* 25* 25

Plastic

50

3900

100.0

0.972

1.798

Tellerette

Plastic

25

37037

190.0

0.930

0.899

Sphere

Glass

25 13

66664 561877

134.5 282.2

0.430 0.400

1.335 1.364

Bed saddle

Ceramic

38 25 13

24928 80080 691505

164.0 260.0 545.0

0.700 0.680 0.650

1.568 1.246 1.364

0.244 0.387 0.232

Intalox saddle

Ceramic

13

730000

625.0

0.780

1.677

0.488

hydr. = hydrophilic; * = likewise estimated for rectification

Table 5.2. Calculation of liquid-side and gas-side volumetric mass transfer in geometrically arranged packing Stacked Packing

Material

Size mm 50

N 1/m3

cL

Cv

0.754

1.278

0.333

131.3 140.1

0.916 0.911

1.374 1.437

176.6

0.945

1.405

0.377

a m 2 /m 3

m 3 /m 3

7502

155.2

7640 8150 20736

8

Pall ring

Ceramic

Hiflow ring

Plastic

Bialecki ring

Metal

Ralu pack

Metal

YC-250*

250.0

0.945

1.334

0.385

Impulse packing

Metal

250

250.0

0.975

0.983

0.270

Ceramic

50 100 100, n

55.0 91.4 102,7

0.806 0.838 0.816

0.939 1.317 1.170

0.327 0.383

Metal

B1-200 B1-300*

200.0 300.0

0.979 0.930

0.971 1.165

0.390 0.422

Plastic

Cl-200 C2-200

200.0 200.0

0.954 0.900

1.006 0.739

0.412

Plastic

PN-110

110.0

0.936

0.973

0.167

Montz packing

Euroform

50 50, hydr. 35

hydr. = hydrophilic; n = newly stacked; * = likewise estimated for rectification

124

5

Mass transfer in countercurrent packed columns

The following equation can be derived by introducing these dimensionless number relationships in Eqns (5-9) and (5-10): 3_

PvaPh = Cv—x lT2

-^ L

-Dv[

(5-13)

2

(e-hL)

According to Eqn (3-17), the corresponding height HTUV of a transfer unit on the vapour side is given by j_

1

/

2

T U

HTUV = -±- - V (e - hL)2 — a Experimentally determined numerical values for the constant Cv, which is characteristic for the geometry of the packing, are listed in Tables 5.1 and 5.2. The numerical values for the exponents m and n are m = 3/4 and n = 1/3 and have also been obtained from measurements. The term aPhla can be evaluated by the method presented in Section 5.3. The determination of the liquid holdup hL in the M ^ - UV,S range requires evaluation of Eqn (4-27); and in the uv > uV)s range, evaluation of Eqn (4-77). The characteristic to be taken for the length of the path of contact lr is the hydraulic diameter dh, i.e. lT = dh = A -

(5-15)

5.3 Vapour-liquid phase boundary The term aPhla in Eqns (5-4), (5-5), (5-8), (5-13) and (5-14) is the ratio of the area aPh at the phase boundary to the area per unit volume of packing. It has been related by means of a dimensionless analysis to the density QL, the dynamic viscosity r] L , and the surface tension oL of the liquid, the area of the unwetted packing a, the void fraction 8, and the liquid load uL. This relationship, in turn, can be expressed in terms of the Reynolds number ReL, the Froude number FrL, and the Weber number WeL of the liquid phase and is valid up to the loading point. Thus, aph

a

8 0.5

— J

= 3

luL

QI

-0.2 / (

805

2

\0.75 /

oLa j

u\a

\ g

Ret2 Wei:15 FrL0A5

The hydraulic area ah included in the model for the holdup (cf. Section 4.7) is sometimes larger than the area of the phase boundary aPh. This is because it embraces a fictitious quantity that corresponds to the volume of liquid that accumulates in the dead spaces of the packing and does not contribute towards mass transfer between the phases. It was for this reason that ah was considered to be independent of the Weber number We.

5.3

125

Vapour-liquid phase boundary

The difference between the hydraulic area ah and the area of the phase boundary aPh in packed countercurrent columns is evident from Figs. 5.2 to 5.4, which were plotted from Eqns (4-74) and (5-16). Rectification columns differ from those designed for absorption or desorption in that the physical properties of the phases are subject to change over the height of the column. Thus a surface tension gradient is formed in the liquid phase from the top to the bottom of the column and influences the area of the phase boundary. Systems are said to be "positive" if the surface tension increases in the direction of liquid flow; "negative", if it decreases; and "neutral", if it remains practically constant. The shear stress induced by a surface tension gradient is given by doL

dx

(5-17)

~dx~ ~&H

where da L /dx is the differential change in surface tension from the top H = 0 to the bottom H = H of the column and x is the mole fraction of the lower-boiling component in the liquid phase. To is in equilibrium with the shear stress in the liquid film TS, which is given by {cf. Fig. 4.1 and Eqn (4-1)} duL,s ds

(5-18)

If the packed column is divided into elements of height AH, in which the driving force consists of differences Ax in the low-boiling mole fractions within the boundary layer of the

1.2 1.0 0.8

Pall ring *****

u.b

8 at o

*a — i

2

i

.^

o

CD

sz

*—

CL.

E

a

0.3

cz "c a CD

1.2 1.0 0.8

1 °

06

Plastic, dumped 50 mm ,

'

a = 87m 2 /m3

--

NOR-PAC r ng

0.4 Fig. 5.2. Hydraulic and phase contact areas as functions of the liquid load

m3

a = 111 Trl /

0.4

a o

0.3 5

10 15 20 25 30 35 40 Liquid load u L [ m3 / m2 h ]

126

5

Mass transfer in countercurrent packed columns

Fig. 5.3. Hydraulic and phase contact areas as functions of the liquid 10

15

20 25 30 35 40 load

Liquid load U|_ [m

3

liquid phase, and if ujso is substituted for the change duLslds in the liquid velocity within a layer of thickness ds, the following relationship can be derived from Eqns (4-13), (5-17), and (5-18): o

=

T\LUL

_So_

=

L

Ax dojdx

AH

(5-19)

The dimensionless quantity S is a measure for the mass transfer effected by the surface tension gradient. The Peclet number PeL in the liquid phase is given by PeL =

uL

(5-20)

It characterizes the mass transfer brought about by flow and molecular diffusion, and its ratio with the term S in Eqn (5-19) is the Marangoni number MaL, i.e. MaL =

do> dx

AJC

DLr\La

(5-21)

where doL/dx is the rate of change in surface tension along the height of the column with respect to the composition x in the liquid phase; AJC is the difference between the concentration in the bulk to that at the surface of the liquid and is given by (cf. Fig. 1.5)

5.3 Vapour-liquid phase boundary

127

-a cz a a

CO

a

QJ

CZ

a

a

0.2 Fig. 5.4. Hydraulic and phase contact areas as functions of the liquid load

10

15

20 25 30 35 40

Liquid load uL [m 3 /m 2 h]

= x-x*

L

=

(x-xe)

(5-22)

The difference in concentration depends on the distribution of the resistance to mass transfer in the two phases, i. e. on the ratios HTUJHTUOL for the liquid phase and HTUvIHTUov for the vapour phase. These two ratios are related as follows: HTUL HTUQL

~

HTUV ~ HTU

~

kov ~ I3

(5-23)

where v is given by HTUV HTUL

(5-24)

128

5

Mass transfer in countercur rent packed columns

The ratio v can be determined from Eqns (1-29), (5-5), and (5-14). Thus, _5_

£k.

JL

MX.

v = Cv myx ML

QL_ ( V Q V ) 2 QV -

J_

DL2

-

where ML and Mv are the molecular masses of the respective phases. The difference in concentration can then be calculated from the following equation: Ax = ~^(x-xe)

(5-26)

The evaluation of numerous studies on rectification systems has shown that the area aPh of the phase boundary remains constant in positive and neutral systems and that Eqn (5-16) can thus be applied. In negative systems, however, the interfacial area aPh is reduced by the surface tension gradient and surface destabilization. Allowance for this effect can be made by —

= (1 - 2 . 4 • 10-4|MflL|0'5) - ^

(5-27)

The mass transfer efficiencies HTUOv {Eqn (3-11)} determined by experiment in rectification systems differ from those calculated from Eqns (5-27), (5-4), and (5-13) by an average of 14 %. The increase in liquid holdup within the range above the loading point also causes an increase in the area aPh of the phase boundary. It can be now assumed that, in analogy to Eqn (4-70), the following relationship applies above the loading point: _ = + \ a }Uv>Uvs a \ a a / \ uv>m Thus the interfacial area at the flood point will be given by

ow I

a

In this case, the volumetric mass transfer coefficient for the range in question can be calculated from the above equations. Figures 5.5, 5.6, and 5.7 convincingly demonstrate the good agreement between the efficiencies determined by experiment and those calculated from the NTU-HTU concept, including the model equations developed above. They show the relationship between the packing efficiency and the capacity for absorption, desorption and rectification systems. The packing concerned in each case was Hiflow rings of various sizes and materials.

5.3

129

Vapour-liquid phase boundary

50-mm Hiflow rings, metal. ds= 0.45 mm. Z = 2400 1/m2 Ammonia-Air/Water. 1 bar. 293 K. uL = 10 m 3 /m 2 h. H = 1.45 m •a?

"

4

5 a.

=n

CO

^

/

Experimental data

z

•— / / Model calculated curve

—-V

CO

a

0.4

0.8

1.2

1.6

2.0

2.4

Gas capacity factor Fv [m~

2.8 1/2

3.2

1

s" kg

1/z

3.6 4.0

]

Fig. 5.5. Comparison of the load-efficiency relationship calculated from the model correlation with that determined in desorption experiments

50-mm Hiflow rings, plastic. ds= 0.3 mm. Z = 1400 1/m2 Carbon dioxide-Water/Air, 1 bar. 293 K. uL = 15 m 3 /m 2 h, H = 1.33 m

- E xperime ntal data CD

^

\

°- S co

D

V

^

a g

§ i 3

"B"—U

"EH:3—nHol M LJUcl

a

D

n ^—

V-— / /

rnlnilnfnrl U

0.4 0.8

1.2

1.6

rnr\;

UUI V

1

t-

0.2

2.0 2.4 2.8

Gas capacity factor Fv lm"

\

1/2

1

3.2 3.6

12

s" kg '

Fig. 5.6. Comparison of the load-efficiency relationship calculated from the model correlation with that determined in absorption experiments

130

5

Mass transfer in counter cur rent packed columns

25-mm Hiflow rings, plastic, d s = 228 mm, Z = 2036 1/m2 Chlorobenzene/Ethylbenzene, 67 mbar, L/V = 1, H = 1.5 m en

I Experimental data 1 } ° C

CD

—o—

/

txr°

a—£Q ,.J

o o

io

—

Model calc jlated (:urve

o

0

0.4

0.8

1.2

1.6

2.0

2.4

2.8

3.2

3.4

Vapour capacity factor F v [m 1 / Z s"1 kg 1 / z ] Fig. 5.7. Comparison of the load-efficiency relationship calculated from the model correlation with that determined in rectification experiments

5.4 Relationship between mass transfer and fluid dynamics The factors that influence fluid dynamics and mass transfer in beds of packing are the flow velocities of the phases and the physical properties of the system, e.g. the density, viscosity, and diffusion coefficient. Other parameters are introduced by the packing, e.g. the void fraction, the surface area per unit volume, and a factor that allows for the shape and surface structure of the packing. They are all related by the pressure drop per transfer unit, which is referred to here as the specific pressure drop and is defined by &p NTUn

H

HTUn

(5-30)

The equation can be applied if mass transfer is predominantly in the vapour phase, which is the case in most rectification and many absorption and desorption systems. Under these circumstances, mass transfer is a function of Reynolds number Rev (and thus the capacity factor Fv) and the Schmidt number Scv acccording to Section 8.3, i. e. approximately HTUQV

=

HFv

uL = const.

(5-31)

The following simple relationship for the specific pressure drop at a constant liquid load uL can be obtained by combining Eqns (5-30) and (5-31):

NTUn

Sc,

=

C

ty

uL = const.

(5-32)

The liquid load uL depends on the mass flow ratio L/V, the densities of the vapour QV and the liquid o L , and the vapour capacity factor Fv, i.e.

5.4

Relationship between mass transfer and fluid dynamics

131

In other words, the specific pressure drop modified by the Schmidt number is a function of the liquid and gas loads. According to a recent suggestion, it can be expressed as follows in terms of the various parameters:

This equation allows the results of rectification studies to be correlated and compared with those obtained in absorption experiments. The phase ratio L/V can be determined by rearranging Eqn (5-33), i.e.

T-"ft; T,

<«5>

Rectification experiments are often performed at a phase ratio of L/V = 1. In this case, Eqn (5-34) becomes t

= 1=AF?

(5-36)

V

In most absorption studies, however, the liquid load is kept constant, and the gas load is varied or vice versa, as is evident from the diagrams presented in Chapter 3. The equation that applies in this case is derived from Eqns (5-34) and (5-35), i. e. A

-—

• Scv

3

= B uLn F{?-n = BULFV"

(5-37)

Figures 5.8 to 5.10 show the results of rectification experiments under total reflux, i.e. L/V = 1; and Fig. 5.11, absorption tests in which the load in the one phase was kept constant and that in the other was varied. It can be seen that they confirm the above relationships, the general form of which is shown qualitatively in Fig. 5.12. Fig. 5.11 indicates that packing may have two ranges of liquid loads - in one of which n < 0; and in the other, n = 0 -. The latter can be expected at liquid loads of u^ > 10-15 m 3 /m 2 h, i. e. in absorption processes. The liquid loads in vacuum rectification are quite often less. A comparison of Eqn (5-32) with Eqn (5-37) reveals that the exponents in, m, and n are theoretically related by in = m + n

(5-38)

If the liquid loads are higher than about 15 m 3 /m 2 h, uL no longer exerts an effect on the modified pressure drop per transfer unit, with the result that the exponent n in Eqn (5-37) becomes zero. Consequently, it is only in this higher loading range that rectification and absorption experiments can be described by a common exponent, i.e.

132

5

Mass transfer in countercurrent packed columns

100

e_

80 -•eg. imm Hiflow ring.meta ii =0.22m.H=U8m M:=39435 1/m3 N 2 z = 600 1/m a iloro-/Ethylbenzene 40 pr = 67mbar,L/V=1

/

-1 Q-

30 /

i/

20 Rectificat on L/V=1

<

r

\ CD

10

n 1 / N

/Abe ;ornl inn

ft

4

n / i

/ 3

6

2

o25mm Hiflow r.rnetal ds =0.3 m,H 440 m N=39917 1/m3 Z=1350 1/m2 NH3-Air/H20 uL = 10m3/m2h p=1barJ=293K

1.5 0.6

0.8 1.0

2 1/2 1/2

3 1

Fig. 5.8. Modified specific pressure drop as a function of the capacity factor in rectification and absorption

l/2

Capacity factor Fv [nff s~ kg ]

(jn)uL > i5m3/m2h = m

(5-39)

It can be derived from the above equations that the constants A and B are related by B = A

QL

(5-40)

The only case in which the constants are the same is that of higher liquid loads, when n tends to zero, i.e. m 3 /m 2 h

-

(5-41)

5.4

133

Relationship between mass transfer and fluid dynamics

60

3

n 25mm NOR-PAC.PP (Js=0.3m,H=1.40m 3 1s|=47837 1/m 40 2 i?=600 1/m 30 %-Air/H 2 0,u L =10rn 3 /m 2 h p=lbar.T = 293K

JT 20

Absorp tion uL = 10m:/ m 2 h ^

10

q

1 J

A¥

If

4

M T ILi

f-

— RecTiTication t/V=1

i

"g

4 /

Fig. 5.9. Modified specific pressure drop as a function of the capacity factor in rectification and absorption

0.6

0.8 1

G25mm NOR-PAC.PVDF ds=0.22m.H = U 7 m N = 45400 1/m3 Z = 2250 1/m2 Chloro -/Ethylbenzene p T --67mbar.L/V--l 2 1/2

-

3 1

1/2

Capacity factor Fv [m" s" kg ]

These equations were evaluated in the light of the results obtained in numerous studies on pressure drop and mass transfer in the rectification and absorption systems listed in Table 5.3. It was thus revealed that the difference between the calculated and experimental figures are slight if the numerical values listed in Table 5.4 are allotted to the exponents m, m and n. Numerical values for the constant A that were determined for dumped packing are presented in Table 5.5; and for regularly stacked packing, in Table 5.6. Inserting the numerical values for m and n in Eqn (5-34) yields relationships for the pressure drop per transfer unit in the range of lower {Eqn (5-42)} and higher {Eqn (5-43)} liquid loads, i. e.

134

5

Mass transfer in countercur rent packed columns

40

30 h

-e-50-mmHiflowring,PVDF hydroph.

_ 20 --

d s =0.22 m, H=1.47m N=7163 1/m3 Chtoro-/Ethylbenzene P T =67mbar ,L/V=1

10

L/V= 1

en Q.

Absor ptinn 3 2 u L =10rn /m h

3

o a>

CL

2

1 0.8 0.6 0.6

u

4 / / \

6

e drop

<

rceumcuuun

ir

1 /

/ 0 50-mm Hifiow ring.PP

y1 I

1

d s = 0.3 m.H=1.37 m N=6997 1/m3 Z=600 1/m2 NH 3 -Air/H 2 0 uL= 10 m 3 /m 2 h p = lbor,T = 293K i

-

1

Fig. 5.10. Modified specific pressure drop as a function of the capacity factor in rectification and absorption

0.8 1 Capacity factor Fv [m" 1/2 s'kg 1 ' 2 ]

r- \-0.33 3

2

=

A

luL < 15m /m h

\NTUn OV luL

> 15 m 3 /m 2 h

= A

(5-42)

T 15 mlh 3600 uL

-0.33

2_ Sc

(5-43)

All that these equations contain, apart from the variables that describe the loading conditions and the physical properties of the system, is a constant A that is specific for a given packing. Values for the pressure drop per transfer unit calculated from these relationships deviate by 14 % on an average from the measured values.

5.4

135

Relationship between mass transfer and fluid dynamics

20 5597/HI* CD.

-1/2 -1 ,

1/2 i s kg i h^—i 147

Fv[n

10 8

£ TZJ

cT 6 - 'CO<_>

7} y

V

>

4

a-

i.

fcW- °H -1.56

*^ D

3

1017

2

—| NH3-Air/H20/1bar)293K 1 3

Fig. 5.11. Modified specific pressure drop as a function of the liquid load

4

6

8 10

20

30

40

Liquid loadu L [m 3 /m 2 h]

/

Eqn. (5-33) log-log tan a = m /

/

I |

Eqn.

(5-33)

log-log

tan 3 = -n

iV 1

1 T

^ ^

^

1

/k

•

*

i

*

!

F

V2vl

Fig. 5.12.

1 1 |_ 1 !^ U L1

Qualitative diagram for modelling the specific pressure drop

1 1 1 1

1

•

136

5

Mass transfer in countercurrent packed columns

Table 5.3. Systems investigated in correlating the specific pressure drop System

Chlorobenzene / ethylbenzene Chlorobenzene / ethylbenzene Chlorobenzene / ethylbenzene Chlorobenzene / ethylbenzene Chlorobenzene / ethylbenzene Chlorobenzene / ethylbenzene Toluene / n-octane Toluene / n-octane Toluene / n-octane Ethanol/water Ethylbenzene / styrene trans-1 cw-Decahydronaphthalene Methanol / ethanol 1,2 Dichloroethane / toluene Ammonia-air / water

Qv

Pr mbar

kg/m

33 67 133 267 533 1000 103 133 267 1000 133 13 1000 1000 1000

0.140 0.268 0.510 0.967 1.827 3.241 0.373 0.473 0.900 1.294 0.483 0.066 1.303 3.200 1.188

3

Vy-106 m 2 /s

DylO6 m 2 /s

SCy

52.4 28.7 15.8 8.8 4.9 2.9 19.1 15.3 8.5 8.2 15.9 105.8 8.4 3.2 15.1

64.8 35.8 19.9 11.1 6.3 3.7 21.0 17.0 9.5 14.5 19.9 120.0 9.1 4.0 23.8

0.809 0.803 0.793 0.791 0.785 0.780 0.908 0.904 0.894 0.567 0.798 0.881 0.929 0.806 0.633

Table 5.4. Exponents in the correlations for determining the modified specific pressure drop u L [m 3 /m 2 h]

m

in

n

< 15

2.33

2

-0.33

2.33

2.33

0

Table 5.5. Calculation of pressure drop in random beds of packing Dumped Packing

Pall ring

Material

Size mm

N 1/m3

a m 2 /m 3

m 3 /m 3

8

A

cP

Metal

50 38 35 25

6242 15772 19517 53900

112.6 149.6 139.4 223.5

0.951 0.952 0.965 0.954

36.98 66.59 64.49 61.18

0.763 1.003 0.967 0.957

Plastic

50 35 25

6765 17000 52300

111.1 151.1 225.0

0.919 0.906 0.887

36.30 65.36 81.66

0.698 0.927 0.865

Ceramic

50 25

6215 36621

116.5 175.1

0.783 0.790

56.94 112.39

0.662 1.242

Ralu ring

Plastic

50 50, hydr.

5770 5720

95.2 95.2

0.938 0.939

27.91 22.24

0.468 0.439

NOR PAC ring

Plastic

50 35 25, Type B 25, 10 webs 22

7330 17450 50000 48920 69274

86.8 141.8 202.0 197.9 249.0

0.947 0.944 0.953 0.920 0.913

20.36 28.23 38.31 28.74 34.31

0.350 0.371 0.397 0.383 0.397

5.4

137

Relationship between mass transfer and fluid dynamics

Table 5.5. (continued) Dumped Packing

Material

Size mm

Hiflow ring

Metal

50 25 90 50 50, hydr. 25

N 1/m3

A

cP

a m 2 /m 3

e m 3 /m 3

5000 40790

92.3 202.9

0.977 0.962

20.14 45.75

0.421 0.689

1340 6815 6890 46100

69.7 117.1 118.4 194.5

0.968 0.925 0.925 0.918

18.04 19.77 18.66 47.57

0.276 0.327 0.311 0.741

1904 5120 13241 110741

54.1 89.7 111.8 261.2

0.868 0.809 0.788 0.779

26.15 36.07 50.09 84.42

0.435 0.538 0.621 0.628

Ceramic

75 50 38 20, 4 webs

Hiflow ring; Super

Plastic

50

6050

82.0

0.942

20.21

0.414

Hiflow saddle

Plastic

50

9939

86.4

0.938

25.13

0.454

TOP-Pak ring

Aluminium

50

6871

105.5

0.956

32.39

0.604

Raschig ring

Metal

50 35 25 15

6630 19300 52200 241600

112.2 152.4 229.7 367.7

0.949 0.929 0.948 0.947

115.10 158.39 206.18 297.81

2.637 3.254 3.112 2.921

Ceramic

25

50599

202.2

0.720

314.17

1.329

VSP ring

Metal

50, No. 2 25, No. 1

7841 33434

104.6 199.6

0.980 0.975

32.25 59.77

0.773 0.782

Envi Pac ring

Plastic

80, No. 3 60, No. 2 32, No. 1

2000 6800 53000

60.0 98.4 138.9

0.955 0.961 0.936

16.81 19.19 29.57

0.358 0.338 0.549

Bialecki ring

Metal

50 35 25

6278 18200 48533

121.0 155.0 210.0

0.966 0.967 0.956

45.97 68.29 114.54

0.719 1.011 0.891

DIN-PAK

Plastic

70 47

9763 28168

110.7 131.2

0.938 0.923

22.12 27.64

0.378 0.514

Glitsch-CMR

Metal

No. No. No. No. No.

9914 3.0 64495 1.5 1.5 Turbo 62432 169930 1.0 548923 0.5

100.0 185.7 173.5 249.4 354.8

0.980 0.632 0.627 0.641 0.882

26.87 48.63 36.75 51.70 75.31

0.435 0.632 0.627 0.641 0.882

Glitsch ring

Metal

30PmK 30 P

28379 33190

175.4 175.0

0.976 0.956

45.50 70.94

0.851 1.056

Intalox saddle

Ceramic

38

19528

143.3

0.813

122.38

1.343

Plastic

50

8656

122.1

0.908

78.97

0.758

138

5

Mass transfer in countercur rent packed columns

Table 5.6. Calculation of pressure drop in geometrically arranged beds of packing A

cP

0.754

37.74

0.233

176.6

0.945

37.30

0.460

YC-250*

250.0

0.945

21.02

0.191

Metal

250

250.0

0.970

16.56

0.292

Gempak

Metal

A2 T 304

202.0

0.979

21.62

0.344

Impulse packing

Metal

250

250.0

0.975

32.52

0.262

Ceramic

100

91.4

0.838

34.96

0.417

Metal

Bl-200 Bl-300*

200.0 300.0

0.979 0.930

30.83 24.68

0.355 0.295

Plastic

Cl-200 C2-300

200.0 300.0

0.954 0.900

41.61 31.06

0.453 0.252

Plastic

PN-110

110.0

0.936

29.80

0.250

Stacked packing

Material

Size mm

Pall ring

Ceramic

50

Bialecki ring

Metal

35

Ralu pack

Metal

Mellapak

Montz packing

Euroform

N 1/m3

a m2/m3

m3/m3

7502

155.2

20736

E

= likewise estimated for rectification

Combining these relationships for Ap/NTUOv with those for AplH, as described in Chapter 4, yields the following expression for the height HTUOy of an overall transfer unit:

Ap/NTUp Ap/H

HTUnv =

(5-44)

The corresponding relationship for the uL < 15 m 3 /m 2 h range of liquid loads is given by {Ml UOv)uL

< 15 m 3 /m 2 h ~

(5-45)

^

and that for the uL > 15 m 3 /m 2 h range, by (5-46) ds These equations allow for the physical properties of the system, the bed geometry, the loading conditions, and the constants A and CP for the packing. The latter is required for the calculation of \L from Eqn (4-67). They are valid at loads of up to 90% of the flood

5.5

Mass transfer at high liquid loads

139

capacity and allow the height of a gas phase transfer unit to be calculated to within an accuracy that corresponds to an average deviation of 13 % from the measured values. If controlled mass transfer is predominantly in the vapour phase, the relationships discussed between the mass transfer efficiency and the pressure drop would entail that the pressure drop per unit of separation efficiency would be largely governed by the Schmidt number Scv for the vapour phase. It is evident from Fig. 5.13 that the relationship between the Schmidt number and the vapour mole fraction varies considerably according to the composition of the mixture concerned. It therefore follows that, if various packed columns were to be tested with different systems, the only magnitude that would allow their performances to be compared is the modified specific pressure drop (Ap/NTUov)Scv2/3. An example of a comparison along these lines is shown in Fig. 5.14. The operating conditions were those listed for random beds in Table 5.7, and the packings compared were 50-mm ceramic Pall rings and 50-mm ceramic Impulse packing.

5.5 Mass transfer at high liquid loads It was demonstrated in Section 4.9 that the flow pattern may change as a result of phase inversion at high liquid loads, whose level depends on the geometry and size of the packing. In some cases, loading conditions of this nature have to be realized in industrial-scale equipment. According to Fig. 4.21, these cases depend on the nature of the packing and the

1.6 -1,2-Propylene glycol / Ethylene glycol 13.3 mbar

1.4

1.2

M a i knnn Hell IUI IUI

A

1 \

/Eth anol *bar\

Ethylbenzene/Styrene^ 133 mbar < \ / / \

0.8

s

vyChlorobenzene/Ethylbenzene 66.7 mbar

0.6 Ethanol/ Water 1 bar 0.4

0.2

Fig. 5.13. Schmidt numbers for some rectification systems

0.4 0.6 Vapour mole fraction y

0.8

1.0

140

5

Mass transfer in countercurrent packed columns

O

-a

CD Q. CO

0.5 0.6 0.8 1.0

1.5

2

3 V2

1

V2

Gas capacity factor Fv [m~ s" kg ]

Fig. 5.14. Modified specific pressure drop as a function of load for (random and arranged) ceramic packing

Table 5.7. Conditions for the tests in which the results shown in Fig. 5.14 were obtained System

d s [m]

H[m]

N[l/m 3 ]

Conditions

Ammonia-air / Water

0.2 0.25

1 0.85

• 7600 O 7600

1 bar, uL = 15-43 m 3 /m 2 h

Ethanol/Water

0.5

1

(j) 7600

1 bar, LIV = 1

Ammonia-air / Water

0.3 0.22

1 2

A 6520 • 6520

1 bar

Ethanol/Water

0.5

1

Chloro- / Ethylbenzene

0.22

1.5

1 bar, LIV=

1

A33, A 67, A 133 bar, LIV = 1

5.6

Mass transfer in absorbers accompanied by chemical reaction in the liquid phase

141

system and arise if the flow parameter at the loading point is (L/V) (QVIQL)I — 0-4 (cf. Figs. 4.13 to 4.15). The results of experiments performed to study this problem are shown in Fig. 5.15, in which the values of HTUOv for an ammonium-air/water system have been plotted against the liquid load uL for a constant gas load Fv. In accordance with the theory, HTUOv first of all decreases as the value for uL increases and reaches a minimum at loads at which phase inversion can be expected. At even higher loads, it remains constant at this low value or rises slightly.

25-mm Hiflow ring, plastic, ds=0.45 m, H =1.5 m, Z = 920 nrr2

\ i\

0.26

0.22

•£ 0.18 cz a

5hnco i n\/o nnin nose lllvtfi iiuu puiiii

[:

kg 1 ' 2 .

v,s=l

m

1.5 ' •

a o

s -1 kg 1/2

,FV=2

7 ^ ~ 0.75 -

•1 —

V

'

-

i

^

—

|

' —

, = 55.4 m3/m2h

aNH 3 -Air/H 2 0. STP

0.10 0

20

100 3

120

2

Liquid load u L [m /m h] Fig. 5.15. Efficiency as a function of the liquid load above and below the phase inversion

5.6 Mass transfer in absorbers accompanied by chemical reaction in the liquid phase Whereas the relationships discussed above concern separation processes in which mass transfer is solely by physical means, chemical absorption is resorted to for removing pollutants from industrial off-gases and power station flue gases. The systems listed in Table 3.10 were investigated to gain information on the differences in performance between physical and chemical absorption. In all cases, the carrier was air at NTP, and the mass transfer components were ammonia and sulfur dioxide. The ammonia was absorbed in water and aqueous sulfuric acid; and the sulfur dioxide, in aqueous sodium hydroxide. In the last two systems listed, absorption was accompanied by a rapid chemical reaction in the solvent, as is indicated in Table 3.10. The packing selected for the studies is shown in Fig. 5.8. Its latticework structure allows extremely low pressure drops and comparatively high capacities and presents hardly any problems in scale-up (cf. Section 8.5).

142

5

Mass transfer in countercurrent packed columns

Table 5.8. The packings investigated in the chemical absorption studies and their geometrical data Packing

NOR-PAC PVDF

Hiflow PP

Hiflow Metal

Height

27 mm

50 mm

28 mm

Diameter

27 mm

50 mm

25 mm

Thickness

2 mm

1.5 mm

0.4 mm

Shape of the packing investigated

N [1/m3] 2

3

3

3

44500

6500

37200

180

114

185

a [m /m ] E [m /m ]

0.927

w [kg/m3]

82

0.930 58

0.965 300

Figure 5.16 shows the relationships that were thus established between HTUOv, vv, Ap/NTUov, Fv and L/V. It reveals that the efficiency of the systems in which mass transfer in the solvent phase is accompanied by a rapid chemical reaction is considerably higher than that in purely physical absorption. The results plotted in Fig. 5.17 show that the efficiency of absorption accompanied by chemical reaction in the liquid phase depends on the system. If a chemical reaction occurs in the liquid, the resistance to mass transfer on the liquid side can ignored. According to the HTU-NTU model represented by Eqn (1-62), the height of a transfer unit HTUL in the liquid phase can then be neglected with the result that

HTUov-* HTUV and Ap/NTU0V-> &plNTUv. In the ammonia-air/water system, in which the resistance to mass transfer is divided between the two phases, the height HTUV of a transfer unit in the gas phase can be obtained from Eqn (3-16). Examples of comparisons between physical and chemical absorption on the basis of the modified specific pressure drop per gas-side transfer unit are shown in Fig. 5.18. The relationship is practically independent of the system and can be expressed by

NTUV

Ap HTUV Scv-213 = f(Fv) = CF? H

(5-47)

The height of a transfer unit HTUV for absorption systems with rapid chemical reaction in the liquid phase can be obtained from the values of Ap/NTUV determined from Eqn (5-47) and Ap/H from the following approximate equation:

5.6

Mass transfer in absorbers accompanied by chemical reaction in the liquid phase

Vm 2 , uL=i0 m 3 /m 2 h, NTP

d s =300 mm, CD

0.4

_ NH 3 -Air/H 2 0*H 2 5q, •1 NH3- Air/H20 c3

_ 0.3 S £ o

o a> cDco

143

• 0.2 \

\

r—

• ^^"^

"•«

0.1

^

-•-

0.5 0.4 -c: co CT> c:

g

>

0.3

s

n

SB'

•—•* '

•-

!-••

V

0.9 1.0 1.2 CO

f 5 1.6

25-mm N0R-PAC . m N = 478371/m3

TD

5 2.0

50-mm Hiflow H = 14 m N=69971/m 3

2.5 3.0 4.0 0

Fig. 5.16.

8 16 24 32 0 8 16 Specific pressure drop Ap/NTU0V [mmWG]

Process engineering data for evaluating physical and chemical absorption

U

CTQ

92.

o

o

uat ing

3,

CD

o

o

cal abs

5"

T3_

CO

<"D

TD

o o

CO TD

TD

O TD

CL

<"D

jns

dat;

CD

CD

CD

iso

—»—».—» c n -r** r-o

Liquid/gas ratio L/V UD

• •

_

— ^

©

1

1

CD —

if

•

I

^S

ZIZIN n II ii ii cn •T- ,—- -P- CD •

—-«

\

r1

CO

D

X D

\

*^

ss \

N^

CO CD

N

cz>

—» CD

Gas capacity factor Fytrn'^s' 1 kg1/2]

c o r>o CD e n

metol II

CO

zr

3

CD CD CD

II

o§ 3 3 -^3

II

CL d . "— oo

CD Kj

\ \ i

\

\

CD CO

\

4

<

\

I 1i

X \ V

Height of a transfer unit HTUOV [mj

o*"CD ZE=

CO

\

oo

\

>

Vo >

Z

,

,

o

—* CO

cn

CD

I I

H

U

Tf

41

f

1 L

/

Specific column volume wls]

5.6

Mass transfer in absorbers accompanied by chemical reaction in the liquid phase

_

Ap/NTUV Ap/H

145

(5-48)

Hence, if the number of transfer units to be realized NTUV is known, the height of the column can be estimated from (5-49)

H - HTUV • NTUV

Fig. 5.19 shows the results of studies on geometrically arranged packing with a honeycomb structure. The high efficiency and the extremely low pressure drop are characteristic for this packing geometry.

25mm NOR-PAC PVDF

50mm Hiflow, PP

NH 3 -Air/H 2 0 NH 3 -Air/H 2 0+H 2 S0 4 -

NH 3 -Air/H 2 0 o NH 3 -Air/H 2 0-H 2 S0 4 * S02-Air/H?0+Na0H o

2.0 "§

15

-c

4 /

d//

0.8

4 &

0.4

|

0.3

CO CO

%. 0.2

NH3-Air7H20 NH 3 -Aif7H 2 04i 2 S0 4 S02-Air/H20+Na0H

— C-0.14 5. m = 2 -

--0.211 m =

1.0

25mm Hiflow,metal

't

'/

i

0.1 0.8 1

f

±1273

^±10%

1.5

2

3

0.8 1

1.5 2

Gas capacity factor Fv

3

0.8 1

1.5 2

3

[m' l / 2 s' 1 kg 1 / 2 ]

Fig. 5.18. Modified specific pressure drop as a function of the vapour capacity factor in physical and chemical absorption

5

146

Mass transfer in countercurrent packed columns

Honeycomb 1. plastic d s = 0.28m. H--0.8m CD

1 - s 0.3 o

~—' • c r -

\

0.2 •= 0.15

-

S0 2 -Air71n NaO H uL=10m3/m2h

10

Ibar, 295K

iI

1

r

11

I" 2 S 1-5

/

CD

I °-8

1

f

1

.a 0.6 O CD

/

0.4 0.3

I

/

I

1

ZL t

0.2 0.8 1 1.5 2 3 Gas capacity factor Fv [rrr1/2 r 1 kg 1/2 ]

Fig. 5.19. Height of a transfer unit and the specific pressure drop for a plastics honeycomb packing as functions of the gas capacity factor in the absorption of sulfur dioxide from air by caustic soda

6 End effects in packed columns

The efficiency of packed columns is usually determined by experiment on rectification, absorption, and desorption systems in pilot plants. Strictly speaking, the end effects that thus occur must be taken into consideration in evaluating, correlating, and scaling up the results obtained. If this is not the case and if the beds of packing in the experiments are of low height, the column efficiency could be wrongly estimated.

6.1 Phenomenological description A distinction must be drawn between external and internal end effects, i. e. those whose influence on the results of efficiency measurements is exerted outside the bed of packing and those whose influence is exerted within the bed. The external effects can primarily be attributed to the liquid distributor and, when applicable, to the device for preventing entrainment of the packing. The extent of the effect depends largely on the design and not so much on the phase load. Other factors that may affect measurements of column efficiency are the support plate for the packing and, when applicable, the gas distributor. In pilot plants, the external effects at the head of the column are probably the most decisive, because a gas distributor in this case is usually dispensed with. In fact, if the bed is of low height, a simple, thin wire netting of small area and a very large open cross-section usually suffices as a support. Internal effects may be caused by the inflow of the phases, which is governed by the pattern and the density of liquid distribution effected by the distributor and may even give rise to maldistribution at the inlet. Another factor is the ability of the packing itself to distribute the phases and even its tendency to maldistribution. The shape of the inlet zone thus formed may be responsible for changes in separation efficiency over the height of the bed. This vertical efficiency gradient disappears once flow has been completely developed and equilibrium has been established. Afterwards, the efficiency per unit height of bed remains constant. In pilot plants, these internal effects are mainly restricted to the liquid inlet zone at the head of the column, provided that the inflowing vapour is uniformly distributed over the cross-section at the foot of the column. These effects can be assessed experimentally by measuring the concentration profile in both phases with the aim of determining the local separation efficiency over the height of the column. However, the method entails sampling by means of probes, which disturb or even alter the flow profile. Another, less complicated method consists of determining the packing efficiency at various heights. It requires simpler instrumentation, presents hardly any problems, and does not disturb the flow profile. Consequently, it was given preference in performing the experiments described and evaluated below. The relationship between the efficiency and the height of the bed depends on the strength of the external and internal effects that are described above and presented qualitatively in Fig. 6.1. The symbol N in the diagram signifies the number of separation units, i.e. either the number of transfer units, in which case N = NTU, or the number of theoretical stages, Packed Towers in Processing and Environmental Technology. Reinhard Billet Copyright © 1995 VCH Verlagsgesellschaft mbH, Weinheim ISBN: 3-527-28616-0

148

6

End effects in packed columns

i.e. N = nt\ and H is the height of bed per unit of efficiency. The initial value of N = Nj at the ordinate H = 0 is equal to the efficiency of any likely external effects. In the upper diagram of Fig. 6.1, the slope dNIdH of the function N = f(H) decreases as the height H increases within the AHt range until N attains the value N = Nt at a height of H = Ht. After this point has been reached, N increases linearly with H. A curve of this shape can be expected if the distribution density Z of the liquid distributor is high and uniform, i.e. if inlet maldistribution is insignificant. The qualitative curve shown in the lower diagram of Fig. 6.1 applies for liquid distributors with a low distribution density Z. In this case, the slope dN/dH first of all increases in the AHt zone until a value of H = Ht is attained, after which it remains almost constant. The value Ht depends on the distributor characteristic and the geometry of the packing. In the A Hi zones, the two-phase current becomes adapted to the flow through the channels formed by the geometry of the packing and its position and arrangement with respect to the walls of the column. The zone of influence AHt is characterized by variations in efficiency and thus depends on the design conditions mentioned. It is also governed by the phase loads and the phase ratio. Within it, the number of separation units is greater (upper diagram in Fig. 6.1) or less (lower diagram) by an amount ANt than that for completely developed two-phase flow and for H > Hi within a zone of the same height. The likelihoods and boundary cases that may arise in practice can be determined qualitatively from Fig. 6.1, and certain relationships can be derived for the efficiency dN/dH of the bed within the zones of fully developed flow.

Uniform initial phase distribution Z high -AH

AA

a a. a»

Poor initial phase distribution Z low

-AN,

Packed height H

Fig. 6.1. Qualitative efficiency curve for the inlet zone of a packed column

6.1

Phenomenological description

149

Thus the following equations apply if allowance is made for external and internal effects:

(dN\

N-ANj-N,

dJV \

I N\

777

(6 la)

< br

-

) (f) \

IN \

JH > Hi

\H

lANi.neg. > Nd

Likewise, the following applies if the external effects can be ignored: l6N\ IN-ANA N = T77 77 <-77 \ a / i )H > //, \ ti !Nd = o ti If the internal effects can be ignored,

lN-Nd\ N 7 7 < 7 7 ti

/

(6"3)

ti

and if both external and internal effects can be ignored, I6N\

=

IN\

If it is evident that end effects cannot be left out of consideration in design studies, evaluation of Eqns (6-1) to (6-4) could yield information on the extent to which the results of separation efficiency measurements published in the literature could be adopted, either direct or with appropriate corrections, in scaling up beds of packing to the heights required in industrial practice. The only cases in which corrections are not required arise if Eqn (6-4) is satisfied or if the following condition applies: N » Nd + m ANt = Ni

(6-5)

The increment ANi corresponds to the change in efficiency within the inlet zone AHt. The smaller the values of AHh the more rapidly the inlet distribution is corrected by a bed of packing. Hence, the following function can be regarded as a measure for the extent of the inlet effects in a separation column with an effective height H: A

" r = f(Z)

(6-6)

150

6

End effects in packed columns

where Z is the number of liquid streams, i. e. feeder points on the liquid distributor, per unit area of column cross-section. Figure 6.2 shows the number of separation units N a s a function of the height H with the number of distribution points as parameter. The lower diagram qualitatively represents Eqn (6-6). Zo is the number of distribution points at which the value for ANt theoretically just becomes zero. Obviously, the minimum increase in efficiency can be expected if the number of distribution points Z is 1. As the value of Z rises within the Z < Zo range, the efficiency in the inlet zone increases steadily, but the rate of increase becomes less in the Z > Zo range until the final value is attained at Z = Zmax. Therefore, liquid distributors with a number Z of distribution points greater than this do not contribute towards a further increase in the efficiency of column packing.

6.2 Correlation of end effects The diagrams presented in Figs. 6.3 and 6.4 serve as a basis upon which equations to describe end effects can be derived from the results of experiments. It is assumed that the local efficiency no longer changes with the height once flow has been completely developed in the zone concerned within the column, i.e.

Packed height H

z]
0

No. of liquid distribution points Z

Fig. 6.2. Qualitative description of the effect exerted by the number of liquid distribution points on the efficiency in packed columns including the inlet zone

6.2

Correlation of end effects

151

dN

(6-7)

= const.

The following relationship can then be expressed in terms of the magnitudes represented qualitatively in Fig. 6.3: dN \

_ N-NdANj >Hi~ H

(6-8)

E

Fig. 6.3. Qualitative efficiency curve for a packed column with positive inlet effect

H Packed height H

Variable efficiency dN

Constant efficiency ,_

/dNN

dHx r

\

. . ^ O ^

mTAN, -1 -AN, Fig. 6.4. Qualitative efficiency curve for a packed column with negative inlet effect

J

^

f AN;

i

Hi Packed height H

H

152

6 End effects in packed columns

Another relationship that is evident from the diagram is N-Nd-ANj

_

N-Nj

H

~

H-Ht

(6-9)

Hence the height of the inlet zone is given by

"'

v

"

(6-10)

" I dJV \dHjHZH:

where, according to the diagram, (6-11) Nt = Nd + m ANt and ANt exceeds AN/ by a multiple /, i.e. (6-12) ANi = i ANi' Therefore, the following relationship must exist between i and m: (6-13)

1 Consequently, Eqn (6-10) can be transformed into

{

=

H-

dN

iI

(6-14)

The factor / is a measure for the inlet effect. As a rule, the only means of determining it is by experiment. The following simple relationship applies: AN'

I dN

(6-15)

Combining Eqns (6-12) and (6-15) yields a general relationship for the inlet factor /, i. e.

AHt dN

ANt AN/

(6-16)

In other words, the factor / is identical to the ratio of the positive (Fig. 6.3) or negative (Fig. 6.4) inlet efficiency to the efficiency in the zone of completely developed flow.

6.2

Correlation of end effects

153

The figure to be taken for ANt in Eqns (6-14) and (6-16) can be obtained by experiment in pilot columns with packed heights of H > Ht. In this case, the values to be determined are the equivalents of the separation efficiencies Na and Nb in beds of Ha and Hb height and the efficiency Nd at H = 0 (cf. Fig. 6.5). The results are correlated by means of the following two equations: Na = Nd + ANt + Ha

dN dH lH>Hi

(6-17)

Nb = Nd + AN; + Hb

dJV \ dH j H > H i

(6-18)

in which Hb is greater than Ha by a multiple q, i.e. Hb = qHa

(6-19)

These relationships give rise to a correlation that permits the positive or negative inlet effect ANt to be calculated from the measured values of 7Vfl, Nb and Nd, viz. (6-20)

ZD

Fig. 6.5. Scheme for modelling the inlet effect in scaling up

Packed height H

154

6

End effects in packed columns

As is evident from Fig. 6.5, the height AHt of the inlet zone can be estimated graphically if a minimum of two measured values of TV for the inlet zone, i.e. H < Htj suffices to allow the shape of the curve to be described, at least roughly, as follows:

N=i(H)H
(6-21)

6.3 Experimental results The relationships outlined above can be interpreted in the light of the results obtained in experiments on columns of different diameter ds and beds of various height H. Types of packing of extremely differing geometry were thus investigated; the materials also differed in some cases, ceramics; in others, plastics; and in others again, steel -. The systems chosen for the experiments were ethanol/water for rectification at atmospheric pressure; ammonium-air/water and sulfur dioxide-air/water, for absorption at standard temperature and pressure; and carbon dioxide-water/air, for desorption at standard temperature and pressure. The number of distribution points on the liquid distributor Z was also varied, with the consequence that, as would be expected, differences in the inlet effects could be achieved. The conditions under which the various experiments were performed can be derived from Table 6.1, in which the main data are listed.

