Water and Wastewater Systems Analysis

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WATER AND WASTEWATER SYSTEMS ANALYSIS

DEVELOPMENTSIN WATER SCIENCE, 34 OTHER TITLES IN THlS SERIES (Volumes 1-3 are out of print)

4 J.J. FRIED GROUNDWATER POLLUTION 5 N. RAJARATNAM TURBULENT JETS 6 D. STEPHENSON PIPELINE DESIGN FOR WATER ENGINEERS

7 V. HALEK AND J. SVEC GROUNDWATER HYDRAULICS

B J.BALEK HYDROLOGY AND WATER RESOURCES IN TROPICAL AFRICA 9 T.A. M c M A H O N AND R.G. MElN RESERVOIR CAPACITY AND YIELD 10 0. KOVACS SEEPAGE HYDRAULICS 11 W.H. GRAF AND C.H. MORTIMER (EDITORS) HYDRODYNAMICS OF LAKES: PROCEEDINGS OF A SYMPOSIUM 12-13 OCTOBER 1978, LAUSANNE, SWITZERLAND 12 W. BACK A N D D.A. STEPHENSON (EDITORS) CONTEMPORARY HYDROGEOLOGY: THE GEORGE BURKE MAXEY MEMORIAL VOLUME 13 M.A. M A R l f l 0 A N D J . N . LUTHIN SEEPAGE AND GROUNDWATER 14 D. STEPHENSON STORMWATER HYDROLOGY AND DRAINAGE 15 D. STEPHENSON PIPELINE DESIGN FOR WATER ENGINEERS (completely revised edition of Vol. 6 in the series) 16 W. BACK A N D R. LkTOLLE (EDITORS] SYMPOSIUM ON GEOCHEMISTRY OF GROUNDWATER 17 A.H. EL-SHAARAWI (EDITOR) IN COLLABORATION W I T H S.R. ESTERBY TIME SERIES METHODS IN HYDROSCIENCES 18 J.BALEK HYDROLOGY AND WATER RESOURCES IN TROPICAL REGIONS 19 D. STEPHENSON PIPEFLOW ANALYSIS 20 I. ZAVOIANU MORPHOMETRY OF DRAINAGE BASINS 21 M.M.A. SHAHIN HYDROLOGY OF THE NILE BASIN 22 H.C. RlGGS STREAMFLOW CHARACTERISTICS 23 M. NEGULESCU MUNICIPAL WASTEWATER TREATMENT 24 L.G. EVERETT GROUNDWATER MONITORING HANDBOOK FOR COAL AND OIL SHALE DEVELOPMENT 25 W. KINZELBACH GROUNDWATER MODELLING: AN INTRODUCTION WITH SAMPLE PROGRAMS IN BASIC 26 D. STEPHENSON AND M.E. MEADOWS KINEMATIC HYDROLOGY AND MODELLING 27 A.H. EL-SHAARAWI A N D R.E. KWIATKOWSKI IEDITORS) STATISTICAL ASPECTS OF WATER QUALITY MONITORING - PROCEEDINGS OF THE WORKSHOP HELD AT THE CANADIAN CENTRE FOR ISLAND WATERS, OCTOBER 1985 28 M.JERMAR WATER RESOURCES AND WATER MANAGEMENT 29 G.W. ANNANDALE RESERVOIR SEDIMENTATION

30 D.CLARKE

MICROCOMPUTER PROGRAMS FOR GROUNDWATER

31 R.H. FRENCH HYDRAULIC PROCESSES ON ALLUVIAL FANS 32 L. VOTRUBA. Z.KOS. K. NACHAZEL. A. PATERA ANDV. ZEMAN ANALYSIS OF WATER RESOURCE SYSTEMS 33 L. VOTRUBA AND V. BROZA WATER MANAGEMENT IN RESERVOIRS

DAVD STEPHENSON Water Systems Research Group, University of the Witwatersrand, 1 Jan Smuts Avenue, Johannesburg, South Africa

ELSEVl ER Amsterdam

- Oxford - New York - Tokyo

1988

ELSEVIER SCIENCE PUBLISHERS B.V. Sara Burgerhartstraat 25 P.O. Box 21 1, 1000 AE Amsterdam, The Netherlands Distributors for the United States and Canada: ELSEVIER SCIENCE PUBLISHING COMPANY INC. 52, Vanderbilt Avenue New York, NY 10017, U S A .

ISBN 0-444-42945-X (Vol. 34) ISBN 0-444-41669-2 (Series)

0 Elsevier Science Publishers B.V., 1988 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior written permission of the publisher, Elsevier Science Publishers B.V./Physical Sciences & Engineering Division, P.O. Box 330, 1000 AH Amsterdam, The Netherlands. Special regulations for readers in the USA - This publication has been registered with the Copyright Clearance Center Inc. (CCC), Salem, Massachusetts. Information can be obtained from the CCC about conditions under which photocopies of parts of this publication may be made in the USA. All other copyright questions, including photocopying outside of the USA, should be referred to the publisher. No responsibility is assumed by the publisher for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions or ideas contained in the material herein. Printed in The Netherlands

V

PREFACE

A systematic approach to decision m a k i n g i n water

resources p l a n n i n g

i s presented w i t h p a r t i c u l a r reference t o wastewater re-use. Various methods of system s i m u l a t i o n a n d o p t i m i z a t i o n a r e a p p l i e d number

of

case

studies.

Methods

of

analysis

and

numerical

in a

methods

(Chapter 2, 4 ) a r e described as well a s the b a s i s of p o l l u t i o n a n d water quality

(Chapter 1 ,

3).

The economics

of

desalination

a r e a l s o discussed

(Chapter 7 ) . The a u t h o r has considerable experience in p l a n n i n g and

recycling

systems

i n an a r i d

area,

Southern

premium f o r m i n i n g a n d i n d u s t r i a l development

a n d d i s t r i b u t i o n of water

resources can

purification

Water

i s at

a n d considerable money

spent on water treatment o r use of poor q u a l i t y water.

of money.

water

Africa.

a is

Careful management

i n these circumstances save a

lot

The general theory of o p t i m i z a t i o n subject to q u a l i t y c o n s t r a i n t s

i s presented i n Chapter 6. The internal are

examples

studied

re-circulation

considered

range

(Chapter

(Chapter

and

9)

sewerage systems (Chapter 1 1

from

,

regional

supplies

8). Groundwater stormwater

and

quality

12) a r e also covered.

(Chapter

artificial (Chapter

Computer

10)

to

recharge

5)

and

applications

e x i s t throughout and a number of s i m u l a t i o n a n d o p t i m i z a t i o n programs in BASIC a r e presented. Chapter 13 i s on an often ignored subject, sampling

procedures

in

monitoring

water

the necessity f o r s c i e n t i f i c

quality.

It

was

written

by

Professor Tom Sanders of Colorado State U n i v e r s i t y . The theory and case studies should p r o v e of v a l u e in many aspects of planning

use

of

water

resources

with

quality

constraints.

Wastewater

re-use and conservation therefore a r e promoted b y the approach adopted.

vi

CONTENTS CHAPTER 1 . WATER QUALITY IN INDUSTRIAL SYSTEMS Geochemical source o f p o l l u t i o n Effect o f e v a p o r a t i o n on c o n c e n t r a t i o n s Effects o f poor q u a l i t y w a t e r Scaling P r e d i c t i o n of s c a l i n g a n d corrosion P r e v e n t i o n of s c a l i n g Calcium c a r b o n a t e s c a l i n g Sulphate s c a l i n g A d d i t i v e s f o r t h e p r e v e n t i o n of s c a l i n g Fouling Control o f f o u l i n g O i l emulsion b r e a k d o w n Corrosion Types of corrosion Corrosion p r e v e n t ion P o t a b l e water s t a n d a r d s Agriculture and irrigation CHAPTER 2.

10 10 13 14 15 17

20 21 24 24 26 31 31

NON CONSERVATIVE PARAMETERS

Introduction B a s i c mass b a l a n c e e q u a t i o n Oxygen b a l a n c e in r i v e r s Coupled equations f o r DO a n d BOD Analytical solution C a l i b r a t i o n of a m o v i n g BOD model Oxygen b a l a n c e Fie1d measurements CHAPTER 4.

9

MATHEMAT I CAL MODELLING O F WATER QUAL I TY

Mass Balances M i x e d a n d p l u g f l o w systems Systems a n a l y s i s T e r m i n a l concentration in a w a t e r c i r c u i t A p p l i c a t i o n to a m i n e w a t e r c i r c u i t Computer s i m u l a t i o n model Mathematical b a s i s of model CHAPTER 3.

1 2 2 3 3 3 5 6 6 8

35 35 37 37 39 40 40 45

NUMERICAL METHODS

S i m u l a t i o n o f H y d r a u l i c Systems Two-step method Demonstration o f n u m e r i c a l i n a c c u r a c y I m p l i c i t f i n i t e d i f f e r e n c e schemes Comments on f i n i t e d i f f e r e n c e methods Numerical methods f o r t h e s o l u t i o n o f s i n g l e differential equations The E u l e r method The m o d i f i e d E u l e r method Runge-Kutta methods M u l t i s t e p methods F i n i t e elements Boundaries f o r n u m e r i c a l methods

51 52 52 55 56 57 57 59 60 61 62 62

vi i

CHAPTER 5. MASS BALANCE O F STORMWATER POLLUTANTS Introduction Catchmen t d e s c r i p t i o n Q u a l i t y Observations Fa1lout measurement Relationship between t o t a l p o l l u t a n t load a n d r u n o f f volume Chemical constituents Mass b a l a n c e f o r event of 18 January 1985 on H i l l b r o w catchment Mass b a l a n c e f o r event of 7 M a r c h 1983 on Montgomery P a r k catchment Conclusions

64 64 66 66 67 67 72 73 77

CHAPTER 6. OPTIMUM ALLOCATION O F WATER RESOURCES SUBJECT TO QUAL I T Y CONSTRA INTS

Int roduc t ion The system Solution method Discussion L i n e a r Programming Solution The I i n e a r programming technique w i t h separable programming a p p l i e d S e n s i t i v i t y study f o r v a r i o u s acceptable TDS values

79 80 82 85 85 91 95

CHAPTER 7. ECONOM I CS OF DESALINATION OF WASTEWATERS

I n t roduc t ion A l t e r n a t i v e s f o r optimal reuse of waste water Selection of optimum d e s a l i n a t i o n methods Relevant d e s l i n a t i o n methods I n d u s t r i a l wastewater treatment Reverse osmosis Membrane d e s c r i p t i o n EIect r o d i a I y s i s Ion exchange Cost a n a l y s i s C a p i t a l costs I n d i r e c t c a p i t a l costs Running costs L a b o u r costs Membrane replacement Conc Ius ions

99 99 101 103 1 04 104 105 105 105 107 107 108 108 108 108 111

CHAPTER 8. COMPUTER ANALYSIS JUST I F IES DESAL I NAT ION

I n t roduct ion A p p l i c a t i o n of o p t i m i z a t i o n of water s u p p l y Systems Analysis General o p t i m i z a t i o n problem Program a p p l i c a t i o n Optimization of mine water system Result o f a n a l y s i s Appendix 8.1 MlNSlM Program f o r s i m u l a t i n g flow a n d TDS in closed systems. Tape o r disc management MlNSlM l i s t of symbols

115 116 118 121 122 123 123 128 128 128 128 129

viii A p p e n d i x 8.2 MINOP p r o g r a m f o r o p t i m i z i n g d i s t r i b u t i o n MINOP l i s t o f symbols CHAPTER 9.

136 136 136

INTEGER PROGRAMMING PLANNING OF TREATED WASTEWATER CONVEYANCE FOR A R T I F I C I A L RECHARGE O F AN AQUIFER

Introduction Cost a n a l y s i s Mathematical formu tat ion Results Summary a n d conclusions

141 146 149 151 153

CHAPTER 10. OPTIMAL PLANNING OF REGIONAL WASTEWATER TREATMENT Introduction T h e m a t h e m a t i c a l model Optimization method

155 158 162

CHAPTER 1 1 . SIMULATION OF SEWER FLOW Int r o d u ct i o n Hydraulic analysis F low measurements H i g h e r income r e s i d e n t i a l L o w income r e s i d e n t i a I Apartment b u i l d i n g s Commercial a r e a s Industrial Conclusions Appendix P r o g r a m SEWSIM Effect of local p e a k s Routing effect Non-Circul a r Conduits I nf low components Data Program output Sample d a t a f i l e

166 167 167 169 170 171 171 172 172 174 174 1 74 175 175 1 76 177 177 186

CHAPTER 12. SEWERAGE SYSTEMS MANAGEMENT L e a r n i n g Simulation Program Optimization Optimal Control a s a L i n e a r Programming Problem Sewer M a i n t e n a n c e D a t a P r o c e s s i n g in J o h a n n e s b u r g A p p l i c a t i o n t o J o h a n n e s b u r g ' s System P r o c e s s i n g of Sewer M a i n t e n a n c e D a t a

190 192 193 195 197 198

CHAPTER 13. WATER QUAL I TY MON I TORlNG NETWORKS Necessity f o r Networks M o n i t o r i n g System F r a m e w o r k F a c t o r s in N e t w o r k D e s i g n S e l e c t i o n of Water Q u a l i t y V a r i a b l e s t o M e a s u r e Sampling Station Location Sampling Frequency Discussion

204 205 205 206 207 21 1 215

ix

AUTHOR SUBJECT

INDEX INDEX

21 7

21 9

This Page Intentionally Left Blank

1

CHAPTER 1

WATER QUALITY IN INDUSTRIAL SYSTEMS

GEOCHEMICAL SOURCE OF POLLUTANTS

Many

of

the

surroundings.

chemicals

?n

in

solution

water

originate

M i n e r a l s which form rocks may be dissolved

s u i t a b l e environment. certain

chemicals

assists

the

Acidic

waters

the rock,

in

reaction,

Iron

i n particular

Exposure to a i r ,

sulphide

i s one

a r e known which

such

from

the

in a

b y water to

contains

chemical

dissolve oxygen,

which

can

be

B a c t e r i a a r e also thought to p l a y a n important p a r t

o x i d i z e d to sulphate.

i n the leaching of sulphides.

The

s o l u b i l i t y of

chemicals

i s also dependent

on

temperature

the r a t e of

dissolution

s u l p h i d e from a rock r a p i dIy

.

When

a

chemical

positively

charged

Solubility

depends

s o l u b i l i t y K.

H 20

= H+

i s slow.

sample.

compound metal on

take

the other

dissolves

or

other

I t may

On

cations charges

to

dissolve

water

the

negatively

present

and

ions

the very

appear as

charged

is

In p a r t i c u l a r water i s ionized a s follows:

the

all

h a n d c h l o r i d e s dissolve

in

and

years

and

I n many cases

t o t a l dissolved s o l i d s i n the water amongst o t h e r factors.

anions.

expressed

as

a

(Brownlow, 1979).

+ OH-

The log of the hydrogen H+ ion concentration i s termed the pH: pH = -log(H+) Water w i t h a factors.

7 i s acidic.

pH below

be rendered so b y

many

For example absorption of carbon d i o x i d e C 0 2 from the a i r

I t may

forms

carbonic a c i d which c o u l d reduce the pH as l o w as 3.0. water d r a i n i n g from

O n the other hand

limestone o r s i l i c a t e m i n e r a l s may h a v e a pH g r e a t e r

than 7 ( P e l l e t i e r , 1964). The process of

l e a c h i n g s u l p h i d e from

s u l p h u r i c a c i d i s formed

i n the process.

minerals

i s self

stimulating

as

On exposure of s u l p h i d e b e a r i n g

horizons ferrous s a l t s o x i d i z e to the f e r r i c s t a t e a n d s u l p h i d e i s o x i d i z e d to sulphate:

4FeS2 + 1502 + 10H20

+ 4FeO(OH)

I n m i n i n g environments, further

promote

ferro-oxidans

the

oxidize

oxidizes only S

oxidation both

+' 8H2S04

bacteria

Fe

of

and

(Mrost a n d L l o y d ,

thrive

Fe

and

S

198Oj.

in the S.

whereas

The

acid

mine

bacteria

thiobacillus

water

and

thiobacillus thio-oxidans

EFFECT OF EVAPORATION ON CONCENTRAT IONS

The r a t e of concentration of t o t a l d i s s o l v e d s a l t s b y e v a p o r a t i o n may be p r e d i c t e d f o r any

ambient c o n d i t i o n s u s i n g psychrometric

a d d i t i o n to e v a p o r a t i o n in cooling towers, in

industrial

systems

dry-bulb

temperature

relative

humidity,

v a p o u r / k g of a i r . of 700 m’/s,

and of

ventilated

i s 31OC a n d

will

it

e v a p o r a t i o n of water takes p l a c e

particularly

air

the

in

increase

In

relationships.

water

For a n a i r d e n s i t y of 1.2

systems.

air

Thus

i s conveyed content

kg/m3

in

by

5

if

the

at

38%

g

water

and a ventilation rate be 5 l i t r e s p e r

the amount of water absorbed b y the a i r w i l l

second ( B a r e n b r u g , 1965). The loss of water b y e v a p o r a t i o n leaved b e h i n d s a l t s entered

the

system

c o n c e n t r a t i n g effect, depends on the

in

dilute

and

solution

the

rate

storage

volume of

of

initially. increase

in

which

There

Thus

if

have

therefore

concentration

in

the system.

is

may

in

there

a

time

is a

12

h o u r retention a n d the flow r a t e of service water i s 100 l i t r e s p e r second, the volume

i n the system w i l l

be 100 x

24/1000

3600 x

8640m’.

=

If

e v a p o r a t i o n loss i s 10 l i t r e s a second which i s 864 m 3 / d a y the i n i t i a l of concentration w i l l

be 10 percent

The s a l t concentration replaced.

would

of

the

increase

initial

unless

the

per day. water

was

The r a t e of concentration i s u s u a l l y offset b y the f a c t t h a t

i s a source of p u r e r water used f o r

make-up

t o t a l load unless there i s a blowdown (Porges, The concentration function

concentration

indefinitely

of

of

total

the e v a p o r a t i o n

dissolved r a t e as

b u t even

as

adds

there to

the

1971).

solids

well

this

the rate

at

equilibrium

will

be

the p u m p i n g d i s c h a r g e

a n d r a t e a t which s a l t s a r e introduced as a r e s u l t of make-up l e a c h i n g of chemicals from the environment (Van Staden,

a

rate

water a n d

1970).

EFFECTS OF POOR QUAL I TY WATER

H i g h t o t a l dissolved s a l t s concentration of

problems.

economic

concentration corrosion waters

The

nature

consequences o f

of

give

in

mine

pipework rise

to

exchange equipment.

of

the

poor

water and

scaling

problems

quality

is

and

varies,

water

suspected

equipment.

in water g i v e s r i s e to a number

are

to

be

Sulphates

blockages.

but

in

all

severe. one

of

and

Scaling

the

is

Plant has frequently

common

in in

of the

heat

in some a r e a s

to be r e p l a c e d a f t e r o n l y a

few years i n service i n many systems because of development of mechanized equipment

the

chloride

causes

carbonates

I n many systems there may be s c a l i n g

a n d corrosion in others.

cases

High

has g i v e n

these effects. rise

to

new

The recent

f e a r s of

the

3

consequences of poor q u a l i t y water. to operate and

the

hydraulically

hydraulic

Many of

using oil-in-water

circuits

could

be

these machines a r e designed emulsions.

already

Emulsion

affected

by

stability

poor

quality

water.

SCAL I NG

S c a l i n g i s the phenomenon of chemical deposition on submerged surfaces. The

deposits

place

are

because of

due the

to

crystallization

dissolved

salt

or

precipitation.

concentration

c o u l d be caused b y e v a p o r a t i o n loss of water,

i s also a

f u n c t i o n of

dissolved solids concentration, chemicals

most

3

whilst

solubility

temperature.

Figure 1 . 1

solubility

these

of

(CaS04). of

which

l e a c h i n g of chemicals from

the

The solubility

Other chemicals,

(e.g.

Mg(OH)2),

aluminium

and

scale

salts

ions i n solution. iron,

parameters such

are

as

pH,

calcium

Calcium carbonate

both

other

scales (Betz,

saturation

total

time a n d flow v e l o c i t y .

causing

illustrates

salts.

other

alkalinity,

frequently

and calcium s u l p h a t e

(CaCO ) insoluble

its

takes

o r a change i n temperature.

The s c a l i n g

The

exceeds

a r e s u l t of an excess of chemicals in solution

l i m i t and i s usually

surroundings,

Scaling

is

effects is

dependent

temperature

influenced

particularly

silica

is particularly

highly of

carbonate

by

oxides

a r e also

on

on

the

chlorides

and

of

magnesium

sometimes

found

in

1980).

P r e d i c t i o n of S c a l i n g and Corrosion

T h e factors

affecting

the e q u i l i b r i u m of

have a complex interdependence. predict

the tendency

calcium

carbonate

L a n g e l i e r (1954) developed

of calcium carbonate to form a

p r e f e r r e d to express the equation in terms of pH.

scale.

However

i n solution

an e q u a t i o n to Ryzner

(1944)

there a n y many

i n f l u e n c i n g effects a n d such formulae can o n l y o f f e r a g u i d e to the l i k e l y b e h a v i o u r of the water,

p a r t i c u l a r l y i n respect to corrosion.

Prevention of S c a l i n g

One way of p r e v e n t i n g s c a l i n g o r corrosion would be to d e s a l i n a t e water.

Possible

reverse osmosis,

methods

of

desalinating

mine

water

e l e c t r o d i a l y s i s a n d thermal procedures.

expensive t h e i r possibi I i ties a r e b e i n g re-assessed.

are

ion

the

exchange,

Although these a r e

4 Scale and,

prevention

where

necessary,

p r e v e n t excessive be

is

currently a

controlled

concentration of

supplemented

with

normally

the

use

undertaken

bleed

(waste)

the d i s s o l v e d s a l t s . of

scale

and

by

from

pH

adjustment

the

system

T h i s treatment

corrosion

additives.

3000 2800 2600 2400 2200

zoo0 1800

-E -I

1600 1400 1200 1000

800 600 400 200

100 50

0

0

20

40

60

80

100

120

140

160

TEMPERATURE O C

Fig.

1.1

Effect of temperature on s o l u b i l i t y of s c a l i n g s a l t s

to may

preventative

5 Calcium carbonate s c a l i n g

The f a c t o r s a f f e c t i n g have a complex

the e q u i l i b r i u m of

interdependence.

calcium

carbonate

In a d d i t i o n to temperature,

in s o l u t i o n the presence

Procedure : glven temp. OC TDS mgll Ca mgll Alkallnlty proceed 1-2-3-4-5

PHS Ryzner Stablllty Index RSI=lpH,-pH Calclum Carbonate S a l l n g Ilkely If LSI>O and R S l c 6 Colrorlon Ilkely If RSI>O

Fig.

1.2

L a n g e l i e r S a t u r a t i o n Index Chart f o r Carbonate S c a l i n g

6

of

other

dissolved

tendency

to form

nozzle can

solids,

especially

A

scale.

sudden

induce s c a l i n g ,

total

alkalinity

reduction

and suspended m a t t e r i n the

as n u c l e i f o r scale formation.

-

positive,

a

there

is

pHs,

where K(C,T)

tendency

can

negative

to

scale

and

a

serve

predict

it

if

pH.

is

I f the LSI

negative,

is

calcium

The pHs i s c a l c u l a t e d from the e q u a t i o n :

i s a f u n c t i o n of

represents

which

may to

the

at

+ pCa + pAPk

pHs = pK(C,T)

and

water

as

The L a n g e l i e r S a t u r a t i o n

where pHs i s the s a t u r a t i o n

carbonate tends to dissolve.

affect

such

L a n g e l i e r developed an equation

the tendency of calcium c a r b o n a t e to from scale. Index i s LSI = pH

a n d pH,

pressure

in

be

the

second

computed

logarithm

of

the temperature

dissociation

from the

thermo-dynamic

calcium

and total

constant

and

dissolved

solubility

considerations.

content,

and

pAPk

is

solids, constant

pCa the

is

the

negative

l o g a r i t h m of the e q u i v a l e n t concentration of the a l k a l i n i t y . The LSI can be computed r e a d i l y from F i g u r e 1.2. Ryzner proposed a d i f f e r e n t arrangement of equation.

The Ryzner S t a b i l i t y

-

R S I = ZpHs If

the

the terms

in

Langelier

the

Index ( R S I ) i s :

pH

RSI

is

less

t h a n 6,

scaling

tendency

increases,

and

if

it

is

g r e a t e r t h a n 8, corrosion i s in f a c t more l i k e l y . There

are

however,

many

and

particularly

other

such

effects

formulae

influencing

can

only

scaling

and

corrosion,

provide

preliminary

sulphate

i s higher

guides

i n r e l a t i o n to corrosion.

Sulphate s c a l i n g

The s o l u b i l i t y of v a r i o u s forms of calcium of

calcium

Calcium

but

s u l p h a t e occurs

CaS04.2H20 a n h y d r i te, The

carbonate

(gypsum),

in

is

also

three

highly

different

herni-hydrite

dependent

crystal line

CaS04.)H20

on forms:

(plaster

of

than that

temperature. dihydrate, paris)

and

CaS04.

solubility

temperature

it

of

(Figure

the 1.1

hernihydrite

1.

The

and

solubility

anhydrite increases

decreases with

with

chloride

concentration and i s affected b y t o t a l dissolved solids.

A d d i t i v e s for the p r e v e n t i o n of scale

I n most

systems,

dernineral i z a t i o n

or

softening the water w i t h r e s i n o r Zeolite i s not economically j u s t i f i a b l e .

In

some cases chemical

especially

once-through

systems,

i n h i b i t o r s a r e used to p r e v e n t the formation of

scale.

7 These

agents control

supersaturated

deposits

solution.

The

by

preventing

basic

crystal

mechanisms

of

growth, scaling

even and

in

a

deposit

control a r e :

(1

1

Control of i n t e r p a r t i c l e a t t r a c t i v e forces e.g.

(ii)

Control

of

particle-to

wetting

agents.

surface

These

involve

non-stoichiometrically possible. scal i n g

(iii)

They

.

and

are

forces,

used

Control of p r e c i p i t a t i o n

electrostatic

hence more

rate,

dispersants.

e.g.

low

for

e.g.

surfactants forces.

or

They

act

concentrations

preventing

flocculants.

are

fouling

These

than

are

high

molecu l a r weight pol ymers. Retardation of c r y s t a l growth, e.g.

(iv)

polyphosphates.

Some of t h e reagents used a r e l i s t e d below:

Polyphosphates:

Applied

in

rates

from

0,5

to 5

mg/O.

Absorbed

onto

surfaces of growing c r y s t a l s and i n i n c i p i e n t c r y s t a l n u c l e i .

They

the

successful

apparent

solubility

of

scale

forming

salts.

These

are

the

increase for

carbonates and h y d r o x i d e s b u t not f o r sulphates.

Organic Phosphates: Simi l a r to polyphosphates b u t they a r e more s t a b l e i n cooling

tower

successfu I

systems.

Phosphonic

acids

have

proved

particularly

.

Phosphate:

React w i t h calcium

p r e c i p i t a t e s out.

For

this

to

reason

form

i n s o l u b l e calcium

i t s use

has

largely

phosphate

been

which

replaced

by

d ispersan ts.

Polymers

(especially

polyacrylates):

growths.

Effectively

dispersants

crystals

i n suspension.

as

Absorbed they

Low molecular weight

onto

maintain

surfaces small

of

crystal

particles

of

polymers h a v e r e c e n t l y been

developed f o r t h i s purpose.

The reagents may be used on combination, reduce pH.

o r even together w i t h a c i d to

Carbon d i o x i d e can be added to closed systems to

reduce pH.

F e r r i c c h l o r i d e i s also used. Dispersants

or

sequestrants

are

sometimes

formation of i r o n h y d r o x i d e o r o x i d e in p a r t i c u l a r . agents a r e used to i s o l a t e and

used

to

prevent

scale

Chelants o r complexing

i n h i b i t scale formers.

It

should

be noted

8

that the

crystal systems

must

inhibitors as

be

a r e not

prevented

by

in e l i m i n a t i n g

effective

sol i d s .

suspended

Instead,

foulants

agglomeration

dispersants

such

as

of

entering

these

sol i d s

phosphonates

and

I igno-su I phates. The deposit of problem.

phosphates i n closed systems due to a d d i t i v e s can be a

The d u r a t i o n of effectiveness of

velocities

and

turbulence

can

affect

additives

i s also unknown.

low-concentration

High

dispersants

in

particular. The effects of

chemical

r e q u i r e consideration.

dissolved s o l i d s

on

Deposits may

may erode h i g h - v e l o c i t y total

additives

jets.

the

block

rest

of

pipes o r

the

will

system

machines.

also

Suspensions

Reactions w i t h o t h e r chemicals may a g g r a v a t e

problems.

There

may

also

be

an

effect

on

settlers

and demineralization plants.

FOUL I NG

Besides chemical which can

precipitates

there

are

many

substances

settle out o r block p i p e w o r k a n d m a c h i n e r y .

materialize

in

the

form

of

films

bridging

c a v i t i e s where water v e l o c i t i e s a r e slow.

openings

The

or

in suspension

deposits

building

may

up

in

The m a t e r i a l deposited may be:

Sediment from ore o r the atmosphere t r a n s p o r t e d in suspension Floc created b y chemical treatment Iron oxide ( r u s t ) Chemicals

used

for

scale

or

corrosion

inhibition

which

subsequently

cause deposits Oils Foam from chemical r e a c t i o n s o r a e r a t i o n B a c t e r i o l o g i c a l slime collected o r accumulated i n the system

The tendency water v e l o c i t y

to s e t t l e i s a

function

a n d a p p e r t u r e bore.

of

particle

Turbulence

due

size, to

shape,

flowing

density,

will

water

m a i n t a i n some p a r t i c l e s i n continuous suspension a l t h o u g h the concentration w i l l b e highest n e a r the bed i n the case of p a r t i c l e s denser t h a n water.

Once p a r t i c l e s particles.

s e t t l e out

Alternatively

they

they

may

may

stick

migrate

to

the

along

surface, the

bed.

or

to

other

Under

some

conditions the bed m a t e r i a l may move a s dunes w i t h p a r t i c l e s b e i n g p i c k e d up b y the flow upstream of resulting

rippled

surface

the dune c r e s t a n d deposited downstream. can

aggravate

friction

loss

in

conduits.

The In

9 addition

to

the

reduction

in

cross

sectional-area,

the

of

capacity

the

conduit i s reduced due t o the h i g h e r d r a g on the perimeter. Deposits may block f i n e pores o r o r i f i c e s completely. filter

media

particles

rapidly

block

thus

The gaps between

requiring

backwashing.

In

machines w i t h f i n e j e t s o r screens s i m i l a r blockages a r e possible. Deposits may

remain

i n flocculated

blanket

form,

or

time and i n c r e a s i n g deposits p r e s s i n g down from above.

consolidate

with

They may s t i c k

to

the surface due to chemical bonding. B i o l o g i c a l matter such as b a c t e r i a l slime o r f u n g i can build up w i t h i n a

water

system

sometimes

provided

carbon

and

r e q u i r i n g oxygen f o r

nutrients

silica,

are

such

as

present.

g r o w t h ) o r aerobic.

nitrogen,

They

may

phosphorous be

and

anaerobic

Some b a c t e r i a t h r i v e on

(not

iron o r

s u l p h a t e and cause d e t e r i o r a t i o n .

Control o f f o u l i n g

Deposits i n machinery and p i p e systems can be prevented o r reduced b y controlling

particle attraction

forces,

preventing

settling

by

turbulence,

i n s t a l l i n g s e t t l i n g b a s i n s o r keeping the p a r t i c l e s out of the system closed c i r c u it s )

(e.g.

.

Dispersants

are

p a r t i cI e- to-surface

used

forces.

o r create r e p e l l i n g charges.

control

to

particle-to-particle

and

n e u t r a I i ze e l e c t r o s t a t i c a t t r a c t ion charges

They

One problem w i t h

these

i s that

if

there

are

sedimentation b a s i n s i n the system they may h i n d e r s e t t l i n g there. High concentrations of dispersants may in f a c t be used f o r systems.

desludging

Surface w e t t i n g agents a r e sometimes used to p r e v e n t deposition of

o i l and grease. Biological

fouling

may

be

controlled

by

disinfection.

Shock

dosing

treatment appears more e f f e c t i v e a n d economic t h a n continuous dosing. Chlorine

i s widely

used as

o x i d i z i n g agent a n d reduces

a

the

biocide

hypochlorous a c i d a n d h y d r o c h l o r i c acid. of

less than 1 mg/t

i s usually

to combat

pH when

sufficient

dissolved

bio-matter. i n water

It

is

an

by

forming

A free r e s i d u a l c h l o r i n e

content

i f contact p e r i o d i s a n h o u r o r

more. Hypochlorite i s also used occasionaly. Non-oxidizing lesions

i n the

biocides act b y surface a c t i v a t i n g o r b y c a u s i n g s u r f a c e metabolism.

compounds ( q u a t s ) .

Into

this

category

fall

quarternary

ammonia

10

0 I L EMULS ION BREAKDOWN

Emulsions of amongst other the

form

of

in

oil

things. minute

water

are

used

for

driving

The emulsions consist o f droplets.

The

emulsion

oil is

prototype

dispersed

stabilized

machinery

in

water

by

in

electrical

charges on e m u l s i f y i n g agents. Chemicals emulsions

(such by

and

polymers

neutralizing

(coagulation), altering

as

precipitating

the e m u l s i f y i n g

cationic

o i I-in-water

emulsions.

are

opposite

repulsive or

out

i t can

particularly

Once charges

charge

charges

Crystallizing

so t h a t

film

polymers

of

polarity)

between

particles

emulsifying

readily

effective

break

agents

be broken.

Cations

separating

in

oi I

h a v e been n e u t r a l i z e d ,

or

dilute droplets

a n d suspended s o l i d s w i l l be absorbed on the surface of floc o r w i l l

break

out a n d f l o a t on top thereby d e s t r o y i n g the emulsion p r o p e r t i e s . Although

it

is

desirable

suspension w h i l s t in service, may

be d e s i r a b l e

place a t

to separate

controlled

machinery f u r t h e r been used

to

to

after

locations

the o i l to

in the cycle.

break

maintain

the

the emulsion and

prevent

emulsion

oil-in-water

i s d i s c h a r g e d to waste

the

water.

subsequent

This

slime

should

to

aluminium

raise

the

pH

emulsions.

again

Cationic

in

Acid a n d a l u m i n i u m s u l p h a t e ( a l u m ) h a v e

oil-in-water

hydroxide.

take

and caking

The

acid

lowers

the

about 3 a n d alum coagulates the o i l b y n e u t r a l i z i n g the charges. added

it

and

the

polymers

aluminium

are

is

preferred

pH

precipitated

and

to

Lime i s

often

used

as in

double a i r f l o t a t i o n (DAF) u n i t s which c o l l e c t s the o i l on the surface.

CORROS ION

Corrosion

is

electrochemical

the

attack

action.

due p r i m a r i l y

to

and

degradation

Pipework

highly

and

saline or

general o r i n i s o l a t e d p o i n t s .

of

machinery

acidic

water.

metal are

by

subject

chemical to

or

corrosion

The d e s t r u c t i o n may

be

I t may reduce the l i f e o f p i p e and steelwork

b y many years. I r o n corrodes

in

water

as

water since i t i s less noble i.e. Fe + 2H20 = Fe(OHl2

insoluble,

replaces

the

hydrogen

ion

in

i t i s less c a t h o d i c :

i s oxidized

which

further

to

i s usually ferric

i n solution

hydroxide,

b u t i s u l t i m a t e l y changed to f e r r i c

manifests a s p i t s i n the i r o n surface, 1.3).

It

+ H2

I n the presence of oxygen, ferrous oxide

follows:

oxide,

Fe203.

a form o f oxygen

in water,

Fe(OHl3.

This

the is

The

reaction

corrosion.

(Figure

11 TABLE 1.1

Nernst s c a l e of s t a n d a r d e q u i l i b r i u m p o t e n t i a l s r e l a t e d to the s t a n d a r d h y d r o g e n electrode a t 25OC (Metal immersed i n a normal s o l u t i o n of one of i t s s a l t s )

Metal

Electrode r e a c t i o n s

E q u i I ib r i u r n p o t e n t i a l (volts)

K

Potassi urn

=

+ e++ Ca + 2eK+

Calcium

Ca =

Sod i um

Na = Na+ + e-

Magnesium

Mg =

Al urn in iurn

~t

Manganese

Mn =

Zinc

Zn = Z n

C hrom i urn

Cr =

++ + Mg

= AI+++

++ Mn

- 2.922 - 2.87

-

2e-

+ 3e+ 2e-

++ + 2e+++ Cr + 3e++ Fe + 2e-

2.712 2.34 1.67

1.05 0.762 0.71

- 0.440

I ron

Fe =

Coba I t

Co = Co

2e-

-

Nickel

Ni =

2e-

- 0.250

Tin

Sn =

2e-

-

++ + ++ Ni + ++ + Sn

0.277

0.136

Lead

Pb = Pb++ + 2e-

Hydrogen

H2 = 2H+

- 0.000 b y convention

Copper

cu =

+ 2e++ cu + 2e-

+ 0.345

cu+

+ 0.522 + 0.800

Copper

cu

Silver

Ag = A g +

P I a t inum

Pt = P t

Gold

Au =

Gold

AU

a-

Fig.

1.3

=

+ e-

+ e+ 2e-

++ +++ Au

= AU+

+ 1.2 a p p r o x .

+ 1.42 + 1.68

+ 3e-

+ e-

Cathodic area

0.126

area Iron

Corrosion c e l l on the surface o f i r o n in water

12

L \

\

1

-

\ \ \

%

\ \ \

Potential o f Metal Eh relative 0 t o hydrogen

-1

F i g . 1.4 If they

the,

may

\

\ \

-

Oxidation Corrosion

-

%

-

Corrosion

-

Immunity due t o low i r o n p o t e n t i a l

% %

\

-

A s i m p l i f i e d form of the P o u r b a i x D i a g r a m f o r i r o n corrosion

or some of

the,

be eroded b y

iron

flowing

oxides water

are

present

especially

if

as

protective

sediment

layers

i s present.

C a v i t a t i o n can also erode the surface l a y e r s . The metal i s thereby exposed a n d corrosion i s accelerated. The e q u i l i b r i u m between i r o n and v a r i o u s compounds water

was

studied

by

Pourbaix.

He presented

i n the presence of

h i s results

in

a

diagram

( F i g u r e 1 .4 ) which shows three zones:

A corrosion zone f o r

low

pH

or

high

electrical

potential

relative

to

l i q u i d solution.

A corrosion i n h i b i t i o n zone f o r

h i g h pH due

to

passivation

by

a

film

found on the surface

A cathodic protection zone f o r low i r o n p o t e n t i a l r e l a t i v e to a s t a n d a r d elect rode.

13

Hydrogen

is

used

as

a

reference

electrode

in

the

of

i t s salts,

the s t a n d a r d

gives

in a normal solution of one

p o t e n t i a l s of metals immersed

r e l a t i v e to

The

Table 1 . 1

p o t e n t i a l of the i r o n w i l l depend on the reference system. the e q u i l i b r i u m

diagram.

hydrogen

electrode

25OC.

at

There

U h l i g (1963)

a r e many texts on f a c t o r s a f f e c t i n g corrosion e.g.

Types of Corrosion

in the presence of

There are many ways i n which corrosion can occur water.

Corrosion i s commonly an electro-chemical

phenomenon which occurs

a t an anode when electrons flow from an

anode

positively

oxygen.

corrode.

charged

anode

to

react

with

Ways i n which the electrons m i g r a t e

to a

cathode,

The

for

leaving

cathode

corrosion

a

does

not

to occur,

are

( U h l i g , 1963).

described below

G a l v a n i c Corrosion: When e l e c t r i c a l l y electrolyte,

dissimilar

metals

are

in

contact

a p o t e n t i a l difference i s established.

metal corrodes,

in o r

through

an

The more a c t i v e ( a n o d i c )

as i t i s least noble.

Selective Lea china: One element of an a l l o y can be corroded more r a p i d l y t h a n another.

Pitting: A shell of iron

surface.

permeable magnetite o r Salts

may

concentrate

ferric

h y d r o x i d e may

form

under

the

the

shell

and

over

an

resulting

env ironmen t becomes i n c r e a s i n g I y corrosive.

Stress Corrosion : Metals

in

stress

may

corrosive environment. to s a l t b u i l d - u p

exhibit

abnormal

Once a c r a c k

s i m i l a r to p i t t i n g .

corrosive

i s formed

properties

Chlorides a n d amonia appear

chief aggressors i n t h i s type of corrosion.

in

i t r a p i d l y deteriorates

Welding may also

a due

to be the

induce l i n e s

of corrosion unless stress r e l i e v e d .

A c i d Corrosion : Acids,

o r even carbon d i o x i d e i n solution,

ion concentration. chelants,

e.g.

NTA

they concentrate.

can

increase the hydrogen

T h i s r e s u l t s i n general loss of metal b y corrosion. (nitrilotriacetic acid)

may

also

Some

become c o r r o s i v e

as

14

B a c t e r i a l Corrosion : B a c t e r i a can cause biochemical a c t i o n which r e s u l t s i n corrosion.

This

t y p e of corrosion i s often encountered i n s u l p h u r i c c o n d i t i o n s .

E l e c t r i c a l Corrosion E l e c t r i c c u r r e n t s , d.c.

i n p a r t i c u l a r , may cause severe corrosion.

anode i s formed where the c u r r e n t

leaves

the

conductor,

corrosion

I f an occurs

there.

Reagent Corrosion : Certain

scale

preventing

agents

such

as

acids

and

chelants

and

complexing agents can promote corrosion

T h e effectiveness of a l t e r n a t i v e corrosion p r e v e n t i o n methods depends on the p r e v a i l i n g circumstances a n d system to be protected. cooling

systems

possible. the

relatively

high

concentrations

I n l a r g e c i r c u i t s a n d c o o l i n g systems,

treatment

dosage

concentration control

must

be

less;

sometimes

of

I n small

chemical

closed

dosage

are

i n o r d e r to be economic, little

more

pH

than

and

( b y b l e e d i n g o f f a n d r e p l a c i n g w i t h f r e s h w a t e r ) can

be accomp I i shed. I n c h i l l e d water human beings.

circuits

the

circulating

I n these circumstances

used i s non-toxic.

water

may

be

i t i s imperative that

T h i s requirement has the effect of

consumed any

severely

by

treatment

l i m i t i n g the

number of chemical corrosion i n h i b i t o r s which can be considered.

Corrosion p r e v e n t i o n

Corrosion can be reduced b y c h a n g i n g the c h a r a c t e r i s t i c s of

the water

o r c o a t i n g the metal. Metal i s sometimes i n f a c t coated n a t u r a l l y b y scale. A u n i f o r m deposit of calcium carbonate can be created b y dosing

w i t h lime,

soda ash o r c a u s t i c soda.

o r unstable,

and cannot be r e l i e d upon f o r 100 percent protection.

Deaeration of water w i l l also reduce i t s c o r r o s i v i t y . vacuum

deaeration

if

feasible.

Oxygen

corrosion a r e thus removed to some extent. remove oxygen

i n the water.

sulphate: 2Na2S03

+ O2

the water

The deposit i s f r e q u e n t l y non u n i f o r m

= 2Na2S04

and

carbon

I n closed systems, dioxide

which

aid

Sodium s u l p h i t e can be used to

The r e a c t i o n w i t h w i t h

oxygen

forms

sodium

15

Corrosion passivates magnetite

i n h i b i t o r s a r e a v a i l a b l e commercially. the

surface

(Fe304).

precipitates.

by

Other

forming

a

inhibitors

protective

react

and poly-

oxide

chemically

I n t o the l a t t e r category fa1 I zinc,

phosphate and ortho-

One t y p e of

to

and

include

film

such

form

insoluble

calcium carbonate,

as

calcium

phosphates.

Other i n h i b i t o r s act b y a b s o r b i n g o r b y p a s s i v a t i n g . protective f i l m

inhibitor

chromate,

nitrate,

The

molybdate

l a t t e r form a

and

tungstate.

Silicates also appear to work on s i m i l a r p r i n c i p l e s . In

general

oxygen.

the

corrosion

I t increases

significant

when

rate

is

dependent

w i t h c o n d u c t i v i t y up to a

the

pH

drops

below

4

(see

on

c o n d u c t i v i t y . pH

limit, Fig.

whereas

1.5).

and

it

i s most

Oxygen

content

increases corrosion r a t e , e s p e c i a l l y a t h i g h e r temperatures. Chromates a r e p a r t i c u l a r l y e f f e c t i v e corrosion up to 300 m i l l i g r a m s

per

litre

in open

I i t r e i n closed c i r c u i t s a r e used. a

deterrent.

Additives

of

circuits

inhibitors. and

I t i s therefore costly,

zinc

and

phophate

Concentrations

2000 m i l l i g r a m s

per

and its toxicity

reduce

the

is

chromate

r e q u i remen t s. To overcome the t o x i c i t y problem of chromates, and polyphosphate m i x t u r e s have been developed. of

calcium

milligrams

orthophosphate

at

per

inhibitor

Iitre,

an

Simultaneous p a s s i v a t ion of salts a t

orthophosphate such

as

phosphonate

the cathodic zone to form a p r o t e c t i v e

such

as

To p r e v e n t p r e c i p i t a t i o n

concentrations

above 5 can

the anodic areas a n d p r e c i p i t a t i o n

( r e f e r r e d to as d i a n o d i c protection, F i l m i n g amines

s u i t a b l e ortho-phosphate

layer

a p r o p r i e t r y name),

octadecylamine

act

differently.

7

be

added.

of

calcium

i s thereby (Betz,

to

possible

1980).

They

form

a

p h y s i c a l b a r r i e r , often monomolecular i n n a t u r e .

POTABLE WATER STANDARDS

Although

i n d u s t r i a l water

i s not often

intended f o r human

the q u a l i t y should b e adequate to ensure should be non-toxic,

no

harm

if

it

consumption

i s consumed.

It

and i f d r u n k in l i m i t e d q u a n t i t i e s showld show no i l l

effects.

The upper l i m i t s to dissolved s a l t s f o r p o t a b l e water a r e d i f f i c u l t

to f i x .

They

depend

on

the amount

consumed

and

it

should

be b o r n

in

m i n d t h a t men could d r i n k up to 2 l i t r e s a s h i f t . M i c r o b i o l o g i c a l m a t t e r in the water can be more concern salts.

After d i s i n f e c t i o n ,

not n o r m a l l y present made.

Toxic

nitrates,

with chlorine,

i n mine service water,

substances

some algae,

normally

include

organic

heavy

than dissolved

bacteria and viruses are

b u t r e g u l a r checks should be

metals,

phosphates and

concentrated

fluorides,

some poly-electrolytes

(the

16

l a t t e r two a r e used in t r e a t i n g water sometimes) Highly

mineralized

water

a f f e c t the sweating process, Often

human

possibility

of

perception unsafe

possesses

laxative

properties.

It

may

blood p r e s s u r e o r the c a r d i o - v a s c u l a r (taste,

water.

smell

Phenols,

or

colour)

chlorine

and

will organic

also

system.

identify

the

matter

are

e a s i l y detected b y taste. Suggested l i s t of l i m i t s to c e r t a i n substances f o r p o t a b i l i t y Table

1.2.

Table

1.3

indicates

the

maximum

allowable

i s given

in

concentrations

of

o t h e r t o x i c substances.

Fig.

1.5

The effect of pH on the corrosion r a t e .

TABLE 1.2

Recommended p o t a b l e water s t a n d a r d s .

Substance

Concentrat ion mg/e

A I k y I ben zenesu Ifona t e ( ABS )

,

tast e-produc in g

C h l o r i d e ( C 1 1,

250.0

taste-producing

Carbon chloroform e x t r a c t

(CCE),

taste-producing

0.2

possi b I y t o x i c

0.01

Cyanide (CN) I r o n ( F e ) , taste-

a n d colour-producing

Manganese ( M n ) , tasteN i t r a t e (NO ) ,

3

and colour-producing

p r o d u c i n g methemoglobinemia

P heno I s , t as t e-p r o d uc i n g a n d tox ic Sulphate (SO)&),taste-producing Total dissolved solids, Zinc

0.5 0.1

Arsenic ( A s )

laxative

( Z n ) , taste p r o d u c i n g

and l a x a t i v e

0.3

0.05 45.0 0.001 250.0

500.0 5.0

17

TABLE 1 . 3

Toxic concentrations in water

Substance

Concentration, mg/t

0.5

Arsenic (As) Barium ( B a )

1 .o

Cadmium (Cd)

0.01 6+) Cr

Chromium (hexavalent,

0.05

Cyanide ( C N )

0.02

Lead ( P b )

0.05

Selenium (Se)

0.01

Silver (Ag)

0.05

AGRICULTURE AND IRRIGATION

I r r i g a t i o n i s a major consumptive

use of water.

Crops cannot

tolerate

h i g h s a l t loads and y i e l d s d e t e r i o r a t e unless remedial a c t i o n i s taken.

The

f o l l o w i n g t a b l e shows levels of s a l t s which a f f e c t crops.

TABLE 1.4 Water Q u a l i t y which affect crops

T DS

mg/P

Lower l i m i t

Upper l i m i t

500

2000

150

350

Root a b s t r a c t i o n : Chloride

mg/P

L e a f water a b s t r a c t i o n (sprinkling) Chloride Nitrates

mg/P mg/P

Rapid assessment of The

conductivity

in

TDS

mS/m

100

1000

5

30

i s often is

possible

approximately

dissolved s o l i d s c o n c e n t r a t i o n ) i n m g / t

b y measuring equal

d i v i d e d b y 6.5.

to

the

conductivity. TDS

(total

F i g 1.6

shows the decrease

s o i l moisture salinity.Some

due to t h e i r p u r i f y i n g a b i l i t y . than f r u i t ,

yield

in

crops

are

for

some crops

more r e s i s t a n t

For instance,

as

than

a

function

others

to

of

salts

vegetables a r e more r e s i s t a n t

b u t a r e less p r o f i t a b l e .

There i s also the

gradual

deterioration

in s o i l

to contend

b u i l d s up due to e v a p o r a t i o n a n d t r a n s p i r a t i o n of water. leached out b y a p p l i c a t i o n of excessive water,

but,

for

with.

Salt

The s a l t s can b e instance,

at

least

25% more water would be r e q u i r e d to ensure good s o l i d c o n d i t i o n s w i t h the TDS l e v e l s of 800 mg/e.

More i r r i g a t i o n equipment

i s also r e q u i r e d

to cope

w i t h the h i g h e r flows. The a l t e r n a t i v e i s to change the c r o p p i n g p a t t e r n .

Crops r e q u i r i n g

water o r a d a p t a b l e to s a l i n e water would h a v e to be developed.

\

I

I

I

Lucerne\

\

\

I

C o n d u c t i v i t y of g r o u n d w a t e r (mS/m) Fig.

1.6

Crop y i e l d as a f u n c t i o n of water q u a l i t y

less

19 REFERENCES

Barenbrug, A.W.T., 1965. Psychrometry and psychrometric charts. T r a n s v a a l a n d O.F.S. Chamber of Mines. Johannesburg. Betz. 1980. Handbook of I n d u s t r i a l Water C o n d i t i o n i n g , 8 t h Ed., Betz, Trevose, 440 pp. Brownlow, A.H., 1979. Geochemisty, P r e n t i c e H a l l , N.J. 498 pp. L a n g e l i e r , W.F. 1954. Journal America1 Water Works Assn., 46, 461. Mrost, M. a n d L l o y d , P.J., 1980. B a c t e r i a l O x i d a t i o n of W i t w a t e r s r a n d Slimes, I .A.E.A. Johannesburg. P e l l e t i e r , R.A. 1964. M i n e r a l Resources o f South - C e n t r a l A f r i c a . O x f o r d U n i v e r s i t y Press. Cape Town. 277 pp. Porges, J. 1971. Handbook of Heating, V e n t i l a t i n g a n d A i r C o n d i t i o n i n g . 6 t h Ed., Newnes-Butterworths, London. Ryzner, J.W. A p r i l 1944. A new index f o r d e t e r m i n i n g t h e amount o f calcium carbonate scale formed b y water. JAWWA, 36, 472-473. U h l i g , H.H. 1963. Corrosion a n d Corrosion Control. John Wiley a n d Sons, N.Y. Van Staden, C.M.V.H., 1970. Steps Taken b y t h e M i n i n g I n d u s t r y to Prevent a n d Overcome Water P o l l u t i o n . Water f o r the F u t u r e Convention, Pretoria.

CHAPTER 2

MATHEMAT I CAL MODELL ING O F WATER QUALI TY

A f i e l d to which many systems concepts can be a p p l i e d q u a l i t y deterioration are

examples

predict

the

rate

concentrations of

in

where

industrial

quality

of

will

build-up

i n water

t h e complex n a t u r e of for

all

Cooling

of

in

dissolved

r e t i c u l a t i o n systems,

the o r i g i n s and methods of

accounting

systems. deteriorate

industrial

these

water

effects

in

and

time.

salts even

concentration

of

real

washing

It

is

or

easy

to

equilibrium

an

understanding

This

i s because of

systems.

system

water

systems

not

the

with

salts.

recirculation a

i s t h a t of

One

appears

way

of

be

by

to

m o d e l l i n g the system on a computer. Once a model i s produced a n d v a l i d a t e d ,

i t may be used to

improve the

operation of e x i s t i n g s e r v i c e water r e t i c u l a t i o n systems and f o r o p t i m i z i n g the design of new systems. The

build-up

of

impurities

in

water

can

together w i t h the water r e c i r c u l a t i o n cycle.

simulated

mathematically

The flows of water

o r i n vapour form i n the a i r in and out of The processes of e v a p o r a t i o n , condensation,

be

i n conduits

the system can be c a l c u l a t e d . p o l l u t i o n a n d make-up

can a l l

be modelled.

MASS BALANCES

For

the

purposes

of

mathematical

system must b e described described

in

terms

analytically. the

of

a

mass

balance

I n other more complex

equations

in

simulation

in terms of equations.

finite

equation

situations

difference

form

water

of

One-stage

and

which is

it

systems,

can

be

necessary

solve

the

systems can be

them

solved

to

express

numerically.

D i f f e r e n t types of models and the assumptions t h e r e i n a r e described below. Parameters whereby

pollution

i s measured may e i t h e r

be c o n s e r v a t i v e o r

non-conservative.

I n a c o n s e r v a t i v e system i n p u t to a n y p a r t of the system

equals

Thus,

outflow.

evaporation parameter

will is a

if

the

be neglected chemical

parameter in a

compound

studied

conservative it

is

is

model.

assumed

water

flow

Similarly

there

is

then if

the

no

reaction,

the

start-up

deposition o r s o l u t i o n i n a c o n s e r v a t i v e model. The model

may

be

mine as

steady-state concentrations

or

time-varying.

build

up

During

p e r i o d of

a

unsteady.

After a w h i l e the system may reach e q u i l i b r i u m . That

case of s a l t s in s o l u t i o n ,

the

system

is

said

to

be

is,

in the

the increases i n mass of d i s s o l v e d s o l i d s

in t h e

21 system

due

to

leaching

or

evaporation

equals

the

by

loss

pumping

or

deposition.

MIXED AND PLUG FLOW SYSTEMS

In a

plug-flow

through

the

pipes a n d d r a i n s a t a c e r t a i n r a t e , conveying i m p u r i t i e s a t t h a t r a t e .

The

s a l t s content as

water

a t any

with

completely

system,

An

input

so

that

the

divided

by

the

total

the

i s assumed

volume

of

and

cross

of

in a

in

at

that

will

salts

series of point.

be

the

instantaneously

increases water

travel

by the

the

mass

system.

Real systems w i l l

In

a

same

at

salt

This

probably

steps

through

of

the

input

simplified

to describe systems which e x h i b i t

change i n concentrations.

tubulence

to

arrives

to spread

concentration

p l u g flow and completely mixed, to

assumed

concentration

mechanism i s often s a t i s f a c t o r y r a t e s of

is

concentrations

system,

systems

water

p o i n t can therefore be affected

different

mixed

every p o i n t .

the

gradual

be between

as there w i l l be d i f f u s i o n and m i x i n g due

connections.

In

general

salts

are

conveyed

by

advection ( l a t e r a l t r a n s p o r t ) and dispersion.

Examples

The simplest i l l u s t r a t i o n of the use of the mass b a l a n c e equations i s f o r a

steady-state

concentration

Q

system.

i n mg/e.

is

I n f l o w of

flow

rate

e/s

in

water a n d of

outflow r a t e :

F i g 2.1 Point Node

Flow Balance Mass Balance

a, ale, .*.C

3

+ +

a2 = a3 a2c2 = a3 = alcl+a2c2 Q1

+Q2

or

MP/d,

salts per u n i t

C

is

the

time e q u a l s

22

e.g.

Q2

i f Q1 = 5 MP/d,

C 1 = 400 mg/P,

=

10 M e / d

( w a t e r flow r a t e )

C2 = 100 mg/P ( s a l t c o n c e n t r a t i o n )

C3 = 200 m g / t

then

a n d the t o t a l mass of s a l t discharged p e r day

Q3C3

=

=

15 x 200 = 3000 k g / d

A completely m i x e d

system can

(2.4)

be described

Subscript i r e f e r s to i n f l o w , e to e x i t ,

by

differential

equations:

s to i n i t i a l conditions:

Volume S Conc. C

Fig. 2.2

QiCi

=

=

.*.