Table 6.1. Conditions and systems investigated in the experiments in which the results shown in Figs. 6.6-6.15 were obtained Packing

Material

Size d [mm]

Packing height H[m]

Diameter ds [mm]

System

Raschig ring

Ceramic

8 25

0.25-4

100 500

Ethanol/Water 1 bar

Pall ring

Metal

35

2-3.95 2-3.75

500 800

Ethylbenzene/ Styrene 67 mbar

600

50

1.33-3.95

500

600

2.00-3.75

800

Methanol/Ethanol 1 bar Ethylbenzene/ Styrene 67 mbar

No. of distributors Z [1/m2]

Hiflow ring

Metal

20

0.3-1.15

300

Air/CO2-Water SO2-Air/Water 1 bar

15

Tellerette

Plastic

47 70

0-1.35 0-1.40

300

NH3-Air/Water 1 bar

490

Envipac

Plastic

32

0-1.33

300

NH3-Air/Water 1 bar

490

6.3

Experimental results

155

The characteristic relationship between the efficiency and the bed height is shown qualitatively in Fig. 6.3 and was determined by experiment. The results of some of these studies that were carried out in the 1950s and 1960s are presented in Fig. 6.6. The measurements were performed in beds of ceramic Raschig rings in the one column with a smooth shell and in another with a corrugated shell. The system was an ethanol/water mixture that was rectified at atmospheric pressure under total reflux. It can be deduced from the shape of the curves that maldistribution and the attendant formation of an inlet zone with variations in efficiency can be prevented by a corrugated shell and uniform liquid feed. Figure 6.7 shows the results obtained in desorption experiments with a water-carbon dioxide/air system at standard temperature and pressure. The packing was metallic Hiflow rings. Since the liquid distributor had a comparatively low droplet density, the shape of the curve corresponds, as would be expected, to the type shown in Fig. 6.4. By virtue of the bed's own ability to distribute the liquid, the local efficiency per unit height, which is poor in the inlet zone of the column, is progressively improved until it attains the same value as that in the zone of completely developed flow. The example given in Fig. 6.8 represents a case in which no internal inlet effects occur. Other results of experiments on desorption, absorption, and rectification systems are presented in Figs. 6.9-6.15.

Raschig ring ceramic — A — 8 mm, d s = 100 mm, Z = 1650 1/m2 Raschig ring ceramic — o — 25 mm, d s = 750 mm, Z = 425 1/mz Ethanol/Water 1 bar, L/V = 1, dn t /dH f nt/H

Fv = 1-32 m- | / z s" 1 kg i

2 Packing height H i m ]

i

I

j

3

Fig. 6.6. Efficiency of a packed rectification column as a function of the height

156

6

End effects in packed columns

25-mm Hiflow ring met.; d s =288 mm; Z =15 1/m2 C0 2 -H 2 0/Air at STP; Fv = 1.015 m ^ s " 1 kg 1/2 NTUL/H,

dNTUL/dH

\

—

6

\

17> S

^

^ - - ^

777

III V

rm-.

41

TTT.

I31

2 ! LiL =

2.77-10"3rn3/m2s

gj

c

--'

0.5

0

o £

1.0

0.5

1.0

1.5

Packing height H [ m ]

£

Fig. 6.7. Efficiency of a packed desorption column as a function of the height

25-mm Hiflow ring met.; d s =288mm ; Z=123 1/m2 S0 2 -Air/H 2 0 at STP; FV = 1 rn^s"1 kg 1 ' 2 NTUov/H, dNTUov/dH

3 3 uL = 8.315^10" rn /m 2 s V CD

\ \

-^

< \ CD

rv*

1

I

\ uL=5.543-1

r

[1/n

J3

nz CO " ^

•§=5

*>

^

m 3 /m z s

uL = 8315-10" 3 m 3 /rn 2 <

3

'

—

•

•

•

— —

—

*<— —^ L >

dNTU(

LU

uL=5. 543 • 1 0 " 3 m 3 /m 2 s^ i

0

0.5 1.0 Packing height H i m ]

1.5

Fig. 6.8. Efficiency of a packed absorption column as a function of the height

6.4

157

Column design and scale-up

32-mm ENVIPAC, plast.; d s = 288 mm; Z = 490 1/m 2 C0 2 -H 2 0/Air at STP, FV = 0.94 m-^s-'kg" 2 NTU L /H,

CJNTUL/CJH

6 *v

-—•

4

»——•

^ — — • • . — • — •

2

— -

2 3

u L =: 3.95 •10' m =

s

_ e

0E

0

cz

~ 6 ^.

-£ 4

c

-S 2

,

——

— -

_

4 E o

2

* UL =

^

——-

5.97 •10"

-Q

5

/m

n L

a> o

^-

=3

^

•>. .— " " " " " • *

^\ r

2

3

?.9O •10" m

3

-

^

b

0 0

0.5

1.0

1.5

Packing height H [m] Fig. 6.9. Efficiency of a packed desorption column as a function of the height

6.4 Column design and scale-up It is evident from the relationships discussed above that it is absolutely essential to make allowance for end effects in designing industrial-scale separation columns. In the first place, experimental data on the efficiency of the intended packing and the relationships derived from them must be checked in order to determine under which conditions they are valid. An efficiency of (N/H)P, as determined in pilot-plant experiments in a column of effective height HP, generally differs from the value (N/H)T for a technical-scale column of height HT = HP. Thus the figure for a pilot column is given by

158

6

End effects in packed columns

47-mm DINPAC. plastics; ds = 288 mm Z = 490 1/m2 CO2-H2O/Air at STP, Fv = 0.94 rTr l / 2 s-'kg 1 / 2 NTUL/H, dNTUL/dH

"^ 6 ^-—

~ 4

'

I 2

3 3 2 UL=J5 97 in~ m /m

a

Z

0

— -— -

i i

i

i

i

i

i

i

i

i

i

i

i

u

i i .

io .g •

, -H

4

L_U

, '

2

2 •10"

3

m3/m2 Q

n 0

0 0.5

1.0

1.5

Packing height H t m ] Fig. 6.10.

Efficiency of a packed desorption column as a function of the height

6.4

Column design and scale-up

159

70-mm DINPAC, plastics ; d s =288 mm Z = 490 1/m 2 C0 2 -H 2 0/Air at STP, Fv = 0.94 m- 1 / 2 s- 1 kg l / 2 NTUL/H,

(JNTUL/CJH

D •

4

——I — -— ——

•^ — —

2

^—*

— — ^

'

•

— —

—

•••H

Y0*0*

4 =i95 1 •1U V

s

\ *^

£ 4

^il

__!_• -

— —

-

1

—

4

g

•

10"

"CD

s

O

1

OO CD

CJ

c cz 0 .9^ o

.##

. — ——-— .

^^

•

Z.90 •10" 0.5

Y

•

— — • •

_^ —^^

0

^

2J

U L = 5.97

•

k- —^ »—-—.—— —•» ^——

—*— jQr

6

3

3

2

m / in

1.0

Packing height H [ m ] Fig. 6.11. Efficiency of a packed desorption column as a function of the height

—

—

—

t_LJ

4 2

1.5 0

160

6

End effects in packed columns

H\

[H/p

dN -i\dHlp \

H>H.

Nd \

Hp

(6-22)

ip

and that for a technical-scale column, by N_\ =(AN_\ +{Nd HJT \dHJT>H>Hi

+

(6-23)

Combining Eqns (6-22) and (6-23) gives

HlT

\HjP

\\

Nd + ANt \ _lNd + ANA }_\!dN_\ H jp \ H j T \ [\dHJp

50-mm Pall ring,metal, d s = 500 mm, Z = 600 1/m 2 Methanol/Ethanol 1 bar L/V = 1 ; dn t /dH.

I8

(6-24)

nt/H

1.5 2 Capacity factor F v [ r r r 1 / 2 s " 1 k g l / 2 ]

QJ

_IJN\ \ dHJT

2.5

6 «= -o

4 >

Fv = 2.5 m- 1 / 2 S"1 k g 1 / z 0 0 Fig. 6.12.

1

2 Packing height H i m ]

3

Efficiency of a packed rectification column as a function of the height

6.4

Column design and scale-up

50-mm Pall ring.metal, d s = 800. Z = 490 1/m 2 ; L / V = 1 Ethylbenzene/Styrene 130 mbor dn t /dH,

161

nt/H

15 2 Capacity factor F v [ m~ 1 / z s" 1 k g 1 / 2

CD r _Q U

4 F v = 2 5 ; 1 5 ; 0 7 5 m'm s" 1 kg 7 .9*

2

o

0

0

1

2

3

o

Packing height H [ m l Fig. 6.13. Efficiency of a packed rectification column as a function of the height The end effects in the technical-scale column can be regarded as identical to those in the pilot plant if the phase distributors and support plates are of the same design in both cases, if the column diameters dSj and ds>P do not differ significantly from one another, or if the packing has no tendency to maldistribution. In these cases, the following applies for the inlet Nd

Nd H

(6-25)

H

and the following, for the zone of fully developed flow:

id///p

\d///r

(6-26)

Eqn (6-24) can then be simplified to give (6-27)

162

6

End effects in packed columns

12 10

35-mm Pall ring,metal ds = 500mm, Z = 600 1/m2

o 2 1.5 2 Capacity factor Fv [rrr 1 / 2 s"1 kg 1/2

10 CD

.Q

I l l Ethylbenzene / Styrene 130 mbar dn t /dH, n t /H

8

e 6

0 0

2

1

3

Packing height H [ m ] Fig. 6.14.

Efficiency of a packed rectification column as a function of the height

Hence the efficiency ratio r\T for columns of different height, i. e. HP and HT, is given by

H N_

H ip

1 N_ H IP

J

(6-28)

The significance of this equation is clearly illustrated by Fig. 6.16, in which it is presented qualitatively as a general function, i.e.

(6-29)

6.4

12 10

~a> o

Column design and scale-up

I I I I T 35-mm Pall ring,metal ds=800 mm, Z = 490 1/m2

1.5

Ethytbenzene/Styrene 130 mbor L/V = 1. dn,/dH, n,/H I I I i i i i \ i r 2 2.5 Capacity f a c t o r F v [ m ~ 1 / 2 s " 1 k g 1 / 2 ]

F v =15 m- 1 / 2 s " 1 k g 1 / z Packing height H i m Fig. 6.15. Efficiency of a packed rectification column as a function of the height

Fig. 6.16. Ratio of the efficiency in an industrial-scale plant to that in a pilot plant as a function of the column height

Packed height HT

163

164

6 End effects in packed columns

The curves shown in the diagram apply for experimental beds of different height, HP1 and HP2 > HP]. They tend towards a theoretical limit at a height HT^> °°, i. e. (T\T)HT^X^>

\ -

N d

+

ANl

(6-30)

If HT —» HP, the limit is unity, i.e. (Tlr)/fr->//,-> 1

(6-31)

Under the given conditions, the following relationship must apply in the zone of completely developed flow: ldN_\ \dHJH>Hi

=

NT-Np HT-Hp

_ AN AH

K

}

Rearranging to solve for HT yields HT=Hp + (NT - NP) -r—\

(6-33)

Hence, the height of bed HT required to achieve a separation efficiency corresponding to a value NT can be obtained direct from the results of a pilot-scale experiment in which (dN/dH)H> Hi has been determined, in which case the one experimental point Np for the case of HP > Ht suffices. If the height HT of the bed is to be determined from the efficiency per unit height (N/H)P of the pilot column, the value obtained would be too small by an amount AH/HT, which is given by

AH HT

NT (N/H)

T

NT (NIH)P

NT (N/H)T

(6-34)

AH/HT can also be expressed in terms of the efficiency ratio r\T, as defined by Eqn (6-29), i.e.

Theoretically, AHIHT can be expressed as a function of the total number of theoretical stages NT, which is given by NT=Nd

+ ANt + HT - ^ \ an /

(6-36)

6.4 Column design and scale-up

165

The requisite height of bed HT can then be determined by rearranging Eqn (6-36), i. e. (6-37)

dH lH>Hj If the efficiency of the pilot plant were to be taken into consideration, the height of the packed bed would be given by

(6-38)

The figure thus obtained is less than that derived from Eqn (6-36) by the following amount:

The term AH/HT can be expressed as a function of NT by combining Eqns (6-37), (6-38), and (6-39) or by combining Eqn (39) with Eqns (6-33), (6-38), and (6-22). Thus, ^ HT

1

'

N N Ndd + ANj NT

1 N + AJV 1 HP IdN\

(6-40) ; <•

\dHJH>Hi The values thus obtained lie between the following limits: - for the limiting case of NT —» NP, (6-41) T I Nr -+ NP

- and for the limiting case of an infinitely large number of theoretical stages NT I AH \HT

1 1 +

HP

I dN\ \ dH ) H> Hi

If there are no end effects, Eqn (6-40) would be reduced to

f] "• T f{Nd

-0 + A Nt) -+ 0

(6-43)

166

6

End effects in packed columns

A special case arises if Eqn (6-7) does not apply, i.e. if dN Q\H

(6-44)

=£ const.

If the differential coefficient were thus to change over the entire height of the column, the relative increment of height AH/HT would have to be determined from the following relationship, which can be derived from Eqns (6-29) and (6-35): N AH

= 1-

(6-45)

- = HH)

In this case, the relationship N = f (H) would have to be determined experimentally.

Raschig ring,ceramic 8mm.Fv=Q.84 m-l/2s-1kgl/2ids=1OOmrn.Z=l65O 1/m2 — 25mm,Fv=1.32 m-1/2s-1kg1/2Jds=750mm,Z=425 1/m2 Ethanol/Water 1 bar, L/V=1 1

s s,

>

- Hp ^^

1^

s

0.9

— —

I 0.8

— —— —— —

0.7

—

m

1 3 Packing height H i m ] 0.3

»——-— — i

& 0.2

r/

CD

i0.1

/ —

CD

*. ,. — \— ^—»—<—- — \ ,13

——

/ /

10 15 No. of theoretical stages n t

20

Fig. 6.17. Efficiency ratio and relative increase in height as functions of the number of theoretical stages

6.5

167

Examples of scale-up

6.5 Examples of scale-up The results of evaluating Eqns (6-28) and (6-40) along the lines indicated in Figs. 6.6 and 6.8 to 6.12 are presented in Figs. 6.17 to 6.22. In the diagrams for rectification systems, N is represented by the corresponding number of theoretical stages nt\ and in those for absorption and desorption systems, by the number of transfer units NTUOv o r NTUL. These diagrams convincingly demonstrate the necessity of allowing for end effects in scaling up.

32-mm ENVIPAC, plastics, ds= 288 mm, Z=490 1/m 2 C0 2 -H 2 O/Air at STP. Fv = 34 m" 1/2 s -1 k g l/2 —uL=8.95 mVm 2 S

— uL = 290 m 3 /m 2 s 1.0

s

\ Vv

F0.9

\

y-2m ^^——| •—^., Ib m * ****** ^—. —•—.

f/p-

•

*

^

,

—

— ^

—

,

'

•

^

-

,

1

«| — — ^

^

—

—

—

-

—

— -

0.6 2 3 Packing height H i m ] 0.5

*—' —" ~—~Z -ism

0.4

—•

'

——"

—

—

——

CO

§0.3

y

o

•S.0.2 a>

p ^

/ /

5

— - —

—

A / f

^ 0.1

5——

—

-—

—

— -

—

-

—

— —

— - —- —-

.

M •

y 10 15 Number of transfer units NTUL

20

Fig. 6.18. Efficiency ratio and relative increase in height to be allowed for in scale-up as functions of the height of the bed of packing or the number of transfer units

168

6

End effects in packed columns

25-mm Hiflow ring, metal; d s =288mm ; Z =123 1/m 2 S0 2 -Air/H 2 0 at STP. Fv = 1 nr 1 / 2 s- 1 k1/2 10

i0.9

. 1 0.8

u,=5.543-10"3. 8.315"i0~ 3 m 3 /m 2 sI I I 2 3 Packing height H i m ]

0.7 0.2 — L

.315 •10" 3m Vm

2

»

s-

/

to

s

/

0 0.3

-—

_— —

s

"

~

~

—

—

Ill

1

~~I

?

3 3 u L =ww-iu " m /nx s

i

0.2 0.1

•"

1^'

0.1 CD

1"

/

J

— — V\ P =r5 m .*——

^iii'-*

—

'

—

^

/

y

^^

—

—• •

•

-

—

—

•

•

—

Up=2 m

/ / 5 10 Number of transfer units

15 NTUQV

Fig. 6.19. Efficiency ratio and relative increase in height to be allowed for in scale-up as functions of the height of the bed of packing or the number of transfer units

6.5

169

Examples of scale-up

DINPAC,plastics d s =288 mm, Z = 490 1/m2 47 mm, 70 mm C0 2 -H 2 0/Air at STP Fv = 0.94 m- 1 / z s" 1 kg1'2, uL--2.90 m 3 /m 2 s

0.6 2 3 Packing height H i m ] 0.5

-— — — -—— —— — — *~— .. — — — ' —

0.4

—

—

-

0.3 /

/

f 0.2 / /

/

/ /

/

~° 0.1 CD

i

't / /, X /

—

HP-2

—

—

—

—

•

—

- ••

.

•

—

—

—

-

—

•

m

•

—

•

—

—

—•

10 15 Number of transfer units NTUL Fig. 6.20. Efficiency ratio and relative increase in height to be allowed for in scale-up as functions of the height of the bed of packing or the number of transfer units

20

170

6

End effects in packed columns

50-mm Pall ring, metal, d s =500 mm, Z=600 1/m2 Methanol/Ethanol 1 bar, L/V=1, HP = 2 m 1.0

J I I 1—I

;S =1 0-9

175,2.

—*-

1i——_, —

—

3 4 P a c k i n g height H i m ]

- ^ o.i

10 15 Theoretical stages nt Fig. 6.21. Efficiency ratio and relative increase in height to be allowed for in scale-up as functions of the height of the bed of packing or the number of theoretical stages 50-mm Pall ring,metal; d s = 800 mm; Z = 490 1/m2 Ethylbenzene/Styreng 130 mbar; L/V = 1 ; HP = 2 m

—•

^

—• —1 —

— >~

>

f 0.9

... — — _

— —

_B__i

•^^-^

4J^-

I1 S -1

1

l/nl/2

' kg" 2

O

I 0.8 UJ

— —

3

4 Packing height H [ m

0.7

—• .-0.4 HZ

V

CD 0.3 CO

y

S

.§0.2

1

1

^0.1

/

_ ^

k. 1/z

AH

It

0 0

_____

I m" 1 / 2 S - 1 | ^y t—1—1—M

_**^5

No. of theoretical stages

10

T

M 15

nt

Fig. 6.22. Efficiency ratio and relative increase in height to be allowed for in scale-up as functions of the height of the bed of packing or the number of theoretical stages

7 Liquid distribution at the inlets of packed columns It is evident from the results presented in the last chapter that the number of liquid distributor outlets greatly affects the inlet efficiency at the upper part of a packed bed, because it governs the quality of liquid distribution at the inlet cross-section and thus the extent to which the packing is wetted. The higher the degree of wetting and thus the greater the phase contact area, the more efficient the mass and heat transfer within the bed of packing. General theoretical considerations and the results of pinpointed experiments allow a relationship to be derived between the number of distributor outlets and the maximum efficiency for a given packing under given conditions. It will thus be seen that the efficiency decreases with the distribution density.

7.1 Theoretical considerations It is permissible in theory to represent a bed of packing as a number of parallel flow channels, each with a hydraulic diameter dh that is given by

dh = 4 -jj-

(7-1)

where a is the surface area per unit volume of the packing and e is the void fraction. The void fraction in a packed column of diameter ds is related to the cross-sectional area of an individual channel Ah by

(f)

(7-2)

and to the number nh of flow channels, by

t - ^Li

(,-3)

7* Since e < 1, the total number of flow channels nh is always less than the ratio of the cross-sectional area of the column to that of an individual channel, i.e. — ris2 4

nh < —

=

d2

-Y

= cp2 = nb

(7-4)

where nb represents the boundary case, i.e. the maximum towards which nh tends if e —» 1, and (p is the diameter ratio as defined by

Packed Towers in Processing and Environmental Technology. Reinhard Billet Copyright © 1995 VCH Verlagsgesellschaft mbH, Weinheim ISBN: 3-527-28616-0

172

7 Liquid distribution at the inlets of packed columns

Eqn (7-4) can therefore be rewritten as

nh <

'd'

= nb

16

(7-6)

Examples of the feasible geometries for the inlet cross-section of a packed column are shown schematically in Fig. 7.1. Dumped toroidal packing is illustrated on the left; and arranged packing with triangular and rectangular flow channels and vertically staggered elements, on the right. The number of flow channels per unit area of column cross-section Zj, is given by (7-7)

Zh =

7* In the boundary case of 8 -» 1, Zh tends towards a maximum Zb, i. e. Zh<

4

1

it d}

7l=z»

(7-8)

If the liquid is to be distributed evenly over all the flow channels, the number of distributor outlets ought to be equal to the number of channels Zh. However, the only points at which the liquid need be fed are those at the flow channel intersects, as illustrated in Fig. 7.1. The number of these points Z7 thus represents the minimum theoretically required. In practice, the number of outlets Z required to feed all the flow channels lies within the following limits: Z, < Z < Zh

Dumped packing

(7-9)

Regular packing

1

q= 6

6

Fig. 7.1. Schematic graph illustrating the inlet geometry of random and geometrically arranged beds of packing

7.2 Effect of inlet liquid distribution on the efficiency of packed columns

173

Now let Z differ from Zb by a factor q, which is given by

This factor, referred to as the feeder coefficient, can be taken to determine the number of outlets required to feed all the flow channels in the inlet cross-section of the packing. In the light of the above considerations, there ought to be an optimum value qopt that corresponds to the number of outlets Zmax at which the packing inlet efficiency is a maximum and cannot be improved by a further increase in Z, i.e. if Z > Zmax. In this case, qopt can be regarded as the performance parameter for the inlet liquid distribution. Logically, Zmax is less than the boundary or limiting value Zh\ and normally, less than Zh, i. e. the number of distributor outlets that is equal to the number of flow channels. It can be derived from Eqns (7-2) to (7-4) that Zh is defined by

The corresponding total number of flow channels n^ is given by ds 16

a2 s

(7 12)

"

7.2 Effect of inlet liquid distribution on the efficiency of packed columns The value of qopt for various types of packing and for distribution densities of Z < Zb can be obtained experimentally by determining the mass transfer efficiency at various load factors below the flood point, i.e. Fv < Fv,Fh a n d at constant liquid-vapour ratios LIV or constant liquid loads uL. The efficiency in this case can be expressed as the number of theoetical stages per unit height of bed ntIH or as the overall height of a transfer unit HTU0. Some results of studies along these lines on random beds of packing are submitted in Figs. 7.2, 7.3, and 7.4; and on systematically stacked beds, in Figs. 7.5 and 7.6. The curves thus obtained confirm that the efficiency increases with the number of distributor outlets Z until a point Z > Z max is reached, above which the rate of increase is negligible. The experiments concerned were the rectification of a chlorobenzene/ethylbenzene mixture at 67 mbar and the absorption of an ammonia-air/water system at 1 bar.

174

7 7

-

Liquid distribution at the inlets of packed columns i

i

r

T

I

]

T

50-mm Hiflow rings PVDF

e

H 0

Chlorobenzene/Ethylbenzene 67 mbar L/V = 1 d s --0.22m ; H =1.5 m

^ 4

— 25-mm Hiflow rings metal

;107 0 ; 600 V ; 1560 O i

0.4

0.8

1.2

i

1.6

i

i

2

i

2.4

Capacity factor F v [ ( T r

i

i

2.8 1/2

1

s" kg

3.2 1/2

3.6

4

]

Fig. 7.2. Effect of the number of liquid distribution points on the rectification efficiency

4 3

••_

2

s

i

I 0-mm H iflow rings r eramic

t

ZL 1

/

2

[V m ]

\

i — — 3 7

27 • 80 • 2036 •

Chlorobenzene /Ethylbenzene 67 mbar L/V = 1 d s - - 0 2 2 m ; H=1.5m 1 Glitsch CMR 2 " metal 1—

z 0.4

0.8

1.2

i=

—c i—

— — ——

^- > -a 10.

—i

\

••

In

1/m2 ] = 27 B; 107 a ; 2036 •

2

2.4

Capacity factor F v I m

2.8 1

s" kg

3.2

3.6

]

Fig. 7.3. Effect of the number of liquid distribution points on the rectification efficiency

7.2 Effect of inlet liquid distribution on the efficiency of packed columns 1

0.6

i

1

1

i

175

I

2

Z [ 1 / m ] - - 1 5 5 O ; 400 • ; 730 • ; 2400 • 0.5 ^

*~—

0.4

<-<

Z °-3

»-—

\<*>—

^

't

^

•s = C).45(T1;

L

H

H = 2m

E: Z3

£

NH 3 -Air/H 2 0,1 bar, uL = 10 m 3 /m 2 h

0.2

GO

25-mm Hitlow rings, metal

g 0.6

^ Z = 15 1/m2

§

7

I1

I 0.5 0.4

s, 2

y

—

Z = 1350 1/m

•

IT"

^ 4

-•^

£ 0.3 d s = 0 3 m ; H = 1.4m

y

0.2 0.4

i

0.8

1.2

1.6

i

2

i

2.4

Capacity factor Fv [ m ^ V

i

2.8 1

3.2

3.6

12

kg ' ]

Fig. 7.4. Effect of the number of liquid distribution points on the absorption efficiency

Chlorobenzene/Ethylbenzene 67 mbar, L/V = 1

MBllapak 250 '/ rlc; = 0.28ft m -1 U

£• 3

jt—<

= 1.5 "iln _—^

Z [ 1/m 2 ]--2250 TT ; 2150 v ; 1560 v UJ

1 0

0.5

1

1.5

2

Capacity factor F v [aT

2.5 1/2

3 1

s" kg

1/z

Fig. 7.5. Effect of the number of liquid distribution points on the rectification efficiency

3.5 ]

4

7

176

Liquid distribution at the inlets of packed columns

Chlorobenzene/Ethylbenzene 67 mbar L/V d s = 0.22 m ; H = 1.4 -1.5 m 7 6

Ij

V\

5

• Sulz 3f lr

DV c n n DA JUU

\^

Z [1/m 2 2036 D 80

27 0

4

5

•

3

^ —

r^ i NT

B 4 —e—o—

•y— QJ

M 2

Z [1/m

2

]-n Montz

3

I

e— o — o O; 2036 e

B1 300

1 ,

"•- - • — <>—**j—0—|K>

hv—^ Z 11/m2] = 6 0 0 o 2150 • ; Ralupak 250 Y , i

1

25 Capacity factor Fv [ m '

1/z

3 1

35

ll 1/? l/nl/z 1

s"' kg ]

"

4

Fig 7-6>

"

Effect of t h e n u m b e r

of

liquid distribution points on the rectification efficiency

7.3 Maximum packing efficiency in inlet zones A term introduced to evaluate experimental results is the relative efficiency e of the packed bed. In rectification studies, it is defined by nA j nA )

(7-13)

7.3 Maximum packing efficiency in inlet zones

111

and in absorption and desorption studies, by (NTU/H)Z
HTUZ^Z HTUz
max

K

}

Solving Eqn (7-10) for q gives /

e

\2

V

)

(7-15)

)

a I

Zb

qopt can then be obtained by plotting the following function: e = f(q)fv

in which fvis

= const.

(7-16)

the relative vapour load factor and is kept constant, i.e.

fy = ( T H \

L

zr = V

Below the loading point at which its flow rate is practically unaffected by that of the vapour, the liquid runs off the walls of the packing. In this case, it can be assumed that qopt and thus Zmax are independent of the vapour load factor Fy, i.e. at relative load factors of /y<0.75.

In Fig. 7.7, qopt is the value on the axis of abscissae at which e tends to unity. At this point, the packing efficiency is a maximum and cannot be improved by a further increase in q or an increase in the number of distributor outlets above Zmax. Once qopt is known, Zmax can be determined from the following equation: a'2

*

— \
(7-18)

It is demonstrated in Fig. 7.1 that the value of qopt depends primarily on the packing geometry at the inlet and that a difference thus exists between the figures for random and those for stacked packing. The packing geometry, in turn, determines how the liquid spreads out and is distributed over the cross-section of the packing and therefore greatly influences the inlet efficiency. The associated differences in Zmax, as determined by experiment, between random and stacked beds are discussed below. Zmax for dumped beds of packing The efficiencies of the types of dumped packing listed in Table 7.1 were determined in rectification experiments in which the number of liquid distributor outlets was varied. The results were evaluated by the procedure described above and are presented graphically in Fig. 7.7 in the form of the function described by Eqn (7-16) with fv as parameter. It can be seen that hardly any relationship exists between the relative efficiency e and the vapour flow rate at relative load factors of fv < 0.75.

178

7 Liquid distribution at the inlets of packed columns

Rectification Chlorobenzene/Ethylbenzene 67 mbar L/V = 1 1

1

0.8 0.6

jfJ

i •B—^

•

—

—

a_ • -

SI

pas.

?

• i

n •"

•

1

n C u 7J

° 0.4 >-.

o

I

]

£ 0.8

J.

EH

= i

n

— —

1 capacity f y = 0 . JU Relative

" 0.6

2

3

4

6

8 10

2

3

4

6

8 10"

2

3

Distribution coefficient q Fig. 7.7. Relative efficiency of packing as a function of the distribution coefficient in rectification

The types of dumped packing listed in Table 7.2 were the subject of absorption and desorption studies. The evaluated results are presented in Fig. 7.8 in the form described by Eqn (7-16). It can be seen that they agree well with those plotted in Fig. 7.7. Thus the value calculated for qopt is the same in both cases, i.e. qopt,dumP = 0.3

(fore = 1; L/V = 1)

(7-19)

The maximum number Zmax of liquid distributor outlets for random beds of packing can be obtained by substituting this numerical value for qopt in Eqn (7-18). Thus

-1max, dump

= 2.388 • 10"

(7-20)

Hence, Zmax can be determined graphically from Fig. 7.9, in which it it has been plotted against the area-to-volume ratio a with the void fraction e as parameter. The horizontal parameter shown as dashed lines in the diagram is the hydraulic diameter dh, which is related to a and 8 by Eqn (7-1). It is evident from the diagram that the smaller the value of dh, the greater the number of outlets Zmax required to ensure the maximum efficiency.

179

7.3 Maximum packing efficiency in inlet zones Table 7.1. List of packings (together with their geometrical data a and e) investigated in the rectification experiments with the different numbers Z of liquid distributor outlets Packing

Material

Size

a[m2/m3]

E

z[l/m 2 ]

Symbol

Pall Rings

Metal PVDF

25 mm 25 mm

223 225

0.954 0.887

107; 2036 27; 107; 2150

O •

Glitsch CMR Cascade MiniRings

Metal

0.5" 1" 1.5" 2" 2.5"

357 233 182 156 78

0.955 0.971 0.973 0.988 0.994

27; 600 107; 2036 27; 107; 2036 27; 107; 2036 104; 2036

B

Hiflow Rings

Metal Ceramic Ceramic PVDF PVDF

25 20 35 25 50

203 261 108 194 118

0.962 0.779 0.833 0.918 0.925

27; 27; 27; 27; 27;

mm mm mm mm mm

107; 600; 2036 80; 2036 80; 2036 104; 2036 107; 2150

m • • O

•

o <>

Table 7.2. List of packings (together with their geometrical data a and e) investigated in the absorption and desorption experiments with the different numbers Z of liquid distributor outlets Packing

Material

Size

ds[m]

a[m2/m3]

E

z[l/m 2 ]

Symbol

Glitsch CMR

Metal

1"

0.22

233

0.971

122; 1360

Hiflow Rings

Metal

25 mm

0,288 0.450 0.600

199 182 201

0.962 0.965 0.962

15; 122; 1350 155; 400; 730; 2400 45

m O

Plastic PP

25 mm

0.288

229 233

0.9143 0.9189

15; 490

A A

50 mm

0.288

112

0.9286

15; 490

V

Absorption NH 3 -Air/H 2 0 J Fv = 0.66 m"1/z s" 1 kg 1 / z m O A -,1/2 Desorption C02 -H 2 0/Air, Fv = U 7 nr 1 / 2 s"1 kg A V mmm

I S1 0.8

a —-*

—

—

• _

rr

*—

TT

—

1 bar, L/V =1 " 2

3 4

6 8 10"2 2 3 4 6 8 10"1 Distribution coefficient q

2

3

Fig. 7.8. Relative efficiency of packing as a function of the distribution coefficient in absorption and desorption

180

7

Liquid distribution at the inlets of packed columns

2000

Z3

T3

ID

50

75

100

150

200

300 2

3

Area per unit volume a[m /m ]

Fig. 7.9. Maximum number of liquid distribution points as a function of the dimensions of a bed of packing

Zmax for arranged beds of packing The results of the corresponding studies on arranged beds of packing are presented graphically in Fig. 7.10. As can be seen, the slope of this log-log relationship is less than that of the corresponding relationships shown in Figs. 7.7 and 7.8 for random packing. Thus the value of qopt calculated in this case is = 0.15

(fore = 1; LIV = 1)

(7-21)

The fact that this numerical value of qopt is lower than that for random packing can be ascribed to the superior self-distribution characteristic and the staggered arrangement of the stacked packing. Hence irregularities in the flow pattern at the inlet can be compensated

7.3 Maximum packing efficiency in inlet zones

181

Rectification Chlorobenzene/Ethylbenzene 67 mbar L/V = 1 1 0.8

s

•S

•

5-0.6 a,

v=

0.75 -

,

ys

CD

c

• | 0.8

1

-2

#

1 0.6

— Relative capacity f v = 0.5

0.4 10

1.5 2

3

4

8 10"2 15 2

6

3 4

6

8 10"1 1.5

Distribution coefficient q Fig. 7.10. Relative efficiency of packed columns as a function of the liquid distribution coefficient in rectification

more rapidly than those in random beds. The optimum number of liquid distributor outlets calculated from this value for the stacked beds of packing listed in Table 7.3 is therefore given by

Zmax,arr=

(7-22)

1.195 • 10"2 ( ~

It can be read off in Fig. 7.11 against the area per unit volume a and the void fraction e for an arranged bed with flow channels of dh hydraulic diameter.

Table 7.3. List of packings (together with their geometrical data a and e investigated in the rectification experiments with the different numbers Z of liquid distributors Packing

Size

a[m2/m3]

e

z[l/m2]

Mellapak

250 Y

250

0.96

27; 2150

V

Ralupak

250 YC

250

0.963

600; 2150

Montz B l smooth

300 350 500

300 350 500

0.972 0.965 0.96

27; 2036 27; 80; 2036 27; 107; 2143

O •

Montz B l perforated

300 350 500

300 350 500

0.972 0.967 0.96

27; 2036 27; 80; 2036 27; 107; 2143

o

500-60

500

0.96

27; 80; 2036

A

Sulzer BX

500

500

0.95

27; 80; 2036

•

Symbol

7

182

Liquid distribution at the inlets of packed columns

100

Fi

g - 7 1 1 - Maximum number of liquid distribution points as a function of the dimensions of a bed of packing pacing

™n ™n mn tnn 200 300 400 500 » -L , r ? / 11 Area per unit volume a [ m / m J ] 150

Desorption C0 2 -H 2 0/Air. 1 bar, Fv=1.47 m'V2 s"1 kg1'2 50-mm Hiflow rings, plastic, ds = 0.288m

• * - — .

0.9 £

0-8

10-7

— « '—^. D *—,

1 • - — .

—o

•

!

—

^ 1.6 m k

-

—

—

k^

08

0.6

—

A

—

—

-

1—

—

—

—

O-

— m

"

—

A_

* * — .

^—«

• — ^ ,

—

.

—•

Z-- 15 1/m

^ .

•——«,

1

—c

——»

—

—

^

0.6

5

6

—

-

—

•

n=

—

7

9

'

-

10

11

10 uL [m 3 /m 2 -s] 10

15

20 25 30 Liquid load uL [ m 3 /m 2 h ] 3

Fig. 7.12.

35

4 5 Liquid/gas ratio L'/V

Relative efficiency as a function of the liquid load in desorption

40

12

183

7.4 Effect of phase ratio on relative efficiency

NH 3 -Air7H 2 0. 1 bar, F v =lfTT 1/2 s' 1 kg 1/2 50-mm Hiflow rings, plastic, d s = 0.45 m

i.o 7

10 L = U

/

r«/

1/ III

o

d CD 1

0.6

>

_

T7-"

— —»

U.ifim

"a

0.4

8

6

10

12

14

103uL[m3/m2s] 0

10

0

1

2

20 30 40 Liquid load u L [m 3 /m 2 h] 3

4

5

6

7

Liquid/gas ratio L/V

Fig. 7.13. Relative efficiency as a function of the liquid load in absorption

7.4 Effect of phase ratio on relative efficiency Values for the relative efficiency calculated as described above are, strictly speaking, valid only for columns that are operated at a phase ratio of L/V = 1. The results of further studies that were performed to determine the effects of other values of L/V are shown in Figs. 7.12 and 7.13. The gas flow rate uv and thus the capacity factor Fv were kept constant, with the consequence that the effect of the liquid flow rate uL was readily apparent. It was thus established that the following equation applies: (7-23)

=

V

Uy

QV

Qv

The relationship between the relative efficiency e and the L/V ratio or the liquid flow rate uL is shown in the diagrams. It applies to both desorption, in which the resistance to mass transfer is on the liquid side, and absorption, in which resistance is predominantly on the gas side. The extent to which the relative efficiency e deviates from the values for L/V = 1 can be expressed quantitatively by the relative efficiency ratio, i.e. (7-24)

The corresponding results obtained in desorption and absorption experiments are presented in Figs. 7.14 and 7.15 respectively. The relationship shown in Fig. 7.14 can be repre-

7

184

Liquid distribution at the inlets of packed columns

sented by the following equation, which has been confirmed for LlV < 15 in systems with resistance in the liquid phase but only for LlV < 7 in systems with resistance mainly in the gas phase:

JLp

(7-25)

Desorption C0 2 -H 2 0/Air, 1 bar, d s = 0.288 m. HP=1.4 m - ^ - a = 229, £ = 0.914; Z--15 l / m 2 ; q = 3-10' 3 -vQ--H2; £ = 0.928; Z=15 1/m 2 ; q = 1310' 3 s

1

o 0

0.8 0.7

•—su — —

i 0.9

—;

/-» -—« —V-

"tfV1 — ..

—

'•

A 25-mm Hiflow rings, PP, Fv = 0.66m' 1/z s"1 kg 1/z v 50-mm Hiflow rings, PP Fv--147 m" 1/z s"1 kg 1/z

1 0.5 o

£ 0.4 0.8

1

15

2

3 4 5 6 7 8 910 Liquid/gas ratio L/V

15

Fig. 7.14. Efficiency ratio as a function of the liquid-gas ratio in desorption

Absorption NH 3 -Air/H 2 0,1 bar, d s = 0.45 m, HP = 1.6 m a = 112; £ = 0.928; Z = 13 1/m 2 ; q--!4-10" 3 '

3 (19 - 0.8

K

07

I" 0.5 ^ 0.4

_

\—i

E °'6 •2

^ « - f4^

0.8 1

Absor ptio n

i—

^THT-L

DesorDtion

—

50-mm Hiflow rings, plastic, F v =1 m"1/2 s"1 kg 1/2 1.5

2 3 4 5 6 7 8 910 Liquid/gas ratio L/V

15

Fig. 7.15. Efficiency ratio as a function of the liquid-gas ratio in absorption and desorption

7.6 Estimation of relative efficiency

185

7.5 Effect of height of packing on relative efficiency The relationships established in the experimental studies described above allow the relative efficiency of the packing to be estimated whenever the number of liquid distributor outlets is less than the maximum and the packing height is about H = 1.5 m. Owing to inlet effects and the packing's self-distribution characteristic, the average relative packing efficiency, as defined by Eqns (7-13) and (7-14), depends on the height of the bed. This is strikingly illustrated in Figs. 7.16, 7.17, and 7.18. A change in the reference height H « 1.5 m entails a corresponding change in the relative efficiency. As would be expected and is evident from these diagrams, the effect of reducing the number of distributor outlets on the efficiency per unit height becomes less as the height increases. In other words, the lower the value of //, the less the value of e and vice versa. The relative efficiency ratio in this case is defined by *

L

(7_26)

It is shown as a function of the bed height H in Fig. 7.19. Allowance must be made for this aspect in order to avoid misinterpretation in evaluating the efficiency of column packing. In particular, the effect that the number of liquid distributor outlets has on the inlet efficiency must be taken into account in scaling up as described in Chapter 8.

7.6 Estimation of relative efficiency If the number of outlets in the liquid distributor of a packed column is reduced to a value of Z < Zmax, the anticipated decrease in efficiency Ae can be described by Ae - ( ^ > r r ( ^ < ^ (nt/H)z

(7.27)

> zmax

This equation can be solved if the relative efficiency e is known. The value can be obtained from Figs. 7.7, 7.8, and 7.10. If the reference height is H « 1.5 m ± 5 %, the curves plotted in these diagrams can be described by a function of the following form: ez
= C ql/v=\;H=\.5

(7-28)

The dashed-line curves in the diagrams represent the most adverse conditions and have been taken for determining the values for C and n in Eqn (7-28). Relative efficiency of dumped packing The following values of C and n apply for random beds: Cdump = 1.13

(for LIV = 1; H = 1.5)

(7-29)

ndump

(for L/V

(7-30)

=0.1

= U H = 1.5)

186

7

Liquid distribution at the inlets of packed columns

50-mm Hiflow rings, plastic

r0 2 -H 2 0/Air, 1 b(ir 1/2 0.9 .- Fv = 1.47 m-

kg"

2

^-c

CD O

S

0.8

r y

% 0-7

71

7 _

A

0.6 0.4

0.6

0.8

1

1.2

0.2138 n1 2 5 1/ m 1.6

1.4

1.8

Height of packing H i m ] Fig. 7.16. Relative efficiency as a function of the bed height in a packed desorption column

50-mm Hiflow rings, plastic 0.9

i

i

i

i

d s = 0.4^) m 2 Z = 13 1/m

^ H3-Air/H20 1 bar

nciency

CD

0.8 0.7 - f jL

IVG

CD

-3 ,-V2s-'

.75

. V2

^ ^

2 = 1 0 m /m h it 3

^ ^

0.6

«—-

a

/ '

CD

0.5

.

\

f n IV = u

3

i/2 2

r'k gV2

r

8.4 m /m h -^ i

0.4 0.4

0.6

0.8

1

1.2

1.4

i

1.6

1.8

Height of packing H [ m ] Fig. 7.17. Relative efficiency as a function of the bed height in a packed absorption column

7.6 Estimation of relative efficiency

187

Chlorobenzene/Ethylbenzene 67 mbar; L/V ^ 1 Rolupcik 250 YC metal; ds-- 0.22 m i *—•

0.8

\

£ 0.6 o 0.4

/

41/

f

. — -

•*• •

•

S

•

—

-

—

—

•

Or-

Z--200 1/m2

\ \ i

- fv--0.5-: •y=2 m

0.2

i

0.2

M

M

—1

0.4

s kg i

i

i

0.6 0.8 1 1.2 Height of packing H t m ]

1.4

1.6

Fig. 7.18. Relative efficiency as a function of the bed height in a packed rectification column

50-mm Hiflow rings, plastic; Z = 15 1/m2 o • ; Z = 131/m 2 v _[m 3 /m 2 h] = 38.4 O; 2 3 * | C0 2 -H 2 0/Air 1 bar, Fv= 1.47 m' 1 " s" 1 kg 1 / 2 d<= 0.288 m \ o

Ap

S 0.9 \

^ 0.8 QJ CJ

£

r

-1.5 m

< \

-

0.6 0.5 0.5

0.6

FvOm-^s^k

;UL 38>/ > m /m h v

C "

Fv=1 m"l/2s"1kc

0-7

3

n /(Ti

NH3-Air/H20. ds ] ; UL = 10 r = 0.45 m 0.7 0.8 0.9 1 1.5 Height ot packing H [m]

2

ii

•

2.5

Fig. 7.19. Efficiency ratio as a function of the bed height in a packed desorption and absorption column

188

7

Liquid distribution at the inlets of packed columns

If the number of liquid distributor outlets is Z < Zopt, substituting Eqn (7-29) for C, Eqn (7-30) for n, and Eqn (7-15) for q in Eqn (7-28) gives rise to the following expression for the relative efficiency in random beds of packing: ( f o r L / V = \\H=

1.5)

(7-31)

This relationship between e and Z is, strictly speaking, valid for a reference height of H « 1.5 m and LIV = 1 and is presented graphically in Fig. 7.20. If the relative efficiency ratio, as defined by Eqn (7-25), is taken into consideration to allow for different values of LIV and the value of qopt remains unchanged, C and n will depend on LIV. In this case, the relationship shown in Fig. 7.21 would apply, i. e. 0 04

C= 1.13

-

(for/f = 1.5)

(7-32)

(for//=1.5)

(7-33)

Surface area per unit volume a [rn 2 /m 3 ] 50

100

Dumped packing

75

100

150

200 250

0.9 0.8

150 200 300 400 500 750 1000 1500 2000

Number of distributor outlets Z [ 1 / m 2 ] Fig. 7.20. Relative efficiency as a function of the dimensions in a packed column and the number of liquid distribution points

7.6

Estimation of relative efficiency

189

Substituting Eqn (7-32) for C, Eqn (7-33) for n, and Eqn (7-15) for q in Eqn (7-28) and allowing for the relative efficiency ratio, as defined by Eqn (7-25), yields an expression for the relative efficiency in random beds for the case in which LIV > 1. Thus, I 8 L \0.04 4JIZ e = 1.13 -rV / \a

01

/f\ 0.25

W

(for H = 1.5)

(7-34)

Relative efficiency of arranged packing The corresponding values for C and n in systematically arranged beds of packing of the types investigated for the case of LIV = 1 and H = 1.5 are as follows: Carr = 1.14

(for LIV = 1; H = 1.5)

(7-35)

narr = 0.07

(for LIV = 1; / / = 1.5)

(7-36)

Thus, if Z < Z op ,, substituting Eqn (7-35) for C, Eqn (7-36) for n, and Eqn (7-15) for q in Eqn (7-28) yields the relationship that corresponds to Eqn (7-31) for random beds, i. e. (for L/V = 1; H = 1.5)

earr = 1.361 [ —

(7-37)

i a

Although insufficient experiments have been performed to reveal the effect of the phase ratio LIV on the relative efficiency of stacked packing, it is reasonable to assume that Eqn (7-25) can be applied for rough estimates.

0.5 10

10

10

Distribution coefficient q

Fig. 7.21. Relative efficiency as a function of the distribution coefficient in packed columns with the liquid-vapour ratio as parameter

8 Scale-up for end effects and phase distribution In Chapters 6 and 7, it was demonstrated that the evaluation of measurements to determine the column efficiency in a pilot plant must allow for end effects and the initial distribution density realized by the liquid distributor. Otherwise grave errors may occur in scaling up on the basis of these measurements or relationships derived from them. The necessity arises because the most pronounced changes in efficiency can generally be anticipated in the upper zone of the column immediately below the inlet. It is only in the lower zones that the efficiency can be expected to remain in equilibrium. Typical curves plotted from the results of systematic studies will again be taken as an example to explain this fact. They are reproduced in Figs. 8.1 and 8.2 and strikingly demonstrate the extent to which the inlet efficiency of a column is affected if the number of liquid distributor outlets is greatly reduced. According to the diagrams, there are two main zones in the bed of packing: the inlet zone, in which the local efficiency continuously changes; and the lower zone, in which the local efficiency remains constant, i.e. the number of transfer units, NTUi in desorption or NTUOv m absorption, increases almost linearly with the height H. It is also evident from the diagrams that the increase in NTU is independent of the number of liquid distributor outlets Z. In other words, the NTU = f (H) curves for Z = constant are practically parallel in the lower zone. The conclusion can thus be drawn that the development of two-phase flow is complete in the zone of constant local efficiency and depends

1

1

I

.

\

A

,

\

CO d

4

o

~

o

°

6

CD _O

i —i

*—•—-

m

0

u

0.2

•

U

s—'

_1 —— \5 -

k

.—•—'

^——«

2 i

|1

..

:

1

1

• '

1 bar 38.4 rcr/m2h _

ZD

£

i

i i —i—i—•

4

i

-

co2 -H20 /Air

^

'i

---

- 25-mm Hiflow rings PP, ds= 0.288 m Fv = 0.66m" 1/2 s" 1 kg 1/2

E

l r—

J

MH3-Air/H20. 1 bar JL= 5.4 m 3 /m 2 h

1

.

I I I .

Ai

'—i

i

0.4

0.6

0.8 1 1.2 1.4 Packing height H i m ]

1.6

1.8

2

Fig. 8.1. Efficiency as a function of the height of bed with the number of liquid distribution points as parameter

Packed Towers in Processing and Environmental Technology. Reinhard Billet Copyright © 1995 VCH Verlagsgesellschaft mbH, Weinheim ISBN: 3-527-28616-0

192

8

Scale-up for end effects and phase distribution

Absorption NH3-Air/H20.1 bar, Fv = 1 firms' 1 kg1/z, uL = 38.4 m J /rrh 1

1

1

1

1

1

1

50-mm Hiflow rings, plastic

•I 6 =3

* * *

^

. -

. —

E

r

t—"

*

* . — -

. — — •

d s = 0.45 m -

ii

i

0 0

0.2

0.4

0.6

0.8 1 1.2 1.4 Packing height H [ m ]

1.6

1.8

i

2

2.2

Fig. 8.2. Efficiency as a function of the height of bed with the number of liquid distribution points as parameter

solely on the packing's self-distribution characteristic and no longer on the effects of the inlet current distribution. An explanation to this effect has already been given in Chapters 6 and 7. Another fact that is known from Chapter 6 and can also be derived from the diagrams is that there is a certain number Zo of liquid distributor outlets that gives rise to hardly any inlet effects. Thus the flow pattern that is characteristic of the packing's self-distribution effect already exists in the inlet zone, and the local separation efficiency is theoretically constant over the entire height of the column. The inlet efficiency is improved if Z > Z o , because the liquid distribution at the head of the column allows more effective exploitation of the area available per unit volume, i.e. the average dN/dH is higher in the inlet zone. However, if Z < Zo, the inlet efficiency is negative, because the surface of the packing in the inlet zone is only moderately wetted, i.e. the average dN/dH is comparatively low. Yet another fact that arises from the diagrams is that the relationships tend towards a finite value at H = 0. It can be ascribed to external end effects, e.g. reflux distributors and support plates, that are embraced by the measurements under certain sampling arrangements and are thus normally included in the evaluation of packing efficiency; but this has already been mentioned in Chapter 6. A qualitative impression of the relationship between end effects and the relative efficiency can be obtained from Fig. 8.3. The N = f(H) curves in the lower part of the diagram qualitatively represent the efficiency determined by experiment and were derived from the quantitative curves presented in Figs. 8.1 and 8.2, in which N = NTUOv and N = NTUL. The associated relative efficiency is represented by the set of curves in the upper part of the diagram. Two cases of efficiency, e and e, are shown: in the one, the end effects Nd have been included {Eqn (8-1)}; and in the other, deducted {Eqn (8-2)}, i. e.

8

Scale-up for end effects and phase distribution

193

Assumption: Nd independent of Z

CD O

a a. QJ

Fv = const; u L or L/V = const

Nd

Packing height H Fig. 8.3. Efficiency as a function of the height of bed with the number of liquid distribution points as parameter (qualitative)

N

= f(H)

(8-1) (8-2)

In the light of these relationships, it can be appreciated that a knowledge of the experimental conditions is essential in scaling up separation columns from experimentally determined values for the efficiency. In other words, design calculations must be based on known values for the height HP of the pilot column, the end effects Nd, the relationship between the efficiency and the inlet characteristic, and the relative efficiency e, which depends on the number of liquid distributor outlets. Relationships of this nature assume the form of Eqns (7-32), (7-35), and (7-38) in Chapter 7.

194

8

Scale-up for end effects and phase distribution

8.1 Scale-up model Once a sound basis for planning has thus been established, the model shown in Fig. 8.4 can be derived. It allows a qualitative comparison of the relationship between the number of separation units and the height of the bed of packing that exists in a pilot plant (Case a), an industrial-scale plant with the maximum number of liquid distributor outlets (Case b), and an industrial-scale plant with fewer liquid distributor outlets (Case c). In Case a, the height is HP, and the number of transfer units pertaining to Zmax liquid distributor outlets is NPjmax\ in Case c, in which Z < ZmflJC, it is merely NP. The number of separation units that must be realized in Cases b and c is NT. If the number of distributor outlets is Zmax, the minimum bed height required is HT>min\ and if Z < Zmax, the height required would be HT > HTjmin. The limiting value for the efficiency at a bed height of if = 0 is the contribution made by the end effects Nd. The quantities AN{ and ANi>max are characteristic of the effect exerted by

Industrial-scale columns

Pilot column

Packing height H Fig. 8.4. Graph for modelling the effect of the number of liquid distribution points on the efficiency and in scale-up

8.1 Scale-up model

195

the inlet current and therefore depend on the number of liquid distributor outlets Z and Zmax respectively. The qualitative TV = f (//) diagram in Fig. 8.4 is based on the assumption that the height HP in the pilot plant and the heights HT>min and HT in the technical-scale plant are greater than that of the inlet zone Hi, in which the local efficiency dN/dH is subject to continuous change. In the H > Ht zone, dN/dH is constant and, owing to the geometry of the model, identical to the following ratio: dtf \

=

dH)H>

Hi

(1-e)^,^ HT-

( g 3 )

HTj

The relative efficiency e in this equation is defined by Eqn (7-13) for rectification systems and by Eqn (7-14) for absorption and desorption systems. It is fixed by the efficiency ratio that corresponds to the height of the pilot plant HP, i.e.

(«)*, = —^

(8-4)

The maximum efficiency per unit height that can be achieved by the optimum number of liquid distributor outlets Zmax and a height HP is given by

(8 5)

nr- = (f) lip

-

\tijpjmax

In this case and if Z > Zmax, the requisite height of an industrial-scale column would be

(8 6)

"

r"

Hence, HT is always greater than HT>min by an amount that is equal to the second summand in Eqn (8-6), and this summand, in turn, depends on e = f (Z). In other words, the increase in bed height that is necessitated by nonoptimum liquid distribution is given by Hr-fhnun_n

H n T.min

JN\

( 1 e )

^

1

H,

\ " I P,max <3W \

(8 7)

"

TW\H tl

This equation was evaluated in the light of studies on random beds of metallic and plastics rings. The value taken for e was obtained from Eqn (7-34). The results are presented in Fig. 8.5, which convincingly demonstrates the effect exerted by the number of distributor outlets Z on the height of the packed bed. In scaling up by the method illustrated in Fig. 8.4, allowance for potential end effects can be made by means of the quantity Nd. The effect of the inlet current ANt on the relative efficiency e depends on the number of liquid distributor outlets Z and is defined by

196

8

Scale-up for end effects and phase distribution AiV, = No - Nd - NPiBUX (1 - e)

(8-8)

= N0-Nd-HP[ — \

(l-e)

The imaginary quantity No is the sum of Nd and Ni>max and is obtained from the maximum number of distributor outlets, i.e. (8-9)

No = Nd + ANl>n

0.5 I

1 0.4 5

I

- 5 0 - m m Pall ring metal L/V = 1 - 2 5 - m m Hiflow ring PP L/V =2

0.3

• 47-mm Dinpac PP

X

0.2

L/V =2

I o.i
5

0

a

1

0.9

>

0.7 nfi

0

0.1

0.2

0.3 0.4 0.5 0.6 Feeder ratio Z/Z ma x.

0

50 100 150 200 250 300 No. of feeders Z [ 1 / m 2 ] for 50-mm Pall ring metal

0

200 400 600 800 1000 1250 No. of feeders Z [ 1 / m 2 ] for 25-mm Hiflow ring PP

0

100 200 300 400 No. of feeders Z [1/m z ] for 47-mm Dinpac PP

Fig. 8.5. Effect of the number various types of packing: 50-mm metal Pall rings 25-mm PP Hiflow rings 47-mm PP Dinpac

0.7

0.8

0.9

1

1500 500

of liquid distribution points on the efficiency and in scale-up for rectification system desorption system desorption system

8.2

Inlet and end effects in industrial-scale plants identical to those in pilot plants

197

Substituting for No in Eqn (8-8) yields an expression for the effect of the inlet stream on the efficiency, i.e. ANt =

ANi>max-(l-e)NP,max (8-10)

=

ANi,max-{l-e)HP[-—\

According to the model, the local separation efficiency in the inlet zone ought to be practically constant and independent of height if the distribution brought about by a given number of outlets Zo corresponds to the self-distribution characteristic of the packing. In this case, the inlet effect ANt tends to zero, i.e. (ANdzo^O

(8-11)

The inflow length Ht is of no significance in calculating the height of the bed of packing as long as it is less than HP and HT. All that is then required is the numerical value of ANt, which can be obtained by three measurements, viz. at H = 0 for the determination of Nd and at Hj > Ht and H2 > Ht for the determination of No and (dN/dH)H > H.. The experiments also revealed that the number of liquid distributor outlets for which the local efficiency does not alter with the height in the inlet zone is usually less than, or at the best, equal to the maximum. This can be ascribed to the geometry and hydraulic diameter of the packing, the system concerned, and the phase ratio. However, the number of distributor outlets is not the only factor that may influence the inlet efficiency. Others are the design of the outlets and their spacing relative to the inlet cross-section of the packing. The figure for the spacing in the experiments was about 150-200 mm.

8.2 Inlet and end effects in industrial-scale plants identical to those in pilot plants The relationships discussed have emphasized an important point to observe in scaling up and thus in avoiding setbacks in column operation, i.e. the quality of the initial liquid distribution must be taken into consideration, because it governs the packing efficiency in the inlet zone. Convincing evidence of its importance is given by the model presented in Fig. 8.4. For it demonstrates that, if end and inlet effects occur, the efficiency per unit height NT/HT in an industrial-scale column differs from the corresponding efficiency NP/HP in a pilot plant column of HP < HT height by a certain ratio \\Tj which is given by

T.

NT/HT

^^ " NP/HP

T8 ( 8 121 12) ( 8 "1 2 )

According to the model, this efficiency ratio applies for a certain value of Z and thus of e. Thus,

198

8

Scale-up for end effects and phase distribution

r ) r = l -

Nd + AJV,- max - (1 - e) NP,n Hp

Hi

(8-13)

Inserting Eqn (8-5) in Eqn (8-13) results in the following relationship: Nd + ANiitnax

~m—

1

1

HP

HT

(8-14)

prmax

The relative difference in the required height A H/HT corresponds to the difference generally caused by inlet effects between the efficiency per unit height in pilot plants and that in industrial-scale columns. It can be derived for a given value of Z and thus of e from the model depicted in Fig. 8.4. According to Eqn (6-40), the relationship can be expressed as follows: AH dN (8-15) = f Nd + ANh NT HT Ht A column packed at random was taken as an example for solving Eqns (8-14), (6-40) and (8-15). The results are shown in Figs. 8.6, 8.7 and 8.8. The extent to which scale-up is influenced by end and inlet effects is very obvious in these diagrams. It is thus convincingly demonstrated that values for (N/H)P measured in a pilot plant do not suffice by themselves for calculating the bed height required for efficient separation. Other information is essential, viz. the height of the pilot plant HP, the number of liquid distributor outlets Z {i.e. the relative efficiency e that defines the characteristic value for the inlet stream in Eqn (8-10)}, and - last but not least - the end effects Nd. Obviously, Eqns (8-14), (6-40) and (8-10), which define the effect of the relative efficiency, i.e. of the number of liquid distributor outlets, are accurate only in as far as the conditions relating to the model in Fig. 8.4 are satisfied. This applies to the assumption that the local efficiency dN/dH is constant and independent of Z in the section below the inlet zone, i.e. for H ^ Hh Numerous investigations have verified that this assumption is adequately satisfied in a bed of packing with good self-distribution. If this is not the case, i.e. if the value for dN/dH when H ^ Ht also depends o n e , a corresponding correction must be made to the equations in the model. Nevertheless, the relationships that have been derived here can be applied with sufficient accuracy for practical purposes to most modern types of packing.

8.3 Inlet and end effects in industrial-scale plants different to those in pilot plants Eqns (8-14), (6-40) and (8-10) are valid if the number of liquid distributor outlets Z per unit area of column cross-section in the pilot plant is the same as that in the industrial-scale column and if the end effects Nd are also the same in both cases. However, if the end effects differ, i.e. Nd>T ^ NdjP, and if the values for Z and thus the values for the relative efficiency e also differ, i.e. eT ^ eP, the efficiency ratio r\T will be given by

8.4

Determination of the limiting number of liquid distributor outlets

1

-U2SL _

T|r=l-

( 1

_

ep)

Hp

199

|

N

ep

ANi max

'

HT

"

^

"

«

(8-16)

Likewise, the following equations can be derived for the relative difference in the required height of bed:

1

_ NdJ + AJVi>r NT

irmax

|

JVrf.p + A ^ - P HP

(81?)

1 IdN \dH ) H > H i

- (1 - eT) HP [^-\

(8-18) (8-19)

Results of numerical evaluations are presented in Figs. 8.9, 8.10 and 8.11. Those that apply to the pilot plant are valid for a value of ZP = Zmax that was kept constant; and those that apply to the industrial-scale plant, for a value of Z = ZT that was varied. The end effects were the same in both plants. The difference between the curves shown in these diagrams and those shown in Figs. 8.6, 8.7 and 8.8 is obvious.

8.4 Determination of the limiting number of liquid distributor outlets The only conditions under which the efficiency per unit height in the industrial-scale column will be the same as that in the pilot plant are those that permit a value of r\T = 1 to be attained. It follows from Eqn (8-13) that the requisite number of distributor outlets is that that would allow the relative efficiency to reach the following limit:

e = e0 = 1

j-—T

(8-2U)

Hp

\~Rl \ tl

} p,max

If Nd = 0, this equation gives rise to the condition that the efficiency per unit height is practical identical to the local efficiency and remains unchanged over the entire height of the column, i.e. there is no inlet effect if AN/

\

(eo)Nd = o =

1

*-viv i, max

l

Hp

-

(

\~R) \ M I P,max;Nd = 0

8

2

1

/o

Tt\

)

200

8

Scale-up for end effects and phase distribution

50-mm Pall ring.metal, ds= 500 mm, HP= 1.5 m Methanol/Water 1 bar, L/V = 1. Fv = 1.5

R

s" 1 kg 1/2

0.95

o i

2

0.90 /

d

LLJ

—.

0.85 2.5 3.5 Packing height H T l m ]

1.5

0.30

g 0.25

- 7-max ——»——-

CD

0.20 "200 0.15 ^3 CD

10 1 / m 2 /

0.10

,

1 15 25 Number of separation units

35

Fig. 8.6. Effect of the number of liquid distribution points on scale-up, if the number of distribution points in the cross-section of the pilot plant is the same as in that of the industrial-scale plant and if the end effects are of the same magnitude

8.4

201

Determination of the limiting number of liquid distributor outlets

25-mm Hiflow ring,PP. d s =288mm. HP = 1.5m 12 NH 3 -Air/H 2 0 NTP, uL = 5.4 m 3 /m 2 h, Fv--0.66m-1/2s-1 kg ' Nd=0,5; ANi,mox=1.88, (N/H)P max -4.92 m-)(dN/dH)H>Hi=3.3 m

0.95

150 — —— —

——.

° 0.90 \

0.85

"

•

•

•

'

0.85

—

—

•

—

•

0.75

1.5

2.5 3.5 Packing height HT [ m ]

—

,

4.5

0.30 1

0.25 0.20 /

•W 0.15 o 0.10 0.05

A 1fy

1

/ /

500

^ ^

—

—

—

—

•

A^. """"

{/, Lr-""

_— ^

1

15 25 Number of separation units

35

Fig. 8.7. Effect of the number of liquid distribution points on scale-up, if the number of distribution points in the cross-section of the pilot plant is the same as that of the industrial-scale plant and if the end effects are of the same magnitude

8

202

Scale-up for end effects and phase distribution

47-mm DINPAC.PP. ds= 288 mm, HP=1.5 m C0 2 /H 2 0-Air NTP,uL=10.4 m 3 /m 2 h, Fv = 0.94nf v

_ 0.95

N V

Z= 1 Dr\

"v

L ^10

CD CO

ficienc^

j 0.90

kg1/2

<

LJJ

%

0.80

^ - .

,

^ ^

**"

• " ^ ^

^ ^ ^ ^

2.5 3.5 Packing height HT [ m ] ^« ^ . b -«.—-

1.5 0.30

•5-

0.25

E

A /

0.20 0.15 0.10

4.5 WO

^

"20

// y

1 {

If

f... 15 25 Number of separation units

35

Fig. 8.8. Effect of the number of liquid distribution points on scale-up, if the number of distribution points in the cross-section of the pilot plant is the same as that of the industrial-scale plant and if the end effects are of the same magnitude

8.4

Determination of the limiting number of liquid distributor outlets

203

50-mm Pall ring metal, ds= 500 mm, HP= 1.5 m Methanol/Woter 1 bar, L/V = 1, Fv = 1.5 m"1/2 s" 1 kg 1/z

2.5 3.5 Packing height Hj [m]

4.5

0.30 <\

-— ' ^^ h

125—h+ ,

1-

.

0.20 -V, 0.15

• «

-

7"" -

| m » - »^

— |

i

1

0.10 15 25 Number ot separation units NT

35

Fig. 8.9. Effect of the number of liquid distribution points on scale-up, if the number of distribution points in the industrial-scale plant differs from that in the pilot plant

204

8

Scale-up for end effects and phase distribution

25-mm Hiflow ring,PP. d s =288mm, HP = l 5 m NH 3 -Air/H 2 0 NTP. uL--5.4 m 3 /™ 2 ^ Fv^OBBm-^s" 1 kg 1/2 Nd=0.5;ANiimQX=l88-(N/H)pimQX=4.92m1(dN/dH)H>Hr3.3m-1

\ 0.95

\ \ \

Nd

\

^ 0.90

N

T'=

Nd't = Nd

P - max.

\

N

^_

1 0.85

^ -"

~OO£

%

0.80

%

7

O

——«.