M i x e d flow node

d (SC) Q C + -

e

dt

Q C +

SdC x

SdC

dt =

Qi C i-QeC

Fig. 2.3

Diffuse node

Integrating that C = C T = S

Qe

f o r constant S

en

and e v a l u a t i n g

the

constant

of

integration

from

the

fact

at t = 0 : QiCi-QsCs ( QiCi-QeC

(2.8)

1

23

QiCi/Qe-

QiCi

-- Qe

C =

or

e(

c

and a t t =

m

o r S = 0,

o r Be = -

,

(ai/ae)ci

=

i f Q . does not equal Qe,

Observe that losses, e.g. The

(2.9)

1

Qet/S

a t t = 0, C = C s ,

e.g.

Cs

there must be i n t e r n a l

gains or

due to evaporation.

previous

example

could

r e q u i r e s specific numbers,

it

is

be

studied

often

numerically.

the o n l y

Although

practical

way

of

this

solving

more complex problems. Assume S = 1000 m 3 , Q . = lm’/s Choose

~t

100

=

= Q

e’ The choice of ~t

5.

C s = 0, Ci = 500 mg/P. can affect

the speed of

the accuracy of r e s u l t s a n d the numerical s t a b i l i t y of must

be

determined

considerations. NOW Q.C.

- Q C

.’.

1

I

I

C2 = C

t

= 5-

5

by

trial,

from

experience

or

from

It

theoretical

c 2 -c 1

(2.10)

At

8 . ( C . -C 1

solution,

the computations.

1

1

) = C1

+ 0.1(500-C1)

(2.11)

The computations can be set out in t a b u l a r form as follows:

t

500-C1

c1

xo.l

c2

0

0

500

50

50

100

50

450

45

95

200

95

405

40

135

300

135

365

37

172

326

1 74

17

343 mg/t

0

0

0

1000

(2.9)

Equation comparable

with

would the

indicate

result

C =

316 mg/e

indicated

by

the

at

t

=

numerical

lOOOs, solution

which of

is 343

mde. A

plot

of

C

versus

t

is

called

a

pollutograph,

and CQ versus t a

loadograph. T h e numerical computations f o r change of p o l l u t a n t above

table

are

very

similar

to

flood

routing calculations

load i n t h e

assuming

for

example the Muskingum method. Reservoirs a r e g e n e r a l l y assumed to be completely mixed,

whereas r i v e r s

24 a r e sometimes assumed to be p l u g flow.

I n fact

i n b o t h there

i s a degree

of m i x i n g due to:

a)

Molecular

diffusion

b)

Turbulent mixing,

c)

Short

due

to Brownian

movement

in

(negligible

most

h y d r a u l i c systems).

circuiting

made across

due to eddies i n the stream. or

the

t r a c k i n g e.g.

water

body

by

reservoirs

in

the

flow.

The

a

track

is

stagnant

where

water

in

corners i s c a l l e d dead water d)

Wind m i x i n g

e)

Thermal m i x i n g a n d i n v e r s i o n (e.g.

Henderson-Sel lers,

The degree of m i x i n g can affect concentrations

1979).

so much t h a t m o n i t o r i n g

systems need to account f o r i t (Sanders, 1983).

SYSTEMS ANALYSIS

A

more

sophisticated

approach

than

the

simulation

above i s the use of systems a n a l y s i s a n d o p t i m i z a t i o n

method

assistance of computers i f necessary. The methods a l l o w to be selected from numerous a l t e r n a t i v e s alternative

The

o p t i o n from a few

standard

engineering

selected designs.

The

described

techniques,

the

with

an optimum design

(Thomann,

1374).

approach

is

to

l a t t e r approach

select is

the

tedious

best where

there are many a l t e r n a t i v e s . The

design o p t i m i z a t i o n

configuration

i n which

not been f i x e d .

the

approach

involves

the

numerical

v a l u e of

creation

of

independent

a

general

variables

A n o v e r a l l economic o b j e c t i v e i s defined a n d the system

has is

described i n terms of equations o r c o n s t r a i n t s .

TERMINAL CONCENTRATION I N A WATER C I R C U I T .

The t o t a l dissolved system w i l l

water

is

control

i n a closed water

b u i l d up due to e v a p o r a t i o n and a d s o r p t i o n o r

c o n c e n t r a t i n g effect

relative

s o l i d s concentration

replaced. proportion

will

continue indefinitely

Make-up of

rate

water of

will

the e q u i l i b r i u m d i s s o l v e d s o l i d s

leaching.

unless s a t u r a t i o n occurs,

replace

replacement

recirculation

to

polluted

water

concentration.

in

water

and

circulation

The or the will

Computation of

the

e q u i l i b r i u m concentration i s performed a s follows:

F

I

:~

ai ~ = aD

+

ae

(2.12)

25

c

I

c,

t

a.

P l u g flow

C

t

b.

Completely mixed system

t

c.

Fig. 2.4

D i f f u s e systea

Comparison of p l u g f l o w a n d m i x e d systems.

26 S a l t s : QiTi + QiTe -

(2.13)

- QPTP

where Qi

i s the

water

input

rate

(.e.g.

l i t r e s per' second

or

megalitres

per d a y ) ,

Q

P

i s the d i s c h a r g e pumping r a t e

Q

i s the e v a p o r a t i o n r a t e

T.

i s the concentration of s a l t s i n the replacement o r makeup water stream.

T

e

is

the

concentration

build

up

due

to

leaching,

expressed

in

terms of the incoming water flow r a t e here.

Tp

i s the concentration

in the pumped

water

which

i s the

same as

the c i r c u l a t i n g water f o r a mixed flow system.

I f Q i s i n m e g a l i t r e s a d a y and T k i l o g r a m s of s a l t p e r d a y .

then QT

i n mg/t

Solving f o r T

the

P'

salt

has

the

u n i t s of

concentration

in

the

system,

(2.14)

Thus f o r no l e a c h i n g ( T the pumping r a t e , T

=

0 ) and a n e v a p o r a t i o n r a t e equal to 50% of

=

1.5 Ti

i.e.

P be 150% of that of the make-up

the e q u i l i b r i u m s a l t concentration

will

water.

APPLICATION TO A MINE WATER CIRCUIT

South A f r i c a n g o l d mines use n e a r l y underground

(Holton a n d Stephenson,

f o r dust control

a n d cooling.

3000 metres below

surface,

Owing

rock

2000 m i l l i o n l i t r e s of water

1983).

The

to

great

the

temperatures

e f f i c i e n t method of c o o l i n g i s b y means of rock.

The water

water

is

depths

can

a day

used p r i m a r i l y i.e.

r e a c h 65°C.

often

over

The

most

s p r a y i n g c h i l l e d water onto the

i s also used f o r ore moving and to a

l i m i t e d extent

for

h y d r a u l i c emulsions in machinery. The

geological

formations

Free State and T r a n s v a a l

in

which

gold

i s mined

which s u f f e r water

imported from a d j o i n i n g catchments such as i n Natal purposes. encouraged

The

cost

both

to

pol l u t e d wastewaters

of

conserve

is

the requirement

therefore

water

i n t o surface

g o l d mines a r e therefore 10% of

water

and

streams.

high to The

made

up

from

minimize water

surface

in

the

Orange

is

i n fact

Water

f o r domestic d r i n k i n g

and

l a r g e l y met b y r e c y c l i n g is

are

shortages.

re-use the

water

is

discharge

of

of

requirements of

the

and only approximately water

resources.

Some

27

mines also have s u r p l u s

underground

water

from

infiltration

and

this

is

used where possible.

# Pure w a t e r

Remaining concentrated S a l i n e water

F i g . 2.5

Model of s a l t b u i l d u p due to e v a p o r a t i o n

The q u a l i t y content

of

surface

i s typically

water where there

less

i s any,

water than

is

good

and

500 mg p e r

i s also g e n e r a l l y

the

litre.

total The

Although

h a r d and contains magnesium and calcium carbonates,

on

the

i s r a r e l y above lOOOmg per

other

hand

the

natural

water

litre. is

In

,Qi

Fig.

2.6

of

ground

I

Model of s a l t e q u i l i b r i u m due to pumping

the water

the dissolved

the Orange

known

concentrations of chlorides.

Average salinity

quality

solids

good as the water o r i g i n a t e s

l a r g e l y from dolomitic a q u i f e r s in the upper s t r a t a .

concentration

dissolved

to

is

salts

Free State

contain

high

28

Despite the general p u r i t y of make-up

water,

a n d o r g a n i c s a l t s u n d e r g r o u n d can t y p i c a l l y per Iitre.

concentrations of d i s s o l v e d

vary

10000 mg

3000 to

from

T h i s water can therefore o n l y be used f o r l i m i t e d purposes.

has to be machines

taken and

to

ensure

with

heat

that

it

is

exchange

not

used

for

drinking,

In

apparatus.

many

mines

Care

certain

in

there

is

s c a l i n g a n d f o u l i n g of m a c h i n e r y a n d p i p e w o r k because of the poor q u a l i t y of

water

and

in

other

mines

there

is

corrosion

of

pipework

and

other

metal-work. Reasons for primarily are

the

l e a c h i n g from

to

brought

from

concentration effect i n cooling and

for

towers.

corrosion

contributor

deterioration

owing

the

the

source

due

to

service

mined ore. of

the

scaling

the

small

be

attributed

In a d d i t i o n c e r t a i n

pollutants

water

to the e v a p o r a t i v e

The chemical and

in mine

dosing of inhibition dosage

water

can

and

there

loss of

water

water can

rates

for

be

is

a

secondary

underground and

purification

ruled

relative

to

purposes

as

out

the

a

major

increase

in

dissolved solids i n the water.

Evaporation

Groundwater

F i g . 2.7 After water,

Mine water r e t i c u l a t i o n system i d e n t i f y i n g p o s s i b l e sources of

chemical

salts

appearing

r a t e of appearance of

s a l t s in

the

water.

The

complicated

n a t u r e of

geochemical environment make% a n exact q u a n t i t a t i v e estimation of in

any

in

the

l a b o r a t o r y a n d s i t e t e s t i n g were performed to e v a l u a t e the p o s s i b l e

particular

l e a c h i n g can

circumstance

be assessed

with

impossible.

Nevertheless

these methods.

Once

relative

pilot

tests

the

leaching r a t e s of had

been

29 conducted to i d e n t i f y the prime effects of water qua1 i t y d e t e r i o r a t i o n , parameters were s t u d i e d i n more d e t a i l . the

crushed

ore

originating

from

I t appeared t h a t

blasting

or

parameter i n a f f e c t i n g the r a t e of geochemical leaching. the reef

i.e.

the ore b e a r i n g stratum,

w i t h the water affects the amount of ore.

Temperature

water,

affects

the

the

drilling

these

fineness

was

a

of

prime

The composition

also i s a factor.

The contact

of

time

l e a c h i n g from any p a r t i c u l a r mass of

chemical

reaction,

as

does

the

pH

of

the in

a n d i n i s o l a t e d cases p o s s i b l y the presence of b i o l o g i c a l matter,

particular

thio-bacillus

ferro-oxidans

and

thio-oxidans.

The

presence

of

a i r appeared i n a l l cases s u f f i c i e n t to s a t u r a t e the water w i t h oxygen a n d therefore was not a l i m i t i n g factor.

Conditions unless otherwise stated 209 fine,

3OoC, a i r b u b b l e d t h r o u g h 2e

/' 5-409 fine crushed ore 100

-

00E

s,E

-

.-f> .-

60

-

" a

c

P

40-

d0VS

F i g . 2.8 L a b o r a t o r y l e a c h i n g tests on crushed o r e

L a b o r a t o r y tests were performed b y immersing samples , o f ore crushed to various

finenesses

one

in

to

two

litres

of

water.

Temperature

was

controlled b y means of a b a t h and a i r was b u b b l e d t h r o u g h the samples agitate

and

water

were

month

and

provide performed

sufficient

oxygen.

simultaneously.

conductivity

and

various

Datum

Tests

tests

were

dissolved

measured r e g u l a r l y as well as pH a n d temperature.

with

pure

for

longer

run salt

to

distilled than

parameters

a

were

30

The r a t e of l e a c h i n g of a t y p i c a l b a t c h of 2.8.

I t will

the f i r s t

be observed that

day a n d then

the l e a c h i n g r a t e s

gradually

the ore were depleted.

samples

decelerated

Confirmatory

i s indicated

were

most

the

reduction

crushed ore,

in

leaching

tests w i t h

rate,

d i f f e r e n t sizes of

The

rapid

during

in

as the s o l u b l e chemicals initial

water

a t v a r i o u s levels i n d i c a t e d t h a t s a t u r a t i o n of the water for

in F i g .

effects

particles and

of

concentrations

was

not

different

temperature,

the cause passes

of

presence of

air

a n d a g i t a t i o n were s t u d i e d i n d i f f e r e n t samples. v a r i e d from 5 to 30

The increase i n t o t a l dissolved s o l i d s in the water grams of dissolved s o l i d s per k i l o g r a m of crushed ore. The

following

a n a l ysed : sodium

inorganic

sulphates,

as

well

concentration

chlorides,

as o t h e r

of

salts

were

carbonates,

elements

in

sulphates

detected

in

the

nitrates, relative

milligrams

the

in

per

water

c a l c i urn order

Iitre

per

cent

sulphur

by

In the presence of

mass).

(mg/P)

r e a c t i o n was is

often

well

precipitated

known

in

both

as

iron oxide

coal

mining

and and

and The

The

SO4

of

was

i n mg/e.

in the ore

oxygen

s u l p h i d e forms in p a r t i c u l a r were o x i d i z e d to sulphates.

which

magnesi urn,

indicated.

t y p i c a l l y one h a l f of t h e t o t a l d i s s o l v e d s o l i d s concentration can be a t t r i b u t e d to the h i g h s u l p h i d e concentration

samples

This to

(up

water

8

some

i r o n from the

the

chemical

reaction

gold

mining

pollution

problems i s i n d i c a t e d below:

+ O2 + H20 4 FeO(OH) + H2S04

(2.15)

The pH of the s o l u t i o n remained between 6 a n d 8 f o r most cases.

By the end of

to below f o u r .

t h i r d week

the f i r s t

week

in

the pH often dropped

As the pH dropped an a c c e l e r a t i o n i n the l e a c h i n g r a t e ,

i n d i c a t e d b y an evidenced.

the second o r

increase

i n conductivity

The presence of

and total

b a c t e r i a was noticed

dissolved,

in

solids,

as was

i s o l a t e d samples a f t e r

a month of t e s t i n g , b u t not i n a l l samples in which the p H dropped o r r a t e of l e a c h i n g was noted to be p a r t i c u l a r l y It

is

therefore

geo-chemical

concluded

that

the

the

high.

leaching

reaction

is

primarily

to

be

r e a c t i o n a n d b i o l o g i c a l r e a c t i o n can be s a i d

small

a in

the environment studied. The

application

particularly generated exposed

of

the

by

mining

surface

of

It

leach a t

a

high

underground

fine

laboratory.

Tests

in

only

which

which

this

compared the

results

not

field

may

of out

Only

explain

with could

to

the

is

settles

to the s h a f t .

r a t e and as

is

operations

the

d r a i n s t a k i n g water back

rate

laboratory

complicated.

the total

field mass

importance, rapidly

the surface the

in

maximums

only

indicate

of but the

ore

also

the

horizontal

low

measured increase

is

fine

l a y e r appears

relatively

the

conditions

to

leaching in in

the total

31

dissolved solids of

the o r d e r of

100 to 300 mg/e

per

cycle

as

the

water

r a n from the workings back to the s h a f t . I t was therefore not possible to equation

form

into

r e l a t i o n s h i p s were

the

i n s e r t the complete chemical process

computer

therefore

used

model

and

of

these

will

the

system.

have

to

in

Empirical

be

verified

for

considerably

during

the

each mine and each o r e mined

COMPUTER SIMULATION MODEL

The day

r a t e s of

use of

and are highest

often

stored

various

in

the

stages.

rates

in

the

additions logical

underground

is

cascade

dams

at

dams in

volumes of

various

underground o r

water

all

conduits

the

quality storage

be

can

also

affect of

internal

volume,

simulating

the

in

is

surface

therefore

dams

modelled.

water removed w i t h the ore,

method

vary

Water

Fluctuation

p r e d i c t unless the

evaporation,

water

d u r i n g the d r i l l i n g a n d ore moving s h i f t s .

as

difficult

well

External

as

to

the

flows

flow

such

as

seepage a n d i n t e r m i t t e n t make-up

flow

process

rates was

and

with

quality. a

The

digital

most

computer

model. This was adapted to a micro computer w i t h considerable success. A

general

simulation

models of mine water

program

systems.

was

p a r t i c u l a r mines.

The sizes of dams,

conduits and the

usage

hydrographs

The o p e r a t i n g r e l a t i o n s h i p s rate,

criteria

for

then

be

used to

which,

adding

programmed as p a r t of

for

the

then

be

example, water,

source code.

model.

simulating i n general

p o s i t i o n s and

the

can

for

make-up

the model

simulate

developed

Models a r e constructed

Flow

starting

the

by

the

salt

pumps

The computer

rates,

for

the c a p a c i t i e s

specified

define

specific form

volumes

leaching etc.

program and

of

user.

are will

dissolved

s a l t s concentrations a r e d i s p l a y e d a t specified time i n t e r v a l s as output.

Mathematical Basis of Model

The computer model easy

updating

concentrations differential

and

was p r e p a r e d

in a

modification.

The

a r e described

equations.

i n models b y

Alternative

modular

structured

to s u i t

salt

means of

first-order

methods

the p a r t i c u l a r equations.

for

and

volumes

of

solving

n u m e r i c a l l y are b u i l t i n t o the s i m u l a t i o n p r o g r a m and selected

fashion

varying

the

ordinary equations

the methods can

I n many cases a fast

i s s u i t a b l e w h i l e i n o t h e r cases a more a c c u r a t e a l g o r i t h m

be

algorithm

i s r e q u i r e d to

solve the equations w i t h s u f f i c i e n t accuracy on a numerical basis. In a

mine

water

system

many

processes occur

simultaneously

and

the

32 net effect i s e i t h e r to increase o r decrease the d i s s o l v e d s a l t concentration of flows a n d water volumes w i t h time. storage element, volume of outflow.

such a s

water

dams,

i n storage,

on

the

mass

of

salts

a n d the s a l t c o n c e n t r a t i o n of a n y

Denote Q1 a n d Q2 as the i n f l o w a n d outflow

a n d C 2 as the corresponding

Cl

The s a l t concentration of water

depends

in a

and

the

inflaw and

to a dam,

a n d denote

I f M i s the mass of

s a l t concentrations.

dissolved s a l t a n d V the dam volume a t a c e r t a i n time t,

the r a t e o f

then

change of water volume a n d s a l t mass w i t h time i s

(2.16)

dM dt

and

If

-

= Qi.Cl

perfect

(2.17)

Q2.C2

mixing

is

assumed

concentration of the outflow M

c2

=

to

occur

in

the

dam

then

the

salt

is:

(2.18)

0

A mine water model b a s i c a l l y consists of e q u a t i o n s ( 2 . 1 6 ) and ( 2 . 1 7 ) f o r each storage element wherein

the volume and s a l t mass change w i t h time.

Other r e l a t i o n s h i p s govern flow r a t e s a n d changes i n s a l t concentrations of flows between storage elements. S t a r t i n g w i t h known o r assumed

initial

d i f f e r e n t i a l equations a r e n u m e r i c a l l y methods.

Values

time-increment

M,

of

V

and

C

V a n d C the

v a l u e s f o r a l l M,

solved u s i n g E u l e r a n d Runge-Kutta are

determined

at

each

iteration

d u r i n g the s i m u l a t i o n a n d can be d i s p l a y e d as o u t p u t .

s t a b i l i t y and accuracy of the solution depends v e r y much on

The

the time step

a n d numerical method selected. Considerable e f f o r t h a s to be expended it

i n g a t h e r i n g data for

the model

i s found. Owing to the u n p r e d i c t a b l e changes i n m i n i n g p a t t e r n s as the

of

characteristics

therefore

the

Reef

change,

the

b e i n g extended o r a l t e r e d .

continually

form

a

complex

storage

i s designed

monitored as

it

volumes and

times

of

distribution

to operate

makeup

water

were

reticulation

pattern

The c o n d u i t s and dams system

which

automatically.

therefore

often

is

Flow

often

rates,

difficult

to

in t h i s system

point

typical

for

variation

alternative

indicates

a

and Fig.

2.10 i n d i c a t e s the water q u a l i t y v a r i a t i o n

in

flow

operating

rate at

the

conditions. workings in

the

not

stored

ascertain.

The model can thus oe used to p r e d i c t the water q u a l i t y a t a n y any

is

constructed

time a t Fig,

2.9

underground water

to the surface a t the same g o l d mine over a p e r i o d of a week.

pumped

33

2.9

Fig.

Flowrate from Coldwell to u n d e r g r u n d (M4/d)

T h e i n i t i a l conditions varied

l2hOO

24h00

12h00

to

an extent.

in starting

That

i s the

up a n d

initial

running

water

the model

quality

could

could be

be

varied

assuming that d i f f e r e n t make-up q u a n t i t i e s of surface water c o u l d be used to replace poor q u a l i t y water i n the surface storage dams over a weekend when m i n i n g a c t i v i t i e s were m i n i m a l .

By comparing a l t e r n a t i v e management

p o l i c i e s i n t h i s manner i t i s possible to r e a c h a f o r m a i n t a i n i n g the water q u a l i t y usage

underground

was

minimum cost

a t a c e r t a i n selected

assumed

fixed

by

the

level.

mining

therefore o n l y storage dam c a p a c i t i e s and make-up

procedure

The r a t e of

operation

and

r a t e c o u l d be v a r i e d

in

t h i s way. I t i s also possible t h a t m i n i n g methods c o u l d water q u a l i t y .

I t was recognised t h a t the contact

be v a r i e d

to affect

time between f i n e ore

suspension and i n the r e t u r n water systems h a d a n important

bearing

the

methods

rate

returning water

of the

quality.

deterioration water

were

in

the

water

therefore

quality.

investigated

In t h i s manner the effects of

therefore r e q u i r i n g less surface make-up

p o l l u t i o n can

water

10000 8000

5000 4000 2000

TueS

F i g . 2.10

Yed

Thur

Fri

Sat

Sun

Hon

Tues

Salt concentration i n the settlers

to optimize

in on

of the

be minimized,

a n d r e d u c i n g m i n i n g costs

i n e l i m i n a t i n g to a l a r g e extent s c a l i n g and erosion.

12000

Alternate

i n order

the

34

REFERENCES

Henderson-Sellers, B. 1979. Re se rv o i rs , M c M i l l a n , 1 2 8 ' p . Holton, M.C. a n d Stephenson, D . , 1983. A computer model of c i r c u l a t i n g s e rv i c e wa t e r i n South A f r i c a n g o l d mines. I n t . J. M i n e Water , 2 ( 2 ) p 33-42. Sanders, T.G. ( E d . ) , 1983. Design of Networks for M o n i t o r i n g Water Q u a l i t y . Water Resources P u b l i c s . 328 p . Thomann, R . V . , 1974. Systems A n a l y s i s a n d Water Q u a l i t y Management. McGraw H i l l , 286 p .

35. CHAPTER 3

NON CONSERVATIVE PARAMETERS

INTRODUCTION

Mass

balances

are

not

always

possible.

waters change concentration n a t u r a l l y . d i f f e r e n t salts. total

Many

Some r e a c t chemically

I f a l l the s a l t s before and a f t e r

concentration of

dissolved

salt

in

same. Sometimes oxygen i s taken out of

mg/e

in

constituents

still

to r e s u l t

in

r e a c t i o n a r e s o l u b l e the

in

the water

the

water

remains

the

to release hydrogen gas

which i s more v o l a t i l e and escapes.

For instance ammonia

Oxygen i n water i s the cause of many changes. oxidized

to

nitrites,

n i t r a t e s cannot

biological

these

turn

in

be e l i m i n a t e d except

or biochemically, Absorption

and

of

oxidized

chemical

to

nitrates.

replacement,

is

The

absorption

as i s now done in some waste water treatment processes. oxygen

matter

by

are

in

and other

water.

Decay

chemicals

i n water

i s generally

may occur

approximated

by

due a

to

first

o r d e r equation

- _

at

-

KC

BASIC MASS BALANCE EQUATION

The

one-dimensional

balance

equation

allowing

for

dispersion,

and sources or s i n k s i s d e r i v e d below Source

I

SdtAdx

direct i o n

Decay Kc Adxdt

F i g . 3.1

Mass b a l a n c e

decay

36 Net increase i n mass of C i n element in time d t i s dC.Adx

= dt

(SAdx

-

aa

KC Adx - C a x dx

-

as

a x d x + a x ( A € aa sx ) d x j

Q

For a u n i f o r m channel A = constant and t = constant a n d Q = constant

...

s-

ac

-a + t k C + v

a2c

(3.3)

E,,I-~=O

1 )

i s r a t e of increase in concentration of p o l l u t a n t

2)

i s decay r a t e

3)

i s advection

4)

is diffusion

5)

i s source

E i s the t u r b u l e n t viscosity

which

diffusion

represents

coefficient.

transfer

of

It

is similar

momentum

to

between

the k i n e m a t i c layers

f r i c t i o n model, e.g. du = p E - against a wall, dy where

in

a

(3.4)

T

(3.5)

, where U=

v'(T/P)

= shear

velocity

a n d k i s the von Karman constant, 0.4. But i t

i s not t h a t simple

b u t macro turbulence, the action,

i n channels

tracking,

as

dead water,

not o n l y

molecular

s t r a t i f i c a t i o n etc.

diffusion complicate

therefore one needs to c a l i b r a t e models.

E l d e r ( D e i n i g e r , 1973) suggests

E = A h J(ghS)

where h = depth a n d A = coefficient

(3.7)

( a v e r a g i n g 0.07).

Normally d i f f u s i o n i s n e g l i g i b l e in r i v e r s , except estuaries. Thus one gets the Streeter-Phelps equation

-a_t

-

-_

- v ac

ax

KC

(3.8)

( o m i t t i n g sources)

(3.9) (3.10)

K ranges from 0.01

per day i n laboratory conditions

1980) w i t h p u b l i s h e d f i g u r e s f o r r i v e r s a v e r a g i n g 0.1

( a s found b y A r n o l d , per day.

37

t

or

C

X

F i g . 3.2

Decay curves

OXYGEN BALANCE I N R I V E R S

Oxygen concentration oxygen).

in a r i v e r i s measured in terms of DO ( d i s s o l v e d

Shortage o f oxygen

i s measured as

(COD) o r a biochemical oxygen demand (BOD). 1.45 x days,

a

BOD5 where BOD5 i s the BOD as measured a s t a n d a r d test (AWWA,

chemical

oxygen

The long term

in a

demand

BOO i s about

laboratory

over 5

1965).

Coupled equations for DO a n d BOD

I f DO concentration i s designated C and BOD i s L then

-a _t

a2c

ac

- E 7 ax - v~

-

K,L

+ K,(C

- C) * S c (3.11)

38

Dissolved Oxygen Sag Curve

Dernond Dissolved Oxygen

P-.L._-I

n-:-A

Lriilcui ruin1

R e oxygenot ion C u r v e Deoxygenalion Curve

Distance Downstream or Time

E f f luen t Outtall

Fig. 3.3

The d i s s o l v e d o x y g e n sag curve

J, Olcygen 0

F i g . 3.4

Carbonaceous plus

Carbonaceous and nitrogenous o x y g e n demand c u r v e s

39

where C aL and a t

= s a t u r a t i o n conc. =

E

a2L ax

7-

of oxygen (3.12)

aL v- K,L, ax

t S

L

These simultaneous equations can be solved a t p o i n t s a l o n g a r i v e r a n d over

time

K,

increments,

K~~~~

=

e (T-20)

i.e.

it

is

a

function

of

temperature.

charac t e r i s t i C

At n - l

F i g . 3.5

Solution g r i d

A s a n example of t h e solution of these two equations a

method

can

diffusion

be

employed

where

A x

f v

(Deininger

1973,

p

122).

One

two-step can

get

explicit pseudo (3.13)

A t

unless a c a r e f u l numerical procedure i s used. Where

the

river

is

depleted

of

oxygen,

the

BOD

equation

must

be

replaced b y KIL i.e.

( C - C ) - Sc 2 s the q u a n t i t y of oxygen consumed i s equal

(3.14)

= K

introduced i n the same time

(Thomann,

to the

quantity

of

oxygen

1972).

Ana I y t ica I solution dC I f - = - K L + K (C - C ) dt 1 2 s a n d oxygen d e f i c i t D = C - C

2:

_ - - KIL

-

(3.15) (3.16)

K2D

Integrating gives KILO -K,t -K,t D = (e -e Kz-Ki

(3.17)

-K, t

1

One can also e v a l u a t e K,

+ Doe

(3.18) and K2 a t t C ( D e i n i n g e r 1972 p 126).

40

CALIBRATION OF A MOVING BOD MODEL

As an a p p l i c a t i o n of the c a l i b r a t i o n of a r i v e r r i v e r in South A f r i c a was analyzed. effluent

from

major

municipal

underdeveloped township. t h r o u g h reed beds.

The

decay

the K l i p

The K l i p r i v e r h a s d i s c h a r g i n g sewage

works

and

runoff

into i t

from

an

The stream i s also h i g h l y m i n e r a l i z e d a n d flows DO o v e r

Measurements of BOD a n d

show r a p i d n a t u r a l self a e r a t i o n . o t h e r sources.

oxygen model,

summer

The waters a r e e v e n t u a l l y

and

winter

recycled w i t h

A numerical model p r e d i c t s d a i l y v a r i a t i o n s i n BOD a n d DO.

coefficient

and

sources

and

sinks

were

fitted

by

linear

programming opt im iza t ion. The

Klip

banks are area.

river

rises

in

three major

the

watershed

of

sewage

works

municipal

the

a

Separate s a n i t a r y sewers a r e p r o v i d e d g e n e r a l l y

l i t t e r i n g r e s u l t s in h i g h l y p o l l u t e d s u r f a c e The

population

consumption

within

of

the

the

m i l l i o n l i t r e s per day,

area

is

watershed

the

large

its

residential

but

a

tendency

Of

a

total

to

runoff.

nearly of

On

Witwatersrand.

and

2

million.

Klip

r i v e r of

water

500

approximately

n e a r l y 50 percent i s r e t u r n e d to the K l i p r i v e r v i a ( u n t r e a t e d ) i .e.

sewage p u r i f i c a t i o n works o r separate storm sewers

2m3/s.

The base flow of the r i v e r i n the reaches s t u d i e d amounts to o n l y lm’/s.

OXYGEN BALANCE

The dissolved oxygen content (DO) of ability

to support

A

life.

lower

water

i s a useful

level of 4 m g / t

i n d i c a t o r of

i s r e g a r d e d as the

its

limit

f o r f i s h l i f e i n the area studied. The

r a t e of

which

dissolved

demand i s dependent on

oxygen

reduces

the

biochemical

the level of free oxygen concentration.

l i m i t i s the s a t u r a t i o n concentration, C S (mg/e) = 14.6 - 0.41T

+ 0.008T‘

oxygen

The u p p e r

C s , estimated to be

- 0.000778T’

(3.19)

where T i s i n “C The DO i n a p o l l u t e d stream v a r i e s a l o n g the l e n g t h

i n accordance w i t h

the r a t e of takeup a n d the r a t e of re-oxygenation

(Fig.

to b i o d e g r a d a t i o n of carbonaceous o r g a n i c matter,

oxygen

nitrification, high

sulphur

oxidizing

i n o r g a n i c chemicals a n d p l a n t

concentration

in

oxygen requirement i s f a i r l y b y the h i g h llime content, Temperature demand.

and

sludge

the

high.

waters,

due

to

3.3).

respiration. mining

T h i s i s counterbalanced

as the waters o r i g i n a t e from a deposits

in

winter

also

I n addition

i s required With

activity,

for a the

to some extent dolomitic

influence

the

area. oxygen

41 Owing to deposits of t h a n 0.2 m/s) the

summer

in the slow

d u r i n g w i n t e r months,

rains

reoxygenation matter,

sludge

the

was

deposists

observed.

while benthal

stream v e l o c i t y

(less

BOD was observed to increase.

were

The

deposits

moving

scoured

sludge

out

arose

were considered

and

a

primarily

from

relatively

After

more

rapid organic

inactive

(Velz,

1970). There

are

nitrogen.

two

primary

biochemical

oxygen

abstractors;

carbon

and

The BOD removal c u r v e t y p i c a l l y e x h i b i t s a n i n i t i a l hump due to

carbon a n d a

subsequent

hump

due

to

nitrogen

(Fig.

3.4).

The

decay

equation smooths the c u r v e out. The coupled d i f f e r e n t i a l equations d e s c r i b i n g DO a r e 3.11

the v a r i a t i o n of

BOD a n d

and 3.12 r e w r i t t e n i n the form

(3.20) (3.21) A method of e v a l u a t i n g the coefficients K, sink

system, the

S

term,

and

so

total

equations 3.20

the

Linear

difference

3.21

and

and

equations

the above case,

Minimise

{

between

and

the

programming may

f u n c t i o n subject to c e r t a i n

K2,

the

actual

a n d the source a n d

represented

the

that

would

concentrations

concentrations

be used f o r

lead

to by

in

the

observed

the system

river

predicted

m i n i m i s a t i o n of

constraints provided

real

an objective is

In

linear.

the o b j e c t i v e f u n c t i o n would b e

z I Predicted BOD - observed BOD I

+Z

subject

that

would be to f i n d values f o r these parameters

minimum

field.

P,

I

Predicted DO

to the c o n s t r a i n t s

-

observed DO

formed

by

the

I}

(3.22)

system of

equations

and

to

the

c o n s t r a i n t that the e r r o r p l u s the p r e d i c t e d v a l u e must e q u a l the observed value. I n other

words

the

calibration

of

the

model

can

be

carried

out

by

m i n i m i s i n g the sum o f the absolute errors. Another method would be b y .means of This

has

been

attempted

survey on 21 March, and

3.21.

The

I inear

elsewhere,

least squares f i t t i n g

using

the

data

1979 (McPherson a n d S h a r l a n d , '

programming

method

has

been

from

techniques.

the

sampling

1979) equations 3.20 used

be

Kleinecke

(1971 f o r estimating geohydrologic parameters of groundwater basins.

O L - . ; ' . ' - . . . . I . . . . . 1 . . . . . .

6h00

l2hOO

18h00

Fig.

3.6

24h00

1 1 . .

...

I . . . . . .

06h00 06h00 12h00

. . a .

18h00

A

l

.

.

24h00

.

.

.

I

I1

.....

I

.

.

06h00 06h00 12h00

,

.

.

.

..... .....

18h00

Results of S i m u l a t i o n using minimum e r r o r c a l i b r a t i o n p a r a m e t e r s

I

24h00

I ,

06h00

43

I

1-1 x - t grid

F i g . 3.7

Considering the concentration-space how

x

1+1

the above coupled equations

grid

3.20

in

and

Fig.

3.21.

3.7 can

i t can be

be shown

formulated

for

l i n e a r programming e v a l u a t i o n of the parameters as follows: The BOD concentration a t a p o i n t

P can be w r i t t e n

in terms of

implicit

f i n i t e differences as:

- (L 2At

i,n + L i + l , n - Li,n-l

+

Li+l,n-l

1

For I i n e a r programming purposes two requirements must be met: (i) (ii)

a l l terms must be l i n e a r a l I v a r i a b l e s must be non-negative

I n the above f i n i t e difference form these c o n d i t i o n s a r e not s a t i s f i e d . F i r s t l y the term l i n e a r since both source/sink

the

+ L. + L. t , i /4 . ( L i - , , n 1-1 ,n-1 1In K1 and the L. a r e unknowns.

K

1,n

+ Li,n-l) Secondly

i s not the

net

term may be e i t h e r p o s i t i v e o r negative.

To overcome these problems the prediced L. a r e r e p l a c e d b y the known 1,n observed values b . a n d the source/sink term i s s p l i t i n t o a n i n p u t term 1,n + S and an output term - T where one of S a n d T w i l l be p o s i t i v e a n d the other zero.

The equation then becomes

44

( L 1. ,n

--

-UAt 2 Ax

+

-

Li+l,n)/2

+

(Li+l,n

+

+

(Li,n-l

-

Li+l,n-l

L .i+1 ,n-1 ) / 2

1

L .i,n - L i , n - l

- At T i

At Si

(3.24)

T h i s can be r e w r i t t e n as

1

(2

Li,n-l

*

1

U At

d

+

+

Li+l,n-l

(Z -

+

bi+l,n-l

+

UAt ~ x

-

-

(-1 ) i,n 2

-)-L. UAt 2Ax

UL!)

1

i+~,n

‘Z

+

2AX

K1 iAt

- +

AtSi

(bi+l,n

bi,n

+

bi,n-l

1

- AtTi = O

I n addition

(3.25)

another

set

of

equations

can

be w r i t t e n

in

terms

d i f f e r s from the e r r o r b y which the p r e d i c t e d v a l u e of L . 1,n of L . 1

. ,n

- Vi,n

L. + Ui,n ‘,n

Again

actual

= b.

the

value

(3.26)

i,n

the requirements that

the s p l i t t i n g of the e r r o r

of

the v a r i a b l e

must

be p o s i t i v e

necessitates

i n t o a p o s i t i v e e r r o r U o r a n e g a t i v e e r r o r -V,

one of which w i l l be zero i n the solution. Similarly

a

includes a

set

of

reaeration

equations term

can

which

be

i s also

written

for

non-linear

equation unless

3.22.

This

the observed

values a r e s u b s t i t u t e d f o r the p r e d i c t e d values. These equations a r e g i v e n below

- ci+l,n

1 (2

+

-

A t Pi

C.

1,n

+ M.

+

UAt

-126x

At R i

1,n

-

N.

1,n

=

o

=

d.

(3.27) 1,n

(3.28)

45

Equations 3.27 a n d 3.28 can be w r i t t e n f o r a l l p o i n t s i, except point,

a l o n g a study

to

be

the

last

i s a v a i l a b l e over

a

a n d di,n a t each v a l u e of n may i ,n observations taken a t o t h e r times. O n l y

The observed values b

p e r i o d of time. have

reach f o r which observed d a t a

inerpolated

from

equations 3.26 and 3.28 can be w r i t t e n f o r the p o i n t f u r t h e s t downstream. The o b j e c t i v e f u n c t i o n now becomes

;

+ V. + Mi,n + N. {; (Ui,n 1,n 1,n subject to the c o n s t r a i n t s g i v e n b y equations 3.27 a n d 3.28.

Minim i se

(3.29)

F I ELD MEASUREMENTS

The

length of

stream

modelled

6

was

km.

It

was

divided

reaches and two sets of samples were taken a s representative, mid w i n t e r and one i n mid summer.

into

four

one set

in

Samples were taken e v e r y hour f o r 24

hours of each section, which was p r o b a b l y a b i t sparse.

DO was measured

w i t h a p o r t a b l e meter.

and 20-day

COD a n d pH,

The samples were tested f o r 5-day

conductivity,

ammonia,

and suspended sol i d s were estimated

from

light

nitrate,

determined.

and

dark

nitrite,

chloride,

Photosynthetic oxygen

bottle

tests,

and

time

of

BOD,

alkalinity

release

was

passage

and

dispersion were determined w i t h f l u o r e s c i n dye, Various linear

methods

programming

were

employed

was

used

to

to

calibrate

minimize

the

the

simulation

absolute

model

value

of

: the

differences between observed and s i m u l a t i o n concentrations of BOD a n d DO. The

method

I inear,

is

the

described

theoretical

elsewhere.

In

concentrations

order were

render

the

equations

approximated

to

by

observed

values whenever p r o d u c t s of two unknowns appeared in the equations. may

have

been

the

result

of

often

apparently

high

unaccounted f o r sources a l o n g some of the reaches. extended

to

non-l i n e a r

equations

(McPherson

and

decay

This

rates

and

The methods a r e b e i n g Sharland,

1979)

with

encouraging results. The i n p u t parameters f o r the p l o t s g i v e n

in Table 3.2

were d e r i v e d b y

t r i a l a n d e r r o r f i t s i n the model. Even then,

there appeared

i n e x p l i c a b l y h i g h BOD o r COD sources a l o n g

the r i v e r reaches. These were a t t r i b u t e d to b e n t h i c deposits o r r u n o f f from adjacent

sewage

irrigation

works,

and

seepage

from

the

industrial

and

other townships to the north. The accuracy of the BOD measurements a t mg/4)

i s questionable,

the levels observed

due to the complex way of d e t e r m i n i n g i t .

(5 to

10

Various

46 researchers have proposed

TOC

(total

oxygen

carbon)

demand.

or

Due

to

COD

as

f r a c t i o n of COD,

the change i n COD may be a more a p p r o p r i a t e parameter

more

high

inert

and t h i s in f a c t gave b e t t e r r e s u l t s t h a n the BOD model.

The sampling frequency of 1 h o u r was r a t h e r coarse. plotted

the

(chemical

oxygen demand)

t h a n COD,

i n d i c a t o r s of

organic

it

was

likely

realized

due

to

that

pollution

surface

runoff

than

loading varied to

Once r e s u l t s were rapidly.

the e f f l u e n t

from

This the

was

sewage

works. The

decay

r a t e of

the

COD

was

which

i s h i g h i n comparison w i t h

data.

This

may

be due

to

high

estimated laboratory

turbulence,

to

be

up

to

3,O

per

day,

results

and other published

or

high salinity

the

of

the

water promoting reactions. Photosynthesis was noticeable o n l y on v e r y overgrown of 3 mg/P/day

reaches.

A value

was t y p i c a l .

Oxygen s i n k s were found to be l a r g e in w i n t e r

( u p to 75 mg/P/day)

but

n e g l i g i b l e i n summer ( t h e r a i n y season). The dissolved oxygen content

was found to be s u f f i c i e n t

to support

life

(above 3 mg/P) a t a l l stages. T y p i c a l r e s u l t s a r e i n c l u d e d as Tables 3.1

to 3.3 a n d F i g u r e 3.6.

REFERENCES

1%5. Standard Methods for the American Water Works Association, Examination of Water a n d Wastewater. 1980. M o d e l l i n g Water q u a l i t y in the u p p e r K I i p r i v e r . Arnold, R.W., MSc(Eng) Dissertation, U n i v e r s i t y of the Witwatersrand. Deininger, R.A., 1973. Models f o r Environmental P o l l u t i o n Control. Ann Arbor. D., 1971. Use of linear programming for estimating Kleinecke, geohydrologic parameters of groundwater basins. Water Resources Research, 7 ( 2 ) , p 367-374. McPherson, D.R. and Sharland, P.J., 1979. River Quality Tests. Undergraduate project, U n i v e r s i t y of the W i t w a t e r s r a n d . Thomann, R.V., 1972. Systems A n a l y s i s a n d Water Q u a l i t y Management. McGraw H i l l , N.Y. 1970. A p p l i e d Stream S a n i t a t i o n . Wiley Interscience, N.Y. Velz, C.J.,

TABLE

3.1

Results of c a l i b r a t i o n u s i n g d a t a of 21 M a r c h 1979 ( e n d of summer)

COD C a l i b r a t i o n

BOD C a l i b r a t i o n Value

Value jyrnbo

Parameter

Dispersion coeff i c i e n Decay c o e f f i c i e n t

K1

Reaeration coeff i c i e n

BOD source/sink

DO source/sink

(1) (2)

Photosynthetic DO ( 2 I n e r t source/sink

E

(1

K2

S R1 p1

Units

?each 1 3each 2

leach 3

Reach

:

Method of determination Reaches 1 a n d 2 Tracer studies Reach 3 - C a l i b r a t i o n

0.4

10.0

10.0

0.4

10.0

0.05

1.3

3.0

3.0

2.0

4.0

Ca I i b r a t ion

2.0

2.7

3.0

2.0

2.7

7 .o

Reaches 1 and 2 Formula Reach 2 - C a l i b r a t i o n

-1 80

330

100

75

30

-50

Calibration

8

10

0

30

10

20

Calibration

3

0

0

2

5

5

Bot t I e tests

-1 50

175

80

10.4

Not

) Notes

teach 1 Reach Z

1

applicable

-

(1)

A n e g a t i v e v a l u e i n d i c a t e s a source ( p o s i t i v e b e i n g a s i n k ) .

(2)

A p o s i t i v e v a l u e i n d i c a t e s a source ( n e g a t i v e b e i n g a s i n k ) .

The i n e r t f r a c t i o n o f t h e i n p u t COD was t a k e n a s 60% The BOD5/BOD20 r a t i o was t a k e n a s 0.69.

Calibration

48

TABLE 3.2

Results of model f i t t e d to COD d a t a of 18 J u l y 1978 (mid-w in t e r

Value ymbol

Parameter

--

-

each 1

each

2

each 3

10.4

0.4

10.0

-D i spers ion

E

Method of Det erm i n a t ion

Assumed same a s for March survey

coefficient Decay

K1

0.1

1.3

1 .o

Model f i t t i n g

2.0

2 .7

5 .0

Reaches 1 a n d

coefficient Reaera t ion

K2

2

coefficient

-

formula

Reach 3

-

model

fitting BOD source/

S

sink ( 1 )

-32

175

50

Model f i t t i n g

-1 3

13

-1 5

Model f i t t i n g

5

5

20

50

DO source/sinb

(2)

R1

Photosynthesis

(2) DO

p1

3

Bottle tests

~ n e r tsource/ (1)

-48

sink

Notes:

-

Model f i t t i n g

-

(1)

A n e g a t i v e v a l u e i n d i c a t e s a source ( p o s i t i v e b e i n g a s i n k )

(2)

A p o s i t i v e v a l u e i n d i c a t e s a source ( n e g a t i v e b e i n g a s i n k )

The i n e r t f r a c t i o n of the COD was taken as 60%

49

3.3

TABLE (.I

Program output mol

LISIIng (lor

D.I.

K l l p R l v w Slmlatlm

ENn Vn DFFN

-. . .-. . I

=

aa* KFm SINt 91RE

Po0 SINt I

1.7s 23.40

bn

kruleay

l0.00kruld.y 0.050 1/*y 2.00 I/&Y -190.0 n p / l / d a Y 8.0 n p / l / d a Y

3.0 np/l/dmy -150.0 np/l/dmy

5.30

bn

20.03 krulday 10.00 krulday 3.m I/&y 1.00 I/&Y 100.0 -/1/dmy 0.0 n p / l / d a Y 0.0 np/l/daY

lncrl F n c l l m :

0.00

0.00

m.0 np/i/ea~

-

O l u m l V a r l a l l m of Rolos,mlhesla used IFW

aLn

-

--

O a X I l l * 0.203 bn OELXIII 0.241 bn OaXl3l 0,174 km

NO of pace 1n1ew.I~ NX No of Ilm Inl.walsNT

-

IbI 1yplc.l

Lonplludlnal Oulpul

ULIPRIVER

SIMULATION

DI.l.nc. Ownsirearn

statim

VE IRO-ll

0.007 days

-

Run

Sirnulaled

9 o o w

m

E 27.0 35.6 15.0 52.3 5a.A . . 62.7

0.0 0.250 0.500 0,750

.ooo

I

1.250 1.500 1.7%

24.3 62.4

SIallm M

364

Tlm.

aO.00 h r s

Ov..r".d

moo

27.0

2.8

2.9

3. 0 3.2 3.3

1.5 _._

3.5 3.6 3.5

F

0 0 57.1

3.6

2.W 2 . m

54.6

3.1

2.503

49.7

i.1

0

44.0

3.4 3.5

0

Slallm

17.6 30.9

3.4

U.6

5.m

24.0 23.3 22.9 22.9 23.0 20.2

5.254

23.3

Slmllm No. HI41

0 0 0

0

0 0 22.0

b.0

11.9

4.0

3.9 1.9 4.3 4.1 4.1 4.2 4.2 4.2

0

0

0

0

1.7

M G

0

0 0

1.750 3.W 3.250

3.500 3.750 4.m 4.250 4.503 4.750

50.6

27 123

0 0 0

50 TABLE

3.3

Contd.

( c l T y p i c a l Time V a r i a t i o n Output KLlPRlVER

SIMULATION

-

RUN

eOp a n d 00 VARIATION = I T N TIME AT STATION F TIME

SIMULATED

OBSERVED

N0.5

m a ,

Kn

00

0.0 1.04

57.56 59.69 57.55 53.24 52.68 52.24 52.55 M.55 49.75 49.32

55.0 59.0 56.00 54.00 59.00 59.00 60.97 60.02 55.00 61.23 57.62 58.80 60.95 60.17 60.24 56.00 56.90 56.36 60.46 66.55 57.07 39.95 47.13 53.00 37.50 27.70

3.52 3.51 4.00 4.02 4.26 4.50 4.50 4.57 4.62 4.62 2.37 4.25 4.13 3.66 3.81 3.78 3.56 3.34 3.33 3.52 3.60 3.60 3.62 3.60 3.35 3.39

2.09 2.49 3.06 5.00 6.04 7.07 7.92 8.% 10.00 11.04

12.05 12.92 13.96 15.00 16.04 17.09 17.92 18.96 20.00 21.36 22.09 22.92 23.94 25.0

47.41

51.56 55.93 61.39 66.30 69.45 70.40 69.30 53.32 53.95 60.98 49.00 49.12 51.33 54.72 54.91

4.04

3.76 3.65 3.53 1.54 3.42 3.43 3.48 3.50 3.46 3.47 3.46

.

5 10 15 20 25 30 3 5 44 4 2 50 55 60 6: 0

3.38 3.45 3.52 3.65 3.91 4.21 4.47 4.56 4.71 4.76 4.73 4.65 4.48 4.19

ox on ON

on

0

.

?$ :7 80

0.

0.

.

.. ..

0%

0 .

a

XO SO

.

0

NO NO LO

0

.

.

0

SO

... . .... .

0

.

0.

*O SO

X

no

NO

no

.

0

I

.. . . 0

0 0

0 0

ON

.. I

.

.

0.

0

6

0 0

0

5

10

15

I

20

51

CHAPTER 4

NUMER ICAL METHODS

SIMULATION OF HYDRAULIC SYSTEMS

Simulation of systems described b y d i f f e r e n t i a l equations can be done in a number of ways:

F i n i t e elements Characteristics

-

Implicit

-

Four p o i n t

F i n i t e difference -

Explicit

-

Four p o i n t

F i n i t e difference

0-0

7 'V

Leap f r o g

Diffusive

Backward centred

L a x - Wendroff = d i f f u s i v e / l e a p

E x p l i c i t schemes a r e simple b u t schemes.

not

too

great.

(Deininger,

Ax2/At

or

2

At There

accurate o r

Problems which manifest w i t h e x p l i c i t

i n s t a b i l i t y and numerical d i f f u s i o n . is

as

The

accepted

stable

schemes

criterion

for

as

implicit

i n c l u d e numerical

I n s t a b i l i t y can occur

stability

frog

i f the time step

diffusive

schemes

is

1973);

2E

5 is

s p r e a d i n g of

(4.1

(4.2)

A x2/2 E

an

additional

the p o l l u t i o n

concentrations a t adjacent

problem, gradient

points.

the maximum numerical d i f f u s i o n Using the previous expression f o r be less than €/4.

that

due

to

From a is E At,

of

numerical

diffusion

successive c a l c u l a t i o n s second o r d e r

Taylor

i.e. using

expansion

max = A x 2 / 8 A t . ( D e i n i n g e r 1973) P we get the pseudo d i f f u s i o n cannot

52

Two-step

method

The water q u a l i t y

equation

i n c l u d i n g the d i f f u s i o n term

in two steps to ensure c o r r e c t a d v e c t i o n a n d d i f f u s i o n .

a‘c _ _ EaxZ

ac kC - v -

aC Ax

c. -

=

Cidl

(4.4)

Ax

ci+l -

a2c -

(4.3)

ax

at

use

can be solved

Thus s t a r t i n g w i t h

+ ci-l

2ci

ax7-

(4.5)

A X2

then C . i,n+l

=

The f i r s t equation

for

c.

+ EAt

i,n

and

last

two

advection

a p p r o x i m a t i o n to C .

I,

F i g . 4.1

Ci-l,n+Ci+l,n-2Ci,n Ax2

n+l

terms

and

on

decay

the can

-

- kC.

vAt ‘i+l,n-‘i,n

1,n

A X

right be

hand

side

used

to

(4.6) in

the

above

the

first

get

a n d then the d i f f u s i o n term.

Basic r e c t a n g u l a r x - t

grid

Demonstration of n u m e r i c a l i n a c c u r a c y

The

convection

term

in

the

water

quality

i I l u s t r a t e problems a n d i n a c c u r a c i e s d u e to a n

Neglecting the d i f f u s i o n a n d decay term, ‘i

,n+l

= C. 1,n

-

v

~

t‘i+l,n

equation

will

be

used

we h a v e

- ‘i,n A X

to

i n c o r r e c t n u m e r i c a l scheme.

(4.7)

53

We should have a wave of concentration move downstream a t a r a t e unattenuated o r changed i n concentration.

C i ,n

i-1

i it1

it2

AX

F i g . 4.2

Theoretical advection

I f Ax = vAt then u s i n g a f o r w a r d difference e x p l i c i t method

‘i

,n + l

i.e.

=

c.

=

2 which i s wrong,

- c.i , n )

1,n - (‘i+l,n = 1 - (0-1)

i t should be 0

dont use a f o r w a r d difference

ac/ax

Instead use a b a c k w a r d difference ac/ax Then ‘i,n+l

c .t,n -

= =

-

(‘i,n

1

1 - (1-0) = 0, correct.

on the other h a n d i f we use

=

‘i-l,n

1 -

0-0 =

1,

AX =

= (Ci+l = (Ci

-

-

Ci)/~x

Ci-l)/Ax (4.7b)

2vAt,

also wrong.

2 I f we continued w i t h t h i s scheme, the v a l u e of C o s c i l l a t e s (see below)

1

0

0.5 F i g . 4.3

O s c i l l a t i n g scheme

v,

54

O n the other h a n d i f one uses a

backward

difference

with

Ax

=

2vAt

n u m e r i c a l d i f f u s i o n occurs a s i n d i c a t e d below.

1

-

F i g . 4.4 I f At if

>

Numerical d i f f u s i o n Ax/v we get n u m e r i c a l i n s t a b i l i t y , e.g.

At = 2 Ax/v,

C.

= Ci,n

1

-

-

* Ax

( C .i,n - ‘i-1,n

1 (4.7d)

2 (1-0) = -1.

C o n t i n u i n g so, a n o s c i l l a t i n g c u r v e occurs:

I

F i g . 4.5

Instability

\

55

I m p l i c i t f i n i t e d i f f e r e n c e schemes

i-1

F i g . 4.6

i

X

i +1

I m p l i c i t scheme

(4.10) z c, - vAt becomes C. ('i,n+l ~,n+l i,n unknown and a set of i equations

method

is

unconditionally

equations can be l e n g t h y , use

the

hydrodynamic

since v .

I , n+l

stable

- 'i-1 , n + l is

with

A l l values

established

but

especially

equation

).

solution

for

of

i

the

a-t n + l a r e

unknowns.

for

non

l i n e a r systems,

the

term

v

( V i , n + l - ' i - l , n+l) i s parabolic.

ax

this

e.g.

is

('i,n+l

-

if

we

non-linear (4.11)

Ax

So r a t h e r use 'i,n

The

simultaneous

i

V.

I - 1 , n t l ) which i s l i n e a r .

(4.12)

A X

Methods of solution of i equations include ( F r i e d , 1975)

i)

Direct methods e.g.

ii)

I t e r a t i v e method

-

m a t r i x methods and Gauss e l i m i n a t i o n . i.e.

assume reasonable v a l u e s f o r

all

C's and

i t e r a t e the equations s u b s t i t u t i n g assumed values on the r i g h t h a n d side

until

the

left

h a n d side

o n l y converges i f At <

agrees

with

assumed

values.

This

AX/V.

... III)

Relaxation methods (Timoshenko,

iv)

A l t e r n a t i n g d i r e c t i o n i m p l i c i t procedure

1951). (Fried,

1975),

i.e.

compute

56

derivitive

w i t h respect to x

i m p l i c i t l y and y e x p l i c i t l y

a n d then

v i c e versa ( s t a b l e ) .

One (e.9.

also

gets

combined

explicit/implicit

McDonnel a n d O'Conner,

methods

for

more

accuracy

1977).

Comments on f i n i t e difference methods

E x p l i c i t method:

1.

T h i s must be designed to be s t a b l e i.e.

a n y e r r o r s due to 2nd o r d e r

terms in the T a y l o r expansion (we took j u s t the f i r s t o r d e r ) must decay d u r i n g comp u t ion. The

time

interval

For e x p l i c i t shown

must

t h r e f o r e be smaller

hydrodynamic

to be s t a b l e

if

equation,

2

using

-

Jgy

=

than

for

Fourier

wave

implicit series

celerity

it

i.e.

method. may

be

speed

of

computation g r e a t e r t h a n speed of a d i s t u r b a n c e i n the system.

2.

I t must

be accurate.

Check

with a

few

space a n d

time

intervals and

a g a i n s t an a n a l y t i c a l s o l u t i o n i f there i s one.

3.

I t shohld minimize numerical d i f f u s i o n

4.