UJ

_ 150. 0.75

—

~~~

—

•

—

2.5 3.5 Packing height Hj [m]

0.70 U.X)

. .

nU. ^n JU

....

U./b 0.20

/ /

0.15 5

y

/ 15 25 Number of separation units Nj

35

Fig. 8.10. Effect of the number of liquid distribution points on scale-up, if the number of distribution points in the industrial-scale plant differs from that in the pilot plant

8.4

Determination of the limiting number of liquid distributor outlets

205

47-mm DINPAC, PP. ds= 288 mm, HP = 1.5 m C0 2 /H 2 0-Air NTP, uL = 10.4 m 3 /m 2 h, F v ^ . ^ m ^ QX.= 3.73 m-l.(dN/dH)H>H|= 1

kg11/z

\ I

\ M

ii

0.95

INd

'

\ \ \

_ 0.90

\

\

\

\

1 0.85

Zp" : Zmax.

\

\

\

N

* %

1 0.80 o .

'

LiJ

0.75

•

~JOn

•••V/fi

-

^

*

-

•

0.75

1.5

2.5 3.5 Packing height H, [m]

=E 0.35

•—• —

4.5

1

i

S 0.30

\

_ 0.25 /

CT) QJ

/

0.20 0.15

]_

t

15 25 Number of separation units NT

35

Fig. 8.11. Effect of the number of liquid distribution points on scale-up, if the number of distribution points in the industrial-scale plant differs from that in the pilot plant

206

8

Scale-up for end effects and phase distribution

If e < e0, it would be logical to assume that NP/HP < NT/HTj i.e. that the inlet effect is negative. As has already been mentioned, there is a certain number of liquid distributor outlets that gives rise to a situation in which no positive or negative inlet effects occur. This limiting value Zo corresponds to a relative efficiency of (eo)Nd = o, as defined by Eqn (8-21), and to an efficiency per unit height of N

-Nd HP

iP,max p,max;Nd

=0

(8-22)

Zo can be obtained by substituting e = {eg) Nd = o for £ m Eqn (7-34). Thus, [0.1

(L/V)0-25]-1

(8-23)

An

1.13

Values of Zmax and Zo determined in two different beds of packing are listed in Table 8.1. A comparison of these figures gives an impression of the great extent to which Zo is less than Zmax. Table 8.1. List of characteristic operating values in a pilot plant for determining the number of liquid distribution points that is unlikely to give rise to either positive or negative end effects Packing

L/V

AN,.max

Pall, metal 50 mm

112.6

0.951

1

0.3

DINPAC, PP 47 mm

135.3

0.921

2.8

1

NP,

5.6

Nd

N H [1/m T7

0.5

1.67

335

92

1

3.07

516

73

8.5 Effect of phase maldistribution The efficiency of packed columns is affected not only by the number Z of distributor outlets per unit area but also by the uniformity with which the phases are distributed over the column cross-section. This applies particularly to the liquid phase. If it is not uniformly distributed and if the ratio of the column diameter ds to the size of the packing d is djd > 10, an impairment in separation efficiency NIH is likely, as has been confirmed in practice. If the degree of liquid maldistribution M is 0 < M < 1, the deterioration in separation efficiency AE can be estimated from the column efficiency Ec by means of the following equation: ' N\ IN H H (8-24) AE = = \-Ec N

8.5

207

Effect of phase maldistribution

According to the Huber and Hiltbrunner theory, the column efficiency Ec is given by the following equation if the maldistribution M takes effect over the entire height of the column: 1

Ec =

(8-25) r + 1

where djd is the ratio of the column diameter to the size of an element of the packing and r is the reflux ratio. An idea of the extent of the theoretically feasible loss in efficiency can be obtained from Fig. 8.12, which was derived by evaluating Eqn (8-25). According to this diagram, hardly any significant loss in efficiency need be anticipated in columns with the diameter ratio mostly encountered in pilot plants, viz. djd < 10, even if the values of M are comparatively large. In modern, uniformly dumped or geometrically stacked beds of packing with no tendency to channelling, the distributor characteristic largely governs the degree of maldistribution M in the inlet zone and the extent to which the surface of the packing is wetted. It can be seen from Fig. 8.13 that the number of distributor outlets is a not inconsiderable factor and is generally much higher in pipe and related types of distributors than in simple box types. Hence the quality of liquid distribution depends not only on the number Z of the outlets but also on the uniformity with which they are fed. The mass transfer experiments described in Chapter 5 were performed in pilot columns to evaluate the characteristics of packed beds. The liquid phase was uniformly fed in accordance with the aspects mentioned above, and the number Z of distributor outlets was sufficiently large to ensure the utmost efficiency. The ratio of the column diameter to the size of the packing was about djd = 10 or less; in other words, the likelihood that liquid maldistribution M could affect the packing efficiency could be almost ignored {cf. Eqn (8-25)}.

0.5 *

Vapour /Liqijid ratio L/V =1

3 0.4

&0.3 y

0.2

>

0.1

•IT - " •

10 Fig. 8.12. (8-25)

\^

^' 14

_4-

— — —

18 22 26 30 34 38 42 Ratio column diameter/packing diameter rjs/d

46

50

Efficiency as a consequence of maldistribution and calculated from Eqns (8-24) and

208

8

Scale-up for end effects and phase distribution

0.4 h-Water STP—N ID

I 0.2 •XD

— ——

\

0.1 ZJ

•JU ]/

— --

•

10 12 14 16 Liquid load UL in m3/m2h

18

Fig. 8.13. Maldistribution caused by trough-type and perforated-pipe distributors

At ratios of djd > 10, maldistribution M is likely to occur and effect a loss in efficiency. The higher the ratio, the greater the loss. For instance, if djd = 50 and M = 0.2 apply over the entire packed height, the loss in efficiency may be theoretically as high as 50 %. Maldistribution M over the height of the column is undoubtedly a characteristic of the packing. Consequently, it may depend on the vapour load fv {cf. Eqn (7-17)} in the column as well as on the quality of the distribution at the inlet. Thus = t(fy) = i(FvIFy,Fl)

(8-26)

The curves shown in Fig. 8.14 were plotted from the results obtained on rectification systems in columns of various diameters packed with metal Pall rings. The liquid-to-vapour ratio was LIV = 1. They show the column efficiency Ec as a function of the diameter ratio djd with the relative vapour load factor fv as parameter. The corresponding equation is

Pall rings.metal.d = 15.25.35.50 mm. L/V = 1

15 20 25 30 35 40 45 50 Ratio column diameter/packing size d s /d Fig. 8.14. Column efficiency of beds of metal Pall rings as a function of the diameter ratio of the column and the rings

8.5

Effect of phase maldistribution

_ f tds_ . ~ \d'Tv

209 (8-27)

It can be seen from the diagram that the larger the value of fv and thus the greater the load, the higher the efficiency and the less the effect of the djd ratio. If the stripping factor \, as defined by Eqn (1-30), is I ~ 1, Ec can be estimated by the Schliinder equation, i.e.

1 1-M

(8-28)

1 1+M

If the liquid is uniformly distributed over the inlet cross-section of the column and the quality of the distribution is retained throughout its entire path, the efficiency can be expected to remain constant over the entire height of the bed. A proviso is that the Schmidt number, i.e. the quotient of the kinematic viscosity and the diffusion coefficient, and the Marangoni number of the liquid phase in negative systems do not undergo any significant change along the concentration profile. In measurements on an ammonia/air-water system in columns of 0.3, 1.0 and 1.4 m diameter, no loss in efficiency was observed in beds of modern reticulated packing, e.g. Norpack rings. The yardstick adopted for the efficiency was the HTU, and the points plotted for these 25-mm and 50-mm rings all lay on their respective curve (cf. Figs. 8.15 and 8.16). It can therefore be concluded that the liquid distribution in beds of Norpack rings is uniform regardless of the column diameter.

NH3-Air/WQter<293 K.I ban M O m W h

50-mm NOR-PAC ring plastic, H = 1m \ 0.4 0.3

J

<: T

- o - ds=i.O m - —o— ds=1.4 m -

0.2 Fig. 8.15. Efficiency of Norpac rings in columns of various diameters

0.3 0.4 0.6 1 2 3 Gas capacity factor Fv [m"1/2 s"1 kg 1/z ]

The fact that the quality of liquid distribution is independent of the column diameter was confirmed by evaluating Eqn (5-32), which defines the pressure drop per unit efficiency (cf. Fig. 8.16). Consequently, no dimensional corrections are necessary in scaling up columns packed with Norpack rings or comparable types of packing.

210

8

Scale-up for end effects and phase distribution

NH 3 -Air/Water.29i KJ bar uL=10 m 3 / m 2 h

30 20 15

—<> - d s = 0.3 m • —c> - ds=1.0 m • > - ds=1.4 m -

10

9

I

s

Q. <

/

a Y /

y

CD t_

/ •

CO

1

2 X

a / 25-mm NOR-PAC rin g plastic H= -1.4 ni 0.8

i

i

i

0.6 1 1.5 Capacity factor Fvln

Fig. 8.16. Modified specific pressure drop in beds of Norpac rings in columns of various diameters

A pronounced relationship between the efficiency and the column diameter in the range between 0.22 m and 1.0 m was also not observed in rectification experiments with Mellapak 250 Y (cf. Fig. 8.17). A slight decrease in efficiency with an increase in column diameter could, at the most, be expected at higher loads corresponding to Fv ~ 2.5 m~1/2 s"1 kg1/2 (cf. Fig. 8.18).

8.6 Gas or vapour distribution In pilot-scale packed columns, gas distribution can be regarded as uniform. In industrial practice, however, maldistribution of the gas phase may occur in columns of large diameter, particularly if the bed of packing is of comparatively low height and the gas is admitted radially into the column. These conditions lead to an increase in pressure in the vicinity of the wall on the opposite side of the column. As a consequence, local differences in pressure may exist in the horizontal cross-section of the column immediately below the bed of packing, and local differences in pressure drop may occur in the stream of gas flowing through the bed. Under these circumstances, optimum gas distribution in the inlet zone is an absolute necessity for high packing efficiency. It can be achieved by baffles, e.g. in the form of a

8.6

Gas or vapour distribution

211

Mellapcik 250 Y, Chlorobenzene/Ethylbenzene, L/V=l. 67mbar _

I

4

2

7 V

v LA/

A/

n

^

metal 0 10

1

^

8 s CD

Z

1 /m 7 -S 1 / ;ids=0.22m.H=,.25m 2

h / - T1/

—o-Z=1350 1/m J —•— Sulzer plant, ds=1.00 m, H = U 0 m

6

Q.

Irop

r

CO

4 ibar

« >

2

)ec.

(

CO

Q.

0 0.4

0.8 1.2 1.6 2 2.4 2.8 3.2 3.6 Vapour capacity factor Fvtnr 1/2 s"' kg1'2]

Fig. 8.17. Performance of a structured packing in columns of various diameters

Chlorobenzene/Ethylbenzene, L/V= 1 Mellapak 250 Y, Fv=2.5 m ^ s ' 1 kg1/2

1

4 -50-100 mbar

HI

£ 3

9. 2—

400-1000 mbar metal

Fig. 8.18. Efficiency of a structured packing in relation to the column diameter and pressure, data of Sulzer

0.1

0.25 0.5 1 1.5 2 Column diameter dstm]

212

8

Scale-up for end effects and phase distribution

pipe bend with a central downward outlet or of an inlet pipe with the lower side open. If severe demands are imposed on the uniformity of gas distribution, distributor plates may be installed. The column shell influences the lie of the packing in the vicinity of the wall and thus causes an increase in the effective void fraction. However, this wall effect does not have a great influence on the efficiency in packed columns of large diameter and in beds with a large effective void fraction.

8.7 Effect of mass transfer coefficient on scale-up In Chapter 5, attention was drawn to the constants CL and Cv for the determination of volumetric mass transfer coefficients and the height of a transfer unit. They were derived from the results of experiments in pilot columns with relative diameters of djd < 10, beds of packing of HP ~ 1.5 m height, and liquid distributors with Z > Zmax outlets. Hence the corresponding equations given in Chapter 5 allow the maximum attainable efficiency, i.e. {NIH)P>max, to be calculated, and the relationships discussed in Chapter 8 should be taken into consideration in scale-up.

9 Phase redistribution in columns A question that continually arises in planning packed columns with large diameters and great heights is the spacing of the redistributors, especially those for the liquid phase. No recommendations on the subject in general can be found in the literature, and planning is usually based on the experience gained in industrial practice. If packings differ in geometry, it is very likely that their fluid-dynamic characteristics also differ. This applies particularly to the flow pattern in the inlet zone and to the extent of maldistribution. Consequently, if the inlet distribution is the same but the packing differs, great differences may still occur in the length of the path traversed before flow is completely developed. Within this length, the efficiency per unit height may vary considerably. For this reason, the most favourable bed height at which redistributors should be installed is subject to great variation.

9.1 Estimation of optimum number of phase redistributors Effective liquid distributors make a substantial contribution towards the costs of a separation plant. Consequently, optimization must be resorted to in determining the bed height Hr at which it would be advisable to instal them. In other words, redistributors cannot be economically justified unless the improved efficiency that they effect leads to savings in packing and column shell costs that exceed the costs of their installation and maintenance. This fact is evident from the schematic diagram in Fig. 9.1, which represents two columns that have to perform the same separation task - the one with, and the other without, redis-

]L —

Fig. 9.1. Column sketched with and without redistributors to supplement the model shown in Fig. 9.2 Packed Towers in Processing and Environmental Technology. Reinhard Billet Copyright © 1995 VCH Verlagsgesellschaft mbH, Weinheim ISBN: 3-527-28616-0

distributors

214

9

Phase redistribution in columns

tributors -. The effective height H in a column with nr redistributors is the sum of the heights Hr of the individual packed zones, i.e. H = ^Hr

(9-1)

If the individual zones are of the same height, H=(nr + l)Hr

(9-2)

The effective height HT in a column without redistributors is greater than that in the corresponding columns with redistributors by an amount AH (cf. Fig. 9.1), i. e. HT=H+AH

(9-3)

The criterion adopted for the optimum number of redistributors is that the costs in each case should be the same, i.e. — d?(H + AH) cP + nds(H+

AH) cs = — ds2HcP + nds H cs + nrcr

(9-4)

where cP [DM/m3] is the costs per unit volume of packing, cs [DM/m2] is the costs per unit area of column shell, and cr [DM] is the costs for one redistributor in a column of diameter ds. Rearranging Eqn (9-4) and substituting Hr(nr + 1) for H {Eqn (9-2)} then gives Hr =

= ———

(9-5) — d}cP + nds cs

If the column diameter ds is given, the third term on the right of Eqn (9-5) is a constant. Therefore,

— d? The factor K represents the redistribution costs that can be attributed to the costs per unit height of the packing and the column shell. Consequently, it is a material constant for a column of given diameter ds. The first part of Eqn (9-6) can be rewritten to give

r

l + — nr

9.1

Estimation ofoptimum number ofphase redistributors

215

If there is only the one single redistributor, Eqn (9-7) can be simplified to

In the theoretical limiting case of nr —» °°, i. e. if the bed of packing is of very great height, Eqn (9-7) becomes

(9 9)

-

The number of redistributors nr from the aspect of optimum costs can be obtained from Eqns(9-2) and (9-7), i.e. (9-10) Application of the above equations necessitates a knowledge of the function AH/H = f(H) for the packing concerned. The term AH/H depends on how uniformly the phases are distributed at the inlet, i. e. on the efficiency of the distributors. It also depends on the geometry and texture of the packing, i. e. on how the packing itself distributes the phases and whether it has a tendency towards maldistribution. An expression for AH/H can be derived from the qualitative relationships illustrated in Fig. 9.2, in which the number of separation units N is shown as a function of the height H of the packing. The upper diagram applies for packed columns without redistributors; and the lower, for columns with nr distributors. The case illustrated in the diagrams is that in which the efficiency of the distributor and the redistributors is very high. Consequently, the local separation efficiency of the packing in the inlet zone of height Ht at the head of the column, or in that immediately below the redistributor, is better than the efficiency in the packed zone below the inlets. In the latter case, the flow can be regarded as practically constant, as has been observed in many experiments (cf. Chapters 6 and 8), i. e. N

Nd + ANt

In a column without redistributors, a bed of height HT is needed to realize an overall efficiency NT. However, if nr distributors are installed in the column, the height of the bed required is merely H=HT-AH

(9-12)

Since the efficiency per unit height in the zone below the inlet or redistributor is constant {cf. Eqn (9-11)}, the following relationship applies: N\ H L

Nd+ ANt Hr

(N \ \H T

Nd + AiV, H

( 9 B )

216

9

Phase redistribution in columns

AN T Hr 'H r >H.

Nr

0

Fig. 9.2.

Hf

| With nr redistributors

Packing height H Graphical model to illustrate the effect of redistribution on the column efficiency

Now let Y\T be the ratio of the efficiency of the column without redistributors (N/H)T to the efficiency (N/H)r of an individual zone in a column with nr distributors, i.e. N T[T

(9-14)

=

and let Nr

«, + i

U ,

'

(9-15)

9.1

Estimation of optimum number of phase redistributors

217

Substituting y\T from Eqn (9-14) and (N/H)r from Eqn (9-15) in Eqn (9-13) then gives ,

Nd + ANt I 1

1 \

,

Nd + ANt I

Hr

H)r The ratio AH/H, which is essential for the evaluation of Eqns (9-5), (9-6), (9-7), and (9-10), can be related to T)rby rearranging Eqn (9-12) and expanding to give AH _HT-H_ H H

NT/(N/H)T-NT/(N/H)r NT/(N/H)r

_

I r,r

lV

"1/J

Hence, if the height of a column without distributors exceeds the effective height of a column with nr distributors by an amount AH (cf. Fig. 9.1), the relative increase in height AHIH is given by AH H

1 (N/H)r Nd + ANt

1

NT Nd + AN,-

I

-1

1 1 Hr HT

1 1 1

(9-18)

I +

I

Eqn (9-17) can be further rearranged to give

^W = ^W~l

(9 19)

"

The term HT in Eqn (9-19) is the height of a bed without redistributors and can be defined by substituting NT for N and HT for H in Eqn (9-11) and rearranging. Thus HT = [NT - (Nd + AW,)] — - \

(9-20)

The term H is the effective height of a bed with rcr redistributors and is given by (9-21) H)r Substituting Eqn (9-20) for HT and Eqn (9-21) for H in Eqn (9-19) then gives rise to AH

/

Nd

+

AAM/jV\ ^

218

9

Phase redistribution in columns

Alternatively, Eqn (9-11) can be rearranged to solve for N, and the following expression can thus be obtained for Nr: Nr =

t

6N\

+ Hr

(9-23)

J

Inserting this relationship in Eqn (9-22) then gives Nd

Nd Hr

Nr

dN\

-1

(9-24)

If the expression on the right-hand side of Eqn (9-22) is substituted for AH/H in Eqn (9-7), a relationship can be found for the height Hr of the one section in a column with nr distributors, i.e. K

1 N NT

nr

1

(9-25)

)\H)rldN

The total bed height H in a column with nr distributors can be obtained by substituting H for (nr + 1) Hr {cf. Eqn (9-2)} in Eqn (9-7). Thus 1

H = nrK —)

(9-26)

) / Eqn Eqn (9-22)

The limiting case of a very large number of separation stages NT, corresponding to HT-> oo, follows from Eqn (9-18), i. e. AH\

I

1 (N/H)r Hr Nd + ANt

(9-27)

It also follows from Eqn (9-22), which gives rise to Eqn (9-28), and from Eqn (9-24), which gives rise to Eqn (9-29). Thus AH

1 cUV\

AH

Nd + ANt

H

Hr

-1

(9-28)

(9-29)

9.2

Costs relationships

219

Equating Eqns (9-27) and (9-28) or Eqns (9-28) and (9-29) yields the following relationship for the height of one section if the number of separation stages tends to infinity:

^

N_\

_ldN\

(930)

Since NT, it follows that nr also tends to infinity. In this case, Eqn (9-25) becomes

A comparison of Eqn (9-30) with Eqn (9-31) leads to the conclusion that, if very great values of NT are realized, the costs for columns with redistributors will not be on the same level as those for columns without redistributors unless the costs factor K tends towards the following limit:

K

^T

Nd + AJV,.

(932)

According to the model, this relationship is valid if the following applies:

One incontestable fact that emerges from these considerations is that the bed height Hr at which redistributors can be economically installed cannot be determined by a simple rule of thumb. The factors that really count in its determination are the end effects at the inlets, the efficiency in the zone of completely developed flow, and the acquisition costs for the redistributors. If the costs factor K, as defined by the expression on the right-hand side of Eqn (9-6), is greater than the value calculated from Eqn (9-32), Hr must be higher than the figure obtained from Eqn (9-30).

9.2 Costs relationships The spacing at which redistributors can be economically installed between sections of packing of Hr height is governed by the costs factor K, which is defined by Eqn (9-6). Eqn (9-32) clearly states that the limiting value KNT _+ ^ for this costs factor is fixed by the ratio of the end effects and efficiency in the inlet zone to the efficiency in the zone of completely developed flow. Rectification and desorption experiments to verify these relationships were performed in pilot plants on packing produced in various shapes and sizes from various

220

9

Phase redistribution in columns

materials. The main dimensions of the columns in the pilot plants and the distribution density of the liquid distributors were varied. The results of these experiments, which have already been discussed in Chapter 6, are reproduced in Figs. 9.3 and 9.4. The values required for the determination of the limiting costs factor KNT _ oo can be read off from the curves in this diagram in conjunction with the qualitative diagram presented in Fig. 9.2. These values are listed in Table 9.1. An important outcome of the studies is that the costs for a column with redistributors cannot be the same as those for the corresponding column without redistributors unless the factor K defined by Eqn (9-6) is identical to a limiting value that depends on the efficiency in the inlet zone and is defined by Eqn (9-32). It can be easily proved that the number of redistributors nr and their spacing Hr are irrelevant if this condition applies. In other words, the costs C remain constant as long as Hr is greater than Ht. According to Eqn (9-4), the costs for a column with nr redistributors is given by C = H\—

d} cP + JT dscs) + nrcr = HcPs + nrcr

(9-34)

where cPs are the costs per unit height of column for the bed of packing and the column shell, as defined by Eqn (9-6), i.e. (9-35)

= ~7 ds cP + Jt dscs

14 A o

12

Ethanol/Water, 1 bar Ethylbenzene /Styrene, 130 mbar Methanol /Ethanol, 1 bar

10

Z) CI

a CDCD

0

1

3

Packed height H [m] Fig. 9.3.

Number of theoretical stages as a function of bed height in rectification

9.2

221

Costs relationships

DINPAC plastics, ds--288 mm Z = 490 1/m2 C02-H20/Air, STP uL=5.97 m 3 /m 2 s, Fv=0.94-10"3 m 3 /m 2 s

47-mm racKing "

— — •

——'

—CD to

a

«

?

no ~ n r n 11 n f

§ "2

Uc

i f

l

Jr * — — — ——— I —

s-

^ ^ ^-— 70-mm Pac king — i

i

1.5

0.5 1.0 Packed height H [m] Fig. 9.4.

Number of transfer units as a function of bed height in packed desorption columns

Table 9.1. Empirical data for describing inlet effects in packed columns. Used to evaluate the diagrams in Figs. 9.6-9.10. Material

H [1/m2]

Nd

ANi

[m] 500

600

0.5

0.5

(if)

K lim

1.9

0.526

Pall ring 50 mm

Metal

Pall ring 35 mm

Metal

800

490

0.5

1.9

2.125

1.129

Raschig ring 25 mm

Ceramic

750

900

0.5

1.5

3.125

0.64

Tellerette 70 mm

Plastic

288

490

1

0.8

1.53

1.176

Tellerette 47 mm

Plastic

288

490

1

0.65

2.05

0.805

System

jctifica

o

&

Desorption

Packing

222

9

Phase redistribution in columns

cPs is related by the factor K to the costs of the redistributors cr as follows:

Cps =

cr K

(9-36)

Rearranging Eqn (9-23) to solve for Hr gives

Hr = [Nr - (Nd

(9-37)

dN

The relationship between NT and Nr is obtained from Eqn (9-15), i. e. NT = Nr (nr + 1)

(9-38)

Hence the total costs are given by

=

1

cPt\[NT-(nr

nrK\

in

ldN

(9-39)

The limiting value for the costs factor K can be found by differentiating Eqn (9-39) with respect to nr and equating the derivative to zero, i.e. dC = 0 dnr

(9-40)

The result is the same as that given by Eqn (9-32) and is independent of the number of redistributors nr and thus of their spacing Hr. The following relationship can be derived from Eqns (9-23), (9-34), (9-35), and (9-36): K

C = cPs NT Nd + ANt + Hr

K dN dH

NT

(9-41)

The limiting value for the costs factor K can again be found by differentiating this equation with respect to Hr and equating the derivative to zero, i.e. dC_ - 0 dHr

(9-42)

Again, the result is the same as that given by Eqn (9-32). The case in which no distributors are installed can be represented by substituting nr = 0 for nr in Eqn (9-39). Thus,

9.2

1 1 dN\ dH

L

Costs relationships

223 (9-43)

H.

Since Hr = HT in this case, it can be seen that Eqn (9-43) is identical to Eqn (9-20). Therefore, HT — CpstiT

(9-44)

— Cnr

Eqns (9-39) and (9-41) apply for Hr > H(, i.e. for the range in which the spacing Hr between two redistributors is equal to or greater than the height Ht of the inlet zone, in which the efficiency dN/dH generally changes. If Hr < Ht, the relationship to apply would be that derived from Eqns (9-23) and (9-41), i. e. C = cPs N7

1

1 +

K

K

Hr

NT

(9-45)

The functional relationships between the characteristic costs and design parameters are illustrated qualitatively in Fig. 9.5. The various parameters represented as functions of the spacing Hr between redistributors are defined as follows:

T = packed height without redistributors

c o ZD CD

o "a a

Fig. 9.5. Qualitative relationship between packed height, costs, and the number of redistributors

Packed height between redistributors Hr

224

9

Phase redistribution in columns

the costs ratio per separation unit by C

1

(9-46);

the various costs factors by (9-47);

-lim < K < Klin

the number of liquid distributors by (9-48),

in which case Nr is obtained from the relationship TV = f(//) or from Eqn (9-23) if Hr > Ht; and the relative reduction in bed height by (9-49).

0.6 <J

CJ)

<= j y 0.4

\

I

AH/HT

o O ZD

CD - ^

~° ^ CD I_

12

1

NT= 30

0.2

CD Q.

i

j

—

HT-9 m

—

i

0.5

£ - 0.4 C_3

O

o

"a

0.3 CD

X

0.4, 0.6/0.8 Klim I 1 25-mm Raschig ring, ceramic

S g. 0.2 0.1 0.4

0.8

1.2

1.6

2.0

2.4

2.8

3.2

Packed height between redistributors Hr Fig. 9.6. Qualitative relationship between packed height, costs, and the number of redistributors in a column with 30 separation stages and packed with 25-mm ceramic Raschig rings

9.3

Examples

225

9.3 Examples The functions N = i(H) shown in Figs. 9.3 and 9.4 serve as an example to demonstrate the dependence of the relationships derived above on the inlet effects exerted by the packing. They were determined by experiment and were used to calculate the values of Knm listed in Table 9.1. The results of the evaluation are presented in Figs. 9.6-9.10. They confirm that the costs per separation unit in columns with redistributors need be no higher than those in columns without redistributors if a theoretical costs factor Klim applies. In this case, however, redistributors allow the height of the columns to be reduced. Thus, if the redistributors occupy a height hr, the savings in column height that they can effect are given by

If)

= ^^

^

=l l-±lH(n, l H r ( n , + +1)1)+ + nnMM

(9-50)

In many cases, a reduction in column height may suffice by itself as a criterion for the installation of redistributors, even if the costs are thus higher than those for a column without redistributors. Columns with redistributors are always more expensive if the costs factor K is higher than Klim •

Redistributors must always be installed if there is a tendency towards liquid maldistribution or if the stream of liquid is likely to be destabilized over the height of the column. Under these circumstances, the model discussed is invalid, because the conditions for its compilation no longer apply, i.e. efficiency improvement in the inlet zone with correspondingly developed flow and efficiency stabilization below the inlet zone.

226

9

Phase redistribution in columns

=E

0.6

12

\ N T = 30

I

. red

\ o a a.

"a

cz

AH;

^

0.2

ct:

4 —

HT=12.8 m 1

0

HT

"/fir""

z.?

*—•

0.6

a CO

a Q.

~> "I

a)

"* 1 ^

0.4 tini

(1 /

CL> CO

_>

Ifi

\

0.5

—

0.3 35-mm

D

1.2

1.6

all ring, metal

0.2 0.4

0.8

2.0

2.4

2.8

3.2

Packed height between redistributors Hr Fig. 9.7. Qualitative relationship between packed height, costs, and the number of redistributors in a column with 30 separation stages and packed with 35-mm metal Pall rings

12

0.6 N T = 30

0.4 0.2 HT = 12.8 m

q •—

\wiwr

0 0.7

I f 1 °6 (_)

{=

^ -.—. "a

e 0.5 a °-

---

_co

o .-n?K,:

—OfiKugi

^

"§ g. 0.4 (_>

—lim

n

r&_

1

50-mm Pall ring, metal

0.3 0.4

0.8

1.2

1.6

2.0

2.4

2.8

3.2

Packed height between redistributors H r Fig. 9.8. Qualitative relationship between packed height, costs, and the number of redistributors in a column with 30 separation stages and packed with 50-mm metal Pall rings

9.3

Examples

227

12

0.6 \

NT= 30

0.4

cz o co

/AH/HT

<_ o cu t=;

Hr=13.8 m

nr

0 0.6 0.5 •" Ktim

•

n a

'Im:

2K,imn-

...

0.4

CL

0.3

o

47-mm DINPAC. plastics 0.2 0.4

0.8 1.2 1.6 2.0 2.4 2.8 Pocked height between redistributors Hr

3.2

Fig. 9.9. Qualitative relationship between packed height, costs, and the number of redistributors in a column with 30 separation stages and filled with 47-mm plastics Dinpac packing

0.6

< .g7

12

\

Ni ==

N

0.4

/ AH/H

30

r

n "r

0.2 HT

=

4

= 18.4 m

0

ID

0.8 \ 0.7

\ \

\

— /'• i"i

0.6 a

s CO

Q_ QJ CO t_

00

cu

o

05

CL

0.41=^ 70-mm DINPAC. plostic|

0.3 0.4

0.8

1.2

1.6

1 2.0

2.4

2.8

3.2

Packed height between redistributors H r Fig. 9.10. Qualitative relationship between packed height, costs, and the number of redistributors in a column with 30 separation stages and filled with 70-mm plastics Dinpac packing

10 Design of distributors Chapters 6 to 9 have shown how indispensable distributors are in packed columns - for distributing either the liquid at the head or the gas at the bottom of the column or for redistributing the phases at given heights -. Their design is governed by the principle on which they operate (cf. Fig. 10.1). It merits great importance because distributors serve to overcome maldistribution, which - according to Eqn (8-25) - may greatly impair the efficiency of large-diameter columns. Allowance must be made in design for differences in liquid load, because it is obviously more difficult to distribute small than large amounts of liquid (cf. Table 10.1).

Distributor

Principle

Design

Liquid transport Capillary

by capillary forces

Profiled slot

Sieve

qp

passage as liquid jets

CL)

CL •o ID

Y///A ' X/////1

Liquid discharge

or

as jets

tube

^SZ_c3ir

Overflow

Slot

as liquid jets

30°-160°

Nozzle

Liquid distributed as droplets

Fig. 10.1. The principles of liquid distribution

Perforated

230

10 Design of distributors

Table 10.1. Ranges of liquid loads for various distributors and the flow rates per outlet Liquid load uL [m3/m2h]

Type of distributor

Liquid per feed point 103l [m3/h]

510.5 0.5

tube or box perfor. plate or box profiled slot capillary

> 20 > 10 > 2 0.05-0.5

large medium - very large - 10

10.1 Fundamental design aspects and relationships Distributors must be accurately finished and correctly installed to avoid differences in liquid level. They should be fitted with drip edges, which prevent coalescence of the liquid on the underside and thus ensure trouble-free operation. Capillary plates are suitable distributors for very low liquid loads, viz. uL > 0.5 m 3 /m 2 h, and allow flow rates of about 0.05-0.5 1/h through each outlet. Profiled-slot distributors permit liquid loads of uL = 0.5-200 m 3 /m 2 h, and the flow rate through each outlet is higher than 2 1/h. Perforated-plate and trough-type distributors with liquid discharge are recommended for moderate liquid loads, viz. uL > 1 m 3 /m 2 h. The volumetric flow rate / through an outlet in a trough-type distributor is higher than 10 1/h. A crucial parameter in the selection or design of a distributor is the liquid load uL required for the separation process. Together with the head ho (cf. Fig. 10.2), it allows the flow velocity at an outlet uo, and thus the number of outlets required, to be determined in distributors with liquid discharge or overflow. In this case, the usual equation for flow through orifices applies, i.e. uo = yJ2gho

(10-1)

Usually, the head ho is higher than 5-10 mm. Since the cross-sectional area a of the outlet is known, the volumetric flow rate / can be obtained from 1 = auo

(10-2)

If the outlets are of the shapes shown in Fig. 10.2, q can be easily determined. According to H. Ulrich, W. Deeke and W. Geipel, the following equations apply for outlets in troughtype distributors: (1) For filleted rectangular slots: 2 I = X — b \[2~g}Q

(10-3)

(2) For triangular notches: o

^ = X — yJ2gh$ tan 6

Packed Towers in Processing and Environmental Technology. Reinhard Billet Copyright © 1995 VCH Verlagsgesellschaft mbH, Weinheim ISBN: 3-527-28616-0

(10-4)

10.1

Fundamental design aspects and relationships

231

-Liquid head

Width of slots

I = Liquid flow rate per feeder Notch angle

Fig. 10.2. Schematic graph of distributors with outlets for liquid discharge where Xh the constriction factor (for vena contracta). According to H. Ulrich et al., allowance for the effect of surface tension o on the constriction factor X can be made by means of a characteristic value Nz for the number of feeders, which is given by Nz = —

QLg

dh hn

(10-5)

where Q L is the liquid density, a is the surface tension, and dh is the hydraulic diameter, which depends on the outlet's effective cross-sectional area a and wetted periphery P, i.e. a

(10-6)

Values of Nz for open box-type or trough-type distributors can be read off against the constriction factor in Fig. 10.3. The flow rate / of liquid through a circular outlet with a diameter d on the lower side of a perforated-plate or trough-type distributor is given by jt

T

gho-

QL

I

(10-7)

If the outlets have been carefully rounded off, the constriction factor is X = 0.9-1. The term Apv allows for the pressure drop in the vapour as it passes through the distributor; it is the amount by which the pressure at the outlet exceeds the pressure at the surface of the liquid.

232

10

Design of distributors

0.6 Liquid (Dutlet slots

0.5

//

>< b 0.4

I

/

I1

0.3 0.2 0.1

/ y

/ 0.4

0.8

^^

\y

1 1

y

/

/

/ /

1.2 1.6 2 2.4 2.8 3.2 Characteristic for No. of outlets Nz

3.6

Fig. 10.3. Diagram for the determination of the constriction factor for the outlets in distributors of the type shown in Fig. 10.2

Experiments have shown that all the outlets in distributors with liquid overflow will be reliably fed if the feeder characteristic, as defined by Eqn (10-5), is Nz > 2. This figure corresponds to a liquid flow rate of / = ca. 0.01 m 3 /h per slot in trough-type distributors with rectangular slots of 5-mm width; and of / = ca. 0.005 m 3 /h per notch, in those with triangular notches. Once / is known, the number Z of distributor outlets per square metre of column crosssection that is required to cope with a liquid load uL in m3/m2h can be obtained from

z<

I

(10-8)

Liquid distributors that operate on the principles outlined in Fig. 10.2 can be quite easily designed with the aid of Eqns (10-3) to (10-8) and Fig. 10.3. Deviations from the tolerances specified in manufacture and assembly are responsible for differences in the head ho and flow rate /. Consequently, it would be an advantage to instal some means of adjustment in the components of a distributor. For instance, differences in head of Aho = 1 mm between the lowermost and uppermost ends of the distributor would lead to maldistribution of about 10%, i.e. M = 0.1, or more depending on the design. It is evident from Eqns (8-25) and (8-28) that the associated reduction in column efficiency Ec represents the borderline case that can be barely disregarded. However, as can be easily proved, differences in head of Aho = 4 mm simply cannot be tolerated. Experiments with the various types of distributors illustrated in Fig. 10.2 have verified the relationships expressed in Eqns (10-4) to (10-7) and Fig. 10.3. The breadth b of the slots was varied between 4 and 6 mm, the notch angle 2 6 was 90°, and the head was varied between 20 and 40 mm.

10.2

Types of phase distributors

233

Obviously, uniform distribution can be achieved more easily at high rather than at low liquid flow rates. Thus, if the liquid load is uL ~ 1 m 3 /m 2 h and the head is ho = 1 mm, the number of liquid outlets Z required per square metre of column cross-section would be Z = 150 in a plate distributor with perforations of d = 3 mm diameter. In the same column operating at the same load but under a head of ho = 3 mm, the number required would be Z = 80. If the column were fitted with a profiled-slot distributor, the number of outlets required would be Z = 200/m2. At such low loads, capillary-plate distributors would account for the highest number of outlets. Plates with spouts or trough-type distributors with liquid overflow that permit flow rates of 20 1/h per outlet are suitable for liquid loads ranging from uL = 5 m 3 /m 2 h to very high values. It is general practice to predistribute the liquid in the designs described above. By this means, perfect hydrodynamic functioning of the distributor itself and thus optimum liquid distribution over the column cross-section can be ensured. Predistribution is unnecessary in pipe distributors, in which the liquid is discharged either through perforations or by nozzles. These distributors are suitable for liquid loads ranging from low to very high. Distributors consisting simply of spray nozzles fitted above the bed obviously have a comparatively restricted operating range in which the sprays can be uniformly distributed over the column cross-section.

10.2 Types of phase distributors There are numerous designs of phase distributors. The few that have been selected for discussion here are characteristic of those used in industrial-scale columns. The trough-type distributors shown in Fig. 10.4 are suitable for average to high liquid loads in columns of 0.6 m diameter or larger. If the liquid loads are small, bolts should be installed to allow alignment of the individual troughs. If the liquid load is less than 5 m 3 /m 2 h, perforated plates (cf. Fig. 10.5) or distributors with spouts (cf. Chapter 3) are recommended. Perforated-pipe distributors (cf. Fig. 10.6) still give satisfactory performance at liquid loads of 0.75 m 3 /m 2 h in columns of any given diameter. If they are properly designed, they also allow very low liquid loads of about 25 m 3 /m 2 h to be uniformly distributed. The same applies to distributors consisting of spray nozzles, but these are not depicted here. Before they are installed, liquid distributors for columns of very large diameter should be subjected to experiments on a test rig in order to determine the standard deviation in liquid distribution (cf. Fig. 10.7). Devices for liquid redistribution are advisable in many separation tasks. An integrated structure consisting of support plates, liquid collectors, and phase distributors (i.e. for the liquid and gas phases) can be used for this purpose (Fig. 10.8). The dimensions entered in Fig. 10.9 are useful for arranging distribution within a column. Other column fittings, e.g. support plates, packing retainers, and liquid collectors for product withdrawal are shown schematically in Fig. 10.10.

234

10

Design of distributors

22

21

18

—i

i- 1

1- I

15

1

160

0611

•

1

140

30°

VT7

0 2600

at-H+l

lil

Fig. 10.4.

Box-type liquid distributor

Liquid feed box Fig. 10.5.

Sieve plate

Gas channel

View of a sieve plate liquid distributor, design of Raschig

10.2

Fig. 10.6.

Pipe-type liquid distributor

Types of phase distributors

235

236

10

Design of distributors

Fig. 10.7. Montz liquid distributor of large diameter under test for measuring the distribution accuracy

Fig. 10.8. Drawing of a redistributor for both liquid and gas phases, including support tray and liquid collector

Fig. 10.9. Characteristic dimensions for the arrangement of phase distributors

120-270-

238

10

Design of distributors

Vapour Reflux Liquid distributorCover plate Packing Support tray Liquid collector

n nnn

Distributor Cover plate Packing Redistributor Packing Support tray

Vapour ^

Fig. 10.10. Schematic diagram indicating the location of internals for packed towers

11 Overall evaluation of packing In view of the spiralling costs of energy, considerable care must be devoted to the choice of packing during the planning stages of economic thermal separation plant. It must permit high loads, have good separation efficiency, and allow low gas-side pressure drops. The dynamic liquid holdup, i. e. the residence time of the liquid, must be small, and the packing must be immune to fouling and corrosion. If all these requirements are entirely met, the operating conditions can be regarded as optimum. In practice, however, they are fulfilled to different extents by different types of packing.

11.1 Materials of construction The ease with which the material of construction can be shaped, processed or machined greatly influences the geometry of a packing. Thus the basic geometry of a metal Pall ring is not completely identical to that of a ceramic or plastics design. Even the thickness of the material differs to a not inconsiderable extent. The process engineering characteristics of the packing are greatly influenced by these geometric factors and also by other properties that can be ascribed to the material of construction, e. g. the wettability of the surfaces and the apparent density of random beds (cf. Fig. 11.1). It is therefore obvious that the properties of the materials mostly used in process engineering, e.g. steel, ceramics and plastics, should be taken into account in assessing packing performance. The fact is that one of the first questions usually raised in planning a given separation process is what would be the most suitable material for the task. Formerly, packing was produced predominantly from metals and ceramics. In the last twenty years, however, plastics have gained a growing foothold in thermal separation processes. One of the main reasons for this is the steady improvement that has been made in their resistance to heat and chemicals and their mechanical strength. A field in which plastics packing has been adopted on a particularly wide scale is ecological engineering, i.e. in air purification and effluent treatment. The plastics primarily used for the production of packing in industrial-scale absorption and desorption plants are polyethylene (PE), polypropylene (PP), poly(vinyl chloride) (PVC), and poly(vinylidene fluoride) (PVDF). The ease with which they can be moulded is exploited in the production of packing of optimum geometry for two-phase flow. These plastics have a very high tensile strength at break, with the consequence that packing produced from them is almost unbreakable under operating conditions and that the likelihood of wear can be practically excluded. Their low density allows reductions in column costs and facilitates handling. Yet another advantage of plastic packing is a significant reduction in down time, because it obviates the precautions that have to be observed in charging ceramic packing and thus allows the column to be filled more rapidly. In practice, the time required for charging plastic packing is only one-tenth of that for ceramics. Hence, in the event that the acquisition costs of plastic packing are higher, the difference can be made good by the savings achieved in reducing the down time.

Packed Towers in Processing and Environmental Technology. Reinhard Billet Copyright © 1995 VCH Verlagsgesellschaft mbH, Weinheim ISBN: 3-527-28616-0

240

11

Overall evaluation of packing

Methanol/Ethanol 1 bar. L/V = 1, d s = 500mm, H=2m

25mm Pall ring Plastic o Ceramic v Metal D

I [1/m 3 ] 57000 43000 47500

I -i-

< 60

A

20 0.2

02

0.4 0.6

04

0.8 1.0 1.2 1.4 1.6 Vapour velocity u v im/s]

1.8

05 08 i 5 U U 16 18 W Vapour capacity factor Fv [m 1/2 s~ 1 kg 1/2 l

2.0 2.2

12 2.4

Fig. 11.1. Efficiency and pressure drop for 25-mm Pall rings produced from various materials Experience has shown that more deposits, which cause an increase in pressure drop, are formed on ceramic than on plastic packing. Thus great differences exist in the down times required for cleaning. This advantage has been exploited in potash and diethanolamine columns, which were formerly charged almost exclusively with ceramic packing. Nowadays, plastic packing predominates in most of these columns. Since plastics have a lower density than that of water, beds of packing produced from them can be cleaned within the column by flotation and washing with water and steam. Other cases in which the low density of plastics can be conveniently exploited concern the retrofitting of plate columns that were previously preferred to columns with ceramic or metal packing simply because they weighed less. There is no doubt that plastics packing can be successfully used in many more fractionation tasks than they are today, particularly in the separation of systems that do not affect the plastics' resistance to heat and chemicals.

77.2

Capital investment

241

11.2 Capital investment

The capital investment costs CQ for a packed column designed for a separation task at a given liquid-to-vapour ratio LIV can be calculated from the following equation: Cc = vv nt V C = — vv nt>iso V C

(11-1)

where Vy is the column volume per unit of separation efficiency and per unit of vapour volumetric flow rate, i.e. the specific column volume nt is the number of theoretical stages required to separate the system into the desired products, V is the volumetric flow rate of the vapour through the column, and C is the costs per unit volume of the packed column. If the number of theoretical stages ntfiso in an isobaric column is known, i. e. a column in which there is theoretically no pressure drop, the term nt can be determined from the theoretical column efficiency r\c (cf. Chapter 1). It can be easily proved that r\c is of no significance except in vacuum separation processes involving a large number of theoretical stages. An idea to this effect can be obtained by comparing packings with different efficiency/pressure drop/load characteristics but operated at the same vapour load per unit cross-section. In this case, the differences in the pressure drop per theoretical stage will give rise to differences in the ease with which the mixture can be separated into its components and therefore to differences in not only vv but also r\c, and thus nt and V as well. Consequently, the operating costs will also differ, and the only basis on which the optimum column could be designed would be a comparison of the total costs. It can thus be seen that the costs C per unit volume of a packed column do not constitute the only criterion that decides the choice of packing. However, if the comparison is based on equal pressure drops per theoretical stage Ap/nt, it will be found that r\ c, nt and V are the same in each case and that the costs of the column will be influenced solely by vv and C. The costs for the shell and the bed of packing in a column are usually fixed by the manufacturer in accordance with the supply schedule. Since the contribution made by the shell towards the costs per unit volume decreases with an increase in diameter, the corresponding values of C are less. Comparatively low values for the pressure drop per unit theoretical stage Ap/nt are achieved by metal packing with thin walls; and extremely low values, by gauze packing. The engineering performance data for these types of packing lie within the ranges depicted in Fig. 11.2. The Pall ring is regarded as one of the best and, over the last 35 years, one of the mostused types of packing for random beds in industrial-scale columns. For this reason, its performance data are often taken as a reference in evaluating new developments. The relevant figures for metal Pall rings are listed in Table 11-1. Thus, one of the criteria adopted is the ratio Cs of the costs of the packing to be evaluated to those of a random bed of 50-mm Pall rings, i.e.

242

11 Overall evaluation of packing =

Cc (packing x) Cc (50-mm Pall ring)

_ ^

In this case, the value for Cc is determined by inserting nt = 1 and V = 1 m3/s in Eqn (11-1). However, if the rectification process involves a large number of theoretical stages, this simplification can apply only if the pressure drop per theoretical stage Ap/nt is the same in each of the beds of packing compared. If the comparison is based on the assumption that the vapour capacity factor Fv is the same in both cases, the higher reflux ratio r will entail that both nt and V will be greater in beds with a high value for the pressure drop per theoretical stage Ap/nt than in those with a low value. This is evident from the qualitative diagram shown in Fig. 1.6. An example of a comparison between a random bed of metal Pall rings and a gauze packing is presented in Table 11.2. It can be seen that the only separation processes in which the gauze packing incurs less costs than the 50-mm Pall rings are those in which specific pressure drops of less than 1 mbar are specified. The curves plotted in Fig. 11.2 and the values listed in Table 11.2 delineate the range of performance data for almost all modern types of packing with moderate pressure drops per theoretical stage. The criterion on which a selection would be based from the economics Table 11.1. Process engineering ratings, costs, and costs factors for columns packed with random beds of metal Pall rings Size