One can use v a r y i n g g r i d s where g r e a t e r a c c u r a c y i s r e q u i r e d :

F i g . 4 . 7 V a r y i n g g r i d s p a c i n g (zooming)

57 NUMER I CAL METHODS FOR THE SOLUT ION OF SINGLE D IFFERENT IAL EQUATIONS

Numerical solutions appear i n the form of a t a b u l a t i o n o f the values of the functions of v a r i o u s values of as a f u n c t i o n a l r e l a t i o n s h i p .

the independent time v a r i a b l e

Numerical methods h a v e the a b i l i t y

p r a c t i c a l l y any equation b u t they

h a v e the d i s a d v a n t a g e t h a t

and

not

to s o l v e

the e n t i r e

t a b l e must be recomputed i f the i n i t i a l c o n d i t i o n s a r e changed.

I f a f u n c t i o n f ( t ) can be represented b y a

power series

i n a certain

i n t e r v a l then i t can be represented b y the T a y l o r series expanded about a p o i n t t = to,

i.e.

about the i n i t i a l value:

I

Y ( t ) = y (tO)+Y ( t o ) ( t - t O ) + y

II

( t o ) (t-t0)2+y

2!

L e t t i n g n represent

I1

( t o )(t-t0)3+

-

...

(4.13)

3!

the p r e v i o u s step

at

time

to a n d n + l

represent

the

next step a t t +h, the series can be w r i t t e n as:

0

Yn+l=~n+hyn l+h2 -yn I I + c y n 2 6

Ill+

*..

(4.14)

Consider the examp Ie p r o b lem

(4.15)

w i t h i n i t i a l conditions (4.16)

Y(0) = 1 This

is

a

linear

time

variant

1st

order

differential

equation.

The

a n a l y t i c a l solution to the problem,

y = 2e-t-1 w i l l be used to compare the t numerical r e s u l t s o f some of the methods a n d t o i l l u s t r a t e the e r r o r a t a n y step.

The E u l e r Method

The E u l e r method

i s the simplest b u t least accurate of a l l the methods

discussed. (4.151,

To o b t a i n a n exact numerical s o l u t i o n to the example problem II I l l, y I V a l l the d e r i v a t i v e s y , y must be e v a l u a t e d a n d

...

s u b s t i t u t e d i n t o the T a y l o r series (4.14). Knowing the i n i t i a l values of y n' I II Y,+~ c o u l d be e v a l u a t e d a f t e r a time increment h. The yn , yn

...,

values of a l l the d e r i v a t i v e s c o u l d then

be c a l c u l a t e d a t

could be evaluated a f t e r the next time increment a n d so on. a r b i t r a r y functions cannot e a s i l y be formulated derivatives y l ' ,

Y l I I , etc.

a r e easy

n+l,

and y n+2 D e r i v a t i v e s of

in computer programs.

to e v a l u a t e f o r

the example

The

(4.14)

58 b u t t h i s i s not g e n e r a l l y

the case.

The E u l e r method t r u n c a t e s t h e T a y l o r

series b y e x c l u d i n g the terms a f t e r the f i r s t problem o f

h a v i n g to

evaluaate

the

d e r i v a t i v e a n d e l i m i n a t e s the

second

and

subsequent

derivatives.

Then yn+l=yn+hynl+O(h')

error

Neglecting h ' y n " / 2 t r u n c a t i o n e r r o r of

(4.17)

and order

the

h'

subsequent

(4.14)

in

i s denoted O ( h * ) .

which

e r r o r a n d r e s u l t s from one step o n l y , t h a t the g l o b a l e r r o r

terms

i.e.

This

from n to n+l.

results is

in

a

the l o c a l

I t can b e shown

accumulated over many steps becomes O(h),

i.e.

an

e r r o r of o r d e r h. S u b s t i t u t i n g the example (4.15) Yn+l=Yn+h.

i n t o the E u l e r a l g o r i t h m (4.17)

gives:

(Yn+tn)

(4.18)

The i n i t i a l c o n d i t i o n y ( O ) = l means

that

y=O

at

increment h=0.02 a n d l e t t i n g the step number n=O a t

t=O.

Choosing

t=O,

the

time

the v a l u e s f o r y

can be evaluated a t successive time increments a s follows:

y =y + h ( y o + t O ) = 1+0.02(1+0) 1 0 +t ) = 1.0200+0.02( y =y +h 2 1 Yl 1 y =y +h y +t ) = 1.0408+0.02( 3 2 2 2

= 1.0200

(4.19)

.0200+0.02)

= 1.0408

(4.20)

.040+0.04)

= 1.0624

(4.21)

= 1 .ow0

(4.22)

= 1 .lo81

(4.23)

y4 y5 etc.

Anal y t i c a1 solution

.

c

F i g . 4.8 The Euler method

The numerical solution a f t e r 5 steps g i v e s the exact a n a l y t i c a l g l o b a l e r r o r i s 0.0022,

i.e.

solution as

i s y(0.10)=1 .lo81

y(0.10)=1.1103.

two-decimal-place

t

whereas y=2e -t-1

Hence

accuracy.

the a b s o l u t e

Since

the

global

59

e r r o r of the E u l e r method i s p r o p o r t i o n a l must b e reduced

at

least

22-fold

to h,

to g a i n

i.e.

O(h),

four-decimal

<0.004. T h i s would increase the computational e f f o r t 22-fold. how the slope a t the b e g i n n i n g o f the i n t e r v a l

ynl

t h e step size h

accuracy, Fig.

i s used

4.8

i.e.

h

shows

to determine

the f u n c t i o n v a l u e a t the end o f t h e i t e r a t i o n i n the E u l e r method. The slope a t the b e g i n n i n g of solution i s a s t r a i g h t l i n e .

the i n t e r v a l

i s a l w a y s wrong

unless t h e

Thus t h e simple E u l e r method s u f f e r s from t h e

d i s a d v a n t a g e of l a c k of accuracy,

r e q u i r i n g a n extremely s m a l l step size.

The M o d i f i e d E u l e r Method

F i g 4.8 a n d the subsequent discussion suggest how the E u l e r method c a n be

improved

with

little

additional

computational

effort.

The

arithmetic

average o f the slopes a t the b e g i n n i n g a n d the end o f t h e i n t e r v a l i s used ( o n l y the slope a t the b e g i n n i n g i s used in t h e E u l e r method).

1

1

yn+l

= Yn

+ h'n

(4.24)

+',+I 2

The E u l e r a l g o r i t h m must f i r s t can

be

estimated.

Applying

be

the

s u b s t i t u t i n g y1 = x+t i n t o (4.24)

used

same

to

predict

example

(4.15)

so as

I n+l before a n d that

y

gives

Y n + l --yn+h(Yn+tn)

+ (~,+~+t,+l) 2 S u b s t i t u t i n g the E u l e r e q u a t i o n (4.18)

'n+l

yn+l

= yn+h('n +t n 1 + (yn+h(Yn+tn)

+

(4.25) gives

f o r Yn+l

tn+l

1

(4.26)

2 Using h=0.02 a n d the i n i t i a l conditions:

y =l,t

0

=O

0

(4.27) =

1 + 0.02

(1+0)

+

(1+0.02(1+0)+0.02)

(4.28)

2 = 1.0204

(4.29)

60

+

1.0204

y 2=

0.02(1 .0204+0.02)+(1.0204+0.02(1.0204+0.02)+0.04) (4.30)

2

= 1.0416

(4.31)

y5= 1.1104 c f a n a l y t i c a l s o l u t i o n 1.1103

1 in the f o u r t h decimal p l a c e .

The answer agrees to w i t h i n

a s much work was done a s in the E u l e r method b u t times more that

would h a v e been needed

with

decimal p l a c e a c c u r a c y .

I t can be shown t h a t

of

method

the

Modified

Modified Euler

Euler and

the

are

simple

methods

method

not

to

twice the

attain

the l o c a l a n d g l o b a l

and

O(h3)

Euler

that

Nearly

certainly

O(h2)

are

referred

four

errors

respectively.

often

22

The to

as

second a n d f i r s t o r d e r methods r e s p e c t i v e l y .

Runge-Kutta Methods

The Fourth-Order

Runge- K u t t a methods a r e amongst

t h e greatest a c c u r a c y p e r u n i t o f c o m p u t a t i o n a l e f f o r t .

those which p r o v i d e The development of

t h e method i s a l g e b r a i c a l l y complicated a n d i s g i v e n completely and

Hainer

(1978)

while

Gerald

(1980)

derives

the

in Stummel

Second-Order

Runge-Kutta a l g o r i t h m a n d e x p l a i n s the p r i n c i p l e s b e h i n d t h e methods. t h e Runge-Kutta

methods use the simple E u l e r method a s a f i r s t

Improved estimates a r e

then

made u s i n g p r e v i o u s estimates

time-values

time

interval

within

the

estimates i s used to c a l c u l a t e are

the

most

widely

used

yn+l.

h.

weighted

The Fourth-Order

because of

f o l l o w i n g i s a p a r t i c u l a r Fourth-Order

A

their

power

method w h i c h

and different

average

of

Runge-Kutta and

Al I

estimate.

all

the

methods

simplicity.

The

i s commonly used a n d

w h i c h i s i n c l u d e d i n the s i m u l a t i o n p r o g r a m :

Yn+l

= y + I ( kl +2k2+2k3+k4) n6

(4.32)

(4.33)

= h f ( t n + i h , yn+gkl )

(4.34)

k3

= hf(t,+ih,yn+$k2)

(4.35)

k4

= hf(tn+l,yn+k3)

(4.36)

k2

61

Again

the problem g i v e n

in

(4.14)

above

T h i s time y ( 0 . 1 )

dy/dt=f(t,y)=t+y,y(O)=l.

whereas ~ ( 0 . 1 ) was c a l c u l a t e d

is

solved

as

an

example:

i s c a l c u l a t e d in one step

i n f i v e time increments

(h=0.02)

(h=0.1)

using

the

simple a n d modified E u l e r methods above.

kl

=h(tn+yn)

=o. 1 (0+1

= 0.10000

(4.37)

k 2 =0.1 (0.05+1 .05)

= 0.11000

(4.38)

k 3 =0.1 (0.05+1 .055)

= 0.11050

(4.39) (4.40)

= 0.12105 k 4 =0.1(0.10+1.1105 1 y(0.1)=1.000+ -(0.10000+2x0.11000+2x0.11050+0.12105) 6 =1.11034

(4.41 (4.42)

T h i s agrees to f i v e decimals w i t h the a n a l y t i c a l r e s u l t a n d i l l u s t r a t e s a f u r t h e r g a i n i n accuracy w i t h less e f f o r t t h a n r e q u i r e d b y the p r e v i o u s Euler methods. method

I t s computationally

because,

while four

each step r a t h e r than two,

steps

to

than

the modified

Euler

the f u n c t i o n a r e r e q u i r e d

the steps can be many-fold

l a r g e r for

for

the same

The simple E u l e r method would h a v e r e q u i r e d of the o r d e r of 220

accuracy.

only

more e f f i c i e n t

e v a l u a t i o n s of

achieve five-decimal

one

evaluation

of

accuracy

the

y(O.1)

in

function.

The

b u t each step

efficiency

of

the

involves

Euler

and

Runge-Kutta methods can be r o u g h l y compared b y c a l c u l a t i n g the number of function

evaluations

required

for

the

p a r t i c u l a r example the Runge-Kutta

same o r d e r

Runge-Kutta 4 would be about O(h 1.

algorith

In

accuracy.

this

method i s a p p r o x i m a t e l y 50 times more

e f f i c i e n t than the simple Euler method (220/4). Fourth-Order

of

(7.35)

is

The local e r r o r term f o r the 5 O(h ) a n d the g l o b a l e r r o r

M u l t i s t e p Methods

The

simple

Euler,

Modified

s i n g l e step methods

Euler

because

they

and

Runge-Kutta

use o n l y

the

methods

are

i n f o r m a t i o n from

called

the

last

I n t h i s they have the a b i l i t y to perform the next step w i t h

step computed.

a d i f f e r e n t step size a n d a r e i d e a l f o r b e g i n n i n g the s o l u t i o n where o n l y the

initial

method

is

conditions to

utilize

polynomial

that

this

the

into

are the

available. past

approximates next

time

The

values

the

of

principle y

derivative

interval.

Most

and/or function

multistep

behind yl and

to to

methods

a

multistep

construct

a

extrapolate have

the

d i s a d v a n t a g e that they use a constant step size h to make the c o n s t r u c t i o n of the polynomial easier.

Another d i s a d v a n t a g e of m u l t i s t e p methods i s t h a t

62 several past p o i n t s a r e a v a i l a b l e a t the s t a r t . the i n i t i a l

required

whereas

only

the

initial

conditions

are

The s t a r t i n g v a l u e s a r e g e n e r a l l y c a l c u l a t e d

conditions using

a

single-step

method

such

as

a

from

Runge-Kutta

method.

F I N I TE ELEMENTS

imp1 i c i t

An

method

involving

mass

balance

across

element

boundaries

(Connor a n d Brebbia,

1976) i s p o p u l a r i n f i x e d systems b u t has not g a i n e d

much

hydraulic

popularity

in

necessitating i t e r a t i v e methods.

systems

owing

to

changing

boundaries

The steps a r e as follows:

D i v i d e body i n t o elements ( 2 o r 3-

dimensional)

Define the nodal unknowns The

flow

across

an

external

boundary

can

be

approximated

as

a

ma themat i c a l f u n c t i o n .

F i g . 4.9 F i n i t e elements

One

sets

up

simu I taneousl y

equations

giving

balance

for

each

element

and

solve

.

Boundaries for numerical methods

Conditions on a b o u n d a r y may be e i t h e r constant p o t e n t i a l water

level

or

cencentration)

i.e.

flow

across

boundary,

flow across) o r mixed (same f u n c t i o n ) . One can use pseudo p o i n t s e.g. hi-,

= h. f o r no flow

h. -h. = h . - hi+, f o r flow p e r p e n d i c u l a r to b o u n d a r y . 1-1 I S i m i l a r schemes may be used f o r concentration d e f i n i t i o n .

( o r head o r

stream1 ines

(no

63 REFERENCES Connor, J.J. and B r e b b i a , C.A. 1976. F i n i t e e l e m e n t s f o r f l u i d f l o w . Newnes-Bu t t e r w o r t h s . D e i n i n g e r , R.A., 1973. M o d e l s f o r E n v i r o n m e n t a l P o l l u t i o n C o n t r o l . Ann A r b o r Science. F r i e d , J.J., 1975. G r o u n d w a t e r P o l l u t i o n , E l s e v i e r . G e r a l d , C.F., 1980. A p p l i e d N u m e r i c a l A n a l y s i s ; 2 n d Ed. A d d i s o n VJesley. 1977. H y d r a u l i c B e h a v i o u r of E s t u a r i e s . McDonell, D.M., O ' C o n n e r , B.A., Macmi I Ian. K., 1978. I n t r o d u c t i o n to N u m e r i c a l A n a l y s i s ; Sturnel, F . a n d H a i n e r , S c o t t i s h Academic P r e s s L t d . Timoshenko, S. and Goodier, J . M . , 1951. T h e o r y of E l a s t i c i t y , McGraw H i l l .

64 CHAPTER 5

MASS BALANCE O F STORMWATER POLLUTANTS I NTRODUCT ION

Pollution

l o a d i n g s from two catchments i n Johannesburg

1986) were i n v e s t i g a t e d . a n d t h e other, stormwater down

a

Montgomery

densely

r u n o f f and d r y weather

sources

process.

Hillbrow,

One,

of

pollutants and

I t i s r e p o r t e d that

t y p e of relate

contribution pollutant

hypothesis.

The

which

loads

to

in

source

i s detected

of

CATCHMENT DESCR I PT ION

Montgomery P a r k Catchment

runoff

A

area.

al.,

catchment

comparison of

b o t h catchments n a r r o w e d understanding

1979),

this

(Green et

suburban

pollution

here.

and

is a

city

from

(Wanielista,

landuse,

unpredictability

up

flows

assisted

a n d Kemp (1982) i s borne out though.

F i g . 5.1

built

non-point

70% of the load i n u r b a n r u n o f f

Park,

and

Bradford paper

qua1 i t y

the

washoff

is

responsible f o r

it

is largely this

(1977)

attempts

contributes

indicated

by

to

to

his

Simpson

65 The

Montgomery

Johannesburg estimated

at

remainder

and

Park

catchment

10.53

measures

15000.

includes

The

developed

parks,

a

is km2

6

situated

(1053

area

is

cemetery

km

ha).

The

75% of

the

and

north-west population total

undeveloped

s o l i d waste t i p in the catchment f r o m w h i c h seepage occurs. is fairly

hilly,

slopes

system

comprises

5.1).

Rainfall

over

ranging

the

from

natural catchment

0.02

and is

recorded

a u t o g r a p h i c r a i n gauges.

Runoff

catchment outlet

the measuring element

bubble

type

i n which

recorder.

Electrical

0.15

to

m/m

artificial

the The

There i s a

The catchment

m/m.

channels at

is

and

area.

development i s housing and some commercial a n d l i g h t i n d u s t r y .

drainage

of

five

The (see

main Figure

locations

by

i s measured a t a g a u g i n g s t a t i o n a t the

conductivity of

i s a Crump the

water

weir was

with

a

recorded

continuously since March 1983. The

Hillbrow

catchment

measures

67.2

u r b a n a r e a comprising h i g h - r i s e b u i l d i n g s , a school

and

is

illustrated

in

F i g u r e 2.

ha

and

is

a

fully

developed

some h i g h d e n s i t y housing a n d The

population

i s estimated

at

12000. There are f o u r r a i n g a u g e s a n d a streamgauge for t h i s catchment. Both

catchments

have

separate

seoarate from waste sewerage systems.

F i g . 5.2

H i l l b r o w Catchment

stormwater

drainage

systems

i .e.

66

Q U A L I T Y OBSERVATIONS

Fa1lout measurement

An

attempt

was

made

to

assess

the

level

of

TDS

occurring

as

atmospheric f a l l o u t on t h e Montgomery P a r k catchment. After a p e r i o d of 28 d a y s without

any r a i n f a l l ,

down" w i t h d i s t i l l e d water,

the r a i n g a u g e s in the catchment t h i s water

b e i n g collected

in a sample bottle.

I t was found t h a t the TDS w i t h i n the f u n n e l s averaged 9.5 was

deposited

equivalent kg/ha

a

fallout

over

28

kg/ha/annum. of 0.72

onto

funnel

loading

days.

If

was

188

the

0.020

m2 i t

Montgomery was

was

Park

omitted

mg.

catchment

this

would

i n a funnel

f a l l o u t was collected

Since t h i s

deduced

that

the

was

4.75

represent with

an

62

area

location n e a r the H i l l b r o w catchment over a p e r i o d of I t was found t h a t the TDS w i t h i n the funnel

d a y s w i t h no r a i n f a l l . case

on

washout

Atmospheric

mz a t a

a r e a of

were "washed

mg

in

resulting

an

atmospheric

loading

18

in t h i s

rate

of

48

kg/ha/annum. Stormwater r u n o f f qua1 i t y analyzed

to determine

data

whether

were

collected

for

relationships could

selected

storms

and

be e s t a b l i s h e d a n d

to

o b t a i n the p r o p o r t i o n s of the d i f f e r e n t constituents. C e r t a i n researchers h a v e observed a c o r r e l a t i o n between the number o f dry

d a y s preceding

runoff

(e.g.

maintain

that

Bedient,

1980).

An could

attempt be

a

Sartor no

such

was

related

storm

et

the

1974;

relationship

made to

and

al.,

to

the

see

level

of

p o l l u t i o n of

et

exists

(e.g.

whether

number

of

Colwill

the

al.,

Whipple

peak

antecedent

1984)

dry

the

resulting

while et

concentration days.

A

=568 P where C

C

1977;

TDS

of

regression

a n a l y s i s was performed on a l l the d a t a a v a i l a b l e a n d the best f i t from a l i n e a r r e l a t i o n s h i p ,

others

al.,

resulted

viz.

+ 68N

(5.1

i s the peak TDS concentration

in mg/l

and N

1

i s the number of

P antecedent d r y d a y s w th a maximum v a l u e of 5. The c o r r e l a t i o n c o e f f i c i e n t corresponding

i s 0.12

which

i s poor.

There

i s an

increase

in

TDS

with

l e n g t h of time between storms i t appears. a

further

condition

In

classes

tes

following relationship

Cp = 1020

-

,

TDS

proposed

by

was

and

with Stall

antecedent (1974)

used

moisture and

the

emerged.

163 AMC

w i t h a c o r r e l a t i o n coefficient of 0.29. mg/l

correlated

Terstriep

(5.2) C

i s the peak TDS concentration

P a n d AMC i s the antecedent moisture c o n d i t i o n class.

in

67

Relationship between Total P o l l u t a n t Load and Runoff Volume

A

regression

volume

data

established obtained

analysis

to

determine

between

from

was

these

linear

performed

whether

on

any

parameters.

pollutant

definite In

approximations

the

all

with

relationship

cases

the

reasonably

-

load

flow

could

best

high

be

fit

was

correlation

coefficients. Considering d a t a from Montgomery P a r k alone r e s u l t s in the equation

W = 3395 with

a

+ 23V

(5.3)

correlation

coefficient

W

0.84.

of

i s -the

mass

of

transported

dissolved solids i n k g a n d V i s the volume of r u n o f f in m’. With the i n c l u s i o n of the d a t a from H i l l b r o w ,

W = 1186

+

the e q u a t i o n becomes

= 0.27V

(5.4)

w i t h a c o r r e l a t i o n coefficient of 0.90. Treated

separately,

the

relationship

between

pollution

load

and

low

flow volume i s

+ 0.55V

W = 3.24

(5.5)

w i t h a coefficient of c o r r e l a t i o n of 0.97

Chem ica I Const ituen t s

The r e s u l t s of t h e chemical analyses of the “ g r a b “

samples collected

both the H i l l b r o w a n d the Montgomery P a r k catchments a r e l i s t e d

in

i n Tables

1 to 5 . These

results

were

analyzed

quantify

to

the

presence

chlorides and bicarbonates as i t was considered t h a t anions

present

bicarbonate,

in

wind

water.

The

highest

nitrates,

anion

concentration

was

followed b y sulphates d u r i n g storm r u n o f f a n d c h l o r i d e in d r y

weather conditions. be

the

of

these were the m a j o r

blown

Sulphates a r e predominant

from

neighbouring

mine

i n Johannesburg

waste

tips

which

and

could

have

high

Sulphates also reach concentrations over 300 mg/l

s u l p h a t e concentrations.

i n water supplies f o r the area. T h e p r o p o r t i o n of n i t r a t e s , total

dissolved

weather

flow

these anions runoff

salts

analyzed. whereas

( a v e r a g e d over

is

sulphates, c h l o r i d e s a n d bicarbonates to the

much I n the

this both

lower

in

storm

runoff

l a t t e r case 68.6% of

proportion

is

catchments)

as

low

as

indicating

than

the

in

TDS

38.8%

in

probable

constituents t h a t do not n o r m a l l y apear in the d r y weather flow.

the

dry

consists the

of

storm

washoff

of

68

TABLE

5.1

I l l

OM

Results o f chemical a n a l y s e s o n r a i n f a l l a n d r u n o f f samples f o r H i l l b r o w on 03/01/85

~~

conduct1V l t Y

TDI

taman

--

ma/.

.PI 1

2Ohl 1

6.20

14.31

138

1010

0.2

12

5.1

36

20hl4

6.30

13.12

112

242

0.3

10

4.1

31

20118

6.05

11.81

134

160

0.8

10

3.0

36

2ohz3

6.00

9.69

102

770

4.1

10

3.0

24

.?Oh26

5.55

9.91

100

512

8.6

11

5.1

10

2013 1

5.85

10.88

126

232

5.3

13

5.1

24

20150

5.45

13.37

120

110

15.0

16

1.1

10

2lho1

5.90

15.43

170

102

12.9

21

8.2

27

*/A

5.55

6.60

18

2.7

4

3.8

6

-

TABLE

&gl*

Yrh

T l l

5.2

pM

63

I

Results o f chemical a n a l y s e s on r a i n f a l l a n d r u n o f f samDles f o r H i l l b r o w o n 18/01/85

ODMYCLlVltY

UIICNt.

taWn

.s/*

1811

i ~ n 2 i 6.35

46.10

346

64

tO.l

6U

37.0

122

18/2

14132

6.35

35.50

265

84

57

30.0

90

18/3

lh138

6.15

2h.50

182

380

a3

12.3

85

18/U

14144

6.35

13.40

104

130

a.1

17

10.3

S6

18/5

14hM

6.15

8.88

69

2Oh

go.1

13

8.2

20

1016

14h52

5.05

8.23

65

u4

0.3

14

7.1

14

1811

1hh54

6.20

6.29

55

92

0.1

14

6.1

12

18/8

lhh57

5.60

7.03

65

56

0.2

12

10.2

7

18/9

15Mo

5.65

6.14

u

8

0.2

11

4.1

10

18/10

15hO4

5.10

5.95

60

(1

0.2

10

6.1

7

13/11

15hO9

5.85

5.92

49

0.2

11

6.1

7

18/12

15hl6

5.10

6.58

50

Y1

0.3

10

5.1

1

b.07

P.ZO

18

8.2

6

R

*/A

\

41

69 TABLE

LwIe mark

T i n

5.3

on

R e s u l t s o f c h e m i c a l a n a l y s e s o n r a i n f a l l and r u n o f f s a m p l e s f o r M o n t g o m e r y P a r k on 07/03/83

CO n a W t l v l t Y

auspewd

***

sol12

~~tntm

-1

I

-1 1

9 1I

-1 I

chiorlam

c. c.rbmet.

-1

1

-1 1

6.25

13.26

104

95

eo. 1

10

6.3

30

5.85

10.31

86

200

0.1

16

5.2

20

so113

6.00

12.91

112

450

2.2

Ylll

6.20

22.30

166

44

1.5

RFl/l*

1.25

10.86

52

TABLE

Su1ph.t.

so1 id. mSlm

50111

roa

taken

5.4

0.4

13

6. 3

31

25

16.0

16

..

..

21

R e s u l t s o f c h e m i c a l a n a l y s e s on d r y w e a t h e r f l o w s a m p l e s from Montgomery P a r k

TOI

8usp.na.a soilas

-11

-1

I

104

10

210.0

100

34

15

1625

4

91.0

15

480

456

314

12

10.0

16

45

175

544

12

11.8

64

101

202

446

10

30.4

kz

86

1@3

320

24

b.0

18

29

not aow

262

14

0.1

25

10

620

la

2.0

40

120

not aow not

row

70 TABLE

5.5

As

one

Results of chemical analyses o n d r y weather flow samples from H i l l b r o w

would

expect,

the

concentration

weather flow i s much lower t h a n

t r a n s p o r t r a t e of sediments as well the

samples

analyzed,

averaged o n l y 27 mg/l

the

of

suspended

i n the storm r u n o f f ,

solids

in

as p o s s i b l e erosion d u r i n g storms.

suspended

solids

in

dry

indicating a higher

the

dry

weather

compared w i t h a n average of 236 mg/l

for

For flow

the storm

flows. Comparing Tables 4 a n d 5 ( d r y weather

flows)

2 and 3

Tables 1,

with

r e v e a l s t h a t the TDS concentrations a r e c o n s i d e r a b l y h i g h e r in d r y flows

than

samples

in

storm

flows.

i s 644 mg/l

while

events a r e

125 mg/l,

The

average

average

1 1 3 mg/l

TDS

values

and

of

runoff.

The base load o f TDS from Montgomery

from

refuse

tip,

which

averages

averaged over the catchment

I t was mentioned

that

the

TDS

117 m g / l ,

weather flow has about f i v e times as h i g h a

a

for

for

to

detect

a

flushing

mg/l,

Park

runoff

the

at

The p r o p o r t i o n s of n i t r J t e s than

the

were

in the stormwater

are

also

the

that as

appears or

flow runoff

the

dry

stormwater

to be

largely

150 kg/ha/annum

o b t a i n e d on

runoff. viz.

the

effect

The

high

346 mg/l

much

higher

sampled in August and October 1982 (see T a b l e

and

TDS 265

to f i n a l

in accordance w i t h

1977; Helsel et a l . ,

I n the case of

rising

making i t possible

in TDS concentration

flush"

Cordery,

runoff.

of

runoff,

decrease

indicate a "first

the f i n d i n g s of many o t h e r s (e.g.

flow

start

stages of

followed b y a time-dependent

l e v e l s of about 60 mg/l

three

( B a l l , 1984).

samples of

effect

the

indicating

160000 kg/annum

weather

weather

concentration

l i m b of the h y d r o g r a p h of 18 J a n u a r y 1985 in H i l l b r o w ,

concentrations a t the e a r l y

dry

in

the

the d r y

1979). dry

weather

weather

flow

5. 4 ) the l e v e l s of n i t r a t e

71 mar

PH (mpnl 10

18 18

160-

14

6.5

14

140-

12

0.0

12

120-

10

5.5

10

100-

8

5.0

8 8 4

2

21

Fig.

5.3

Plot of p o l l u t a n t c o n c e n t r a t i o n event on H i l l b r o w on 03/01/85

--.-.

Nllrole

45

----Suop.

-

\

Sulohale

-.-

TO9

time f o r r a i n f a l l - r u n o f f

-

HW+I+WI

VS.

Conducllvlly pn cc CMorldoo

Solids

Flowale

-.18

40-

6.1

-.18

35-

8.t

-.14

30-

5.e

-

5.t

25

20 15105-

14h25 30

Fig.

5.4

35

40

50

45

P l o t of p o l l u t a n t c o n c e n t r a t i o n event on H i l l b r o w on 18/01/85

vs.

55

15hoo

5

10

15 T h

time f o r r a i n f a l l - r u n o f f

72

a r e so h i g h as to suggest resulting

overflow

p o s s i b l e blockage o f a s a n i t a r y sewer

entering

the

stream.

It

was

observed

w i t h the

for

all

three

r u n o f f events t h a t the n i t r a t e concentrations increased over the d u r a t i o n of each

hydrograph,

reaching their

maximum on

the recession

limbs of

respective h y d r o g r a p h s . A possible e x p l a n a t i o n f o r t h i s phenomenon lighting activity w i l l course of

the storm,

r u n o f f w i t h time. these

the

i s that

increase the n i t r a t e l e v e l s in t h e r a i n f a l l d u r i n g the r e s u l t i n g i n i n c r e a s i n g n i t r a t e concentrations

There

concentrations

were

between

however

large

events.

initial

concentrations from the H i l l b r o w catchment were 0.2 the r u n o f f on 3 J a n u a r y

1985 w h i l e

and

mg/l

final

nitrate

a n d 12.9 mg/l

in

the maximum n i t r a t e concentration

in

the r u n o f f on 18 J a n u a r y 1985 d i d not exceed 0.3 concentration of 2.2 mg/l

the

in magnitudes of

differences

The

in

mg/l.

A maximum n i t r a t e

was recorded i n the r u n o f f from the

Montgomery

P a r k catchment on 7 M a r c h 1983. The recommended n i t r a t e l i m i t i n domestic water i s 6.0 mg/l There

does

w i t h a n upper l i m i t of 10.0 mg/l

not

apear

to

be

any

definite

(SABS,

1984).

time-related

decrease

increase in the l e v e l s of the o t h e r c o n s t i t u e n t s i n the r u n o f f .

or

For example

s u l p h a t e concentrations increase w i t h time i n the r u n o f f from H i l l b r o w on 3 J a n u a r y 1985 w h i l e the converse i s t r u e f o r the r u n o f f on 18 J a n u a r y 1985 from the same catchment. Plots of p o l l u t a n t concentrations w i t h time f o r

the H i l l b r o w events a r e

presented i n F i g u r e s 5.3 and 5.4.

Mass Balance for event of 18 J a n u a r y 1985 on H i l l b r o w Catchment

A

rainfall

d e p t h of

6 mm was

measured

for

t h i s event

concentration in the r a i n f a l l was 18 mg/l

(see Table 2).

expressed

as a

rainfall

0.18

kg/ha

total.

For a

in

l o a d i n g r a t e of catchment

corresponds to 4030 rn3 of

size of

rainfall

over

kg/ha/mm

67.2 the

ha

this

catchment

and

TDS

the

T h i s can a l s o be of

or

rain

depth of mass of

1.08

rainfall 73

k g of

pollutants. For t h i s event a r u n o f f volume of 475 m’ pollutant

were

estimated.

There

p o l l u t a n t from the catchment.

was

thus

a n d a t o t a l load of

121 k g of

a

48

kg

the

runoff

1.8

kg/ha

net

washoff

E x p r e s s i n g the p o l l u t a n t

i n terms o f catchment a r e a a n d r a i n f a l l g i v e s 0.30

of

load i n

kg/ha/mm

or

of

total. The

sources

of

these

p o l l u t a n t s have

densely developed a r e a l i k e H i l l b r o w , of deposits

from

wind

and

w h i c h i s u s u a l l y present.

motor

not

the most

vehicles

and

been

identified,

but

in

a

l i k e l y sources a r e washoff s o l u b l e f r a c t i o n s of

litter

73

Since the r u n o f f was o n l y 12% of the r a i n f a l l experienced a

net

washoff

of

pollutants,

with

washed o f f than was deposited b y the r a i n f a l l ,

and

the catchment

66% more

pollutant

still being

i t i s conceivable t h a t

this

washoff may reach even h i g h e r percentages f o r events where the p r o p o r t i o n of

runoff

rainfall

to

is

greater.

Such

events

would

result

h a a v i n g a greater depth of h i g h e r i n t e n s i t y r a i n f a l l .

It

from

storms

i s also p o s s i b l e loss of moisture,

t h a t i n p u t d u r i n g one storm i s stored and released a f t e r to be washed o f f d u r i n g a subsequent storm.

A

p l o t of

hydrograph,

p o l l u t o g r a p h a n d TDS v a r i a t i o n

with

time

for

t h i s event i s presented i n F i g u r e 5.5.

Mass Balance for event of 7 March 1983 on Montgomery Park Catchment

On 7 March 1983 a t o t a l depth of 14 mm of the Montgomery P a r k catchment. exceeding f i v e concentration Hillbrow

on

days of

of

the

no

18 October

so

rain,

rainfall 1985

is

it

is

much

when

loading

rate

p o l l u t a n t s deposited

of

on

0.52

this

only

two

was

surprising than

recorded on

dry

that

that

days

km’

The

the

in

passed.

The

r e s u l t i n g in a

total

mass

of

was

thus

7666

catchment

TDS

measured

had

(see Table 5.31,

kg/ha/mm.

10.53

not

higher

measured TDS of the r a i n f a l l was 52 mg/l rainfall

rainfall

T h i s event was preceded b y a time p e r i o d

soluble kg

in

147420 m3 of r a i n f a l l . A r u n o f f volume of 5508 m3 w i t h a corresponding c u m u l a t i v e r u n o f f

of 1479 k g of dissolved p o l l u t a n t s was measured. pollutant

load

can

be

represents o n l y 4% of

expressed the

deposited b y the r a i n f a l l . a

net

gain

of

6187

kg

as

rainfall

0.10

and

kg/ha/mm.

pollutant,

or

k g / h a o r 0.42

pollutant

pollutant

net

deposition

of

( l o s s of

that

occurred

m a t t e r ) from

this

volume

19% of

that

deposited.

kg/ha/mm

catchment w h i l e net washoff occurred i n the densely Since there i s a deposit

runoff

therefore experienced

81% of

corresponds to a net g a i n of 5.87 i.e.

The

the TDS washed o f f

I n t h i s case the catchment of

load

I n terms of r a i n f a l l

in

of the

This

rain-borne peri-urban

developed catchment.

r a i n as

indicated b y

the

Montgomery P a r k catchment i t can be expected t h a t a s i m i l a r deposit would occur in H i l l b r o w , so the l i t t e r load must be h i g h e r . Once

again

it

is

p o l l u t a n t s washed o f f

difficult

to

attempt

t h i s catchment.

to

identify

the

sources

of

R e f e r r i n g to Tables 5.2

a n d 5.3

it

w i l l be seen that n i t r a t e levels in the r u n o f f a r e h i g h e r f o r t h i s catchment than

for

possible

the

Hillbrow

washoff

fertilizers.

This

of seems

catchment

decaying a

on

18

vegetation,

reasonable

January animal

deduction

as

1985,

signifying

faeces the

and

Montgomery

the

garden Park

74

r--,/-• --.----.

L*'

14hOO Fig.

16h00 5.5

lEhoO TIME

Hydrograph, p o l l u t o g r a p h a n d TDS f o r H i l l b r o w f o r event on 18/01/85

I 1,20

E 0,90 "

-

/--'

-

E

W

I-

U

d 0,60

s

s

-

LL

0,30

I

15h00

17h00

19hOO

2lhoo

23h0

TIME Fig.

5.6

Hydrograph, p o l l u t o g r a p h a n d TDS f o r Montgomery P a r k f o r event on 07/03/83

75

catchment consists of p r e d o m i n a n t l y s u b u r b a n r e s i d e n t i a l developments w i t h gardens.

Another

ground

(either

minerals).

source

in Montgomery

previously

deposited

I t i s noted that

Park

by

c o u l d be

rain

leachate from

seeping

or

in

the

from

soil

the p r o p o r t i o n of sulphates a n d carbonates i n

r u n o f f i s s i m i l a r to the r a i n , b u t c h l o r i d e s increase. It

appears

that

sulphates

d i f f e r e n t land-uses,

and

chlorides

are

the respective levels b e i n g of

unaffected

by

the

two

the same o r d e r f o r b o t h

catchments which also i n d i c a t e s they may be a i r - b o r n e

i n t o the catchment.

I t has also been observed that there a r e ( i l l e g a l ) discharges of

industrial

wastes i n t o the separate stormwater system in H i l l b r o w . The

hydrograph,

pollutograph

TDS

and

variation

with

time

for

this

event a r e i l l u s t r a t e d i n F i g u r e 5.6. I n the mass b a l a n c e of p o l l u t a n t s o u t l i n e d above i n both

the H i l l b r o w

pollutant runoff.

load

in

and

the

To determine

runoff

whether

g a i n of p o l l u t a n t s i t

to

the

i s also necessary

the

rainfall

to

causing

the that

the TDS concentration

know

TDS

levels

in

the r a i n f a l l

(Montgomery P a r k ) a n d 78 mg/l

concentration of 118 mg/l

relate

of

In the present p r o j e c t r a i n f a l l q u a l i t y

the r a i n f a l l as well a s the r u n o f f .

( H i l l b r o w ) , 52 mg/l

in

load

to

the catchment h a s experienced a net loss o r

was o n l y analyzed f o r three events, mg/l

i t was found p o s s i b l e

the Montgomery P a r k catchments

being

18

( H i l l b r o w ) . A TDS

i n r a i n f a l l was observed b y Madisha

(1983) a t a

location near the H i l l b r o w catchment. Assuming a r a i n f a l l l o a d i n g r a t e of 0.52 kg/ha/mm l o a d i n g r a t e of 0.71

and an average r a i n f a l l total

weight

computed f o r

of

dissolved

twelve

solids

deposited

rainfall-runoff

on

events f o r

e l e c t r i c a l c o n d u c t i v i t y d a t a were a v a i l a b l e .

f o r Montgomery P a r k

kg/ha/mm the

for

two

which

both

Hillbrow,

the

catchments

was

discharge

and

These r e s u l t s a r e presented in

Table 5.6. I t can be deduced from Table 5.6

runoff

expressed

in

terms

of

rainfall

Montgomery P a r k and 1.54 kg/ha/mm i s i n accordance Lanyon, of

with

1980; Mikalsen,

stormwater

is

the

is

from

the average 0.40

pollution

kg/ha/mm

of

of r a i n f a l l f o r H i l l b r o w .

f i n d i n g s of

1984), v i z .

higher

that

that

other

researchers

i n general

commercial

load of

rainfall

for

This f i n d i n g

(e.g.

Polls and

the level of p o l l u t i o n

and

downtown

land-use

developments than from r e s i d e n t i a l developments. Another

i n t e r e s t i n g deduction from Table 6 i s t h a t

deposited on the Montgomery P a r k catchment t h a t

more p o l l u t a n t

was

was washed o f f f o r

five

out of the seven events w h i l e t h i s was o n l y the case f o r events in the H i l l b r o w catchment.

two out of

five

The h i g h e r percentage imperviousness in

the H i l l b r o w catchment i s p o s s i b l y the reason f o r t h i s phenomenon.

76

TABLE

Comparison of p o l l u t i o n loads i n r a i n f a l l a n d r u n o f f w i t h r a i n f a l l depths

5.6

wation and

lainfall

U l p h t of

U i p h t 01

Ratio O f

dapth

dap0alt.d

106 In

runofr

load in

106

rumrr

I M d to

wnorr

data

?Oi I U t l O l

rainfall (-1

-

tho1

Ihal

I hg/h./rl

laad

mntwuw Pa~h 01/03/03

14

7666

1479

0.19

W/I2/01

11

7118

7356

1.03

0.54

12/12/83

17

9309

13086

1.41

0.73

21/01/85

46

25100

23451

0.93

0.40

30/10/85

55

30116

15872

0.53

0.27

0.10

3 I / 10185

24

13141

7680

0.59

0.30

0111 1/85

67

36607

26391

0.72

0.37

-

Avarmpa 10s for

ni I IbIOr

71 -/I

nlllb-

13/09/011

1

48

247

5.15

3.60

16/09/04

14

669

217

0.32

0.21

H)/lO/04

2

96

01

0.ou

0.60

21/10/04

1

48

193

4.02

2.07

18/01/85

6

73

121

1.66

0.30

-

r e l a t i o n s h i p s between d e p t h o r r a i n f a l I a n d

H a v i n g established of

pollutant

compu ted

washed

off

a

catchment,

precipitation

of

catchment

763

or

1190

loads

amount can

be

example

and

1981),

assuming a

the

total

mean

mass

of

will

be of the o r d e r of 80000 k g p e r

For

the

Montgomery

loading

will

be a p p r o x i m a t e l y

kg/ha/annum.

amount of a n n u a l p o l l u t a n t

for

(Adamson,

mm

p o l l u t a n t s washed o f f t h i s catchment annum

pollutant

.

Considering the H i l l b r o w annual

annual

Park

catchment

the

320 000 k g o r

305 kg/ha/annum. Assuming a n average d r y weather flow of 0.0015 m’/s H i l l b r o w a n d 310 d r y d a y s p e r annum flow

volume

of

a p p r o x i m a t e l y 40300 m’.

results

i n an

This

results

or

130 m’/day

annual in

dry

an

in

weather

annual

dry

weather p o l l u t a n t load of a p p r o x i m a t e l y 22100 k g o r 330 kg/ha/annum.

The

average d r y weather flow

i n Montgomery P a r k

the

annual

dry

off

which

corresponds

kg/ha/annum.

weather

flow to

a

this

total

catchment pollutant

i s about 0.004 is

due to d i r e c t stormwater r u n o f f i s about 3.6

approximately

load

Therefore i t can be deduced t h a t

m’/s

of

60500

so

110000 m’ kg

or

57

the a n n u a l p o l l u t a n t load

times t h a t due to d r y weather

77

flow

for

the

Hillbrow

catchment

and

about

5.3

times

that

due

to

dry

sources

are

weather flow f o r the Montgomery P a r k catchment. The

pollutant

loading

rates

derived

from

the

different

summarized i n Table 5.7.

TABLE

5.7

Summary of dissolved loads i n kg/ha/mm

CONCLUSIONS

Despite the l i m i t e d monitoring,

the f o l l o w i n g

tentative

conclusions c a n

be drawn. The t o t a l dissolved p o l l u t i o n from H i l l b r o w ,

a densely

load i n stormwater

a n d surface

populated c i t y a r e a i s about

which

i s about 3 times as great

Park.

The m a j o r i t y

from

a

s u b u r b a n catchment,

(70%-80%) occurs d u r i n g storm r u n o f f

Only about 430 kg/ha/annum

drainage

15000 kg/ha/annum Montgomery

in both

cases.

f a l l s o r i s washed out of the atmosphere.

The

m a j o r i t y i s therefore l i t t e r and from vehicles in the case o f H i l l b r o w ,

and

decaying vegetable matter o r leachate from Montgomery P a r k . There i s a net g a i n of p o l l u t a n t s from H i l l b r o w b u t in Montgomery P a r k the t o t a l washoff atmosphere.

i s about

the same o r d e r as the t o t a l deposited from

A s a l a r g e p r o p o r t i o n of r a i n seeps i n t o the ground,

store TDS to be released i n f u t u r e r u n o f f .

the

i t could

There i s a net g a i n of n i t r a t e

in Montgomery P a r k however.

Dry

weather

concentrations

seepage from a p o l l u t e d l a n d f i l l 1984)

and

illegal

waste

are

higher

in the case of

discharge

in

Hillbrow.

r u n o f f increase w i t h number of p r e v i o u s d r y sweeping would reduce loads.

in

both

catchments,

Montgomery

Park,

Concentrations

days,

due

signifying

to

(Ball,

in

storm

that

street

78

The m a j o r i t y o f d i s s o l v e d s a l t s i s washed o f f d u r i n g the r i s i n g the storms except n i t r a t e s w h i c h e x h i b i t a l a g . alternativley this.

the i n f l u e n c e of atmospheric

l i m b of

Release from the g r o u n d o r

l i g h t i n g could

Before p r e d i c t i o n b y m o d e l l i n g c a n be u n d e r t a k e n ,

b e the cause of intensive

further

i n v e s t i g a t i o n w i l l be r e q u i r e d .

REFERENCES

Adamson, P.T., 1981. Southern A f r i c a n Storm R a i n f a l l . D i r e c t o r a t e o f Water A f f a i r s , Department o f Environment A f f a i r s , Technical Report TR 102. B a l l , J.M., 1984. D e g r a d a t i o n o f g r o u n d a n d s u r f a c e w a t e r q u a l i t y in r e l a t i o n to a s a n i t a r y l a n d f i l l . MSc(Eng) D i s s e r t a t i o n , U n i v e r s i t y o f t h e W i twatersrand. Bedient, P.B., Lambert, J.L. and Springer, N.K., 1980. Stormwater p o l l u t a n t load-runoff r e l a t i o n s h i p s . Jnl. Water P o l l u t i o n Control Fed., 52, 2396-2404. B r a d f o r d , W.J., 1977. U r b a n stormwater p o l l u t a n t l o a d i n g s : a s t a t i s t i c a l summary t h r o u g h 1972. J n l . Water P o l l u t i o n Control Fed., 49, 613-622. C o l w i l l , D.M., Peters, C.J. a n d P e r r y , R., 1984. Water q u a l i t y o f motorway runoff. Transport and Road Research Laboratory, Dept. of the Environment a n d Dept. o f T r a n s p o r t , TRRL Supplementary Report No. 823. Cordery, I., 1977. Q u a l i t y c h a r a c t e r i s t i c s o f u r b a n stormwater in Sydney, A u s t r a l i a . Water Resources Research, 13, 197-202 Green, I.R.A., Stephenson, D. a n d Lambourne, J.J., 1986. Stormwater p o l l u t i o n a n a l y s i s . U r b a n H y d r o l o g y a n d D r a i n a g e Research Contract, Water Research Commission Report No. 115/10/86. Helsel, D.R., Kim, J.I., G r i z z a r d , T.J., R a n d a l l , C.W. a n d Hoehn, R.C., 1979. L a n d use i n f l u e n c e s o n m e t a l s in storm d r a i n a g e . Jnl. Water P o l l u t i o n Control Fed., 51, 709-717. Madisha, J.L., 1983. I n v e s t i g a t i o n p r o j e c t o n u r b a n stormwater p o l l u t i o n in Braamfontein. Department o f Civil Engineering, University of the W i twatersrand. Mikalsen, K.T., 1984. Assessment of water q u a l i t y changes r e s u l t i n g from urbanization, a g r i c u l t u r e and commercial f o r e s t r y in the s t a t e of Georgia, U.S.A. Proceedings o f t h e T h i r d I n t . Conf. "Urban Storm Drainage," Goteborg, Sweden, 801-810. 1980. P o l l u t a n t c o n c e n t r a t i o n s from hogeneous Pol Is, I . a n d L a n y o n , R., l a n d uses. Jnl. Environmental Eng. Div., ASCE, 106, 69-80. S a r t o r , J.D., Boyd, G.B. a n d A g a r d y , F.J., 1974. Water p o l l u t i o n aspects of street s u r f a c e contaminants. Jnl. Water P o l l u t i o n Control Fed., 46, 458-467. Simpson, D.E. a n d Kemp, P.H., 1982. Q u a l i t y a n d q u a n t i t y o f stormwater r u n o f f from a commercial land-use catchment in N a t a l , South A f r i c a . Water Sci. Tech., 14, 323-38. South A f r i c a n Bureau o f S t a n d a r d s (SABS), 1984. S p e c i f i c a t i o n f o r w a t e r f o r domestic supplies. SABS 241. Stephenson, D. and Green, I.R.A., 1987. Mass b a l a n c e o f stormwater p o l l u t a n t s . Water S.A. T e r s t r i e p , M.L. a n d S t a l l , J.B., 1974. The I l l i n o i s u r b a n d r a i n a g e a r e a s i m u l a t o r , ILLUDAS. I l l i n o i s State Water Survey, U r b a n a , B u l l e t i n 58. Wanielista, M.P., 1979. Stormwater Management Q u a n t i t y a n d Q u a l i t y . Ann A r b o r Science P u b l i s h e r s I n c . M i c h i g a n . Whipple, W., Hunter, J.V. a n d Yu, S.L., 1977. E f f e c t s o f storm f r e q u e n c y on p o l l u t i o n from u r b a n r u n o f f . Jnl. Water P o l l u t i o n Control Fed., 49, 2243-2248.

79

CHAPTER 6

OPT I MUM ALLOCAT ION OF WATER RESOURCES SUBJECT TO QUAL I TY CONSTRA I NTS I NTROOUCT ION

We a r e r e a c h i n g economic

benefit

an

cost

age of

compromise.

analysis,

1960's

The

1970's

the

saw

h a i l e d the e r a

the

appearance

of

of the

environmentalists and i d e a l i s t s a n d the 1980's appear to be p r o d u c i n g more realistic

planners.

Multiple

objectives

including

economic,

sociological,

p o l i t i c a l and environmental w i l l be considered b u t h o p e f u l l y perspectives.

High i d e a l s can o n l y r e s u l t

may h a v e detrimental The w a t e r i n g

down

effects

of

i n slow-down

development

e n g i n e e r i n g projects

stagnate the engineering profess ions

on

industry

and

of to

of

i n the correct

growth and t h i s

underdeveloped countries. meet

high

i d e a l s can

lose v a l u a b l e b r a i n power

also

to o t h e r

.

Water resources a r e regarded b y many as a never d i m i n i s h i n g asset. account mined.

of

annual

This i s a

replenishment fallacy,

basin deterioration, and

more

the

usage occurs

and poorer q u a l i t y water

for

it

apart

n a t u r e of so

is

there

assumed

from

the will

the

over-exploitation

resource can be g r e a t e r

i n our r i v e r s .

resource

cannot

and

be a l t e r e d .

waste

water

New g r o w t h can o n l y

On be

drainage

As

more

discharges be met from

these r i v e r s o r from water f u r t h e r a f i e l d i f surface waters a r e to be r e l i e d on. We can often not a f f o r d the l u x u r y of p u r e mountain waters p i p e d from many hundreds of kilometres away. water to acceptable s t a n d a r d s and n u t r i e n t removal f o r a l l uses. obtained

from

different

which quality

i n some cases.

i s particularly high.

containers

while

poorer

i n d u s t r i a l purposes. quality

water

a r e predominately water.

supplies.

be necessary

This

will

be

purify

waste

The cost of d e m i n e r a l i z a t i o n

quality

i s t r a n s p o r t e d separately water

Although separate expensive

h i g h density

to

T h i s cost may not be w a r r a n t e d

I n many countries p o t a b l e water

domestic and of

will

It

there

residential

i s used piped may

and

for

water be

or

general supplies

some

could j u s t i f y

areas high

Other areas r e q u i r i n g lower q u a l i t y c o u l d receive separate is particularly

the case

i n m i n i n g areas

in South

Africa

where these studies were i n i t i a t e d . P a r a l l e l studies a r e i n v e s t i g a t i n g the cost o f d e m i n e r a l i z a t i o n and h i g h q u a l i t y p u r i f i c a t i o n b u t that i s o n l y one of the options.

The others a r e to

seek f r e s h surface o r groundwater resources f u r t h e r away, poorer q u a l i t y of i n d i c a t e d here.

local resources o r to a l l o c a t e i n

to make do w i t h

an o p t i m a l

manner

as

80

Methods of research c o u l d e i t h e r adopt the g l o b a l systems approached o r a more s i m p l i s t i c b u t p e r h a p s easier

understood methodology.

number of sophisticated techniques f o r o p t i m i z a t i o n of water

systems

readily,

subject

to

constraints.

in fact sometimes too r e a d i l y ,

these methods may from a computer politicians.

form

follow

ideal

program

the

objectives.

subject

i s not easy

Simple g r a p h i c a l

to describe a n d present. to

various

The

There a r e a

linear and nonlinear use

of

computers

adopted b y eager students. matter

for

to e x p l a i n

dissertations

Whereas

the o u t p u t

to r e g i o n a l p l a n n e r s a n d

displays or tabular

results

a r e much easier

Simple h a n d c a l c u l a t i o n s o f t e n enable the a n a l y s t

alternatives

and

in m i n d

bear

marginal

costs

or

multiple

By f o l l o w i n g the e n t i r e p l a n n i n g process t h r o u g h the a n a l y s t

also able

to c l a r i f y

is

a l t e r n a t i v e objectives a n d

t h i s approach which i s adopted

i n the s i m p l i s t i c

allocate

priorities.

s t u d y below

It

is is

(Stephenson,

1982).

THE SYSTEM

Consider the t r a n s p o r t a t i o n problem depicted sources of

water a r e a v a i l a b l e

resources

indicated

as

10,

(A,

20

i n Fig.

6.1.

A number of

B a n d C ) a n d they each have

and

15

megalitres

per

day

limited

(Ml/day),

r e s p e c t i v e l y . T h e t o t a l a v a i l a b i l i t y may exceed the requirements of

demand

of users W,

in t h i s

example.

X,

and Y

The cost of

though, transport

a n d a g a i n i n the t r a n s p o r t a t i o n

which r e q u i r e 8,

12 a n d 16 M l / d a y

a l o n g each r o u t e i s i n d i c a t e d i n F i g . t a b l e a u Table 6 . 2 .

A s f a r as

6.1,

i t has been

described the system i s a simple t r a n s p o r t a t i o n example w h i c h could e a s i l y be optimized,

i.e.

the flow

a l o n g each r o u t e to r e s u l t

t r a n s p o r t a t i o n system c o u l d be d e r i v e d r e l a t i v e l y e a s i l y .

F i g . 6.1

Supply requirements a n d a l t e r n a t i v e s

i n a minimum t o t a l

81

The s i t u a t i o n

i s complicated b y the Fact t h a t

have c e r t a i n water q u a l i t y requirements.

TDS ( t o t a l dissolved s o l i d s ) i s in mg/l

i m p u r i t y , e.g. of

W,

X

and Y

respectively.

are

that

the TDS s h a l l

not

a n d the requirements

exceed

Note t h a t Ml/day m u l t i p l i e d b y mg/l

11

10,

8 mg/l

and

g i v e s k g / d a y of s a l t s ,

The TDS of the source waters from A,

mass flow rate. and 8 mg/l

the i n d i v i d u a l consumers

The measurements of the r e l e v a n t

B a n d C a r e 6,

a

11

respectively.

T h e lower l i m i t on TDS may be achieved b l e n d i n g d i f f e r e n t sources o r ,

i f economic,

the resources.

The l a t t e r option,

assuming

source

any

by

selecting

correct

sources,

p u r i f y i n g p a r t o r a l l of a n y of

namely p u r i f i c a t i o n ,

i s p u r i f i e d and adding

could be h a n d l e d b y

the cost

to

the conveyance

cost. Often the r e l a t i o n s h i p between cost of p u r i f i c a t i o n a n d r a t e of nonlinear

such as

w i t h desalination

be

reverse

becomes more complex.

I n such case,

possible

1978).

Alternatively

employed to seek a n optimum.

I f only par t

(Stephenson,

need be p u r i f i e d ,

separable a

osmosis

and

flow

the

is

system

programming methods a r e gradient

method

may

be

( a v a r i a b l e p a r t ) of a source

the d e s c r i p t i v e equations a r e more numerous b u t

linear

programming methods may be employed to optimize the system. I n the present example

(Fig.6.1)

the resource a n d demand c o n s t r a i n t s

may also be w r i t t e n a s l i n e a r c o n s t r a i n t s :

Demand

aAW + aBW + aCW= Q~~ + aBX + aCX = aAy + aBy + aCY =

8 12 16

The q u a l i t y c o n s t r a i n t s may be w r i t t e n : 6QAW + l l Q B W + 8QCW 1 1 0 x

+ 6QAy + 6QAx

8

llQBx

+ 8QCX 511 x 12,

llQBy

+ 8QBx

5

8 x 16

Provided there i s a feasible solution the set of m be analyzed b y l i n e a r programming methods. and n

the number

of

demand p o i n t s .

m

+

2n c o n s t r a i n t s c o u l d

i s the

Alternatively

the

number of

sources

availability

and

82

demand c o n s t r a i n t s c o u l d be considered i n a t r a n s p o r t a t i o n m a t r i x qua1 i t y c o n s t r a i n t s h a n d l e d separately of l i n e a r programmes ( D a n t z i g , This

is

u s i n g t h e p r i n c i p l e of decomposition

1963; Stephenson,

based

described

below.

additional

on

the

c o n s t r a i n t s on the d i s t r i b u t i o n s .

1969). A t h i r d method i s

transportation

computers

a n d more

interaction

between

method

with

The r e s u l t i n g advantages o v e r

the l i n e a r programming a l t e r n a t i v e s a r e s i m p l i c i t y , for

a n d the

the

rapidity,

no necessity

water

resources

planner

linear

programming

a n d the system. It

is

assumed

the

reader

is

familiar

with

and

t r a n s p o r t a t ion programming techniques.

SOLUTION METHOD

The d a t a a r e a r r a n g e d in a t a b l e a u s i m i l a r (Table

6.1).

Each

l a b e l led "slack"

demand

is

represented

by

to a

a

transportation row,

each source and there

i s an additional

column

including

A

since resources exceed demand here.

tableau

column

a

labelled "artificial

slack"

since the i n i t i a l assignment may not s a t i s f y q u a l i t y c o n s t r a i n t s w i t h o u t I n f a c t , a s there a r e three a d d i t i o n a l c o n s t r a i n t s , three a d d i t i o n a l of

the

artificial

v a r i a b l e s in the f i n a l slack

flow

variables

necessarily so f o r s a l t mass flow is

not

necessary

to

assign

should

artificial

cost

it.

one would expect u p to

programmme. be

s l a c k s since they

row

represents

The cost very

coefficients

large,

are of

the

but type.

not It

the

following

eliminate

artificial

coefficients

in

method.

TABLE 6.1

Transportation slack

X

Y

matrix

with

shuffling

to

83 An

initial

satisfied flow

-

i s made i n Table 6.1

assignment

r u l e (Loomba,

1964).

At each assignment,

water flow and

l i m i t s the number,

salt

balance.

i n b l o c k CY,

but

u s i n g the

Northwest corner

two types of c o n s t r a i n t must be Thus

i n most

blocks,

AW,

e.g.

TDS b a l a n c e l i m i t s flow

2.25

to

( a flow of 6 would otherwise have been assigned to t h i s b l o c k ) .

Ml/day

The f i r s t step a f t e r m a k i n g the i n i t i a l assignment should be to evacuate flows

from

the

artificial

slack

column.

s a t i s f y flow c o n s t r a i n t s and TDS Ml/day

corner

re-allocation,

6.1,

Thus 8/48

in k g / d a y .

each

re-assignment

that

indicates 8 Ml/day

r e s u l t i n g in TDS flow of 48 k g / d a y .

each

Note Observe

the

water

two

of

a

closed

and select

re-allocations

circuit

the lowest are

at

source

whether

water

to

evacuate

or

TDS o f

TDS

limit

allocation. block

in

a n d the

I t i s r e l a t i v e l y easy to check

p e r m i s s i b l e flow

necessary

a

must

flows

/

a r e w r i t t e n i n the bottom l e f t of each b l o c k followed b y

TDS flow mg/l

limits.

6 at

the

I n Table

LY.

a

feasible

(non o p t i m a l ) solution r e s u l t s . Now the o p t i m i z a t i o n proceeds a s f o r any t r a n s p o r t a t i o n exercise, for

the

column

additional and

row

constraint

cost

on

coefficient

vacant block w i t h a c t u a l costs

it

each and

re-al location. comparing

i s decided

to

After

calculating

implied

costs

in

each

re-allocate

to

block

BY.

Although flow consideration would l i m i t the a l l o c a t i o n to 1 M l / d a y , c o n s t r a i n t s l i m i t i t to 0.4 M l / d a y . eliminated.

Then a l l the slack i n TDS f o r

Table 6 . 2 r e s u l t s .

TABLE 6.2 T r a n s p o r t a t i o n m a t r i x step two

except

quality row Y

is

04 I t w i l l be observed t h a t there i s more than one p o s s i b l e cost coefficient f o r some blocks,

depending on which block i s used as a p i v o t .

This arises

because the number of occupied blocks i s g r e a t e r t h a n n + m - 1 a n d m a r e the number of a r t i f i c i a l slack column.

rows and columns

i n the t a b l e a u

where n

excluding

the

Each possible combination should be i n v e s t i g a t e d .

Where the p i v o t sequence AW,

AX,

B X , B Y , BS, CY i s used,

the maximum

difference between i m p l i e d cost a n d a c t u a l cost c o e f f i c i e n t appears i n block

C X , and i s 8 v s 4

( T a b l e 6.3).

It will

a r o u n d the closed p a t h CX-AX-AY-CY-CX 1.4

and then 0.9

ml/day

can

be found

t h a t b y proceeding f i r s t

a n d then CX-EX-BY-CY-CX

be a l l o c a t e d

to

CX

block

without

that f i r s t violating

flow and q u a l i t y c o n s t r a i n t s .

TABLE 6. 3

T r a n s p o r t a t i o n m a t r i x optimized

Dunand :

Subsequent improvement,

calculations i.e.

will

reveal

is

no

further

cost

no more i m p l i e d costs exceed a c t u a l costs once new cost

coefficients a r e ca Icu I a ted

.

The optimum p l a n , w h i c h s a t i s f i e s q u a l i t y F i g . 6.2.

there

requirements,

i s indicated

in

85

D iscussionl All

water

poorer

users do

quality

is

not

require

tolerable,

the

allocation

same of

high

quality

alternative

water.

sources

Where

may

be

considered. O v e r a l l economy of p u r i f i c a t i o n a n d d i s t r i b u t i o n r e s u l t .

F i g . 6.2

Optimum a l l o c a t i o n subject to c o n s t r a i n t s

A technique f o r a l l o c a t i n g water resources b y a form of programming simple and

has not

been

demonstrated

computer orientated.

with The

an

example.

transportation

The

technique

resulting distribution

system

is is

depicted a n d can r e a d i l y be updated as q u a l i t i e s of the sources v a r y .

T h e method distribution

i s therefore of use f o r management

systems

as

well

as

design.

In

and o p e r a t i o n of

fact

even

more

so,

water since

construction costs a r e not as a r u l e e a s i l y l i n e a r i z e d whereas pumping costs a r e g e n e r a l l y p r o p o r t i o n a l t o the r a t e of flow.

L I NEAR PROGRAMM I NG SOLUT ION

The p r e v i o u s sections high1 ighted the shortcomings of the t r a n s p o r t a t i o n and

transportation

extended

techniques.

The

techniques

onerous simp1 i f y i n g assumptions be made about parameters. an approach which do not model

require

They

that

thus o f f e r

the d i s t r i b u t i o n comprehensively

enough.

The most severe shortcomings are: a ) Qua1i t y

constraints

cannot

be

considered

in

Transportation

Programming.

b ) Optimization

of

the

amount

of

water

to

be

desalinated

and

hence

blended cannot be achieved in e i t h e r of the T r a n s p o r t a t i o n techniques.

86 c)

Non-Linear

cost f u n c t i o n s h a v e to be a p p r o x i m a t e d b y

l i n e a r functions

in both techniques.

Linear

programming

shortcomings can

techniques

be overcome.

In

provide linear

means

whereby

programming

q u a n t i t y c o n s t r a i n t s , a n d any o t h e r l i n e a r c o n s t r a i n t s , to

yield

an

optimum

solution.

However,

neither

al I

both

these

quality

and

can be m a n i p u l a t e d

a

non-linear

objective

f u n c t i o n n o r c o n s t r a i n t s c a n be used unless they a r e converted to a

linear

or

linear

piecewise

linear

form.

This

can

be

achieved

by

using

programming in c o n j u n c t i o n w i t h separable programming. This section describes how the d i s t r i b u t i o n problem i s transformed a

representative

mathematical

model

suitable

for

analysis

using

into

linear

programming (Grosman, 1981).

The sets of d a t a r e q u i r e d a r e summarized below;

Qua1i ty

Quantity

Water Board

500

mg/P

100.0 Me/d

Groundwater

600

mg/e

11.5 Me/d

Wastewater

1750 mg/l

Sources :-

Desalinated wastewater

Variable

175 mg/P

Variable

Demands:Transfer

1750 mg/e

7.0

Me/d

System 1

700 mg/e

9.5

Me/d

System 2

700 mg/e

0.7 Me/d

System 3

700 mg/e

0.5

Waste ( S l a c k )

1750 mg/P

The water b o a r d s u p p l y i s assumed o t h e r sources, b e used.

this is high,

Me/d

unused

to be 100 Me/d.

I n r e l a t i o n to the

a n d consequently o n l y a p o r t i o n

thereof

may

The p o r t i o n to be used w i l l b e optimized.

Wastewater to y i e l d a n

y i e l d s 10 Me/d,

improved qua1 i t y

This v a r i a b l e portion

i s an

of which a v a r i a b l e p o r t i o n i s d e s a l i n a t e d available unknown

from

and

the d e s a l i n a t e d

hence

it

should

wastewater.

be optimized.

The recovery r a t i o n of feed flow to product flow in a d e s a l i n a t i o n p l a n t 0,69 f o r t h i s case. U U

+ D /0.69 + 1.45 D

Expressing the above i n mathematical terms,

= 10

= 10

where U = Used MSW i n Me/d

D = Desalinated Wastewater in MP/d

(6.10)

is

87

Two

new

variables

(U

and

D)

and

a

new

constraint

Eq.

6.10

are

i n t r o d u c e d to c a t e r f o r t h e d e s a l i n a t i o n of a v a r i a b l e p e r c e n t a g e o f waste. U was assumed t o b e 7.5 Mk‘/d,

D w a s 1.73 Me/d.

The

m a g n i t u d e o f t h e s l a c k a l l o c a t i o n t o w a s t e (W) w i l l c o n s e q u e n t l y v a r y .

h e n c e f r o m Eq.

The

v a r i a t i o n i s a c c o r d i n g to E q . 6.11

6.10,

where the sources a r e b a l a n c e d a g a i n s t

the demands:

W + 7.0 + 9.5 + 0.7 + 0.5

-

D = (10

but

U ) 0.69

hence W = 93.8 + U + ( 1 0 W = 100.7 + 0.31

100 + 11.5 + U + D

=

f r o m Eq. 6.10 -

(6.11)

U ) 0.69

U

(6.12)

From a T r a n s p o r t a t i o n E x t e n d e d a n a l y s i s U w a s 7.5 Mt/d

was o n l y

with

a

1

maximum

hence W

MP/d, value

10

of

was

4.03

Me/d,

MP/d.

(that

Me/d,

However,

is

a n d t h e 100 U varies

without

now

desalination).

T h e r e f o r e from Eq. 6.12 W L 103.8 Me/d

(6.13)

The a c c e p t a b l e q u a l i t y assumed f o r t h e System 1 (S), System 2 ( V ) a n d System 3 ( M ) i s s t i l l 700 m g / Q . T h e n e x t s e c t i o n r e v i e w s a n a n a l y s i s of

a

r a n g e of acceptable q u a l i t i e s . The

only

unrealistic

linear programming, flow.

The

cost

assumption

i s that

the

coefficients

necessary

total

are

costs

are

summarized

this

in

analysis,

linearly below

r e l a t e d to in

Table

using feed 6.4.

Ab b r e via tio n s f o r the sources a n d demands a r e a l s o i n d i c a te d .

TABLE 6.4

Cost c o e f f i c i e n t s (c/m’)

u s e d in l i n e a r p r o g r a m m e

DEMANDS

I (c/m’

I TRANSFER I SYSTEM 1 I SYSTEM 2 1 SYSTEM 3

w l O / S

1

I

v

l M

WB

R

0.0

0.0

24.0

32.5

39.5

GROUND WATER

F

5.0

2.5

3.0

11.5

14.0

u

7.5

6.0

0.0

1 .o

0.0

D

44.0

43.0

38.0

-_ cn

WASTE

W

u

K

3

SI

WASTE WATER DESAL. WASTE WATER

46.0

51 .O

88 The f o r m u l a t i o n of t h e m a t h e m a t i c a l model b e g i n s b y e x p r e s s i n g the o b j e c t i v e f u n c t i o n i n terms of t h e e x p r e s s i o n

n

z =

x

c c.

J

(6.14)

J

Hence

+ O.O(RB) + 24.O(RS) + 32.5(RV) + 39.5(RM) + 5.0(FW) + + 3.0(FS) + 11.5(FV) + 14.O(FM) + 7.5(UW) + 6.0(UB) + O.O(US) + l.O(UV) + O.O(UM) + 44.O(DW) + 43.O(DB) + 38.O(DS) + 46.O(DV) + 51.5(DM) + O.O(U) + O.O(D)

Z = O.O(RW)

2.5(FB)

(6.15) where t h e terms

brackets represent

in

the

f l o w of

water

from

a

specific

source ( f i r s t l e t t e r ) to a s p e c i f i c demand (second l e t t e r ) a n d c o n s t i t u t e t h e The term U and D r e p r e s e n t the

unknowns. Desalinated

wastewater

respectively.

yields of

Consequently

the

they

wastewater have

zero

and cost

c o e f f i c i e n t s a n d a r e a l s o unknown. The o b j e c t i v e

2 must b e m i n i m i z e d s u b j e c t

function

to

the

following

l i n e a r constraints.

Source C o n s t r a i n t s :-

RW

+

RB

+ RS

t

R V t RM 5 100.0

FW + FB + FS + FV + FM = UW

+

(6.17)

+ UV + UM

=

U

(6.18)

+ DS + DV + DM

=

D

(6.19)

UB + US

DW + DB

(6.16)

11.5

Demand C o n s t r a i n t s : R W + FW + UW + DW

+ DB

RB + FB + UB RS + FS

+ US + DS

103.8 =

=

R V + FV + UV + DV =

RM + FM + UM + DM =

( f r o m 6.14)

(6.20)

7.0

(6.21)

9.5

(6.22)

0.7

(6.23)

0.5

(6.24)

Quality Constraints:500 R W 500 RB

+ +

600 600

500 RS + 600

+ FW + 1750 UW + 175 DW I 103.8 (1750) FB + 1750 UB + 175 DB 5 7.0 (1750)

+ +

FS + 1750 US + 175 DS

5 9.5

( 700)

+ 600 + FV + 1750 UV + 175 DV 5 0.7 ( 700) 0.5 ( 700) 500 RM + 600 + FM + 1750 UM + 175 DM 5

500 RV

(6.25) (6.26) (6.27) (6.28) (6.29)

89

B I end i n g Constraints:U

+ 1.45 D

= 10 ( from 6 . 1 0 )

( 6 .3 0 )

Non-nega t i v i t y constra i n ts:-

A l l unknowns It

is

(6.31 )

0

necessary

convert

to

unknowns on the r i g h t h a n d side.

UW + UB

DW

+

DB

The

+ US + UV + + DS + DV + set

optimized,

of

6.19

and

to

a

form

DM

-

(Eq.

no

Hence:

(6.32)

D = 0

subject to the objective

(6.33) 6.16,

6.17

6.20

and

f u n c t i o n of

Eq.

6.15,

to

6.33

can

be

u s i n g the manual

Since the r e s u l t a n t m a t r i x i s r a t h e r l a r g e ,

a computer

programme to solve I i n e a r programming problems b y the Simplex i s preferred.

with

UM - U = 0

constraints

Simplex Technique.

6.18

Eq.

Technique

The f o l l o w i n g i s noted :

a ) D i a g r a m m a t i c a l l y the solutions i s as i n d i c a t e d i n F i g . 6 . 3

b ) The

water

obtained

consequently

from

the

water

board

a l l o c a t e d to waste as slack.

is

not

This

is

required, interpreted

and

is

to mean

that i s i s not necessary to o b t a i n water from the water b o a r d . c ) Most

of

the

wastewater

ground

water

i s allocated

system

1

and

most

of

the

i s a l l o c a t e d to the t r a n s f e r .

I

/f

Optimal solution programming

WASTE

J

1750mg/L

/

11 .5MP/d

Fig. 6.3

to

to

the

distribution

problems

using

linear

90 The amount of water zero.

d r a w n from the d e s a l i n a t e d

T h i s implies t h a t no d e s a l i n a t i o n

being able

to

optimize

this

wastewater

i s required.

variable

is

source

is

The importance o f

enhanced

by

comparing

the

change in the values of the o b j e c t i v e f u n c t i o n . The

v a l u e of

the o b j e c t i v e

$453/day

compared

Solution,

solely

function

with

the

a

result

as

i s now

$1043/day,

Transportation of

allowing

a

decrease

of

Programming

Extended

an

variable

unknown

desal i n a t ion f r a c t i o n to be opt imized. The optimum solution

was reached,

unknowns were n e g a t i v e o r zero. function

would

occur

if

groundwater

to

$lO/day/unit

of water.

water,

waste.

i f water was

transfer.

TABLE 6.5

Table 6.5

a

The

since a l l

the shadow v a l u e s of

The

lowest

increase

of

water

was

unit cost

would

The highest

increase

in the o b j e c t i v e

allocated by

the

c/m'

or

increase would be $336/day/unit

a l l o c a t e d from

the d e s a l i n a t e d

wastewater

to

of the

summarizes the shadow values in ascending o r d e r .

DEMAND

SHADOW VALUE ( $ / d a y /un i t

Groundwater

Waste

10

Water Board

Transfer

15

Desal.

waste

System 2

225

Water Board

System 2

238

System 3

242

System 1

244

System 1

257

System 3

280

Desal.

Ww

Water Board Desa I.

WW

Water Board Desa I.

WW

Waste

331

Desa I.

WW

Transfer

336

g ) The assumption that cost i s l i n e a r l y r e l a t e d to feed flow Hence the r e s u l t s o b t a i n e d a r e not a ' t r u e '

the expected assumed,

from

1

only

Shadow v a l u e s of empty c e l l s u s i n g l i n e a r programming.

SOURCE

correct.

the

feed

and

assumptions

flow

hence

r a t e s from a

cost

( a n d consequently

was of

b y the comparisons i n Table 6.6.

each

source

derived. the cost

I t may,

overestimates cancel the underestimates.

to

The

each

demand

are

not

Initially,

inaccuracies

coefficients) however,

is clearly

optimum.

of

were the

borne o u t

be a r g u e d t h a t

the

91

TABLE 6.6

Errors

incurred

by

using

linear

cost

functions

instead

of

non-l i n e a r cost functions.

SOURCE

ASSUMED FLOWS OPT I MUM FLOWS AND CORRESPONDING FROM FIG. 6.3 COSTS AND CORRESPONDING COSTS

DEMAND

FLOW

COST

(Ml/d)

(c/m’)

FLOW

PERCENTAGE DIFFERENCE IN COSTS

COST

(Ml/d)

(c/m3 1

(c/m’)

Groundwater

System 1

3.0

3.0

8.7

1.6

47%

Wastewater

Waste

2.0

7.5

3.8

5.2

31 %

Wastewater

Transfer

2.0

6.0

5.3

4.5

25%

Groundwater

Transfer

5.0

2.5

1.7

3.1

-24%

THE

LINEAR

PROGRAMM ING

TECHN IQUE

WITH

PROGRAMM I NG

SEPARABLE

APPL I ED

The

assumption

function,

has

programming, programming, been

could

be

curve.

cost

throughout

transportation

that

the

function, the

and

discussion

programming

assumption

g r a p h s and t h a t employed

to

approximates n o n - l i n e a r accuracy

linear

made

depends on

in fact

avoid

on

onerous

by

of

objective

transportation and

Iinear

I t has consistently the

nature

of

the

the technique of s e p a r a b l e programming

this

functions

the

is

hence

extended

a n d the a p p l i c a t i o n of these techniques.

mentioned

cost-flow

a

of

been

assumption.

Separable

Programming

b y piecewise l i n e a r approximations.

d e v i a t i o n of

the

For non convex separable functions,

linear as

a p p r o x i m a t i o n from

i n t h i s case,

The the

the technique

does not guarantee a g l o b a l optimum. This

section

employs

the

separable

conjunction w i t h l i n e a r programming, mathematical model of

the system

f o r the objective function.

programming

to p r o v i d e a n o p t i m a l

technique,

in

solution.

The

i s described in the next section,

except

92 T h e model i s thus expressed as below:Minimize the o b j e c t i v e f u n c t i o n Z

subject

to

the

l i n e a r o r piecewise

linear

constraints

Z =

CRW

CRB t CRS

f

CRV

f

CRM

f

+ CFW

f

CFB + CFS

f

CFV

+ CUW

f

CUB + CUS

f

CUV + CUM

t

CDB

+

f

CDW

where CXY demand

Y

CDS

t

represents in

the

separable programming.

+

CDV total

dollars/day,

CFM

f

CDM

(6.34)

cost of

and

supplying

represents

water

a

DJXY represents the J t h

from

functional increment

source

X

equation

D or

to of

S f o r the

XY combination. CRW

=

CRB =

0 0

CRS = 117 DORS + 107 D l R S

+ 223 D2RS + 565 D3RS

1658 D4RS

f

CRV = 124 DORV + 108 D l R V t 227 D2RV + 565 D3RV

CFW =

37 DOFW +

25 D l F W

CFB =

13 DOFB +

19 D l F B +

4 0 D2FB +

CFS =

42 DOFS

20 D l F S +

24 D2FS

CFV =

4 9 DOFV t

22 D l F V

CFM =

42 DOFM +

20 D l F M

f

CUW =

6 2 DOUW +

38 DlUW

CUB =

42 DOUB

+

34 D l U B

cus

=

52 D2FW

f

f

1670 D4RV

f

CRM = 117 DORM + 107 D l R M + 223 DZRM + 565 D3RM

1658 D4RM

f

113 D3FW

+

80 D3FB +

+

29 D3FS

351 D4FW 156 D4FB

+

89 D4FS

t

26 D2FV +

30 D3FV +

+ + +

+ 89 D4FM 64 D2UW f 131 D3UW + 407 D4UW 5 7 DZUB + 109 D3UB + 236 D4UB 24 D2FM

f

29 D3FM

2 D2UV

f

3 D3UV

101 D4FV

0

CUV =

4 DOUV +

CUM =

0

CDW = 251 DODW CDB = 231 DODB

+ +

1 DlUV

229 DlDW 227 D l D B

f

+

6 D4UV

+ 583 D2DW + 1594 D2DW + 4595 D4DW + 574 DZDB + 1572 D3DB + 4424 D4DB

+ 1464 D3DS + 4287 D4DS + 1466 D3DV + 4194 D4DV 189 DODM + 193 D l D M + 517 D2DM f 1464 D3DM + 4287 D4DM

CDS = 189 DODS + 193 D l D S + 517 D2DS CDV = 193 DODV CDM =

+

194 D l D V

+

519 DZDV

(6.35) subject to source c o n s t r a i n t s 6.16, demand c o n s t r a i n t s 6.20

to 6.24,

qua1 i ty c o n s t r a i n t s 6.25

to 6.29,

6.17,

6.32

a n d 6.33,

b I end in g c o n s t r a i n t s 6.30, U

+

1.45 D = 10

Non-nega t i v i t y c o n s t r a i n t s , adjacent c o n s t r a i n t s f o r separable v a r i a b l e s : -

(6.30)

93

I f a n y DJXY i s non-zero, the v a l u e 1 ,

all

DJXY values

t h e preceding

must

take

on

and a l l the succeeding DJXY values must take the v a l u e 0.

where

RS

+

DORS + 0.6 DlRS

= 0.3

R V = 0.3 DORV t 0.6

+ 4.5 D3RS + 13 D4RS

1.6 D2RS

DlRV + 1.6 DZRV + 4.5

D3RV + 13 D4RV

RM = 0.3 DORM + 0.6 DlRM + 1.6 DZRM + 4.5

D3RM + 13 D4RN

+ 1.6 DZFW + 4.5 D3FW + 13 D4FW + 0.6 D l F B + 1.6 D2FB + 4.5 D3FB + 13 D4FB

FW = 0.3 DOFW + 0.6 DlFW FB = 0.3

DOFB

FS = 0.3 DOFS + 0.6

+

D l F S + 1.6 D2FS

DOFV + 0.6 D l F V + 1.6 DZFV

FV = 0.3

D3FS + 13 D4FS

4.5 4.5

.t

D3FV + 13 D4FV

+ 4.5 D3FM + 13 D4FM DlUW + 1.6 DZUW + 4.5 D3UW + 13 D4UW D l U B + 1.6 DZUB + 4.5 D3UB + 13 D4UB DlUV + 1.6 DZUV + 4.5 D3UV + 13 D4UV DlDW + 1.6 DZDW + 4.5 D3DW + 13 D4DW D l D B + 1.6 DZDB + 4.5 D3DB + 13 D4DB DlDS + 1.6 DZDS + 4.5 D3DS + 13 D4DS DlDV + 1.6 DZDV + 4.5 D3DV + 13 D4DV DlDM + 1.6 DZDM + 4.5 D3DM + 13 D4DM

FM = 0.3 DOFM + 0.6 D l F M + 1.6 DPFM UW = 0.3 DOUW

+

UB = 0.3

DOUB

+ 0.6

UV = 0.3

DOUV + 0.6

0.6

DW = 0.3 DODW + 0.6 DB = 0.3 DODB t 0.6 DS = 0.3 DODS + 0.6 DV = 0.3 DODV + 0.6 DM = 0.3 DODM + 0.6

(6.36) and where XY represents the unknown q u a n t i t y from source X to demand Y.

linear

programming

solution

was

Extended/370

in

obtained

(MPSX/370)

the

i n t o 6.34

equations,

conjunction using

supplied

represents the

.

S u b s t i t u t i n g the set of equations of 6.35 a s independent

i n MP/d,

i n 6.36

These set of equations

g r i d equa t ions of sepa r a b I e programm i n g

of equations of 6.36

of water

with

IBM

a n d r e t a i n i n g the set

the system

separable

Mathematical

i s solved u s i n g

programming. Programming

The

System

Software Package.

I n o r d e r to ensure the solution obtained

i s close to a

global

optimum

(as opposed to a local optimum) i t i s necessary to complete two computer runs.

The f i r s t ,

XSETLB = -1

with

after

the

the

control

programme,

l i n e BCDOUT

programming f o r non-convex

in

separable functions,

guarantee a g l o b a l optimum.

The reader

the

the control

second

the

information.

line

Separable

as in t h i s case,

i s r e f e r r e d to

Program Reference Manual (1976) f o r f u r t h e r

with

programme.

does not

the MPSX/370

IBM

The s a l i e n t r e s u l t s

and conclusions apear below: a ) Diagrammatically b ) The

100 MP/d

lOMP/d

is

returned.

t h e solution i s i n d i c a t e d below i n F i g . 6.4.

taken

assumed

from to

the

have

water

been

board

taken

is

from

in the

fact

not

board,

Hence the s u p p l y from the b o a r d i s also optimized.

used. it

is

If all

94

F i g . 6.4

Optimal

solution

using

l i n e a r programming

conjunction

in

with

separable programming

Most of

the

wastewater

ground

water

i s allocated

and

most

the

of

i s transferred.

The amount of water d r a w n from d e s a l i n a t e d implies that

no d e s a l i n a t i o n

the abundance of f a i r l y mg/e.

1

to system

i s required.

wastewater

The m a i n

good q u a l i t y g r o u n d water

I n t h i s case the acceptable s t a n d a r d of

i s zero.

reason f o r

This

this

w i t h a TDS of

700 mg/e

i s only

is 600

just

above the q u a l i t y of the groundwater s u p p l y . The

v a l u e of

$352/day

the o b j e c t i v e

compared

about solely

with

as a r e s u l t

function

the of

linear the

is

now

$691/day,

programming

i n t r o d u c t i o n of

a

solution.

decrease This

of

comes

a more r e p r e s e n t a t i v e

cost f u n c t i o n , u s i n g separable programming. Since

the o b j e c t i v e f u n c t i o n

obtained

is

not

necessarily

i s of the

the

non-convex

global

optimum.

type, When

the

solution

using

the

95

XSETLB=-1 command

( s e a r c h i n g from

lower

bound to u p p e r

v a l u e of the o b j e c t i v e f u n c t i o n was $714/d.

bound)

the

When d e l e t i n g t h i s command

( s e a r c h i n g from upper bound to lower b o u n d ) the v a l u e was reduced to $691/d.

Fig.

6.5

i n d i c a t e s the

$691/d

is

still

a

local

optimum.

The

g l o b a l optimum i s around $650/d. g ) There

is

no

difference

in

allocation

between

this

solution,

and

the

solution u s i n g l i n e a r programming ( w i t h o u t a n o n - l i n e a r cost f u n c t i o n ) .

h ) The accuracy optimum.

It

of

i s w i t h i n 5% -

the solution

would

be

improved

by

a

10% of

refinement

the of

true

the

global

grid

and

f u n c t i o n a l equations w i t h i n the v i c i n i t y of the c u r r e n t a l l o c a t i o n s .

S e n s i t i v i t y Study f o r v a r i o u s acceptable TDS v a l u e s

The case studies presented were based on a n acceptable Total Solids ( T D S ) of 700 mg/P System 3.

It

for

i s necessary

water

to

used on

examine

the

1,

System

the

optimal

Dissolved

System 2 a n d

solutions

for

various

possible acceptable TDS values i n o r d e r to e s t a b l i s h the best q u a l i t y .

This

would lead to the establishment of an optimum TDS value,

total

in terms of

combined costs, r e q u i r e d a t the demand zones mentioned above. here i s between 500 mg/O

The r a n g e of acceptable TDS values examined and 1200 m g / P closer

steps

i n discrete steps of 50 mg/O from 600 mg/P upwards, between

500

mg/O

and

r e q u i r e d to the mathematical model

mg/e.

i n Eq.

the e x i s t i n g system,

i g n o r i n g a l l q u a l i t y aspects.

to Eq.

presents the optimal

The

only

i s the s u b s t i t u t i o n of

values f o r 700 mg/P

Table 6.7

6.27

600

6.29.

water of

in

the r e l e v a n t TDS

Results a r e

a l l o c a t i o n of

and

modification

also

water

given

from

for

each

source to each demand,

the amount of wastewater used a n d the amount of

desalinated wastewater.

I t also

or

local

optimum,

and

shows

i n d i c a t e s whether the s o l u t i o n i s a g l o b a l the

value

of

the

objective

function

for

v a r i o u s selected TDS values. Fig.

6.5

procuring,

indicates desalinating

graphically and

the

variation

distributing

for

in

the

various

total

cost

acceptable

of TDS

values. From Table 6.7 a n d F i g . 6.5

the f o l l o w i n g conclusions a r e a p p a r e n t :

a ) The g r a p h i s c h a r a c t e r i z e d b y two p a r t s :

one w i t h acceptable q u a l i t i e s

g r e a t e r than 600 mg/e a n d the other w i t h q u a l i t i e s less t h a n 600 mg/O. The former has a f l a t slope of 0.2, l a r g e TDS

increases.

reverse tendency.

The

latter

i n d i c a t i n g small cost decreases f o r

has

a

slope

of

8.5,

displaying

the

96

TABLE

6.7

Comparison of optimal solutions f o r v a r i o u s TDS v a l u e s

RW 0.651

RB

4.339

3.409

2.661

3;591

7.000

RS RV RM 4.522

3.318

FW

2.059

FB

0.800

1.730

7,000

FS

7.265

8.382

9.500

8.674

7.848

7.022

6.196

FV

0.535

0.618

0.700

0.639

0.578

0.517

0.467

FM

0.382

0.441

0.500

0.457

0.413

0.370

0.326

3.326

3.800

3.800

8.139

7.209

6.278

4.941

6.200

uw UB

6.349

3.800

0.700

5.270

us uv

0.826

1.651

2.478

3.304

8.800

0.061

0.122

0.183

0.243

0.700

UM

0.043

0.087

0.130

0.174

0.500

10.000

10.000

10 .ooo

10.000

DW DB

DS

2.235

1.118

DV

0.165

0.082

DM

0.118

0.059

U

6.349

8.175

D

2.518

1.259

10.000

TYPE G L O B A L G L O B A L G L O B A L

.

OBJ. FN 1573 (R/d)

1213

698

LOCAL

691

GLOBAL

633

GLOBAL

LOCAL

GLOBAL

61 2

64 9

359

97

I1

1

FIG. 6.5

V A R I A T I O N I N T O T A L COST FOR

V A R I O U S A C C E P T A B L E TOS V A L U E S

LLL 1 6

u 7

800

900

1000

TOTAL D I S S O L V E D S O L I D S (mg/e)

1100

1200

The a b r u p t change in slope a t 600 mg/e p r o c u r i n g Desalinated wastewater water of

improved q u a l i t y

d e s a l i n a t i o n incrases,

for

i s a r e s u l t of the necessity f o r

lower

i s required,

acceptable

the amount

a n d consequently

TDS values.

of

water

As

requiring

1,

the a l l o c a t i o n s to System

2

and 3 increase. The p r e v i o u s argument v a l i d a t e s the selection of reach,

slightly

to the r i g h t of 600 m g / t .

a

quality

The exact

within

quality

the

would

be

Each successive increase i n acceptable TDS should cause a decrease

in

determined a f t e r a g r a p h was d r a w n .

the t o t a l least-cost. Not a l l the successive TDS increases manifest a decreased cost f o r p r e v i o u s TDS.

This

o b j e c t i v e function. t h a t 700 mg/4, they

not

do

occurs

as

However,

on

a

result

of

inspection

the of

non-convex

Fig.

6.5,

it

is

evident

1000 mg/e a n d 1100 mg/e a r e in f a c t local optima, follow

the

produced i n Table 6.7

expected

trend.

Consequently

the

f o r these TDS v a l u e s a r e also not

These problems may be overcome be p e r f o r m i n g a

the

separable

since

allocations

true

sensitivity

optima.

analysis,

o r p o s s i b l y b y r e v i s i n g the g r i d a n d f u n c t i o n a l equations. The absolute completely.

lowest cost The

occurs

resulting

when

cost

is

all

quality

$359/d,

a

aspects a r e

decrease

of

ignored

$34/d

in

comparison w i t h the s o l u t i o n u s i n g t r a n s p o r t a t ion programming a lone. Trends of

increases,

decreases a n d changes i n a l l o c a t i o n s as

v a r i e s a r e e v i d e n t from Table 6.6.

1)

An

increase

in

allocation

the TDS

Two t y p i c a l forms are: from

500

mg/Q

to

600

mg/e

and

a

decrease thereafter - Groundwater to System 1 . 2)

No

allocation

thereafter Most of

-

until

after

600

mg/e

and

a

steady

increase

Wastewater to System 2 .

the groundwater

is

allocated

to

System

1,

and

most

of

the

wastewater t r a n s f e r r e d a t low TDS values d i s c h a r a g e d to waste.

REFERENCES

Dantzig, G.B., 1963. L i n e a r Programming a n d Extensions. P r i n c e t o n U n i v . Press, Princeton. Grosman, D.D., 1981. Optimum a l l o c a t i o n of mine s e r v i c e water subject to q u a l i t y c o n s t r a i n t s . C i v i l Eng. in S.A. Lcomba, N.P., 1964. L i n e a r Programming. McGraw-Hill, NY. Stephenson, D., 1969. Optimum allocation of water resources by mathematical programming. J . H y d r o l . 9, 20-33. Stephenson, D., 1978. Optimum p l a n n i n g of r e g i o n a l waste water treatment. I n : Modelling the Water Q u a l i t y of the H y d r o l o g i c a l Cycle (Proc. Baden Symp., September 1978), 351-360. IAHS P u b l . No. 125. Stephenson, D., 1982. Optimum a l l o c a t i o n o f water resources subject t o q u a l i t y c o n s t r a i n t s . Proc. Exeter Symp. IAHS, P u b l i c . 135, 299-305

99

CHAPTER 7

ECONOMICS OF DESALINATION OF WASTEWATERS

I NTRODUCT ION

M u n i c i p a l wastewater

i s generally

and to n e u t r a l i s e the b i o l o g i c a l

treated

activity.

to remove suspended

It

i s disinfected and

innocuous before b e i n g discharged i n t o streams. water

however,

is,

not

affected

noticeably

The m i n e r a l content of

by

treatment

either

wastewater treatment works a n d a t the water p u r i f i c a t i o n works. o n l y i s there a m i n e r a l b u i l d - u p and

to some extent

contributed

to

by

domestic natural

phosphates and other

in the water

pollution, sources.

nutrient

but

in

the

at

the

Thus not

due to i n d u s t r i a l p o l l u t i o n

also

Thus

matter

rendered

this

mineral

addition

m i n e r a l s coming from

to

the

content

the

is

nitrates,

residential

type

areas, we also h a v e n a t u r a l m i n e r a l s such as calcium a n d s u l p h a t e b e i n g contributed dissolved

to

the

solids

system

thus

from

stormwater

discharged

by

runoff.

wastewater

The

works

total into

mass the

of

rivers

averages m i l l i o n s of tons p e r day. The magnitude of the problem of removing the dissolved m i n e r a l s i n the water

i s enormous.

There

reuse of t h i s wastewater.

a r e many

options

open,

however,

for

optimum

Some of the p o s s i b i l i t i e s a r e suggested below:

ALTERNATIVES FOR OPTIMAL REUSE OF WASTE WATER

Present p o l i c y for many affected water s u p p l i e s i s e f f e c t i v e l y

to d i l u t e

p a r t l y treated and r e t u r n e d wastewaters w i t h f r e s h water from r i v e r s a n d other

upstream

acceptable according concern.

sources.

limit, to

for

world

Provided

example health

500

that

the

mg/e

organisation

per

some of

the

wastewater

then

there

where

Alternative

other to t h i s

of f u r t h e r sources of f r e s h water (Stephenson a n d Corbetis, I t may be more p r u d e n t less c a p i t a l capital use

i s thought

steady

of

then

at

an

solids

is

little

in future users

will

i s the use

1984).

to adopt more o p e r a t i n g i n t e n s i v e schemes a n d

intensive schemes i n the l i g h t

i n t e n s i v e water

is

dissolved

i t may be necessary

downstream

have s i m i l a r o r more concentrated problems.

quality total

standards,

I n o r d e r to achieve t h i s d i l u t i o n ,

to discharge

water litre

supply

schemes.

high capital

economic

risks

,In p a r t i c u l a r

where

cost

of

schemes should

base load s u p p l y b a s i s whereas o p e r a t i n g

g e n e r a l l y be reserved f o r times of drought

be

involved

in

conjunctive used

on

a

i n t e n s i v e schemes would

i n s u r f a c e resources which a r e

100

Clarlflcatloi

Grit 500

Sand

50

10 1

0.1

Silt 0,Ol

SAND

FILTERS

Clay

0.00

EVAPORATION

Collolc

R E V E R S E OSMOSIS ,001

-

0001

I 1

F i g . 7.1

I 10

100

1000

10000

too

Selection of p u r i f i c a t i o n method based on water q u a l i t y

101

capital

intensive.

operative

intensive

procedures highly

Demineralisation than

those

i.e.

operating

and

surface

suitable

intensive

resources

for

as

desalination

development.

of

desalination

they

use

processes

large

sea

are

more

Desalination

water

are

of

power,

amounts

often for

example d i s t i l l a t i o n processes. On the o t h e r h a n d the t o t a l d i s s o l v e d s o l i d s content

of

sea

i s n e a r l y 35 000

water

t a l k i n g of dissolved s o l i d s contents of

mg/t

per

litre,

whereas

1 000 mg/P

less than

we

per

are

Iitre

in

into aquifers

is

wastewaters f o r a r t i f i c i a l recharge of g r o u n d water a q u i f e r s . The p o s s i b i l i t y of now

under

l i m i t e d treatment

consideration.

It

is

before d i s c h a r g i n g

possible

that

by

trickling

the

water

t h r o u g h the a q u i f e r s there w i l l b e n a t u r a l a e r a t i o n which would reduce the b i o l o g i c a l oxygen demand as well as p r o v i d e a degree of f i l t r a t i o n great

interest,

natural

n e u t r a l i s a t i o n of wastewaters

ion

some of

exchange

resulting

the dissolved

c o u l d be discharged

to

in

or

Alternatively,

the

s o l i d s content.

lower

levels o f

a n d of

demineralisation

the a c q u i f e r

thereby

l i f t i n g the fresher waters which have seeped there b y n a t u r a l means such as from r a i n w a t e r and i n f i l t r a t i o n from surface streams. Not o n l y

will

this

t y p e of

artificial

recharge

r e d u c i n g pumping costs b y keeping a h i g h water

have the a d v a n t a g e of table,

but

it

may

solve the problem of dewatering of dolomitic compartments which to geotechnical collapse

and

problems. dire

Previous

consequences

dewatering in

also

is linked

exercises have r e s u l t e d

residential

areas

and

at

in

mining

development so p a r t i e s concerned would be nervous about d e w a t e r i n g even i f o n l y i n t e r m i t t e n t l y to s u p p l y i n times of drought. Other

possibilities

particular

areas

possibility

of

to

include other

minimal

the

selected

if

treatment

local

recycling

In

areas. water

is

of

this

used

wastewater way

for

from

there

is

successive

a

lower

q u a l i t y - r e q u i r i n g uses. Yet another p o s s i b i l i t y i s the r e c y c l i n g w i t h f r e s h water pumped from r i v e r s

instead of

pumping costs a n d p i p i n g costs,

the n a t u r a l

as well

recycling.

as storage costs,

In

this

way

would be saved

f o r the water would be recycled a n d not have to be pumped.

SELECT ION OF OPT I MUM DESAL I NAT ION METHODS

Although h i g h d e s a l i n a t i o n costs a r e a deterrent desalination

for

water

supply,

considerably

more economic

than

an may

optimised first

to the general

system

appear.

The

may

in

location,

use of

fact

be

scale,

type and a d a p t a b i l i t y of a d e s a l i n a t i o n o r d e m i n e r a l i s a t i o n p l a n t can a l l be p u t to use i n r e d u c i n g t o t a l water costs. d e s a l i n a t i o n p l a n t may a v o i d the

Thus the location o f

necessity of

d i s p o s i n g of

in-house

effluents

into

102

collecting

sewers,

then

through

and

pumping

costs

Distribution

municipal are

wastewater

thereby

partly

treatment

reduced,

works.

w h i c h offset

d e s a l i n a t i o n costs. Studies f o r optimum location of d e s a l i n a t i o n p l a n t s have been conducted with the

the

assistance

reticulation

of

computer

system

and

simulation

alternative

programmes.

locations

for

The

depiction

desalination

p l u s a n a l y s i s h a v e p r o v e d t h a t such p l a n t s c a n be economically There may be s a v i n g s plants are

underground.

water

piping

and

pumping

in

There

costs.

is

costs

in

also

the

Desalination

has

c o n s i d e r a b l y b e t t e r water q u a l i t y

than

the

further

costs

of

imp1 i c a t i o n s

in

reducing

particular saving also

for

in

been

use of

heads

purchase

river

corrosion

installed.

high

shown

of

to

if

raw

give

water.

and

of

plants

This

a

has

deterioration

to

pipework due to other chemical a c t i v i t i e s such as s c a l i n g . The method of cost of energy.

d e s a l i n a t i o n may also depend to a

Whereas

l a r g e amounts of energy and a r e therefore fired

boilers,

low

energy

consumption

f r e q u e n t l y use e l e c t r i c i t y

from the g r i d systems. of

oil-from-coal more

for

heat

the

desalination

exchange

type

water

distribution may

methods.

before

prove

of most

sending ice

such

as

on

the

require

reverse

There a r e many

or

l a r g e amounts of

evaporation

Some mines c h i l l

contemplated

freezing

form

systems generate

suitable

cooling. even

some

extent

n o r m a l l y u n d e r t a k e n u s i n g coal

systems

which

have

large

d e s a l i n a t i o n methods such as e v a p o r a t i o n

heat

Some

and

Thus may

industries

The

In

such

vapour

be

require

underground and

underground.

viable.

industries

generation.

s u r p l u s heat

it

osmosis

have cases

compression

method i s also r e c e i v i n g close a t t e n t i o n i n t e r n a t i o n a l l y a t the moment. The scale of

the d e s a l i n a t i o n p l a n t a n d the q u a l i t y of

the

raw

h a v e a considerable effect on the optimum method of d e s a l i n a t i o n . size of p l a n t w i l l

water

Scale o r

i n f l u e n c e the o p e r a t i n g costs a n d these can be expected

to reduce the l a r g e r p l a n t a n d c a p i t a l costs such a s housing w i l l

reduce

p e r k i l o l i t r e of water t r e a t e d the l a r g e r the p l a n t . For low total dissolved sol i d s contents membrane-type

processes such a s

reverse osmosis a n d e l e c t r o d i a l y s i s h a v e p r o v e d most economical.

For very

low

problems

concentrations

ion exchange

i s economical.

There

a r e many

associated w i t h the membrane t y p e processes in p a r t i c u l a r where there i s a h i g h s u l p h a t e content. the c r y s t a l i s a t i o n dissolved a l s o effect

of

I n such cases seeded the

sulphates

s o l i d s in suspension. the f i n a l

on

The number o f stages

water q u a l i t y .

The

cost

removed may be a minimum f o r one p a r t i c u l a r k i l o l i t r e treated,

systems h a v e often p r e v e n t e d

the membrane a n d

per

in

ton of

kept such

the

dissolved

method whereas

total

p l a n t s cai solid

the cost pel

i f one i s not concerned w i t h the amount of s a l t s removed

103 F i g u r e s 7.7

may be cheaper f o r another system.

a n d 7.8

compare the costs

on these b a s i s f o r d i f f e r e n t methods. Multi-stage

demineralisation

applications. methods

are

brought

to

Thus

if

a

usually a

low

the

total

is

possible

that

most

Iitre,

also

water

be

suitable

is

quality

efficient

dissolved

than 10 m i l l i g r a m s per

It

may

high

and

solids

the

stages

final

particular multi-stage

effluent

concentration,

most economically

succession

for

required,

for

can

be

example,

less

t h r o u g h successive stages.

employ

different

techniques

e.g.

reverse osmosis coupled w i t h ion exchange. The

dispossl

of

the

brine

demineralisation

of

the b r i n e i s

l i t t l e concern

sea,

this

of

i s not

waste

the

most d e s i r a b l e that even

possibly

cost of

case

transport

in

where

also

a

Whereas the

problem

the

case of

the

brine

and

cases the b r i n e may

form

the cost of

disposal

be

to

to

of

sites

it

p l a n t s on

disposed

if

This

it

is

stored.

t h r o u g h successive

is

and

minimises

the

In

such

stages of

would b e designed d i f f e r e n t l y

stages

the

It

of.

h i g h concentration

inland.

have to be concentrated

the p l a n t . These concentration

of

desalination

has

before disposal

comes

concentration

when

volume

the b r i n e be b r o u g h t to a v e r y

solids

to

is

waters.

the

to

e f f l u e n t p u r i f i c a t i o n stages a n d may work on a d i f f e r e n t process a g a i n . Heat exchange p l a y s a n processes.

important

in the o p e r a t i n g costs of many

part

Thus i f e v a p o r a t i o n techniques a r e used

then

the e f f l u e n t

which

is a t a h i g h temperature can be used to heat the incoming stream to b r i n g it

to

nearly

evaporation could

be

evaporation

methods.

used

temperature. immaterial

to

In

cool

temperature

the the

case

of

i t may not

be wise

as

freezing

incoming

T h i s would be possible

but

such

stream if

in

multi-stage

processes of

the f i n a l

water

the to

ice

near

flash product

freezing

p r o d u c t temperature

i f c o l d water

i s a product

were

a s well

as

p u r e water. I t i s thus evident be

bought

practicability

in

that

the

of

desalination

form

the

of

a

be

designed

in

conjunction

costs

are

to

with

t h a n 50 cents p e r k i l o l i t r e ,

can

a s a whole.

the

be achieved.

plant In

The

plant.

d e m i n e r a l i s a t i o n process

considering the p l a n t and a l l factors

desalination

and d e m i n e r a l i s a t i o n cannot

package

of

this

only

easily

economics

and

be selected

when

The e n t i r e process must the

factory

case

effective

comparable w i t h r a w water,

if

optimum

costs

less

can be achieved.

RELEVANT D E S A L I N A T I O N METHODS

The p o t e n t i a l

for

desalination

r e s u l t there was a n increase

is

i n water

internationally

recognized

and

as

a

d e s a l i n a t i o n c a p a c i t y of 40% d u r i n g

104

the l a s t 5 years

(65% of which a r e m u l t i - s t a g e

flash distillation

seawater

p l a n t s a n d 25% reverse osmosis seawater a n d b r a c k i s h water p l a n t s ) . Membrane osmosis

was

methods

appear

restricted

y e a r ago a n d now

250000 m’/d

moving

Membrane

and

to

for

future

size p l a n t s

l a r g e scale

for

development.

brackish

plants.

water

Reverse until

Some examples

are

10 the

p l a n t in Jeddah f o r sea water treatment a n d the 400000 m’/day

p l a n t i n Yuma ( U S A ) ,

favourably

promising

small

to

f o r d e s a l i n a t i o n of d r a i n a g e .

methods

are

i n energy

scaling.

Where

competitive

consumption brine

with

as

disposal

well is

thermal as

a

processes,

susceptibility

problem

comparing

to

however

corrosion

(for

example

i n l a n d ) the cost of a d d i t i o n a l f a c i l i t i e s may d e t r a c t from the membrane processes.

I n d u s t r i a l Wastewater treatment

The

increased

research

and

costs

development

r e d u c i n g energy been

energy

work

consumption.

investigated

and

their

size of the p l a n t (Binnies,

during for

the

al I

Different

last

desalination

methods

applicability

1981; Larson,

decade

of

depends

have

directed

methods

towards

energy on

the

recovery costs

have

and

the

1979).

Some examples a r e : 1)

RO p l a n t energy can be recovered b y

installing

a

turbine

on

line

in

the ( h i g h p r e s s u r e ) b r i n e stream. 2)

Underground

installation

of

RO

plant

can

be

justified

based

on

u t i l i s a t i o n of the s t a t i c pressure instead of h i g h p r e s s u r e pumps. T h i s can be a p p l i c a b l e underground. In

the

to the m i n i n g

industry

has

it

(demineral i z a t i o n )

(USA)

plant,

production

The energy consumption costs w i l I n o r m a l l y be h i g h .

USA

for

been

suggested

domestic

and

that

where

the

RO

for

advanced

municipal

a l t e r n a t i v e f o r s o l v i n g the problems of Denver

f o r f r e s h water

water

treatment

wastewater

supply.

demineralization

is

This

is

methods the

best

is applied

included

in

iri

a

single

and

fresh

a n d i s now b e i n g contemplated elsewhere.

Reverse Osmosis

T h e n a t u r a l phenomenon

of

osmosis

occurs

water a r e separated b y a semi-permeable through when

the membrane

equilibrium

two solutions

to

dilute

i s established

the and

the

salt

water

membrane a n d f r e s h water flows

saline

i s c a l l e d osmotic pressure,

when

water.

This

water

flow

stops

p r e s s u r e d i f f e r e n c e between the

m a g n i t u d e of

which

the

depends

105 on

the s a l i n e

the s a l t

solution

solution

concentration.

greater

than

(DSS,

membrane free of s a l t

If

osmotic,

however, fresh

pressure

water

i s exerted

diffuses

through

in

the

1980).

1980; L u d w i g ,

Membrane Description

The cellulose

acetate membrane which

1 0 0 ~ thick,

approximately

approximately 0,2p

thick

of

which

in general

is currently

only

one

layer

is

active

use

is

and

is

(2000A) on top of the membrane surface w i t h the

r e s t a c t i n g as p h y s i c a l support f o r

the exerted pressure.

acts as a f i l t e r to r e t a i n the ions such as Na'

and

This t h i n

layer

Cl-.

E Iectrod ia I y s i s

I n the E l e c t r o d i a l y s i s process,

water

flows

between

alternately

placed

c a t i o n and a n i o n permeable membranes.

A

direct

electric

current

i s the

driving

force

for

the

ion

migration

through the membranes. A series of a l t e r n a t i v e c a t i o n a n d a n i o n membranes w i t h a p l a s t i c spacer between i s assembled hundred membranes

and

their

separating

i n t o membrane stacks. spacers

are

usually

Several

assembled

between a s i n g l e set of electrodes to form a membrane stack. The ion selection membranes a r e b a s i c a l l y

ion exchange r e s i n s i n sheet

90%. Normally

form w i t h s e l e c t i v i t i e s g r e a t e r

than

consists of one to s i x stages,

w i t h removal p e r stage v a r y i n g from 30

E l e c t r o d i a l y s i s systems to

60% ( n o r m a l l y 50%). Energy consumption i s based on F a r a d a y ' s Law, according

100 mg/e

removal

of

dissolved

ionised

solids

from

5m3

( D C ) a r e r e q u i r e d w i t h voltages 1 - 2 V.

amper-hours

kWh i s needed f o r

5m'

of

water

treated

in

to which f o r

of

200

water,

Therefore about 0,3

addition

to

which

2kWh

is

r e q u i r e d f o r pumping. Several

hundred

internationally

for

Electrodialysis

process

water

waters n o r m a l l y of less t h a n 3000 Reverse introduced

polarity

mg/t

(electrodialysis

commercially

to

plants

treatment

reduce

or

have

been

portable

water

i n s t a l led from

feed

has

been

salinity. reversal)

polarization

configuration and

scaling

in

the

membranes.

I o n Exchange

The ion exchange process has been used f o r many years

for

softening

106

iter

ter

'1

Fig. 7.2

10

100

1000 10 000 Product Solinity mg/l

S u i t a b l e feed s a l i n i t i e s a n d product s a l i n i t y f o r v a r i o u s d e s a l i n a t i o n processes. Recovery r a t i o s also i n d i c a t e d

100 1

107

of water and d e m i n e r a l i z a t i o n f o r v a r i o u s

i n d u s t r i a l uses.

r e s t r i c t e d to waters of not more than 1000 mg/4 The called

process zeolites

the c h a r a c t e r i s t i c

which

found

were

exchange r e s i n s have s u p e r i o r are

insoluable

solids

r e v e r s i b l e exchange Resins

normally

CP-

absorbs

with

mobile Na+

other

of

some

exchange a n d Ca

++

ions

neutral

fixed

ions of

ions

anions

cations

and

and

the other

+.

release

or

OH-;

these

+

ion

capable

in

of

solutions.

release

are

The ions release H

r e s i n s and base r e s i n s respectively.

the

be d e f i n i t i o n

sign and

for

Artificial

anions

opposite cations

minerals

suitable

f o r Na

exchange c h a r a c t e r i s t i c s a n d

containing

absorb

and

to

l i k e exchange of Mg'

i s normally

t o t a l dissolved solids.

i s based on

softening of water,

It

H+

called

a n d OH-

or

acid the

in

solution which combine to form H20. Ion exchange s a l i n i t y higher

is unlikely than

prove

to

1000 mg/4.

economical

However,

it

for

can

water

b e used

treatment

of

in c o n j u n c t i o n

w i t h a membrane process.

COST ANALYSIS

The

cost

cents/m' to take

of

desalination

of water produced. i n t o account a l l

techniques

i s often

expressed

in

terms

This approach can be m i s l e a d i n g as

the v a r i a b l e s

it

a f f e c t i n g t h e cost s t r u c t u r e .

of

fails Before

proceeding w i t h cost estimation the f o l l o w i n g parameters h a v e to be f i x e d :

1)

Product requirement,

p l a n t load f a c t o r a n d recovery.

The v a r i a b l e s affect the q u a n t i t y a n d q u a l i t y of r e l a t i o n s h i p between product the plant

operational

water

efficiency.

quantity,

Values

the f i n a l

feed

water

assumed f o r

product,

the

quantity

the cost

i n t h i s p a p e r a r e ; recovery r a t i o (Rc) 70% - 65% a n d p l a n t

and

estimate

load f a c t o r

90%.

2 ) Rate of

interest

which

for

present

purposes

is

taken

10% w i t h

as

a

redemp t ion p e r i o d of 20 years.

3)

P l a n t l i f e i s taken a t 30 years. The c a p i t a l and r u n n i n g costs a r e affected b y the above parameters.

C a p i t a l Costs

Capital development equipment

d i sposa I

.

costs

include

(roads, and

Civil

Engineering

electricity

controls

as

well

and as

water

and etc.

installation

plant

1. of

as

well

They

also

intake

as

and

site

include brine

108

I n d i r e c t C a p i t a l Costs

10 - 12% long term

interest

r a t e i s included d u r i n g p l a n t construction

a n d also labour costs w h i c h amount to 5

- 6% of the t o t a l c a p i t a l costs.

R u n n i n g Costs

Running costs a r e g e n e r a l l y d i r e c t l y p r o p o r t i o n a l and

include

energy

costs,

chemical

costs,

to p r o d u c t t h r o u g h p u t

labour

for

operation

and

ma i n tenance, membrane r e p lacemen t , o p e r a t i n g a n d maintenance costs. For

membrane

plants

100% load factor feed

water

of

it

2c/kWh.

characteristics,

is

reasonable

Chemical the

to

cost

process

assume

and used

electricity

treatment and

the

costs

cost

with

vary

with

plant's

recovery

ratio.

L a b o u r Costs

These depend on the requirements o f the p l a n t w i t h respect and

control.

also

It

depends

on

the

affects i t s maintenance l a b o u r cost.

of

reliability

the

to o p e r a t i o n

plant,

as

this

Costs g i v e n here a r e f o r p l a n t s u p to

10 000m3/day c a p a c i t y (medium s i z e ) .

Membrane Replacement

For E l e c t r o d i a l y s i s which

on

the

average

(ED)

20% of

have a

7

capital

year

cost

life.