0,81 Fv

15-15-0.4

25-25-0.6

2.02

2.30

F V ,F

Ap nt

Cs

Cs

Ap nt

VV

vv

Fv

H

3.66

2.7

0.09

1.5X

5

2.4

0.08

1.2°

3

2.11

0.09

1.4X 1.1° 1.6X 1.3°

1.0x

5

2.76

0.09

1.1°

3

2.49

0.09

3.02

2.4

0.10

l.lx

1.2° l.lx

1.3° 35-35-0.8

2.40

2.71

2.6

0.11

x

5

2.83

0.09

1.0x

1.0°

3

2.59

0.09

0.9 x

0.9

1.0°

0.9° 50-50-1.0

2.47

2.18

2.4

0.13

1

5 3

2.89 2.65

0.11 0.11

1 1

80-80-1.5

2.61

1.47

2.6

0.18

1.4 X

5

3.17

0.13

l.lx

1.4°

3

2.77

0.16

Dimension

Fv n r m k g 1 / 2 s

Material

x

Carbon steel

n t /H 1/ni

Ap/n t mbar ° Stainless steel

1.1°X 1.5 1.4°

vv m3/m 3 /s

77.2

Capital investment

243

^ Packin g Dumped Regular

•

• • Pall ring Gauze . 50-mm metal Sulzer BX -

12

> /

/ p

—Ethylbenzene/Styrene 133 mbar

CO

CL

J /

cz

. — —- — — —

0 0.4

(V,

0.2

t

CD

0 Fig. 11.2. Graphical comparison of random beds of packing and a structured packing

1

1.2

2.0

1.6 ,.

•,

.

.

2.4 r

2.8

r -1/2 -1 i

Capacity factor Fv[m

3.2

1/21

s kg ]

Table 11.2. Engineering and costs comparison between a random and a geometrically arranged bed of packing Column Internals

3 Cs

Specific pressure drop Ap/n t 1 vv Cs Fv

0.5 Fv

Cs

Fv

vv

Pall ring 50

2.65

0.11

1

1.69

0.22

1

1.15

0.,32

1

Sulzer BX

3.11

0.08

3.2

2.7

0.06

1.3

2.4

0..06

0.8

Dimension Material

Ap/n t mbar

Fv

m"1/2 kg1/2 s-1

Stainless steel

v>/ m 3 /m 3 /s

244

11 Overall evaluation of packing

aspect is the costs as determined from Eqn (11-1). From the engineering aspect, however, the tendency to fouling would be another factor to be taken into consideration. Frequently, the decision in favour of a particular type of packing is based on an analysis of the total costs with due regard to specific local conditions, e.g. the layout of the equipment. If different types of column internals are compared on the basis of Eqn (11-1), a fundamental distinction must be drawn between cases in which Fv = 0.8 FFh where Fm is the capacity factor at the flood point, and those in which Ap/nt is a constant. The latter is important for evaluating all separation processes in which a limit is imposed on the pressure drop.

11.3 Evaluation for the separation of thermally unstable mixtures The parameters that influence the thermal stability of a substance are the operating temperature and the residence time. The latter is governed by the volume of liquid / retained in the bed of packing and the liquid flow rate VL or - if the liquid velocity uL and the height H of the bed are given - by the liquid holdup hL, i.e.

The specific residence time tjnt is defined as the period during which the liquid is held up over a bed height that corresponds in terms of efficiency to a theoretical stage, i.e.

nt

(11-4)

uL \ ntIH

It attains its lowest value in column internals for which the term hL/(nt/H) is a minimum when uL remains constant. Eqn (11-4) can also be writen in the following form: ^- = hL-^LVV=KhVy nt uL

(11-5)

In other words, the specific residence time tjnt is directly proportional to the column volume per unit of efficiency vv. The constant of proportionality Kh is a dimensionless hydrodynamic quantity that is specific for a given type of packing and is given by h

L

L

^

L

Thus, for a given column volume per unit of efficiency vv and a given liquid/vapour ratio L/V, the bed of packing with the shortest residence time will be that in which the liquid holdup hL is lowest for the load factor concerned. Hence, the average total residence time of the liquid in the bed is a function of parameters that depend on the load, i.e. hL and vv, and parameters that are defined by the separation task, i.e. the number of theoretical stages nt and the volumetric phase ratio, i.e.

11.3

Evaluation for the separation of thermally unstable mixtures tL = Kh vv nt = hL vv nt ——

245 (11-7)

uL The volumetric phase ratio in this case is given by

The product of hL and vv is identical to the liquid holdup h'L per unit of separation efficiency and vapour volumetric flow rate, i.e. h'L = hL vv

(11-9)

Consequently, the suitability of column internals for the rectification of thermally instable mixtures is essentially defined by two equations, i.e.

—

= f(FV)

LI V,PT = const

(H-10)

nt —

= f(

The following relationship can be obtained by combining these two equations: ) t

(11-12)

I L/V,pT = const

The terms (tLlni)um and (Ap/nt)um define the maximum permissible limits for the specific residence time and the temperature at the foot of the column. If they are known, it can be determined which of the columns under investigation represents the most favourable costs. The condition that must be satisfied in this case is (11-13)

Another condition that must be met is that the choice should be in favour of the column with the lowest costs per unit of column efficiency and unit volumetric flow rate, as defined by v,C

= j - ^ Kh

(11-14)

nt

where C is the costs per unit volume of the packed column. Eqn (11-10) relating to plastics packing is presented graphically in Fig. 11.3. It can be seen that the minimum residence time coincides with the vapour capacity at the loading point, above which the liquid holdup rises considerably with an attendant, renewed increase

246

11

Overall evaluation of packing

in the residence time. This minimum corresponds to a pressure drop per theoretical stage lS.plnt = 2.2 mbar. Eqn (11-12) is presented graphically in Fig. 11.4. In this case, the example taken to plot the curve was metal packing in the range below the loading point. Another fact that can be derived from Figs. 11.3 and 11.4 is that the residence for the liquid is less in beds of packing with a large area per unit volume a than in beds with smaller values of a.

Chlorobenzene/Ethylbenzene 67 mbar. L/V=1

-CD

0.8

1.2

1.6

2.0

2.4

2.8

3.2

3.6

Vapour capacity factor F v [m" 1/2 s"1 kg 1 ' 2 ] Fig. 11.3. Specific residence time of the liquid phase in a column packed with plastics Hiflow rings as a function of the capacity factor

20

i

i

i

i

i

i

Chlorobenzene/Ethylbenzene 67 mbar. L/V--1 10

X CMR

1.5 Turbo ,a=173rn 2 /m 3 -

Metal^ ^\ —.»

7^1—.

Gempak2AT,a = 200m 2 /m r 3 0.1

0.2

0.3 0.4

^ —

0.6 0.8 1

Spec, pressure drop Ap/n t [mbar]

Fig. 11.4. Specific residence time of the liquid phase as a function of the specific pressure drop in a random and in an arranged bed of metal packing

11.4

Evaluation in terms of minimum column volume

247

11.4 Evaluation in terms of minimum column volume Rectification is the most energy-intensive thermal separation process. The planning stage involves thermodynamic and hydrodynamic analyses of the design, materials, and operating parameters and a knowledge of the process engineering parameters required for the evaluation of the intended column internals. The only means of ensuring optimized energy consumption and minimum column volume is to instal efficient high-performance packing with a low inherent pressure drop. Considered from this aspect, the volume Vc of the enrichment section in a rectification column of height H through which vapour with a molar mass \iv and a density QV flows at a velocity uv and a molar flow rate V is given by VC = V— QV

—H

(11-15)

Uy

The molar flow rate V is given by V = D (r + 1)

(11-16)

where D is the molar flow rate of the overhead product and r is the reflux ratio. Eqn (11-16) applies to the entire enrichment section of the column if the individual components of the mixture have almost the same vaporization enthalpy. Strictly speaking, it applies to the stripping section only if the mixture to be separated flows through the column at its boiling point, i.e. tF = tb. The terms nt/H and vv associated with the vapour capacity factor Fv can be introduced by means of the relationship expressed in Eqn (1-36). Eqn (11-15) then becomes yc = D iiv — vv (r + 1) nt

(11-17)

Qv

Other parameters that affect the volume Vc are the operating pressure and the nature of the system to be separated. The following two general relationships then apply: QV, r, nt = f (/?, system)

(11-18)

vv = f (p, system, internals)

(11-19)

The term (r + 1) governs the energy consumption, and the separation term (r + l)nt exerts a great influence on the column volume. This product passes through a minimum at a certain reflux ratio r, i.e. VC,min

n = f (Ap//Ir)

(11-20)

If the rectification process involves a large number of theoretical stages, this minimum value increases with the pressure drop per theoretical stage Ap/nt, as is clearly evident from the example shown in Fig. 11.5. It is also obvious from the diagram that modern packing is

248

11 Overall evaluation of packing

Ethylbenzene/Styrene. pj =51 mbar, tp = t b x F --0.591 , x D --0.992 . x B = 0.0035 60

\

\

\

» 55

s

\ X \

X

I SO

-^ r

^ 45

1

—.

o

^ .

—-»

40 460

N ___

\

440

\

1 •

—i

\

420

, —

cT

T 400

H

iI

OfV

/

/

J 380 X /'

g 360

•K >

— —

^1

340 i

320

—~*

300 rpi ^

re "-'^

rr. rr -yn bU °^ '-^ ReflUX ratio r

7r ' ^

pn "^

Fig. 11.5. Effect of the specific pressure drop on the column dimensions in the vacuum rectification of an ethylbenzene/styrene mixture

definitely superior to traditional fractionating plates from the aspect of the volume Vc of the enrichment zone, because it gives rise to much lower values of Ap/nt and vv. Since a decrease in the value of Ap/nt entails a reduction in the reflux ratio r {cf. Eqn (1-49)}, another great advantage of lower pressure drops in separation processes that involve a large number of theoretical stages is a substantial cut in the energy consumption. According to Eqns (1-48) and (1-49), the reflux ratio in a real column r exceeds that in a theoretical isobaric column riso by a factor vG, which - in turn - exceeds the minimum rmintiso by a factor v. There must be a value of v that corresponds to the minimum volume Vc,min

11.4

249

Evaluation in terms of minimum column volume

and the separation term [(r + l)nt]min and to which Eqn (11-20) would apply. The relationship to the pressure drop per theoretical stage would then be / Ap\ [(r + \)nt]minVG

= f —

(11-21)

]> V

n

t

\

The additional energy consumed by this pressure drop is given by vGQiso

riso + 1

v 1

(11-22)

rmin,i,

It can be expressed as follows as a function of the presssure drop per theoretical stage: / Ap \

= ff

(H-23)

Ethylbenzene / Styrene , pT = 51 mbar . t F = t b x F : 0,0591 ,x D = 0,992 , xB--0,0035 -S "5

1-8

^-—-

X

h r

•

'm n. sc

«

1.4

3

1.2

[(r*1)nt]min

0.3

03 a ,

CD

a c

—•

AQ /QIS0

;0.2

GU

-ci

0.2 J-s

\

-

CD C 3 C/) <1 O CD

0.1 —— —

O

0

.

_ — •

— ^

0.1 < |

NA

< ^ , —— 1

\

a

2

3

4

5

6

Specific pressure drop Ap/n t [mbar]

o

0

*

Fig. 11.6. Effect of the specific pressure drop on energy consumption and the number of theoretical stages

250

11

Overall evaluation of packing

The associated increase in the number of theoretical stages Antlnt>iso can also be expressed as a function of the pressure drop per theoretical stage, i.e. l(r + l ) n l ] m i -

= fH -

n

t,iso

\

n

t

(H-24) I

These relationships are presented graphically in Fig. 11.6. The data taken as an example were derived from Fig. 11.5. The effect of the pressure drop on the energy consumption and the number of theoretical trays is immediately evident. The curves apply to the case in which the column volume Vc is a minimum. In other words, they need not necessarily correspond to the operating conditions under which the minimum total costs, i.e. the sum of the capital investment and running costs, can be expected. The extent to which the two cases agree depends on the local costs for energy and the materials of construction.

11.5 Theoretical considerations in the design of column internals Modern manufacturing and finishing techniques allow column packing to be realized in multitudinous geometrical forms with a wide variety of surface structures, as is evident from the designs discussed in Chap. 2. Thus great scope is available in varying the hydrodynamic and performance characteristics. The materials of construction represent another important design factor. It is obvious from the preceding sections of this chapter and the remarks on the experiments discussed in Chap. 3 that there is no single type of packing that can provide a perfect answer to all the demands that are encountered in practice: high outputs, low pressure drops, short residence times, immunity to corrosion, resistance to fouling, and low costs. Consequently, a logical procedure in selecting packing would be to apply Eqns (11-1) and (11-2) in order to determine which would be most economical of the types that have previously been screened for compliance with process requirements, e.g. short residence time and low pressure drop in the rectification of thermally unstable mixtures. Many aspects on separation efficiency have to be considered in addition to the operating requirements and the properties of the system. Most importance is attached to the basic geometry and dimensions of the packing. The volumetric mass transfer coefficient, i.e. the product of the mass transfer coefficient p and the area of contact aph at the phase boundary, is a useful performance criterion (cf. Chap. 5). It is defined in terms of the phase load u in a horizontal cross-section of the column and the height of a transfer unit HTU (or the number of transfer units NTU per unit column height H), i.e.

The specific column volume, in analogy to Eqn (1-36), can be introduced in this equation, i. e. 1

uNTUIH

HTU

u

' $aPh

(11-26)

11.5

Theoretical considerations in the design of column internals

251

According to the theory of nonstationary diffusion, the mass transfer coefficient |3 for the phase concerned depends on the corresponding diffusion coefficient D and the period of contact required for renewal of the phase boundary, i.e.

P = - \ / -

(H-27)

where — = constant = 2jt~ 05 . c The duration of contact can be reduced by design measures. For instance, it is known that small packing separates more efficiently than large; and regularly stacked packing with interrupted flow channels, more efficiently than falling-film. In both cases, x is small, with the consequence that both the specific column volume v {cf. Eqn (11-28)} and the total volume Vc, through which the phase in question flows at a volumetric rate V {cf. Eqn (11-29)}, are also small:

— Vc = vVNTU

(11-28) (11-29)

A knowledge of the residence time in the column is particularly important in planning the rectification of mixtures that are sensitive to heat. It depends on the liquid holdup {cf. Eqn (11-3)}, the liquid load uL, and the volume Vc {cf. Eqn (11-17)} of a column of height H and diameter ds. The value for the liquid phase is given by

L

(

UL -

)

d}

The value for the vapour phase can be obtained from this equation by introducing the terms for the effective void fraction ee for the gas {Eqn (4-55)} and the superficial gas velocity uv, i.e.

tv

=

£eVc

= -^-H

JT 2 — ds Uy

(11-31)

Uy

The residence time tL is related to the duration of contact xL through the liquid holdup hL, which depends on the length lx of the path of contact over which the surface of the liquid is renewed in the bed of packing concerned. The average liquid velocity over this path is given by uL = —

(H-32)

252

11

Overall evaluation of packing

The total number of paths of contact per unit height of column, i.e. for H = 1, that is permitted by the geometry of the packing is given by

«c = 7-

(H-33)

1

Therefore, rL and tL are related by the following equation:

Substituting for tL from Eqn (11-30) then yields the following relationship between the duration of contact and the liquid holdup: xL = - ^ uLnc

(11-35)

Finally, substituting for nc from Eqn (11-33) gives xL = - ^

(11-36)

This equation states that the less the product hLlx of the liquid holdup and the path of contact for a given liquid load, the less the duration of contact xv. It is an unambiguous statement that must be observed in designing packing geometry. In analogy to Eqn (11-32), the average superficial velocity of the gas or vapour phase is given by Uv=— xv

(11-37)

In other words, the vapour traverses the path lx in a period of time xv, which is related as follows to the residence time tv: (11-38) Substituting for tv from Eqn (11-31) gives rise to Eqn (11-39); and combining Eqns (11-33) and (11-39), to Eqn (11-40): TV = —^—

uvnc Uy

(11-39)

77.5

Theoretical considerations in the design of column internals

253

These equations relate geometric parameters for the packing, i.e. the void fraction 8 and the length of the path of contact / t , to certain operating conditions, i.e. the liquid holdup hL and the superficial gas velocity uv. Hence, the duration of contact of an entire phase depends on the local phase velocity and the number of paths of contact per unit of effective column height. The figure for the liquid phase can be obtained from Eqn (11-41), which is derived by combining Eqns (11-32) and (11-37); and for the gas phase, from Eqn (11-42), which is derived from Eqns (11-33) and (11-37):

xL = ^J— uLnc

(11-41) (11-42)

uvnc The corresponding residence time for the liquid phase is given by Eqn (11-43); and for the gas phase, by Eqn (11-44):

tL = -¥-

(11-43)

UL

tv=-^-

(11-44)

Uy

According to these two equations and to Eqns (11-30) and (11-31), a definite relationship exists between the residence time, the load, and the height of the bed. If the liquid load uL is given: the smaller the product of the liquid holdup hL and the height H, the shorter the residence time tL. If the vapour load uv is given: the smaller the product of the effective void fraction ee and the height //, the shorter the residence time tv. Rearranging Eqn (11-28) allows the duration of contact e to be expressed in terms of the specific column volume v, the area of contact at the phase boundary aph, and the coefficient of diffusion D, i.e. (11-45) It follows from this equation that if the duration is short, the product of the specific column volume v and the area of contact aph must be small. Its value for the vapour {Eqn (11-46)} and liquid {Eqn (11-47)} phases can be obtained by further rearrangement of Eqn (11-45). Thus

aph = c Vj±-

(11-47)

254

11

Overall evaluation of packing

According to Eqn (11-1), the price of a rectification column is governed by the product of the specific column volume and the costs per unit volume. Consequently, development work must be aimed at selecting design parameters that involve the minimum outlay on materials of construction and machining. Combining Eqns (11-40) and (11-46) gives rise to (11-48) It follows from this equation that, if the void fraction 8 is given, the specific column volume vv relating to the vapour phase can be reduced by shortening the length of the path of contact lx. Analogous information can be derived from the corresponding equation for the specific volume vL relating to the liquid phase, which is obtained by combining Eqns (11-36) and (11-47), i.e. V

L = —

\

ITT-li

(H-49)

Design measures aimed at frequently interrupting the flow paths for the two phases, and thus their redistribution, have a beneficial effect on mass transfer and therefore reduce the specific colume volumes. The liquid holdup hL also depends on the design and the loading conditions, and the advantageous effects that can be achieved if its value is low are evident from Eqn (4-73). The area a per unit volume and the area of contact aph at the phase boundary can be best exploited by packing that permits high vapour velocities and can be uniformly wetted. According to Eqns (11-48) and (11-49), low values for the specific column volumes vv and vL can thus be attained. An illustrative example is given by Table 11.3, in which the specific column volume Vy for a random bed of Pall rings is compared to that for stacked Pall rings operated at the same pressure drop per theoretical stage Ap/nt. It can be seen that the column space occupied by the stacked bed is only about 40 % of that of the random bed.

Table 11.3. Difference in specific column volume between random and geometrically arranged beds of Pall rings. Comparison based on the specific pressure drop Metallic Pall ring packings, ring size 25 mm Ap/nt [mbar] -» vv^ [m3/m3/s]

Dumped Stacked

0.5

1

5

0.453 0.180

0.244 0.080

0.093 0.036

77.6

State of the art in the development of packing

255

11.6 State of the art in the development of packing The properties expected of packing are great separation efficiency and a high superficial velocity, yet the minimum possible pressure drop in the stream of gas or vapour. The more that these requirements are met, the less the volume of the internals that are required for a given separation task, i.e. that necessary to achieve a specified capacity and overall efficiency. Thus a measure for the efficiency is the specific column volume vv {cf. Eqn (1-34)} that is required to cope with a given liquid load or a given phase ratio. Its reciprocal can be regarded as the volumetric efficiency of the packing. A criterion that is frequently adopted for evaluating packing is the pressure drop per unit of efficiency, which is referred to as the specific pressure drop. If it is low, the packing is eminently suitable for the separation of mixtures that are sensitive to heat, because it allows operation at moderate product temperatures. Packing with a low specific pressure drop is essential for the realization of optimum energy consumption in separation equipment. In many cases, it also entails a reduction in capital investment costs, particularly for vacuum rectification processes that involve a large number of transfer units. Hence the specific column volume and the specific pressure drop decisively govern the economics of column packing. The operating characteristic for the packing is another criterion for selection. Some of the numerous products that have to be separated on an industrial scale tend to foul or corrode the packing in a column. Experience has shown that the simpler the geometry of the packing and the smoother its finish, the less this tendency. An example of suitable geometry is honeycomb packing, in which parallel rows of sheet metal, foil, or plastics film are stacked crosswise in a regular geometric arrangement. The only means of finding out the extent to which the performance of random and stacked beds of packing can be improved is to determine by experiment the parameters that specify the geometry and texture. The wide differences in the thermodynamic behaviour and physical properties of the various systems to be separated by thermal techniques entail corresponding differences in the operating conditions. Thus the liquid loads in vacuum rectification are usually much less than those encountered in rectification at atmospheric or higher pressures or in absorption and desorption processes. Consequently, the liquid/vapour load ratio in a column may vary considerably from the one process to another. Moreover, the efficiency of most beds of packing depends on the load and pressure; and the maximum load, on the liquid/vapour ratio and the pressure. It can thus be seen that there is no one type of packing that gives optimum performance in each and every industrial application. This also explains the numerous designs of packing on the market. In view of these facts, engineers responsible for planning thermal separation plants often have difficulty in selecting the optimum packing for a given application, particularly since the pertinent empirical values derived from laboratory or plant studies are not always available. However, evaluation of the results presented in various publications permits the performance of packing of different geometries and textures to be assessed in outline. The criterion that is generally adopted in evaluating various types of packing is: the greater the area per unit volume a, the better the mass transfer. However, this applies only if the yardstick for packing performance is the specific column volume vv. Another criterion is: the greater the effective void fraction, the less the pressure drop and the larger the bed capacity.

256

11

Overall evaluation of packing

A measure for the degree to which the area available per unit volume in the bed of packing can be exploited is the performance-related area a'. It represents the area per unit efficiency and unit vapour volumetric flow rate, and is given by (11-50)

a — a vv

The volume of packing material v' present in a bed can be expressed in terms of the separation efficiency and the flow rates, i.e. (11-51)

— a s vv = — a' s = (1 - e) vv

If vv has been determined for various beds, the area required to realize the one theoretical stage and unit vapour volumetric flow rate can be obtained from the function (11-52)

a' = f(fl)

These conclusions have been verified by the results of comprehensive studies of recent and later date that were performed under comparable conditions on various beds of packing and that embraced different design principles, different materials, and different surface structures, e. g. expanded metals, fabrics, and smooth surfaces (Fig. 11.7). The results obtained in evaluating the less recent studies are presented in Fig. 11.8, which shows the performance-related area a ' a s a function of the area per unit volume a for some packings of completely different geometries and textures (cf. Table 11.4). The points plotted Table 11.4. Symbols for traditional types of packing as illustrated in Fig. 11.8 Packing

Dimensions

Symbol

Metal gauze

Sulzer

BX

T

Sheet metal, folded and perforated

GHH

Square

•

Metal grid

Glitsch

Fine

Metal grid

Glitsch

Course

• •

Ceramic, rough

Raschig ring

25 mm

A

Plastic, corrugated and performated

BASF ring

25 mm

O

Sheet metal, smooth

Raschig ring

25 mm 35 mm 50 mm

A A

Sheet metal, discontinuous

Pall ring

15 mm 25 mm 50 mm 80 mm

O O

Structure

Expanded metal, discontinuous

Pall ring

25 mm 50 mm

A

o 6 e e-

77.6

State of the art in the development of packing

257

PacMiam-

Gutsch 3no, .jjor-jc

b!;iS,".!*; bfiCl,

Fig. 11.7. Examples of traditional packing for geometrically arranged and random beds

metal

Pail ring, exp. met

in the diagram were derived from experiments performed in the same pilot plant, with the same test system, and under the same conditions. It allows the limits to be estimated within which the separation efficiency can be influenced by design measures. According to the diagram, the degree of exploitation of the available surface decreases with an increase in its area a, i.e. more area a' has to be installed per unit efficiency and unit flow rate. Figure 11.8 also permits the conclusion that changes in the surface structure of packing of given basic geometry merely lead to a moderate change in the efficiency per unit area. Despite the very expensive material of high interfacial activity that is required for its production, metal gauze packing is less efficient per unit area than, say, a random bed of traditional metal Pall rings. In qualitative terms, this entails that, if the one theoretical stage is adopted as a measure for the efficiency under conditions that correspond to about 80 % of the maximum possible capacity, the area per unit volume of the gauze packing required to realize this

258

Is*

Overall evaluation of packing

on o/) — c

*E e

11

max. loac

A

. - —-

c ^-« «— ^-*

—

^—,

—

•

-—•

.—--

in

,—

, zu a

g 10 " S 40

Ethylbenzene/Styrene 133 mbar Liquid/Vapour ratio L/V = 1

-—

a CD <

- ^.— -*

S 30

-—

a

,—«•

•2 20

•

CD CU

m

60

^

—

•

-o

100

o

o

c

Spec, pressure droP 3 mc f ar i

140

180 220 260 300 340 380 Area per unit volume a [m 2 /m 3 ]

420

460 500

Fig. 11.8. Relationship between the performance-related and the geometric areas of traditional random packing and arranged packing as listed in Table 11.4

one stage would be about 50 % more than that required for a random bed of 25-mm metal Pall rings. This fact must be regarded from the aspect of the target set in all new and further developments, i.e. to improve upon the process engineering characteristics of existing designs and thus the economics of separation plants and processes. It will then be seen that there is a limit to the number of design measures that can be adopted, individually or combined, to improve packing effectiveness. Comprehensive experimental studies over the years have also confirmed that physical, technical and economic limits are imposed on development work aimed at improving the efficiency of packing of given basic geometric configuration. By virtue of its low pressure drop in vacuum rectification with a large number of theoretical stages, high-performance column packing offers many advantages. An important factor in the selection of packing is the pressure drop per theoretical stage Ap/nt, because - if the pressure at the head of the column is given - it governs the pressure at the bottom and thus the product temperature and energy consumption. In addition, if the principle of the heat pump is considered, the total pressure drop between the head and bottom of the column determines the economics of the separation process. Consequently, the specific column volume vv should be adopted as a criterion if the packings to be compared have the same pressure drop per theoretical stage. The first energy crisis triggered off a growing demand for column packing with a low pressure drop. As a consequence, a pronounced trend set in towards stacked and random beds with a moderate pressure drop per theoretical stage Ap/nt. Since gauze packing is very expensive and tends to foul in a number of applications, the compelling idea arose to

77.6

259

State of the art in the development of packing

replace the gauze by structured sheet metal yet to retain the beneficial features of a wellknown type, e.g. Sulzer Packing BX. The aim was to achieve a higher efficiency than that attainable with smooth sheet metal. These considerations led to Mellapak 250 Y and other designs of similar basic geometry. They also gave rise to new structures and designs with and without perforations. The evaluation of results of experimental studies on some of these packing variants is presented in Fig. 11.9. It can be seen that the question of which surface structure on the sheet metal should include perforations is practically immaterial from the aspect of the attainable minimum specific column volume. The results of the experiments presented in Fig. 11.10 reveal that the efficiency of a perforated structured surface is somewhat higher than that of a smooth unperforated surface but no better than that of an unperforated structured surface. Unmistakable evidence for the efficiency at the surface of some modern packing elements shown in Fig. 11.11 is provided in Fig. 11.12, which represents the function a' = i{a) {cf. Eqn (11-52)}. The curve demonstrates, just as convincingly as those in Fig. 11.8, the decrease in the degree of exploitation of the available surface that occurs with an increase in its area a. Equally convincing evidence is given in Table 11.5 to the effect that, despite the differences in surface structure and the completely different basic geometry, the surface efficiency of random beds of modern packing may be just as good as that of geometrically arranged beds operated under the same conditions.

Chlorobenzene/Ethylbenzene 67mbaf\ L/V = 1

0.12 \\

•V \\

0.10

lellapak 250 Y lontz pock. B1-300 / •alupak 250 YC

\

V \\ \

0.08

\

^ 0.06

J

<;hoc

CD

f 0.04 i

0.08

I

Sontz pack. A1

/ —.

V

0.06

alzer pack. BX

- Gauz( Fig. 11.9. Specific column volume as a function of the specific pressure drop for sheet-metal and metal-gauze packing

0.02 0

0.5

1

1.5

2

2.5

Specific pressure drop Ap/n,[mbar]

3

260

//

Overall evaluation of packing

Chlorobenzene/Ethylbenzene L/V-1, PT*67mbor

~ 25

-u-

CO m

Montz-pock B1-300 o Structured a Structured+perforatecl a Smooth

II*

20

I•

a, 15 E ig o

\

> 10

c?

c:

q> o

"

•LJ..

1

iCL-

0 0

0.5

1

1.5

2

2.5

3

3.5

Specific pressure drop Ap/n t [mbar] Fig. 11.10. Effect of the surface structure on the specific column volume as a function of the specific pressure drop in a bed of arranged packing

Table 11.5. Process engineering ratings and data on the surface effectiveness of selected types of metal packing System: Chlorobenzene/Ethylbenzene 67 mbar, liquid/vapour ratio 1 F v vapour capacity factor v v specific column volume a area per unit volume a' performance-related area Packing

Ap/n t [mbar]

1

2

3

Mellapak 250 Y a = 250 m 2 /m 3

F v [m 1 / 2 s 1 kg1/2] v v [m3s/m3] a' [m2s/m3]

2.56 0.067 16.75

3.025 0.053 13.25

3.3 0.078 19.5

Gempak 2 A T-304 a = 200 m 2 /m 3

F v [m 1 / 2 s"1 kg1/2] v v [m3s/m3] a' [m2s/m3]

2.46 0.087 17.5

3.24 0.055 11.0

3.6 0.048 9.6

Glitsch No. 1.5 T CMR a = 173 m 2 /m 3

F v [m 1 / 2 s 1 kg-] v v [m3s/m3] a' [m2s/m3]

1.8 0.137 23.70

2.5 0.082 14.18

3.1 0.056 9.69

Hiflow ring 50 mm a = 92 m 2 /m 3

F v [m 1 / 2 s 1 kg1/2] v v [m3s/m3] a' [m2s/m3]

2.04 0.192 17.86

2.68 0.134 12.46

3.02 0.101 9.39

11.6

State of the art in the development of packing

By virtue of their outstanding process engineering characteristics, random beds of performance packing are now also used for very large capacities, e.g. plastics Hiflow in columns of 9 m diameter and 35 m height. Hence, there are many types of packing, than structured, that have been developed to keep pace with the growing demand and an interesting alternative in certain processes.

Fig. 11.11. Examples of recent types of packing

261

highrings other allow

11

262

Overall evaluation of packing

Chlorobenzene/Ethylbenzene 67 mbar, liquid/vapour ratio L/V=1 Specific pressure drop 3 mbar

60

100

140

180

220

260

300 2

340

380 420

3

Area per unit volume a [m /m ] Fig. 11.12. Relationship between the performance-related and geometric areas for recent types of packing

11.7 Optimum area per unit volume in beds of packing Economic evaluation of column packing entails that the efficiency must be weighed up against the costs involved in its realization. They depend on the basic price for the materials of construction, the volume of materials per unit volume of product, and the running costs. In general, the process engineering aspects are confined to the efficiency, pressure drop, and capacity, but an economic study lays emphasis on the costs-to-performance ratio. If the shape of the packing is given, this necessarily raises the question of the optimum area aopt per unit volume, which can be derived from costs considerations by the procedure outlined in Fig. 11.13. The first step is to determine as a function of the area per unit volume a the costs Kp of the performance-related area a', which depends on the costs per unit area Cp of the packing installed, i.e. Kp = a'Cp = avvCp

(11-53)

The area as of the column shell per unit flow rate and unit efficiency is given by ndsH

as = Jt

2

4 = -r vv "J

l

— ds uvnt

(11-54)

11.7

Optimum area per unit volume in beds of packing

263

costs K - ^ ^ - ^ ^ ^ —mS-\

Kmin

•

"""

1 1 a opt.

....•••*"

Costs

^ shelf

"^-

ds = const. Area per unit volume a [mz/m3] Fig. 11.13. Graph for the determination of the area of a packed column that permits minimum costs

The column shell costs Ks corresponding to as are (11-55) where Cs is the costs per unit area of shell. The sum K of the costs items is js

js

,

Cs

-ty-

=i (a)

(11-56)

At the value for aopt, K passes through a minimum, which is given by Ks) da

= 0 - > aopt

(11-57)

If the column is of large diameter, the effect exerted by the costs Ks corresponding to the area as is reduced. Four types of metal packing, one of them structured, will now be taken as an example to illustrate these relationships. The specific column volume vy, as defined by Eqn (1-34), is shown as a function of the area a per unit volume in Figs. 11.14 to 11.18. The relationship can be described by an equation of the following form:

264

11

Overall evaluation of packing

VV=

W-A+.

(11-58)

where A and B are constants. The costs function follows from Eqns (11-56) and (11-58), i. e. (11-59) The costs Cp per unit of packing installed are given by Eqn (11-60); and the costs Cs per unit area of column shell, by Eqn (11-61): Cp = C + Da

(11-60)

Cs = E + Fds

(11-61)

where C and D are costs factors that apply to a specific packing, and E and F are the corresponding factors for the column shell. Eqn (11-61) applies if the column diameter ds and thickness s lie in the range ds < 1 m, s = 6 mm through ds ~ 2 m, s = 8 mm to ds ^ 3 m, s = 10 mm and the material of construction is stainless steel (18 Cr 10 Ni 2.5 Mo - German steel number 1.4571). The total costs K are therefore given by —+ B a

a(C + Da)

4[^ + F

(11-62)

Numerical values for the factors A and B (derived from Figs. 11.15, 11.17, and 11.18) and for C, D, E and F (estimated from manufacturers' data) are listed in Table 11.6. Eqn (11-62) is presented graphically in Figs. 11.19, 11.20, and 11.21. The curves are valid for traditional random packing (represented by Pall rings), modern random packing

Nominal ring size d [mm "e

13

50

35

25

15

yre le ' 33 nba r, -t V ma>:. ccipac it v CO .80 f^eto 1 R DSCflio rino

F hyl "IPfTIGDG \

kH i 10

100

Fig. 11 14. rings

200 300 Area per unit volume a [m 2 /m 3 ]

7

400

Relationship between the specific column volume and the area of beds of metal Raschig

11.7

265

Optimum area per unit volume in beds of packing

(represented by Glitsch Cascade Mini-Rings), and stacked packing (represented by Montz Bl). It can be seen that the total costs K depend greatly on a and ds and that the optimum area aopt per unit volume is a function of ds.

50

Nominal ring size d [mm ' 25

35

3 13 CL>

t 12 \ 11

15

' ' I r Q /C> t .thy Iben zene/ o tyrene 133 mbar, -- =

\\

1

c:a.8 0% max. capacity

Metal Pall rings

"i 10

i

r 100

200

— 400

300

Area per unit volume a [m 2 /m 3 ]

Fig. 11.15. Relationship betwen the specific column volume and the area of beds of metal Pall rings

Nominal ring size d [ m m '

50 35 12

15

25 1 1

11

Methanol/Ethc nol i 1

9 \ _ O

i

10

i_

DCir.

L

-'

V

r:a.80°/«3 mo* r.nn acity

\

N

\

«1etc I Pall f"innc 1 200

—

400

300 2

3

Area per unit volume a [m /m ]

Fig. 11.16. Relationship between the specific column volume and the area of beds of metal Pall rings

11

266

Overall evaluation of packing

Nominal ring size d[inches]

2.5

2

1.5 1.5T

1T

\ 1e\

PL

0.5

1

/ C 1L . .1 U _. _

Ihiuruuenmi e/t thylDenzene o/ muui, V 1 -

c ^\

: a . 8 0 % max. capacityI \

o 7 ^"•^^

IB S.

5

— —

letal Gl tsc ) C 3SC(ide Mini Ri igs 1 1 1 n

100

200

300 2

•o

400

3

Area per unit volume a [m /m ] Fig. 11.17. Relationship between the specific column volume and the area of beds of Glitsch CMR packing

10

i I I I :• - Chlor Dbenzene/Ethylbenzene 67 mbar,4- = 1

c a . 8 0 % max. capacity

/ )

^ 7 >

Mellapak 250 Y

S.

° 6

Lh

"o 5

—^

f^lontz niGta [ I

200

300

i

pprl^inn •a

500

400 2

3

Area per unit volume o [m /m ] Fig. 11.18. Relationship between the specific column volume and the area of arranged beds of packing

11.7

Optimum area per unit volume in beds of packing

267

Differentiating Eqn (11-62) with respect to a gives rise to aopt, as is indicated by Eqn (11-57). Thus ^- + F\= alpt (AD + BC) + 2 BDalpt

(11-63)

If the numerical values for the factors A to F listed in Table 11.6 are inserted in Eqn (11-63), the graphical relationship illustrated in Figs. 11.22, 11.23, and 11.24 can be obtained by plotting the optimum area aopt per unit volume against the column diameter ds. According to the curves reproduced in Fig. 11.22, the value of aopt corresponding to a shell diameter of ds > 2 m is aopt < 120 m 2 /m 3 , and the associated optimum diameter of the Pall ring is d > 50 mm. The value for stacked Montz Bl or packing of similar geometry and efficiency is aopt = 200/300 m 2 /m 3 . The dashed lines in the diagrams apply for the case in which the costs of the packing may vary by ± 25 %. If D = 0, Eqn (11-63) is simplified to

Substituting Cs for (E + Fds) {Eqn (11-61)} and Cp for C {Eqn (11-60)} then gives

In other words, the optimum area aopt per unit volume is governed by the costs ratio CJCp and the column diameter ds.

Table 11.6. Costs function factor for some types of packing Factors for cost functions

Ethylbenzene/ Styrene 133 mbar Pall ring

Chlorobenzene/Ethylbenzene 67 mbar Glitsch CMR Montz packing Bl

A (m2/m3/s)

7

4

16

B (m /m /s)

0.07

0.04

C (DM/m2)

14

6

0.018 22 + 6/ds

D (DM/m)

0

0.077

0

3

3

E

(DM/m2)

F

(DM/m3)

640 for 0 .5 m < ds < 4 m 180 for 0 .5 m < ds < 4 m

268

11

Overall evaluation of packing

Ethylbenzene/Styrene133 mbar, L/V=1, Fv = 0.8F Vmax Nominal ring size d [mm] 80 50 35 25

Area per unit volume a [m 2 /m 3 ] Fig. 11.19. Effect of the diameter of a column packed with metal Pall rings on the total costs and the area that permits minimum costs

Chloro-/Ethylbenzene 67mbar, L/V=1, Fv--0.8F Vmax. Nominal ring size d [inches] 2.5 2 1.5 1

700 en

costs Kit

_E

600 500 400 300

15E

\

800 \ \

v \ V \\

\ \

1E

i Kmin

\

> A

y/

^—

7

s

/

7 /

y /

^\y

/

/

/ />

/ -^

Metal Glitsch CMR 200

i

i

i

100 200 Area per unit volume a [m z /m 3 ]

300

Fig. 11.20. Effect of the diameter of a column packed with metal Glitsch CMR on the total costs and the area that permits minimum costs

11.7

Optimum area per unit volume in beds of packing

269

Chloro-ZEthytbenzene 67mbar,L/V=l

1100

\

\

1000

Kmin \

0

?5rr)

\

= 800

\j

.

\

7.5

y

——. -

\

4? 900

7

/

at ?

1 700 1

a

*

— — —- -

— —

. -

d—

—. ———

° 600

4

500

m

Ann,

[

r-7

n

1

ne

L II ietci I

200

PIjcki

-

—

—

— ———

"

— — —

m

-

-

-

——

Bl-

300 2

400 3

Area per unit volume a [m /m ] Fig. 11.21. Effect of the diameter of a column packed with metal Montz Bl on the total costs and the area that permits minimum costs

250

Stainless Steel Pall ring

\ 200 s

o

150

\\ \

s

***

CD

a

25

°

•

100

^

—

•

35 •*

*-—' —«. —•

•

^•—

'75 •cP

m

—

CD

— — —— - —

50 M _ __

50 0

1.0

1.5

2.0 2.5 3.0 3.5 Column diameter d s Im]

4.0

4.5

5.0

Fig. 11.22. Optimum area as a function of the diameter of columns packed with metal Pall rings

270

11

300 ^ "

1 1

1 1

250

a. o

Overall evaluation of packing

200

a

Stainless ste el Glitsch-C MR

V

£ 150 a "a

I

1— r—

— —. — * —

• 2.5

'——.

p ~~

•

50

0.5

1

1.5

2

2.5

3.5

3

Column diameter ds [ m ] Fig. 11.23.

Optimum area as a function of the diameter of columns packed with metal Glitsch CMR

400

1 1 • Stainless steel

\ \

350 \

\

- Montz packings B1-

\

I

\

°° 300

•cP-

O QJ

r

I

250 - ^

5 °

z

-c

•

—

0.5

1.0

1.5

2.0

—

. —

•

—

—

.

•

-

*

2.5

——

—

—. * -

—

—

—

-

^"7—

P

200

—

3.0

3.5

4.0

•

>-—-

-

4.5

r 5.0

Column diameter ds [ m ] Fig. 11.24.

Optimum area as a function of the diameter of columns packed with metal Montz Bl

11.8 Limits to the further development of packing It is evident from the above analysis that the design measures that can lead to a noticeable improvement in efficiency per unit area are restricted in number, regardless of whether they are applied individually or combined for modifying existing packing or for developing new types. In many cases, the improvements that can be achieved are no better than moderate. As is evident from Fig. 11.25, the enlargement of the area per unit volume always leads to a reduction in the specific column volume vv and thus to an increase in the volumetric efficiency Ev, which is defined by

E -J---2t,y —

—

vv

a

(11-66)

11.8

_ 28

1

1 \

Ethylbenzene/Styrene 133 mbar

\

1

\

Chlorobenzene/Ethylbenzene 67 mbar \

L/V-1 Specific pressure drop 3 mbar \

\

u

\

16

\

\

\

"-V

60

•—--.

ckino •—«.

20

I rQdit'mr)nl •—«. •——

_

P" — —

100 140

— -

1

180

220

=====

260

300 340 z

380

420

460 500

3

Area per unit volume a [m /m ] Fig. 11.25. Specific column volume and volumetric efficiency as functions of the area for beds of traditional and modern packing

The curves in Fig. 11.25 were derived from those shown in Figs. 11.8 and 11.10 and from the following relationship:

Vy

=

(11-67)

They reveal the limits that are imposed on the development of column packing. The limit to which the volumetric efficiency Ev tends corresponds to an area per unit volume a — 350 m 2 /m 3 , and cannot be significantly improved at higher values of a. The process engineering criteria adopted for the technical evaluation of column packing include the liquid holdup hL per unit column volume, the vapour flow rate at the loading uVjS and flood uv>Fi points, the pressure drop per unit height of bed Ap/H, and the volumetric mass transfer coeffients in the liquid |3Lap^ and vapour ^yaPh phases. These parameters also govern the packing performance from the economics aspect, because they decide the specific column volume vv. The relationships for their determination are dealt with in Chapter 4 and 5. The other parameters in these relationships concern the system to be separated, the operating conditions, and the design. The system parameters are the phase densities QL and QV and dynamic viscosities r\L and r\v; the operating parameters are the volumetric flow rates uL and uv and the liquid/vapour ratio L/V; and the design parameters are the packing's area per unit volume a, the relative void fraction 8, and the empirical factors that define the packing's shape and surface, i.e. the factors in the relationships for the liquid holdup Ch, the flow rate at the load Cs and flood Cpi points, the pressure drop Cp, and the volumetric mass transfer coefficients on the liquid CL and gas Cv sides.

7 8 9 10 12.5 15 20 25

QJ O

eff

•

(_>

'olu metr

20

271

Limits to the further development of packing

272

11

Overall evaluation of packing

The relationship for the liquid holdup (hLS)P follows from Eqns (4-73) and (4-74), i. e. h L t S = Ch a 0 5 1 6

(11-68)

The relationship for the vapour flow rate at the load point uVyS for a given system is obtained from Eqns (4-26) and (4-29), i.e.

fs = Cs (e - hLiS) A/ ^f

~ uv,s

(H-69)

The corresponding relationship for the vapour flow rate at the flood point can be derived from Eqns (4-35) and (4-41), i. e.

=

/F/

Another factor that affects hydrodynamic evaluation is the pressure drop per unit height of bed (Ap/H)s at the loading point. In the model, it is described by Eqn (4-58), with 5L = ^s/w> and Eqn (4-26) with uv = uvs- The relationship for the theoretical design factors that influence the pressure drop at the loading point in the model can be obtained from these two equations, i.e.

JAp,S '•

It can be concluded from Eqns (5-4), (5-13) and (5-16) that the design parameters that affect mass transfer on the liquid side are the area per unit volume a and an empirical constant CL, which is characteristic for the packing geometry and texture and is given by fL = CLa1/6~?>LaPh

(11-72)

Likewise, mass transfer on the gas side depends on the area per unit volume a, a factor Cv that is characteristic for the packing geometry and texture, and the void fraction available for the flow of vapour (e - hL), i.e. (H-73) Pall rings have been used successfully in industry for more than 35 years and are a convenient reference for comparing the hydrodynamic parameters selected for evaluation. Thus differences in the liquid holdup hL can be expressed by the ratio of the value for the packing concerned to that for 50-mm Pall rings, i.e. ru hL s

'

=

h£ hL,s (Pall-50)

=

fhis

!h±± (Pall-50)

(U 1

K

11.8

Limits to the further development of packing

273

Differences in the flow rates at the loading and flood points can be expressed by the corresponding ratios, i.e.

Uv Fl

'

Uy,S

fs

uvs (Pall-50)

/ 5 (Pall-50)

uv>Fl (Pall-50)

(11-75) (11-76)

fViFt (Pall-50)

The ratio for the pressure drop at the loading point is

hP,s p

'>

(Ap/H)s

(Pall-50)

(11-77)

fAp>s (Pall-50)

The corresponding ratios for mass transfer on the liquid rL and gas rv sides are given by the following equations:

h $LaPh (Pall-50)

(11-78)

fL (Pall-50)

ftyflp/, fy

(11-79)

rv = § a (Pall-50) " f (Pall-50) v Ph v

Three types of packing have been chosen to demonstrate the application of Eqns (11-72) to (11-79) in the light of the results of experimental studies (Table 11.7). Two of them are

Table 11.7. Characteristic data for some types of metal packing Glitsch rings

P-Modifications 30 P

No. 0.5

30 PmK

CMR 304

Shape in metallic version

d[m]

0.030

0.030

h[m]

0.030

0.030

0.5-10-

s [m] 3

N [1/m ] 2

3

a [m /m ] 3

w [kg/m ]

0.28-lO"

0.005 3

0.2 -10- 3

32509

28445

560811

169

180

357

0.958

8

3

0.015

319

0.975 200

0.955 348

11

274

Overall evaluation of packing

similar, viz. the 30 P metal and the 30 PmK Glitsch rings. They differ from one another in wall thickness s and in the fact that the ends of the former are smooth and those of the latter form a collar; in other words, the parameters that differ are a and 8. The third packing to be discussed is the CMR Glitsch ring No. 0.5, whose shape and size differ completely from those of the other two. The values measured for the liquid holdup are shown as a function of the liquid and vapour loads in Figs. 11.26 to 11.28. After the loading point has been exceeded, the liquid holdup rises rapidly until, in the bed of CMR Glitsch No. 0.5 rings, it attains a value as high as 30 % of the void fraction at the flood point. The corresponding pressure drop measurements have been plotted in Figs. 11.29 to 11.31. The pronounced rise in pressure drop with an increase in the liquid load, and thus in the holdup, is clearly evident.

PT 10

^

8 . Air /hl 2 O.1bar,293K - Glitsc h 30P metal 6 lm.N=32509m-3 - H=1.3fDm. Z=1013 m-2

r

cr

cr

£

Fv =1nH'

1

1.5 2

3

4

-1 kgi/2

6 3

1—

8 10 3

15

2

Liquid load 10 -U|_[m /m s ]

0.3 0.4

0.6 08 1.0

Gas capacity factor F v [nr

1.5 2.0 1/2

1

3.0 1/2

s" kg ]

Fig. 11.26. Liquid holdup as a function of load in a random bed of metal Glitsch 30 P packing as listed in Table 11.7

11.8

275

Limits to the further development of packing