For

is

spent

reverse

on

membranes

osmosis

treating

b r a c k i s h water the l i f e of the membrane i s o n l y 3 years. In

F i g u r e 7.3

Osmosis

include

capital

costs.

the

the

capital

site

Figure

cost

for

development

7.4

shows

both

costs,

the

Electrodialysis equipment

operating

costs

costs

and

Reverse

and

indirect

(running

i n c l u d i n g l a b o u r , energy a n d costs f o r both membrane processes. i s based upon a feed water w i t h a s a l i n i t y mg/e

costs)

This data

in the r a n g e of 1 000 t o 3 000

t o t a l dissolved sol ids.

The

capital

approximately

cost

for

$700/m3/day

the for

reverse a

osmosis

120rn3/day

$170/m3/day f o r a 10 000m3/day feed c a p a c i t y The cost a l l o w s f o r

feed

plant,

d i f f e r e n t equipment designs

process

varies

capacity

from

plant

to

based upon 3 stages.

and manufacturer's

prices

a n d s i t e costs which a r e dependent on t h e s i t e . The c a p i t a l cost

for

E l e c t r o d i a l y s i s depends

the feedwater hence the number of

stages

l a r g e l y on

involved

the s a l i n i t y

of

i n the process a s well

109

D E S R L I N R T I O N PROCESSES CFTXTRL L RUNNING co-

ro11 nLcmtornmysxs L IINLRSL

osnos~s

c

8

Fig

n \

I Fig.

7.4

Running cost versus P l a n t size (Feed) f o r ED & RO ED process RO process

(

(

-.-.d )

I10

D E S A L I N A T I O N PROCESSES ENERGY R f O U I R M W S (hl4hk) FOR CLCCTRODIRLYSIS h REVERSE OSMOSIS

Fig. 7.5

Energy Demand versus Feed Salinity for ED & RO

F i g . 7.6

Energy Demand versus P l a n t size (Prod) for ED & RO

ED

process (-.-.-

)

RO. p r o c c s d

)

111

as the p l a n t size. of

120m3/day

The costs v a r y from $760/m3/day

feed

capacity

10000m3/day feed c a p a c i t y .

a

to

$200/m3/day

f o r two 4-stage

for

2

a

I t can be seen i n F i g u r e 7.3

stage

plant

plant

of

t h a t c a p i t a l costs

f o r E l e c t r o d i a l y s i s a r e g e n e r a l l y h i g h e r than other methods. In

running

osmosis,

costs

varying

however

from

25c

electrodialysis 7c

to

as

osmosis from the same p l a n t c a p a c i t y 7.3

and 7.4

account

for

different

opposed

is

cheaper

( F i g u r e 7.5).

water

-

45c

to

than

reverse

for

reverse

in

Figures

1Oc

The costs

characteristics

and p l a n t

design

factors. water

The

temperature,

influence energy

and

pH,

turbidity,

pretreatment

costs.

suspended

Also

recovery

matter ratio

etc.

can

(Rc) v a r i e s

between 70 a n d 85% f o r E l e c t r o d i a l y s i s a n d 65 a n d 85% f o r reverse osmosis which can affect the energy requirement. The t o t a l for different

theoretical

cost of the water v a r i e s from 40c

to 20c

per

m3

size p l a n t s f o r E l e c t r o d i a l y s i s and 52c to 22c p e r m3 i n the

case of reverse osmosis (1983 f i g u r e s ) . In

Figure

7.5,

energy-consuming

it

can

be

seen

f o r a feed s a l i n i t y

that

Electrodialysis

is

r a n g e of 500 - 3 000 mg/Q.

less

This

is

due to the fact that energy demand i s d i r e c t l y p r o p o r t i o n a l to removal f o r the E l e c t r o d i a l y s i s .

The

energy

costs

account

for

different

plant

sizes,

assumed of the o r d e r of 1 000m3/day, F i g u r e 7.6 shows the v a r i a t i o n in energy requirements f o r d i f f e r e n t size p l a n t s . Energy f o r reverse osmosis changes w i t h recovery v a r y i n g from 70% to 85%. The e l e c t r o d i a l y s i s c u r v e assumes a recovery r a t i o of 75%.

CONCLUSIONS

It

is

evident

demineralization.

that

there

are

many

From

the

point

of

variables view

of

affecting the

the

costs

applicability

of

p a r t i c u l a r process and the optimum process f o r a p a r t i c u l a r a p p l i c a t i o n t h e f o l l o w i n g factors a r e r e l e v a n t :

Load factor

-

Locality

- affects power cost, construction a n d l a b o u r costs.

r e l a t e s c a p i t a l to r u n n i n g costs.

C a p i t a l cost a n d interest r a t e . Power and other o p e r a t i n g costs. TDS of r a w water. Q u a l i t y requirements f o r e f f l u e n t Method of b r i n e disposal.

of a

112

I f the costs a r e expressed a s cents p e r k i l o l i t r e , may p r o v e most economic,

i f they a r e expressed a s cents p e r

whereas

of dissolved s o l i d s removed,

of

k g of

per

membrane

and

ion

salt

removed

exchange

r e l a t e d to the amounts o f s a l t removed and they low TDS waters.

F i g u r e 7.7

however,

include scaling

There i s a tendency to use thermal methods

f o r h i g h TDS waters as the cost h a n d the cost

the incoming steam

In the case of e v a p o r a t i o n methods,

i s d i r e c t l y r e l a t e d to t h e TDS.

other

kg

another method may be optimal.

Methods r e l a t i v e l y i n s e n s i t i v e to the TDS o f the thermal methods.

one p a r t i c u l a r method

and

7.8

depict

is

low.

processes

are

therefore

the costs of

On

are lowest

different

the more for

method

p l o t t e d ( a ) versusflow r a t e a n d ( b ) versus r a t e of TDS removal. It

appears

industrial

that

wastwaters

membrane

type

(provided

Recent advances i n membranes now rates at

processes

adequate

are

most

economical

pre-treatment

is

i n c l u d e those c a p a b l e of

low pressures p r o v i d e d o n l y

limited

solids

removed

for

practical).

passing

high

i s required.

Using present d a y p r i c e s i t i s f e a s i b l e t h a t costs w i l l

be competitive w i t h

b u l k water

is

supplies from a f a r

reduced r e t i c u l a t i o n costs,

and

in

addition

there

a n d the p o s s i b i l i t i e s of use of

the

i n c e n t i v e of

the e f f l u e n t s f o r

specific a p p l i c a t i o n s o r f o r g r o u n d water recharge.

REFERENCES

B i n n i e a n d P a r t n e r s , 1981. D e s a l i n a t i o n methods a n d costs, Water Systems Research Programme, U n i v e r s i t y of the Witwatersrand. DSS Engineers Inc., 1980. Data Collection a n d A n a l y s i s of Commercial Membrane D e s a l i n a t i o n P l a n t s . 1979. D e s a l i n a t i o n of sea water a n d b r a c k i s h Larson T.J. and L e i t n e r G., water, A cost update. D e s a l i n a t i o n , 30, p525-539. L u d w i g , L., 1980. Reverse osmosis i n the d e s a l i n a t i o n of b r a c k i s h water a n d sea water, Desalination, 36, p 153-178. Stephenson, D. a n d Corbetis, S.S., 1984. Economics of D e s a l i n a t i o n of Wastewaters f o r the W i twatersrand. Water We1 I Assn. Conf. Johannesburg.

\ \

113

114

Fig. 7.8

Desalination costs per k g of dissolved solids removed as a function of f e e d s a l i n i t y , f l o w r a t e a n d method

115

CHAPTER 8

COMPUTER ANALYSIS JUSTIFIES DESALINATION

INTRODUCTION

Industry

uses

water

for

cleaning,

t r a n s p o r t amongst other purposes.

air

conditioning,

dilution

and

Water may be r e c y c l e d a n d d e t e r i o r a t e s

in q u a l i t y due to contact w i t h contaminants a n d discharges i n t o t h e system

(Holton

and

1983).

Stephenson,

The

total

dissolved

(TDS)

solids

concentration i n some waters can exceed 10000 mg/l. The

poor

pipework

water

and

refrigeration the

poor

quality

can

machinery.

plant

water

was

In

lead a

are

corrosion

particular

extremely

quality

to

severe.

the

health

and

system,

deterioration

hazard,

of

the

associated

with

corrosion

Other problems and

of

surface

effluent

discharge regulations. The problem has

been

aggravated

by

in

deterioration

surface

water

q u a l i t y over the last few years. The approach adopted resources,

can

(Stephenson,

in this

be a p p l i e d on

re-distributing

water

smaller scale f o r operating-cost

in

a much wider

to

scale

optimize than

the

economical

i n d u s t r i a l water systems.

sources

such

as

herein

way

to

discharge

The b a s i s f o r

desalination

lies

in

the

in

total,

problems

as may

the

water

be

may

reduced

as

of

described

purpose

meet

of

quality

justifying fact

that

be of the

high other costs.

a

higher

volume

of

( b r i n e ) i s c o n s i d e r a b l y less i f d e s a l i n a t i o n i s performed.

There

are

alternative

ways of

justifying

high

operating-cost

such as d e s a l i n a t i o n in comparison w i t h more conventional r i v e r water.

They l i e i n c o n j u n c t i v e use - namely

schemes to s u p p l y the base sources

the

use

namely p u m p i n g costs o r storage dam

Less water may be r e q u i r e d Effluent

most

the

I t could be a p p p l i e d on a r e g i o n a l b a s i s o r on a

costs may thereby be saved,

effluent

namely

1986). The computer program developed f o r

constraints i s universal.

quality.

study,

when

drought.

there

is

a

load,

use of c a p i t a l - i n t e n s i v e

and r e s o r t i n g to s t a n d y

shortfall

in

surface

systems

sources such as

resources

low c a p i t a l - c o s t e.g.

during

a

A l t e r n a t i v e l y d e s a l i n a t i o n could proceed on a r e g u l a r small scale,

d i s c h a r g i n g i n t o a r e s e r v o i r (e.g.

a q u i f e r ) which c o u l d be tapped i n times

of shortage elsewhere. The f i t t i n g i n o f a d e s a l i n a t i o n u n i t w i t h a system i s thus more l i k e l y to j u s t i f y from

a

desalination than a straight

plant

or

from

more

comparison

conventional

of

sources.

u n i t costs The

of

water

optimization

of

116

multi-source

systems

computer

is helpful.

analysis

can

reveal

be

balance

used.

of

builup

requires

over

at

nodes

analysis

various

Simulation

TDS

equation

careful

There a r e

time. will

ways

and

in

of

the

A

simultaneous

give

this

which

water

is

distribution

steady

where

computer

solution

system of

TDS

state

the

systems will

the

mass

loads,

and

o p t i m i z a t i o n can produce the best ( g e n e r a l l y the most economic) p l a n . The type of d e s a l i n a t i o n p l a n t most s u i t a b l e f o r a n y g i v e n system w i l l also depend on the circumstances (Stephenson a n d Corbetis, values

mentioned

demineralization processes,

e.g.

here

could

be

described

(usually

confined

reverse

osmosis,

to

as

TDS

lower

are

requiring

often

1983). The TDS desalination

water).

most

Membrane

suitable,

or type

although

freeezing d e s a l i n a t i o n i s now r e c e i v i n g a t t e n t i o n . Various attempts a t o p t i m i z i n g complex have

been

reported

(Rinaldi

al,

et

systems

1984).

In

i n v o l v i n g water general,

the

quality

problem

is

non-linear

so

little

use.

Search methods

used.

The technique described i n t h i s p a p e r i s one such method which uses

l i n e a r programming

packages

(Smeers a n d

(Loucks et

Tyteca,

known c h a r a c t e r i s t i c s o f

the system to speed

the cost

are

of

desalination

not e x p l a i n e d

studies have been r e p o r t e d ( A b u l n o u r et a l ,

1981)

al,

1967)

must

the search. in detail

are

generally

of be

The method a n d

here

although

such

1983).

APPL I C A T ION OF OPTIMIZATION O F WATER SUPPLY

The options studied,

in view

of

the poor

quality

of

the

water

on

an

i n d u s t r i a l system were:

1.

Accommodate

the

poor

quality

at

the

expense

of

higher

maintenance

costs of pipework a n d machinery.

2. Prevent d e t e r i o r a t i o n of the water a t the source o f p o l l u t i o n . 3.

Remove the TDS i n the water b y means of a d e s a l i n a t i o n p l a n t .

4.

Use g r e a t e r q u a n t i t i e s of f r e s h water.

5.

Re-distribute

the water i n a way w h i c h m a i n t a i n s h i g h e r q u a l i t y a t key

points.

Alternative 1 , was

quickly

namely c o n t i n u i n g w i t h the present

r u l e d out

pipework and machinery.

by

assessing

the

cost

of

poor

regular

quality

water,

replacement

of

Research was also i n p r o g r e s s to reduce l e a c h i n g

a t the source of p o l l u t i o n b u t no p o s i t i v e recommendations c o u l d b e made. The most economical combination of a l t e r n a t i v e s the computer program developed for the purpose.

3-5

was

investigated u s i n g

117

No.3 Shaft

Flsrure water

Mlm u r v l c a water

... . .....

-L

-. -

-----

C b r water return Ilne Carcmd. rvstem overflow F a d rate; Sludge llmr MIM wwklngs u r d water 6 nrsure water

chamber water system dam

F i g . 8.1 Section through a t y p i c a l mine

The water

d i s t r i b u t i o n system

not accurately documented. another

and

it

i s often complex

I n general,

i s collected

i n d r a i n s and

pumped

after

s e t t l i n g to remove suspended p a r t i c l e s .

dust

suppression

and

cooling.

(Stephenson,

1983) a n d

water i s p i p e d from one w o r k i n g to

Minimum

to

The water

flows

are

waste

or

recycled

may

be

used f o r

required

but

the

d i s t r i b u t i o n p a t t e r n a n d the amount r e c i r c u l a t e d o r pumped can b e v a r i e d .

118

Water from d i f f e r e n t evaporation

or

locations

draught

i s often blended.

towers

before

i s cooled

Water

refrigeration

by

an

in

spray

indirect

heat-exchange p l a n t i n c o o l i n g systems. The e v a p o r a t i o n i n the warm a r e a s as well a s i n e v a p o r a t i o n dams a g g r a v a t e s water.

F i g . 8.1

water

taken

the TDS concentration

in

the

i l l u s t r a t e s a section t h r o u g h a t y p i c a l mine w o r k i n g s w i t h

from

a

fresh

water

source

at

underground f o r cooling a t surface cooling

the

towers,

surface,

returned

from

and p a r t l y replaced b y

f r e s h water before r e c y c l i n g .

SYSTEMS ANALYSIS

One s h a f t

program

described

here.

must

equal

zero.

8.2,

reproduced

The h y d r a u l i c p r i n c i p l e

system i s the c o n t i n u i t y equation, node

in F i g .

i n the complex d i s t r i b u t i o n system depicted

be reduced to the flow d i a g r a m of F i g .

It

is

t h a t is,

possible

used

by

for

8.1

can

the computer analyzing

the

net i n f l o w minus outflow a t a n y

on

this

d i s t r i b u t i o n system out of a number of closed

basis

loops.

to close the system b y means of a dummy node i.e.

to

make

up

any

I t may be necessary

a n y loose i n p u t

to a n d

outflow from the system can be taken from o r to the dummy node.

Such a

dummy

quality

node

is

handled

differently

from

c o n s t r a i n t o r mass TDS b a l a n c e a p p l i e s to i t .

F i g . 8.2

Graphic of system a n a l y z e d

other

nodes

as

no

119

I t may be shown t h a t the minimum number of closed loops

in a network

1981):

of pipes and channels i s (Smith et a l ,

L = P - N + l where P

i s the

number

connecting N nodes.

conduits

of

Additional

loops

may be defined b y i n c l u d i n g pieces of o t h e r loops a n d the selection of

the

best loops can speed a n a l y s i s i f manual h y d r a u l i c a n a l y s i s i s performed. A n algorithm for f i n d i n g

nodes comprised p a r t of to

identify

conduits

as

flowing

s e p a r a t i n g adjacent loops, stage.

loops i n a system described o n l y

the program.

i.e.

in terms of

For p r a c t i c a l purposes i t

from

one

node

loops a r e not

to

another

i s easiest

and

not

i d e n t i f i e d a t the d a t a

as

input

The d e f i n i t i o n of loops a t d a t a i n p u t stage i s also irksome when

comes to r e v i s i n g ,

adding

flows i n t h e network,

to o r

however,

subtracting

conduits.

flows should a l w a y s b a l a n c e a t nodes.

simplest way of e n s u r i n g t h i s i s to a d j u s t

flows b y a d d i n g a flow

closed loops.

MAIN PROGRAM

SUB PROGS

~

IDENTIFY SYSTEM READ CONDUIT DATA IDENTlfY NODE CONS SEEK ML LOOPS

.

I I

I I

HYDRAULIC NETWORK ANALYSIS FOR CONDUITS I

I

I

SOLVE SIMULTANEOUS

MASS W C E TDS EOS AT ALL NODES XPT 0 ADJUST FLOW IN LOOPS IN BEST WAY UNTIL AU TDS's WITHIN LIMITS

RETC COST

F i g . 8.3

Program flow d i a g r a m

I

I

I I

TRYMTERNATNEDESM PUNT LOCATIONS AND-SCALE

it

D u r i n g r e v i s i o n of The

around

1 20

A computational a l g o r i t h m f o r loops

was

inserting

developed. dummy

The

selecting

algorithm

conduits and

nodes.

was r e q u i r e d as o n l y flow balance, nodes.

For instance,

8.3.

t h e minimum include

Special

h a n d l i n g of

closed

these

by

conduits

A flow d i a g r a m f o r the procedure i s g i v e n in

s t a r t s w i t h each p i p e in t u r n

i n the system.

flow

to bottom

(from

of

branches

not TDS b a l a n c e occurs a t some dummy

To ensure t h a t each p i p e i s i n c l u d e d in a

direction

number

unclosed

e v a p o r a t i o n can be represented a s a n e g a t i v e flow f o r

a dummy node w i t h zero TDS. Fig.

can

top

node

It

node)

loop,

proceeds from one

the procedure in

pipe

the

positive

to

another

l e a d i n g from i t . Where there i s more t h a n one p i p e e x i t i n g from a node, new

loop

i s created f o r each b r a n c h .

loop closure and then a n y p i p e s dropped.

in

At the

step not

a check in a

ignored.

A

negative

flow

from

node

i s made f o r

closed

Whenever a closed loop i s formed a check i s made,

w i t h o t h e r loops to ensure no d u p l i c a t i o n . are

each series

loop

are

pipe b y pipe,

Loops w h i c h h a v e n e g a t i v e f l o w s zero

(which

has

zero

TDS)

p r e s c r i b e d to represent e v a p o r a t i o n since node 0 i s a l w a y s a t zero TDS.

START WITH W C H PIPE IN TURN GO FROM TOP NODE TO BOTTOM OF SUCCESSIVE PIPES Where there Is a branch-off store plpedata up to branch for another loop CHECK FOR LOOP CLOSURE ELIMINATE REDUNDANT PIPES CHECK FOR LOOP DUPLICATION BY COMPARING PIPE FOR PIPE AND ELIMINATE DUPLICATES

GO BACK TO CHECK FOR BRANCH LOOPS

F i g . 8.4 Loop seeking a l g o r i t h m

a

is

121

Once a l l the loops a r e i d e n t i f i e d , a n increment i n flow i s added to one loop a t a time to determine the corresponding change in TDS a t each node

and the corresponding cost

increase.

comparison w i t h t a r g e t TDS,

i s i d e n t i f i e d a n d the

The

node

with

the

worst

TDS,

in

in TDS a t

improvement

the node p e r u n i t increment i s established.

T h i s i s repeated f o r each loop

a n d the one w i t h the maximum of d(TDS)/dC

i s selected where C i s the cost

of c i r c u l a t i o n .

The maximum necessary increase in flow i s made a r o u n d the

loop consistent w i t h

quality

constraints.

The procedure

i s repeated

until

a l l TDS's a r e w i t h i n specified l i m i t s . I t i s necessary time

an

i n the system each

to r e c a l c u l a t e TDS's a t each node

increment

is

made

to

flows

around

a

loop.

This

is

done

by

i t e r a t i n g f o r each node in succession the mass b a l a n c e equation z Q ( T + P)/YQ

T' =

flow from an upstream node to the node a t w h i c h T I

where Q i s the be determined.

and P

T i s the TDS a t the upstream node,

( o r decrease i n the case of

desalination)

of

TDS a l o n g

i s to

i s the p i c k u p

the conduit.

The

summation i s over a l l c o n d u i t s l e a d i n g to the node.

General o p t i m i z a t i o n problem

The problem to be solved can be described as follows: flow

requirements a n d maximum TDS requirements a t

network,

should

be

purchased

d e s a l i n a t i o n should flows

certain

as well as q u a l i t y of r a w water a v a i l a b l e ,

in water a t c e r t a i n p o i n t s a n d the network

in

each

objective

conduit

function

transport

per

from

to

Iitre

d e s a l i n a t i o n in c / l

the

raw

be performed? At and

quality

be minimized along

any

layout,

water

same

(TDS)

at

include

conduit,

each of

e.g.

a

what amount of water

time

cost

in

points

r a t e of d e t e r i o r a t i o n

source

the

g i v e n minimum

and the

what

node. raw

of

yields in

the

water,

Costs

cost

of

and

cost

of

pumping

f o r a l t e r n a t i v e l e v e l s of treatment (mg/l

level

program

removal).

A t r i a l a n d e r r o r process i s r e q u i r e d to e s t a b l i s h the best p o s i t i o n of the

desalination

plant

or

( p r o p o r t ion of TDS removed ) The

costs

were

a l t h o u g h non-linear

.

assumed

plants,

to

be

and

the

linearly

best

level

proportional

of

to

treatment

flow

rate

o b j e c t i v e functions could be h a n d l e d b y the program.

C a p i t a l costs of c o n d u i t s were not

i n c l u d e d a s the c o n d u i t s a l r e a d y

a n d can h a n g l e l a r g e r flows t h a n w i l l n o r m a l l y occur emergency c o n d i t i o n s ) .

Flows can be c o n t r o l l e d b y

exist

( t h e y a r e based on

valves

in

g r a v i t y lines and pumping power in the case of p u m p i n g lines.

the case of

122 PROGRAM APPL I CAT ION

The program handles

up

to

was

on

run

100

128 kb

a

conduits.

It

is

s i m u l a t i o n a n d g r a p h i c s program.

16

x

often

bit

run

m i c r o computer conjunction

in

The s i m u l a t i o n p r o g r a m a l l o w s

v a r i a t i o n in d r a w o f f s f o r meeting s p e c i f i c w a t e r demands, which

can

fluctuate

over

a

period.

It

does

not,

which with

for

a

time

a n d f o r storage

therefore,

assume

c o n t i n u i t y of flow a t nodes a n d i s useful f o r more r e f i n e d studies t h a n the o p t i m i z a t i o n program graphics

system

such

is

as

useful

r e q u i r e s co-ordinates

time

for

varying

quality

visualization

of nodes as i n p u t .

of

(see

the

8.5).

Fig.

system,

The

although

it

A common d a t a f i l e can b e used

f o r a l l programs a n d t h i s f i l e can be amended ( c o n d u i t s a l t e r e d ,

added o r

s u b t r a c t e d ) as a n a l y s i s proceeds. The o p t i m i z a t i o n p r o g r a m commences w i t h minimum flow d a t a . o n l y be increased to reduce TDS a t a n y p o i n t . p l a n t s must e.g.

be selected

i f s l i p stream

by

trial,

desalination

as

well

i s resorted

The location of d e s a l i n a t i o n

as

the

to,

level o f

it

desalination,

i s equivalent

removal. Although i t would be a simple m a t t e r to a u t o m a t i c a l l y desalination

plants

along

successive

conduits,

the

c o n s t r a i n t s l i m i t i n g d e s a l i n a t i o n p l a n t s to s p e c i f i c not

warrant

automatic

repositioning

of

Flows can

number

of

locations o r

plants.

Brine

to p a r t

investigate physical

l e v e l s does

disposal,

space

requirements and access a r e of p a r t i c u l a r concern i n mines.

0

1

2

F i g . 8 . 5 Deterioration simulation

3 of

TDS

5

4

at

a

,DAY 6

strategic

/

point

as

indicated

by

123

OPTIMIZATION O F MINE WATER SYSTEM

Mines s u f f e r from poor water q u a l i t y due to poor r i v e r q u a l i t y , concentrations of c h l o r i n e i n ground water, which

necessitates

particular

extensive

mine's

method

recycling.

of

a n d a severe shortage of water

(1985) r e p o r t e d on a

Baker-Duly

solving

large

the

problems

using

a

simulation

program. The p a r t i c u l a r mine presented as a n example of

the a p p l i c a t i o n of the

c u r r e n t o p t i m i z a t i o n p r o g r a m suffered the v a r i o u s problems out1 i n e d above. The s i m p l i f i e d system a n a l y z e d here i s depicted

i n Fig.

8.2,

r e a l mine i n v o l v e d 3 s h a f t s w i t h cross flows from one shaft the system

analyzed

2140m below surface, the

there

surface,

respectively.

lowest

level

and

and

i s one m a i n two

shaft

sub-shafts

from

down

the

the

water

water board. from

surface

In

down

to

There a r e s e t t l e r s f o r removing suspended sol i d s a t at

the

bottom o f

i s recycled

with

'fresh'

P r i o r to the study

groundwater

resulting

the

2430 and 2620m below

to

the

main

shaft.

s e t t l e r s i s d i v e r t e d i n t o sumps a n d thence pumped to of

whereas

to another.

totalled

22

23

I/s

water was

I/s

and

purchased thus

Water

higher from

purchased,

evaporation

a

the Part

regional

the makeup

amounted

i n a d i s c h a r g e to waste on the surface o f 29 I/s.

from

levels.

16

to

I/s

Owing to the

h i g h heads, cost of p u m p i n g to waste was h i g h a n d the purchase p r i c e of f r e s h water was also h i g h . making marginal

The q u a l i t y of ' f r e s h '

improvement to the system f o r

water was

in f a c t poor,

the p r i c e p a i d .

q u a l i t y was of p a r t i c u l a r concern a t the r e f r i g e r a t i o n p l a n t s , was directed s t r a i g h t to them. U n f o r t u n a t e l y , also sent to the r e f r i g e r a t i o n p l a n t s , poor q u a l i t y .

That

was

mine workings where the water h a d come i t s contamination,

and e v a p o r a t i o n a t

water

water from c o o l i n g dams was

a n d t h i s water was of

because the dams

As

f r e s h water

received

warm

i n t o contact

the w o r k i n g s

particularly

water

from

the

w i t h ore,

with

all

a n d the s p r a y i n g on

the dams had concentrated the dissolved s o l i d s even more b y e v a p o r a t i o n . T h e fact t h a t water i n the s p r a y dams was of p a r t i c u l a r l y poor q u a l i t y a n d that

i t h a d to be improved c o n s i d e r a b l y before re-use,

indicated

the

most a p p r o p r i a t e p o s i t i o n f o r a d e s a l i n a t i o n p l a n t .

RESULT OF ANALYSIS

Table 8.1 to

the

i n d i c a t e s flows a n d TDS's a t a l l p o i n t s in the system p r i o r

analysis

a n d Tables

8.2

a n d 8.3

present

the

optimum

TDS's r e s u l t i n g from the a n a l y s i s f o r the best p o s i t i o n of plant.

flows

and

the d e s a l i n a t i o n

1 24 Table quality over

8.1

was

was

obtained

arbitrarily

l i t t l e more

than

from

assumed

a

week

the

simulation

start

to

program,

500

at

to e q u i l i b r i u m

TDS's

of

where

before

mg/P

over

water

increasing

4000

mg/l

at

p I aces.

TABLE 8.1

Water Flows a n d TDS without d e s a l i n a t i o n

Cost, $/a = 1.056825E+6

~~

Pipe number

Node 2

Node 1

1 2 3 4 6 6 I 8 9 10 11 12 13 14 16 16 17 18 19 20 21 22

0 1 3 6 0 0 2 4 0 5

1 3 6 I 11 I 4 6

8 9 I 10 I 11 0

12 12 2 3

8.2

Table

4

summarizes

nodes 8 a n d 7,

(W

(will

(CPU

Equilibrium TDS (WlU

23 23 8 8 -8

800 0 0 0 0 0 0 0 1800 400 0 0 0 0 200 0 200 1800 0 0 0 0

80 0 0 0 0 0 0 0 0 0 6 0 20 0 0 0 0 0 10 60 16 0

i91 193 183 3296 4133 3296 2419 2298 2298 8180 8295 3174 8188 8138 8826 4183 3826 3138 3180 0 0 2419

-8

8 7 9 2 10 12 11 12 10 8 0 0

8

Increase TDS Cost

36 61 18 69 62 67 67 36 40 26 18 4 60 8 21 16

6

the

TDS's,

removing 1000 mg/l.

with

a

desalination

operating

cost

million/y.

I n f a c t a maximum TDS of 2000 mg/l

specified f o r

this

any re-distribution

run

a d e s a l i n a t i o n cost

whereas

plant

between

The h i g h e s t TDS in the system

mg/l a n d no a d d i t i o n a l f l o w s above minimum were r e q u i r e d . assuming

~

Water Flow

of

a maximum o f

100 c / k l ,

anywhere 1334 mg/l

i s 1334

The net system would

be

$2.9

in the mine was

resulted

without

or increase of flows.

For the r u n w i t h no d e s a l i n a t i o n i t was found t h a t i t was impossible to

achieve

a

maximum

TDS

as

low

r e c i r c u l a t i n g more f r e s h water. water

was

relatively

high

but

as

1334

mg/l

everywhere

purely

T h i s i s p a r t l y because the TDS of even

with

better

quality

raw

by

the r a w

water

a v a i l a b l e ) considerable geochemical d e t e r i o r a t i o n o c c u r r e d u n d e r g r o u n d ,

(if

so

125

there

were

limits

to

what

could

be

achieved.

Anyway,

even

maximum TDS of 1603 mg/l,

which exceeds the d e s a l i n a t i o n a l t e r n a t i v e f o r b e t t e r water. hand,

if

TDS

the

recirculation

limit

solution

with

a

the cost of c i r c u l a t i n g water was $6.5 m i l l i o n / y

was

became

relaxed

to

comparable

2000 with

mg/l, the

On

the

the o t h e r

cost

desal i n a t ion

of

the

solution,

namely $2.5 mi 1 I ion/year. should

It

be noted

that

the costs

purchases a n d d e s a l i n a t i o n . used

to pump

maintenance,

to

the m e t a l l u r g i c a l

especially

plant

replacement

c o n s t r a i n t s (maximum TDS)

only

B r i n e disposal

of

were set

include

where

corroded

it

was

only

a

question

of

it

whether

to

more

The

i s omitted

in s a v i n g s

use

Cost, $/a = 2.912175E+6

~~

1

Node1

3 4

0 1 3 6

6

0

6

0 2 4

2

7 8

9 10 11 12 1s 14 16 16 17 18 19 20 21 22

0 6

8 8 9 7 10 7

11 0 12 12 2 3

Node2 1 3 6 7 11 7 4 6 6 8 7 9

2 10 12 11 12 10 8 0 0

4

WatcrFlow

lncmrrTD8 Cod

BpuilibriumTD6

(Ud

(=g/l)

cwn,

(CW)

23 2s 8 8

800 0

30 0 0 0

-8

0

0

-8

0

0

36 61 18 69 62 67

0

0

0

67

36 40 26 18 4 60 8 21 16

0 0

797 798 783 448 843 448 1179 1339 1839 1844 448 1342 1348 681

0

0 0 0 100 0 20 0

200

0

799

0

0

643

200 1800 0 0 0 0

0

799

0 10

681 1344 0 0 1179

1800 400 -1000 0

0

60

16

0

is

cost

of

as

the The

i n replacements

raw

TABLE 8.2 New Water Flows and TDS w i t h d e s a l i n a t i o n

Pipe number

water

problems.

desalinate.

Max TDS 1344 mg/l,

raw

the b r i n e

i s used.

pipes,

to e l i m i n a t e corrosion

d e s a l i n a t i o n system cost i s more than j u s t i f i e d and

pumping,

i s not costed as

water

or

to

126

One

factor

additional

omitted

cooling of

The r a w water

at

this

stage,

the recirculated

however, water,

is

if

the

less

i s g e n e r a l l y a t a lower temperature

requirement

raw

water

for

i s used.

(2lOC) t h a n the water

r e t u r n e d from the mine w o r k i n g s (28OC). The a d d i t i o n a l cost of o p e r a t i n g a desalination

plant

underground

where

access

is

limited,

is

also

not

p r o p e r l y e v a l u a t e d a t t h i s stage. The most economical s i t i n g o f the d e s a l i n a t i o n p l a n t this

reduces p u m p i n g cost

highest TDS concentration

to as

the

surface.

this

results

It

i s u n d e r g r o u n d as

s h o u l d be a t

i n minimum p l a n t

the p o i n t capacity

of per

u n i t removed. The

example

illustrates

the

use

of

the

program

facilitated

rapid

comparison of a l t e r n a t i v e water management systems on a cost a n d q u a l i t y basis. costs

I n general quoted

additional cleaner

are

factors

water,

conservation

of

i t demonstrates t h a t , often

in

favouring less

excess

despite the f a c t t h a t raw

desalination

corrosion

natural

of

and

resources,

water in

industrial

blocking,

less

costs,

pumping

less costs,

Pipe number 1 2 3 4 6 6 7 8 9 10 11 12 13 14 16 16 17 18 19 20 21 22

Node 1

Node 2

Water Flow (116)

namely: greater

and

0 1 3 6

0 0 2 4 0 6 8 8 9 7 10

I 11 0 12 12 2 3

1 3 6 7 11 7 4 6 6 8 7 9 2 10 12 11 12 10 8 0 0 4

176 176 118 118 -8 -8 36 94 18 112 113 212 212 78 194 146 138 116 213 118 176 68

Cost, $/a = 6.544681E+6

Increase TDS Cost ( W l ) (c/W 800 0 0 0 0 0 0 0 1800 400 0 0 0 0 200 0 200 1800 0 0 0 0

30 0 0 0 0 0 0 0 0 0 6 0 20 0 0

0 0 0 10 60 16 0

Equilibrium TDS (mg/l) 800 799 798 1239 1303 1233 1106 1216 1216 1604 1233 1609 1603 1489 1697 1303 1697 1489 1604 0 0 1106

often

systems,

Optimum Flows to reduce TDS to 1603 mg/e

Best o b t a i n a b l e without d e s a l i n a t i o n ,

are

effluent,

consumption. TABLE 8.3

desalination

there

lower

water

127

REFERENCES

A b u l n o u r , A.M., S o r o u r , FA.H., Hammouda, F. and A b d a l Dayem, A.M., 1983. S q u e e z i n g d e s a l t e d w a t e r c o s t s b y p r o p e r c h o i c e o f t h e d e s a l t i n g t e c h n o l o g y a n d w a t e r management. D e s a l i n a t i o n , 44, 189-198. B a k e r - D u l y , H.L.G., 1985. O p t i m i z a t i o n o f w a t e r r e t i c u l a t i o n s y s t e m s a t L o r a i n e G o l d M i n e L i m i t e d , Proc. Mine V e n t i l a t i o n Society of South A f r i c a Conf. H o l t o n , M.C. and Stephenson, D., 1383. A c o m p u t e r model o f c i r c u l a t i n g s e r v i c e w a t e r i n S o u t h A f r i c a n g o l d m i n e s . I n t l . J. M i n e Water, 2 ( 2 ) 33-42. L o u c k s , D.P., R e v e l l e , C.S. and Lynn, W . R . , 1967. L i n e a r p r o g r a m m i n g m o d e l s f o r w a t e r p o l l u t i o n c o n t r o l . M a n a g e m e n t Science, 14, 8166-8181. Rinaldi, S., Soncini-Sessa, R., Stehfest, H. and T a m u r a , H., 1979. M o d e l l i n g and C o n t r o l o f R i v e r Q u a l i t y , McGraw H i l l , New Y o r k . Smeers, Y . and T y t e c a , D., 1981. On t h e o p t i m a l l o c a t i o n o f w a s t e w a t e r treatment p l a n t s , I n : J. T h i s s e and J. Z o l l e r ( E d s . ) , L o c a t i o n and A n a l y s i s o f P u b l i c F a c i l i t i e s , N o r t h H o l l a n d , Amsterdam. 1981. C i v i l E n g i n e e r i n g Systems S m i t h , A.A., H i l t o n , E. and L e w i s , R.W., A n a l y s i s and D e s i g n . Stephenson, D., 1983. D i s t r i b u t i o n o f w a t e r in g o l d m i n e s i n S.A., Intl. M i n e Water J . , 2 ( 2 ) 21-30. Stephenson, D., 1986. Computer analysis justifies desalination. Desa I i n a t i o n , 58, 155-167. Stephenson, D. a n d C o r b e t i s , S . , 1984. Economics o f d e s a l i n a t i o n o f w a s t e w a t e r s f r o m t h e W i t w a t e r s r a n d , Proc. I n t l . Conf. o n Water Resources and Desalination. Johannesburg, South A f r i c a , Water S u p p l y Improvement Assn.

128

APPENDIX 8.1

MlNSlM PROGRAM FOR SIMULATING FLOW AND TDS IN CLOSED SYSTEMS

The

program

is

for

simulating

r e t i c u l a t i o n systems.

It

concentration

nodes,

at

all

flow

TDS

and

and

plots

it

at

any

in

changes

i s based on nodes a n d l i n k s ,

and

water

TDS

calculates

selected

node.

Volume

v a r i a t i o n s a t nodes a r e p e r m i t t e d a l t h o u g h zero volume nodes can a l s o be specified.

will

The program

selected scale o r v i e w i n g

also draw

angle.

The

a

picture

program

of

is

the

system

BASIC 3.0

in

at

for

any

HP

a

9816 micro computer. To

account

for

TDS

build-up

along

a

route,

one

may

specify

the

increase in TDS a l o n g the r o u t e in mg/l. I f d e s a l i n a t i o n i s done, When

evaporation

a n e g a t i v e increment i n TDS i s inserted.

increases

TDS

the

concentration

specifies a n e g a t i v e flow to t h a t node from another

at

any

node

one

'0'

node such as node

a t the node of o r i g i n a n d zero increase i n TDS a l o n g the l i n k route. The volume a t each node i s set v a l u e i s zero o r n e g a t i v e , equal

outflow.

during

the

nodes,

It

day

is

from

a no-volume

therefore a

zero

node i s assumed a n d

not

possible

to

specify

volume

node.

From

other

t h e a v e r a g e flows

must

variations

positive

volume

Then

in o r d e r

i n t o a n d out of a l l nodes

not the p e a k s w h i c h a r e s p e c i f i e d in the

should b a l a n c e d u r i n g each d a y ,

i.e.

I f this

inflow

flow

the flow can be s p e c i f i e d over so many h o u r s a d a y .

not to cause extreme volumes,

data.

i n i t i a l l y a t a s p e c i f i e d value.

Q.Tin should = 0 over 24 hours.

A maximum of 5 p i p e s o r l i n k s a r e p e r m i t t e d to each node.

When before

inputting data

reading

in

dummy p i p e from

data

make sure on

the

the

( I ) node h a s been

'top'

'bottom'

(J)

node.

' 0 ' to the node i n question

Node 0 need not be so defined node 0 a r e p l o t t e d b u t

it

r e d e f i n e the TDS a t node 0,

wise

to

necessary

to d e f i n e

as no p i p e s from

i s not

If

use

a

i t s co-ordinates.

i t are plotted.

have pipes

defined

to 0 a s

Pipes they

to

will

w h i c h c o u l d otherwise b e used as a s i n k f o r

e v a p o r a t i o n and a source f o r f i s s u r e s w h i c h would then increase i n TDS b y a given figure. Costs a r e c a l c u l a t e d i n D o l l a r s p e r annum

if

prices

i n c/kl

are input

in d a t a .

Tape or Disc Management The

programme

MlNSlM

can

be

copied

onto

new

tapes.

Data

files

129

cannot.

They

have to be typed i n l i n e b y l i n e a f t e r the f o l l o w i n g

i s set

u p on the tape. CREATE "DATMIN",

100,88.

T h i s creates a f i l e o f

100 records

(for

p i p e s ) each 88 b y t e s long p e r m i t t i n g 11 x 8 b y t e numbers p e r record. erase a p r e v i o u s d a t a f i l e m i g h t have to

be closed

purge

manually

it

a n d re-create

after a

it.

bomb out.

executing the program i t pauses and asks whether

Note a

data

Alternatively

100 To file

while

graphics o r re-write

of

d a t a i s r e q u i r e d . A new tape could be inserted a t t h i s stage.

MlNSlM L i s t of Symbols A1 A2 B1-9 C c2

E( F( ) G( G1 GO

H( H1 I( J(

K ( I ,MI L( 1 L1 MO M M1 M2 M3 M5 N NO N1

N2 N3 N4 P( PO Q( 91

1

ZQ

R( S( s1 T1 T2 T3 T4

a n g l e of v i e w i n g p l a n e from X a x i s , degrees a n g l e of v i e w i n g p l a n e from 2 a x i s , degrees dummy i n p u t f o r a l t e r a t i o n s p r i c e c/kP t o t a l cost/rands p e r annum i n i t i a l volume, m3. Use n e g a t i v e o r zero v a l u e to s i g n i f y constant outflow over 24h. Must then b a l a n c e flows over 24h not a t peaks. new mg/P a t node p o l l u t a n t concentration mg/P a t node G counter f o r p l o t s used in c a l c u l a t i o n of TDS a t nodes head, m not used size of device top node of p i p e bottom of p i p e number of p i p e s connecting i n t o node ( u p to 5 p e r m i t t e d ) length, m distance to device p i p e counter Pipe number of nodes connecting p i p e counter counter f o r i n i t i a l flow c a l c u l a t i o n s p i p e no. of device node counter device p e r p i p e node a t w h i c h TDS i s to b e p l o t t e d 1 = TDS concentration p l o t r e q u i r e d 2 = volume a t node, m3 0 = o l d data, 1 = new, 2 = r e v i s e d 1 = g r a p h i c d i s p l a y , 0 = none, 2 = r e c o r d d a t a a n d stop i n p u t p o l l u t a n t concentration a t node 2, mg/e i n t o p i p e in it i a I concentration flow P / s

1

design flow i n p i p e P / s volume m3 S coun'ter f o r p l o t s d u r a t i o n of simuln. d a y s s i m u l a t i o n i n t e r v a l , hours d r a w o f f hours/day (1st hours of d a y ) time i n t e r v a l s f o r d r a w o f f p e r i o d

1 30 T5

device type; 1 = f l a n g e , 2 = v a l v e , 4 = a r r o w , 5 = square no. i t e r a t i o n s p e r d a y i t e r a t i o n counter d a y counter d a y counter screen X co-ordinate screen Z co-ordinate X m i n on screen X max on screen Z m i n on screen Z max on screen X co-ordinate Y co-ordinate Z co-ordinate

3 = tank,

Data Input

The computer asks f o r the f o l l o w i n g d a t a to be typed i n i n t e r a c t i v e l y :

Ll L2 L3 L4 L5 L6 L7

L B et seq

System name Simulation p e r i o d , d a y s Time increment, d a y s Period in h o u r s p e r d a y d u r i n g which d r a w o f f occurs. The b a l a n c e of the time water may flow to r e f i l l r e s e r v o i r s . I n i t i a l TDS of the e n t i r e systems, mg/P Node no. a t which a p l o t o f TDS versus time i s r e q u i r e d Type 0, 1 o r 2 depending on whether the o l d d a t a f i l e , a new one o r a r e v i s i o n of the o l d one i s r e q u i r e d Type the f o l l o w i n g separated b y commas, w i t h one l i n e p e r pipe o r conduit; Top ( u p s t r e a m ) end node no. Bottom (downstream) end node no. x-co-ordinate of bottom node ( h o r i z o n t a l l y from a d a t u m ) y-co-ordinate of bottom node ( v e r t i c a l l y ) z-co-ordinate of bottom node ( i n t o screen) Volume of storage a t bottom node, m’ Design flow in P / s ~ n p u tp o l l u t i o n , mg/e Cost a l o n g route, cents p e r u n i t o f flow (ke) Type a row of n i n e zeros to end t h i s d a t a L a t e r the program may c a l l f o r a d d i t i o n a l g r a p h i c s d a t a p e r pipe : Pipe no. (counted from the top of the l i s t ) Position ( d i s t a n c e from top end o f p i p e ) to a device Device t y p e ( 1 = f l a n g e , 2 = v a l v e , 3 = t a n k , 4 = a r r o w , 5 = square) Size, m to d r a w i t Cost p e r u n i t size

The d a t a w i l l then be f i l e d f o r subsequent re-use b y the second program MINOP. Examples of o u t p u t , g r a p h i c s a n d i n p u t a r e g i v e n in the char, ter.

131 Program listing 1 I RE-STORE"MINS1M'

10 I MINE WATER RETIC SIMULATION I"M1NSIM" 1 1 GRAPHICS OFF 12 DUMP DEVICE I S 707,EXPANDED 1 4 PRINTER I S 707 2 0 ASSIGN O P a t h l TO "DATMIN" I CREATE "FILNAM",100,88 ag"DATM1N" 2 1 D I S P "SYSTEM NAME"i 22 INPUT NS 2 4 PRINT NE 99 ) , J ( 99 ) ,K( 99.5 ) 2 5 INTEGER N ,NO ,N1 ,N2 ,N3 ,N4 ,M ,M0 ,M1 ,M2 ,M5 ,S I ,I( 2 7 D I M X ( 9 9 ) , Y ( 9 9 ) .Z( 9 9 ) ,U( 9 9 ) ,W(99) ,P( 9 9 ) , H ( 9 9 ) ,6( 9 9 ) , S ( 9 9 ) 30 D I M E( 9 9 ) ,R( 9 9 ) ,P( 9 9 ) ,L( 9 9 ) .F( 9 9 ) ,C( 99 ) 31 D I S P "DURN OF SIMULATION,DAYS"I 3 2 INPUT 1 1 33 D I S P "TIME 1NCREHENT.HOURS"t 3 4 INPUT 1 2 3 5 D I S P "FLO OVER HOURS/DAY"i 36 INPUT T3 37 D I S P " I N I T I A L TDS,mQ/l"( 3 8 INPUT P0 39 D I S P "PLOT TDS AT N0DE"i 4 0 INPUT N1 4 2 DEG 4 3 D I S P "OLD OR NEW OR REV D A T A ( 0 / 1 / Z ) " i 45 INPUT N3 61 NZ-1 62 T4-T3/T2 I I T S / d 66 1 7 - 2 4 / 1 2 70 G(O )=0 80 X ( 0 )-0 90 Y(0j-0 1 0 0 Z(0)-0 110 E ( 0 ) - 0 111 FOR N-1 TO 9 9 112 S ( N ) = 0 113 E ( N ) - 0 114 F ( N ) = 0 115 X ( N ) = 0 116 Y(N)=0 117 Z(N)=0 118 C(N)-0 1 1 9 NEXT N 120 c2-0 122 G( 1 )=P0 1 2 5 M1=0 130 FOR M=1 TO 9 9 1 4 0 I F N3C>1 THEN 190 1 4 5 I NEW PIPE DATA 150 DISP "N1 ,N2,X2,YZ,ZZ,U2,l/s,tmg/l,c/"i 1 6 0 INPUT I ( M ) , J ( M ) , X ( J ( M ) ) ,Y( J ( M ) ) ,Z( J ( M ) ) ,E( J ( M ) ) , R ( M ) ,P(M) ,C( M ) 170 OUTPUT @ P a t h 1.Mi I ( M ) , J ( M ) , X ( J ( M ) ) .Y( J ( M ) ) ,Z( J ( M ) ) ,E( J ( M ) ) , R ( M ) , P ( M ) ,C(M) 1 8 0 GOT0 2 10 1 8 5 I OLD PIPE DATA 1 9 0 ENTER @ P a t h 1, M i I ( M ) , J ( M ) , X ( J ( M ) ) , Y ( J ( M ) ) , Z ( J ( M ) ) ,E( J ( M ) ) ,R(M),P(M),C(M) 2 1 0 I F I ( M ) + J ( M ) = 0 THEN 228 212 S(J(M))=E(J(M)) 218 G(J(M))-P0 2 2 0 C2=CZtC( M )rR( M )*315 225 M l = M l + l

132

226 228 230 231 232 233 234 235 245 246 ?48 249 251 253 254 255 256 257 258

262 263 264 265 267 268 269 270 271 272 274 276 278

286 706 705 707 708 710 71 1 720 730 740 750 760 770 780 790 800 810 820 830 835 840 845 850 851 854 855

NEXT M I F N3<2 THEN 256 FOR M0=l TO 99 I REV P I P E DATA DISP "PIPE N o . " i INPUT M C2=CZ-C( M ) * R ( M ) * 3 1 5 DISP "N1 , N 2 , X 2 , Y 2 , ~ 2 , U 2 , l / s , t m g / l , c / " i INPUT I ( M ) , J ( M ) , X ( J ( M ) ) , Y ( J ( M ) ) ,Z( J ( M ) ) ,E( J ( M ) ) , R ( M ) , P ( M ) , C ( M ) OUTPUT B P a t h l , M i I ( M ) , J ( M ) , X I J ( M ) 1 , Y ( J ( M ) ) ,Z( J ( M ) ) ,E( J ( M ) ) , R ( M ) , P ( M ) ,C(M) I F I ( M ) t J ( M ) = 0 THEN 256 I F MCMl THEN 251

Ml=MI+l S ( J ( M ) )=E( J ( M ) ) G( J ( M ) )-P0 CZ=C2+C(M)*R(M)*315 NEXT M 0 FOR M - l TO M 1 L ( M ) = S Q R ( ( X ( J(M))-X(I(M)) ) ^ 2 + ( Y ( J ( M ) ) - Y ( I ( M ) ) ) * 2 + ( 2 ( J(M))-Z( I ( M ) ) ) ^ 2 1 NEXT M PRINT "N1 N2 X2 Y 2 22 U2 Q t m g c / " FOR M=1 TO M 1 PRINT USING 2651 I ( M ) , J ( M ) , X ( J ( M ) ) , V ( J ( M 1 ) ,Z( J ( M ) ) ,E( J ( M ) ) , R ( M ) . P ( M ) , C ( M ) IMAGE 20,2D ,5D, 4D,5D ,4D ,3D, 4D,3D NEXT M D I S P "LAYOUT GRAPHICS(0=NO,l=YES,2=RECORD DATA & STOP ) " I INPUT N4 I F N4<2 THEN 2 8 0 ASSIGN O P a t h l TO "DATMIN" FOR M=1 TO 99 OUTPUT @ P a t h 1, M i I ( M ) , J ( M ) ,XC J ( M ) ) , Y ( J ( M ) ) ,Z( J ( M ) ) ,E( J ( M ) ) , R ( M ) ,P(M) ,C(M 1 I F I ( M ) t J ( M ) = 0 THEN 2910 NEXT M I F N4-1 THEN 1570 ALPHA OFF GINIT GRAPHICS ON I F N2>1 THEN 8 5 0 WINDOW - . 5 , T I . - 2 0 0 , 2 * G ( I )t3000 C L I P 0 ,T1 ,0 ,2*Gc 1 )+3006 AXES 1 ,100 C L I P OFF MOUE T1-1,10 LABEL " O A Y " FOR T0=1 TO T I MOVE TO-.5,-200 LC\BEL UALO(T0) NEXT T0 FOR G I - 0 TO 2 * G ( l ) + 2 5 0 0 STEP 500 MOUE -.5,G1 LABEL UALS(G1 ) NEXT 61 MOUE .5,2*G( 1 )+600 LABEL "TDSmg/l NODE"LUALB(N1 ) 60TO 890 WINDOW -.5,Tl ,-10,E(NI ) t l U C L I P 0 , T l .-10,E(N1 ) + I 0 AXES 1 , l C L I P OFF

133 857 868 860 862 864

MOUE T l - 1 ,0 LABEL "DAY" FOR T0=l TO T1 MOUE T0-.5,-10 LABEL UALS(T0 ) 866 NEXT 1 0 8 6 8 FOR S l - 0 TO E ( N 1 ) t l O STEP 10 870 MOUE -.5,S1 872 LABEL UCILL(SI ) 874 NEXT S1 876 MOUE B,E(Nl ) + I 0 878 LABEL "UOLn3,NODE"bUALO(Nl) 890 I END OF LABELING 900 FOR N=1 TO M l t l I NODES CONS 905 M2=0 906 FOR M0=l TO 5 907 K ( N ,M0 )-0 908 I ( K ( N , M 0 ) ) = 0 909 J(K(N,M0))=0 910 NEXT MO 915 FOR M0=1 TO M 1 1 PIPES 920 I F I ( M 0 ) < > N THEN 940 925 MZ-M2tl 927 K ( N ,M2 )-M0 930 GOTO 960 940 I F J(M0)<>N THEN 968 945 M2=M2+1 950 K(N,MZ)=MB 960 I F M2-5 THEN 970 968 NEXT M0 970 NEXT N 975 I F NZ>l THEN 990 980 MOUE 0,G(N1 ) 985 GOTO 1090 990 MOUE 0,S(Nl ) 1090 FOR T=1 TO T l ! DAYS 1100 FOR T9=1 TO T7 1105 I F T9>T4 THEN 1160 1110 FOR M=1 TO M1 1145 Q ( M ) = R ( M ) 1155 NEXT M 1157 GOTO 1200 1160 I F E ( I ( M ) ) < = 0 THEN 1200 1195 Q(M)-0 1200 TDS a STORAGE TINS 1210 FOR N-1 TO M 1 + 1 1220 I F E ( N ) > 0 THEN 1340 1225 Gl=Q 1228 Q1=.001 1230 FOR M0-1 TO 5 I 2 3 5 I F J ( K ( N , M B ) ) O N THEN 1280 1236 I F G( I ( K ( N , M 0 ) ) )+P(K(N ,M0) )<=0 THEN 1255 1240 G1=( G( I ( K ( N ,M0) ) ) t P ( K ( N , M I ) ) )*Q(K(N .M0) )+G1 1255 01 =Ol + Q ( K ( N ,M0 ) ) 1280 NEXT MO 1282 G l = G l / Q l 1285 GOTO 1440 1340 G l m 0 1 S>0 1345 G0=G( N )*S( N )

134

1350 FOR MO-1 TO 5 1360 I F J(K(N,M0))<>N THEN 1390 1370 G1-61+(6( I ( K ( N,M0 ) ) )+P(K( N ,M0 ) ) )*Q( K ( N ,M0 ) ) 1375 S(N)=S(N)tQ(K(N,MB) )*T2*3.6 1380 GOT0 1420 1390 I F I(K(N,MB))<>N THEN 1420 i 400 GI=GI-G(N')*Q(K(N ,MQ ) ) 1412 S(N)=S(N)-Q(K(N,MQ) )*T2*3.6 1428 NEXT M 0 1430 61-( 61 *T2*3.6+60 ) / S ( N ) 1440 F ( N ) = G l 1472 NEXT N 1474 FOR N-1 TO M l + l 1476 G(N)=F(N) 1488 NEXT N 1492 I F N2>1 THEN 1488 1485 DRAW T - l t T g * T 2 / 2 4 , 6 ( N l ) 1486 60TO 1490 1488 DRAW T - l t T 9 * T 2 / 2 4 , S ( N l ) 1490 NEXT T9 1492 NEXT T 1494 DUMP GRAPHICS 8707 1496 GOT0 2920 1570 DISP "XMIN ,XMAX ,ZMIN ,ZMAX ,XANGL ,ZANGL' I 1580 INPUT ~ 0 , ~ 9 , ~ 0 , ~,AZ 9 , ~ 1 1590 GINIT 1592 GRAPHICS ON 1595 DEG 1600 WINDOW UQ,U9,W0,W9 1601 FOR M=1 TO M 1 ! NODES 1602 U(M)=X(M)*COS(Al ) t Y ( M ) + S I N ( A l ) 1604 W ( M )-Z( M )+COS( A2 ) t (Y ( M )tCOS( A1 )-X( M )*SIN( A 1 ) )*SIN( A2 1608 NEXT M 2170 FOR M=1 TO M l ! PIPES 2190 PEN 1 2195 I F I ( M ) - 0 THEN 2225 2196 I F J(M)-0 THEN 2230 2200 MOUE U ( I( M ) ) ,W( I( M ) ) 2210 DRAW U ( J ( M ) ) , W ( J ( M ) ) 2220 LABEL Uc\L$( J ( M ) ) 2223 GOT0 2230 2225 MOUE U( J ( M ) ) ,W ( J ( M ) ) 2228 LABEL UALO( J ( M ) ) 2230 NEXT M 2235 FOR N0=l TO 3 2240 FOR N=1 TO 100 2241 I F N>Ml THEN 2415 2242 I F NO-1 THEN 2256 2243 I F N0=3 THEN 2269 2246 M5-N I ARROWS 2247 I F I ( N ) = 0 THEN 2410 2248 L l = L ( N ) / 2 2249 I F J ( N ) - 0 THEN 2410 2250 T5=4 2251 Hl-L1/10 2254 C0-0 2255 GOTO 2320 2256 M5=N ! TANKS 2258 L l = L ( N ) 2260 1 5 1 3

)

135 2262 H l = E ( J ( N ) ) / 2 5 2264 C0=0 2266 GOT0 2320 2268 ALPHA ON 2 2 7 0 DISP "PIPEn ,X ,TYPE ,SIZE .COST/' 1 2280 INPUT M5,Ll ,T5,H1 ,C0 2 3 2 0 I F M5-0 THEN 2420 2340 X5=X( I ( M 5 ) ) + L l / L ( M 5 ) * ( X ( J(M5 1 )-X( I ( % ) ) ) 2350 Y5=Y( I ( M 5 ) )+Ll /L(M5 ) * ( Y ( J( M5 ) )-Y( I(M5 ) ) ) 2360 Z5=Z( I ( M 5 ) )+L1 /L(M5 )+(Z( J(M5) )-Z( I ( M 5 ) ) ) 2 3 7 0 US=XS*COS(AI ) t Y 5 * S I N ( A 1 ) 2 3 8 0 W5=Z5*COS(A2 )t(YS*CDS(Al )-XS*SSN(Al ) ) * S I N ( h Z ) 2390 ON T5 60TO 2460,2490,2540,2590,2850 2400 I l=FLANGE,Z=UALUE,3=TANK,4=~RROW,S=S~UARE 2 4 1 0 NEXT N 2415 NEXT N0 2420 MOUE U0,WB 2430 C2=1NT(C2 ) 2440 LABEL " R/s="LUALO(C2) 2445 DUMP GRAPHICS 2 4 5 0 60T0 7 0 0 2460 MOUE US ,W5tHI / 2 2 4 7 0 DRAW US ,W5-H1/2 2480 GOT0 2410 2 4 9 0 HOVE U5-H1/2,WStH1/2 2500 DRAW U 5 t H I 12 ,WS-HI / 2 2510 MOUE U5+Hl/2,WS+H1/2 2520 ORAW U5-H1/2,U5-H1/2 2530 GOTO 2410 2540 MOUE U5-HI / 2 ,WStWI 2550 DRAW U 5 - H l / 2 ,W5 2560 DRAW U S H 1 / 2 ,WE 2 5 7 0 DRAW U5+Hl/Z,W5+Hl 2580 60TO 2410 2590 I F U ( J ( M S ) ) < > U ( I ( M S ) ) THEN 2601 2591 IF W ( J ( f l S ) ) > W ( I ( M 5 ) ) THEN 2594 2592 U8=270 2 5 9 3 GOTO 2608 2594 U8=90 2595 GOT0 2608 2601 UE=ATN( (U( J( M 5 ) )-W( I( M5 ) ) ) / (U( J ( M 5 ) )-U( I( M5 ) ) ) ) 2602 I F U8>=0 THEN 2606 2603 I F W ( J(M5) ) < W ( I(M5) 1 THEN 2608 2604 GOTO 2607 2606 I F U ( J ( M S ) ) > W ( I ( M S ) ) THEN 2608 2607 U8=U8t180 2608 UG=U5-Hl*COS(U8-45) 2610 W6=W5-Ht*SIN(U8-45) 2 6 2 0 U7-U5-Hl*COS(U8t45) 2630 W7-W5-Hl*SIN(UEt45) 2 8 1 0 MOUE U6,W6 2820 DRAW U5,W5 2830 DRAW U7,W7 2 8 4 0 6QTO 2410 2850 MOUE US-H1/2,WStHl 2860 DRAW U5-H1/2 ,W5 2a70 DRAW u 5 + ~ 12 1 ,w5 2880 DRAW U5tH1/2,W5tHI 2890 DRAW U5-H1/2,W5tHl 2900 60TO 2410 2920 END

136

APPENDIX 8.2

MINOP p r o g r a m f o r o p t i m i z i n g d i s t r i b u t i o n

MlNOP List of Symbols p r i c e c/ke cost t o t a l cost dummy TDS max. TDS desired, o r G of node w i t h m a x . T D S increment i n TDS max. increment i n TDS t o t a l TDS - mg/s i n t o node t o t a l flow i n t o node TDS G(I) - H(I) max. TDS top node bottom node p i p e no. connecting to node ( u p to 5 p e r m i t t e d ) number of p i p e connecting number loops best loop no. branches i n loop p o s i t i v e loop p i p e s out node loop counter number loops a n d b e g i n number loop number connecting p i p e s to node p i p e number p i p e counter number of nodes number of p i p e s in loop number of connecting p i p e s from node dummy p i p e s out node number of p i p e s in loop r e d u c t i o n i n no. p i p e s in loop, o r , p i p e to node w i t h max. TDS p i p e number i n loop b e g i n p i p e f o r loops name node counter no. nodes p i p e no. i n p u t TDS, mg/e flow e/s dQ/dC dQ co-ord. not used i n MINOP 0,

I1

137

Notes on program

The program i s in BASIC for an HP 9816 series 200 micro computer. data f i l e i s obtained from the M l N S l M program in appendix 8.1.

The

138 Program

MINOP

listing

101 RE-STORE"MIN0P" 20 I "MINOP " OPTIMZS FLOS I N NETWORK SUBJECT TO TOS L I M I T S 3a PRINTER IS 707 40 A S S I G N @ P a t h 1 TO "DATMIN" 5 0 I D I S P "SYSTEM NAME"! 60!INPUT NO 7 0 I P R I N T NC DIM Q( 9 9 ) ,G(99) ,P( 9 9 ) ,C( 9 9 ) , L ( 9 9 ) ,H( 9 9 ) 80 , M 2 ( 5 0 , 5 0 ) , M 3 ( 9 9 ) .M4 ,M INTEGER I ( 9 9 ) , J ( 9 9 ) , K ( 9 9 , 5 ) , K 1 ( 9 9 , 9 ) , L l ,L2 ,L3,M,M0,Ml 90 S.M6(99),M7,M8,M9,N,Nl 1 0 0 M I 1 0 1 NO.PIPES 110 G ( 0 ) = . 1 120 N l = l 130 DISP "MAX TDS DES1RED"i 1 4 0 INPUT 6 0 1 5 0 FOR M=l TO 9 9 ENTER @ P a t h 1,M; I ( M ) , J ( M ) ,X ,Y ,Z ,E ,Q( M ) ,P( M ) ,C( M ) 160 H( .I(M ) )=G0 170 I F I ( M ) t J ( M ) = 0 THEN 2 5 0 180 I F I(M);=Nl THEN 2 1 0 190 Nl=I(M) 200 If J ( M ) < = N l THEN 2 3 0 216 N1 =.Jc M ) 220 MI-Mltl 230 2 4 0 NEXT M 250 H(0)-100000 2 6 0 FOR M0=l T O M 1 D I S P "ANY CHANGES? PIPENo,TOPn,BOTn,FLOI/s,POLmg/l , c / h 1 (O's=none ) " I 2 70 280 INPUT M , I ( M ) , J ( M ) ,QC M 1 ,P( M ) ,C(M ) 290 I F I ( M ) + J ( M ) = 0 THEN 3 2 0 I F M > M l THEN M l = M l t l 300 310 NEXT MO I NODES 3 2 0 FOR N-0 TO N l G( N )=G0 330 340 M3( N )=0 L( N )=0 350 FOR M=l T O M l I P I P E S FROM NODE 360 I F I ( M ) < > N THEN 4 0 0 370 M3( N )-M3( N ) t1 380 K l ( N ,M3( N ) )=M 390 NEXT M 400 FOR M0=1 TO M 1 I P I P E S TO NODE 410 I F J ( M Q ) < > N THEN 4 5 0 420 L( N )=L( N ) + 1 430 K ( N L ( N ) )=NO 440 NEXT M0 450 4 6 0 NEXT N 4 7 0 G( 0 1-0 4 8 0 L1=01LOOFS 4 9 0 FOR.M9=1 TO M1 IBEGINPIPE FOR LOOPS L 0 - L l t l ITRY LOOP 500 L8=0 51 0 M G ( L 0 ) = l I N O . P I P E S I N LOOP 520 M2(L0,1 )=M91PIFES I N LOOPI 530 LE=LBIPOS LOOP 540 FOR L 3 = 1 TO MlIBRANCH ROUTINE 550 L8=0 560 L4=M3( J ( M 2 ( L0 ,M6( L0 ) 1 ) ) 570 FOR M5=1 TO L 4 I P I P E S OUT NODE 580 ~

139 5 90 600 610 620 630 640 650 660

I F M5-1 THEN 670 L6=LG+lIANOTHER POS LOOP FROM BRANCH M6(L6 )=M6(L0) FOR M7=1 TO M6(L6)-1 MZ(L6 ,M7)42(LB,M7 )ICOPIES PIPES I N PREU LOOP NEXT M7 M 2 ( L6 ,M6(L6 ) )=K 1 ( J ( M 2 ( L 0 ,M6( LO ) - 1 ) ) ,M5 ) GOTO 690 M6(L0)=M6(L0)+1 IN0 PIPES I N LOOP 670 M2( L 0 ,M6( L 0 ) )=K 1 ( J ( M 9 ( L0 ,M6( L0 1- 1 ) ) ,M5 ) I NEXT PIPE 680 NEXT M51 CHEK LOOP CLOSURE 690 FOR M5-2 TO M6(L0) 700 71 0 FOR M7=1 TO M5 IF I( MZ(L0 ,M7) ) < > J M ( Z ( L 0 ,M5) ) THEN 800 720 L1=L1 t 1 730 M6(L1 )4lS+I-M71SHUFFLE UP PIPES 740 FOR M8=l TO M 6 ( L l ) 750 M Z ( L I ,M8 )-M2( L 0 ,M8+M7- 1 ) 760 NEXT ME 770 L6=1 780 GOTO 840 7 90 NEXT M7 800 NEXT M5 81 0 GOTO 1000 820 I CHEK DUP LOOP 830 I F L l ; = l THEN 1000 840 FOR LZ=1 TO L1-1 850 M=O 860 FOR M7=1 TO M6(Ll ) 870 M=Mt 1 880 ME-1 890 I F M Z i L l ,M)OM2(L2,M8) THEN 980 900 91 0 M8=M6+1 M=Mt 1 920 IF M:=MG(LI) THEN 950 930 M= 1 940 950 I F M8:=M6(L7) THEN 9G8 Ll=Ll-llREMOUE OUP L O O F 960 GOTO 1000 970 NEXT M7 980 NEXT L2 990 I F L 8 < - 0 THEN 1030 1000 I F L 6 ‘ = L 0 THEN 1040 1010 L0=L0+ 1 1020 1030 NEXl L3 1040 NEXT M9 I 0 5 0 FOR L:=l TO L I 1060 FOR M=I TO M 6 ( L 2 1 IQ701PRINT L:,MZ(L2,W) 1080 NEXT M 1090 NEXT L2 1100 GOSU8 1120 1110 GOTO 1300 1120 FOR L4=1 TO Mi 1130 G5-0 1140 FOR N=i T O N l 1150 Gl=.l 1160 G’L=.I 1170 FOR O=l TO L ( N ) Gl=Gl t Q ( K ( N,O ) * ( G : I ( k‘: N , O ) ) ) t F ( K ( N ,O ) ) ) 1180

140

1190 62=62tQ(K(N,O)) 1200 NEXT D 1210 63=6(N) 6(N )=GI 162 1220 64=AES( 6( N )-63)/G(N ) 1230 1240 I F 64<65 THEN 1260 1250 6544 1260 NEXT N 1270 I F 65<.00I THEN 12901 MAX FC 1280 NEXT L 4 1290 RETURN 1300 FOR M=1 TO N1 IITNS 1310 RI=BIDQ/DC 1320 R3=0IDQ 1330 FOR L 2 = l TO LllEEST LOOP 1340 C1=0 1350 H1=0 1360 M0=6 1370 FOR M8=1 TO MSfL2 ) C1 =C1tC(MZ(L2 ,M8 ) ) 1380 1390 I F Q ( M 2 ( L Z 3 M 8 ) ) < 0THEN 1540 1400 M0=M8 Q( M2( L2 ,M8 ) )=Q( M2( L2 ,M8 ) ) t1 14 10 1420 I F J(M2(L2,M8))=0 THEN 1470 1430 I F G( J ( M 2 ( L2 ,M8 ) ) )-H( J( M 2 ( L Z ,M8 ) ) )<=HI THEN HI =G( J( M 2 ( L2 ,M8 ) 1 )-H( J ( M 2 ( L2 ,M8 ) ) ) 1440 1450 M7=MZ(L2,MB)IPIPE TO NODEWITH MAX TDS 1460 60=G(J(MZ(LZ,M8))) 1470 NEXT ME 1480 I F H l i = l THEN 1540 1490 GOSUE 1120 1500 I F ( G Q - G ( J ( M 7 ) ) ) / C I ~ ' = R 1THEN 1540 1510 Rl=(G0-G( J(M7) ) ) / C l R3=(G0-H( J(M7)) ) / t G Q - G ( J ( M 7 ) ) ) 1520 1536 L3=L2 1540 FOR M8=1 TO MQ Q( MZ(L2 ,ME) )=Q(MZ(L? , M a ) ) - 1 1550 1560 NEXT M8 1570 NEXT L t 158@ FOR M7=1 TO M6(L3i 1590 Q ( M ~ ~ L ~ , M ~ ) ) I Q ( M ~ ( L )~t ,RM3 ~ ) 1600 NEXT M7 1610 NEXT M 1620 C 2 = 0 1630 PRINT " P n N l N2 1 / s tTDSng1 c / L 1 T D S 2 ' 1640 FOR M-1 TO M1 1650 PRINT USING 1660;M,I(M) , J ( M ) , Q ( M ) ,P(M) , C ( M ) ,G( 1660 IMAGE 2D ,4D ,4D ,4D ,6D ,50 ,SO 1670 C2=C2tC(fl)*Q(M)*315 1680 NEXT M 1690 C2=INT(C2 ) 1706 PRINT "COST ,R/a="i C Z 1710 ASSIGN 0Pathl TO 1720 EN0

INEXT LOOP

!NEXT PIPE 1470

J(M))

141

CHAPTER 9

INTEGER PROGRAMMING PLANN ING OF TREATED WASTEWATER CONVEYANCE FOR ARTIFICIAL RECHARGE OF AN AQUIFER

INTRODUCTION

The

international

growth

has been p e r s i s t e n t l y h i g h . l a r g e p r o p o r t i o n of living.

i n water

demand over

the

last

few

decades

T h i s r a t e of growth i s l i k e l y to c o n t i n u e a s a

the p o p u l a t i o n

is

increasing r a p i d l y

in

standard

of

The a v a i l a b i l i t y of new sources of water h a s tended to l a g b e h i n d

demand. Even i f new sources were a v a i l a b l e the cost of p r o v i d i n g to meet any

possible

drought

extreme

in

developing

account of the u n r e l i a b i l i t y of r i v e r flow.

areas

could

be

high,

on

Surface water can o n l y be used

i f a l t e r n a t i v e sources a r e a v a i l a b l e to meet essential

t o i t s f u l l e s t extent

demands i n times of d r o u g h t .

For t h i s reason the w o r l d i s now

l o o k i n g to

groundwater a n d wastewater to meet s h o r t f a l IS.

A scheme i s i n v e s t i g a t e d here to s u p p l y from groundwater o n l y a t

the

r a t e a t which i t can be n a t u r a l l y replenished.

Separate studies a r e b e i n g

conducted on t e r t i a r y

but

wastewater now

treatment of

to a r t i f i c i a l l y

wastewater

recharge groundwater

r e c e i v i n g consideration.

Such

research

with

is

cannot be expected to re1 ieve c u r r e n t droughts,

the

a

idea of

using

wastewater

long

term

the

is

only

project

and

w h i c h however p r e c i p i t a t e d

research i n t o a l t e r n a t i v e sources of water. It

i s proposed

resources

in

to

such

use groundwater

a

way

that

supplemented b y groundwater, Surface water

resources

can

groundwater reserves can r i v e r s (Paling, owing

to

natural

1984).

purification

and

resulting in a then

be u t i l i z e d

be d r a w n on

The

limited suitable

i n conjunction w i t h surface

deficiencies

r a t e of

surface

to

water

can

be

availability.

a g r e a t e r degree since

in times of

shortfalls

also

being available,

limited

water

higher overall

recharge w i l l

wastewater the

in

permeability

in surface

be r e l a t i v e l y the of

slow

possibility the

soil.

of The

h y d r a u l i c s of the recharge process should be i n v e s t i g a t e d w i t h s i t e tests. The case study a n a l y z e d i s the Witwatersrand area,

a h i g h growth r a t e

conurbation based o r i g i n a l l y on m i n i n g . Groundwater constitutes a t present o n l y one percent of the average d a i l y

2400 M l / d farming

to

and

the

Witwatersrand

gardening

purposes

supply

area. are

to t h e Rand Water Board of

Privately however

in

owned

boreholes

common

use

as

for

a

I

4

Fig. 9.1

Dolomite deposits i n the Witwatersrand a r e a

143

supplement to the formal

programmes intensified The

initiated,

of

around

source of

low r a i n f a l l

introduced,

of

of

1.

9.1

(Figure

Black

geological System, time

quartzites

is

in

outcrops

away

of

several

years

emergency

available

groundwater

weathered

zones,

Reef

from

of

occur

sources

deposits,

the centre a t

Series,

the

the

cavities

in

a

quartzites

a

wide

one

slope of

ten

and

Ventersdorp

the

mined

Pretoria

syenite

sanctioned

for

the

Series

dykes

groundwater compartments.

on

overly

Since some of

dewatering

in

these

the

order

pebble

W i twatersrand w h i c h were

The

series,

number of

some

small

and

Witwatersrand.

create a

shales and

virtually

vertical

independent

allow

safer

forming on the surface.

because of

The outcrops of

have

mining,

groundwater levels i n these compartments have dropped considerably. compartments have not been dewatered

and

r e s u l t i n g compartments to

and

circle

approximately

the l a t t e r renowned f o r i t s a u r i f e r o u s reefs,

extensively

intersections b y

which

These

the South dolomite o v e r l a y s

conglomerates

been

study

groundwater

thick, d i p gently To

one

the

dolomite deposits,

kilometer

at

and

Johannesburg

degrees.

F o l l o w i n g a series of

.

main

fissures

supply.

1980's water r e s t r i c t i o n s were

i n the e a r l y

the danger of

the Other

sinkholes

dolomite a r e g e n e r a l l y covered b y

a l l u v i a l deposits of v a r y i n g depth. Published studies on a r t i f i c i a l treated

wastewater

a r e almost

considerable depth,

recharge

entirely

u n d e r l a i n b y an

of the performance of

by

infiltration

conducted

with

in p r i m a r y

impermeable

layer.

partially

aquifers

Important

these schemes a r e the permanence of

of

aspects

the i n f i l t r a t i o n

r a t e and the reduction i n contaminants b y b a c t e r i o l o g i c a l processes a n d b y adhesion to soi I p a r t i c l e s .

1980),

(Bouwer et a l . , (Mathew

et

aquifer

Careful

selection

of

the

the p u r i f y i n g c a p a c i t i e s of in

the

Witwatersrand

the U.S.A.

1984) and A u s t r a l i a

I s r a e l ( l d e l o v i t c h and M i c h a i l ,

1982).

al.,

extensive testing of secondary

Successful p r o j e c t s a r e r e p o r t e d from

infiltration

site

and

the combined p r i m a r y and

area

will

have

to

precede

a

wil I

create

a

fluctuating

decision on the q u a l i t y of the i n f i l t r a t i o n water. An

actively

operated

groundwater t a b l e and

groundwater

reservoir

increased groundwater

flow

velocities.

Therefore a n

increased a c t i v i t y of s o l u t i o n a n d erosion processes i n the dolomite may be expected,

in

subsidence. certain

some

Built-up

compartments

cases areas

followed

by

the

occurence

located over some of

u n s u i t a b l e for

the

of

sinkholes

the dolomitic

envisaged

scheme.

areas

and leave

Simulation

of

groundwater movements a n d m o n i t o r i n g of the n a t u r a l freshwater/wastewater interfaces w i l l have to be done. Artificial

recharge

not

only

increases

the

available

amount

of

Fig.

9.2

S e w a g e w o r k s and r e c h a r g e s i t e s

145 groundwater,

it

schemes

groundwater

for

also

enables, use

by

its

more

stable

supply,

to

with

surface

waters.

conjunction

in

develop

A

s i m p l i s t i c model ( P a l i n g , 1985) indicates t h a t b y c o n j u n c t i v e use o f surface a n d groundwater the minimum guaranteed d r a f t can b e increased b y 10% of the total s u p p l y compared w i t h the s i t u a t i o n in w h i c h each source s u p p l i e s individually.

in the Witwatersrand a r e i s s t i l l m a i n l y o r g a n i z e d on

Sewage treatment a

municipal

watershed wastewater

basis.

which

collection

approximately

Johannebsurg

divides

the

is

located

three

two

with

(megalitres p e r

m u n i c i p a l i t i e s i s processed

the works

in

concerned,

500 M l / d

East of Johannesburg

operates

town

a

works

distinct combined

day).

South

areas

as

effluent

Sewage

from

in the m u n i c i p a l i t i e s of

as

output

of

as 6 Ml/d.

scheme c o u l d

Germiston,

the

surrounding

i n works w i t h c a p a c i t i e s a s small

a p o t e n t i a l a r t i f i c i a l recharge

of far

Boksburg,

involve Benoni,

B r a k p a n and S p r i n g s ( F i g u r e 9.2 and Table 9.1).

Table 9.1

Sewage works a n d Recharge site.

No.

Name

Discharge ( M l / d )

E l e v a t i o n (m)

a v e r a g e 1984

It that

1

Davey ton

8

1600

2

Mc Comb

6

1580

3

Jan Smuts

11

1610

4

Rynfield

11

1620

5

Ancor

30

1580

6

Benon i

15

1640

7

Mapleton

--

1580

8

Dekema

56

1530

9

Rondebul t

39

1560

10

Vlakp laas

44

1520

has been form

historical

t r i b u t a r i e s of

p r a c t i c e to

the' Vaal

discharge

River

the

upstream o f

in

effluent the

streams

intake

of

the

local Rand Water Board.

I n d i r e c t reuse in t h i s form h a s been p r a c t i s e d i n

the

since

Witwatersrand

area

1923

and

p u r i f i c a t i o n in streams and reedbeds, water.

I n t e n s i v e m o n i t o r i n g of

the

takes

place

after

and after d i l u t i o n with

streams

by

alleged fresh

the Rand Water

self river

Board

in

146

recent years h a s i n d i c a t e d a considerable contamination mainly

by

industrial

discharge

and

leaching

of

o f these

the

streams,

numerous

goldmine

dumps. Dolomite compartments are

limited.

suitable

Dewatered

compartments

with

for

artificial

compartments

built-up

a r e a s on

top

recharge and abstraction

the

gold

mining

have

been

mentioned.

in

area

and

Another

impediment c o u l d be t h e p e r c o l a t i o n from contaminated streams. Effluent

from

t r a n s p o r t e d to been a

established

sewage

water

works

by

pipeline.

the dolomite compartment

cheaper

alternative,

b u t closed

pipes

would

are

have

Canals

prefered

to

might for

be have

sanitary

For sewage works i n close p r o x i m i t y to each o t h e r in comparison

reasons.

w i t h the distance to a n y seepage a r e a combined c o n d u i t s be most economic whereas o t h e r sources may j u s t i f y minimizing

total

seperate conduits.

network

to be optimized.

I n the W i t w a t e r s r a n d s i t u a t i o n

clearly

distinct

clusters

are

which

of

network

enabled

model to be reduced to a minimum. works

cannot

be

the

Although

justified,

b u t may

be

considered

complexity

the

as

a

r e l o c a t i o n of e x i s t i n g sewage

future

economically s i t e d over the seepage areas. of economy of scale,

could

The

of

treatment

cost

probably

problem

discernable,

conveyance

would

new

works

T h i s would

may

be

more

use the a d v a n t a g e

increase conveyance cost due to the g r e a t e r

peak to average flow r a t i o f o r r a w sewage. Integer

network

programming

f i e l d of sewage conveyance. c e n t r a l i z a t i o n of Florida,

wastewater

has

Wanielista

found

treatment

Leighton a n d Shoemaker

several

a n d Bauer facilities

(1984) used

it

applications

(1972) a p p l i e d in

the

in

a

in

Econ R i v e r

similar

the r e g i o n a l i z a t i o n of wastewater c o l l e c t i o n and treatment

the

i t to the basin

fashion

for

systems

in Long

P i p e diameters were based on maximum p e r m i s s i b l e flow v e l o c i t i e s

decided

I s l a n d , New York.

COST ANALYSIS

for

p r a c t i c a l reasons.

The

was selected in each case.

next

larger

commercially

available

Based on a cost p e r metre

w i t h the length of the p i p e l i n e section known,

the t o t a l

pipe

size

in f i g u r e 9.3

and

costs f o r

supply

a n d construction may be c a l c u l a t e d . For

purposes

calculated using

of

estimating

the Darcy

pumping

equation.

w i t h the r e l a t i o n s h i p s i n Table 9.2. the

range

Q

interpolated.

=

10

-

50

Ml/d.

heads,

the

The costs f o r

friction pumps

was

head

was

estimated

The equations were based on d a t a f o r For

intermediate

heads

the

costs

are

w

c)

V

m

.r

0

-

u

0 0

E-

.

c

0 0 N

-

0

0

0 OD 0

0 L n

0

w 0

0

0 0 N

D

0 N 0

0

E

D 0

E 0

z N

D

D

z

D m 0

0

W 0

0 0 0

0

N 0

147

148 TABLE 9.2

The

Pump costs

Head (m 1

Cost

20

207.5

(Q i n Ml/d)

($1

40

217.5

* *

60

230.0

* a

costs

for

the

pump

motors

Q + 4625

Q + 4725 + 5800

were

based

on

the

shaft

power,

increased b y a 20% safety m a r g i n (see Table 9.3).

TABLE 9.3

Motor costs

Motor Power

Voltage

(kW)

(V)

0 - 250

400

250 - 1900 1900 - 6570

The number of

costs ($/kW

60

1000 - 3300

70

6600 - 11000

80

i n s t a l l e d pump sets depends on the flow

a n d the c o n t i n u i t y of t h i s b a s i c a n d one back-up

flow

volume.

set of pumps

was

For

h e l d to

under 50 M l / d a n d two b a s i c a n d one back-up F i n a l l y the costs f o r p i p e l i n e ,

the present

to be h a n d l e d

calculations

be s u f f i c i e n t

for

one

flows

sets f o r b i g g e r flows.

pumps a n d motors

are

added

procedure i s repeated f o r each of the 113 v a r i a b l e s p e r c l u s t e r .

up.

This

149

MATHEMAT I CAL FORMULAT ION

In

the

papers

by

Wanielista

Shoemaker

(1984) r e g i o n a l

plants

dealt

is

with

and

wastewater

in

one

Bauer

(1972)

conveyance

comprehensive

computer

W i twatersrand a r e a e f f l u e n t conveyance to recharge be

broken

down

in

a

number

of

Witwatersrand was developed that could

and

Leighton

to c e n t r a l i z e d model.

sites can

A

subsystems.

and

treatment For

the

successfully

network

of

the

In

incorporate a l l the subsystems.

p a r t i c u l a r the most complex subsystem comprises the s i x treatment works the

Benoni,

proposed

Brakpan

infiltration

and area

Springs municipalities at

Mapleton

1

(node

(node 7 ) .

The

6)

to

network

and with

in a its

possible flow d i r e c t i o n s i s presented in f i g u r e 9.4. I t i s the subsystems which could p o s s i b l y s u p p l y which a r e considered here.

At design stage i t i s u n c l e a r whether e f f l u e n t

should be conveyed from node 3 to node to minimize the costs. in the optimization

between nodes

5 o r the o t h e r way r o u n d in o r d e r

Both options a r e therefore l e f t f o r possible selection

procedure.

3 and 6.

The

The same considerations i n t r o d u c t i o n of

excludes the a p p l i c a t i o n of a dynamic Smith et a l . ,

the Mapleton a q u i f e r

apply

programming

approach

as

the

Rynfield

-

0----------------ODaveyton

,'; \,

-0'

i

MC

Maple1:on

Network w i t h possible flow d i r e c t i o n s

Comb

link

directions used b y

(1983). On the other h a n d integer programming can be

a p p l i e d to solve t h i s problem i n the f o l l o w i n g way.

F i g . 9.4

to

two p o s s i b l e flow

150

Each

plant

has

a

certain

design

o r i g i n a t i n g from a p l a n t must a t

discharge.

Every

pipeline

least be a b l e to convey

this

section

discharge.

As most l i n k s a r e supposed to convey e f f l u e n t from o t h e r p l a n t s a s w e l l , a series of flow r a t e s can be defined as a r e s u l t of d i f f e r e n t combinations o f By r e p r e s e n t i n g each flow r a t e in each p i p e l i n e section

d i s c h a r g e volumes. b y a seperate

i n t e g e r decision

v a r i a b l e the network o p t i m i z a t i o n c a n then

be formulated a s a n i n t e g e r programming problem.

The number of v a r i a b l e s

depends on the number of network nodes as well as on the number of In the present

w i t h t h e i r specific d i r e c t i o n .

example

the network

links

can

be

described b y 113 v a r i a b l e s . The flow required connected function

rate

pipe with can

dictates

diameter these

be

under

and

certain

pump

requirements

expressed

as

the

can

The

cost

factors

CCi

*

Ci

are

be

sum

v a r i a b l e s and the r e l a t e d cost factors, Objective f u n c t i o n =

conditions

capacities.

of

determined. the

products

below the

The of

the costs

objective

the

integer

or

Xi calculated

for

each

p i p e l i n e section as i n d i c a t e d i n the cost a n a l y s i s . developed to c a l c u l a t e

mentioned

Subsequently

thse cost

factors,

maximum flow volume from each node,

flow

volume

and

each

A separate p r o g r a m was

based on

the

input

of

(1)

the

( 2 ) the e l e v a t i o n of each node,

(3)

( 4 ) the maximum p e r m i s s i b l e flow v e l o c i t y a n d ( 5 )

the l e n g t h of each l i n k ,

the e f f e c t i v e p i p e roughness. P r o v i s i o n was made to e l i m i n a t e c e r t a i n

links

o r s u p p l y nodes i n o r d e r to m a i n t a i n the f l e x i b i i t y r e q u i r e d to a d j u s t network

for

other

program

was

program

makes

clusters

extended

u s i n g the I .B.M.

it

in

of such

immediately

treatment a

way

suitable

plants. that

for

the

The

cost

format

submission

of

for

the

calculation the

output

optimization,

mixed i n t e g e r programming p a c k a g e MPSX-370/MIP.

The c o n s t r a i n t m a t r i x

i s based on two simple p r i n c i p l e s

which exploit

the essential f e a t u r e of decision v a r i a b l e s : a) Y -

C Xi

5

zero

T h i s expression variables.

i s used to describe

I f Y = 1 at

least one X.

the

relationship

must b e present.

between

different

I n t e r a c t i o n s of

this

t y p e a r e m a i n l y of a p r o g r e s s i v e n a t u r e , but some r e g r e s s i v e steps h a d to be i n c l u d e d e.g.

i f l i n k 4-6 conveys Q1 + Q4, the

l i n k s 2-3,

2-5

and 2-7

may convey o n l y Q2.

b)

L X . = zero o r . u n i t y . For the r i g h t h a n d side t o equal one,

v a l u e one. zero.

only

I f the r i g h t h a n d side i s set a t

I f a l l p o s s i b l e flows

from a

one

zero,

particular

variable all

node a r e

a n d then set a t one, o n l y one flow w i l l be selected.

assumes

v a r i a b l e s must grouped

the be

together

151

The

combination

of

these

two

expressions

guarantee

unique

paths

through the network a n d together w i t h the o b j e c t i v e f u n c t i o n the p a t h w i t h the lowest costs w i l l be found.

RESULTS

Optimal artificial

effluent recharge

network

scheme c a r r i e d

appeared to i n d i c a t e f i g u r e 9.5a.

lising

velocity

2.2

of

configuration

configurations

the minimum

the flow m/s

would

the

be

around total

volumes total

$13.4

were computed

in

table

Under

Optimized c o n f i g u r a t i o n shown in f i g u r e 9.5b The r e l a t i o n between flow Since the p i p e diameter of

the

flow

velocity,

of

the

maximum

problem c o u l d be expanded

individually

separately,

to

one

potential inspection

a s estimated

and

a

for

maximum this

same

flow

the

( ~ / 4 D ) 2.

the s q u a r e root

velocity

to

1.2

m/s

million (figure 9 . 5 ~ ) .

slightly

by

the

inclusion

of

shows the s i t u a t i o n in which two c l u s t e r s

recharge

site.

Each

cluster

is

optimized

r e s u l t i n g in a cost of $11.2 m i l l i o n f o r the n o r t h e r n c l u s t e r as

indicated previously,

and $5.1

million for

the western

cluster,

bringing

the t o t a l to $16.3 m i l l i o n .

F i g . 9.5

in

selected

conditions

is Q = v

i n v e r s e l y p r o p o r t i o n a l to

reduction

sources 8 , 9 a n d 10. F i g u r e 9.6a supply

the

visual

was

costs

a

would cost $11.2 m i l l i o n .

r e s u l t e d i n a minimum construction cost of $17.5 The o r i g i n a l

9.1

r a t e and p i p e diameter

i s thus a

length

construction

million.

A

Mapleton.

pipe

for

Network o p t i m i z a t i o n . Node 1 to 6 represent sewage works and node 7 the i n f i l t r a t i o n site. See also T a b l e 9.1 a n d f i g u r e 9.1

152

L i n k a g e of networks. Node 1 to 6 a n d node 8 to 10 represent sewage works a n d node 7 the i n f i l t r a t i o n site. See a l s o Table 9.1 a n d f i g u r e 9.1

F i g . 9.6

An a l t e r n a t i v e arrangement from

the

northern cluster

via

which may save cost node 9

(see f i g u r e

i s to

supply

The

9.6b).

effluent

change

in

i n p u t d a t a f o r the n o r t h e r n c l u s t e r i n v o l v e s f i v e new v a l u e s f o r the l e n g t h of

the

the l i n k s between node 2, other,

resulting

in

a

3, 4, cost

5, of

6 on the one h a n d a n d node 9 on $11.1

million.

The

fact

that

the

c o n f i g u r a t i o n of the optimal network remains the same as i n f i g u r e 9.6a

is

coincidental. The

cost

increasing million

optimization

the flow

for

this

via

cluster.

of

the

node 9, The

western

resulting

total

cost

cluster i n an

thus

is

performed

optimized

amounts

to

cost $17.2

Hence the lay-out of the sewage works i n t h i s case i s such that of the two c l u s t e r s does not r e s u l t i n any f u r t h e r cost reduction.

+'

nodes 1 , 2

nodes 1 , 2 , 4 , 5 , 6

node 7 node 3 node 3'

-

-

- supply

points demand p o i n t l o c a t i o n of booster station alternative s i t e for

-

booster stati a,

F i g . 9.7

Optimum location f o r a booster s t a t i o n

a

after

of

$6.1

million. linkage

153

SUMMARY AND CONCLUS IONS

Integer programming p r o v e d to be a useful tool f o r the e v a l u a t i o n o f a least-cost

configuration

designed

to

a

It

takes

interrelations. computer

of

suit

node optimization

cases

with

seven

approximately

half

to c a l c u l a t e the cost factors and

f o r integer optimization.

I .B.M.

a p i p e l i n e network.

network

mixed can

support

a

and

second

p r o g r a m was

rather

on

an

complex

I.B.M.

3083

to compile a p r o g r a m s u i t a b l e

For a c l u s t e r of s i x s u p p l y nodes a n d one demand i n less t h a n 30 seconds u s i n g the

r e s u l t s were obtained

integer

be

The

nodes

programming

handled

by

package

subdividing

a

MPSX-37O/MIP.

system

into

Complicated

subsystems

and

o p t i m i z i n g each c l u s t e r i n d i v i d u a l l y . The f l e x i b i l i t y

of

the program enables one

to

i n t r o d u c e changes w i t h

minimal e f f o r t a n d to compare the r e s u l t i n g a l t e r n a t i v e s . This

feature

may

be

illustrated

by

the

follohing

example

of

an

economic o p t i m i z a t i o n of the location of a booster s t a t i o n ( f i g u r e 9.7). By v a r y i n g the d i s t a n c e between node 3 a n d

the other f i x e d

sequential search w i l l r e s u l t i n the optimum solution. o f MPSX-370/MIP prevent

the

applicability

each run g i v e a

can f o r

search

from

becoming

i s accompanied b y

a

The "range"

sensitivity

random

analysis

process.

the d i s a d v a n t a g e

nodes a

that

facility

and

The

thus

general

no p r o v i s i o n s a r e

made f o r i n t r o d u c i n g the costs f o r obstacles l i k e r o a d s a n d r i v e r s . Computer sewage

effluent

resulted visual

analysis

in a

the

conveyance

cost

inspection.

of

most

economic

an

artificial

to

r e d u c t i o n of A

lower

flow

16% over velocity

an

pipeline

configuration

groundwater optimum

increased

recharge

solution

the

total

based

for site on

construction

costs as the influence of a n increased p i p e diameter s t r o n g l y outweighs the reduced

cost

in

pumping

sewage works a f u r t h e r

equipment.

Depending

on

the

lay-out

of

the

r e d u c t i o n in the combined costs c o u l d p o s s i b l y be

a t t a i n e d b y i n t e g r a t i o n of i n d i v i d u a l clusters.

REFERENCES

H., Rice, R.C., Lance., J.C., and Gilbert, R.G., 1980. Bouwer, R a p i d - i n f i l t r a t i o n Research a t F l u s h i n g Meadows Project, Arizona. J. Water Polut. Control Fed., Vol. 52, No. 10, p 2457. I d e l o v i t c h , E. and M i c h a i l , M., 1984. S o i l - a q u i f e r Treatment - A New Approach to an O l d Method of Wastewater Reuse. J. Water P o l l u t . Control Fed., V o l . 56, No. 8, p 936. Leighton, J.P. and Shoemaker, C.A., 1984. An I n t e g e r Programming Analysis of the Regionalization of L a r g e Wastewater Treatment a n d Collection Systems. Water Resources Research, Vol. 20, No. 6, p 671.

154

Mathew, K., Newman, P.W.G. and Ho, G.E., 1982. G r o u n d w a t e r R e c h a r g e w i t h Secondary Sewage E f f l u e n t . A u s t r a l i a n Water Resources C o u n c i l , Technical P a p e r No. 71, C a n b e r r a . 1984. O p t i m i z a t i o n of C o n j u n c t i v e Use of G r o u n d w a t e r and P a l i n g , W.A.J., S u r f a c e Water Resources in t h e Vaal B a s i n . Proceedings o f t h e H a r a r e Symposium, IAHS P u b l . No. 144. P a l i n g , W.A.J., 1985. Economic O p t i m i z a t i o n of A l t e r n a t e Water Resources f o r the W i t w a t e r s r a n d . Water Systems Research Programme, U n i v e r s i t y o f the W i t w a t e r s r a n d , Report No. 4/1985. P a l i n g , W.A.J. and Stephenson, D., 1985. I n t e g e r P r o g r a m m i n g of T r e a t e d Wastewater Conveyance f o r A r t i f i c i a l Recharge o f a n A q u i f e r . J. Int. SOC. Ecol. M o d e l l i n g ( 7 ) . Smith, A.A., H i n t o n , E. a n d Lewis, R.W., 1983. C i v i l E n g i n e e r i n g Systems, A n a l y s i s and Design, John Wiley G. Sons. 1972. C e n t r a l i z a t i o n of Waste Treatment W a n i e l i s t a , M.P. and Bauer, C.S., F a c i l i t i e s , J. Water P o l l u t . Control Fed., V o l . 44, No. 12, p 2229.

155

CHAPTER 10

OPTIMAL PLANNING OF REGIONAL WASTEWATER TREATMENT I NTRODUCT ION i s a n elevated r i d g e in the

The Witwatersrand o r 'White Waters Ridge' h e a r t of South A f r i c a

formed

by

the

gold-bearing

quartzite

emerging above the surface of the s u r r o u n d i n g c o u n t r y . was

originally

secondary

in

discovered

industry

and

1886

tertiary

and

this

commercial

about f o u r m i l l i o n i n h a b i t a n t s of the area.

It

sparked

rock

strata

i s where the

development.

gold

growth

There

are

of now

The present water consumption

which i s s u p p l i e d b y the Rand Water Board,

averages 1700 Ml/day

and i s

i n c r e a s i n g a t a r a t e of 6 p e r cent a year. The Witwatersrand r u n s i n a n east-west watershed

(Fig.

10.1).

It

is

the

source

d i r e c t i o n a n d forms a n a t u r a l of

the

number

o r i g i n a l l y there were many s p r i n g s a l o n g the r i d g e , Waters R i d g e ' .

The

water

supply

of

streams

and

hence the name 'White

to Johannesburg

was o r i g i n a l l y

pumped

from the ground as the water resources of the a r e a were not p l e n t i f u l account

of

the

fact

that

the

r a t h e r than a r i v e r b a s i n ) .

elevated

ridge

was

an

origin

The streams to the n o r t h form

of

(on

streams

tributaries

of

the Limpopo R i v e r , a n ephemeral r i v e r w h i c h flows eastwards to the I n d i a n Ocean.

The streams to the south flow

i n t o the Vaal

River,

a tributary

of

the Orange R i v e r , which flows westwards to the A t l a n t i c Ocean. It water.

i s from The

constructed

the Vaal

Vaal in

River

Barrage,

1923,

r e l i a b l e sustained

50

followed

y i e l d of

that

the W i t w a t e r s r a n d d r a w s

km

by

these

south

the

sources

Water Board h a s r i g h t s to 2400 Ml/day. to downstream users. The Vaal, flashy Vaal

or

r i v e r a n d c a r r i e s much s i l t Dam.

On

the

other

hand

it

of

Vaal

the

is

3300

'murky'

(170 mg/l has

now

supplemented

by

r e l a t i v e l y untapped Tugela R i v e r , 300 km away. t a p p i n g the Orange R i v e r a t

The and

was

combined the

Rand

i s translated

is a

on the a v e r a g e ) beyond

relatively

o r i g i n a t i n g m a i n l y from s a l t s being

Ml/day

r i v e r as i t

( a v e r a g e 100 m g / l ) is

1933.

its

Some water must also be passed on

The Vaal

River

of

Witwatersrand,

in

Dam

most

little

dissolved

leached from water

diverted

the

salts

farmlands. from

the

P l a n s were considered f o r

i t s source a n d d i v e r t i n g these waters to the

Vaal b a s i n . These d i v e r s i o n schemes a r e expensive. On

the other

h a n d wastewater

treatment

technology

i s now

r a p i d l y and the cost of treatment i s a p p e a r i n g more a t t r a c t i v e . about 50 p e r cent

of

water

i s used consumptively

on

advancing Since o n l y

the Witwatersrand,

f

157

there

i s scope f o r

happening

water

indirectly.

Witwatersrand

finds

reclamation Most

and

water

i t s way,

In f a c t

recycling.

returned

a f t e r treatment,

to to

the

this

i s now

sewers

on

streams which

to the Vaal Barrage.

The Rand Water Board (1977) pumps 1000 M l / d a y

the Barrage. Most of

the b a l a n c e of

i t s supply

the

discharge

i s taken d i r e c t l y

from

from

the

Vaal Dam through a p i p e l i n e , which may be supplemented

i n the f u t u r e b y

a canal

leading

pumping

Some of

the e f f l u e n t

from

the

dam

from

wall

to

the Zuikerbosch

the Witwatersrand

which

finds

station.

i t s way

to

the

Vaal Barrage a n d i s not r e t u r n e d to the Witwatersrand

b y the Rand Water

Board,

The q u a l i t y of

i s consumed b y communities f u r t h e r downstream.

effluents

entering

the

Vaal

Barrage

thus

affects

the

cost

of

the

treatment

before f u r t h e r use of the water i s possible.

A

number

of

possible

schemes

to

re-use

the

wastewaters

of

the

Witwatersrand a r e possible:

1.

P a r t i a l treatment of waste water treatment p l a n t s on the Witwatersrand, and

return

of

the

effluent

f u r t h e r p u r i f i c a t i o n occurs. r i v e r water then, and/or

to

the

Vaal

Barrage

via

streams,

where

The e f f l u e n t s a r e d i l u t e d b y r e l a t i v e l y p u r e

a f t e r re-treatment,

pumped back

to the W i t w a t e r s r a n d

passed dOWnStream of the Barrage.

2.

Convey

3.

Reclaim e f f l u e n t on the Witwatersrand to a sub-standard

4.

Reclaim

wastewaters

Barrage,

from

the

Witwatersrand

to

the

banks

of

the

a n d p u r i f y them a t a combined works before r e - c y c l i n g .

i n a separate d i s t r i b u t i o n system f o r non-hygienic to

a

high

standard

and

re-cycle

and re-cycle

it

purposes.

together

with

the

water

pumped from the Vaal R i v e r .

5.

Install a

low-capital,

h i g h operating-cost,

reclamation f a c i l i t y

Witwatersrand and m a i n t a i n t h i s as a standby droughts. reliably

Draw be

from

drawn,

the Vaal

River

and

the

use

a

on

the

in case of n a t u r a l r i v e r

much h i g h e r d r a f t

reclamation

plant

than

when

could

shortfalls

occur.

6.

Install

low-capacity

reclamation

facilities

on

the

discharge the p u r i f i e d e f f l u e n t i n t o storage dams;

o r underground.

Draw on the Vaal

Witwatersrand

and

e i t h e r on the surface

R i v e r to a h i g h degree

as

for

(5)

and use the stored e f f l u e n t when s h o r t f a l l s occur in the Vaal R i v e r .

7.

Pass

partly

treated

effluents

downstream

of

the

Vaal

Barrage

in

constructed condu i t s.

Past p l a n n i n g and construction been

on

a

local

municipal

basis,

of waste water whereas

bulk

treatment water

facilities

supply

was

has the

158

r e s p o n s i b i l i t y of

the r e g i o n a l

Rand Water

Board.

The establishment This w i l l

r e g i o n a l waste water a u t h o r i t y i s now b e i n g contemplated. comprehensive facilities

planning

at

and combined

least

cost

to be achieved.

sewage o u t f a l l s can

be

s a v i n g s i n cost due to scale.

The location of

selected

overall

to

treatment,

result

in

least

cost

Regional

planned

i.e.

of

a

enable

treatment

with

treatment

of

consequent

facilities

sewers,

can

be

wastewater

and water s u p p l y .

I t i s w i t h these ideas i n m i n d t h a t a p r o j e c t to s t u d y the water s u p p l y

a n d waste water system of the Witwatersrand was embarked on.

THE MATHEMAT I CAL MODEL

The

system

of

dams,

streams,

wastewater

treatment

plants,

water works and c o n d u i t s between the W i t w a t e r s r a n d a n d the Vaal g r o w i n g more complex over the years. authority should

responsible

have

at

for

its

overall

disposal

As p o i n t e d out,

planning

data

a n a l y s i s models to f a c i l i t a t e p l a n n i n g . optimizing

planning

of

wastewater

is

Such

facilities

s u i t e of

A

treatment

is

a regional planning

desireable.

assimilation

potable River

computer

works,

a

and

body

systems

programs

for

sewers

and

outfall

water works should be a t hand. The system

i s described

in some cases not

linear,

to a r r i v e a t a least-cost

l a t e r b y equations a n d

The

chapter by

a

goes

master

on

to

methods

are

a r e needed

A s i m p l i s t i c mathematical model of p a r t o f

plan.

the system i s assembled below,

basins

constraints which

a n d n o n l i n e a r programming

and methods o f s o l u t i o n a r e o u t l i n e d l a t e r .

describe

program,

a

which

method

could

of

also

linking

neighbouring

consider

various

time

horizons. The set of c o n s t r a i n t s developed below i s f o r s t a t i c c o n d i t i o n s in a p a r t i c u l a r b a s i n . S t a t i s t i c a l l y averaged v a l u e s of flows,

water q u a l i t i e s

and

by

consumptions

distributions

are

would

taken. be

To

allow

for

variations

probability

possible

but

would

increase

F i g u r e 10.2.

The

diagram

embodies

theoretically

computat iona I time man yfo Id. Consider

the

simplistic

the f o l l o w i n g concepts: the Witwatersrand

system

in

the water requirements of a m a j o r consumer such a s

( 3 ) c o u l d be met from s u r f a c e resources

t r e a t e d wastewaters r e t u r n e d to the r i v e r a t from

(5).

The

wastewaters

from

(3)

could

Reclaimed

water

is

assumed

d i s t r i b u t i o n systems as r i v e r water.

to

partially

( 2 ) o r reclaimed waste water

be treated a t

t e r t i a r y treatment a t ( 5 ) o r d i s c h a r g e d i n t o the r i v e r a t treatment.

(11,

be

( 4 ) followed b y (6) after

circulated

in

the

limited same

The problem i s to determine what each

f l o w should be a n d what s t a n d a r d of treatment i s d e s i r a b l e .

159

SUE-SKTEM I

'. \ Fig.

\ 10.2 Water c i r c u l a t i o n d i a g r a m

Each source, node.

consumer,

treatment p l a n t o r j u n c t i o n

i s r e f e r r e d to as a

The v a r i a b l e s a r e the flow r a t e s between the nodes numbered

d i a g r a m and the respective p o l l u t a n t

concentrations,

i n the

.

and

are

all

designated Q. I-J

Pi-j

respectively

for

flow

from

node

to

i

node

The

j.

flows

expressed i n Ml/day. The p o l l u t i o n (TDS) o r a (BOD).

load may be conservative such as

non-conservative

total

dissolved solids

v a r i a b l e such as biochemical oxygen demand

I n the former case there must be a mass b a l a n c e of

pollutant

in

the system and i n the l a t t e r case the effect of the r i v e r a n d b a r r a g e s i n d i l u t i n g the p o l l u t a n t must be assessed. model.

BOD i s considered

Values of BOD a r e expressed i n mg/l

M l / d a y and p o l l u t i o n in mg/l

and

i n the present

the product

i s p r o p o r t i o n a l to the t o t a l

of

flow

in

load in tons/day

discharged b y a stream o r conduit. The object of

the study

i s to minimize

the cost

convenient to convert a l l costs to a common basis, redemption on c a p i t a l cost p l u s r u n n i n g costs, kilolitre.

Cost

coefficients,

or

variable.

Some

of

coefficients,

the

cost

water i n closed conduits, anticipated theoretically

incremental feasible,

are

It

is

a l l expressed in cents p e r

therefore

for

the system.

required

instance

for

for

each

conveyance

of

a r e n o n l i n e a r a n d must be approximated b y the

costs. it

rates,

of

say a n n u a l i n t e r e s t a n d

is

Although necessary

nonlinear to

objective

simplify

the

functions

model

as

far

are as

possible since there a r e f u r t h e r n o n l i n e a r c o n s t r a i n t s as w i l l be r e v e a l e d f u r t h e r on. capital

cost.

I f there a r e e x i s t i n g c o n d u i t s these w i l l But

existing capacity,

if

the

f u t u r e flow

along

a

route

e f f e c t i v e l y h a v e zero is

likely

to

exceed

i t i s o n l y the incremental cost of the new c o n d u i t s a n d

works which need to be considered. s i z i n g the v a r i o u s works.

Allowance f o r peak f a c t o r s i s made in

160

Associated

with

each

rate Q. .

flow

is a

conveyance cost

coefficient,

I-J

which

The v a r i a b l e p o r t i o n of

i s designated Ci.

the cost component

which

i s a f u n c t i o n of flow o n l y i s t h u s

‘1-2

’ ‘3‘3-6

‘2’2-3 Note that Q6-7

‘1

+

considered.

is

fixed

(10.1)

‘4‘4-3

+

its

so

cost

is

not

variable

i.e.

P u r i f i c a t i o n costs comprise a component p r o p o r t i o n a l component pollutant

proportional load

to

load removed,

pollutant

Q . . ( P . .-P.

removed,

conditions after

works

need

not

be

The cost of conveyance i n n a t u r a l channels i s zero.

I-J

I-J

treatment.

The

I-]

to

i.e.

effluent

of

.

and a

proportional

2

subscript

l a t t e r component,

produce a n

I-J

or

I-J

where

i s d i f f i c u l t to e s t a b l i s h a n d i n fact

a r e designed

.

Q. .P.

load

. ) l-J/2

to flow Q .

to

refers

to

cost p r o p o r t i o n a l

i t i s often assumed

reasonable

to

that

standard

with

treatment costs p r o p o r t i o n a l to flow r a t e . Vie w i l l consider the general case a n d designate

the coefficients

+ Q3-4

Since Q3-6

respectively.

of

Q

3-6 P3-4 a n d Q2-6 P2-3 as C5

is a

constant,

the

and

flow-proportional

C6 cost

can b e omitted. The equations o r c o n s t r a i n t s d e s c r i b i n g the system a r e formulated

Hall

(1977) formulated the system w i t h

similar

constraints,

but

next.

at

that

time was unaware of a simple method of solution. For flow b a l a n c e a t the v a r i o u s nodes: At

some source nodes such as

case we consider

(1

1,

the

yield

may

u n l i m i t e d augmentation possible,

be

limited

a t a cost.

but At

in our

consumer

nodes the s u p p l y must be s u f f i c i e n t :

42-3 ‘6-7

+

Q4-3

(10.2)

= a1

(10.3)

= a2

At consumer nodes the wastewater o u t p u t i s known:

(10.4)

‘3-4

+ ‘3-6 = a3 At treatment p l a n t s a n d o t h e r nodes the flows must balance:

Q3-4 - 44-2 ‘1-2

‘2-6

+ +

-

(10.5)

Q4-3 = 0

‘4-2

- ‘2-3

‘3-6

- ‘6-7

Note t h a t a l t h o u g h

-

‘2-6

=

‘6-8

=

the

(10.3) i t complicates

(10.6) (10.7)

v a r i a b l e Q6-7 the

cost

constants which may b e desired.

could

function

be e l i m i n a t e d

and

The number of

minimized i n simple cases b y s u b s t i t u t i n g Q

4-3

for

Q3-9 and Qg-6.

(10.2)-(10.7) c o n s t r a i n t s of

are the

It in

will fact

less-than

be all or

any

observed equations.

They

a slack

variable,

but

could

w i t h more meaning

in

The than

to

the

i s nevertheless a n d Q3-6 constraints

called

so

type,

v a r i a b l e s would be i n t r o d u c e d to form equations. fact

variables

the

equation

changes

f o r Q4-5 a n d

that

greater-than

later

using

equally which waste,

well

case

be

slack

Q6-8, i s i n

a purely

algebraic

161

slack

variable.

I n equation

(4)

the

waste

water

output

is

This constant i s in fact a f u n c t i o n of the consumption

constant.

given a2,

as

a

but i t

i s easier to i n s e r t a constant. There a r e other forms of c o n s t r a i n t s on the flow v a r i a b l e s

waste

water

barrage

C13-6

(10.2).

which c o u l d

For instance b a s i n c h a r a c t e r i s t i c s may l i m i t the amount of

be incorporated.

which

could

(economically)

O r i f the s u p p l y C12-3

be

discharged

beyond

the

was considered as two components;

one through e x i s t i n g c o n d u i t s a n d one t h r o u g h new conduits,

there

would

be a l i m i t on the c a p a c i t y of the e x i s t i n g conduits. The next set of c o n s t r a i n t s a p p l i e s to the p o l l u t a n t s .

Certain

l e v e l s of

p o l l u t i o n may be known: P I - 2 = a4

(10.8)

I n fact i t i s assumed f o r the BOD study t h a t P1-2 = 0. There may be t o l e r a b l e l i m i t s on c e r t a i n l e v e l s o f p o l l u t i o n : ‘4-2 ‘2-3 ‘6-7

5 5 5

a5

(10.9)

a6

(10.10

a7

(10.11

There i s an extent of n a t u r a l p u r i f i c a t i o n i n r i v e r s :

- ’4-2/2

’4-2

(10.12

= a8

(10.13) ( f o r f l o w 2 - 6) P2-3 - P2-3/2 = ag I n the case of TDS as the p o l l u t a n t there would b e n e g l i g i b l e r e d u c t i o n of P a t waste water treatment p l a n t s a n d the TDS a f t e r reclamation p l a n t s could be taken as zero. a n d P5-3 = 0,

-

‘3-4

‘4-2

i n the case of BOD,

i t can be assumed P1-2 = 0

and there i s some reduction i n P a t 4 a n d 9: (10.14)

=

(10.15)

- ‘9-6 = all ‘3-4 A mass balance of p o l l u t a n t s must be m a i n t a i n e d a t nodes:

(10.16)

(10.17)

Q3-4P3-4+Q3-6P3-4-Q2-3P2-3-Q4-3p5-3 Note P2-6 e q u a l s P2-3,

P4-5

= al 2

(10.18)

equals P4-2

a n d P3-9

e q u a l s P3-4

so these

s u b s t i t u t i o n s a r e made f o r s i m p l i f i c a t i o n . It

is

implicit

in

the

optimization

program

that

all

variables

are

non-negative a n d r e a l so these c o n s t r a i n t s a r e not s t a t e d e x p l i c i t l y . The general (10.2)-(10.17).

model

then

is

to

minimize

(10.1)

subject

to

constraints

A method of solution i s o u t l i n e d in the n e x t section.

162

OPTIMIZATION METHOD

It will linear

be

except

two-dimensional

observed for

that

the

constraints

objective

function

(16)-(18).