Figure 11.32 shows the results of the separation efficiency experiments and the corresponding pressure drop measurements. The Glitsch 30 P and 30 PmK rings have practically the same efficiency, but the associated pressure drops differ considerably over the packed bed. Both the efficiency and the pressure drop of the Glitsch ring No. 0.5 CMR 304 are decidedly higher than the corresponding figures for the other two packings. The relationship between the specific column volume Vy and the pressure drop per theoretical stage lS.plnt is given by

Vy

=

Qv

(11-80)

Fv (nt/H)

Figure 11.33 shows that, at any given value of Ap/nt, the value of vv required to achieve the one theoretical stage and unit vapour capacity is significantly less for the Glitsch ring No. 0.5 CMR 304 than for the other two packings. Figure 11.34 demonstrates that the Glitsch ring No.5 CMR 304 is also superior to the other two in respect of the volume of packing required to achieve unit efficiency and unit volumetric vapour load v' {cf. Eqn (11-51)} at a given pressure drop per theoretical stage. The diagram includes the corresponding curves for the specific mass of the packing vv', which is related to v' through the weight per unit volume w of packing, i.e.

i—

hz = 1 m-1/2

i

s -1

I

jj

B

S1

kg n

i

Air/H20,1bar. 293 K . -Glitsch 30 PmK ds=0.3.N=284< H=l.32m.Z=10 13m-2

•s ZD

CJ

1.5 2 3 4 6 8 10 Liquid load 103-uLlm3/m2 s]

I

15

1 10

4u -o •V. o - o -oc o - -ol —

•UL=

o-

53 Fig. 11.27. Liquid holdup as a function of load in a random bed of metal Glitsch 30 PmK packing as listed in Table 11.7

0.4

r

i

r \ J

30

CKXX

20rriVm2h

I i

—ok>—•opcoo 10

0.6 0.8 1.0

1.5 2.0

3.0

Gas capacity factor F v l n r 1 / 2 s-1 kg 1/z ]

15

11

276

Overall evaluation of packing

(11-81)

w = v w

Numerical values for the area per unit volume a, the thickness of an element of packing s, and the weight of unit volume of packing w are presented in Table 11.7, and Eqns (11-51) and (11-52) were evaluated with values of vv taken from Fig. 11.33. Yet another feature that underlines the superiority of the Glitsch ring No. 0.5 CMR 304 in this comparison is the average liquid residence time per theoretical stage tLlnt {cf. Eqn (11-5)}, which is an important factor in the separation of thermally unstable mixtures. The relevant functions are presented in Fig. 11.35. Factors on which the residence time depends are the liquid holdup hL, the separation efficiency nt/H, and the liquid flow rate uL, which in this case is given by QV

(11-82)

_ 20 n

f

,5

>n

1kCVI

Fv=1m-'

jy

=2 10

- A ir/H 2 0.1 bar.293K bl tsch No.0,5C ^IR3U4 dc;=0.3m,N=560 811m-3 H=1.11m, Z=101: 1m- 2

§•

5 6 15

2

3

4

6 3

8 10 3

15

2

Liquid load 10 -Ui [m /m s] 40 n

30

V0

20 ZD -CD

4

- -°n

15 o10 8 6

u

>—

I

JH1

>o-oc

! ZOmVmZh 0-

n

\J 5

o

yet*

0.3 0.4 0.6 0.8 1.0 1.5 2.0 3.0 Gas capacity factor F v [rrr 1/2 s"1 kg 1/2 ]

Fig. 11.28. Liquid holdup as a function of load in a random bed of metal Glitsch No. 0.5 CMR 304 packing as listed in Table 11.7

11.8

277

Limits to the further development of packing

Characteristic geometrical data and (separately determined) model parameters for the three Glitsch packings discussed above are listed in Table 11.8 together with the corresponding values for 50-mm Pall rings. Table 11.9 lists the results obtained in evaluating Eqns (11-73) to (11-79). Again, 50-mm Pall rings were taken as reference. The above relationships for the performance of column packing give an idea of the limits within which packing elements of given basic geometry may be developed. According to Eqn (2-4), the relative void fraction increases with a decrease in the thickness s of the packing element. Substituting this relationship for in Eqn (11-69) gives rise to the following for the design parameters that influence the loading point: (11-83)

Air./H 2 0.1bar. 293K Glitsch 30 P metal ds=0.3m, N=32509m-3 H=1.36m, Z=1013m-2 Fig. 11.29. Pressure drop as a function of load in a random bed of metal Glitsch 30 P packing as listed in Table 11.7

0.4

0.6 OS 1.0

Gas capacity factor

1.5 2.0 F v [nr

1/2

3.0 4.0 j

s~ kg V2 ]

278

11

Overall evaluation of packing

200

i

150 o 100 h -o 0 © 60 • 50

„

i?

] 0 10 20 30 40

A

& I'Kr

ffffi A /

3

i

I°

MA

Sk

1 . 20

m

<3 a- 1S

0

w/

10 8 6 5

«

A ir /I 1/ Air/t^0,1 bar 293 K

/j • / ft

2

'A

Wi

m

I 40

QJ

/

4V

. filter h ulllSL

30 PmK d s =0. 3m. N=28445 H=1.3 2m. Z=1013m- 2

y

v/ f

0.4

0.6 0.8 1.0

Gas capacity factor

1.5 2.0 Fv[rTr1/2

Fig. 11.30. Pressure drop as a 4.0 function of load in a random bed of metal Glitsch 30 Pmk packing as listed s~1 kg1/2] in Table 11.7 3.0

Table 11.8. Characteristic data for packing as listed in Table 11.7 compared to those for 50-mm Pall rings Packing 30 P 30 PmK 0.5 CMR 304 50 Pall ring

a

E

ch

Cs

cF1

cP

cL

Cv

31100

164.0

0.959

0.851

2.564

1.760

1.056

1.577

0.398

29200

180.5

0.975

0.930

2.694

1.900

0.851

1.920

0.450

552000 356.8 6242 112.6

0.955

1.338 0.784

2.644

2.178

0.882

0.495

2.725

1.580

0.763

2.038 1.192

N

0.951

0.410

11.8

279

Limits to the further development of packing

400 U|_[m3/m2h o 0 -o10 0 20 e 30 • 40

300 200 150

—

100

)—

«f

i

1 80

4A

/

l\ •?rr)

(JD

JL'p/ J

e

_ 50 ^ 40

'OS/

1 30

7/

e

| |

/

20

J •J

15 10 8

m

¥

w, i 7

6 5 4

p

Air/H 2 0.1 bar, 293 K Glitsch No.0,5CMR 304 ds=0.3m,N=560811m-3 H=1.11m. Z=1013m- 2

— —

f-—

3 Fig. 11.31. Pressure drop as a function of load in a random bed of metal Glitsch No. 0.5 CMR 304 packing as listed in Table 11.7

0.4

0.6 0.8 1.0

15 2.0

Gas capacity factor

F v [m-

1/2

3.0 4.0 1

s" kg 1/z ]

Table 11.9. Comparison of the metal packings listed in Table 11.7 with 50-mm metal Pall rings with respect to liquid holdup, Eqn. (11-74); loading and flooding flow rates, Eqns. (11-75) and (11-76); pressure drop at the loading point, Eqn. (11-77); and volumetric mass transfer coefficients in the liquid and gas phases, Eqns. (11-78) and (11-79). Reference system: water/air at STP, uL = 10 nr7m2h Packing

r

h,s

rUvs

r

uVF1

r Aps

rL

rv

30 P

131

0.83

0.90

1.38

1.41

0.928

30 PmK

1.465

0.90

0.96

1.36

1.74

1.14

0.5 CMR 304

2.747

0.677

0.72

1.851

2.074

1.227

Reference packing: 50-mm metal Pall rings

uL = 10-

m3 m2h

hL.s m 3 /m 3

Uy.s

2.45

2.23

m/s

Uv.Fl

m/s 2.98

PvaPh

(Ap/H) s mbar/m

s"1

s"1

32.5

7.04 • 10"3

6.86

MPH

280

11 Overall evaluation of packing

The corresponding relationship for the flood point can be derived from Eqn (11-70), i. e.

I - — as

-hL)Fi

(11-84)

fFi — Cfi

Hence the potential allowed for increasing the load by decreasing the wall thickness is limited. It is also evident from Eqns (11-83) and (11-84) that the factors that decidedly affect the load are Cs and CFt. They govern the resistance factors | 5 and §F/ at the loading and flood points {cf. Eqns (4-29) and (4-41)} and thus the associated vapour and liquid flow rates uV}S and uVtFl {cf. Eqns (4-28) and (4-35)}. The importance of these factors and parameters is impressively demonstrated in Figs. 11.36 and 11.37, which were plotted from the solutions to Eqns (4-28), (4-29) and (11-82) and the values listed in Table 4.1. Despite the fact that the packings concerned are of the

T* 4 -o—

——'_-o •

—

•o— r

o

i

"1

£1

ULJ

I

0 240

" -

200 160 CZL

' _

Chloro-/Ethylbenzene 67mbar, L/V= , H = 1.5m " ds= 0.22m, Z=600m"2 Glitsch No. 0.5 CMR 304 o N = 552037m-3 Glitsch 30 P metal a N -- 31968 m"3 Glitsch 30 PmK, metal v N = 29151m"3

120

1

dI // // -4 7 / /I1 / /

f

<

/ /

80 r-

CD

7?

/

/ /

40 SS=—— 0.4 Fig. 11.32. Table 11.7

0.8 1.2 1.6 2.0 2.4 Vapour capacity factor F v [nr 1/z

2.8

3.2

3.6

Efficiency and pressure drop as functions of load for the various metal packings listed in

11.8

281

Limits to the further development of packing

same size, significant differences exist even between packings of the same material, particularly plastics. Theoretically, the wall thickness also exerts a comparatively slight effect on gas-side mass transfer, as is evident from the following relationship, which has been derived from Eqns (2-4) and (11-73): (11-85) - — as-hL In theory, mass transfer on the liquid side is unaffected by wall thickness. However, an exception may arise if a change in wall thickness effects an attendant change in the packing density of a random bed and thus in the area per unit volume a and liquid holdup hL. A reduction in the thickness of the packing element may also give rise to a decrease in pressure drop to an extent that can be determined from the following relationship, which applies to conditions at the loading point and can be derived by substituting (1 - V2 as) {cf. Eqn (2-4)} for 8 in Eqn (11-71): (11-86) - — as-hL If the Glitsch 30 P and 30 PmK rings are taken as an example, it can be demonstrated

Metallic Glitsch packings Chlorobenzene/Ethy(benzene 67mbar, L/V=1

20

•3 10 >

I 5 Fig. 11.33. Specific column volume as a function of the specific pressure drop for the various metal packings listed in Table 11.7

I \ \ \ \ \ ^>^N \ °° \

. . . . .

-

•

—

*

-

-

,

—i

— —

0.5 1 15 2 2.5 Spec, pressure drop Ap/n t [mbar]

1

3

282

11

Overall evaluation of packing

that a decrease in wall thickness in conjunction with a minor design change - in this case an alteration in the ring collar - may effect an increase in the void fraction and thus a substantial reduction in pressure drop at all flow rates. An increase in load at the flood point, however moderate, may also be achieved by this means. Structuring the surface of the packing may have a beneficial effect on mass transfer if it allows better liquid distribution and thus an increase in the phase contact area. The effect of the packing's surface area on process engineering parameters, particularly the capacity factor, is evident from the above equations and is demonstrated in Fig. 11.38, which was plotted from experimental data. The size, shape, and finish are the main packing factors that influence the process. They are expressed in the equations by the empirical C factors, numerical values of which are listed in Table 11.8 for some types of packing. The figures give an idea of the technical limits that are imposed on improving the efficiency.

Metallic Glitsch packing Chiorobenzene/Ethy[benzene 67mbar, L/V=1

\ \ 60 cp CD

\

\

JOP

N

\

40

%

< 20

— —

0 10

CD >

I \ \ \\ \ \ \ 0

>

\

tyfi \ ^

^ s

• * • —

* - — ^ — - ,

•—»

CD CO

0.5 1 1.5 2 2.5 Spec, pressure drop Ap/n t [mbar]

—

—

Fig. 11.34. Volume of material and mass of packing, both expressed in terms of the efficiency and the volumetric vapour flow rate, as functions of the specific pressure drop for the various metal packings listed in Table 11.7

11.8

283

Limits to the further development of packing

Tables 11.10 and 11.11 list process engineering parameters required for the global evaluation of random and stacked beds. The reference value selected for the comparison is the pressure drop per theoretical stage Ap/nt, which is responsible for differences in the load factor Fv and the column diameter ds. The yardsticks adopted for the material requirements are the specific column volume vv and the weight w' and area a' of packing per unit of separation efficiency and throughput. Significant factors in evaluating packing for systems that are sensitive to heat are the liquid holdup h'L per unit of efficiency and throughput and, as a consequence, the liquid residence time per theoretical stage tLlnt. Another factor to which consideration must be given in the design of random and stacked beds of packing is the mechanical strength or the physical constants of the material. The idealized stress-strain diagrams shown in Fig. 11.39 for 50-mm Pall rings illustrate this point. The assumptions made in plotting the graphs were that the load is always applied in the radial direction and that the open joint lies in the centre of the ring. The applied pressure in terms of bed height was calculated from theoretical considerations. As would be expected, the thickness of the ring exerts a considerable effect on the load under which plastic deformation occurs. In further experiments, it was ascertained that the deformation in rings with spot-welded joints was only one-quarter of that in unwelded rings. It is obvious from the above remarks that fluid dynamic and efficiency studies are absolutely essential in the design of column packing and that they necessitate well-equipped pilot plants. Some of the author's pilot plants are illustrated in Chapter 3 and in Fig. 11.40

20 ,

15

h

61Itr,

10

b

S

'tsch

6

%

13

^

1.5

~ A D O

1 0.1

2.3 2.1 1.9 0.2

'

30,

?Op-- ^

05 n

rtr

LMfx

Loading capac ty 2

;

[ m i/2

0.4

s-i

Chlorobenzene/Ethylbenzene 67 IT bar, L/V = 1

" ^

ka V 2 l

0.6 0.8 1

1.5 2

3

4

5 6

Specific pressure drop Ap/n t [mbar] Fig. 11.35. Relationship between the specific liquid residence time and the specific pressure drop in rectification columns with the metal packings listed in Table 11.7

284

11

Overall evaluation of packing

Table 11.10. Parameters for comparing random beds of high-performance metal packing Dumped packing

Ap/n t [mbar]

Glitsch No. 1 CMR w = 390 kg/m 3 a = 249 m 2 /m 3 E = 0.969 N = 169930 nr 3

Fv [ m - ¥ k g 1 / 2 l v v [m3s/m3] w' [kg s/m3] a' [m2s/m3] h[ [m3s/m3] t L /n t [s]

1.56 0.127 49.53 31.623 2.03 • 10"3 7.18

2.28 0.076 29.64 18.924 1.55-10"3 5.49

2.88 0.041 15.99 10.209 0.966-10' 3.42

Glitsch No. 1.5 CMR w = 306 kg/m 3 a = 186 m 2 /m 3 e = 0.972 N = 64495 m-3

Fv [m-¥kg1/2] v v [m3s/m3] w' [kg s/m3] a' [m2s/m3] hi [m3s/m3] t L /n t [s]

1.8 0.1327 41.92 25.48 1.75-10"3 6.2

2.48 0.083 25.40 15.44 1.66-10"3 5.87

2.96 0.055 16.83 10.23 1.1-10"3 3.89

Glitsch No. 1.5 T CMR w = 215 kg/m 3 a == 173 m 2 /m 3 8 = 0.970 N = 62432 nr 3

Fv [m^'VV' 2 ]

v v [m3s/m3] w' [kg s/m3] a' [m2s/m3] h' [m3s/m3] t L /n t [s]

1.8 0.137 29.46 23.70 1.86-10-3 6.58

2.5 0.082 17.63 14.18 1.5-10"3 4.985

3.1 0.056 12.04 9.69 1.14-10"3 4.05

Pall rings 25 mm w = 390 kg/m 3 a = 215 m 2 /m 3 e = 0.942 N = 53200 nr 3

F v [m^'Vkg 1 ' 2 ] v v [m3s/m3] w' [kg s/m3] a' [m2s/m3] h[ [m3s/m3] t L /n t [s]

1.34 0.154 60.06 33.11 1.845-10"3 6.542

1.92 0.108 42.12 23.22 1.595-10"3 5.656

2.4 0.072 28.08 15.48 1.236-10' 4.384

Pall rings 50 mm w - 210 kg/m 3 a = 113 m 2 /m 3 8 = 0.942 N = 6358 irr 3

F v [m^'V'kg 1 ' 2 ] v v [m3s/m3] w' [kg s/m3] a' [m2s/m3] hi [m3s/m3] t L /n t [s]

1.6 0.248 52.08 28.02 2.773 • 10"3 9.832

2.26 0.171 35.91 19.32 2.334 • 10-3 8.277

2.74 0.127 26.67 14.35 1.927-10" 6.832

Hiflow rings 50 mm w - 173 kg/m 3 a = 92 m 2 /m 3 e = 0.977 N = 4739 nr 3

F v [m-^V'kg 1 ' 2 ] v v [m3s/m3] w' [kg s/m3] a' [m2s/m3] hi [m3s/m3] t L /n t [s]

2.04 0.192 33.22 17.86 2.147 • 10~3 7.612

2.68 0.134 23.18 12.46 1.797-10"3 6.372

3.02 0.101 17.47 9.39 1.419-10" 5.032

11.8

Limits to the further development

of packing

285

Table 11. 11. Parameters for comparing types of high-performance structured metal packing Packing

Ap/n t [mbar]

0.5

1

2

3

Gempak 2AT - 304 w = 165 kg/m 3 a = 200 m 2 /m 3 8 = 0.979 dr = 0.63 mm

F v [m s kg v v [m3s/m3] w' [kg s/m3] a' [m2s/m3] hi [m3s/m3] t L /n t [s]

1.76 0.133 22.02 26.69 1.5-10 5.31

2.46 0.087 14.44 17.5 1.285 10 4.55

3.24 0.055 9.075 11.0 0.966 • 10 3 3.425

3.6 0.048 7.92 9.6 0.919- io- 3 3.259

Mellapak 250 Y w = 200 kg/m 3 a = 250 m 2 /m 3 8 = 0.96 d, = 0.96 mm

Fv [rn^Vkg v v [m3s/m3] w' [kg s/m3] a' [m2s/m3] hi [m3s/m3] t L /n t [s]

2 0.086 17.2 21.5 1.098- l O 3 3.894

2.56 0.067 13.4 16.75 0.962 10" 3.414

3.025 0.053 10.6 13.25 0.889 • 10"4 3.152

3.3 0.078 15.6 19.5 0.432 • IO 5.078

Ralupak 250 YC w = 290 kg/m 3 a = 250 m 2 /m 3 8 - 0.965 dx = 0.84 mm

Fv [nr^Vkg v v [m3s/m3] w' [kg s/m3] a' [m2s/m3] hi [m3s/m3] t L /n t [s]

2.2 0.073 21.17 18.25 2.098 • l O 3 7.439

2.7 0.056 16.24 14.0 2.012 107.135

3.1 0.048 13.92 12.0 1.839-10-3 6.522

3.22 0.064 18.56 16.0 2.5559.059

Montz packing BI - 300 w = 242.1 kg/m 3 a = 300 m 2 /m 3 8 = 0.93 d, = 1.4 mm

Fv [ m ^ V k g v v [m3s/m3] w' [kg s/m3] a' [m2s/m3] hi [m3s/m3] t L /n t [s]

1.8 0.077 18.64 23.1 0.923 • l O 3 3.271

2.35 0.06 14.53 18 0.862 10~3 3.057

3 0.051 12.35 15.3 0.8143 • 10-3 2.888

3.25 0.048 11.62 14.4 0.8814 103.125

286

11

Overall evaluation of packing

2.0 INTALOX sa jdle 1.8 Bialecki ring

1.6 -

1.2 i

>/ / /

/

—

/

/

/

/ 1:

0.8

u>

7^

0.6

/ /.

0.4

/ •y, >

0

V jr

/

V

/

/

ririg -

,* Bialeck i

N0R-PAC ring

ri

, L Plast ic

/

0.2

yep

^ Pall ring

/

/

/.' I y.

Packing size 50 mm

/

1 / . / .'

f

/, f

1

1.0

/. /

Pall ring ^

/

/

/

y

/

V*

/^/ .

ng.

Hiflow r

/

•*

/

o cz o

/

.•

/

> / - /_

/x

1.4

V

/

1

2

4

i

6

/I

8 10 0 2 Liquid/Gas ratio L / V

Metal 6

8

10

Fig. 11.36. Resistance coefficient at the loading point as a function of the liquid-gas ratio in packed columns, system air /water at STP

11.8

Limits to the further development of packing

287

2.8 i

\

Metal

- Plastic -

\ \

2.6 \

^

2.4

1= 5 2.2

6 2.0 3 3

1.8

i\

NOR-PA C ring-

iT

/VSP r

\

I ji~T

\

V

.Pali ring

\ \ \

V

\ \*

CO

a

CO


1.4

1.2

/

Biaiec
\

\

^^

\

\

1.6

ing

\

*^ \

s.

- Hiflovn ring' /

\Bialecki ring

> /

Packing size 50 mm

^^

/

/

Pall ring

] NTALOX saddle

1.0 8

10

0

2

6

8

10

Liquid/Gas ratio L/V Fig. 11.37. Gas velocity at the loading point as a function of the liquid-gas ratio in packed columns, system air/water at STP

288

11

50

Overall evaluation of packing

Pall ring nominal diameter d [mm] 25 35

15

CMR ring nominal diameter d[inches] 2 1.5 1 0.5 1.5 E

200 300 Area per unit volume a [ m 2 / m 3 ]

400

Fig. 11.38. Effect of the area of random beds of packing on the capacity factor

Equivalent bed height H [m] 5 5

12 10

10 10 10

15 15 15

20 20

25 = 1 mm

s = 0.8 mm

s= 0.7 mm

I I I I I I I 50-mm metal Pall ring with open joint Ingot steel

0 12 16 20 24 Load per packing element P[kg]

28

Fig. 11.39. Stress-strain relationship for 50-mm metal Pall rings

32

11.8 Limits to the further development of packing

Fig. 11.40. Pilot plant installed in the author's laboratories for thermal separation processes

289

12 Retrofitting columns by the installation of packing On the strength of the advantages that they offer in process engineering, packed columns are progressively encroaching upon territory that was formerly the exclusive domain of plate columns. A well-known example is the industrial-scale vacuum separation of ethylbenzene/styrene mixtures, for which purpose bubble-cap plates were initially used in compliance with tradition. They were subsequently superseded by special slotted-sieve and valve plates; and these, in turn, are now losing ground to structured sheet-metal packing. At the present time, packing is attracting attention not only for new installations but also for retrofitting existing columns. The aims of substituting modern, high-performance packing with a low pressure drop for the former column internals are to save energy, increase the capacity, and improve the product quality. This applies particularly to separation processes in refineries, to chemical and petrochemical production plants, and to food processing.

12.1 Advantages of retrofitting The relationship between energy costs and the expenditure on equipment is evident in Fig. 1.7. The pressure drop per theoretical stage Ap/nt causes the relative volatility to decrease in the direction from the top to the bottom of the column. In other words, the mean value am is less than that in theoretically isobaric rectification aiso, i.e. in the boundary case when Ap/nt = 0. The minimum number of theoretical stages ntymin and the minimum reflux ratio are correspondingly greater; thus nt>min > nt>minyiso, and rmin > rmin>iso. As is evident from Figs. 1.7 and 1.8, the number of theoretical stages in real rectification, when Aplnt > 0, is also greater, i.e. nt > nt>iso; and, according to Eqn (1-52), the reflux ratio as well, i. e. r > riso. The procedure outlined below permits calculation of the savings in energy and the reduction in the number of theoretical stages that can be achieved by retrofitting and makes due allowance for the specific pressure drop Aplnt. The steps (a)-(p) can be deduced from Figs. 1.7, 1.8 and 12.1 and the thermodynamic fundamentals and relationships that describe rectification processes. (a) The nature of the task implies that the mole fractions of the more volatile component in the feed xF, overhead product (distillate) xD, and bottom product xB are given. The pressure pT at the top of the column is also given and can theoretically be optimized to allow minimum separation costs. Known parameters are the molar enthalpy of the feed hF and h'F at the inlet and boiling temperatures, respectively, and the molar condensation enthalpy Ahv of the vapour stream in the inlet cross-section. Hence the factor / that describes the thermal state of the feed can be calculated from Eqn (1-12). (b) The relative volatility aIjiso of a molar mixture with a concentration x*tso, yfjso at the intersect / of the equilibrium curve and the g-line can be determined by iteration from phase equilibrium equations. Thus, the following applies for an ideal binary mixture:

Packed Towers in Processing and Environmental Technology. Reinhard Billet Copyright © 1995 VCH Verlagsgesellschaft mbH, Weinheim ISBN: 3-527-28616-0

292

12 Retrofitting columns by the installation of packing

1

X F /f Xp Liquid mole fraction x

Fig. 12.1. Qualitative diagram representing the minimum number of theoretical stages and the enrichment curve required to obtain the minimum reflux ratio in isobaric and real rectification

xn1

where Au A2, Bj, B2, C7, and C2 are the Antoine constants for a given boiling point T and the corresponding pressures of the more volatile Pj and less volatile P2 components 1 and 2. The phase equilibrium concentration of the more volatile fraction x*iso can then be obtained from the following equation, which is valid for a = aI>iso, y = y*iso, x = x*iso and a pressure /?/ = pT:

f xUso (a[Jso

-

'

•

-

/

_

XF

(12-2)

!

(c) Once aItiso and x*iso have been obtained, the phase equilibrium concentration of the less volatile component y*iso can be calculated from the following equation:

xUso

(aUso

-

(12-3)

12.1 Advantages of retrofitting

293

There is no need for iteration if the feed is admitted into the column at the boiling point, i.e. if hF = hF and / = 1, in which case x*iso = xF. Under these circumstances, a*wo = a*- corresponding to pt = pT and T(xF) can be determined direct from Eqn (12-1); and thus yfJso = yFJso, from Eqn (12-3). (d) It is evident from Fig. 12.1 that the minimum reflux ratio in isobaric rectification is given by (12-4) (e) Thus the reflux ratio r in real rectification can be obtained from Eqn (1-49) by assuming a value for the factor vg\ and the energy parameter e can therefore be calculated from Eqn (1-47). In Fig. 1.8, the value of s, the stage-number parameter, can then be read off on the axis of ordinates against this value of e and the corresponding pressure drop per theoretical stage Ap/nt. This step is demonstrated in the qualitative diagram shown in Fig. 1.7. A knowledge of the parameter s is essential for determining the number of theoretical stages in real rectification from Eqn (1-45). (f) The term nt>min>iso in Eqn (1-45) applies to the minimum number of theoretical stages in isobaric rectification. It can be defined by the Fenske. equation if the mean relative volatility amJso in the range of concentrations under consideration can be accepted, without reservation, as being sufficiently accurate for practical purposes. Thus In nt,min,iso =

l-xB

xD - xD

xB

J

J In a.m,iso

- 1

(12"5)

The minimum number of theoretical stages required in the enriching zone of the column, in which the mean relative volatility is am}enr!iso, is given by In ^t,min,enr,iso

XD

l-XF

-xD

xF

- 1

(12-6)

(g) Eqn (1-45) can be rearranged to give the total number of theoretical stages nt in real rectification, i. e. (12-7) The number of these stages that is accounted for by the enriching zone is given by ^ t, min, enr, iso

n,,enr =

\

s

' $

, ._

.

(12-8)

(h) The pressure pF in the cross-section of the feed inlet can now be obtained from nlenr, i. e. (12-9)

294

12 Retrofitting columns by the installation of packing

(i) The relative volatility a7 applies to the intersect of the curves that are valid for the feed inlet cross-section. As described in step (b), it can be determined by means of Eqn (12-1), but applies in this case to real rectification. Therefore, x7*can be obtained from the following relationship:

im

r

i+*;(«,-!)*'

/-i

(1210)

/-I

(j) Now that Jt*and a7 are known, the phase equilibrium concentration yf can be determined from

Again, iteration is unnecessary if the mixture is at the boiling point when it flows into the column, because x*= xF and a 7 = aF at /?7 = pF and T(xF). (k) The minimum reflux ratio rmin for the real column can then be obtained from -y*

The following relationship ought to exist between rmin and the minimum reflux ratio in an isobaric column rminjiso Xl iso

- (r • i \ y*'™ r 'mm ~ \rmin,iso ^ l) *

' *

i ^

Xl iso

>

*

±L i * — 1

n? ITl V 1 ^" 1 " 3 /

(1) The reflux ratio in isobaric rectification can be obtained by rearranging Eqn (1-52). Thus Fmin, iso

/ 1 /-» 1 A \

riso =

r = vrmin>iso

(12-14)

The factor v in Eqns (1-48) and (1-50) can then also be determined. (m) Since rmin>iso and v are now known, the energy parameter for isobaric rectification eiso, as represented on the axis of abscissae in Fig. 1.7, can be calculated from Eqn (1-46). (n) The value for siso corresponding to eiso on the isobaric (Apfnt = 0) curve in Fig. 1.8 can be read off on the axis of ordinates. Rearranging Eqn (1-44) and inserting this value for siso then gives the number of theoretical stages in the isobaric column, i.e. nUlso =

H

t

~ 1

+ Siso

(12-15)

$iso

(o) The values obtained for nt and nt>iso in steps (g) and (n) can be taken to calculate the theoretical column efficiency r\c from Eqn (1-42). Alternatively, r\c can be calculated from Eqns (1-53), (1-54) or (1-55), because the terms in these equations are now also

12.1

Advantages of retrofitting

295

known. Yet another means by which r\c can be obtained is to determine the increase in the number of theoretical stages Ant that is caused by the specific pressure drop Ap/nt, i.e.

Ant = nt- nt>iso =

_*~i"° ^1

T Km,*™ + 1)

S) {L

(12-16)

Siso)

In this case, the theoretical column efficiency, i. e. the number of theoretical stages in a theoretical isobaric column, expressed as a ratio of that in a column with pressure drop, is given by

=

n,Mo + An,

An, 1 +

(p) The amount Ar by which the reflux ratio in a real column exceeds that in an isobaric column is defined by Ar = r- riso =

* ~ 6iso

(rminMo

+ 1)

(12-18)

yi - e) {i - eiso)

It allows an expression to be obtained for the efficiency in terms of energy r\e, i. e. the energy consumption in a theoretical isobaric column to be expressed as a ratio of that in a real column. Thus

u

=

riso + 1 riso + Ar + 1

= l +

1_ Ar riso + 1

v

;

Relationships for the relative increase in the energy consumption QIQiso and in the number of theoretical stages Ant/nt)iso can be obtained by following the steps (a)-(p) in the procedure outlined above. With the aid of Fig. 1.8, they can be expressed as functions of the pressure drop per theoretical stage Aplnt, i.e.

4^ Qts

An, nt,iso

— - 1 = f (Ap/n,) 1

- 1 = f(Ap/nt)

(12-20) (12-21)

T\C

Both relationships are presented graphically in the numerical example given in Fig. 12.2. The diagram convincingly demonstrates the advantages that can be derived from installing packing instead of plates. The upper curve was plotted from the sole aspect of achieving the utmost savings in energy, i.e. for a constant number of theoretical stages (nt = const.), and the parameters that were taken into consideration were nt>min>iso, riso and s. The two lower curves represent the case in which the intention was both to save energy and to reduce the

12

296

Retrofitting columns by the installation of packing

number of theoretical stages, i. e. the minimum reflux ratio factor was constant (v = const.) and the parameters were rminJso, ntMnMo and ntJso. The headings on the diagram indicate the ranges of pressure drops that apply to arranged packing, random packing, and plates.

12.2 Potential for retrofitting with low-pressure-drop packing It is clearly evident from Fig. 12.2 that the energy consumption and the number of theoretical stages in intensive-rectification columns can be substantially reduced by substituting low-pressure-drop packing for fractionating plates. Theoretically, it is also feasible to retrofit the column so that the number of theoretical stages remains unchanged. In this case, the severity or the fineness of the cut can be increased, and purer products can be obtained.

Regular or corrugatedsheet packing 0.30

Dumped pack ag

Trays

11M Tt1

0.20

-^

r t min.is o=27.4 n t = 58 r,s0-4-4 s - 0.5,?

e:D 0.15 CO

0.10 0.08

si

/

! )\

0.03

3—-

ft

/

/+ 3

4

/

y

/

s W

y /

=

^-

0.20 0.15

0.06

"

0.04

nt,iso=52

0.03

-.

6

0.30

nt m i n . i s o " L11 '-QJ v = 1.3

k

/

0.10 0.08

-i

/ min.iso

y

0.015

y

y

yA

0.02

A

y

/

/

/

y y

/

y

/

/

A

y /

y

j

/

/

0.06 0.04

y/

—

y

/ 3—/ y

y

/

CD

0.02 0.015 8 10

15 20

40

60 80

Specific pressure drop A p / n t [mm WG ] Fig. 12.2. Increase in energy consumption and in the number of theoretical stages as a function of the specific pressure drop in vacuum rectification involving a large number of theoretical stages. Evaluated with the aid of Fig. 1.8.

72.2

Potential for retrofitting with low-pressure-drop packing

297

The condition for equilibrium at the point y = yt\ x = xj is —

(12-22)

Consequently, the minimum reflux ratio rmin is given by (cf. Fig. 12.1) a, ^"min

(12-23)

1-x?

a7

The rate of heat emission Q is described by Q =

h'B-h'F

xD - xB

(12-24)

where v is the factor for the minimum reflux ratio {cf. Eqn (1-50)} and rmin depends on the pressure pF in the feed cross-section and thus, according to Eqn (12-9), on the pressure drop per theoretical stage Ap/nt. Another means of determining the effect of Ap/nt on Q arises from the following equation, which can be obtained by rearranging Eqn (1-47): • • -\-' pc 'r min,iso

(12-25)

1 -e

Consequently, the following relationship can also be derived from Eqn (1-57); and it can be evaluated with the aid of Fig. 1.8:

CD

a

ID C=

Hnin.iso t V g " " i )

Fig. 12.3. Application of Fig. 1.8 for retrofitting estimates

Energy parameter

298

12 Retrofitting columns by the installation of packing XF -

XB

-*-

1-e

Ahv

+ h'D - h'B\ + h'B - h'F

(12-26)

The significance of the pressure drop per theoretical stage Ap/nt in retrofitting and designing separation columns is further demonstrated in Figs. 12.3 and 12.4. These diagrams represent a method of comparing column internals with different pressure drops per theoretical stage, i.e. (Ap/nt)j and (p/nt)2. The two types of column compared are denoted by the subscripts 1 and 2, and the method permits a comparison in the following five cases: (A) The minimum reflux ratio factor v, as defined by Eqn (1-50), remains constant. (B) The reflux ratio r {Eqn (12-25)} and thus the energy parameter e remain constant. (C) The number of theoretical stages nt {Eqn (12-7)} and thus the stage-number parameter s remain constant. (D) The product vapour load V remains constant. (E) The column is operated at a constant pressure drop per theoretical stage Ap/nt. In Cases (A) and (B), the difference in the number of theoretical stages is given by An't = nh - nh =

^ " ^

(nt,min,iso

+ 1)

(12-27)

In Cases (A) and (C), the difference in reflux ratio is given by Ar' = r2 - n =

e 2 (1_ e 2~^_ei)

(rminjso + 1)

(12-28)

Eqns (12-27) and (12-28) can be solved numerically with the aid of Fig. 1.8. The percentage reduction in the number of theoretical stages that can be achieved by installing the internals denoted by the subscript 1 instead of those denoted by the subscript 2 can be determined from the following equation: 100 = ^ nh

100

(12-29)

nt.

The corresponding savings in energy can be calculated from the following equation: Ql

~QQl

100 = y ^ y y

100

(12-30)

In Case (A), the reduction achieved in the number of theoretical stages is less than that in Case (B), and the savmgs in energy are less than those in Case (C). On the other hand, no energy is saved in Case (B), and no reduction in the number of theoretical stages is effected in Case (C). In Case (D), the opportunity of retrofitting with stacked packing with a low pressure drop can be exploited to increase the capacity F. If the vapour flow rate V is the same in both cases, i. e. V = const., the distillate flow rate D in a real column can be compared to that in a theoretical isobaric column Diso by means of the following equation: V = Diso (riso + 1) = D (riso + 1 + Ar)

(12-31)

72.2

Potential for retrofitting with low-pressure-drop packing

299

The inlet capacity in the isobaric case is given by Eqn (12-32); and that in the real case, by Eqn (12-33): F 1

XD

=D

ISO

J-^lSt

F= D

XF

xD-

-xB -xB

(12-32)

xB

(12-33)

xF-xB The efficiency in terms of capacity is therefore given by F 1

1

ISO

(12-34)

1 +

where Ar is as defined by Eqn (12-18). In other words, the efficiency is the same in terms of capacity r\F as it is in terms of energy r\e, as defined by Eqn (12-19). The lower the value of Ap/nt, the greater that of v]F. As a consequence of the pressure drop in a theoretical stage Ap/nt, the capacity in real rectification is less than that in theoretical isobaric i.e. AF

F

- F

r

r

iso

F iso

= 1 -x\F =

i(Ap/nt)

(12-35)

F

x

ISO

Hence, the following equation applies if column internals with a specific pressure drop (Ap/nt)2 are replaced by internals with a lower value (Ap/«,)/ and the vapour flow rate is assumed to be the same, i.e. Vj = V2 = const, (cf. Fig. 12.4): = D2 (r2

Product vapour rate V

< O

Fig. 12.4. Qualitative comparison of column internals with various specific pressure drops Case D: if the vapour load is kept constant Case E: if the specific pressure drop is kept constant

CD d. CO

Capacity factor Fv

(12-36)

300

12

Retrofitting columns by the installation of packing

The inlet capacity F2 in Case 2 and that Fj in Case 1 are given by

F2-

D

F, - D

~ -xB

XD

xF-

• X

XD

xF-

~

B

-xB • X

(12-37)

B

The percentage increase in capacity is therefore Fj-F2 i

F2

100

(12-38)

r2 + 1

in which Ar' is as defined by E q n (12-28). In Case ( E ) , an increase in capacity F can also be achieved by retrofitting, because the loads permitted by modern packing of appropriate dimensions are higher than those obtained by plates of equivalent Ap/nt. It is evident from the qualitative diagram shown in Fig. 12.4 that the increase in capacity in this case is given by Fi ~ F2

— P - — 100 r2

FVi - Fy2

—

tv2

100

(12-39)

where FVl and Fy2 are the vapour capacity factors at which the value Ap/nt = constant in packings 1 and 2. The benefits offered by high-performance packing with small values of Ap/nt are reviewed in Table 12.1. They apply to both the planning of new and the retrofitting of existing columns. It is evident from the table that advantages can be obtained in the number of theoretical stages nt and thus the column height i7, the reflux ratio r and thus the column diameter ds, the energy consumption Q, and the capacity F. If the calculations reveal that the height of the column to be retrofitted Hj is less than the original height H2, i.e. Hi < H2l full exploitation of the available height H2 will give rise to more clean-cut separation, i.e. to improved product quality. An impression of the advantages that modern packing has over conventional sieve plates can be obtained from Table 12.2. The example taken was the vacuum rectification of a mixture with a thermally unstable bottoms product. The principle of the heat pump was applied by compressing the overhead vapour to heat the bottoms. There is no mistaking the considerable improvement that was achieved in the economics of the process by the installation of packing.

72.2

301

Potential for retrofitting with low-pressure-drop packing

Table 12.1. Characteristics for planning new columns and retrofitting existing columns with lowpressure-drop packing (Ap/nt)i -< (Ap/n t ) 2 = const.

V =

e =- const.

s = const.

V = const.

Ap/n t = const.

n tl < n t2

n t i < nt2 n t] > ntl (v)

n tl = n t2 n t i < n tl (v)

= n t2 n tl <: n t , ( v )

n tl = n t2 nti < n tl (v)

An ;

An ; > An|(v)

An; = 0

An; = 0

An; = 0


H, < H 2

H, < H 2

' '< r 2

dsi


Qi < Q

2

Hi /

\

<

H2

Hi

<

H2

H, < H, (v)

H, < H, (v)

i < r2 ri > r,(v)

ri = r 2

Ar' 1 - 0

Ar' > Ar'(v)

Ar' :> Ar'(v)

Ar' = 0

d S i = ds2 dSi < dSi (v)

d S i < d s2 dSi > dSi (v)

ds, -: d s 2

dSi = ds2 dSi < d sl (v)

Q, < Q 2 Qi > Qi W

ri

Ar

IT

P-P\/ »

r

^ -

Hi < H, (Vj ri < r2 ri > ri (v)

-d-d

TT

= r2 < C r i (v)

<S(v)

r

dsi

r, < r, (v)

-> d S i (v)

Q, > Q 2 Qi < Qi(v)

>S(v)

F, = F 2

F, : = F 2

Fi = F2

Fi

A

B

c

D

>

Fi > F 2

F2

E

Table 12.2. Economics of applying the principle of the heat pump. Valid for the separation of a mixture consisting of equal parts by weight of ethylbenzene and styrene fed at a rate of 30 tons/hour into the following columns: (a) fitted with perforated plates (b) packed with Mellapak 250 Y. Based on the following prices: electricity 0.06 SFr/kWh, steam 12 SFr/ton, cooling water 0.6 SFr/kWh (SFr = Swiss Francs). With the courtesy of Sulzer AG, Winterthur Operating data

Sieve tray

Mellapak

Pressure at head of column [mbar]

67

67

Temperature at head of column [°C]

58

58

Number of theoretical stages

54

54

Reflux ratio

8.25

6.5

Pressure at foot of column [mbar]

310

127

Temperature at foot of column [°C]

106

81

15

15

Reboiler temp, difference [°C] Compression ratio Compressor costs Energy savings [%]

9.9

4.5

100

60

30

60

302

12

Retrofitting columns by the installation of packing

12.3 Advantages of packing in steam rectification Even if a vacuum is applied, it is not always possible to separate unstable mixtures at temperatures that are low enough to avoid thermal decomposition. This applies particularly to mixtures of fatty acids, and an example is the separation of palmitic and stearic acids in industrial-scale rectification columns equipped with 20-40 plates. If the pressure at the head of the column is 7 mbar, pressure drops of 43-85 mbar occur under normal operating conditions and are responsible for boiling points of between 267 °C and 279 °C. In separation tasks of this nature, it is absolutely essential to restrict the residence time of the products and the pressure drop to the minimum possible values. Even if this demand is met and even if the vacuum applied is justifiable from the engineering and economic aspects, substances that are unstable to heat cannot always be separated under conditions that preclude thermal decomposition. Thermally unstable substances that are encountered in thermal separation practice include higher fatty acids, unsaturated and high-molecular-weight organic compounds, and essential oils. They can be separated under very favourable conditions by rectifying with an inert vapour as carrier. Steam is mostly used for this purpose, because many of the organic substances that have to be separated in practice are insoluble in water. An example of the reduction in temperature that can be achieved by this means arises in the distillation of palmitic acid. Thus, if the mass fraction of steam is about 15%, the boiling point at a pressure of 13.3 mbar can be lowered by about 19°C; and at a pressure of 133 mbar, by about 36 °C. Rectification with an inert vapour under vacuum is also resorted to for crude oils that may undergo thermal decomposition at elevated temperatures. For instance, the temperature above which Near East crudes may thermally decompose is about 390 °C. The advantages of steam or inert vapour rectification are offset by the high steam consumption and the extent to which the column cross-section must be enlarged to accommodate the steam fraction additionally imposed. This is evident from the following theoretical considerations. Let a mixture's instability to heat entail that the temperature at a given theoretical stage /, as counted from the head of the column, must not exceed a given value th Then the equilibrium pressure corresponding to this temperature th i.e. the sum of the partial pressures of the mixture's components c = 1 to c = n in the product vapour with a molar flow rate V, is given by (cf. Fig. 12.5): c=n

Pv,i = 2 Pa = const

(12-40)

c=l

This equilibrium pressure can be attained and maintained at a constant value if the molar flow rate of steam S is correspondingly large. If the vapour pressure curves for the individual components Pc = f(t) are known, the pressures at the boiling points of the pure components Pi,i,Pc,i,Pn,i can be obtained as is indicated by the qualitative diagram presented in Fig. 12.6. Hence, if the composition of the liquid product phase Xjti,xcj,xn>i leaving the /'th theoretical stage is given, the corresponding partial vapour pressures can be calculated from Pa = la xa Pa

(12-41)

303

12.3 Advantages of packing in steam rectification

p T =const. S'V L

Stage 1

Stage j

Stage n t Fig. 12.5. Scheme for describing the product temperature within the column in steam rectification

m PJ.

Top

Pressure p

tj

Ap

m

Botto S.V [ pB=f(pT(ntlAp/nt) tB=f(S/V,pp)

Top Pi

PHJ Pvj'Pcj H V

Fig. 12.6. Qualitative boiling pressure curves in steam rectification

(xc) Stage j Boiling temperature J

A simplifying assumption that can be made for mixtures that obey Raoult's law is that the activity coefficient y is unity. It is valid for most hydrocarbon systems subjected to steam rectification, and considerably simplifies the calculation of phase equilibria. The value thus determined for the equilibrium pressure pv,i of the product vapour at a total pressure pt above the f th theoretical stage allows the partial pressure of the steam at this stage to be determined as a function of the pressure pT at the top of the column and the pressure drop per theoretical stage Ap/nt for the type of packing concerned under the given loading conditions, i.e.

304

12

Retrofitting columns by the installation of packing

Ps,i = Pi ~ Pv,i =PT+

(i - 1) —

- Pv,i

(12-42)

\ fi I

The total vapour flow rate is the sum of the flow rate of steam and that of the product vapour, i.e. Vtot = S + V

(12-43)

If it assumed that the modified Dalton's law of partial pressures applies, the molar fraction of steam will be given by Eqn (12-44); and that of the product vapour, by Eqn (12-45):

<12 44

- >

Hence, if the molar flow rate of product vapour V is known, the molar flow rate of steam can be calculated from the partial vapour pressures pSi and pVi, i. e. S = V^~

(12-46)

Pv.t

If the individual components each have roughly the same molar vaporization enthalpy, the molar flow rate V of the product vapour and thus its molar fraction yv in the total vapour mixture must be constants, i.e. (yv) v = const = const

(12-47)

In this case, the partial pressure of the product vapour can be determined at any given theoretical stage. Thus,

Pv,t = yvPt = yv

Ap

(12-48)

Consequently, the phase equilibrium temperature corresponding to the composition xc>i in the liquid phase at that particular stage can be obtained. Now suppose that the thermal instability of the substances to be separated entails that a certain upper operating temperature limit may not be exceeded, e. g. the temperature tt laid down for the fth stage. In this case, the partial pressure pVi exerted by the molar volume above the f th stage must remain constant; its relationship to the total pressure is given by Pi = Ps,i + Pv.i

(12-49)

The partial pressure of the steam pSi can be regulated by means of the steam molar flow rate S.

12.3 Advantages of packing in steam rectification

305

The total pressure pt at the /'th theoretical stage is fixed by the pressure pT at the head of the column and the pressure drop per theoretical stage Ap/nt for the packing concerned (cf. Fig. 12.5). Thus, (12-50) The partial pressure of the product vapour pVi can be derived by combining Eqns (12-49) and (12-50). Thus,

Pv,i=Pr+(i-l)

— -Ps,i

(12-51)

The following relationship must apply for the partial pressure of the steam: S

(12-52)

It therefore follows that the volume flow rate of steam required per unit flow rate of product vapour is given by

The condition for steam rectification must be adhered to, i. e. (Pv,i)ti = const. = const.

(12-54)

Consequently, the lower the pressure drop per theoretical stage Aplnt for the packing, the less the flow rate S of steam required. The lowest steam flow rate occurs in an isobaric column, i.e. for Ap/nt = 0, in which case the following applies: % - = -£ZL-l y

(12-55)

Pv.t

If Ap/nt > 0, Siso must be increased by a corresponding amount AS. Since AS is directly proportional to Ap/nt, the pressure drop in an actual column must be compensated by admitting steam at a higher flow rate. This additional rate of steam is given by

It follows from this equation that the lower the pressure drop per theoretical stage, the less the amount of steam that has to be admitted in steam rectification.

306

12 Retrofitting columns by the installation of packing

The ratio of the cross-sectional areas of steam rectification columns, the one with Aplnt = 0 and the other with Ap/nt > 0, is equal to the ratio of the squares of their diameters dSyiso and ds. The temperature is the same in both cases, and the density of the steam is thus directly proportional to the pressure. In other words, Eqn (12-57) applies for steam rectification with Ap/nt > 0; and Eqn (12-58), for Ap/nt = 0: (Qs.dtt = const. ~ Ps,i

(12-57)

\Qs,i,iso)ti = const. ~ PS,i,iso

(12-58)

Therefore, the increase in the column diameter necessitated by the pressure drop within the bed of packing can be described by

ds -

ds,iso)2

Ps,i

(12-59)

"•S, ISO

PS,i,is

Another fact to be taken into consideration is that the ratio of the steam partial pressure in isobaric rectification to that in nonisobaric is equal to the corresponding ratio of their molar flow rates, i.e. (12-60) Rearranging Eqn (12-59) to solve for ds and substituting from Eqn (12-60) yields d5 = ds>iso + Ads = dS}iso + d5>iso \ —lhH£- 7 — = ds>iso 1 + \ / —T— V Ps,i Siso V S

(12-61)

Substituting from Eqns (12-52) and (12-53) then gives

\/ „

T>

S lS

'°

\l

ps.

l Hf

(12-62)

This equation states that the amount Ads, by which the diameter dStiso of an isobaric rectification column has to be increased, is directly proportional to the square root of the pressure drop per theoretical stage Aplnt, provided that the vapour load is constant in the column. It also clearly reveals the advantages of replacing existing column internals by lowpressure-drop packing. Consider, for instance, the case in which the pressure drop per theoretical stage of the existing internals is greater than that of the packing intended as a replacement, i.e.

nt /2

(12-63)

72.3

Advantages of packing in steam rectification

307

According to the previous remarks, this replacement would result in a savings of AS in steam. Eqn (12-64) would then apply for the original internals 2; and Eqn (12-65), for the replacement packing 1:

P T

+

d - l ) ( ^

V . ^

(12-64)

Pvj pT+(i-l) - ^ =

-pVJ

^

d2-65)

The molar flow rate of steam, expressed in terms of the molar flow rate of product vapour, can then be obtained by substracting Eqn (12-64) from Eqn (12-65), i. e.

In other words, the savings ASIV in the molar flow rate of steam is directly proportional to the amount (k -1), by which the pressure drop per theoretical stage of the replacement packing 1 is less than that for the existing internals 2. It can be easily verified by dividing Eqn (12-65) by Eqn (12-66) that the corresponding relative savings in steam is given by AS ^2

S2-S, = —r

k-1 =

(12-67)

S2

,, ,

PT-PVJ

If the total vapour load is kept constant in both cases, the reduction in column diameter that can be achieved by substituting the packing 1 for the existing internals 2 is given by

a

s2

A reduction in capital investment entails that the costs per unit column volume (cf. Chapter 11) for Column 7, as expressed by Eqn (12-69), are also less than those for Column 2, as expressed by Eqn (12-70): =

(dS2

-Adsf df2

CS2 = vV2 C2 where vV2 is the column volume per unit of separation efficiency for Column 2, C2 is the cost per unit volume (m3) for Column 2, and C\ is the cost per unit volume (m3) for Column 1.

(12-70)

308

12

Retrofitting columns by the installation of packing

Packing 1 is considered to be more economical only if the total costs CT>1, i. e. capital and running costs, are less than those for the original internals 2. It is quite feasible that, if the costs for the shell and bed of packing are very high, Column 1 may involve the higher acquisition costs, despite the smaller diameter ds>1, yet the total costs may still be less, i.e. CTJ < CT,2- However, if the costs for the shell and packing are extremely high, i.e. Cj ^> C2, CTJ may exceed CTa, even if dsJ < dSy2A flow chart for an oil refinery is shown in Fig. 12.7 to illustrate steam rectification.

Vacuum station

Water High-pressure steam

Vacuum column /

Saturated steam Heater

Fuel ? oil

Fig. 12.7. Crude oil inert steam rectification plant

The five valve-ballast plates in the distillation zone of a FCC fractionating column were replaced by a bed of Montz Packing Bl/250.60 of 2.6 m total height. A schematic diagram of the upper section of the column is shown in Fig. 12.8. As a result, the separation efficiency was increased from 3 to 4.5 theoretical stages with an associated improvement in the product quality. The packing was arranged in parallel layers, as is shown in Fig. 12.9. Utmost care in stacking the packing is essential in order to maintain the efficiency throughout the height of the bed. Data characteristic of a plant for the distillation of fatty acids before and after changing over from plates to packing are presented in Table 12.3. The advantages achieved from the

12.3

Advantages of packing in steam rectification

309

change-over are immediately evident: the reduction in the pressure drop per theoretical stage allowed a 40 % increase in capacity, a reduction of 25 °C in the temperature at the foot of the column, and 15 % savings in energy. In addition, the column could be operated without carrier steam.