These

p r o d u c t s of v a r i a b l e s .

these products to separate functions,

and

constraints

constraints

are

involve

There a r e techniques f o r c o n v e r t i n g f o l l o w i n g w h i c h a technique known a s

separable programming may be employed to optimize the system. Hadley

(1964) proposed a simple method o f

transforming

a

p r o d u c t QP

b y i n t r o d u c i n g two new v a r i a b l e s M a n d N, such t h a t

+ P)/2,

M = (Q

-

N = (Q

P)/2

(10.19)

then

-

QP = M‘

NZ

(10.20)

and Q = M + N , P = M - N

(10.21) M and N a r e u n r e s t r i c t e d i n s i g n b u t t h i s i s p e r m i t t e d in the d e l t a method

of separable programming (IBM, The

separable

programming

1976). algorithm

is

based

on

the

fact

that

separable f u n c t i o n can be approximated b y piecewise

I i n e a r functions.

p o l y g o n a l a p p r o x i m a t i o n i s represented b y a set

special

of

variables,

a The

so

a n y v a l u e of M can be represented a s follows:

+

M = Mo

GIDl

+ G2D2 +

...Gk D k +...GRDR

(10.22)

where the Ds represent i n t e r v a l s of M a n d the special

v a r i a b l e s GI,

...,GR

a r e defined as follows: f o r M in i n t e r v a l k , G , = G 2 = G k-1 = 1

(10.23)

O(Gk(

( 10.24)

Gk+l

1

= Gk+2,..GR

= 0

(10.25)

M comprises a set o f i n t e g r a l i n t e r v a l s D u p to k - 1 p l u s a f r a c t i o n

i.e.

of i n t e r v a l k . Note that M’

=

where

+

+...

G E G E +... GRER 1 1 k k each i n t e r v a l Ek corresponds

Ma 0

approximations i n Fig.

10.3, Mo = 0,

(10.26) to

an

interval

Dk.

k = 4 a n d Gk = 0.3.

Thus

for

the

The v a l u e of M

can be confined to a known range. Although there i s a p o s s i b i l i t y of a t t a i n i n g a local optimum t h i s chance i s reduced i f the problem i s solved w i t h the special v a r i a b l e s set at

their

verify

upper bound,

the r e s u l t s .

a n d then w i t h

It will

them set

be observed

that

at

2R

their

lower

variables are

i n t o the model f o r each p r o d u c t in the o r i g i n a l c o n s t r a i n t s . d e s i r a b l e to s i m p l i f y

It

initially

bounds,

to

introduced i s therefore

the o r i g i n a l system a s much a s p o s s i b l e to minimize

163

the number o f products. The f o l l o w i n g s i m p l i f i c a t i o n s a r e introduced. i n t o two subsystems (see F i g .

10.21,

which

The system

will

i s subdivided

b e l i n k e d v i a a master

p r o g r a m a c c o r d i n g to D a n t z i g ' s decomposition p r i n c i p l e (Dantzig, a p p l i e d b y Stephenson (1970) to link r i v e r b a s i n s . considered

here and

there

will

be

shadow

1963) a n d

O n l y sub-system

values

imposed o n

1

the

is

cost

coefficients of Q (10.31,

P a n d Q2-6P2-3 b y the master p r o g r a m (C7 a n d C8). 3-6 9-6 (10.71, (10.11 1, (10.13) a n d (10.17) a r e thereby e l i m i n a t e d .

E l i m i n a t i n g Pg-6 C7,Cf5

using

Certain variables i s eliminated, and

(10.151,

= C5 + C7 a n d C I 6 = C6

(10.18)

,

and by

cost c o e f f i c i e n t s become C o g = C3

namely Plm2 substituting

respectively,

the

-

al 1

+ C8. a n d P5-3 a r e zero so c o n s t r a i n t (10.8) from

number

of

(10.12)

and

products

(10.4)

into

i s reduced.

(10.16) Now

the

problem i s :

subject

to: 0.28) 0.29) 0.30) 0.31) 0.32) (10.33) (10.34) ( 10.35) ( 10.36

(10.37) (10.38) Put

t

'4-2~4-2 = M - ~ ' Q2-3P2-3 = M i - N: Q2-6P2-3 = M =

-

N:

M Z - Nt

Q3-4p3-4 Then (10.37)

1

(10.39) (10.40) (10.41) (10.42)

a n d (10.38) c a n b e r e p l a c e d b y e q u a t i o n s (10.43)-(10.52):

164

(10.43 (10.44 (10.45 (10.46 (10.47) (10.48) (10.49) (10.50) (10.51) (10.52)

Each M2 a n d NZ comprises composite p o l y g o n a l

(10.22)

equation

and

computer d a t a i n p u t .

it

necessary

to

functions

define

the

according

intervals

c * ~ Q +~ c4a4-3 - ~

+ c;

(a3P3-&

-

to

in

The o b j e c t i v e f u n c t i o n must a l s o be r e - w r i t t e n

c1a1-2 + c2a2-3 +

min

is

the

as

+ N):

M:

(10.53)

b

t

Fig.

/

10.3 Polygonal a p p r o x i m a t i o n of a s e p a r a b l e f u n c t i o n

T h e problem may

once

the

expanded,

procedures using

the

thus

be solved

are

adequately

decomposition

by

straightforward

programmed, principle,

the

techniques, process

consider

to

horizons. The problem may also be considered i n more d e t a i l here.

Using decomposition

sub-programs

for

1975).

would

This

principles

individual ensure

waste

it

would

water

optimization

programming methods c o u l d be employed

be p o s s i b l e

treatment of

to

each

study

works

may

various

be time

than outlined to

incorporate

(e.g.

component.

pollution

and

along

CIRIA, Dynamic stream

reaches a n d optimize the s o a c i n g a n d s t a n d a r d of waste water p u r i f i c a t i o n

165

works d i s c h a r g i n g

i n t o the stream.

Where m u l t i p l e decisions a r e r e q u i r e d ,

f o r instance f o r a l t e r n a t i v e p u r i f i c a t i o n p l a n t

locations,

m i x e d integer p r o g r a m m i n g c o u l d be employed.

o r sewer o u t f a l l s ,

Computer s i m u l a t i o n s o f the

system a s a l s o r e q u i r e d t o study extreme c o n d i t i o n s a n d cost s e n s i t i v i t i e s t o supplement

the shadow

v a l u e s produced b y the o p t i m i z a t i o n .

There

o t h e r s o p h i s t i c a t e d techniques f o r o p t i m i z i n g n o n l i n e a r waste water (Chiang

and

Lauria,

above-formulated To would

recommended,

be

Pratishthananda

and

Bishop,

1977)

but

the

problem s i m p l i f i e d to a neat solution.

incorporate a l l not

1977;

are

systems

the

concepts

realistic

i.e.

c o u l d be continued

human

though,

in

a and

large number-crunching interactive

i n t e r v e n t i o n a t each step.

as data

are

updated

by

The p l a n n i n g

successive

program

programming

iteration

is

process of

the

master p r o g r a m a n d sub-programs.

REFERENCES

Chiang, C.H. a n d L a u r i a , D.T., 1977. H e u r i s t i c a l g o r i t h m f o r waste water p l a n n i n g . Proc. Amer. SOC. Civ. E n g r s 103 No. EE5, 863-876. CIRIA, 1975. Cost e f f e c t i v e sewage treatment - the c r e a t i o n of a n o p t i m i z i n g model. C l R l A Report 46, London. D a n t z i g , G.B., 1963. L i n e a r Programming a n d Extensions: P r i n c e t o n U n i v e r s i t y Press, Princeton, New Jersey, USA. H a d l e y , G., 1964. N o n l i n e a r a n d Dynamic Programming, pp. 448-465: Addi son-Wesley , Reading. 1977. A method f o r o p t i m i z i n g the c i r c u l a t i o n o f water in H a l l , G.C., u r b a n regions. N a t l . I n s t . Water Res. Council f o r Scient. a n d I n d u s t . Res. P r e t o r i a , R.S.A. IBM, 1976 Mathematical Programming System Extended/370, P r o g r a m Reference Manual, 2nd e d i t i o n , pp. 230-251. 1977. A n o n l i n e a r m u l t i l e v e l model P r a t i s h t h a n a n d a , S . a n d Bishop, A.B., f o r r e g i o n a l water resources p l a n n i n g . Waf. Resour. B u l l . 13 No. 3, 61 1-625. Rand Water Board, 1977. Annual Report. Stephenson, D., 1970. Optimum d e s i g n o f complex w a t e r resource projects. Proc. Amer. SOC. Civ. E n g r s 96, no. HY6, 1229-1246. Stephenson, D. 1978. Optimal p l a n n i n g of r e g i o n a l wastewater treatment. Proc. IAHS Symposium. Model I ing the Water Qua1i t y o f the H y d r o l o g i c a l Cycle. Baden, 125. 351-360.

166

CHAPTER 1 1

SIMULATION OF SEWER FLOW

I NTRODUCT ION

With the development of s u b u r b a n a r e a s w i t h i n c i t i e s to t h e i r

limits i t

i s becoming necessary to consider s u b d i v i s i o n a n d more intense r e s i d e n t i a l densities

i n suburbs which

were

previously

only

sparsely

effect of more intense development on the services,

populated.

The

such a s sewerage,

for

a n area must be considered before such increase i n d e n s i t y i s permitted. study of the consequences of increased l o a d i n g i s d i f f i c u l t , the

effect

may

cause

a

A method of

system.

p a s s i n g the

chain

reaction

identifying

increased

flow

was

down

possible

the

problem

A model

sought.

p a r t i c u l a r l y as

length areas

for

A

of

the

and

sewer

methods

rapidly

of

selecting a

p a r t i c u l a r area o r f o l l o w i n g the flows t h r o u g h a system was developed. There the

i s frequently

system

as

hydrograph,

well

i.e.

a n a p p r e c i a b l e time-lag as

attenuation

routing.

due

to

I n o r d e r to a l l o w

s i m u l a t i o n program seemed to b e the most

as h y d r o g r a p h s flow lateral

for

dispersion

down

of

the

these effects

a

computer

approach.

The

program

logical

can draw d a t a from e x i s t i n g l a n d use i n v e n t o r i e s wherein d a t a concerning a l l stands w i t h i n the m u n i c i p a l and

land

usage

type)

engineering data (i.e. and

condition)

are

are

area

(i.e.

floor

In

addition

retained.

sewer lengths,

compiled.

The

p r o j e c t s such as d a t a r e t r i e v a l

for

slopes, latter

areas,

number o f

data

connections,

data

drawing

may

files

containing

diameters,

be

sections,

rooms

used

drops

for

establishing

other depths

of connections a n d management o f the sewerage system a t a l a t e r stage. there a r e about 135 000 stands w i t h i n

As

the Johannesburg a r e a a systematic

a n d e f f i c i e n t way of s t o r i n g the d a t a was r e q u i r e d f o r t h i s a p p l i c a t i o n . The sewage

process design

of

computerization

flows

effectively.

also

enables

Whereas

it

design sewerage systems f o r

the estimated

over

it

ten

different manholes,

hours of

the d a y ,

components. leaks

from

Stormwater sanitary

accounted f o r separately. may

also

successive

be

considered.

hydrographs

i s now

peak

possible

ingress, fittings

was

engineers

flows to

sewage

estimate

necessary

based on

divide

infiltration and

to

previously

the

through

to

averages flow

into

joints

in

may

be

discharges

The a c t u a l time d i s t r i b u t i o n of sewage d i s c h a r g e s This

will

contribute

therefore h a d to be gathered

affect to

an

the

hydrograph

outfal I.

in o r d e r to p r o v i d e

the

lags

where

Considerable subdivision

a n a l y s i s a n d the development of c o n t r i b u t o r y h y d r o g r a p h s .

for

data the

167

Considerable

work

has been

done

South

in

Africa,

particular

in

by

Shaw (1963) a n d Crabtree (1976), on e s t a b l i s h i n g c o n t r i b u t o r h y d r o g r a p h s . The a c t u a l l a g g i n g of h y d r o g r a p h s a n d consideration of r o u t i n g effects a n d p r o b a b i l i t i e s of d i f f e r e n t

connections

been tackled on a r e a l scale. probably

received

synthesizing

more

inflow

discharging

The a n a l y s i s of

attention

and

the

larger

h a v e not

in storm d r a i n s has

1981)

(Stephenson

hydrographs

simultaneously

flow

due

to

the

scale

of

storm

ease

of

sewer

systems (Stephenson a n d Hine, 1986).

HYDRAULIC ANALYSIS

In employing backwater However,

a

effects,

routing

al I

if

computational

computer

these

time

simulation and

probability

components

would

method

be

were

effects

increased

and

so

on

can

also

be

shown

attenuated (Chan a n d Wang, One computer

model

to

simulates

the flow

types a n d

be

included. program, hydraulic

these effects

individual

and

lavatory

flushes

be

rapidly

theory

to

down sewers a n d accounts

times of

lengths of sewer number 135 000,

in fact a p p r o p r i a t e to a n a l y s e the flow therefore e x i s t s f o r

lag,

one The

some of

probability

time

1980).

time l a g as well as d i f f e r e n t individual

using

in

considerably.

Peaks due

for

could

considered

equations were therefore s i m p l i f i e d b y o m i t t i n g time l a g r o u t i n g was employed.

allowance

abstracting

data

inflow.

as

for the

i t i s often not convenient o r

in each sewer.

from

However

relevant

Another

areas

program

which

a n a l y s i s and even f o r condensing the d a t a so t h a t a number o f

require

lengths of

sewer could be considered together to speed a n a l y s i s (Constantinides, 1982). I t i s possible to i d e n t i f y build

the

correct

program i s to study times

of

day

at

the type of

contributor

the l a g and

which

the

inflow

hydrograph.

flows

One

i n each case i n o r d e r of

a t t e n u a t i n g effect start

and

the

to

of

the

on h y d r o g r a p h s .

The

increase

objects

and

subsequently

decrease a r e therefore important a n d f i e l d measurements were r e q u i r e d .

FLOW MEASUREMENTS

Measurements were made in manholes as n e a r a s possible to the source of sewage in o r d e r to minimize the time to r o u t i n g down the sewers.

l a g a n d t o a v o i d a t t e n u a t i o n due

The flow depths in t h e sewers wer gauged a t

manholes over a p e r i o d of weeks a n d the r e s u l t i n g h y d r o g r a p h s plotted. The v a r i a t i o n s from week to week

were s l i g h t and s i m i l a r

averaged f o r compil i n g the hydrographs.

weeks

The o b s e r v a t i o n s t a k e n a t

were night

168

in

dry

weather

were

assumed

comparing these r e a d i n g s a t dry

periods

infiltration during

was

it

and

and

possible

leakage

after

to

from

summer

indicate

the end of to

leakage

estimate

the

the

plumbing

storms

plus

summer a n d

indicated

infiltration.

the end of

relative

systems. storm

in

proportions

of

Observations

inflow

By

winter

to

the

made

system.

R a i n f a l l i n Johannesburg i s n o r m a l l y r e s t r i c t e d to the summer season when h i g h i n t e n s i t y storms of sewers

were

assumed

short to

duration

flow

occur

during

unsurcharged

surcharged conditions were d i s c a r d e d a s they

the

during

would

afternoons. storm

The

flow

and

h a v e been d i f f i c u l t to

use for e s t i m a t i n g a c t u a l c o n t r i b u t i n g flows. The peak flow r a t e d u r i n g the d a y f o r h i g h e r

1.17

I/min

ingress. system

per

house

leakage,

income housing averages

infiltration

and

stormwater

The amount of leakage from the p l u m b i n g system i n t o the sewerage i s estimated

to

throughout the year.

0.05

excluding

be

0.06

I/min

per

house,

in

sewers

poor

soil.

The

hours

additional

flow

during

the p r e c i p i t a t i o n over

and

after

suggested

two-year

storm of 5 mm/h.

to peak flow

to be 2 mm/h

i s 0.05

design

storms

the catchment.

T h i s flow i s also associated w i t h the one-year

storm over n h o u r s which i s estimated The flow

day

This i s greater for older

v a r y w i d e l y depending on the methods o f c o n t r o l l i n g stormwater gullies.

a

in l e a k i n g sewers i s estimated to be

The i n f i l t r a t i o n

I/min p e r metre of sewer p e r metre diameter.

estimated to a v e r a g e 1 % of

24

over

inflow

recurrence

f o r general

mm/h

which

The e f f e c t i v e c o n t r i b u t i n g area

is

This w i l l into

interval analysis.

is

1%

of

the

50 m

i s about

w i d t h of catchment p e r metre of sewer. Up to 5%, assumed

and

in

50 m wide

some cases.

i s o l a t e d cases even

strip

over

all

more,

of

was

found

sewers

The a c t u a l sewer flows often

the

rainfall

over

an

sewers

in

-

even

to

g l a s s f i b r e flume was used

in

to e n t e r

increased b y over 50%

69% d u r i n g a n d a f t e r a storm. I n the case of the

invert

of

a

the f l a t a r e a s a special manhole.

to measure

has

a

curved

that

the

results are

existence o f s i l t a n d so on. Where possible, to gauge flows. c i r c u l a r chart

a r e changed a t weekly P o r t e r meter was minute intervals.

integrated total intervals.

installed for

flow

a

block

which

273

affected

of

by

flume was

the used

these flumes was on a

r e a d on a

To g i v e continuous

several

not

a conventional

The normal method of r e c o r d i n g a t w i t h an

from

hump

T h i s e l i m i n a t e s the problem of a s c e r t a i n i n g e x i s t i n g sewer g r a d i e n t s . the fact

flows

a

flats.

is

small

and

it

advantage

relatively

bottom

made

Another

possible

This

meter;

flow

the

rates

a

weeks t o g i v e a c c u r a t e d a t a

charts Fisher at

15

169

The

input

hydrographs

were

reproduced

by

the

computer

using

a

F o u r i e r series t y p e of c u r v e f i t .

H i g h e r income r e s i d e n t i a l

An area o f houses

and

1220 h a w i t h

approximately

newer

houses

including

well

town

e s t a b l i s h e d medium-sized

houses

development of the h y d r o g r a p h taken in a h i g h e r (Fig.

11.1).

Equivalent

house u n i t s were

servant

accommodation

is

allowed

for

for

a

150 m2 f l o o r

the area area

to a l l o w f o r the r e d u c t i o n

in flow p e r u n i t of f l o o r a r e a as houses a n d f l a t s

and

selected

income r e s i d e n t i a l

based on

to the power of 0.8

normalized b y r a i s i n g t h a t

was

at

increase in size.

the

rate

of

one

Hotel house

e q u i v a l e n t u n i t f o r every three rooms. Shops, offices,

schools a n d churches

a r e allowed f o r a t the r a t e of one house e q u i v a l e n t

per

area.

Metered (November 1981) 58 5 67 8 1164 24 0

Daily Iota1 kl Average Its Peak 11s Minimum 11s

'"t

.-. 0.

300 m2 of

Calculated 58 7 68 0 1156 24 0

Calculated flow Melered llow

I

I

3

0

9

6

12 Time of day h

15

18

21

24

Comparison of c a l c u l a t e d a n d metered f l o w s in h i g h e r income r e s i d e n t i a l areas

Fig. 11.1

Minimum o r base flow was assumed to be due to i n f i l t r a t i o n a n d manholes o r to leakage w i t h i n equal to 41% of the average, At

5.15

a.m.

which occurs

at

the flow

8 a.m.

the b u i l d i n g s .

start

work

at

This

7

This

was

i n t o sewers shown

to

be

o r 20% of the maximum flow in d r y weather.

rises r a p i d l y flow

a.m.

congestion demands an e a r l y s t a r t

to

within

pattern

residents in Johannesburg get up a t 5 a.m. workers

city.

floor

and for

80% of maximum flow,

suggests onwards.

office

workers

that

higher

Generally, at

8

income

production

a.m.

Traffic

those t r a v e l l i n g the 12 km i n t o the

170 The evening meals,

peak occurs

at

a n d so on,

ablutions

7 p.m.,

about

and

activity

indicating

ceases

at

preparation

midnight.

of

Maximum

flow p e r u n i t was found to average 1.17 I/min.

Low income residential Detailed income

land

use d a t a

residential

area

were

not

available for

11.2).

(Fig.

Details

of

the study houses

of

and

the

low

flats

were

a b s t r a c t e d from c o n s t r u c t i o n d r a w i n g s a n d checked on s i t e before the sewer d a t a were used. Lenasia

-

monitored

The a r e a chosen embraced most of

-

a town 25 km south o f Johannesburg

A

a flume.

with

time

l a g of

comparing the h y d r o g r a p h measured

with

one

the newer

hour

the

sections of

a n d the sewage flow was

allowed

hydrograph

at

for

was when

the p o i n t

of

origin. Monday 461

Daily Iota1 kl Average. 11s Peak. Us Minimum. U s

,Tuesday

Wednesday

462 5 32 1532 0.28

531 14 77 0.15

460 5 30 1450 0.28

Average

Calculaled

461 531 1486

463 54 14 7

0.23

0.3

-- -

15

Calculaled l b w Monday 30 January 1984 Tuesday 31 January 1984 ........... Wednesday 1 February 1984

...

5

a

E

l 1

0

6

3

9

15

12

. 21

18

24

Time of day h

F i g . 11.2.

Comparison o f c a l c u l a t e d a n d metered f l o w s i n low income r e s i d e n t i a l a r e a s

Rapid increases i n flow occurred a t 5.30 smaller peak a t 10 a.m. departure

of

particularly

the on

a.m.,

p e a k i n g a t 7.15

a.m.

i n d i c a t e d g r e a t e r a c t i v i t y i n the home a f t e r

working

population

-

Mondays

the

than

traditional

p r o p o r t i o n of the f a m i l y c o u l d remain a t home,

in

higher

washing which

income

day.

A

A the

areas, greater

i s also indicated b y

the smaller evening peak a t 8 p.m. Maximum flow p e r house u n i t amounted to 0.46 flows

metered

b u i Idings.

are

due

to

the

recent

I/min.

construction

of

The low minimum all

sewers

and

171

Apartment buiIdi n g s

A

large

selected

complex

for

the

known

study

comprises 273 f l a t s

as

Helderberg

in

of

an

apartment

(flats)

a

total

with

of

Berea,

585 rooms.

Johannesburg,

area

(Fig.

Metering

was

was

11.3).

It

c a r r i e d out

close to t h e b u i l d i n g so the time l a g was minimal. Points infiltration

of

interest

and

m o r n i n g peak,

of

leakage,

the

hydrograph

the

sharp

rise

include and

have something

Inflow starts

later

to do than

with

the

i n other

p.m.

television

residential

g r e a t e r p r o x i m i t y of these f l a t s to places of work.

Monday

10

238 2 74 8 66 0 27

Tuesday 2295 2 66 7 45 041

-

Wednesday 241 9 2 82 8 66 0 46

---

-.-

Thursday 2374 276 8 31 052

of

in

the

p.m.

which

flat-dwellers.

possibly

due to

the

Maximum flows appear

2.05

i.e.

Average 2367 275 027

of

fall

a n d 9.30

areas,

level

each d a y except on

viewing

t o be h i g h e r t h a n i n other types of development, Daily lolal hI Average 11s Peak 11s Minimum lls

low

subsequent

the secondary morning peak a t 10 a.m.

the Thursday a n d the d i s t i n c t i v e peaks a t 7.30 may

the

I/min p e r u n i t .

Calculated 240 28

86 03

042

Calculated (low Monday 21 November 1983 Tuesday 22 N o v e m k 1983

G

Time 01 day h

F i g . 11.3

Comparison of c a l c u l a t e d a n d metered f l o w s i n a f l a t a r e a

Commercial a r e a s

For the study of a commerical a r e a ( F i g .

11.4)

business d i s t r i c t of Johannesburg was selected.

a p o r t i o n of t h e c e n t r a l

House e q u i v a l e n t u n i t s were

obtained on the b a s i s of 300 mz of f l o o r a r e a a n d amounted to 3026 u n i t s , i n d i c a t i n g a t o t a l f l o o r a r e a of

90.8

ha.

The development

i s exclusively

commerc i a I. A r a p i d increase in flows occurred a t

occurred a t 1 1 a.m. around

3

p.m.,

6 a.m.

The peak m o r n i n g flow

Flows then d e c l i n e d u n t i l a r a p i d increase o c c u r r e d a t

resulting

in

the

peak

daily

phenomena a r e i n d i c a t i v e of normal o f f i c e hours.

flow

at

4

p.m.

These

The afternoon peak must

b e due to the use of l a v a t o r i e s a n d washing j u s t before s t a f f l e f t work.

172

The base f l o w s

are

high

relative

to

higher

income r e s i d e n t i a l

areas,

w h i c h can be a t t r i b u t e d to a h i g h leakage r a t e . 20-23 April 1982 4955 6 57 4 90 5 31 9

Daily average total kl Average 11s Peak 11s Minimum 11s

150

I

5-8 July 1982 47185 54 6 94 7 30 0

Average 4837 0 56 0 92 6 30 9

Calculalecj 4849 8 56 1 93 2 30 3

-

Calculated llnw

......Weekday tlow 20-23 Aprll 1982 -..... . Weekday l l w 5-8 July 1981

I

I

0

3

6

9

12 Time 01 day h

15

18

21

24

F i g . 11.4 Comparison of c a l c u l a t e d a n d metered flows in a commercial

area

Industrial

Several

industrial

reasonably generally were

areas

were

r e a l i a b l e method of mixed b u t d i d not

established

based

investigated

simulating

include any

100

on

mn

of

in

flows. heavy

floor

detail

to

Types of industry.

area

establish industry

Initially

units

showed

large

which

discrepancies in flows due to t h e predominance of h i g h o r

low water

b y i n d i v i d u a l f i r m s w h i c h bore no r e l a t i o n to f l o o r a r e a .

Variation

f l o o r area p e r u n i t d i d not therefore g i v e consistent to another.

a

were

usage of

the

r e s u l t s from one a r e a

I t was found t h a t a c t u a l water s u p p l y g a v e the best i n d i c a t i o n

of e f f l u e n t discharge.

Water meter r e a d i n g s a r e n o r m a l l y taken e v e r y

months i n Johannesburg a n d stored

in

computer

e x t r a c t meter flows over a three-month average d a i l y flow of 800 I / d a y . f o r t h i s study

files.

It

was

three

possible

p e r i o d a n d then base u n i t s on

to an

An i n d u s t r i a l a r e a o f 160 h a was selected

( F i g . 5 ) . M a j o r i n d u s t r i e s i n c l u d e d yeast m a n u f a c t u r e w h i c h

has a v e r y h i g h water usage.

CONCLUSIONS

The composite h y d r o g r a p h s p r e p a r e d from sewer flow measurements 1 1 .l-11.5)

indicate

varying

peak

times

and

the

i n d i v i d u a l h y d r o g r a p h s i s thereby emphasized. be c u m u l a t i v e a n d as peaks.

The

time

a

l a g of

result

sewer

individual

Out-of-phase

capacities

contributor

importance

need not

of

(Fig.

assessing

peaks w i I I be

hydrographs

the

also

not

sum of adds

to

173

the attenuation effect. The computer s i m u l a t i o n program i s used f o r the p l a n n i n g a n d of

extensions to

the

sanitary

sewer

collection

network.

The

new

routes,

facilities,

size

temporary

diversion

works,

program

is

or subdivision,

used to i d e n t i f y bottlenecks, study the effects of re-zoning plan

design

plan

alternative

size t r u n k sewers a n d estimate loads a t o u t f a l l works.

The

program

is

contributions

and

sections.

is

It

to

linked plotting

proposed

to

to

a

land

program estimate

use

inventory

for

drawing

future

flows

for

sewer using

assessing longitudinal

a

land

use

c l a s s i f i c a t i o n established in the computer d a t a b a n k . Dailylolal k l Average I/s Peak lls Minimum 11s

300 -

Monday

Tuesday

Wednesday

Thursdav

Average

Calculated

10317 1194 216 5 60 2

11157 129 1 208 5 69 9

10565 122 3 208 5 75 0

10423 1206 2165 67 4

10615 1228 2125 68 1

10647 1232 2132 74 5

--..-.-........

Calculaled llow Monday 5 July 1982 Tuesday 6 J U I ~1982 Wednesday 7 July 1982 Thursaay 8 July 1982

,7 E FE R EN C ES Chan, W.Y.W. a n d Wang, L . K . , 1980. Re-evaluating H u n t e r ' s model f o r r e s i d e n t i a l water demand, J. Am. VJat. Wks Ass. Constantinides, C.A., 1982. Comparison o f time l a g and k i n e m a t i c flow i n conduits. Water Systems Research Programme, University of the Witwatersrand. Crabtree, P.R., 1976. Flow a n d i n f i l t r a t i o n g a u g i n g in sewers. N a t i o n a l B u i l d i n g Research Institute, Concil for Scientific and Industrial Research. P r e t o r i a . Shaw, V.A., 1963. The development of c o n t r i b u t o r h y d r o g r a p h s f o r s a n i t a r y sewers and t h e i r use in sewer designs. Civ. Engr. S. A f r . 5, No. 9, 246-252. Stephenson, D., 1981. Stormwater h y d r o l o g y a n d d r a i n a g e , E l s e v i e r , p 276. Stephenson, D. and Hine, A.E., 1986. Simulation of sewer flow. M u n i c i p a l Engineer, 3. 107-112.

174

APPENDIX 11.1

PROGRAM SEWS IM

T h i s i s a micro-computer

(HP9816) o r i e n t a t e d

version of

a

program

to

store d a t a and s i m u l a t e flows down s a n i t a r y sewage networks. Contributor

hydrograph

types of

development

(type 2),

industrial

flows

unit

per

number o f

e.g.

characteristics residential

(type 3)

(P/min/100m2)

programmed

100m’

in

various

lower

class

( t y p e 4). The

actual

peak

b e . inserted

in

the

t h e case of

a n d peak in P/min/HE

for

(type 11,

class

a n d commercial must

(HE) or

house u n i t s

r e q u i r e d f o r each p i p e ,

are

upper

data.

Equivalent

non-residential,

is

f o r each section.

Hydrographs a r e accumulated w i t h time l a g proceeding down a l l sewers. Time l a g s a r e based on f u l l p i p e v e l o c i t y a s h y d r o d y n a m i c a n a l y s i s would be too time consuming a n d not worth the e f f o r t . Hydrographs over a n y p e r i o d of f o r any time i n t e r v a l

(e.g.

maximum) a r e t a b u l a t e d , Also

indicated

overflow

volume

are

e.g.

24h

(starting at

midnight)

selected p i p e s ( s a y 10

and plotted i f required. maximum

i f not

time

l h ) f o r a n y number of

flow

adequate.

for

A

every

summary

pipe,

of

pipe

its

capacity

lengths

and

and inflow

areas i s t a b u l a t e d a t the end. Each sewer i s i d e n t i f i e d b y a number.

The n u m b e r i n g system f o r sewers

can be selected such t h a t the f i r s t two d i g i t s of a 6 - d i g i t the o u t f a l l region,

number i n d i c a t e

the second two the s u b u r b a n d the l a s t

two the a c t u a l

p i p e which i s assumed t h e same as the top end manhole.

Effect o f Local Peaks ( P r o b a b i l i t y a n d R o u t i n g )

The design flow from a house connection f o r sewer design 1,5P/min. effect

of

The a c t u a l peak d i s c h a r g e i s c o n s i d e r a b l y a

number

of

houses

is

accumulated

is typically

h i g h e r b u t when

the

above

the

figure

is

reasonable. A proof t h a t the instantaneous peaks c a n be neglected follows.

A

typical

toilet

f l u s h occurs a t

Frequency of f l u s h i n g p e r house.

a

rate

of

204

in

a t peak p e r i o d s i s once e v e r y 2,5

7

sec

i.e.

3P/s.

minutes = 1/150s

Therefore a f t e r 7 houses mean flow/house assuming o n l y 1 house

flushes a t a time,

i s 1,2P/min

-

w h i c h i s a normal design flow.

i.e.

after

10 houses o r so the flushes a v e r a g e to g i v e a normal flow design f i g u r e . The p r o b a b i l i t y 1/400,

of

any

two houses f l u s h i n g

a n d of 3 houses 1/8000 etc.

from each house together

i.e.

i s remote.

simultaneously

is

(7/150)’

=

remote so the coincidence o f a peak

I n any case those peaks a r e

rapidly

175 attenuated b y the r o u t i n g effect described below.

Routing effect (Graphs from Stormwater Hydrology a n d D r a i n a g e Stephenson,

1981 )

In

order

to

.

shorten

running

h y d r a u l i c r o u t i n g effects.

time,

the

program

does

The f o l l o w i n g section i s proof of

r o u t i n g has a n e g l i g i b l e effect on peak flows.

include fact

that

Routing i s the s p r e a d i n g of

in peak due to

a wave and corresponding reduction

not the

hydrodynamic

forces.

I t i s superimposed on the time l a g effect. f o r 7s in a

Consider the depth corresponding to a flow of 3P/s dia.

150mm

d r a i n a t a slope of 1/100:

From a c h a r t f u l l flow Qf = 2OP/s. Therefore Q/Qf

= 0.15.

Therefore r e l a t i v e depth a t 3 t / s from the c h a r t i s y/D = 0.25 Now f o r

a reduction

in

depth

from

0.25D

to

0.125D

(i.e.

half

original

d e p t h ) from the c h a r t

Ey

0 15*x ~0.013a100 - = 15m 0.003'7

.'. i.e.

x = t2m

depth h a l v e s i n 12m of sewer pipe.

Therefore the r o u t i n g effect

i s v e r y r a p i d to s t a r t w i t h i f the flow

is

v e r y low. On the other h a n d the r o u t i n g effect on a h y d r o g r a p h from 100 houses i s c a l c u l a t e d below: Flow r a t e q = 1.5P/min 0.003 x 8h x 3600. i.e.

x

i.e.

100/60s

depth w i l l

3e/s

=

as

well,

b u t Q(volume)

h a v e over 12rn x 3600 x 0/7

i s now

= 50

km

n e g l i g i b l e r o u t i n g over the f i r s t km o r so and b y then the number of

c o n t r i b u t i n g houses w i l l f a r exceed 100.

Non-Circular

Sewers

Conduits

are

sometimes

non-circular

e.g.

rectangular

culverts

or

egg

176

shaped.

Then

the

'diameter'

i s the h y d r a u l i c r a d i u s , a n d P the

wetted

equal

perimeter,

to A/P

at

full

results.

the c o n d u i t w i l l

and A i s t h e cross sectional flow.

correct time l a g i n the computations, flow c a p a c i t y of

where R

in the d a t a may be r e p l a c e d b y 4R

This

procedure

results

w h i c h i s taken f o r the f u l l

however b e i n c o r r e c t l y

The a c t u a l d i s c h a r g e c a p a c i t y

area, in

flow.

indicated

the The

in

the

is:

A

Q = A v =

-

De2 Qe

4

i.e.

the i n d i c a t e d flow Q

the

true

cross

i n the computer p r i n t o u t should be m u l t i p l i e d b y

sectional

e q u i v a l e n t diameter 4A/P

area i.e.

divided

( nDe'/4)

by

where

De

is

the

true capacity Q = (P2/4nA)Qe.

I n f l o w Components

I n f l o w to each sewer from connections, groundwater

i s assumed to comprise four

stormwater

ingress,

a

function

components; of

i n f i l t r a t i o n which i s a f u n c t i o n of s e w e r

sewer length,

sewage flow

length, and

steady

leakage.

Each parameter can be s u p p l i e d i n the d a t a a n d u n t i l more a c c u r a t e d a t a i s available,

the f o l l o w i n g f i g u r e s a r e suggested:

Sewage I n f l o w equivalent

: Peak net

i n f l o w r a t e of

1.0

litres

per

minute per

house

i s average i n m i d d l e c l a s s r e s i d e n t i a l areas.

:

Stormwater

From

gulleys,

I n f i l t r a t i o n : 0.15

manholes

and

leaks,

mm/h.

1%

About

of

1% x 10mm/h = O.lmm/h.

p r e c i p i t a t i o n r a t e . e.g.

l i t r e s p e r m i n u t e p e r metre of sewer p e r metre diameter.

Increase for o l d sewers.

L e a k s : from c i s t e r n s , equivalent.

Inflow

d r i p p i n g taps etc.

distribution

Q2 a n d 43

assumed

is

a

in

the

program.

The

series any

T21 a n d T31 a n d

(positive

start

half

only)

The f i r s t

are

T10,

wave should s t a r t

at

in

the

T20

of

sin

waves.

type hydrograph

time

peaks occur a r e T11,

hours).

l i t r e s p e r m i n u t e p e r house

Increase f o r o l d e r a n d l a r g e r p r o p e r t i e s .

peaks of each of the 3 s i n waves f o r Q1,

0.15

hours

time and

T10.

at T30

These

when which

The

a r e designated each the

of sin

respectively values

relative

are

those waves

(all

built

in into

177 the program a n d the p r o g r a m must be e d i t e d to change them.

DATA

Data can be stored a n d edited in a separate f i l e , establishment

and

identified

the d a t a

in

identified form.

when SEWSIM As

program a t the time of r u n n i n g should be equal lines.

to and

greater

the d a t a

named a t the time of

i s run. file

Data requirements

is

u s i n g the "GET"

appended statement,

to

the

are main

l i n e numbers

2000 to a v o i d o b l i t e r a t i n g program

than

The d a t a f i l e should end w i t h END. Data can b e i n free format w i t h

commas s e p a r a t i n g numbers. Three items of d a t a a r e not used

i n SEVJSIM.

These a r e

sewer

depth,

drop a n d g r o u n d level. They a r e intended f o r a d a t a l o g g i n g a n d p l o t t i n g program l a t e r . Zeros may be inserted a t t h i s stage.

Program Output

The program sorts the p i p e d a t a m a n h o l e ( s ) . I f there

i s more

the d a t a should be checked.

than

i n t o order

one

and

unconnected

A p i c t u r e i s d r a w n of

identifies

the

(downstream)

lowest

manhole

the system w h i c h

can

be copied u s i n g DUMP GRAPHICS. Then press CONTINUE f o r the p r o g r a m to i n each

r o u t e the flows through the system and t a b u l a t e maximum flow etc. pipe. Hydrographs

are

also

tabulated

for

nominated

pipes.

h y d r o g r a p h s a r e t a b u l a t e d a t the times corresponding reach the e x i t of the system ( t h e lowest time

at

which

the

tabulated

flow

manhole)

occurs

subtract

Note

that

the

to when they would

and the

to get lag

the time

actual of

the

correspond i ng p i pe from the t a b u I a t ed t ime. The h y d r o g r a p h s a r e a l s o p l o t t e d on the screen a t the correct times.

To

p l o t a h y d r o g r a p h DUMP GRAPHICS then/or continue. F i n a l l y a t a b l e summarizing t o t a l p i p e l e n g t h a n d house u n i t s f o r each type of development i s g i v e n .

.

'LO! Fi'E-Sl'OHE"SEWSI~1" W 1'1'8 7 16-2560 - 1b 03.87 15 N d = T 0 2 16 DlJMP O E V I C E I S Nd 18 PRINTER I S Nd 20 D I M M ( 4 0 0 ) . M d ( 4 0 0 ) . D ( 4 0 0 ) .S(408). X ( 4 0 0 ) .Hq(400) . Y ( 4 0 0 ) .H(40GI). I t (400) . T x (400) . T I (400) . Q ( 4 0 0 ) . Q c ( 4 0 0 ) . Q w ( 4 0 0 ) , G ! s ( 4 0 0 ) ,Qi (400) .Ql (400) . Q m ( 4 0 0 ) .Qv(4P)0) . J d ( 4 0 B ) 3v1 DJM I21 (99) . Q 2 ( 9 9 ) , Q 3 ( 9 9 ) . T 1 8 ( 9 9 ) . T 1 1 (99) . T 2 0 ( 9 9 ) . T 2 1 (99) . T 3 0 ( 9 9 ) , T 3 1 (99) . M h ( 9 9 ) , Jh (99) ,at (29.99) ,He(99) .G1 (400) 31 COM NSCZ03 40 I N P U T "NAME '?".NS 60 READ N s . T s . T i . N h , O l l !NO.SECNS. S I M L N h . T I N C h .Nhydqphs.GLmBOTMH 70 FOR Jn=l TO Nh ! HYDROGHAPHS 80 HEAD M h ( J n ) !PIPE NO OF HYGPHS 90 NEXT Jn 100 J2=B 110 FDR K = l TO Ns SECT DATA I20 READ Mb,Itk,Np,Am,Fw,Fs,Fi,Fl ! HOTM MH, ZONE TYPE,Npipes,MANNINljn.I-/MIN/HEQ ,mm/h STORM,INFIl/MIN/M/M.LK/MIN/HEQ 130 J2=J2+Np 140 M d ( J 2 ) = M b 150 FOR J=J2-Np+l TO J2 ! P I P E DATA 160 READ M ( J ) , D ( J ) . X ( J ) , S ( J ) , H q ( J ) ,Y(J) , H ( J ) ,G1 (;I) !NO. ,DIClmm,I..m,Sm/m.H~USE EQU VS(l00m2),DETTHm,DROP BOTMENDmm,GLmMH 180 I F J < = J Z - N p + l THEN 200 190 M d ( J - l ) = M ( J )

12 ! D. STEPHENSON

I

'

200 I t . ( J ) = I t k 205 Q v ( J ) = K 260 T x ( J ) =X ( J) +Am*4". ( 2 / 3 /) ( D ( J )/ 1000) ." ( 2 / 3 )/S( J)". 5 ! L..AG, 5 270 Qc ( J) =. 7 8 5 / A m / 4 . " ( 2 1 3 ) (D( J) / 1000) ( 8 / 3 +S ) ( J) 5+ 1000 !CAPAC I TY ,L./s 280 Qw (J)=Fw+Hq ( J ) /h0/ 1000 !PEAK M3/S INFLOW 290 Q s ( J ) = F s * X ( J ) * l 0 0 / 1 0 0 0 / ~ 6 0 0 ! DO. STORM 300 Qi ( J ) = F i + X (,I) +D ( J )/ 1 0 0 0 / 6 0 / 1000 ! DO. I N F I L T N 310 Q1 ( J ) = F l + H q ( J ) /60/1000 ! DO. L E A K S 320 NEXT J 330 0 (K)=J2-Np+l ! TEMP. TOPMH FOR PLAN P1.OT

*

,*%

340 350 400 410 420 430 440

450 460 470 480 490 500 510

9rn (F:) =Np NEXT K T40=12 T41-17 91(1)=.7 92(1)=.5 93(1)=.6 T10(1)=5 Tll(i)=9 T20(1)=7 T21(1)=13 T30(1)=14 T 3 1 ( 1 ) =20 91(2)=.8 92(2)=.7

520 530 c-13(2)=.6

T10(2)=6 T11 (2)=8 T20(2)=7 T Z 1 ( 2 )=13 T30(2)=16 590 T 3 1 ( 2 ) = 2 0 4500 01(3)=.4

!STORM START h !PEAK h ! RESID4UPCLAS. 1S T P E A K = l ! 2 N D PEAK ! 3 R D PEW !START h 1ST PEW MUST BE 1st HG TO START ' P E A K h 1ST PEAK ! S T A R T h ZND PEAK !PEAK h 2ND PEAK !START h 3RD PEAK !PEAK h 3RD PEAK !RESIDLPOOR

540 550 560 570 580

6llb 620 630 640

! INDUST

02(3)=.S 93 ( 3 ) =. 45

T10(3)=6 T 1 I ( 3 )= I 0 650 T 2 0 ( 3 ) = 4 660 T 2 1 (3)=13 670 T 3 0 ( 3 ) = 1 3 675 T 3 1 ( 3 ) = 1 6 680 01 (4)=.3 690 02(4)=.7 700 03(4)=.45 710 T 1 @ ( 4 ) = 6 720 1 1 1 ( 4 ) = 1 0 /d T 2 0 ( 4 ) = 6 740 T 2 1 ( 4 ) = 1 3

!COMMERCIAL

--.

d

W

i

61 4 IXI

B t.4

m iii L

I

z

2 W

I !-

w

t);

w

a

+

a

r.l

-

1030 1032 1033 1034 1035 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 104.9 1050 1051 1052

1053 1055 1060 1070 1071 1072 1073

1074 1075 1076 1077 1078 1080 J 090

1092 1093 1100

NEXT E GINIT GRAPHICS ON ! DRAW LAYOUT GCLEAR WINDOW - 1 0 0 0 . T l ( N l ) + 1 0 0 0 , 0 , N s + l FOR E = l TO Ns FOR J = B ( E ) TO O m ( K ) + O ( # ) - l MOVE T 1 ( N l ) - T l ( J ) . K DRAW T 1 ( N l ) - T l ( J d ( J ) ) - 2 0 . K L l = T l ( N l ) - T l (J)-20 C S I Z E 3..4 MOVE L1 .K ! D I R l+PT/b LABEL M ( J ) LDIR 0 NEXT J Jmm=Om ( K ) +O ( K ) - 1 I F J d ( J m m ) = 0 THEN 1055 MOVE T 1 ( N l ) - T l ( J d ( J m m ) ) - 1 0 . K DRAW 1 1 (N1 ) - T 1 ( J d ( J m m ) ) , G ! v ( J d ( J m m ) ) NEXT K PAUSE FOR J=1 TO J2 (;7m(J)=0 ! MAX. FLOW Qv(J)=0 !SPILL VOL. NEXT J Ti=0 !COUNTER FOR T H FOR T h = T i TO T s STEP T i ! T I M E h AT BOTTM FOR J=1 TO 52 I N I T I C I L I Z E FLOWS R(J)=0 NEXT J FOR J=1 TO 52 T S T h - T I ( J ) /3h00 !PIPE T I M E FOR REACHNG E X I T A T T h I F T : : . T 1 0 ( I t ( J ) ) THEN 1100 T=T+24 IF T > = T l B ( I t ( J ) ) THEN 1110 !HYOROGRAPH ORDINATE PER PIPE

1290 NEXT J 5 1300 NEXT J

1 3 1 0 FOR J = 1 TO J Z 1320 I F R(J)<=Qm(J)

THEN 1340 1 3 3 0 Qm(J)=Q(J) 1 3 4 0 I F Q ( J ) < P c ( J ) / l 0 0 0 THEN 1360 1350 R V ( J )=Qv (J)+ ( Q ( J )-Qc ( J )/ 1000)+3600+Ti 1360 NEXT J 1370 T i = T J + l 1380 FOR Jn=l TO Nh !HYDRAPH POTNTS 1 3 Y 0 R t (Jn,T j )=a ( J h ( J n )) + l B 0 0 1400 NEXT J n 1.410 NEXT T h 1420 PRINT "SEWER NETWORK ANALYSIS , " 1430 PRINT N8 1440 PRINT 'I P I P E D I A SLOPE HUNITS LAGh M A X L s QCAP XFIJL.1. OFL.Om3" 1450 IMAGE DDDDDD.DDDDD.D. DDDD.DDDDD.DDD. DD.DDDI)D.T)I)DDD.onnI>. D.DDDD. D 146R FnR J=l TO 52 1470 T 1 ( J ) = T l (J)/360cI 1400 Qm (J ) =Qm (J)+1800 1490 P f = a m (J) /Qc (J ) + 1 0 0 1500 PRINT USIND 1450:M(J) ,D(J) . S ( J ) .Hq(J) .T1 ( . 7 ) .Qm(,l) . R c ( , l ) . P f . R v ( J ) 1 5 1 0 NEXT 3 1520 IMAGE DDDDDDDD.# 1525 IMAGE DDDDD.DD.# 1526 IMAGE DDDDD.DD 1 5 2 7 IMAGE DDDDDDDD 1530 PRINT 1540 PRINT "SELECTED HYDROORAPHS AT":Ti ;"h 1NTVL.S STCIHTTNG A T - T l FKIR PTPF 1 5 4 5 PRINT USING 1520;Ti 1550 FOR Jn=l. 7'0 Nh-1 1551 PRINT USING 1520;M(Jh(Jn)) 1552 NEXT J n 1 5 5 3 PRINT USING 1 5 2 7 : M ( J h ( N h ) ) 1 5 6 0 FOR T k = l TO T i 1565 PRINT USING 15'20:Tk 1570 FOR Jn=l TO Nh-1 1571 PRINT I.JSING 1525:Qt (-7n.Tk) 1 5 7 2 NEXT J n 1573 PRINT IJSING 1526:Qt ( N h . T k )

1575 NEXT TIC 1380 GCLECIR 1600 FOR Jn=l TO Nh

1602 1603 1605 1610 1620 1630 1700 1701 1710 1711 1720 1721 1724 1725 1730 1740 1750 1755 1760 1765 1766 1770 1780 1790 1800 1810 1820 1830 1840 1850 1855

QCLEAR ! P L O T HYDROORCIPHS ON SCRNCSIZE 4 Omi=Qm(Jh(Jn)) WINDOW -3,24.5,-0.Qmj*l. 1 CIXES 1,1,0,0,12,10 MOVE l , Q m ( J h ( J n ) ) Qm (Jh (Jn ) ) = I N T (Qm ( Jh (Jn ) ) 1000)/ 1000 L A B E L Qm (Jh (Jn) ) ;" L / s PIPE" :Mh (Jn) MOVE 6,0 LCIBEL. N S

DUMP GRAPHICS & / O R CONT

*

MOVE 22.0 L A B E L "h 24" MOVE -2.10

LhBEL 10 FOR T=2 TO T i Th=(T)*Ti-Tl (Jh(Jn)) T h - T i .Qt ( J n , T - l ) Th,Qt ( J n . T ) T -T1 ( J h ( J n ) ). Q t ( J n , T - 1 ) DRAW T i - T l ( J h ( J n ) ) , Q t ! J n , l ) PAUSE ! T Y P E CONT NEXT Jn FOR 1 = 1 TO 6 MOVE DRAW NEXT MOVE

He(I)=0 NEXT I FOR J = 1 TO 52 H e ( 1 t ( J ) ) = H e ( I t (J)) + H q ( J ) XleX1+X(J) NEXT J PRINT

(El-)

TO DO NEXT t i Y B 13R DUMPFH TO DRAW EX

SEWSIM

DATA

FORM

NAME -2 W !

DATA

..........

NO. OF SECTIONS, 2010

DATA

SIMULATION DURATION h,

T I M E INCREMENT.h,

NO.

HYDROGRAPHS REQUIRED,

G.L.(M)

BOTM M i .

..................

....................................

........................

P I P E NO. OF HYDROGRAPHS

2020

DATA

..........................................................

SECTION DATA: BOTTOM MH NO.,

2030

DATA

( 1 L I N E PRECEEDING EACH SECN.)

ZONE TYPE (1-41,

P I P E DATA:

DATA

PIPES I N SECN,

MANNINGN,

SW/min/HE,

STORM Chnm/h,

I N F I L T N L/mm/m/m,

EAKG L/mi

/HE.

( I L PER P I P E )

P I P E NO.(=TOP MH NO.), 2040

NO.

........................................................................................................................... m -,

LENGTH m ,

SLOPE m/m,

HE=HDWE E a U I V S ( l W m ’ ) ,

(DEPTH TOP MHm,

DROP BOTM mm,

GLm

............................................................................................................................

G i v e e a c h d a t a f i l e a name

Store in ASCII form

e.g.

SAVE

c a l l e d up when SEWSIM i s RUN. “FILENAME”

187

SAMPLE DATA F I L E SEWDAT

(ASC I I

FORMAT)

7000 2001 ZQCI? 2061.3 2804 288'3

DATA 4 , 2 4 , 1 . 4 , 5 0 DATA lil,1'21,211,.311., 1 1 . 3 , 1 , 2 ,. 0 1 J , 1 1 , 0 WTA 111,100,100 ,.0100,100,1.30,49 DATA 1 1 2 , 3 0 0 , 3 0 0 , . 6 1 1 0 0 , l ~ 0 , 1 , 0 , 4 8 DATA 112,2,9, . 0 2 , I , 0 , . 1 , . 0 DATA 1 2 1 , 1 5 0 , 1 B 0 , . 0 1 5 , 1 0 0 , 1 , 0 , 4 7 2806 DATA 1 2 2 , 1 5 0 , 3 0 0 ,.004,75,1,C!Il46 2807 D(?ITA 123,200,i00,.802,95,1.5,30,45 2 0 0 8 DATA 122,3,1,.02,1,0,a..1 2089 DATA 211,150,100,.81,100,1,0,48 2 0 1 0 DATA 123,4,1,.02,1,0,0,0 2 0 1 1 DATA 311,100,iQ0,.002,100,1,0,47 100pI0 END

,.

:YF'B2'mX. 78B VOLUME LABEL: B982.5 F I L E NAME PRO TYPE FiEC/FILE HYTE/HEC

SEWDAT

BEWSIM

Note

_-__ SAME

ASCII PHDG

"SEWDAT",

3

256

7 _IL 3

256

don't STORE

,I...

ADDPESS

50 53

,

0

188

END P I P E WITH NO D . S . P I P E 2

SEWER NETWORK hNALYSIS

112

FOR

DIA SLOPE HUNITS LAGh MAXLs PCAP %FULL OFLOm3 100 .0100 100 .I2 2 4 37.3 0.0

PIPE

111 112

308 150 150 I23 200 211 150 311 100 121 122

.0100 100 .0150 100 .0840 75 .0020 95 .a100 100 .00?0 100

.07 .44 .40 .I6 .45 .31

10 2 4 7 2

2

84

12.1 14.0

12

6 69.3 10 73.3 10 16.7 2 112.5

0.0 0.0 0.0 0.0 0.0 0.0

SELECTED HYDROGRAPHS AT I h INTULS STfiRTING AT -TL FOR P I P E I 31 1 111 121 21 1 1 .I7 0.00 * 29 .03 L. 1

3 4

5 6 7

.03 0.00 0.0Q 0.00 a0

.

.79

8 9 10

1.25 1.56 I .67

11

1.57

1:

1.29 .96

13 13

.97

.03 .03 .03 -03 .03 .68 1.45

1.69 1 .?O

.96 1.11 1.18 1.18

.I7 .I7 .I7 .17 .17 .67 1.03 1.32 I .51 1.58 1.52

1.36 1.33 1.51 1.65 I .56

15

!.18

1.10

16 17 16 19 20 21 22

1.34

.94 .94 1.03

23

.73

.64 .56

.I7

24

.53

.20

.I7

1.40

1.36 1.21 1.17 1.07 .89

1.00 1.01 1 .OO

1 .:7

0.00 0.00 0.00 0.00 0.0Q .32 .7b

1.10 1.36 1.50 1 .5l 1 .41 1 .21 I .47 1 .69 I .43 *

76

.bl .51

.34

.37 .23

0.Q0

.08 0.08 0.08 0.00

...

189

I

1.684 L / s PIPE 121

1.688 L/s PIPE 31 1

-

h 24

190

CHAPTER 12

SEWERAGE SYSTEMS MANAGEMENT

The

in

interest

management

of

sewerage

existing

i n c r e a s i n g flows

and

systems

systems

to

improve

is

has

in

recent

order

to

increased

in

improved

catchment

water

balances.

years cope

The

as

with

design,

s i m u l a t i o n a n d management o f such systems i s t h e s u b j e c t of much r e s e a r c h (Yen,

1987).

Dual

p o l l u t i o n of old

systems

waterways

systems,

pose

particular

problems

i s becoming more o f

including

re-lining

p l a c e (Adams a n d Zukovs,

to

a

increase

older ,areas

as

Rehabilitation

of

in

problem.

i s also

throughput

taking

1987).

The o p e r a t i o n o f a l a r g e u r b a n sewer system was o p t i m i z e d b y S c h i l l i n g a n d Petersen sewer

(1987)

pumpstations,

using

in

system

storage

adequately controlled, severe

economic

conjunction

with

I i n e a r programming.

Brenner,

West

and

ponds

catchment

linear constraints.

Conduit

rate

the

given

by

wastewater

The

treatment

St.

optimization

s i m u l a t i o n model.

t h a t the o p t i m i z a t i o n model was,

as

a

comprises

combined

sewer

pipes,

plant.

Unless

t h e system i s l i a b l e to f l o o d l o w l y i n g s u b u r b s w i t h

consequences. a

The storm/waste

Germany,

o f necessity,

flow

in

run

was

this

was

a s i m p l i f i e d model assuming

s t o r a g e therefore, Venant

model

The reason f o r

a

complex

equations,

function

could

not

of

flow

easily

be

i n c l u d e d in a l i n e a r model. A r a i n d a t a c o l l e c t i o n n e t w o r k was coupled t o a catchment model o n a r e a l time b a s i s t o p r e d i c t flow r a t e s ( F u c h s e t al.,

1987).

LEARNING SIMULATION PROGRAM

The p r o g r a m used a n i t e r a t i v e l e a r n i n g process t o o p t i m i z e o p e r a t i o n o f t h e system.

That

is,

successive r u n s used p r e v i o u s r e s u l t s to

the operating r u l e using a r t i f i c i a l The sewer

system

studied

was

designed

o v e r f l o w i n storms r a n t o r i v e r s a n d lakes. forced t h e system t o b e improved.

to

treat

lower

flows

I n c r e a s i n g p o l l u t i o n awareness

.

The problem was set up t o m i n i m i z e a constraints.

A

formal

system

(referred

e s t a b l i s h e d w i t h t h r e e components:

whereas

At t h e same time a s r e d u c i n g overflows,

p a r a l l e l o b j e c t i v e s were t o reduce p u m p i n g e n e r g y costs a n d

f lood ing

improve o n

intelligence.

to

cost as

function a

avoid

without

production

street

violating

system)

is

191

A w o r k i n g memory w i t h a l l d a t a A r u l e base

A n i n t e r p r e t e r to choose and a p p l y p r o d u c t i o n s Improved control ones.

i s achieved b y a l t e r i n g the r u l e base o r

a d d i n g new

For each u n s a t i s f a c t o r y production a l i s t i s created.

A meta production systems was f u r t h e r added. a f f e c t the w o r k i n g memory b u t can change

Meta p r o d u c t i o n s do not

the content of

The meta system i s e v a l u a t e d b y the control

the r u l e base.