Liquid distributor Distillation zone Fig. 12.8. Example for retrofitting a FCC fractionating column by substituting Montz packing for five valve-ballast plates in order to improve separation

I I

I I

I I

I I

Liquid collector

I I

Table 12.3. Data relating to the rectification of coconut oil fatty acid in a column formerly fitted with bubble-cap plates and after retrofitting with Mellapak packing. With the courtesy of Sulzer AG, Winterthur Characteristic data

Trays

Column diameter ds [m]

2.5

Effective column height H [m]

18.6

Pressure at head of column pr [mbar] Pressure at foot of column pB [mbar]

5 90

Temperature at head of column tD [°C] Temperature at foot of column tB [°C] No. of theoretical stages nt

Energy savings A Q / Q [%]

23

173 255

230

26

32

Capacity increase AF [%] Carrier steam S [%]

Mellapak

40

10 15

310

12

Retrofitting columns by the installation of packing

Fig. 12.9. Montz Pak Bl-250 packing elements for a column of 4-m diameter. The beds of packing were charged through manholes

12.4 Improvement in product purity caused by restricting the pressure drop in beds of packing The total pressure drop between the head and the foot of the column will obviously be high in rectification processes that involve a large number of theoretical stages. Hence, if it may not exceed a given value owing to the product or the process conditions, undesirable limits may be imposed on the separation efficiency and thus on the purity of the product in plate columns. Examples of the limits that may be set by the process conditions arise in the separation of thermally unstable mixtures; in coupled columns with an integrated heating system, e.g. if the heat content of the bottoms in the one column is utilized for the indirect condensation of the overhead product in the other; or if the overhead vapour in the one column is used to heat the bottoms in another that operates under reduced pressure. In cases of this nature, more theoretical stages can be realized by substituting lowpressure-drop packing for the plates (trays), i.e. nuP > ntJ. This is evident from the qualitative diagram in Fig. 12.10. According to this, the pressure drop must be the same in both cases, i. e. Ap = f-^-1 ntJ = \^2-\ nttP = const. nt IT \ nt JP

(12-71)

In other words, the ratio of the number of theoretical stages to the specific pressure drop in the packed column {Eqn (12-72)} is greater than that in the plate column {Eqn (12-73)}:

12.4

311

Improvement in product purity caused by restricting the pressure drop in beds of packing

uv = const, and A p = const. — n t p > n t T — - ( x D P - x B X

X

D,T

) > (xD

D,P

M

1

Ap= const. n

p

t,I

1 888

X

X

B,I

B,P

Packing

Trays

Vapour load u v

Fig. 12.10. Schematic diagram demonstrating the advantages of packing over plates for improving product quality in separation processes with constant total pressure drop

, nt IT nt,p = 7——r— nuT

(12-72)

AEA nt

Jp

AE] r

App = const.

nt JT AE) nt

(12-73)

jp

Thus the degree of separation is also increased. A measure for the fraction of high boilers AB remaining in the overhead product D is *B

_

•

_ ^l

*>D)xB = const., Ap = const.

(12-74)

It can be expressed in the following form: (12-75) This function can be evaluated in the light of the above remarks, to obtain the minimum number of theoretical stages from Eqn (1-60). Information can thus be derived on the improvement in product quality that can be achieved if the plates are replaced by packing. Likewise, the fraction of low boilers AD remaining in the bottoms B is given by

A

B

—

(XB)XD

= const.,

Ap = const.

(12-76)

12

312

Retrofitting columns by the installation of packing

and information on the improvement in the quality of the bottoms can be derived, by analogy, from the following function: (12-77) If the overhead and bottom products are of very high purity, the term xD(l - xB) tends towards unity. In other words, if the relative volatility is given, the term xB(l - x^) decides the minimum number of theoretical stages nUmin. This is clearly demonstrated in Fig. 12.11, in which xB(l - xD) is shown as a function of nt and r^p with a as parameter. The following linear relationships are obtained by plotting on semilogarithmic paper:

- xD) xB •

1

(12-78)

Thus if xB = const., xD is given by X

~ 1 -

D

xB

(12-79)

a'

or, if xD = const., xB is given by 1 xB « 1 -x D

1 a n, +

(12-80)

1

Ratio of specific pressure drops r A p ( n t I = 5 0 ) 1.5

2

2.5

3

3.5

4

10

s e

10'1 2

i 10s

o

10-3

• \

N

\

\

\

\ \

N

\ \

=3

s\

ioJ 10"

50

\

"i \

100 150 Number of theoretical stages nt

\

1%,200

Fig. 12.11. The advantage of low-pressure-drop packing in improving product quality by the scheme illustrated in Fig. 12.10.

13 Applications for packing in liquid-liquid systems Depending on the geometry of their elements and the materials from which they have been produced, random and stacked beds of packing give good results in liquid-liquid extraction as well in gas-liquid separation processes. This has been confirmed in numerous systematic studies performed in the author's laboratories.

13.1 General aspects More energy is required to separate mixtures by rectification if the differences in the relative volatilities of the components are slight or if the fraction of the one component is small. A typical example of the latter case is the recovery of organic compounds from aqueous solutions in the treatment of industrial effluents. A physical method that can be adopted for this purpose is direct rectification, but the high energy costs involved are a major deterrent. An alternative on which current attention is focused is to extract the organic compounds from the waste water by means of a solvent and to recover the solvent from the extract in a second, rectification stage. Flow charts for both methods are presented in Fig. 13.1. The process with the extraction stage may require much less energy, because the vaporization enthalpy of organic substances is three to five times less than that of water. This is clearly demonstrated by Fig. 13.2. Liquid-liquid extraction processes for the recovery of organic compounds from effluents can be successfully carried out in packed columns.

Condenser

b)

Q)

Condenser

Waste water

Extract

Extractor'

Purified

water

Reboiler

Rectification column T I

water

Recycling « ^ _

of solvent

Fig. 13.1. Recovery of organic compounds from production effluents (a) by rectification (c) by liquid-liquid extraction and rectification of the process solvent Packed Towers in Processing and Environmental Technology. Reinhard Billet Copyright © 1995 VCH Verlagsgesellschaft mbH, Weinheim ISBN: 3-527-28616-0

314

13 Applications for packing in liquid-liquid systems

1.0 Water - Methanol/ 2- Octanol

0.5

1.0 1.5 2.0 2.5 Solvent/feed ratio C/F [kmol/kmol]

3.0

3.5

Fig. 13.2. Energy saved by combining liquid-liquid extraction with solvent recovery instead of direct rectification (cf. Fig. 13.1)

13.2 Experimental The flow chart for the experiments is shown in Fig. 13.3. The diameter of the column was varied up to 0.25 m; and the height of the packing, up to 3.2 m. The types of dumped packing tested are shown in Fig. 13.4; and of arranged packing, in Fig. 13.5. Another packing system that was included in the studies is illustrated in Fig. 13.6. It is known as a tube column and consists of vertical tubes in which the packing elements have been systematically stacked beforehand. The derivation of a generally applicable model to describe mass transfer and flooding in extractions columns filled with these types of packing necessitates a fundamental investigation into the hydraulic characteristics of the packing, because they strongly influence the extraction efficiency and the maximum load. Thus the packing performance is affected by the extent to which the two phases are intimately mixed and uniformly distributed over the entire cross-section of the column. The systems listed in Table 13.1 allowed the effect of the main physical properties - density Q, diffusion coefficient D, dynamic viscosity r\ and surface tension o - to be taken into account over a wide range. In some of the systems, the resistance to mass transfer was in the dispersed phase D only; in others, in the continuous phase C only; and in others again, in both phases. The effect exerted on the performance by the direction of mass transfer was also investigated, i.e. from the continuous to the dispersed phase C —» D or from the dispersed to the continuous phase D —> C. In the diagrams, a C —» D system is denoted by "Dispersed phase / Transfer components-Continuous phase"; and a D —» C system, by "Dispersed phaseTransfer component/Continuous phase".

13.2

V16

VK

Experimental

V15

Fig. 13.3. Flowchart for one of the pilot plants used in the experiments

Fig. 13.4. Packings investigated in dumped beds

Pall ring 25 mm, metal

Hiflow ring 25 mm, plastic

Bialecki ring 25 mm, metal

Hiflow ring 35 mm, ceramic

315

316

13 Applications for packing in liquid-liquid systems

Stacked Bialecki rings,-25 mm metal

Montz packing B1-300 metal

Montz packing B1-300 plastic

Fig. 13.5. Packings investigated in geometrically arranged beds

Tubes filled with packing elements

Fig. 13.6. Extraction-tube columns with stacked Bialecki rings

D D D D CD C-

Toluene (D) - Acetic acid/Water

Carbon tetrachlor. (D) - Acetic acid / Water

Dichloroethane (D) - Acetic acid/Water

Isobutyl alcohol (D) - Acetic acid / Water Isobutyl alcohol (D) - Acetic acid / Water

Toluene (D) - Acetone / Water Toluene (D) - Acetone / Water

D,C

c D

D D D D,C

Transfer resistance

c c c c

Transfer direction

Extraction system

QD
QD
QD>QC

QD>QC

QD
Density difference

998.2

985.6

1485 1315

235

998.2

2538

279

0.926

252 1472

1.154

0.353

0.88

0.88 -

D D • 109 D c -10 9 m 2 /s m 2 /s

999.2 998.2

QC kg/m 3

1315 5958

AQ kg/cm 3

Table 13.1. Physical properties of the systems investigated in the studies on liquid-liquid extraction

1.075

1.46

1.0

1.075 1.0

0.586

4.703

0.835

0.586 0.969

r] c -10 3 " \]D • 103 kg/ms kg/ms

351

28

280

351 445

o-10 3 N/m

318

13

Applications for packing in liquid-liquid systems

13.3 Fluid dynamics of dispersed and continuous phases A typical relationship that was established between the phase loads uc and uD and the dispersed-phase holdup in liquid-liquid systems is shown qualitatively in Fig. 13.7. It can be seen that it is analogous to the corresponding relationship in gas/liquid systems. Thus, at continuous-phase loads uc of up to 70% of that at the flood point M C J H , the dispersed-phase liquid holdup hD is independent of the continuous-phase superficial velocity; and, in this capacity range, it is merely a linear function of the dispersed-phase superficial velocity uD, according to the results obtained by experiment.

r ^=0 Flooding J

L

TD O

UD.FI

Continuous-phase load u c Fig 13.7.

Dispersed-phase load UQ

Qualitative description of the hydraulics in packed column extractors

The efficiency of extraction in packed beds is mainly influenced by fluid-dynamic parameters, i. e. the geometry and material of construction of the packing elements, the phase loads and the dispersed-phase holdup, the direction of mass transfer, the physical properties of the system, and the location of the resistance to mass transfer.

13.4 Dispersed-phase holdup The relationship between the dispersed-phase holdup hD is evident from Figs. 13.8 and 13.9. The former applies for dumped 25-mm plastics Hiflow rings; and the latter, for arranged Montz B 1-300 sheet-metal packing with elements of 50-mm height. In both diagrams, the holdup hD has been plotted against the continuous-phase column load uc with the dispersed-phase load uD as parameter. The results obtained in experiments on dumped 35-mm ceramic Hiflow rings have been plotted in Fig. 13.10. It can be seen that, if uc is kept constant at a value of u c < 70% Uc,Fh t n e relationship between hD and uD is linear. Likewise, linear relationships were

13.4

319

Dispersed-phase holdup

25-mm Hiflow ring Plastic, N = 43888 1/m3 ds= 0.154 m, H = 2.2 m 48

Montz packing B1-300 Sheet metal d s = 0.154m, H-2.21 m

m 3 /m 2 s

40 - uD=9.62-10

i

32

32

Toluene (DVWater ~ 1 bar. 293 K

1

24 a sz. a.

24

16

16

1

1

'

1

uD= 2 . 7 8 - 1 0 " 3 m 3 / m 2 s -

—

1 l \ ifnli minn 1 DVWate r 1 bar, 293 K /

"8 CO CD CDCO

5.55-10"J

u—•

8 U

0 0

4

8

12

16

Continuous-phase load

0

4

12

16

load

u c 10 3 [m 3 /m 2 s]

u C 'i0 3 [m 3 /m 2 s] Fig. 13.8. Dispersed-phase holdup as a function of the continuous-phase load for plastics Hiflow rings

8

Continuous-phase

Fig. 13.9. Dispersed-phase holdup as a function of the continuous-phase load for Montz B1-300 packing

established in similar experiments but on stacked 25-mm metal Bialecki rings (Fig. 13.11). In this case, the tests were performed on four different systems, and the results thus clearly demonstrate the effect of the system and that of mass transfer. The experiments also indicated the effect exerted by the direction of mass transfer. The holdup measured in the C —> D direction was greater than that in the D —> C direction, and was associated with the existence of smaller droplets. The resultant increase in efficiency was about 30 %. Yet another item of information that was gained from the experiments was the effect of the transfer component fraction in the phase under consideration. Thus, an increase in the concentration of the transfer component reduces the holdup when the mass transfer is in the D -» C direction. The relationship between hD and uD for continuous-phase loads of Uc < 0.7' UC,FI can be expressed by the following simple equation: hD = Cs uD

(for uc < 0.7 UC,FI)

(13-1)

in which Cs is a characteristic factor for the packing and depends on the system, i.e. it is mainly a function of the densities of both phases QC and QD and the surface tension a.

320

13 Applications for packing in liquid-liquid systems

35-mm Hiflow ring 25-mm stacked Bialecki rings Metal. ds= 0.1m, H=3.2m

Ceramic, N = 16800 1/m3 d s = 0.154 m, H = 2.25 m 40

a. ZD

-a

40

Uc-103 [ m3/i —o— 0 —D—

3.37

32

"—£r—

64

LA f /

24 co

f/ r

/

IP

16 A

co

P

Q

/

/6 Toluene bar,

(DVWater 293 K CCU(D)-Acetic acid/Water

n 0

4

8

2

16

12

6

8

10 3

Dispersed-phase load u D [m /m 2 s]

Dispersed-phase load UD-103

4

[m3/m2s]

Fig. 13.10. Dispersed-phase holdup as a function of the dispersed-phase load for ceramic Hiflow rings

Fig. 13.11. Dispersed-phase holdup as a function of the dispersed-phase load for stacked metal Bialecki rings

The double-layer model described by Gayler et al. and Thornton relates the phase loads uc and uD, the holdup hD, and the relative velocity uR of the dispersed-phase droplets as follows: uc UR

z\hDz\h

\-hD

(13-2)

where 8 is the void fraction of the packing. The velocity of an individual droplet u is described by the Levich function, i.e. 4g

AQ

Q2cCf

O\T

(13-3)

in which Cf is a friction factor and is equal to unity. If w c a n d uD tend to zero, the droplet velocity u tends to a characteristic value uK, which is defined by U

K

—

(13-4)

13.4

Dispersed-phase holdup

321

Thornton proposed that this characteristic velocity be related as follows to the relative velocity uK = -——

uR

(13-5)

i - nD

The droplets attain their terminal velocity in the operating range under consideration. Allowance for the kinematic energy that is lost when dispersed droplets collide with the packing can be made by expressing the velocity of the individual droplets u as a function of the relative droplet velocity, i.e. u = Ch uR

(13-6)

The factor Ch in this equation is characteristic for the packing geometry. Systematic investigations have shown that it can be considered as a constant only within a range of comparatively low holdups hD\ for instance, its deviation in the hD < 0.25 range is merely ± 1 0 % , i.e. Ch = const.

(for hD < 0.25)

(13-7)

This hD range corresponds to uc < 0.7 UC,FI- Rearranging Eqn (13-6) to solve for uR and substituting for u from Eqn (13-3) then gives

Qc

icf=\

Rearranging Eqn (13-2) to solve for hD gives

in which the following applies in the hD < 0.25 range for the right-hand term in the denominator: -^ 8

— i — «£ iiu

(for /*D < 0.25)

(13-10)

I - nD

Thus the term within square brackets in Eqn (13-9) becomes lluR. Substituting the right-hand side of Eqn (13-8) for uR in Eqn (13-9) then gives the following approximate expression for the determination of hD: 2

( -j-T

\ J_

4

(for uc<

0.7 UC,FI)

The holdup factor Ch in this case must be determined by experiment.

(13-11)

322

13 Applications for packing in liquid-liquid systems

Table 13.2. Values for characteristic packing constants Packing

8

Ch

CF1

M03[m]

(C m ) c _ D

25-mm dumped metal Pall ring 25-mm dumped metal Bialecki ring

0.94 0.94

2.976 3.521

0.45 0.45

-

0.29 0.29

25-mm dumped plastic Hiflow ring

0.924

2.667

0.565

-

0.32

35-mm dumped ceramic Hiflow ring

0.83

2.128

0.57

-

0.27

25-mm stacked metal Bialecki ring

0.928

2.151

0.67

50

0.37

50-mm tube column 25-mm tube column

0.94 0.924

2.151 2.151

0.58 -

38 18.8

0.43 0.61

0.93

2.105

0.60

50 135

0.32 0.22

0.897

1.621

0.60

60

0.27

Sheet-metal packing Montz B1-300 Plastics packing Montz Cl-300

Systematic studies have revealed that the holdup factor Ch is independent of the system and is characteristic for the packing geometry. Numerical values are listed in Table 13.2 alongside other packing parameters.

13.5 Phase throughput In the uc > 0.7UC,FI range of continuous-phase superficial velocities, the dispersed-phase holdup increases rapidly with w c , and phase inversion occurs. The hydraulic characteristics in this range thus differ from those in the main operating range. It has been demonstrated by experiment that the following function applies to the loading range in which flooding can be expected: uK = CMu

(for uD -* hD)Fl)

(13-12)

Substituting in Eqn (13-5) then gives the following equation for the relative droplet velocity UR\ uR = CFlu(l-hD)

(13-13)

The experimental results shown in Fig. 13.12 confirm this relationship. Combining Eqn (13-13) with Eqn (13-2) allows the continuous-phase load uc to be expressed in terms of the velocity u of the individual droplets and the holdup hD, i. e.

uc =CF,eu

,hD %-!;{ uDluc

h

(1 -hD) + hD

(13-14) v

'

According to Figs. 13.8 and 13.9, the position of the continuous-phase flood point can be defined by

13.5

T o l u e n e ( D ) / W a t e r t 1 b a r , 293 K. d s = 0.154m,

1

Metnl

| 0.2

IT

5 O

1 1etal I

a

" 25-mm Pall ring

H=2.25m

I

^ 2 5 - m m Bialecki ring

U

-5 0.4 r2

323

Phase throughput

. 1

I

f ^eraniiL

I

I

Sheet metal h = 50mm

0.2

Montz packing B1-300

^ 3 5 - m m Hitlow ring 0

0.2

0.4

1

0.8

0.6

0.6 0.8 0 0.2 (1 -h D )(flooding range) 0.4

0.2

1

0.8

0.4

0.6

0.8

0.6

0.4

0.2

Dispersed-phase holdup h 0 Fig. 13.12. Relationship between droplet velocity and holdup of dispersed phase

due Hhr

(13-15)

= 0

Differentiating Eqn (13-14) accordingly gives the following equation, which can be applied for the determination of the continuous-phase capacity UC,FI at the flood point: uc,n = Cm e u (1 - hD>Fi)2 ( 1 - 2

hDjFl)

(13-16)

The corresponding dispersed-phase superficial velocity uD obtained by combining Eqn (13-13) with Eqn (13-2) is hD(l-hD)2

uD =

w

(13-17)

uDluc

The corresponding position of the dispersed-phase flood point is defined by duD dhD }FI

(13-18);

and the corresponding equation for the determination of the dispersed-phase capacity uD>F/ at the flood point is

324

13 Applications for packing in liquid-liquid systems

uD>Fl = 2 CFl 8 u (1 - hD>Fl) hlFl

(13-19)

Evaluation of Eqns (13-16) and (13-19) requires a knowledge of the dispersed-phase holdup at the flood point, which can be obtained by combining Eqns (13-17) and (13-19), i. e. , h

=

[(uD/uc)2 + __

SuD/uc]m-3uD/uc .

(Ij-ZUJ

4(l-uD/uc) Numerical values for the flood-point constant CFi for various types of packing can be obtained by plotting the results, as indicated in Fig. 13.12. Figures thus determined are listed in Table 13.2. Typical curves for the capacity at the flood point are presented in Fig. 13.13. They are valid for a 50-mm tube column, as illustrated in Fig. 13.6 and stacked with metallic Bialecki rings, and represent operating conditions without mass transfer. The agreement between the theoretical curves and those plotted from measurements is quite good. Fig. 13.14 indicates the effect of mass transfer. In this example, the load at the flood point was increased by about 25 % when mass transfer proceeded from the dispersed to the continuous phase as a result of rapid droplet coalescence. The bed of packing in this case consisted of stacked 25-mm Bialecki rings, which are illustrated in Fig. 13.5. If mass transfer is in the opposite direction, i.e. from the continuous to the dispersed phase, the limiting load would be the same as that without mass transfer.

13.6 Mass transfer in the dispersed and continuous phases From the aspect of industrial applications, the HTU - NTU model described by the following two equations has been found suitable for predicting the efficiency and effective height H of a packed extraction column.

H = HTUQD

' NTUQD

(13-21)

H = HTUoc • NTUQC

(13-22)

If mass transfer proceeds from the dispersed to the continuous phase, the height of an overall transfer unit HTUQD will be given by HTUOD

= HTUD + E(HTUc)

(13-23)

where E is the extraction factor. If mass transfer is in the opposite direction, the following applies: HTUoc = HTUC + 1/E(HTUD)

(13-24)

The extraction factor E is governed by the process conditions, i. e. the phase ratio UDI uc, the slope m of the equilibrium curve for the extraction system, and the phase density ratio QDI Qc- Thus,

13.6

325

Mass transfer in the dispersed and continuous phases

50-mm tube column, metal Bialecki rings d s = 0.0532 m.H = 1.5m

k. r-

21)

•>

LI

16 -Tc)lue ie([))/H 2o-

cu (D)/ H20

k

A

12

Z: ^ \ V

-1

on'

^

1/

bar, z.3j r\

Q

0

4 "ISO

Dutanol D)/l

n 0 4 8 12 16 20 24 Continuous-phase flood load u CFr 1O 3 [m 3 /m 2 s] Fig. 13.13. Characteristic capacity diagram for a tube column packed with metal Bialecki rings for various liquid-liquid systems without mass transfer

25-mm stacked metal Bialecki rings ds=0.154m, H = 2.4m \

0

4

8

i r i i i Toluene(D)-Acetone/H 2 0Toluene(D)-Acetic acid/H20

12

16

20

24

Continuous-phase flood load uc,R-103[m3/m2s] Fig. 13.14. Influence of mass transfer on the capacity of a column packed with stacked metal Bialecki rings

326

13

Applications for packing in liquid-liquid systems

E = m

»!L OS. uc Qc

(13-25)

The expression for the height of an overall transfer unit, HTUQD or HTUoc •> contains the term HTUD or HTUC- The former is related to mass transfer in the dispersed phase {Eqn (13-26)}; and the latter, to mass transfer in the continuous phase {Eqn (13-27)}: HTUD = - ^ -

(13-26)

HTUC = - ^ -

(13-27)

PD aPh

Pc aph

where aph is the phase contact area per unit column volume and (3O (or |3C) is the mass transfer coefficient. The product of aPh and |3 D (or |3C) is referred to as the volumetric mass transfer coefficient. Mass transfer can be adequately described in both directions by the theory of nonstationary diffusion, which Higbie expressed in terms of the diffusion coefficient D in the phase under consideration, the duration of contact x or the length / of the path of contact, and the Fourier number Fo, i.e. (3 = -= \ — V jt y x

(for Fo < 100)

(13-28)

The Fourier number is defined by Fo = 4 - ^

(13-29)

Clys

If the duration of contact x or the length / of the path of contact is short and the Fourier number is less than 100, the diffusion coefficient D can be used to determine the mass transfer coefficient |3. Theoretically, a bubble of the dispersed phase remains in contact with the continuous phase over a path of length / and for a time x until it collides with the packing and renews its surface. The time x is defined by x = /e — uD

(13-30)

Substituting Cs for hDluD {cf. Eqn (13-1)} gives

x = Cs I e

(13-31)

13.7

Extraction efficiency, test results and derivation of model

327

The characteristic length / depends greatly on the packing geometry. The only means of determining its value if the packing is dumped is by experiment. However, if the packing is systematically stacked, e.g. sheet-metal types or in tube columns, a geometrical relationship exists between / and the characteristic size of the individual packing elements, as is evident from Table 13.2. Another parameter that governs the extraction efficiency is the interfacial area aPh, i.e. mass transfer area per unit volume of packing. It is defined by aPh = 6 e -y-

(13-32)

dyS

where dyS is the mean Sauter diameter of the droplets, which depends on the interfacial tension o at the surface of the droplets and the phase density difference AQ, i. e.

V s ^y

(13-33)

where Q is the droplet constant. In the main uc < 0.7 UC,FI loading range, the droplets remain stable. In other words, dvs is independent of load and can be calculated from the droplet constant Cd, for which the following numerical values have been obtained by experiment:

Q = 0.8

(if QD > Qc)

(13-34)

Q=1.0

(if

(13-35)

QC>QD)

At the flood point, the droplet diameter increases by about 20%, i. e. Q,FZ = 1.2 Q

(13-36)

If mass transfer is in the D —»• C direction, i.e. from the dispersed to the continuous phase, the droplet diameter dvs can be expected to increase with an associated decrease in efficiency (cf. Fig. 13.15). If mass transfer is in the C —> D direction, the droplet diameter dvs decreases with an attendant significant improvement in mass transfer (cf. Fig. 13.16).

13.7 Extraction efficiency, test results and derivation of model It has been confirmed by experiments on dumped and stacked packing that the theory of nonstationary diffusion {Eqn (13-28)} can be applied to describe mass transfer efficiency in beds of packing, on the assumption that the duration or path of contact is short. The experiments embraced systems with different physical properties, differences in the resistance to mass transfer, and differences in the direction of mass transfer.

328

13

Applications for packing in liquid-liquid systems

25-mm Bialecki rings, stacked, metal d s =0.1m. H=2.95 m, Toluene(D)-Acetic acid/Water, A=0.3-9 c tkmol/m 3 ] i n l e t -o- 0.1 - o - 0.2 - © - 0.3 Toluene(D)-Acetone/Water, X=1.43

9

£

CD

a

AT Toluene (DJ/Water, uc = (

3 0

2

4

6

8

Fig. 13.15. Mean droplet diameter as a function of the dispersed-phase load for stacked metal Bialecki rings

10

Dispersed-phase load iiD-103[m3/m2s]

25-mm Bialecki rings, stacked, metal d s = 0.1 m, H--2.95 m 6

1

ug-103 =3.372 m 3 /m 2 s uc 103 =2.36 m 3 /m 2 s

5 ^^

m

-^

-^ 4

- Toluene(D)/Acetone^4J 1 j \\<^\—i—(J 1 hnr 7Q1 l^

-D I 0

2

4

I

I

6

i

I 8

10

12

Concentration of acetone in water x [ % w t ]

Fig. 13.16. Mean droplet diameter as a function of the transferred component concentration for stacked metal Bialecki rings

Mass transfer in the D —> C direction The packing efficiency, expressed as the height of an overall transfer unit (HTUOD in the dispersed phase or HTUoc m the continuous phase) is shown as a function of the dispersedphase load UD at a constant phase ratio uD/uc in Figs. 13.17 to 13.20. It is evident from the diagrams that the types of packing concerned hold out good prospects in industrial applications. When dumped, Pall and Bialecki rings have almost the same efficiency in extraction columns, and their performance can be considerably improved by stacking (cf. the curves for the Bialecki rings in Figs. 13.17 and 13.18). The extent of the improvement depends on the shape of the rings.

13.7

329

Extraction efficiency, test results and derivation of model

Metal packing, ds = 0.10 m, H = 1.6 m IsobutanoKDl-Acetic acid/Water, 1 bar, 293 K i

c=

i

I

i

i

I

i

25-mm Pall rings, dumped

1 °-8 _u /u =0.85 D

D-C-

c

o =

o

0.6

25-mm Biaecki rings, stacked

CD CD

i

0.4

1

i

i

i

2

I

1

3

I

i

4 3

5 3

6 2

Dispersed-phase load uD-10 [m /m s] Fig. 13.17. Height of dispersed-phase transfer unit as a function of the dispersed-phase load for metal packings

Metal packing , ds=0.154mJ H = 2.4m Toluene(D)-Acetone/Water, 1 bar, 293 K „

2.0

_§

1.8

1

D

I—

~ CD

c/> cz o

CD CD

Fig. 13.18. Height of dispersed-phase transfer unit as a function of the dispersedphase load for metal packings

/

1.6 - — • - 2 5 - m m Bialecki rings, dumped —a—25-mm Pall rings, damped 1.4 D-C uD/uc=1.429 < 1.2 /25-mm Bialecki rings, stacked 1.0 O u u 0

2

4

6

8

10

12 14

Dispersed phase load UDlO3[m3/m2s]

Figs. 13.19 and 13.20 demonstrate that an increase in efficiency can be obtained by reducing the height h of an element of stacked sheet-metal packing. Thus a reduction in height from h = 135 mm to h = 50 mm improved the efficiency in this case by a factor of 1.64. This fact can be explained by the theory of mass transfer in liquid-liquid systems. These studies also revealed that, if the resistance to mass transfer is only in the dispersed phase, the efficiency (HTUOD) of 50-mm Montz Bl sheet-metal packing hardly differs from that of 25-mm metallic Bialecki rings.

330

13 Applications for packing in liquid-liquid systems

Montz Bl-300 packing Sheet metal, ds=0.157 m. H=2.4 m 1.8

1

/

1-6

h-- 0.13 5 m

Z 14

y

C

- To luerie(D )-Ac .etic ac id/V\/ate - 1 bar, 293 K

cr a

o

* h =0.05m

1.0

/

—n

cp

0.8 —

l

I

0.6

3

3

- uc=2.lMO" m /m^

D-

0

8

12

16 3

20 2

Dispersed-phase load U0 10 [m /m s]

Fig. 13.19. Height of dispersed-phase transfer unit as a function of the dispersedf Montz Bl-300 l 3 0 0 packing ki phase load for

Montz Bl-300 packing Sheet metal d s = 0.157 m, H = 2.4m

o

2.4

! Tnluen e ( D ) - Acetcinp/Wnt Ibar, 293 \(

2.2

o

h -- 0.135 rr

5 2.0 •s CJ> CD

H

7/

o/

J

^ h = 0.'05m

1.8

1

•

- u D /u c = 1.4?

1.6 0

4

8

12

16 3

3

20 2

Dispersed-phase load u D 10 [m /m s]

Fig. 13.20. Height of dispersed-phase transfer unit as a function of the dispersedphase load for metal packings

13.7

Extraction efficiency, test results and derivation of model

331

The studies also embraced the determination of the relationship between the volumetric mass transfer coefficient $DaPh and the dispersed-phase load uD. The curves thus plotted for dumped ceramic and plastics packing are presented in Fig. 13.21; for tube columns with metallic packing of different sizes, in Fig. 13.22; and for stacked metallic and plastics packing, in Fig. 13.23. The two systems studied are representative of resistance to mass transfer in the dispersed phase and of the direction of mass transfer from the dispersed to continuous phase. The diagrams are self-explanatory and need no further explanation. An almost linear relationship also existed between the volumetric mass transfer coefficient (3/)flp/j and the superficial velocity of the dispersed phase uD in all the other cases investigated. Mass transfer in the C —> D direction Similar results were obtained when the direction of mass transfer was from the continuous to the dispersed phase C -» D. In Figs. 13.24 and 13.25, the height HTUOC of an overall transfer unit in the continuous phase is shown as a function of the continuous-phase load wc for a constant phase ratio uDl uc- The high extraction efficiency of both dumped and stacked beds of packing in this case is evident from these diagrams. Fig. 13.25 also clearly indicates that large differences may exist between the efficiency of stacked Bialecki rings and that of Montz sheet-metal packing with extraction systems of this nature. In these systems, the resistance to mass transfer is distributed between both phases. It is evident from the relationships discussed in Sect. 13.6 that the two factors that largely govern the efficiency of a liquid-liquid extraction column are the mass transfer coefficient |5 and the interfacial area aPh. Their product is referred to as the volumetric mass transfer coefficient pfl/v, and can be obtained by combining Eqns (13-11), (13-28), (13-30), (13-32), and (13-33). It is thus given by Eqn (13-37) for the dispersed phase; and by Eqn (13-38), for the continuous phase:

Pz> an = CmuD Pc aph = ^mUD

(a ArTl 3 / 8 r» 1/4 D 1 / 2 igAQ C D

\£

°

^

(13-37) (13-38)

in which Cm is a mass transfer constant that is representative for a given packing and is given by

c-*£][* Eqn (13.38) was adopted to plot the linear relationships shown in Figs. 13.21 to 13.23. The agreement between the theoretical and the experimental results is satisfactory. Allowance can be made for the effect exerted by the direction of mass transfer by means of the following relationship, which was determined by experiment: (Cm)c^D

= 1.5 (Cm)D^c

(13-40)

332

13 Applications for packing in liquid-liquid systems

[Toluene(D)-Acetic acid/Water, 1 bar,293K|

2

4

6

8

10

12

Fig. 13.21. Volumetric mass transfer coefficient for the dispersed phase as a function of the dispersed-phase load for random beds of ceramic and plastics Hiflow rings

14

Dispersed-phase load up •10 3 [m 3 /m 2 s]

Tube columns pocked with metal Biolecki rings

12 z

Dispersed-phase load uD 10 [nr/m s

14

Fig. 13.22. Volumetric mass transfer coefficient for the dispersed phase as a function of the dispersed-phase load for tube columns packed with metal Bialecki rings

13.7

Extraction efficiency, test results and derivation of model

333

Toluene(D)-Acetic ocid/H20;l bar,293K

Fig. 13.23. Volumetric mass transfer coefficient for the dispersed phase as a function of the dispersed-phase load for geometrically arranged beds of metal and plastics Montz packing

0

2

4

6

8

10

12 14

3

3

Dispersed-phase load uD10 [m /m 2 s]

Metal packing, ds = 01 m, H=1.6 m lsobutanol(0)/Acetic acid-Water, I bar, 293 K 0.8 - 2 5-m Tl PCill rings .

dijmp^

i

•Si " i 0.6

c

el

**> 2 5-mm bioiecKi rings>. siuik ?d

0.4

no

n

cp

/uc= O.ob1

U 0.2

Fig. 13.24. Height of continuousphase transfer unit as a function of the continuous-phase load for metal packings

Ki-

0

1

2

3

4

5 3

3

6 2

Continuous-phase load u c l0 [m /m s]

13 Applications for packing in liquid-liquid systems

334

Metal packing , ds=0.154 m, H = 2.4 m Toluene(D)/Acetone-Water. 1 bar, 293 K 2.2 Montz packing B1-300 v h = 0.135m—

1.8

J

1.6 to a o

~

1.4 25-mm Pall rings, dumped i\n a 1.2 -25"mm Bialecki rings, stacked y o

t

0

12 14

0.8 0.6 2

4

6

8

10

Continuous phase load uc-iO 3 [m 3 /m 2 s]

Fig. 13.25. Height of continuous-phase transfer unit as a function of the continuous-phase load for metal packings

In other words, the efficiency of mass transfer in the direction from the continuous to the dispersed phase, i.e. C -* D, is 50% higher than that in the opposite direction, i.e. D —» C. This fact can be explained by the corresponding difference in the droplet diameters. The numerical values of Cm listed in Table 13.2 are valid for the C —» D direction. The application of Eqn (13-40) to Eqn (13.39) implies the following requirement: {Cm)c-

(QV

(13-41)

Applying Eqns (13-11) and (13-33) to this equation yields the following proportional or approximate relationship: (Cm)c

(dys)p{dvs)c-

{hD)c{hD)D-

(13-42)

Substituting the numerical value derived from Eqn (13-40) for the left-hand side of Eqn (13-41) gives (13-43)

13.7

Extraction efficiency, test results and derivation of model

335

In this case, the square root term can be equated to unity. Likewise, substituting the numerical value derived from Eqn (13-40) for the left-hand side of Eqn (13-42) gives (13-44) It also follows from Eqn (13-39) that the effective length / of the path of contact is related to the characteristic fluid-dynamic constants Ch (for the dispersed-phase holdup) and Cd (for the droplet diameter in the dispersed phase) and to the mass transfer constant Cm. The following simple equation thus applies: Ch

/ = 32.41

(13-45)

2

(Cm Cd) Combining Eqns (13-23) and (13-25) to (13-27) with Eqns (13-37) and (13-38) gives the height of an overall dispersed-phase transfer unit HTUOD for mass transfer in the D -^ C direction, i. e. 1

1 (

.

x3/8

(g AQ)

n l/2

_l/4

UD

QC

,

+'

m

QD

n l/2

~

DC

QC

(13-46)

Likewise, combining Eqns (13-24) - (13-27) with Eqn (13-38) gives the height of an overall continuous-phase unit HTUoc for mass transfer in the C —> D direction, i.e. 1

a

UQ

I 1

1

Qc

The effective height H of the column required for extraction can then be obtained from Eqns (13-21) and (13-22) and the number of transfer units NTUOD and NTUOC-

14 Examples for the design of packed columns The relationships discussed in the previous chapters are important for the design and operation of countercurrent packed columns. Examples taken from the fields of desorption, absorption, rectification, and liquid-liquid extraction shall now be given to demonstrate how they can be applied in plant engineering. It is presumed that the reader is acquainted with the principles underlying thermal separation techniques. Fig. 14.1 shows a flow chart for a rectification column with a concentration x of low boilers in the feed F, overhead product D, and bottoms B. These fractions are presented qualitatively in the ylx diagram. The example concerned is the separation of a binary mixture; the equilibrium curve ye = f(x) and the operating lines y = f (JC), viz. BI in the stripping zone and ID in the enrichment zone, are given.

Rectification

Reboiler B = F-D

Fig. 14.1. Qualitative determination of transfer units in rectification

hF = feed enthalpy hp = feed enthalpy at boiling temperature Ah v =vaporization enthalpy at feed section

Packed Towers in Processing and Environmental Technology. Reinhard Billet Copyright © 1995 VCH Verlagsgesellschaft mbH, Weinheim ISBN: 3-527-28616-0

338

14 Examples for the design of packed columns

Fig. 14.2 illustrates the principles of absorption and desorption. The factors given are the gas volumetric flow rate V, the concentration of transfer components y in the gas, the liquid volumetric flow rate L, and the concentration of transfer components x in the liquid. The subscript u indicates the bottom of the column; and the subscript o, the head of the column. The gas load Y of transfer component is related to the mole fraction y by

Likewise, the liquid load X of transfer component is related to the mole fraction x by

X

< 14 - 2 >

= T^

The number of transfer units NTUOv required for rectification between zones with molar fractions ya and yb is given by

NTUov = /a~y"

In 4 ^

Aya - Ayb

(14"3)

Ayb

The terms Aya and Ayb in this equation represent the difference between the equilibrium mole fraction ye>a or ye>b and the vapour mole fraction ya or yb, i.e. &ya = ye,a - ya

(14-4)

An = ye,b-yb

(14-5)

The size of the zones should be selected so that the slope myx of the equilibrium curve is practically the same in each. In contrast, the slopes of the equilibrium curves in absorption and desorption processes can be regarded as constant over the entire range of concentrations between the head and the foot of the column, particularly at low phase loads. In this case, if the gas load is adopted as a measure for the concentration, the number of transfer units in absorption processes will be given by

where Yu and Yo are the gas loads at the foot and head of the column. The terms AYU and AYO are then defined by AYu = Yu-mYXXu

(14-7)

AYo = Yo-mYXXo

(14-8)

The corresponding equations for the liquid load are

NTUOL=

f-f AXU - AXn

In-^ AXn

(14-9)

14 A X M

_

AX0 =

Examples for the design of packed columns

1 mYX

Y

x

339 (14-10)

—Yo-Xo mYX

(14-11)

Likewise, the number of transfer units required in desorption processes will be given by Eqns (14-12) to (14-14) if the gas load is adopted as the measure for the concentration: Y -Y u °

AY

(14-12)

°

Absorption

Desorption

ye-

x,y m yx L/V X,Y L,V r777'

Mole fraction in liquid, gas or vapour Slope of the equilibrium line Molar liquid-to-gas ratio or slope of the operating line Load fraction of transfer component in liquid /gas Carrier stream of liquid /gas phase L _ Y 0 -Y u Y Q = 'U

V

+

*W~

A n — A ii

Fig. 14.2. Qualitative determination of transfer units in absorption and desorption

340

14 Examples for the design of packed columns

Yo = mYXXo-Y0

(14-13)

Yu = mYXXu-Yu

(14-14)

The corresponding equations for the liquid phase are

1 Yo

(14-16)

Yu

(14-17)

mYX

= xu

1 mYX

In a rectification process, as illustrated in Fig. 14.1, the reflux ratio is given by r

> r-*n = T T T T

(14-18)

The molar flow rate at the head of the column would then be V= F

XF XB

~ (r + 1) D ~ %B

X

(14-19)

In an absorption process, as illustrated in Fig. 14.2 (left), the total liquid-vapour ratio must be higher than the ratio of the carrier liquid, i.e. solvent, to the vapour, i.e.

( 14 " 2 °)

Y > T" The flow rate of solvent in this case is given by

Lm = V lu~*°

(14-21)

In desorption, as illustrated in Fig. 14.2 (right), the total vapour/liquid ratio must be higher than the ratio of the stripping gas to the liquid, i.e. V

V

The flow rate of stripping gas in this case is given by Vm = L ^ ^ x

o,m

x

u

(14-23)

14 Examples for the design of packed columns

341

In absorption and desorption, the total molar flow rate of vapour, consisting of the carrier gas and the transfer components, is given by V =V(\ + Y) where V = Vu (1 - yu)

(14-24)

and the total molar flow rate of liquid, consisting of the carrier liquid and the transfer components, by L = L(l+X)

where L = Lo(1 -x o )

(14-25)

The column diameter ds can be expressed in terms of the free cross-sectional area As, i. e. ds = \ —As y JI

(14-26)

If uv is the superficial gas velocity, As can be defined by As = ^

^

Uy

(14-27)

Qy

Thus the column diameter can be calculated from the operating parameters V [kmol/h], uv [m/s], T [K], and p [bar], i. e. ds = 5.4 • 1(T3 \l V — — 17

p

(14-28)

Uy

Fig. 14.3 illustrates liquid-liquid extraction in which the specific gravity of the continuous phase (Subscript C) is greater than that of the dispersed phase (Subscript D). In this case, the total number of transfer units NTUOc derived from the HTU-NTU model is given by NTUoc =

Cc

'°~Cc'u In ^ Aco - Acu Acu

(14-29)

where Aco is the driving concentration difference at the head of the column, as defined by Eqn (14-30), and Acu is the driving concentration difference at the foot of the column, as defined by Eqn (14-31), i. e. Aco = cc,o - ~ - cDtO

(14-30)

AcM = cc,u - — cD>u

(14-31)

Another case to consider is that in which mass transfer is in the C —> D direction and the desired separation efficiency is given by ^E = 1-££JL

(14-32)

342

14

Examples for the design of packed columns

h CQ.O C

Co

Fig. 14.3. Qualitative determination of transfer units in liquid-liquid extraction

Rearranging this equation gives rise to the following: CC,u = (1

(14-33)

-

from which it can be derived that the concentration of transfer components in the continuous phase decreases from cc>o at the head of the column to cc>u at the foot. If the phase ratio in the extractor is uc/uD, the concentration of transfer components in the dispersed phase increases from a value of cD>u at the foot of the column to the following value of cDo at the head of the column: c

(cC,o ~

D,o —

c

D,u

(14-34)

UD

Eqn (13-22) allows the effective height H to be determined from NTUOc and HTUOc\ and, if the volume flow rate Vc of the continuous phase is given, the column diameter ds can be obtained from the load uc < 0.7 uc, FI from the following equation: (14-35)

14.1 Determination of the diameter of an off-gas absorption column with various types of packing Polluted air flowing at a rate of 105 m 3 /h STP is to be scrubbed with water in a packed column. The liquid-to-gas ratio must be varied between LIV = 1 and L/V = 10, depending on the degree of contamination. The maximum permissible load is that at the loading point.

14.1

Determination of the diameter of an off-gas absorption column with various types of packing

343

Under these conditions, what diameter would the column have to be if 50-mm packing of the following types had to be installed? Plastics packing: Intalox saddles, Bialecki rings, Pall rings, and Norpac rings Metal packing: Pall rings, Hiflow rings, Bialecki rings, and VSP rings Solution Properties of the system Density and dynamic viscosity of the gas QV= 1.19 kg/m 3 TJV = 18 • 10~6 kg/ms Density and dynamic viscosity of liquid QL = 998 kg/m 3 TU = 1 • 10"3 kg/ms The values of Cs required to calculate the resistance coefficients § 5 at the loading point from Eqn (4-29) are listed in Table 4.1.

Gas, air 100000 m 3 /h, Liquid: water, STP, loading capacity 5.4

/ Packing size 50 mm

j

5.2

/

- I N TALOX 5;adc le 5.0

/

/ - Bicilec
4.8

/

rOu 11

•y

y

>

Hifl DW

my

y

/

TD

If

1

4.6


A-Pall ring /

f ij

4.4

I !

4.2

4.0

/

/ /

2

1

H1

A

1

0

-NOR-PAC ring

/

- Plast IC

1

3.8

/

4

6

8

10

0

fK A

Bialecki ring

- v SP

2

ing Mr tnl 4

6

8

10

Liquid/gas ratio L/V

Fig. 14.4. Column diameter as a function of the liquid-vapour ratio for the data given in Section 14.1

344

14

Examples for the design of packed columns

The values of § s calculated from Eqn (4-29) for all the packings, together with the associated values for a and 8, which are also listed in Table 4.1, allow the corrresponding vapour flow rates at the loading point uv = uvs to be determined by iteration as functions of the liquid/vapour ratio LIV from Eqn (11-82). The evaluated results are plotted in Fig. 14.4. It can be seen that the column diameter ds required for a ratio LIV = 10 is about 25% greater than that for LIV = 1. The diagram also shows that the differences in diameter associated with plastics packing are greater than those for metal packing.

14.2 Design of a packed column for the rectification of an isobutane/n-butane mixture An isobutane/n-butane mixture flowing at a rate of 500 kmol/h has to be separated in a rectification column. It consists of 60 % of the low-boiling component and 40 % of the highboiling and enters the column at the boiling point. The overhead product has to consist of 99.9% mol of isobutane, and the bottoms may contain only 0 . 1 % mol of this component. The packing is of the Montz Bl-200 sheet-metal type, and the column operates at an overhead pressure of 3.6 bar and a reflux ratio of 15 under the conditions at the loading point. Solution Average properties of the system \iv = 58.124 kg/kmol QV Tjv Dv am

= = = =

\iL = 58.124 kg/kmol

3

QL = 561.3 kg/m 3 t\L = 0.13078 • 10"3 kg/ms DL = 8.44 • 10~9 m 2 /s oL = 8.88-10- 3 kg/s 2

8.398 kg/m 7.76 • 10~6 kg/ms 1.17 • 1(T6 m 2 /s 1.35

Characteristic data for the packing derived from Tables 4.2, 4.4, and 5.2 a 8

= 200 m 2 /m 3 = 0.979 m 3 /m 3

Cs = 3.116 CL = 0.971

Cv = 0.390 CP = 0.355

Product streams designated as in Fig. 14.1

5 D D 5

kmol

°°° ° i r

0.6-0.001

0.999-0.001

3O 3O

L = 300.1 kmol/h • 15 = 4501.5 kmol/h = 4501.5 kmol/h • 58.124 kg/kmol = 261645 kg/h V = 300.1 kmol/h (15 + 1) - 4801.6 kmol/h = 4801.6 kmol/h • 58.124 kg/kmol = 279088 kg/h

14.2

Design of a packed column for the rectification of an isobutaneln-butane mixture

345

Resistance coefficient at the loading point according to Eqn (4-29) 9.806 'U

= 0.514

261645 / 8.398 \ 1/2 /0.131-10 [ 279088 \ 561.3 / \ 7.76 • 10"6

Relationship at the loading point according to Eqn (4-28)

uv,s =

/ 9.806^ 0.514

0.979 2001

12 9.806

2001

12 0.131-10- 3 w L 9.806 561.3

0.131-10- 3 w L 561.3

561.3 \ 1/2 8.398

Relationship at the loading point according to Eqn (11-82) for uL and uv = uVtS

261645 8.398 uL = 279088 ' 561.3uv,s Vapour load at the loading point determined by solving Eqns (4-28) and (11-82) by iteration uv>s = 0.489 m/s Cross-sectional area of column according to Eqn (14-27) As

279088/3600 = 18.88 m2 0.489 • 8.398

Column diameter according to Eqn (14-26) ds = \—'

18.88 = 4.9 m

Column diameter selected for planning: ds = 5 m. Cross-sectional area of the planned column A s = — • 5 2 = 19.635 4 Vapour and liqud loads in the planned column 279088/3600 uv = 8.398 • 19.635 = 0.47 m/s 261645/3600 3 3 2 uL = 561.3 • 19.635 = 6.59 • 10- m /m s

346

14

Examples for the design of packed columns

Theoretical liquid holdup according to Eqn (4-27)

HL

" I

0.131 • 1(T3 • 6.59 • 1(T3 • 2 0 0 2 U / 3 ' 9.806 • 561.3

12

= 0.0422 m 3 /m 2 Particle diameter according to Eqn (4-66)

Factor to allow for end effects {Eqn (4-57)}

fs = 1 +

4 200 -5

-i

= 0.996

Reynolds number for the stream of vapour {Eqn (4-65)} 0.47 • 0.63 • 10"3 • 8.398 (1 - 0.979) 7.76 • 1C

0-996 = 15 200

Reynolds number for the stream of liquid {Eqn (4-69)} 6.59 • 10-3 • 561.3 - 141.42 200 • 0.131 • 10-3

L

Wetting factor for the packing {Eqn (4-68)} W= exp

141.42 200

= 2.028

Resistance coefficient for the stream of vapour {Eqn (4-67)}

Pressure drop in the vapour stream {Eqn (4-58)}

H

200 8.398 - 0.472 1 T— TTT^T = 128.3 n ^ x3 • ~ (0.979-0.0422) ' 2 ' 0.996

= 0-564 • ,

'

Hydraulic diameter {Eqn (5-15)} A

0.979

= 0.01958 m

Pa/m

14.2

Design of a packed column for the rectification of an isobutaneln-butane mixture

347

Area of phase contact {Eqn (5-16)} ^

3

0

9 7 9 - ( 6-59-10^-561.3 \ 200- 0.13078 • 10~3

a

'(6.59- 1Q-3)2 561.3 \ 0 7 5 / (6.59 • 10' 3 ) 2 200 ^ 0 4 5 0.00888 -200 / \ 9.806

~ "

Height of a transfer unit in the liquid phase {Eqn (5-5)}

HTUL =

1 0.13078 • 10-3 \ 1/6 / 0.01958 0.971 561.3 • 9.806 8.44 • 10

6.59 • 10" 200

1.045

- 0.083 m Height of a transfer unit in the vapour phase {Eqn (5-14)}

200 • 7.76 • 10"6 \ 3M /1.17 • 10~6 • 8.398 \ 1/3 0.47 • 8.398 / \ 7.76 • 10~b /

1 1.045

= 0.143 m Determination of the concentration zones (Table 14.1) Calculation for the height of the uppermost zone Xa

= XD = 0.999 kmol/kmol to xb = 0.8 kmol/kmol

Characteristic concentration in the uppermost zone Phase equilibrium concentration corresponding to ya = xa = 0.999 kmol/kmol {Eqn (1-38)} 1 35 • 0 999 * • = 1 + (1.35-1)0.999

= °" 93

Vapour concentration corresponding to xb = 0.8 kmol/kmol on the operating line for the enrichment zone {Eqn (1-13)} yb = —

15

0 999 • 0.8 + -z = 0.8124 kmol/kmol

Phase equilibrium concentration

= 8438 1 /(OS-I

0.8

°-

348

14 Examples for the design of packed columns

Differences in concentration {Eqns (14-4) and (14-5)} Aya = 0.9993-0.999 = 0.0003 kmol/kmol A j b = 0.8438-0.8124 - 0.0314 kmol/kmol Number of vapour-side transfer units {Eqn (14-3)} 0.999-0.8124 NTUov

=

0.0003

o.ooo3-o.o3i4 ' l n "b^TT =

28

'

Mean slope of equilibrium curve {Eqn (1-66)} yx

[1 + (1.3 1.3 - 1) 0.867]2

= 0.8184

Stripping factor {Eqn 1-30)} X = 0.8184

4501.5 kmol/h

Number of theoretical stages {Eqn (1-27)}

Height of an overall transfer unit {Eqn (1-62)} HTUov = 0.143 + 0.8335 • 0.083 = 0.212 m Height of uppermost concentration zone {Eqn (1-64)} if no allowance is made for end effects H = 0.212 • 28.8 = 6.106 m The results thus obtained for all the concentration zones are listed in Table 14.2. Total theoretical height if no allowance is made for end and distribution effects 2 H = 15 m.

14.3 Scaling up measurements performed in pilot plants In mass transfer studies in a column with a new type of packing, a total of NP>a = 5.6 transfer units was measured for a height of HPa = 1.5 m. Hence the number of transfer units per unit height of bed was (NIH)P>a = 3.733 m"1. In a control experiment with a bed height of HPb = 2 m, the number of transfer units measured was NPft> = 6.8. What would the error

14.3

Scaling up measurements performed in pilot plants

349

be if the efficiency determined for a height HPa = 1.5 m were to be taken as a basis in calculating the height HT of an industrial-scale column required to realize NT = 20 transfer units on the assumption that the inlet distribution remains unchanged? For the purpose of the calculation, assume that the height of the inlet zone Ht is less than HPa = 1.5 m. Solution If no allowance is made for end effects, the height of the column would be

Hw

_ _ g t _ = - | L = 5.36 m

If it is assumed that the separation efficiency remains constant in the H > Ht zone, the following applies for Hi < HP dN \

NPb-NPa

6.8-5.6

dHJH>Hi

HP>b-HP>a

2-1.5

„ A -, :.4 m

According to the model presented in Fig. 8.4, the end effects (Nd + ANt) can be determined by rearranging Eqn (6-8) for the case of H = HPa, i. e. ) n lH>Hi = 5 . 6 - 1 . 5 • 2.4 = 2 The relative difference in height required to compensate end effects can then be obtained from Eqn (8-15), i.e.

7 1

-2Q

^ 1+

JJ'2A

According to Eqn (6-35), this corresponds to an efficiency ratio of

rjr = 1 - 4HrT " =

X

" °- 285 = °- 715

The actual column height required can then be calculated from Eqns (6-35) and (6-39), i. e.

350

14

Examples for the design of packed columns

The same result can be obtained from Eqn (6-28). Thus

P_a

Nd + AN(\H

jP,a

1 1.5

2

= 7.49 m 3.733

Hence, the absolute value for the additional height required is AH = 4 ^ " HT = 0.285 • 7.49 = 2.13 m. HT This figure agrees with that for the difference between the values calculated for HT and HT(P), i- e.

AH = HT-HT(P)

= 7.49-5.36 = 2.13 m.

Hence, if the column design were to be based on the measured value for (N/H)P>a = 3.733 m"1, the height of the bed would be too short by an amount AH

HT

100 = 28.5%.

14.4 Design of an absorber for removing acetone from process air The spent air from a production plant contains 1 % mol of acetone and flows at a rate of 2000 m 3 /h at 27 °C. The acetone has to be removed to a final concentration of 100 mg/m 3 by absorption in water in a column packed with 50-mm metal Pall rings. The main dimensions of the column, which is operated at the loading point, have to be determined for the case in which the water consumption is 1.4 times higher than the minimum. Solution Average properties of the gas phase \iv

= 28.96 k g / k m o l

QV

= 1 . 1 6 2 kg/m3

T]v

= 18.13 • 10~ 6 k g / m s

Dv

= 10.8 • K T 6 m 2 / s

1^

= 58.08 k g / k m o l

Molar mass of acetone

14.4

Design of an absorber for removing acetone from process air

Average properties of the liquid phase \iL = 18.02 kg/kmol QL = 997 kg/m 3 T) L = 0.857 • 10"3 kg/ms DL = 1.18 • 10~ 9 m 2 /s oL =12- 10- 3 kg/s 2 Slope of equilibrium curve for the acetone-air/water absorption system YYlYx = 2.314

Packing characteristics (Tables 4.1, 4.3, 4.6 and 5.1) a = 110 m 2 /m 3 E = 0.952 m 3 /m 3

C 5 = 2.725 CL = 1.192 Cy = 0.410

CP = 0.763 Ch = 0.784

Product streams (Fig. 14.2, left) Vu

= 2 0 0 0 ^ • , 1 ^ 2 v ^ m 3 | = 80.25 kmol/h ft 28.96 kg/kmol

yM

= 0.01 kmol/kmol

yM

=

V

= 80.25 (1-0.01) = 79.45 kmol/h

°^^

= 0.01 kmol/kmol

=ino

m3

28.96 kg/kmol 58.08 kg/kmol -1.162 kg/m 3

= 4.291 • 10"5 kmol/kmol 4 291 • 10~5 4 2 9 1

1 -4,291 = 4322

"10

kmol/kmo1

3 kmol/kmo1

L

= 1.4 • 183.04 = 256.26 kmol/h = Lo

x

= 0 + T 9 ; 4 ^ (0.01 - 4.291 • 10' 5 ) = 3.087 • 10~3 kmol/kmol 256.26

u

351

352

14 Examples for the design of packed columns Lo

= 256.26 kmol/h • 18.02 kg/kmol = 4617.7 kg/h

Vo

= 79.45 (1 + 4.291 • 1(T5) = 79.45 kmol/h = 79.45 kmol/h • 28.96 kg/kmol = 2301 kg/h

Resistance coefficient {Eqn (4-29)} 9.806 2.7252

= 0.629

L162

\ 18.13 • 10~6

2301 \ 997 /

Vapour velocity at the loading point {Eqn (4-28)}

uv,s =

9.806 0.629 12 9.806

0.952 1101

12 9.806

-no1

0.857 • 10~3 uL 997

1/6/

997

0.857

uL 997

\i/2

1.162

Liquid velocity at the loading point {Eqn (11-82)} for uL and uv = uv,s 4617.7

1.162

Gas velocity at the loading point determined by solving Eqns (4-28) and (11-82) by iteration uv>s = 1.988 m/s Cross-sectional area of column {Eqn (14-26)}

A

2300.9/3600 1.162 • 1.988

°277

Column diameter {Eqn (14-27)} ds=\—'

0.277 = 0.594 m

Column diameter selected for planning: ^ = 0.6 m Cross-sectional area of planned column As = — • 0.62 = 0.2827 m2

2

14.4 Design of an absorber for removing acetone from process air Vapour and liquid loads in the planned column

Uv=

^

=

2300.9/3600 1.162-0.2827

=1

4617.7/3600 997 - 0.2827

= 44 5 555

-945m/s 3

'

'

1100

3 2 mm / m S

Theoretical liquid holdup {Eqn (4-27)} 0.857 • 10-3 • 4.55 • HT3 • HO2 \ 1/3 )

/

Particle diameter {Eqn (4-66)} dp = 6 •

1

- ^ p 9 5 2 = 2.618 • 10-3 m

Wall factor {Eqn (4-57)} /

\"1

A

= 0.9429 Reynolds number for gas flow {Eqn (4-65)}

v

1.945 • 2.618 • 10~3 • 1.162 (1-0.952) 18.13 • 10-6

°9429 -

Reynolds number for liquid flow {Eqn (4-69)}

u

4.55 • I P 3 • 997 110.0 • 876 • 10- 3 "

4 8 1 2

Wetting factor for the packing {Eqn (4-68)}

Resistance factor in gas flow {Eqn (4-67)}

Pressure drop per unit height in gas flow {Eqn (4-58)} Ap H

110 ()R2

(0.952 - 0.0387)

3

1.162 • 1.9452

1

2

0.9429

= 277.2 Pa/m

353

354

14 Examples for the design of packed columns

Hydraulic diameter {Eqn (5-15)} rf, = 4

. ^ f = 0.0346m

Phase contact area {Eqn (5-16)} Eh. — a . n QS? 0 - 5

a "

3

°-952

-

1 110 • 0.857 • 10-3

(4^55 • 1 0 - y 997 \015 ( (4.55 • 10' 3 ) 2 110 , 0.072 -110 / \ 9.806

— U.u/^

Height of transfer unit in the liquid phase {Eqn (5-5)} 3 0.857 • 101.192 \ 997 • 9.806

L

\ 1/2 /4.55 • 10

0.0346 9

1.18 - KT /

\

110

/

\ 0.672 /

= 0.539 m Height of a transfer unit in the gas phase {Eqn (5-14)} HTTJ HTUv =

l

^^ (0'952 " °° 3 8 7^) T ^ rnos?

n ^ ^ i / 2 0-03461/2

1.945

10.8 • 10-6

/IIP - 18.13 • IP"6 \ 3 / 4 /l0.8 • IP' 6 • 1.162 \ 1/3 / 1 \ \ 1.945 • 1.162 ) \ 18.13 • 10~6 / \ 0.672/ = 0.456 m Differences in gas loads {Eqns (14-7) and (14-8)} AYU = 0.01-2.314 • 3.807 • 10~3 = 2.864 • 10~3 kmol/kmol AYO = 4.291 • 10~5 -2.314 • 0 = 4.291 • 10"5 kmol/kmol Overall number of gas-side transfer units {Eqn (14-6)} 0.01-4.291 - H P 5

MTTI NTUov

=

2.864 - IP' 3

2 . 8 6 4 - 1 0 - 3 - 4 . 2 9 1 - 1 0 - 5 ' l n 4.291 • 10"5

Stripping factor {Eqn (1-68)} - 2.314 • I9*™1* ^ 0.7174 256.26 kmol/h

=

U

^

14.5 Design of a desorber for removing carbon dioxide from process effluents Overall height of a transfer unit {Eqn (1-62)} HTUov = 0-456 + 0.7174 • 0.539 = 0.843 m Height of bed of packing without allowance for end and distribution effects H = 0.843 • 14.826 = 12.49 m

14.5 Design of a desorber for removing carbon dioxide from process effluents The carbon dioxide content of a process effluent flowing at a rate of 4 m 3 /h is to be reduced from 1.5 kg/m 3 to 0.02 mol/m 3 by desorption with air in a packed stripper column operating at 20°C and 1 bar. The carbon dioxide content of the inlet air is 0.03% vol., and that of the air leaving the desorber outlet must not exceed 1 % vol. The desorption column is to be packed with 35-mm plastics Pall rings. Determine its main dimensions. Solution Average properties of the gas phase \iv QV r\v Dv

= = = =

28.96 kg/kmol 1.188 kg/m 3 17.98 • 10~6 kg/ms 15.4 • 10~6 m 2 /s

Data for carbon dioxide \iA = 44.01 kg/kmol QA = 1.818 kg/m 3 Average properties of the liquid phase \iL QL r|L DL oL

= = = = =

18.02 kg/kmol 998 kg/m 3 0.998 • 10"3 kg/ms 1.82 • 10~ 9 m 2 /s 72 • 10- 3 kg/s 2

Slope of equilibrium curve for the carbon dioxide-water/air system rriyx = 1440 Characteristic data for the packing derived from Tables 4.1, 4.3, 4.6 and 5.1 a = 145 m 2 /m 3 8 = 0.906 nr7m 3

Cs = 2.654 CL = 0.856 Cv - 0.380

CP = 0.927 Ch = 0.718

355

356

14

Examples for the design of packed columns

Product streams corresponding to Fig. 14.2, right to

= 4 • 998 = 3992 kg/h = 4 •~ ^ -

X

°

=

= 221.53 kmollh

1 5

" ' 4408l'02998

X

° = 1 + 054 1( Vo-4

= 6154

" 10 " 4

kmol/kmo1

= 6 15

- ° • 10"4 k m o l / k m o 1

L

= 221.53 (1 - 6.150 • 10"4) = 221.39 kmol/h

y

=

"

0 3 10 2 °°0 3 10~ 4I01 I • liliiss3 =°3 -°22

kmol/kmo1

4

Yu

=

t

3 02 • 10~ "3 Q 2 1Q_4 = 3.02 • 10"4 kmol/kmol

= 0.01 • ^

; \-™

= 0.01007 kmol/kmol

18 09 = 0.02 • 10"3 • —^— = 3.614 • 10~7 kmol/kmol Total mass balance

K

= 13,80 (1 + 0.01017) = 13.94 kmol/h - 13.94 • 28.96 = 403.71 kg/h

K

- 13.80 • 28.96 (1 + 3.02 • HT4) = 399.77 kg/h 399

- 7 7 = 336.50 m 3 /h 1.188

Lu

= 221.39 • 18.02 (1 + 3.614 • 10~7) = 3989 kg/h

Resistance coefficient {Eqn (4-29)}

2.654

3989.45 399.77

9.806 1.188 1;2 0.998 • 10" 998 / 17.98 • 10"

0.4 1-0.652

14.5 Design of a desorber for removing carbon dioxide from process effluents Vapour velocity at the loading point {Eqn 4-28)} 9.806 \ 1/2 [ 0.906 1.980 / [ 1451/6 12 9.806

1/2

/ 12 \ 9.806

0.998 • 10~3 uL 998

0.998 • 10~3 uL \1161 998 998 / \ 1.188

Liquid velocity at the loading point {Eqn (11-82)} for uL and uvs 3989.45 399.77

1.188 998

Uy s

'

Gas velocity at the loading point determined by solving Eqns (4-28) and (11-82) by iteration uVjS = 1.195 m/s Cross-sectional area of column {Eqn (14-26)}

As

=

399.77/3600 1.188-1.195

=

Column diameter {Eqn (14-27)} ds = \

— • 0.0739 = 0.316 m

Column diameter selected for planning: ds = 0.32 m Cross-sectional area of planned column As = — - 0.322 = 0.0804 m2 Vapour and liquid loads in the planned column

Uv=

399.77/3600 1.188-0.0804

^rn , -163m/s

=1

3989.45/3600 UL =

998 • 0.0804 =

3 13 8

'

'

10

Theoretical liquid holdup {Eqn (4-27)} 0.998 • 10"3 • 13.8 • 10~3 • 1452 \ 1/3 = 0.0708

357

358

14

Examples for the design of packed columns

Particle diameter {Eqn (4-66)}

=

= 3.890 • 1(T3 rn

6

Wall factor {Eqn 4-57}

Reynolds number for gas flow {Eqn (6-65)} 1.163 • 3.890 • 10~3 • 1.188 (1 - 0.906) 17.98 • 10~6

0.9206 = 2927

Reynolds number for liquid flow {Eqn (4-69)}

=

*«•

13.8 • 10-3 • 998 145 • 0.998

Wetting factor for the packing {Eqn (4-68)}

Resistance factor in gas flow {Eqn (4-67)}

o ^-"•"'

^2927

' 2927 008 M

-™-j 0.906

= 1.284

Pressure drop per unit height in gas flow {Eqn (4-58)} Ap H

_ ~

1.188 • 1.1632

145 '

' (0.906 - 0.0708)

3

1 = 240Pa/m 0.9206

Hydraulic diameter {Eqn (5-15)}

dh = 4 • ° ^ — = 0.02499 m 145

Phase contact area {Eqn (5-16)}

a

=

3

3 • 0.906 - (( 13-8 • 10- • 9983 \ 145 • 0.998 • 10"

p

(13.8 • IP' 3 ) 2 - 998 \ 0 7 5 / (13.8 • 10"" 33))22 145 \'Q-45 = 0.799 0.072 • 145 9.806

14.5

Design of a desorber for removing carbon dioxide from process effluents

359

Height of transfer unit in the liquid phase {Eqn (5-5)} _ L

1

/ 0.998 • 1(T 3 \ 1 / 6 / 0.02499

~ 0.856 \ 998 • 9.806 j

\ 1 / 2 /13.8 • 10~3 \ 2 / 3 / 9

\ 1 . 8 2 • 10~ f

\

145

/

1

= 0.772 m Height of a transfer unit in the gas phase {Eqn (5-14)}

145 • 17.98 • 10"6 \ 3M /15.4 • 10"6 • 1.188 \ 1/3 / 1 \ _ 1.163-1.188 / 1 17.98-10- 6 / \o.799/~ °'187

m

Differences in gas loads {Eqns (14-16) and (14-17)} AXO = 6.154 • 10"4 AXU = 3.614 • 10"7 -

° ' 0 i 0 ^ 7 = 6.083 • 10~4 kmol/kmol 1440 3 02 • 10~4 — = 1.516 • 10~7 kmol/kmol 1440

Number of liquid-side transfer units {Eqn (14-15)}

NTUoL oL

6.154 • 10~4 - 3.614 • 10~7 ~ 66.083 0 8 3 • 105 1 6 • 10"' lO" 7 10-44 - 1 1.516

/ 6.083 • 10"4 = 8.39 \ 1.516 • 10"

Stripping factor {Eqn (1-68)}

221.39 kmol/h Height of an overall transfer unit {Eqn (1-63)} HTUOL

= 0.772 +

X

• 0.187 = 0.774 m

Height of bed if end and distibution effects are neglected {Eqn 1-65)} H = 0.774 • 8.39 = 6.494 m

\

\ 0.799 /

360

14

Examples for the design of packed columns

14.6 Determination of the difference between the theoretical and the real liquid holdup The purpose here is to determine the differences between the theoretical and the real liquid holdups applicable to the loading conditions under which the columns discussed in Sections 14.4 and 14.5 were operated. Solution Known values in Section 14.4 Ch = 0.784 a

= 110 m 2 /m 3

QL = 997 kg/m 3

uL

= 4.55 • 10~3 m 3 /m 2 s

i\L = 0.857 • 10~3 kg/ms

ReL = 48.12

Froude number for the liquid phase {Eqn (4-27)} = L

HO (4-55 • I C Y 9.806

.

=

1Q_4

Hydraulic area {Eqn (4-75)} — = 0.85 • 0.784 • 48.1 0 2 5 (2.322 • 10~ 4 ) 01 - 0.760 a Real liquid holdup {Eqn (4-73)}

= 0.0322 m 3 /m 3 Calculated difference between the theoretical and real holdups AhL

0.0387-0.0322

=

"TiT

^^

=

°'m

Known values in Section 14.5 Ch = 0.718 a = 145 m 2 /m 3

QL = 998 kg/m 3 r\L = 0.998 • 10~3 kg/ms

Froude number for the liquid.phase {Eqn (4-27)}

uL = 13.8 • 10"3 m 3 /m 2 s ReL = 95.17

14.7 Additional column height required to compensate maldistribution

361

Hydraulic area {Eqn (4-75)} — = 0.85 • 0.718 • 95.17 025 (2.816 • 10~3)01 = 1.060 a Real liquid holdup {Eqn (4-73)}

= 0.0736 m 3 /m 3 Calculated difference between the theoretical and real holdups AhL hL

0.0708 - 0.0736 = - 0.039 0.0708

14.7 Additional column height required to compensate maldistribution In a column of ds = 2250 mm diameter packed with 50-mm Pall rings, the liquid distributor gives rise to maldistribution of M = 10%. The phase ratio is LIV = 1. If the maldistribution were to remain effective over the entire height of the column, what would be the additional column height required to compensate the attendant loss in efficiency? Solution The loss in efficiency can be read off from the diagram in Fig. 8.12 against the value 4 _ 2250 _ d ~ 50 ~ 4 5 The numerical value thus obtained is AE = 15%. In other words, the efficiency would be reduced by a factor {Eqn (8-24)}

Hence, the relative increase in height required to compensate the maldistribution is given by

362

14

Examples for the design of packed columns

14.8 Retrofitting a plate column with packing for steam distillation of crude oil In order to avoid thermal decomposition, the partial pressure of the hydrocarbon vapour must not be allowed to exceed 34 mbar at the lower end of the intermediate zone in a vacuum column (pT = 1 0 0 mbar) designed for fractionating crude oil by steam rectification. The plates previously used (subscript 2) gave rise to a pressure drop of 110 mbar between the head of the column and the intermediate zone. After the column had been retrofitted with low-pressure-drop packing (subscript 1), the pressure drop was only 70 mbar. How much steam has thus been saved? Solution According to Eqn (12-50), the pressure drop after retrofitting is given by p -PT=

{i - l) |-^£-] = 70 mbar

The pressure drop before retrofitting is given by

p

-PT=

(i - 1) ( - ^ - 1 = 110 mbar

According to Eqn (12-63), the factor k for the difference in pressure drop is given by

Ano

Ap_\ ~ 70 nt

l57

/i

The relative savings in steam achieved by the installation of packing follows from Eqn (12-67), i.e. AS

^T

1.57-1 = 15? L57 +

100-34 = °- 226 ~1Q~

The volume flow rate of steam per unit flow rate of the hydrocarbon vapours after retrofitting is obtained from Eqn (12-64), i. e. Sj_= V ~

100 + 7 0 - 3 4 34

The corresponding flow rate before retrofitting is obtained from Eqn (12-65), i.e. $2_ _ 100 + 1 1 0 - 3 4 V " 34 "

7

14.9

Reduction in height effected by redistributors

363

Therefore, the savings in steam per unit flow rate of product vapour is as follows:

The same figure can be obtained from Eqn (12-66), i. e. - ^ - = ^ • • 7 0 (1.57-1) = 1.17 The savings in steam achieved by substituting packing for fractionating plates can be determined from the values obtained for AS IV and S2/V, i. e.

100 =5.17 v^~

10

° = 22 - 6 %

14.9 Reduction in height effected by redistributors It is intended to separate a mixture in a packed column with 30 transfer units, 35-mm metallic Pall rings, and optimum inlet distribution. How much height would be saved by installing three redistributors? Solution Assume that the inlet effect and the data describing the efficiency are identical to those listed in Table 9.1. In this case, the effective height of the column without redistributors is given by Eqn (9-20), i.e. (HT)nr

=

o = [30 - (0.5 + 1.9)] • y j ^ = 13 m

The relative reduction in the height of the bed can be read off against nr = 3 in the upper diagram shown in Fig. 9.7. Thus, AH/HT = 0.26 The absolute reduction in height is therefore AH = 0.26 • 13 = 3.4 m Hence, the total effective height of the bed with three redistributors is (HT)nr = 3 = 1 3 - 3 . 4 - 9.6 m

364

14

Examples for the design of packed columns

and the effective height between the redistributors is

r

3 + 1

This value can also be read off on the axis of abscissae against nr = 3 in Fig. 9.7. Assume further that the height occupied by a redistributor in the column is hr = 0.4 m. According to Eqn (9-50), the relative reduction in the total height would then be F^-H

= 1 - — [2.4 (3 + 1) + 3 • 0.4] = 0.169

The absolute saving in the height of the column shell is therefore AHS = 0.169 • 13 = 2.2 m

14.10 Advantages of geometrically arranged packing in fractionating fatty acids A modern plant for processing palm-kernel oil consists of nine distillation stages in tandem. The plans for process optimization included the improvement of product quality by an appropriate choice of column internals. A Hermann Stage method was adopted for the design.

Solution Since the feedstock is sensitive to heat, the distillation stages were designed with structured packing and falling-film evaporators. As a consequence, the residence times were very short, and the bottom temperatures were comparatively low (Fig. 14.5). The effects on the product quality were as follows. The overhead product in each stage ranging from Column 2 (octanoic acid) to Column 5 (myristic acid) is the pure distillate of the unhydrogenated crude acid concerned. Its purity is higher than 99 % during continuous operation and even higher than 99.5 % for lauric (Ci2) and myristic (Ci4) acids. Owing to the unsaturated Cw fraction, the purity of the palmitic acid in the sidestream distillate of Column 8 is only just higher than 97 %. Since the linoleic acid fraction (Ci8») in the feed is higher than that of the oleic acid (Ci 8 ), the sidestream distillate in the next column downstream (Column 9) contains only 85% of oleic acid (Ci 8 H); the remainder consists of 8-10% of linoleic acid (Ci8») and 4 - 5 % of stearic acid. If the trans-fatty acid content is less than 0.5%, the oleic acid content in this fraction is higher than that attained in the Henkel or Alpha-Laval detergent processes. The flow chart shown in Fig. 14.5 for a fatty acid fractionating plant includes the continuous cracker, the glycerol-water evaporation unit, and the pure glycerol distillation column. The two latter also incorporate a Hermann Stage process and the associated engineering. The entire plant has been on stream in Malaysia since 1992.

14.11 Recovery of acetone from production effluents by liquid-liquid extraction

365

O

W)

14.11 Recovery of acetone from production effluents by liquid-liquid extraction A production effluent containing 0.241 kmol/m 3 of acetone is to be purified by liquidliquid extraction with toluene. The packed column is to be designed and operated for 80 % acetone recovery. The intended packing is 25-mm Bialecki rings. The column diameter and the effective height of bed should permit the effluent to flow at a rate of 1557 m 3 /h, the column load may not exceed 35 % of that at the flood point, and the extractant is toluene flowing at a rate of 2829 m 3 /h.

366

14

Examples for the design of packed columns

Solution Characteristic data for systematically stacked Bialecki rings (cf. Table 13.2) E /

- 0.928 = 0.050 m

Cm = 0.67 Ch = 2.151 Cd = 1

Physical properties of the system QD = 857 kg/m 3

QC = 9 9 8 kg/m3

T|D = 0.55 • 10~3 kg/ms DD = 2.478 • 10~9 m 2 /s a = 0.026 kg/s 2 Phase flow ratio uD uc

r| c - 0.893 • 10"3 kg/ms Dc = 1.3 • 10"9 m 2 /s m = 0.64

2.829 = 1.82 1.557

Dispersed phase holdup {Eqn (13-20)} (1-822 + 8 • 1.82) 1 / 2 -3 • 1.82

u h

3

=

4 ( 1 - 1 . 8 2 ) ° '

3 7 5 m

3

/m

Droplet velocity {Eqn (13-3)} 9.81 (998 - 857) 0.026 9982

= 0.1096 m/s

Velocity of continuous phase at the flood point {Eqn (13-16)} uc,m = 0.67 • 0.928 • 0.1096 (1-0.375) 2 (1 - 2 • 0.375) = 6.6 • 10~3 m 3 /m 2 s Velocity of continuous phase under operating conditions uc = 0.35 • 6.6 • 10~3 = 2.31 • 10' 3 m3/m2s Diameter of extraction column {Eqn (14-35)} 4_ 1.557/3600

_

JT ' 2.31 • 10~3

~

>488

m

Velocity of dispersed phase under operating conditions uD = 1.82 • 2.31 • 10~3 = 4.21 • 10"3 m 3 /m 2 s

14.11

Recovery of acetone from production effluents by liquid-liquid extraction

Dispersed phase holdup under operating conditions {Eqn (13-11)}

" * Mass transfer constant {Eqn (13-39)}

Cm

i v °-o5°

Height of overall transfer unit {Eqn (13-47)} 0.0265'8

1

TJrTJJ oc

1

~ 37.32 ' [9.81 (998-857)] 3 / 8 • 9981/4' 1.82

1 (1.3 • 10" 9 ) 1/2

+

1 0.64

1 (2.478 • 10~9)1/2

998 . 857

„ „A = 1.14

Concentration of continuous phase after extraction {Eqn (14-33)} cCu = (1 - 0.8) 0.241 - 0.0482 kmol/m 3 Concentration of solvent after extraction {Eqn (14-34)} cD,o = ~rzr (0.241 - 0.0482) + 0 = 0.1059 kmol/m 3 1.82 Driving concentration difference at the head of the column {Eqn (14-30)} Aco = 0.241 -—^— • 0.1059 - 0.0755 kmol/m 3 0.64 Driving concentration difference at the foot of the column {Eqn (14-31)} Acu = 0.0482 - — | — • 0 - 0.0482 kmol/m 3 0.64 Number of overall transfer units in the continuous phase {Eqn (14-29)}

oc

0.241 - 0.0482 ~ 0.0755 - 0.0482 '

Effective height of bed {Eqn (13-22)} H = 1.14 • 3.17 = 3.61 m

0.0755 n

^

1?

367

15 Recent trends in packing technology Solid particles suspended in the vapour and liquid phases may clog beds of packing in many environmental engineering processes. This likelihood can be overcome by fluidizing the beds. Although fluidization allows higher gas flow and mass transfer rates to be realized, hesitation has been shown in the past in adopting it on an industrial scale for packed towers. The reasons for the reluctance were the lack of design correlations and the difficulties involved in homogeneously fluidizing the bed without an attendant high pressure drop in the bottom grid. Further research on the subject has been instigated by the development of a hollow, thin-wall, ellipsoidal packing element, the performance characteristics of which allow excellent prospects to be envisaged in industrial aplications.

15.1 Fluidized beds of packing The design and operation of a fluidized bed consisting of this hollow, ellipsoidal packing on a supporting grid are illustrated in Fig. 15.1. The pressure drop in the gas stream flowing in the void fraction is brought about by the shear forces that act between the gas, liquid, and packing. When it is in equilibrium with the weight per unit cross-sectional area of packing and the liquid, the bed will start to expand. This stage is referred to as the onset of fluidization. At gas flow rates higher than that at equilibrium, the bed loosens and the elements of packing are free to flow, with the consequence that the interfacial area available for mass transfer is renewed. If the open area of the supporting grid is higher than about 80 %, the density of the packing is the factor that decides whether the phase load at the onset of fluidization will be lower than, equal to, or higher than the flooding load in a comparable fixed bed (cf. Fig. 15.2).

Demister

Gas outlet

A

.Liquid teed x

^"^

Liquid distributor Retaining grid Supporting grid

Liquid outlet Fig. 15.1. Fluidized-bed contactor (left) before onset of fluidization (right) fluidized Packed Towers in Processing and Environmental Technology. Reinhard Billet Copyright © 1995 VCH Verlagsgesellschaft mbH, Weinheim ISBN: 3-527-28616-0

370

15

Recent trends in packing technology

-a =5

Fig. 15.2. Effect of the density Q of the packing on the operating mode of a fluidized packed bed

Gas capacity factor Fv

Qi > Qi > Q3

According to the literature, packing of density less than 300 kg/m 3 allows scrubbers to operate in the nonflooding mode. The density of the hollow ellipsoidal packing, viz. 160 kg/m 3 , is well below this figure.

15.2 Hydrodynamics of fluidized packed beds The load at which beds of the hollow ellipsoidal packing fluidize corresponds to the flooding load in static beds. The relationship between the pressure drop in the fluidized bed and the gas capacity factor F v at constant liquid loads is shown in Fig. 15.3. The conditions for onset of fluidization, i.e. the minimum gas and liquid flow rates, in beds of hollow ellipsoidal packing can be seen in Fig. 15.4. An increase in the liquid load entails a reduction in the free volume of the bed and thus a lower gas velocity at the onset of fluidization. The velocity in the flow channels within the bed and thus the force of friction between the gas and the packing remain approximately constant. An increase in the gas capacity factor normally leads to higher values of the forces that act on the single elements in the bed. Since the bed continues to expand with an increase in the gas flow rate, high local velocities are avoided, and the pressure drop remains almost constant (cf. Fig. 15.3). The relationship between the extent to which the bed expands and the gas capacity factor is shown in Fig. 15.5.

15.3 Mass transfer in fluidized packed beds Fig. 15.6 shows the results of measurements of the mass transfer efficiency, expressed as the height of an overall mass transfer unit HTUcw, in a fluidized packed bed. The measurements were performed on an ammonia-air/water system in a packed column of 0.288 m diameter. It is important to note that the values of HTUOV in Fig. 15.6 are related to the static bed height. The actual height of the bed can then be obtained from Fig. 15.5. Up to the onset of fluidization, the performance is similar to that in most static beds of packing. Owing to the movement of the bed at higher loads, the efficiency remains almost constant as the gas flow rate increases.

75.3

Mass transfer in fluidized packed beds

Liquid load : u L [ m 3 / m 2 h ]

„

a10,o20(o30

50

/ to,

ex.

\

lu

J- 30

/

>

•o—

}—<

CO

L

371

c

0 >—(. o—tr-^ 33u C

—D

Mr

I 20

d s =0.288 m, H stQt = 0.35 m — 1 bar, 293K,Air/Water

CD

10

V

&

0.5

2.5

1.5 Gas capacity factor F v [rfi

3.5

1

1/z

s" kg ]

Fig. 15.3. Pressure drop in a fluidized bed of 0.35 m static height for various liquid loads uL as a function of the gas capacity factor Fv. Bed packed with plastic 35/50-mm Euromatic ellipsoids

Static bed ratio H s t Q t / d s = • 0.3, • 0 . 6 , A 0,9 \M

i

1.3

- Air/Water ,1 bar . 293 K J S = 0.288 m

i

1.2

s r

1.1

I

D

U

1.0

oq 5

10

15

20

Liquid load

25

30 3

35

40

2

u L [m /m h]

Fig. 15.4. Gas capacity factor Fv as a function of the liquid load uL for various ratios of the static bed height to the column diameter Hstat/ds at the onset of fluidization. Bed packed with plastic 35/50-mm Euromatic ellipsoids

372

15 Recent trends in packing technology

Liqid load : u L [ m 3 / m 2 h ]

o i o , a 2 0 , A 30

J

3.0

H s t a ,/d s = 0.6 d<; = 0.288 m 1

2.5

/ 0

2.0 A

ya

1.5 1.0

n u

0 —r~i—

A*Y

ft A

0.5 0.5

1.5

2

2.5

Gas capacity factor Fv [ m

3

3.5

1/2 1

4.5

1/2

s kgg ]

Fig. 15.5. Bed expansion ratio Hexp/Hstat as a function of the gas capacity factor Fv for various liquid loads uL. Bed packed with plastic 35/50-mm Euromatic ellipsoids

Liquid l o a d : u L [ m 3 /m 2 -h • 20, A 3 7 0.25 -^— -^

0.20

.•'

0.15

I 0.10

/

V

A—

*-*

4—

-A" -A- ~A,

• — — .

^

^

-

^

MH 3 -Air/WaterJ bar 293 K, dq= 0.288 m

0.05

i

0 0.5

1.5

2.5

Gas capacity factor F v lrn

3 1/

1

3.5

4.5

12

s kg ' ]

Fig. 15.6. Height of an overall transfer unit HTUOV for various liquid loads uL as a function of the gas capacity factor Fv. Bed packed with plastic 35/50-mm Euromatic ellipsoids

References Billet publications that relate to this book (names of co-authors in parentheses) in chronological order

Zur Vorausberechnung von Fiillkorpersaulen fur die Rektifikation, Chem.-Ing.-Tech. 32 (1960) 8, 517-520. Belastbarkeit von Laborfullkorperkolonnen, Chem.-Ing.-Tech. 32 (1960) 8, 544-550. Vacuum Rectification in High-Efficiency Equipment (L. Raichle), Industrial and Engineering Chemistry 57 (1965) 4, 52-60. Investigations of Various Fractionating Equipments in Test Columns and Application of the Results for Optimization of Separators. In: Primera Convencion Mundial de Ingeneria Quimica, Mexico 1965, Industrial Papelera Nacional S.A., Mexico, D.F., 558 (1966). Recent Investigations on Metal Pall Rings, Chem. Eng. Prog. 63 (1967) 9, 53-65. Rektifikation in Kolonnen mit metallischen Fiillkorpern, Chem.-Ing.-Tech. 40 (1968) 1/2, 43-51. Some Aspects on the Choice of Distillation Equipment (S. Conrad & C M . Grubb). In: /. Chem. E. Symp. Ser. 32, Brighton (1969) 5, 111-126. "Trennkolonnen fur die Verfahrenstechnik": BI-Hochschultaschenbuch Vol. 548, Bibliographisches Institut, Mannheim 1971. Gauze-Packed Columns for Vacuum Distillation, Chem. Eng. 68 (1972), 68-71. Industrielle Destination: Verlag Chemie, Weinheim 1973. Zum Warme- und Stoffaustausch bei der partiellen Gegenstrom-Direktkondensation, Chem.Ing.-Tech. 45 (1973) 13, 887-891. Fliissigkeitsseitiger Stofflibergang bei der Absorption in fiillkorperkolonnen und ihr verfahrenstechnischer Vergleich (J. Mackowiak), Chem.-Tech. 6 (1977) 11, 455-461. Kolonnen mit geordneten Fiillkorpern in parallelen Rohren fur die Flussig-Flussig-Extraktion (G. Husung & J. Mackowiak), Chem.-Tech. 8 (1979) 1, 25-29. Neuartige Fiillkorper aus Kunststoffen fur thermische Stofftrennverfahren (J. Mackowiak), Chem.-Tech. 9 (1980) 5, 219-226. New Aspects of Mass Transfer from Rigid Spherical Droplets into the Continuous Phase in an Extraction Column Filled with Orderly Arranged Packing Elements (J. Mackowiak), Proceedings: 3rd Intern. Chem. Eng. Conf. CHEMPOR '81, Oporto, Portugal 19.-25.04. (1981). Separation Process Design under the Aspect of Energy Saving Proceedings: XII Mendeleev Congress on General and Applied Chemistry, Academy of Sciences of the USSR and the Mendeleev Chemical Society of USSR Baku, USSR 21.-26.09. (1981). Energieeinsparung bei thermischen Stofftrennverfahren, Anwendungen im technologischen Umweltschutz, Dr. Alfred Huthig Verlag, Heidelberg 1983. Fluiddynamisches Verhalten und Wirksamkeit von Gegenstromapparaten fur Gas-FliissigSysteme bei fliissigkeitsseitigem Stoffubergangswiderstand. Festschrift der Fakultat fur Maschinenbau der Ruhr-Universitat Bochum (1983). Operation of Thermal Separation Plants under the Aspect of Environmental Protection, Proceedings of Congress: 4th Int. Symp. on Environmental Techniques Development, Pusan/ Korea (1984).

Packed Towers in Processing and Environmental Technology. Reinhard Billet Copyright © 1995 VCH Verlagsgesellschaft mbH, Weinheim ISBN: 3-527-28616-0

374

References

Hiflow-Ring, ein Hochleistungsfullkorper fur Gas/Fliissig-Systeme (J. Mackowiak), Chem.Tech. 13 (1984) 12, 37-46; 14 (1985) 4, 91-99; 14 (1985) 5, 195-206. Uber den Einsatz von geordneten Fiillkorpern bei der Fliissig/Fliissig-Extraktion (J. Mackowiak & M. Pajak), Chem.-Ing.-Tech. 57 (1985) 8, 684-685. Beitrag zur Auslegung von Fliissig-Fliissig-Extraktoren mit regellosen Schiittungen und geordneten Kolonneneinbauten (J. Mackowiak), VDI Berichte, (1985) 1803-1851. Extraktion als energiesparende Alternative zur Rektifikation (M. Pajak), Chem.-Tech. 15 (1986) 4, 40-47. Untersuchungen der Wirksamkeit von Fiillkorpern aus Kunststoff in Kolonnen groBer Durchmesser (J. Mackowiak, A. Koziol & S. Suder), Chem.-Ing.-Tech. 58 (1986) 11, 897-900. Planning Thermal Separation Plants from the Economic, Ecological and Product-Specific Aspects, Proceedings: World Congress HI of Chemical Engineering, Tokyo, Japan, 21.-25. September (1986). Trends in Development of Packing Devices, Proceedings: Int. Symp. on Separation Process Engineering, Waseda University, Tokyo 1986. Removal of Organic Substances from Industrial Waste-Water by Liquid-Liquid Extraction, Proceedings. 5th Int. Symp. on Environmental Techniques Development, Pusan, Korea DEPCI 86 (3), 111-132 (1986). High Performance Absorption Columns (J.-H. Kim), Proceedings: The First Korea-Japan Symp. on Separation Technology, Kyongju, Korea DEPRI 11 (1), 121-134 (1987). Der VSP-Ring aus Metall, Hochleistungsfullkorper fur Gas/Flussig-Systeme (J. Mackowiak & R. Chromik), Chem.-Tech. 16 (1987) 5, 79-87. Modelling of Fluiddynamics in Packed Columns, Proceedings: IChemE Symp. Sen, Distillation and Absorption 1987, No. 104, A171-A182 (1987). Capacity Studies of Gas-Liquid Two-Phase Countercurrent-Flow Columns (M. Schultes), Proceedings: IChemE Symp. Sen, Distillation and Absorption 1987, No. 104, B255-B266 (1987). Mass Transfer in Regular Packing (Z. Spekuljak), Rev. latinoam. transf cal. mat. - hat. Am J. Heat Mass Tranf. 11 (1987) 63-72. Performance of Low Pressure Drop Packings, Chem. Eng. Comm. 54 (1987) (1-6), 93-118. Packed Column Analysis and Design GLITSCH, Inc., Dallas, Texas 1987, Ruhr-Universitat, Bochum 1989. Relationship between Residence Time, Fluid Dynamics and Efficiency in Countercurrent Flow Equipment, Chem. Eng. Technol. 11 (1988) 3, 139-148. Theory and Practice of Packed Columns, Korea Institute of Energy and Resources, Taejon, Korea 1988. Modern Plastic Packings for More Efficient Separation Processes (XL. Bravo), FAT Sci. Technol. 91 (1989) 8, 329-334. Contribution to Design and Scale-Up of Packed Columns, FAT Sci. Technol. 92 (1990) 9, 361-370. Modelling of Pressure Drop in Packed Columns (M. Schultes), a) Inzynieria Chemiczna i Procesowa 1 (1990) 17-30 b) Chem. Eng. Technol. 14 (1991) 89-95. Fluiddynamik und Stoffubertragung bei der Gegenstrom-Absorption in Ftillkorperkolonnen, Chemie-Umwelt-Technik 1, (1991) 75-81.

References

375

Contribution to Packed Columns Scale-up in Separation Processes, Proceedings of the International Conference on Petroleum Refining and Petrochemical Processing INTERPECI China, Vol. 2, (1991) 929-935. Beitrage zur Verfahrens- und Umwelttechnik aus AnlaB des 25jahrigen Bestehens der RuhrUniversitat Bochum, Ruhr-Universitat, Bochum 1991. Stand der Entwicklung von Fiillkorpern und Packungen und ihre optimale geometrische Oberflache, Chem.-Ing.-Tech. 64 (1992) 5, 401-410. Bewertung von Fiillkorpern und die Grenzen ihrer Weiterentwicklung, Chem.-Ing.-Tech. 65 (1993) 2, 157-166. Predicting Mass Transfer in Packed Columns (M. Schultes), Chem. Eng. Technol. 16 (1993) 1-9. Performance of Liquid Distribution and its Influence on Packed Towers, Proceedings: 5th Int. Energex Conference, 18-22 October, Seoul, Korea 1993. Influence of Liquid Distribution on Packed Tower Design, Proceedings: 3rd Korea-Japan Symp. on Separation Technology, 25-27 October, Koex, Seoul, Korea 1993. Modelling of Packed Tower Performance for Rectification, Absorption, Desorption in the Total Capacity Range (M. Schultes), Proceedings: 3rd Japan-Korea Symp. on Separation Technology, 25-27 October, Koex, Seoul, Korea 1993. Fiillkorperwirbelbetten fur Absorptionsprozesse (A. Daubner), Poster presented at Achema 1994, Frankfurt 1994.

Selected publications for additional information on hydraulics in packed towers Bemer, G.G., Kali, G. A . I , Trans. Inst. Chem. Eng. 56 (1978) pp. 200-204. Bornhutter, K., Mersmann, A., Chem. Eng. Technol 16 (1993), 46-57. Brauer, H., Grundlagen der Einphasen- und Mehrphasenstromung, Sauerlander, Aarau 1971. Chromik, R., Fortschritts-Berichte VDI; Reihe 3 Verfahrenstechnik; No. 273, VDI-Verlag Diisseldorf 1992. Daubner, A., Symposium, T. U. Wroclaw, Karpacz, Poland 1993. Furnas, C. C , Bellinger, E, Am. Inst. Chem. Eng. 34 (1938) 251-286. Gelbe, H., Fortschritts-Berichte VDI; Reihe 3 Verfahrenstechnik; No. 23, VDI-Verlag Diisseldorf 1968. Hines, A.L., Maddox, R.N., Mass Transfers, Fundamentals and Applications, Englewood Cliffs, New Jersey: Prentice-Hall, Inc., 1985. Jesser, B. W, Elgin, J. C , Am. Inst. Chem. Eng. 39 (1943) 277-286. Kaiser, V, AIChE National Meeting, Los Angeles 1991. Kister, H . Z . , Distillation Operation, McGraw-Hill, New York 1990. Kolev, N., Verfahrenstechnik 7 (1973) 3, 71-75. Kunesh, J. G., Lahm, L. L., Yanagi, T , Proc. AIChE Annual Meeting, Chicago 1985. Kutzer S, Mersmann, A., "Verfahrenstechnik der Mechanischen, Thermischen, Chemischen und Biologischen Abwasserbehandlung", Preprints Vol. 2, 2. GVC-Kongrefi 19-21 October Wiirzburg, 1992, pp. 85-89. Landau, R., Birchenall, C.E., Joris, G.G., Elgin, J.C., Chem. Eng. Prog. 44 (1948) 4, 315-326. Maier, K.-H., Geipel, W, Chem.-Ing.-Tech. 63 (1991) 3, 253-255.

376

References

Mackowiak, J., Fluiddynamik von Kolonnen mit modernen Fullkorpern und Packungen fiir Gas/Flussigkeitssysteme, Sauerlander Verlag, Aarau 1991. Mersmann, A., Deixler, A., Chem.-Ing.-Tech. 58 (1986) 1, 19-31. Mohunta, D.M., Ladda, G.S., Chem. Eng. Sci. (1968) 164. Otake, T , Okada, K., Kagaku Kogaku 17 (1953) 5, 176-184. Olujic, Z., AIChE Annual Meeting, Miami Beach 1992. Perry, D., Nutter, D. E., Hale, A., Proc. AIChE National Meeting. Houston, Texas 1989. Schmidt, R., VDI-Forschungsh. 550 (1972). Shulman, H. L., Ullrich, C. E, Wells, N., AIChE J. 1 (1955) 2, 247-252. Shulman, H. L., Ullrich, C. E, Wells, N., Proulx, A. Z., AIChE J. 1 (1955) 2, 260-264. Zuiderweg, E I , Verfahrenstechnik (Mainz) 12 (1978) 1, 674-677. Zuiderweg, E J., Kunesh, J. G., King, D. W, Trans. IChemE 71, Part A (1993) 1, 38-44.

Selected publications for additional information on mass transfer in packed towers Au-Yeung, P H . , Ponter, A.B., Tenside Detergents 20 (1983) 3, 112-117. Au-Yeung, P H . , Ponter, A.B., Can. J. Chem. Eng. 61 (1983) 8, 481-493. Brauer, H., Stoffaustausch einschliefilich chemischer Reaktionen, Sauerlander Verlag, Aarau 1971. Bravo, J.L., Fair, J. R., Ind. Eng. Chem. Process Des. Dev. 21 (1982), 162-170. Deed, D.W, Schutz, P.W., Schutz, P.W., Drew, T.B., Ind. Eng. Chem. 39 (1947) 6, 766-774. Drinkenburg, A. A. H., Inst. Chem. Eng Symp. Ser. 104 (1987) B 179-B 191. Geipel, W, Ullrich, H., Fullkorper-Taschenbuch, Vulkan-Verlag, Essen, 1991. Higbie, R., Trans. AIChE. 31 (1935), 365-388. Hikita, H., Kataoka, T., Nakanishi, K., Kagaku Kogaku 24 (1960) 2-8. Houston, R. W, Walker, C. A., Ind. Eng Chem. 42 (1950) 6, 1105-1112. Hutchings, L.E., Stutzman, L.E, Koch, H. A., Chem. Eng Prog. 45 (1949) 4, 253-268. Joosten, G . E . H . , Danckwerts, P. V, Chem. Eng Sci. 28 (1973) 453-461. King, C. J., AIChE J. 10 (1964) 5, 671-677. Kister, H. Z., Distillation Operation, McGraw-Hill, New York 1990. Kolev, N., Verfahrenstechnik (Mainz) (1969) 3, 241-243. Kolev, N., Semkov, Kr., Chem. Eng.Process. 29 (1991) 83-91. Lewis, W K., Whitman, W G., Ind. Eng. Chem. 16 (1924) 12, 1215-1220. Lynch, E.J., Wilke, C.R., AIChE J. (1955) 1, 9-19. Mohunta, D. M., Vaidyanathan, A.S., Ladda, G.S., The First National Heat and Mass Transfer Conference, Indian Institute of Technology, Madras, December 1971, Paper No. HMT-59-71,pp. 65-78. Martin, Ch. L., Bravo, J. L., Fair, J. R. Proc. AIChE Meeting, New Orleans 1988. Molstad, M.C., Abbey, R.G., Thompson, A.R., McKinney, J.E, Trans. Am. Inst. Chem. Eng 38 (1942) 410-434. Molstad, M.C., Parsly, L . E , Chem. Eng. Prog. 46 (1950) 1, 20-28. Onda, K., Sada, E., Murase, Y, AIChE J. 5 (1959) 2, 235-239.

References

311

Onda, K., Okamota, T., Honda, H., Kagaku Kogaku 1A (1960) 490-493. Onda, K., Sada, E., Saito, M., Kagaku Kogaku 25 (1961) 820-829. Onda, K., Sada, E., Kido, C , Kawatake, S., Kagaku Kogaku 30 (1966) 226-229. Onda, K., Takeuchi, H., Okumoto, Y, /. Chem. Eng. Jpn. (1968) 1, 56-62. Ponter A. B. and Au-Yeung, P. H., Can. J. Chem. Eng. 60 (1982) 2, 94-98. Puranik, S. S. and Vogelpohl, A, Chem. Eng. Sci. 29 (1974), 501-507. Richards, G.M., Ratcliff, G. A., Danckwerts, P. V, Chem. Eng Sci. 19 (1964) 325-328. Roberts, P.V, Hopkins, G.D., Munz, C , Riojas, A.H., Environ. Sci. Technol 19 (1985) 2, 164-173. Semkov, Kr. and Kolev, N., Chem. Eng. Process. 29 (1991), 77-82. Sherwood, T.K., Holloway, F. A.L., Chem. Eng. Prog. 36 (1940) 21-37. Sherwood, T.K., Holloway, F. A.L., Chem. Eng. Prog. 36 (1940) 39-70. Sherwood, T. K., Pigford, R. L., Absorption and Extraction, McGraw-Hill, New York 1952. Shi, M. G. and Mersmann, A., Chem.-Ing.-Tech. 56 (1984) 5, 404-405. Shulman, H.L., DeGouff, J. J., Ind. Eng Chem. 44 (1916) 8, 1915-1922. Stichlmair, J., GVC-Jahrestreffen 1990 der Verfahrensingenieure - ProzeB- und Umwelttechnik - Summary, Poster, Stuttgart, 3-5 Oct. 1990. Stiebing, E. and WeiB, S., Chem. Tech. 43 (1991) 11/12, 418-423. Strigle, Jr. R. E, Random Packings and Packed Towers, Gulf Publ. Comp. Houston 1987. Surosky, A . E . , Dodge, B.F., Ind. Eng Chem. 42 (1950) 6, 1112-1119. Treybal, R., Mass Transfer-Operations, 3rd Ed. McGraw-Hill, New York 1980. Vidwans, A.D., Sharma, M.M., Chem. Eng. Sci. 22 (1967) 673-684. Vivian, J.E., Whitney, R.R, Chem. Eng. Prog. 43 (1947) 12, 691-702. Whitney, R. P., Vivian, J. E., Chem. Eng. Prog. 45 (1949) 5, 323-337. Yilmaz, T., Chem.-Ing.-Tech. 45 (1973) 5, 253-259. Yoshida, E, Koyanagi, T., Ind. Eng. Chem. 50 (1958) 3, 365-374. Zuiderweg, F. J., Harmens, A., Chem. Eng. Sci. 9 (1958) 2/3, 89-103. Wu, K . Y , Chen, G. K. in: Distillation and Absorption Chem. E. Symp. Ser 104, Vol. 2, B225-B231, Brighton 1987.

Index

Absorber, design of 350 Absorption -chemical 43, 141, 143 f - column for 32 - physical 43 - systems 43 - transfer units 339 Area - effective 89 - hydraulic 96 - interfacial 128 - optimum 267

Desorption - column for 32 - systems 44 - transfer units in 339 Diffusion coefficient 119, 121 Diffusion, non-steady-state 119, 121 Din-Pac 24 f Dispersed-phase - capacity 323 -holdup 318,324 Distributor outlets, number of 177 Distributors, design of 229 Droplet diameter 327 - mean 328

B

Beds, void fraction 28 Bialecki rings 59 Boundary loads 87 Box-type liquid distributor 234

Capacity factor 3 Capacity, maximum - of packed column 36 Capillary distributor 34 Capital investment 17, 241 - costs 18 Cascade mini-rings 24 Column - for absorption experiments 32 - for desorption experiments 32 - for rectification experiments 33 - height of 10 Column efficiency 208 - theoretical 13 f, 16 Column height, additional 361 Column internals, design 250 Column packing, types of 23 Column volume - minimum 247 -specific 11, 241, 264 Continuous-phase load 322 Costs - capital investment 241 - comparison between random and geometrically arranged beds of packing 243 - per unit volume 241 - total 18 D Dalton's law 303 Density, gas-liquid systems 38 Desorber, design of 355

Effective area 89 Efficiency - gradient, vertical 147 - improvement of 282 - in rectifications 31 - of extraction 327 - of mass transfer 370 - ratio 162, 166 Efficiency, relative 176, 178, 185, 189 - estimation of 185 End effects - experimental results 154 - external 147 - internal 147 - maldistribution 147 Energy consumption 17, 20 Energy parameter 13 Enrichment zone 5, 7 Entrainment 101 Envi-Pac 24 f Equilibrium curve 5f, 9, 11, 20 Equilibrium of forces, in packed column 73 f Euromatic ellipsoids 372 Evaluation, global - of random beds 283 - of stacked beds 283 External effects 147 Extraction efficiency 327 Extraction factor 324 Extraction-tube column 316 Fatty acid, fractionation of 364 Feed, thermal state of 6 Feeder coefficient 173 Fenske equation 18 Film thickness 75 Flooding conditions 84

Packed Towers in Processing and Environmental Technology. Reinhard Billet Copyright © 1995 VCH Verlagsgesellschaft mbH, Weinheim ISBN: 3-527-28616-0

380

Index

Flood data 66 f Flood point 41, 43, 76, 84, 87, 97 Flow - laminar liquid 76, 78 - turbulent film 78 Flow channels, number of 172 Flow parameter 4, 102 - modified 83 Fluid dynamics 73 Fluidization, performance of 370 Fluidized beds of packing 369 - hydrodynamics of 370 Fluidized-bed contactor 369 - mass transfer in 370 Forces - equilibrium of 74 - frictional 74 - of gravity 74 - shear 74 Fourier number 326 Froude number 124 Funnel distributor 36 G Gas capacity factor - relationship with liquid load 371 f Gas distribution 210 Gas-liquid systems - densities of 38 - physical properties of 39, 41 - viscosities 38 Gas phase resistance, systems with 40 Gempak 27, 57 H Hackette 24, 60 Heat consumption 18 Height - of an overall transfer unit 20, 72, 372 - of a transfer unit 10, 37, 120 - of continuous-phase transfer unit 333 - of dispersed-phase transfer unit 329 Hiflow rings 24 f, 52 f, 60 Higbie correlation 119 Holdup - dispersed phase 318, 324 HTU-NTU - concept 10 - model 20 Hydraulic area 96 Hydraulic diameter 171 I Inlet effects -negative 151 - positive 151 Inlet zone 148 Intalox saddle 25, 61 Interfacial area 128

Internal effects

147

L Laminar flow 76 Levich function 320 Liquid distribution at inlets 171 - principles of 229 Liquid distributors, types of 235 Liquid entrainment 100 Liquid film 74 Liquid flow, laminar 78 Liquid holdup 34, 39, 41, 62, 64, 66, 75 f, 82, 87, 93, 96, 98f, 360 - in geometrically arranged beds 99 - in random beds 98 - real 360 - theoretical 360 Liquid-liquid extraction 313, 365 Liquid-liquid systems 313 Liquid load 76 - at phase inversion point 111 - high 139 Liquid-vapour ratio 11 Liquid velocity, local 74 Loading conditions 82 Loading point 82, 103 Loading range 76, 117 f M Maldistribution 147, 207 f Marangoni number 126 Mass transfer 119, 121, 324, 370 - coefficient 8, 119 - for various packings 69 f - in fluidized packed beds 370 - in the continuous phase 324 - in the dispersed phase 324 - volumetric coefficient 33, 37, 121 Material balance 6 McCabe-Thiele method 5 Mellapak 27 Metal packing, characteristic data 273 - comparison of random beds 284 Metallic rings 49 Mixtures, thermally unstable 244 Molar evaporation enthalpy 6 Montz packing 27, 55 N Nor-Pac rings 24 f Nozzle distributor 35 Number of distribution points 150, 206 - maximum 180, 182 Number of distributor outlets 172, 177 - limiting 199 Number of flow channels 172 Number of theoretical stages 5 f, 12 - minimum 18 - per unit height 9 Number of transfer units 8, 10

Index O Operating costs 17 Operating line - enrichment zone 7 - stripping zone 7 Packed columns - applications for 3 - capacity factor 3 - capital investment costs 241 - design examples 337 - end effects 147 - equilibrium of forces 73 - for rectification 344 - gas velocity 287 - maldistribution 147 - maximum capacity 36 - resistance coefficient 286 Packed column extractors 318 Packed towers, internals 238 Packing - applications in liquid-liquid systems 313 - arranged beds of 85 - ceramic 54 - characteristic data 278 - cost comparison of different types of bed 243 - density 29 - development of 270 - efficieny improvement 282 - gauze 26 - geometrically arranged 27 - mass of 282 - materials of construction 239 - optimum area 262 - overall evaluation of 239 -random beds of 25, 80 - sheet-metal 26 - stacked 26 - surface area 28 - technology, trends in 369 - thickness 28 - types of 23 Packing performance, test systems 37 - experimental results 41 Pall rings 25, 46 Parameters - energy 13 - of flow, modified 83 - stage-number 13 Peclet number 126 Perforated-pipe distributor 34 Phase boundary 8, 124 Phase contact area 9 Phase distributors, types of 233 Phase inversion 83, 102, 106 -coefficient 105, 107 Phase maldistribution 206

381

Phase redistribution 213 Physical properties, gas-liquid systems 39 Pilot colums, distributors 34 - capillary 34 - funnel 36 - nozzle 35 - perforated pipe 34 - profiled-slot 35 Pilot plant 31 Pipe-type liquid distributors 235 Pressure drop 11, 31, 41, 88, 108, 307, 371 - effect on product purity 310 - in a fluidized bed 371 - in geometrically arranged beds 95 - in random beds 94 - per separation unit 5 - per theoretical stage 12, 15 - per unit height 4, 113 - total 5 Pressure drop, modified specific 132 Pressure drop, specific 68, 130 Process engineering, of selected types of metal packing 260 Product purity 310 Profiled-slot distributor 34 R Ralu-Pac 27, 56 Random beds 80, 288 - effect of area on capacity factor 288 - global evalualtion of 284 - packing for 25 Raoult's law 302 Raschig rings 44 Reboiler 6 Rectification 41, 338, 343 - at atmospheric pressure 41 - column for 33 - efficiency 31 - number of theoretical stages 6 - packed column for 344 - transfer units 337 - vacuum 41 Redistribution 214 - effect of 216 Redistributors 213, 237 Reflux - condenser 6 - minimum 18 - ratio 14 Relative efficieny 176, 178, 185, 189 Relative vapour load factor 177 Relative velocity of droplets 320 Residence time 244 - liquid 283 - specific 244 Resistance factor 74, 76, 79 f, 84, 86, 89 f, 92, 103 f Retrofitting 362

382

Index

- of columns 291 - potential for 296 Reynolds number 76, 78, 97

Sauter diameter 327 Scale-up 153, 157, 191 - examples of 167 - gas distribution 210 - measurements 348 - model 194 Separation efficiency 10 Shear force 74, 89 Sieve plate liquid distributor 234 Solvent recovery 314 Stacked beds, global evaluation of Stage-number parameter 13 Steam rectification 302 Stress-strain relationship 288 Stripping factor 10, 21, 36 Stripping zone 5, 8 Sulzer packing 58 Surface tension gradient 125

Top-Pak rings Transfer units

50 339

- height of 10, 37, 120 - in absorption 339 - in desorption 339 - in rectification 337 - overall, height of 72 Turbulent film flow 78 Two-film theory 9

285

Vacuum rectification, nonisobaric 15 Vapour distribution 210 Vapour-liquid ratio 10 Vapour load factor, relative 177 Velocity - of an individual droplet 320 - of vapour 76 Vertical efficiency gradient 147 Viscosities, gas-liquid systems 38 Void fraction 75 - effective 28, 89 Volatility, relative 11 VSP rings 24 f W Wall factor 89 Weber number 124 Wetting, degree of 91