A simple example

interpreter.

demonstates the technique: Stormflow

could

be

stored

in

a

detention

f l o o d i n g would be an u n s a t i s f a c t o r y state.

basin

freely,

while

street

T h i s r u l e could be described b y

a meta f u n c t i o n as flows:

( W E > 1.0)

+

(pump too L O W ) (Value = - 1 )

Whenever the water level in the sewers i s h i g h e r t h a n manhole

level which

may cause street f l o o d i n g t h i s r u l e i s a p p l i e d . At a n y selected time i f the meta

production

rule

is applicable

the

decision

PUMP

=

OFF

is

counter

the corresponding productions a r e decreased b y 1 .

r u l e d i.e.

The facts i n the w o r k i n g memory a t the time may h a v e been

W E = 0.4

where W E = water e l e v a t i o n

R I = 10

where R I = r a i n f a l l i n t e n s i t y .

Another s i t u a t i o n may also have been stored in the experience memory, e.g. WE = low

R I = 10 I t i s possible b e t t e r productions c o u l d h a v e been a p p l i e d . The total l i s t i n memory may now be

WE -

Va Iue

RI -

-3

LOW

9

-1

LOW

10

-6

LOW

a

-10

LOW

11

A new p r o d u c t i o n i s created t a k i n g the c o n d i t i o n p a r t of the o l d one.

A

second condition i s added of the form

N I op x where op i s e i t h e r < o r experience memory,

> a n d x i s the median v a l u e of R I in the l i s t of

weighted w i t h the level of punishment.

Thus s t a r t i n g w i t h the o l d p r o d u c t i o n

(WE = LOW)

+

(pump = OFF)

192

the new p r o d u c t i o n w i l l s w i t c h pump on because the systems knows t h i s

is

connected w i t h h i g h r a i n f a l l i n t e n s i t y . Hence the new p r o d u c t i o n i s

( W E = L O W ) ( N I > 9.75)

+ (pump = O N )

The new p r o d u c t i o n i s assigned a v a l u a t i o n of

0 a n d stored

in

the

rule

base. I f the s i t u a t i o n WE = 0.4

R I = 10 occurs a g a i n the last r u l e s w i l l b o t h a p p l y ,

but

the

l a t t e r r u l e i s chosen

as h a v i n g lowest e v a l u a t i o n l e v e l . Street f l o o d i n g i s t h u s avoided.

OPT I M I ZAT ION

The

same

optimization

problem at

was

discrete

simplified times.

into

Sewers

a

linear were

subcatchments.

Wser

I1

Hbsssliisc

I2

-1

Fig.

12.1 Process v a r i a b l e s f o r the s i m p l i f i e d systems

system

lumped

for

direct

into

three

193

A rainfall/runoff

model

was

used

to compute

r e m a i n i n g system consists o f two o f f - l i n e backwater

effects from

v a r i a b l e s ( F i g . 12.11,

-

the

pumps.

inflow

hydrographs.

ponds a n d two t r u n k sewers w i t h

The

system

can

be

described

by

up

18

namely:

i n f l o w I 1 i n t o the pump sump of the downstream p u m p i n g s t a t i o n , 12 h a l f w a y

The

the

upstream

station,

and

13

into

the

sump

inflow of

the

upstream s t a t i o n .

-

the pumping r a t e s PR3

i n t o the

i n t o the downstream system,

upstream pond,

PRl

P2 from

the

i n t o the downstream pond,

upstream

a n d PKA to

the treatment p l a n t .

- recycled flow from the ponds to the system ( R R l a n d RR3, r e s p e c t i v e l y ) , - the stored sewage i n the t r u n k s (V12 a n d V3, r e s p e c t i v e l y ) and i n the ponds (R1 a n d R3, r e s p e c t i v e l y ) ,

-

overflow

PO1

Wasserlose,

-

flood

into

the

Weser

estuary,

01

into

the

downstream

creek

and 03 i n t o the upstream creek Krimpelfleet,

volumes

respectively

which

cannot

be

handled

by

the

system

(F12

and

F3,

1.

The s i m p l i f i e d model

was

verified.

This

was

done

through

a

detailed

a n d p h y s i c a l l y precise model.

Optimal Control a s a L i n e a r Programming Problem

The task

in

drainage (i.e.

the o p e r a t i o n of

the Bremen combined

m i n i m i z a t i o n of f l o o d i n g ) a n d environmental

m i n i m i z a t i o n of combined sewer f l o w ) as

low

as

sewer

possible.

Since

protection a n d no overflow

it

is

system

p r o t e c t i o n (i.e.

w h i l e keeping the cost of impossible

to

were

achieve

operations

perfect

flood

simultaneously p r i o r i t i e s h a v e to be specified.

They include:

1 . minimum f l o o d i n g (F12, F3) 2. minimum overflow i n t o the creeks (01, 0 3 ) , 3. minimum overlfow i n t o the e s t u a r y ( P o l ) ,

4. minimum pumping i n t o the ponds ( P R l , PR3),

5. minimum use of the ponds ( R l , R3) U n i t costs c a r e specified overflow.

etc.

Using the

for

every

technique of

c u b i c metre flooded,

l i n e a r programming

c u b i c metre

the o p e r a t i o n a l

o p t i m i z a t i o n problem was formulated a s n

z

min t = l

cv3tV3t + cR3tR3t + cv12tV12t + c r l t R l t + cRR3tRR3t + cP2tP2t

+ cPR3tPR3t + cF3tF3t + co3t03t + cRRltRRlt + cPKAtPKAt

+ cPRltPRlt

+ cF12tF12t + cPOltPOlt + c o l t O l t

1 94

12.1

TABLE

O p t i m a l Control S t r a t e g y f o r M a j o r Storm 0708

,----------------

----

0.0 1.0 .----------------

C

1 2

14268 1277 'I4268 10000 14268 10000 ill88 10000 14268 10000 14268 10000 14268 10000 14264 10000 13814 10000 13049 10000 13088 10000 11037 10000 10108 10000 9125 10000 a i r 4 10000 7163 10000 6182 10000 5201 10000 4220 10000 3231 10000 1612 -~~~ 9549 531 6560 531 6490' 531 4420 531 2350 531 260 531 0 531 0

3 4

6 6 7 8 9 10 11 12 13

14

16 16 17 18 19 20 21 22 23 24 25 28 27 28 29 t

.---__-----

R3

c

0.3

1 2 3

4944 9600 9600 9600 9600 9600 9600 9600 9600 9600 9600 9600 6704 7615 6626 5437 4848 3269 2170 1081 0 0

.---------4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

93 ----0.26 -----

PM PRl Po1

t _---

10

1630 0 0 0 3800 1277 3600 9414 691 3600 Be68 9000 3600 6346 6346 3600 2946 2946 3600 1373 1373 3800 603 603

a

$600

3600 3600 3600 3600 3800

0

0 0

0 0

0

0

0

0

3600

0 0

0 0

3800 3600 3800 3600

0 0 0 0

0 0 0 0

3800 3600

0

0

0

0 0

0 0 0 0

0 0 0

0 0 0 451 0 989 0 2070 0 2070 0 2070 0 2070 0 280

0

0

0 0 0 0 0 0 0 0 0

3600 3600 3600 3800 3600 3600 1610 1530

0 0 0 0 0 0 0

0 0 0

0 0 0

0 0 0

0

0

0

0

0

0

0

1280 1280 1260 0 1260 1260 1260 1260 1260 1260 1260 1260 1260 1260

1730 1730 1730 1730 1730 1730 1730 1730 1730 1730 1262 193 0 0 0

1260 1260 1260 1260 1280 1260 171 171 171 171

0 0 0 0 0 0 0 0 0 0 0 0 0 0

171 171 171

PR3 F3 -----------1.0 1001 --__----_ 0 4944 6588 5710 6588 270 6032 0 3656 0 2047 0 2011 0 1577 0 997 0 396 0 0 0 0 0 0 0 0 0 0 0 0

0 0

0

0 0 0 0 0 0

0 0 0

0

896 1069 1089 1089 1089 1089 1089 1089 0 1081

0 0 0 0 0 0 0 0 0

0

1932 6588 6032 3656 2047 2011 1577 997 396 0 0 0 0 0 0 0 0

0 0 0 0

12283 9972 12715 8410 5080 3519 2752 2147 1701 1386 1170 1170 1170 1170 1170 1170 1170 1170 1170 1170

13558 6118 6032 4916 3307 3271 2837 2257 1656 812 171 171 171 171 171 171 171 171 171 171 171

3483 1762 752 ._ 275 205 194 191 189 189 189 i 89 189 189

ias

189 189 189 189 189 189 189 ~~~

195

subject to the c a p a c i t y c o n s t r a i n t s

5 R3 5 V12 5 R1 5 P2 5 PR3 5 PKA 5 PRI 5 PO1 5

V3

1730 m3 9600 rn’ 14268 m’ 10000 m3

0.70 m’/s 3.66 m’/s 2.00 m’/s 8.20 m’/s

5.00 m’/s

a n d the dynamic c o n s t r a i n t s f o r each of the f o u r storage u n i t s

-

V3t+l - V3t

RR3t + P2t + PR3t + F3t

= 13t

= o

R3t+l - R3t - PR3t + RR3t + 03t V12t+l

-

V12t

-

P2t-2

-

+ PKAt + P R l t + F12t

RRlt

R l t + l - R l t - P R l t + RRlt + POlt

The flow

time

from

the

taken as one time step

+

+

12t-1

= o

Olt

inflow

(i.e.

= Ilt

site

12

30 m i n ) and

to

the

downstream

the flow

pump

time between

was

the two

pumping stations as two time steps. The problem was

solved w i t h

presented i n Table 12.1 time step o n l y costs c of

A

s t a n d a r d software.

f o r a 210 m i n storm

and

(0 to 30 m i n from a c t u a l time).

the o b j e c t i v e function.

Sensitivity

c o u l d be specified q u i t e a r b i t r a r i l y ,

typical

inflow The

table

of

is one

includes u n i t

a n a l y s e s showed

provided that

result

forecasts

that

u n i t costs o f

these

different

o r d e r s of magnitude a r e a l l o c a t e d to objectives of d i f f e r e n t p r i o r i t y .

SEWER MAINTENANCE DATA PROCESSING IN JOHANNESBUG

Johannesburg

has

nearly

four

thousand

operate and m a i n t a i n on a continuous basis.

kilometres Many of

of

sewerage

to

the areas a r e prone

to abuse and blockage a n d the n a t u r e o f the topography a n d c l i m a t e make maintenance a h i g h cost i n the system. That is, in

ingress

into

sewers

and

f o r e i g n matter which block

in

many

sanitation

places system

it

is

are

this

suspected, often

may

the sewers.

found

as

in

bring

intense storms o f t e n r e s u l t surface

debris

and

other

There i s a l s o u n a u t h o r i s e d access articles sewers.

obviously Despite

the

not

from

high

rate

the of

1%

g r o w t h i n Johannesburg many o f the sewers a r e o l d a n d some a r e of poor q u a l i t y r e q u i r i n g r e g u l a r maintenance a n d replacement a n d r e p a i r s . While a t f i r s t i t may a p p e a r t h a t r e a d y a v a i l a b i l i t y of l a b o u r i n South Africa

should f a c i l i t a t e c l e a n i n g a n d

should

provide

obviously for

labour

imposes

severe

i d e n t i f y i n g trouble

managers

and

opportunities, problems a t

spots

sewerage

b u d g e t i n g f o r r e p a i r work

at

the

the

higher

i n the system

engineers.

same

time

management

This

levels. would

type

the

of

maintenance

such

a

system

Maintenance of

b e of

of

great

data

such a s to manholes a n d

even

is

logs

value useful

to for

pipes requiring

replacement as well a s m i n o r items such a s manhole l i d s a n d s t e p i r o n s a n d benching

i n manholes.

There i s also much to be g a i n e d

maintenance d a t a in the way o f types of blockage. where f o r e i g n objects a r e f r e q u e n t l y

encountered

from a n a l y s i s of

For instance l o c a l i t i e s can

be

narrowed

down

a n d the i n h a b i t a n t s o f t h a t township made a w a r e of the t r o u b l e s caused b y such p o l l u t i o n .

f o u n d in sewers i t may p o i n t

Where sand i s f r e q u e n t l y

r o a d s r e q u i r i n g s u r f a c i n g as stormwater

can

r e a c h sewers

by

to

unexpected

ways. Overflows a n d inadequate

l i f t i n g of

sewer

manhole

capacities.

lids

in c e r t a i n a r e a s may p o i n t

Alternatively

they

sewer l i n i n g s o r roots w h i c h b l o c k the sewers.

may

indicate

to

corroded

Here a g a i n i d e n t i f i c a t i o n of

frequency and l o c a l i t y o f such inadequacies i n d i c a t e s where maintenance i s most u r g e n t l y r e q u i r e d . The human management side

i s also v e r y complex.

The o u t l y i n g depots

where such maintenance takes p l a c e employ some s i x h u n d r e d people, w h i c h a r e g e n e r a l l y o r g a n i z e d i n t o gangs a t each depot. to managers who take messages a n d t r a n s m i t Even managers a n d f r e q u e n t l y type

of

logs

they

keep

The s u p e r v i s o r s r e p o r t

the teams to problem points.

s u p e r v i s o r s a r e not h i g h l y

are

often

difficult

to

trained

process.

a n d the

However

computerization of the l o g keeping on a n e x p e r i m e n t a l b a s i s a t one of depots has proved s a t i s f a c t o r y a n d w i t h i n t y p e of s t a f f .

the the

the c a p a b i l i t i e s of the e x i s t i n g

T e r m i n a l s connected to the m u n i c i p a l i t y ' s m a i n computer

at

head o f f i c e a r e used a n d once b a s i c k e y b o a r d s k i l l s h a v e been p i c k e d u p then spread sheet g r e a t advantage

type data

l o g g i n g h a s p r o v e d p o s s i b l e and

to the engineers a t

in

head o f f i c e concerned w i t h

fact

of

planning

a n d the engineers concerned w i t h b u d g e t i n g a n d maintenance a n d design. Although

Johannesburg's

obvious

computer w i t h o u t l y i n g t e r m i n a l s ,

solution

is

through

its

mainframe

in f a c t many s m a l l e r m u n i c i p a l i t i e s may

r e s o r t to m i n i o r even m i c r o computers to h a n d l e t h e i r system.

The l a t t e r

would be p o p u l a r w i t h the smaller m u n i c i p a l i t i e s where one s t a t i o n o n l y maintained.

is

197 The use of micro computers also enables micro g r a p h i c s to be used to identify

A

t r o u b l e areas.

blockages.

With

the

screen map can

advent

of

the

highlight

computers

many

zones

with

fields

in

frequent the

Civil

Engineering f i e l d have been opened up to the b e n e f i t s which can accrue in both

the

design

administration

and

areas.

constructional Due

to

initial

areas costs

and and

the

a

management

natural

and

reluctance

to

adopt new methods progress i s sometimes slow b u t i t can u s u a l l y be s a i d that

w h i l e computers do not

necessarily

save money

they

can

definitely

g i v e b e t t e r r e s u l t s a t the end of the day.

AppI i c a t i o n to Johannesburg's system

Thus

it

was

with

this

i n t e n t i o n of

giving

an

improved

Johannesburg h a s persevered w i t h computerization o f many of

service

that

i t s functions.

T h i s chapter o u t l i n e s the progress made in the p r o v i s i o n a n d maintenance of sewerage r e t i c u l a t i o n . The sewers

analysis has

townships

of

sewer

systems

already

been

established

for

s u b d i v i s i o n of

existing stands

and has

future

to

identify and

has

In

flows.

been assessed

potential been

some

overloading

used

cases

to

by

analyse

the

effect

a n d a c c u r a t e estimates of

of

costs

g i v e n f o r a d d i t i o n a l sewerage work (Stephenson a n d Hine, 1982 a n d 1985). Sewer r e t i c u l a t i o n s need r e g u l a r p l a n n e d c l e a n s i n g i f a n d subsequent danger to h e a l t h i s to be avoided.

serious f l o o d i n g

I f r e g u l a r c l e a n s i n g of

p u b l i c sewers i s well o r g a n i z e d many of the blockages which occur can be avoided.

Maintainance of p r i v a t e l y owned sewers i s not the r e s p o n s i b i l i t y

o f the sewerage a u t h o r i t y unblock these sewers owner

b u t i n Johannesburg i t i s the o f f i c i a l p o l i c y to

In many cases the

i f asked to do so b y the owner.

i s the local a u t h o r i t y

so t h a t there i s a vested

interest

to ensure

t h a t these a r e well m a i n t a i n e d so as to reduce the number of blockages. Conventional u s i n g c a r d s etc.

systems h a v e been which

used to r e c o r d the work

h a s been successful

considered t h a t records of

c l e a n s i n g work

but

and

c o u l d be more e f f e c t i v e l y done b y computer a n d

c a r r i e d out

time consuming.

the c l e a r i n g of that

I t was

blockages

r e t r i e v a l of

records

a n d p l a n n i n g o f work would be made easier. Consequently the M a i n t a i n a n c e Data System has been e s t a b l i s h e d a n d i s being applied

where Sewer

Data

has

been

established

giving

sizes

lengths of sewers together w i t h a u n i q u e manhole numbering system.

and

198

Data i s compiled b y depot a d m i n i s t r a t i v e

s t a f f on Forms wich

numerical format s u i t a b l e f o r i n p u t to the computer.

have a

Details are abstracted

from work r e p o r t s d a i l y . Forms used in the f i e l d g i v e township a n d street names which numerical

become

township codes a n d manhole numbers before b e i n g entered

the computer.

into

I n c o r p o r a t e d i n the c l e a n s i n g r e p o r t i s a n inspection of each

manhole a n d sewer l e n g t h i n c l u d i n g the measurement of the d e p t h o f flow.

Processing of Sewer Maintenance Data

The processing of

sewer maintenance

data

has

reached

an

advanced

stage u s i n g the programs and techniques d e s c r i b e d below. The workforce

i s d i v i d e d i n t o gangs w h i c h work

on e i t h e r c l e a n i n g of

sewers o r c l e a r i n g of blockages. The c l e a n i n g of sewers each

day

a n d manhole

i s recorded b y

the gang

numbers a r e o b t a i n e d

from

leaders keyplans

in

the f i e l d

showing

the

sewer network. On

the

following

working

day

information

is

abstracted

a d m i n i s t r a t i v e s t a f f a n d i n s e r t e d i n a numerical format.

TABLE 12.1 Cleansing of Sewers

nEcono OF SYSTEMATIC CLEANINO

L SEWERMANHOLE

CONDITION

by

( T a b l e 12.1)

depot

199 Program UPDATE i s then length

and

slope

which

is

used

to

added

to

provide the

details

data

file.

of

sewer

These

diameter,

details

are

o b t a i n e d from the Sewer Data F i l e ( T a b l e 12 .2 ) A MERGE program

i s used

to

add

new

data

to

a master maintenance

f i l e (Table 12.3). Program MAINTENANCE produces a r e p o r t of the sewers cleaned between g i v e n dates as r e q u i r e d a n d p r i n t e d out a c c o r d i n g to each township. Program GANGS produces a

r e p o r t of

work

c a r r i e d out

by

each g a n g

between g i v e n dates. T h i s r e p o r t could form t h e b a s i s f o r a bonus scheme ( T a b l e 1 2 . 4 ) . Blockages a r e recorded as reported The

details

of

actual

appear on work blockages

which

with

"Private"

number a n d "Main"

time

boundaries

started

recorded.

r e p o r t sheets a n d enable d a t a to be completed. stand

the

time a n d date

completed

within

giving

the

and

are

clearance

are

denoted

by

a

stand

blockages which occur in p u b l i c sewers a r e denoted b y

a manhole reference number. Reports which a r e

found

to

b e problems

i n the

storm water system a r e g i v e n a code which enables

water

reticulation or

the computer

to i g n o r e

t h a t report a p a r t from showing how many of the r e p o r t s h a v e been r e f e r r e d elsewhere f o r a c t i o n ( T a b l e 1 2 . 5 ) . Program

BLOCKMACRO

between g i v e n dates. possible cause

i s shown.

completion of clearance problems,

produces

a

The l e n g t h of The time

report

which

blockages

elapsed between

i s also c a l c u l a t e d

lack of s t a f f etc.

of

to

help

townships

in

time taken to c l e a r the

blockage

the

identify

report

and

administration

The s e v e r i t y of a blockage i s also shown b y

i n d i c a t i n g the number of houses flooded as the r e s u l t of a "main" and for a "private"

and

blockage

blockage i f the house o r y a r d i s flooded ( T a b l e 1 2 . 6 ) .

A macro program produces a r e p o r t of

all

done in u n b l o c k i n g sewers between g i v e n dates.

the

work

each

gang

has

Numbers of blockages a n d

t o t a l time spent i s shown ( T a b l e 1 2 . 7 ) .

A program produces a r e p o r t of a l l the stands a n d sewer lengths where there

has

been

information

can

overloading

of

more be

than very

public

one

blockage

useful

sewers

in

and

repeated blockages on p r i v a t e stands.

in

a

given

identifying

also

when

time

possible

answering

period. defects queries

This and about

TABLE 12.2

E x a m p l e of U p d a t e d Sewer D a t a F i l e

h)

0 0

35032913086120202 51.01.5 35032913186120203 41.01.0 35032913286120203 ti 1.0 1.0 01.5 35032913386120203 &l. 350329 13986120202 5 1.02.0 35032914086120202 51.02.5 35032914186120202 51.03.0 35132915086120103 01.01.0 35132915106120103 61.01.0 35132915286120103 41.02.0 35132915306120103 41.01.5 35132915486120102 51.02.0 35132915586120102 51.02.0 35132915686120102 51.01.5 35132315786120102 SO. 50.5

TABLE 12.3

1

1

2 2

3 2 2 1 1 3

3 5 1 2

1

152 152 152 152 152 152 152 152 152 152 152 152 152 152 152

5 6 2 4 3 6 3 2 2 1

1 6 1

1

5

4

1

1

15.54 70.26 57.79 60.01 49.22 75.68 49.10 76.90 70.73 64.00 62.97 65.40 62.97

100.0 100.0 100.0 00.0 80.0 00.0 110.0

70.0 70.0 60.0 60.0 66.0 46.0 79.2 79.2

63.03

63.00

Sewer M a i n t e n a n c e Records

I S E U E R PlCIINlEWNCE R M R D S

REOUESTED CTLIRT WITEX- 861201 REOUESTED END DRTE I- 861204

sso

TOUNSHIP

-

uwsm MRNMOLE CONDITION

DEBRIS GRNG tcIhlti NO No SIZE ~~~-W R S 2 S 1.0 329130 1.0 3-2131 S 0 3 A 1.0 3--91;2 z2913 1 A 1.0 2 S 1.0 229139 5 1.0 ‘329100 2 2 S 1.0 3,3101

SEWER LENGTH IS.%

!saNn

70--%

57.79

1.0 1.0

60.01

1-s

TOTnLSI

l4RN

~

7.0

BKTS 1.S

A9.22

2.0

75-68

A9.10

2. S J. 0

S77.60

12.S

ISEUER PlCIINlENRNCE RECORDS

0 0 0

0 0 0

0 0 0

0 0 0

DEPTH DF W SLBB COV FRR STEP COP FLOu RS X JNTS PIPE OIL 0 0 0 0 1 0 19. 0 1 0 0 0 0 0 0 1z. 0 0 0 0 0 0 12. 0 6 0 0 0 0 0

0

RUB R f f i MET YO00 GLRSS ROOTS FRT BEN 1NV U 0

1

0

0

0 0 0

0 1 1

0 0 0

0 0

0 0

0 1

0 0 0

0

0

0

1

2

1

0 0

0

0 0

SEUER CONDITION

0

6.

0

0

0

0

0

0

0

0

0

0

0 0 0

0

0

0

0

0

0

6

19.

0

6

0

0

0

0

0

0

0

0

6

22.

0

0 0 0

0

0 1

1

0

0

0

0

0

0

0

29.

0 0

6 0

0 0

0

1

0

0

1

0

0

0

0

0

1

1

6

1

6

0 0

1

c

0 N

86 T V 9

vv ' V S t

vs ' 6 8 I H18N31 1UlOl

00 ' 0 00 ' 0 666/00S

+OOOI

00 ' 0

oo ' 0 00 ' 0

00 '0

00 ' 0

86 'SVV

00 ' 0 vv ' f 6 Z 00 ' 0 9s '68 f 662/002 66f/001 Stj3M3S do S H U N 3 1

:tj313wu1a do U 3 N U 3 1 3

s 'L S T 0

'*

StlllOH NU313

- s7u101 :

-

I 1x3 UISUN31 f SS UI S U N 3 1 'OSZ 3WUN 3a03NMOI d IHSNMOl

N

0 N

TABLE 12.6

Output f i l e

1 S E U L R OLOCKAGC R C C O R D S

R L P U E S I E D S T A C T DATE:87ClUS *L:UC:TED CND D A T i :- 1175107 TOYNSnXP BLOCKAGL DCPORTFD MOUll DATE

-

52

BOSlOWT

PRIVATE: STAND NO

40.

nA1M: SLYER

OF S T A N D S

no

z z ~ i m 8 7 r i . r ~ iz:40

I ~ 7 ~ 1 ~ 0s

--

0 Z O n P L A I h T : R E F i R R E O TO b A T E R S R A N C M EC’PLAIhTS R L F E R R L O 1 0 R O A D S AND YORKS I S E Y i l l BLOCKAGE R C C O R D S

lOYNSHIP

iEPOPTlL

niui ?

DATL C7ulub

-

157

ELDORAEO PAPK

PRIVATE: STAGO

ID 4Jl

1418

87itios i 4 : o o

SEYER

DATL

L’J

o

30.

TIBE

I I C I ? ~ I:DD

JOB

TIRC

1.20

OF S T A W S

-

19n9

BLOCKAGE CLELRED START Fltiisn

RAIN:

AREA(WECTARES>

-

106.1 CIIVATL:

M O U I S FRO@!

RAIN:

I E P O R T l N G TO GANG GANG CORPLETIOM SUMDAT NO S I Z E CAUSE

L F F E C T E D FLOODED FLOODED

6

0

5

1

4

MOUSES 2

11110

I!

MOUSE

n

D

R L C U E S l r O S l 8 R T DATE:117OlOf D L i U C S T L D E k J C A T i :- 6 7 0 1 0 7

@LOCKAGE

-

I L O C K A G E CLEARED START FINISH DATF TlRf DATE T I R E

-

AREACMECTLRES)

JOB

DATE

TINE

TIME

87~106

a:so

0.30

128.6

cnon

MOURS

MA1N:

R E P O R T I N G TO GANG GAYG COfiPLETIOH SUMDAT N O S l Z E CAUSE

.

2

0

2

3

2

PRIVATE:

nousEs T A ~ D HOUSE A F F E C T E D FLOODED FLOFDED 0

1

1

20 3 REFERENCES

Adams, B.J. and Zukovs, G., 1987. P r o b a b i l i s t i c models f o r combined sewer systems r e h a b i l i t a t i o n s a n a l y s i s . In Beck (1987). Beck, M.B. (Ed.) 1987. Systems A n a l y s i s in Water Q u a l i t y Management. IAWPRC Conf. London, Pergamon Fuchs, L., M u l l e r , D. a n d Neumann, A., 1987. L e a r n i n g p r o d u c t i o n systems f o r the c o n t r o l o f u r b a n sewer systems. In Beck (1987). S c h i l l i n g , W. a n d Petersen, S.O., 1987. Real time o p e r a t i o n o f urban d r a i n a g e systems, v a l i d i t y a n d s e n s i t i v i t y o f o p t i m i z a t i o n techniques. In Beck (1987). Stephenson, D. a n d Hine, A.E., 1982. Computer a n a l y s i s o f Johannesburg Sewers. Proc. I n s t n . Munic. Engrs. S.A. IMESAF, 7 ( 4 ) A p r i l . p13-23 Stephenson, D. a n d Hine, A.E. 1985. Sewer Flow Modules f o r V a r i o u s t y p e s o f development in Johannesburg. Proc.. I n s t . Munic. Engrs. S.A. (10) Oct. p31-41. Stephenson, D. and Hine, A.E., 1987. Maintenance program for Johannesburg Sewerage Systems. Yen, B.C. ( E d . ) 1987. Proc. 4 t h I n t l . Conf. U r b a n Storm Water H y d r o l o g y a n d D r a i n a g e , Lausanne.

TABLE 12.7

Outout f i l e

SLYER BLOCKAGE

RECORDS

l E O U E S T E D S T l R l DATE:070105 SEOUESTED END DATE :- 870107 €AM:

1

SIZE:

ToYNsnIP

4 NO. OF PRIYITE

NO. OF nAIN

TOTAL NO. O f

PRIVATE- MAIN-

TOThL-

lOYNCODE lAME BLOCKbCLS BLOCKAGES BLOCKAGES JOB T I M E JOB T I M E JOE T I M E 155 E L D O R l D O PARK2 2 0 0.00 4.25 2 b.25 177 ELDORADO PARK4 4 0 4 7.25 0.00 7.25 342 K L I P S P R U I T YES 1 0 1 0.25 O.OG 0.25 TOTALS:-

7

0

7

12.15

0.00

12.15

204 CHAPTER 13

WATER

QUALITY MON I TOR I NG NETWORKS i Y

Colorado State U ive

b y Thomas G. Sanders,

NECESS I T Y FOR NETWORKS

Environmental

legislation

been responsible f o r recent streams.

Such m o n i t o r i n g

and

general

water

quality

awareness

have

increased m o n i t o r i n g a n d s a m p l i n g of water and

testing

can

be expensive

and

a

in

scientific

approach to m i n i m i z i n g costs w h i l s t m a x i m i z i n g b e n e f i t s i s d e s i r a b l e . The

assumption

trends

in

water

that

a

quality,

measure ambient

water

monitoring

actively

guide

implemented,

in

government's

however,

feasibi I i t y

obtaining

conclusive

compromises a n d

compliance etc.,

is

with

water

water

legal

the

view

being

is

the

of

more

which

to

When from

involved

resources force

of

for

water

efforts.

viewed

available

and

generated

problems

the consequences

detect

legislation

management

is,

can

standards,

into

The

monitoring

That

information w i t h measures,

stream

information

quality

quality

network

incorporated

conclusive

stand-point.

half

monitoring

the U n i t e d States.

envisages

technical

quality

check

quality,

water q u a l i t y management qua1 i t y

water

a

in

many

a r e often

not

f u l l y understood. Monitoring conducted

over

necessarily Simply

performed large

hydrologic

collecting

problem; cases, samples

or

ultimate

of

geographic

in

i n fact,

thought types

use

government

is

that

of

data

the

data.

(defined

covering

such

given

agencies

areas

boundaries)

samples

so major,

little

by

a

by

the

analysis

many

political

often

i t becomes a n end to

in

in

techniques

Consequently,

the

to

be

majority

a

used of

major

In many

itself. of

not

streams.

becomes

representativeness

cases, and

k i lometres of

many

situation

is,

the

or

water

even

the

resources

are

devoted to c o l l e c t i n g d a t a as i t i s the most immediate problem. By

using

most

resources

to

physically

collect

water

resources a r e l e f t to consider the representativeness of a n d space,

d a t a a n a l y s i s o r d a t a use.

m o n i t o r i n g system system

should

be

should

therefore

examined

and

samples,

the sample

little i n time

A b a l a n c e d ( c o l l e c t i o n versus

be developed designed

so

use)

the e n t i r e m o n i t o r i n g

simultaneously

(a

systems

the

system

approach). The purpose of

t h i s chapter

i s to r e v i e w

monitoring

and

then d e l i n e a t e the impacts t h a t such a systems a p p r o a c h of m o n i t o r i n g w i l l h a v e on network design b y c o n s i d e r i n g the w a t e r q u a l i t y

v a r i a b l e s to b e

205 monitored,

the sampling location a n d s a m p l i n g frequency.

MONITORING SYSTEM FRAMEWORK

Before

a

monitoring

network

can

be

m o n i t o r i n g program should be delineated, I n addition,

the decisions

designed

the

goals

of

the

and specific objectives applied.

to be made based

upon

information

network and the subsequent actions should also be well

from

the

developed p r i o r to

the collection o r a s i n g l e b i t of data. The a c t u a l

operation

of

a m o n i t o r i n g system can

be

categorized

into

f i v e major functions:

1.

Sample Collection

2.

Laboratory Analysis

3.

Data H a n d l i n g

4.

Data A n a l y s i s

5.

I nformation U t i I i z a t i o n

These f i v e functions serve as quality

conditions

of

water

management

agency

approvals,

regulations,

qua1 i t y . effects

Without of

those

a

the feedback

quality

loop from

management

i s c o n s t a n t l y m a k i n g decisions pollution

monitoring

decisions,

abatement,

feedback

the

loop

(e.g.

etc.)

past

water

making.

r e l a t i v e to

that

accurately

management's

in-stream

decision

affect

and

site

water

documenting

success

A

the

future

direction are uncertain. M o n i t o r i n g network design operational collection

i s an o v e r r i d i n g a c t i v i t y

f u n c t i o n s l i s t e d above) (e.g.

location

that

a n d frequency)

should c a r e f u l l y with

used to o b t a i n the i n f o r m a t i o n r e q u i r e d a n d making.

Thus,

the

type

actually

( c o v e r i n g the f i v e i n t e g r a t e sample of

data

utilized

analysis

in decision

the design of water q u a l i t y m o n i t o r i n g networks must

i n t o account the decision m a k i n g process,

take

the t y p e and level o f s t a t i s t i c a l

a n a l y s i s a p p l i e d to the d a t a , a n d u l t i m a t e use of the d a t a collected.

FACTORS I N NETWORK DESIGN

M o n i t o r i n g network

design,

guides m o n i t o r i n g operations,

as a p l a n n i n g / d e s i g n can

i t s e l f be broken

componen ts:

1.

Selection of Water Q u a l i t y V a r i a b l e s to Monitor

2.

Sampling Station Location

type function

down

which

i n t o three m a j o r

206

3.

Sampling Frequency

The

term

water

quality

variable

is

used

instead

of

water

quality

parameter because water q u a l i t y i s a random v a r i a b l e a n d c a n be d e f i n e d by

statistical

addition,

parameters

the term

deterministic

parameter

equations

a s the mean a n d

such

or

is

most

models

often

and

standard define

used

to

can

lead

it

deviation.

In

constants confusion

to

of by

i d e n t i f y i n g i t a s a random v a r i a b l e . the

monitoring

system's o p e r a t i o n a l f u n c t i o n s I i s t e d p r e v i o u s l y a n d v i c e versa.

Each

of

these

factors

The degree

of impact, however,

in

network

design

effects

all

depends upon the purpose a n d g o a l s of

the m o n i t o r i n g

system.

SELECT ION OF WATER QUALITY VARIABLES TO MEASURE

to

The selection of the water q u a l i t y

v a r i a b l e to be sampled w i l l

a

of

l a r g e extent

background developing network

frame

the of

its

objectives reference

the o b j e c t i v e s

has

stndards, for

or

on

of

primary

the

of

the

sampling

the

individuals

monitoring

objective

to

network

network.

monitor

the

responsible

for

When

a

compliance

sampl i n g

with

stream

the v a r i a b l e s sampled a r e the ones s p e c i f i e d i n the l e g i s l a t i o n ,

example,

dissolved

(DO).

oxygen

DO

is

sampled

because

s t a n d a r d s specify a minimum l e v e l which should not be v i o l a t e d .

s t a n d a r d l e g i s l a t i o n were those r e l a t e d to water s u p p l y , biochemical oxygen demand a n d dissolved solids,

(BOD),

stream

Dissolved

i m p o r t a n t a n d i n c l u d e d in stream

oxygen a n d o t h e r v a r i a b l e s deemed most

quality

depend

and

temperature,

col iform b a c t e r i a ,

turbidity,

and

suspended

because most i n d i v i d u a l s e n t e r i n g the f i e l d o f water

management d u r i n g

the

last

few

decades

have

a

background

in

s a n i t a r y engineering. Since i n d i v i d u a l s o t h e r t h a n besides s a n i t a r y became interested i n water q u a l i t y , which

should

be

sampled

( e n v i r o n m e n t a l ) engineers

the number of water

routinely

has

increased.

quality This

variables

compounding

syndrome cannot a n d should not be the major v a r i a b l e selection mode f o r a permanent,

routine

accommodated

in

sampling

the

p o p u l a r i t y of synoptic

much

program,

discussed

but

instead

synoptic

can

surveys.

be

The

easily

increasing

s u r v e y s w i t h s a m p l i n g agencies i s p r o b a b l y

due to

the f a c t t h a t the s u r v e y s a r e in fact a n a p p l i c a t i o n of a systems a p p r o a c h to

water

programs, sampling

quality

monitoring.

the objectives, frequency,

the

Unlike

the

permanent,

the use of the d a t a , variables

to

be

routine

the s a m p l i n g

sampled

as

well

sampling

locations, as

the

the data

207 analysis

procedures

and

decisions

to

be

made

should

be

developed

be

developed

completely before the survey i s undertaken. Both

sampling

independently

location

of

the

and

water

sampling

quality

frequency

variable

to

can

be

analyzed,

location and frequency a r e specified f o r the c o l l e c t i o n of ( t h e analyses a r e made l a t e r ) .

However,

water

monitored.

quality

week

at

a

monitoring

variable

single the

being

point

in

relatively

a

river

stable

For

may

river

the

variables

t h e i r n a t u r a l and/or

considered

when

be

more

temperature, coliform

sampling than

but

once

adequate

may

bacteria

water

delineated.

Network

concentration

qua1 i t y

is

concentration,

the

as

former

be

sample

in

if

opposed

being

a

to

an

result

24-hour

(generally

daily

in

space

In

several

period,

while

the daytime,

in a

be to

should

be

(flow

weighted)

grab

samples the

can

addition

units

mean

instantaneous

of

for

hardly

be s p e c i f i e d so

time a n d

respective

a

a

concentrations.

should

network.

their

differs

measurements spaced d u r i n g a single

variation

monitoring

variables,

design

needed

the

to be monitored

man-made

designing

considering

only a

example,

before a water q u a l i t y m o n i t o r i n g network can be designed

systematic fashion, that

both

both c r i t e r i a a r e affected b y the

adequate for m o n i t o r i n g r a p i d l y v a r y i n g Therefore,

as

the water sample

sample

with

latter

flow

comprises a.m.

between 8.00

and

4.30 p.m.1. In

reality,

the

specification

of

the

water

quality

variable

however, water

to

be

In p r a c t i c e ,

monitored p r i o r to i n i t i a t i n g network design would be ideal.

network design i s specified a n d one must know o r determine what

quality

variables

can

be

accurately

monitored

with

the

existing

a

water’

network.

SAMPL I NG STAT ION LOCAT ION

The

location

of

m o n i t o r i n g network design,

a

permanent

i s probably

b u t a l l too often

never

comprises lead i n many cases r i v e r g a u g i n g stations. the

gauging

sampled

is

collectors

station not

and

follow

when

most

properly

is

truly

addressed.

representative generally

of

the

water

the

in

aspect

of

quality

the

Expediency

network a n d cost

near existing

Whether the s i n g l e g r a b sample from the b r i d g e o r

but

users

station

critical

to s a m p l i n g from b r i d g e s o r

known,

e s t i m a t i n g discharge, indicate exactly

sampling

the

is

quality

of

the

assumed data.

measuring

discharge.

water

quality

However, variable

be

Using

measurement anywhere i n the river

water to

lateral

t h i s does

mass

being

by

both

the

river

stage

for

transect not

would

necessarily

concentrations.

In

fact

208

F i g , 13.1

Macrolocation of Sampling Stations W i t h i n a R i v e r Basin Using the Percent Areal Coverage a s the C r i t e r i a S p e c i f y i n g Locat ion

209 research

indicates

the

opposite,

that

will

rarely

a

single

sample

be

i n d i c a t i v e of the average water q u a l i t y i n a r i v e r cross section. Sampling

locations

for

a

c l a s s i f i e d i n t o two levels of

permanent design:

water

quality

network

former

b e i n g a f u n c t i o n o f the specific objectives o f the network

latter

being

independent

of

can

be

macrolocation a n d microlocation,

the

objectives

but

a

the

and

the

of

the

function

representativeness of the water sample to be collected. The political etc.

macrolocation

within

boundaries,

a r e a s of

Macrolocation can

a

river

basin

usually

major p o l l u t i o n

be specified,

coverage u s i n g b a s i n c e n t r o i d s

a s well,

(Sanders et

is

loads,

determined

population

a c c o r d i n g to percent

1986).

al,

This

locates sampling p o i n t s in a systematic f a s h i o n m a x i m i z i n g the e n t i r e b a s i n w i t h a few s t r a t e g i c a l l y an

example

of

locating

sampling

using

areal

methodology

information of F i g u r e 13.1

located stations.

stations

by

centres,

basin

centroids

is and

sub-basin centroids w i t h percent a r e a l coverage a s the c r i t e r i a . The procedure f o r l o c a t i n g sampling s t a t i o n s i s d e r i v e d b y d e t e r m i n i n g the c e n t r o i d o f a r i v e r system. i s a stream

without

defined

i n t e r i o r stream r e s u l t i n g from

value

equal

to

the

i s given

intersection

of

the v a l u e o f two e x t e r i o r

(this

one;

an

tributaries

Continuing downstream i n the same manner,

would have a v a l u e of two. streams intersect,

Each c o n t r i b u t i n g e x t e r i o r t r i b u t a r y

tributaries)

as

the r e s u l t a n t downstream s t r e t c h of r i v e r would h a v e a the

sum

of

the

values

of

the

preceeding

intersecting

stream. At the mouth of the r i v e r , the v a l u e o f the f i n a l r i v e r section w i l l be equal to the number o f c o n t r i b u t i n g e x t e r i o r t r i b u t a r i e s ,

22 in F i g u r e

13.1.

by

D i v i d i n g the

v a l u e of

the f i n a l

v a l u e of the c e n t r o i d of the b a s i n ,

s t r e t c h of

1 1 i s calculated.

h a v i n g a v a l u e equal to t h a t of the c e n t r o i d sections and

i s the

location of

the

the

river

r i v e r basin, of

I n many

sampling station

cases,

when

with

When

this

occurs,

closest to the c e n t r o i d i s chosen.

the

stream

highest

the

initial

river

basin

centroid.

segment

having

the two equal The

two

order

the mouth

t h i s procedure to

The n e x t o r d e r o f sampling

determined b y f i n d i n g the c e n t r o i d v a l u e of a n d below

applying

into

there i s u s u a l l y not a stream h a v i n g a v a l u e e q u a l to

the centroid.

the

The section of r i v e r

d i v i d e s the b a s i n

( t h e assumption i s made t h a t there e x i s t s a s a m p l i n g s t a t i o n a t of the r i v e r b a s i n ) .

two,

a

a

that value

locations

is

sections above

procedure

is

continued

u n t i l a percentage of a r e a l coverage i s a t t a i n e d . The percentage of area coverage specified b y the m o n i t o r i n g agency defined as the number of

sampling

the

this

basin.

sampling

Intrinsic

in

station hierarchy

stations d i v i d e d b y

objective

that

procedure

o r d e r s the

is

importance

is

the m a g n i t u d e of the of

concept each

of

a

sampling

210 station

in the b a s i n

1973). T h i s p r o v i d e s a

(Sharp,

r e a l i s t i c methodology

i n which a r a t i o n a l implementation progam c a n proceed: stations

(highest

available,

order)

additional

are

built

first

and

as

the most

the

important

resources

become

As each succeeding h i e r a r c h y

s t a t i o n s can be b u i l t .

of s t a t i o n s a r e e s t a b l i s h e d the percentage of a r e a l coverage i s increased. Having

established

microlocation

the

specifies

macrolocations

the

river

within

reach

to

a

be

river sampled

microlocation specifies the p o i n t i n the r e a c h to be sampled.

basin,

the

while

the

This point

is

t h e location of a zone in the r i v e r r e a c h where complete m i x i n g e x i s t s a n d

in o r d e r to o b t a i n a

o n l y one sample i s r e q u i r e d from the l a t e r a l transect

(in

representative

space)

sample.

Being

downstream from the nearest o u t f a l l ,

a

function

t h e zone of

of

the

distance

complete m i x i n g can

be

estimated u s i n g v a r i o u s methodologies. Given the assumptions t h a t a p o i n t

source

stream approximates a Gaussian d i s t r i b u t i o n , modelled

using

image

theory,

in a

d i s t a n c e downstream

the

following

straight,

pollutant

a n d t h a t b o u n d a r i e s can equation

u n i f o r m channel

-

-

(J

Y

where

a point

L

be the

source

1977).

2u

Y

(13.1) is

the

from

mixing

source

velocity and D Estimates of D

Y

predict

2oy

distance

D

can

from

p o l l u t a n t to a zone of complete m i x i n g (Sanders et a l . ,

LY

in a

distribution

distance farthest

for

complete

lateral

lateral

boundary,

u

mixing,

a y

is

stream

mean

is

i s the l a t e r a l t u r b u l e n t d i f f u s i o n coefficient.

Y

Y

to

can be made u s i n g e q u a t i o n 13.2

= 0.23 du'

(13.2)

where d i s depth of flow u* i s shear v e l o c i t y

g

i s acceleration flow

due to g r a v i t y R i s h y d r a u l i c r a d i u s S i s slope o r t h e h y d r a u l i c g r a d i e n t (Sanders e t al., Unfortunately,

1977). there may not e x i s t

in a g i v e n r i v e r

of complete m i x i n g due i n p a r t to the random n a t u r e of

mixing

distance,

determination of

inapplicability

of

the m i x i n g distance,

the

assumptions

o r more often

river

l e n g t h o r t u r b u l e n c e to assure complete m i x i n g

river

reach.

On

the o t h e r

hand field

reach any

within

in

used

t h a n not,

v e r i f i c a t i o n of

points

the aforementioned

not

the

enough

the s p e c i f i e d

a completely

mixed

zone p r i o r to l o c a t i n g a permanent s a m p l i n g s t a t i o n c a n be e a s i l y done b y collecting

m u l t i p l e samples

in the cross

u s i n g a we1 I-known one- o r two-way

section

and analyzing

the

a n a l y s i s of v a r i a n c e techniques.

data

21 1 If

there

sampled,

is

not

a

completely

mixed

zone

the

in

river

reach

to

be

there a r e three a l t e r n a t i v e s :

( 1 ) Sample anyway a t a s i n g l e p o i n t a n d assume i t i s r e p r e s e n t a t i v e ( t h i s i s a general approach adopted t o d a y ) ;

( 2 ) Don't sample the r i v e r reach a t a l l , obtained does not q u a l i t y o f the

represent

sample

because t h e d a t a w h i c h would be

the e x i s t i n g r i v e r

quality,

b u t only

In o t h e r words,

volume collected.

the

the data

is

useless;

( 3 ) Sample a t several p o i n t s in the l a t e r a l transect c o l l e c t i n g a composite mean, which would be r e p r e s e n t a t i v e of the water q u a l i t y

in the r i v e r

a t that p o i n t i n time a n d space.

I f the sample i s not r e p r e s e n t a t i v e of the water mass, sampling

as

presentation

well and

as the

the

mode

realistic

m a k i n g becomes inconsequential.

of

use

data of

analysis,

the

data

interpretation

for

I n s p i t e of t h i s f a c t ,

the frequency of

objective

and

decision

c r i t e r i a to e s t a b l i s h

s t a t i o n locations f o r r e p r e s e n t a t i v e s a m p l i n g h a v e received r e l a t i v e l y

little

a t t e n t i o n from many i n s t i t u t i o n s a n d agencies responsible f o r water q u a l i t y monitoring.

SAMPLING FREQUENCY

Once sampling

stations

a r e representative

have been

i n space,

located to ensure

sampling

frequency

samples collected

should

be

specified

so

t h a t the samples a r e r e p r e s e n t a t i v e in time. Sampling frequency basin

is

a

very

a t each permanent

important

parameter

sampling station w i t h i n a

which

must

be

considered

design of a water q u a l i t y m o n i t o r i n g network.

A l a r g e p o r t i o n of

o f o p e r a t i n g a m o n i t o r i n g network

r e l a t e d to

sampling.

However,

the

reliability

d e r i v e d from a m o n i t o r i n g network sampling.

Addressing

is directly

this

and

utility

of

river in

the

the costs

the frequency

water

quality

of

data

i s l i k e w i s e r e l a t e d to the frequency of

anomaly

Quimpo

(1968)

summarized

the

s i g n i f i c a n c e of sampling frequency a n d stated t h a t : On the one hand,

b y s a m p l i n g too often,

obtained i s r e d u n d a n t and t h u s expensive, hand,

the i n f o r m a t i o n a n d on the other

sampling too i n f r e q u e n t l y bypasses some i n f o r m a t i o n

necessitating an extended p e r i o d of observation. Significant v i o l a t ion

,

as

sampling

frequency

is

m a i n t a i n i n g e f f I uent standards,

i n ambient water q u a l i t y ,

very

to

detecting

stream

standards

a n d e s t i m a t i n g temporal changes

l i t t l e q u a n t i t a t i v e c r i t e r i a which designate

a p p r o p r i a t e sampling frequencies h a v e been a p p l i e d to the design of water

21 2 quality

monitoring

networks.

many

In

cases,

professional

judgment

cost c o n s t r a i n t s p r o v i d e the b a s i s f o r s a m p l i n g frequencies.

All

frequencies

upon

are

capabilities, only

the

same

at

once-a-month,

practical

means

each

station

once-a-week,

to

implement

etc.

a

frequencies

as

and

1978).

Adrian,

functions

of

the

variable

(Nyquist frequency),

maximum

to

minimum

flow

cyclic

methods

variations

and

(Ward et

possibly

the

considering

the

include

of

the

b a s i n area

water

and

19671,

Orlob,

specifying

of

a

test

measuring

the

confidence

1976; L o f t i s a n d Ward,

al,

water

quality

the r a t i o of

quality

intervention

1978),

1978), and

the number of d a t a p e r y e a r f o r hypotheses (Sanders and Ward, the power

routing

s a m p l i n g frequencies a t each

The

the d r a i n a g e

(Pomeroy

i n t e r v a l o f the a n n u a l mean

although

program

too often,

there do e x i s t many q u a n t i t a t i v e ,

s t a t i s t i c a l l y meaningful procedures to specify (Sanders

based

and

sampl i n g

s t a t i s t i c a l b a c k g r o u n d o f d a t a collectors,

station

and

and

(Lettenmaier,

1975).

A l l of the aforementioned procedures can b e a p p l i e d to the design of a water q u a l i t y m o n i t o r i n g network w i t h each r e q u i r i n g a d i f f e r e n t statistical

sophistication

assumptions app I y One of variable

the

.

simplest

(iid)

and

as

approaches

concentrations

distributed

insofar

are

is

data

to assume

random,

determine

the

requirements

that

the

independent

number

of

as

well

water

and

samples

level of as

quality

identically

per

year

as

a

f u n c t i o n o f an a l l o w a b l e ( s p e c i f i e d ) confidence i n t e r v a l of the mean a n n u a l concentration analyses of

( t h i s i s analogous to the procedure f o r d e t e r m i n i n g how many a

water

sample

should

be

made

to

determine

a

reasonable

estimate o f the mean water q u a l i t y v a r i a b l e c o n c e n t r a t i o n ) .

[

n =

aizS]

(13.3)

where n i s the number of e q u a l l y is a

constant

number

of

which

samples,

is a

S

is

spaced samples collected p e r y e a r ,

function the

of

the

standard

l e v e l of

deviation

concentrations a n d R i s s p e c i f i e d h a l f - w i d t h

of

significance of

the

water

the confidence

taI2

and

the

quality

interval

of

the a n n u a l mean. Using the same assumption,

t h a t the water

number of samples p e r

year

can

a n a l y s i s procedure as

well.

For

example,

variable i s iid,

quality

be s p e c i f i e d a s a

if

function

annual

of

means

tested f o r s i g n i f i c a n t changes u s i n g the d i f f e r e n c e in means,

the

the data

were

to

be

then to detect

a n assumed level of change, t h e number of samples c a n be specified.

A

more

sophisticated

procedure,

representing

a

higher

level

of

21 3

0.9

0.8

R vs. Number of Somples per Yeor I 2 3 4 5 6 7 8

0.7

0.6

Wore Conn. at Thompsonville Deerfield Conn. ot Montopue City Millers Conn.ot Vernon

Westfield Conn. ot Turners Falls

R

0.5

0.4

0.3

0.2

0. I

I

1

I

I

I

10

20

30

40

50

Number of Somples per Yeor

Fig 13.2

A p l o t n u m b e r o f s a m p l e s per y e a r of the expected h a l f - w i d t h of t h e c o n f i d e n c e i n t e r v a l of m e a n log f l o w , R , v e r s u s n u m b e r of S a m p l e s for S e v e r a l R i v e r s in t h e C o n n e c t i c u t R i v e r B a s i n

214 statistical

analysis,

may not be i i d ,

would

be

to recognize

b u t h i g h l y dependent,

that

water

seasonal v a r i a t i o n ,

a n d determine s a m p l i n g frequency

variability

water

of

the

quality

p e r i o d i c components h a v e daily

discharge,

data

been

variable

removed.

bases

of

quality

veriables

not i d e n t i c a l l y d i s t r i b u t e d ,

as a f u n c t i o n of

series

after

trend

Unfortunately,

other

than

water

time

having

quality

number, r e l i a b i l i t y a n d l e n g t h a r e g e n e r a l l y

variable

of

the and

mean

sufficient

not a v a i l a b l e f o r a p p l i c a t i o n

of t h i s procedure. Once utilized quality

a

uniform

to

objectively

interval

frequencies)

of

the

of

where

station.

Thus,

stations

more

frequently

little.

With

number

reference

of

of

sampling

annual

equality

sampled

these

samples

per

13.2

the

(for

it

can

within

a

varies

where which

of

specifying

in a

the is

mean

number

at

water

a

of

fashion sampling

tremendously

plot

of

samples

will

quality

log r i v e r

the

flow

the

sampling

each

water

be

of

consistent

half-widths

quality

interval

year,

frequencies

mean

stations

selected

the expected h a l f - w i d t h

expected

Figure

the confidence

is

basin-wide

water

than

to

criterion

For example,

approach c a n be a p p l i e d

specifying

half-width

frequency

distribute

m o n i t o r i n g network.

confidence

by

sampling

be

varies expected

versus

collected

at

the each

s t a t i o n w i t h i n the r i v e r b a s i n f o r a g i v e n R a r e determined b y d r a w i n g a horizontal abscissa curve.

line axis

through below

Figure

13.2

and

R

the

may

reading

intersections also

the

on

be used

number

the

i n an

of

samples

horizontal

line

i t e r a t i v e fashion

on

with to

the each

specify

s a m p l i n g frequencies a t each s t a t i o n when a t o t a l number o f samples from the b a s i n

i s specified.

For example,

collected a n d analyzed, horizontally;

a

v a l u e of

the number of

if

R

only

samples s p e c i f i e d

curves a r e summed a n d compared

to

N

samples

i s assumed

N.

If

the

by

and the

sum

a

per

year

line

is

were drawn

i n t e r s e c t i o n of

were not e q u a l

the to N

then another estimate of R would be made u n t i l the sum of a l l the samples i s equal to N. I t should be noted t h a t the expected h a l f - w i d t h o f the a n n u a l mean i s not the o n l y s t a t i s t i c

that

the expected h a l f - w i d t h a n d may

can

be used

to

specify

s a m p l i n g frequencies;

d i v i d e d b y the mean i s a measure o f r e l a t i v e e r r o r

be more a p p r o p r i a t e

when

assigning

sampling

frequencies

in

a

b a s i n where water q u a l i t y v a r i e s tremendously from r i v e r to r i v e r . When developing s a m p l i n g frequencies, important

cycles

concentrations,

which

can

have

one must keep i n m i n d two v e r y

immense

impact

on

the d i u r n a l c y c l e a n d the weekly cycle.

d i u r n a l cycle (which i s a

f u n c t i o n of

the r o t a t i o n

e l i m i n a t e d b y s a m p l i n g in e q u a l time i n t e r v a l s f o r

of a

water

The effect the e a r t h )

24-hour

quality of can

period

the be and

215 the effect of t h e weekly c y c l e ( w h i c h i s a f u n c t i o n of mans' be eliminated be m u l t i p l e s

by specifying of

seven,

that

and

sampling

occasional

i n t e r v a l s for a

sampling

on

a c t i v i t y ) can

network

weekends

cannot

would

be

necessary.

in terms of v a r i a b l e s

Perhaps the major impact between network design to

monitored,

be

operational

sampling

monitoring

consequently,

location,

functions

ultimate

v a l u e of

sampling program that

is

and

the

sampling

the

in

area

monitoring

frequency

of

data

network

and

the

analysis

and,

information.

Any

i s to generate conclusive r e s u l t s from o b s e r v i n g

stochastic process ( w a t e r q u a l i t y concentrations) must be well s t a t i s t i c a l l y designed.

S t a t i s t i c a l l y designed

implies

p l a n n e d ( i n p r o p e r locations and numbers) so t h a t

that

a

planned and

the

sampling

the s t a t i s t i c a l

techniques chosen w i l l be a b l e to y i e l d q u a n t i t a t i v e information.

is

analysis Thus,

the

d a t a a n a l y s i s techniques ( l e v e l and t y p e of s t a t i s t i c s ) to be used must be defined

in

order

to

know

how

to

compute

proper

sampling

frequencies,

locations, etc.

D ISCUSS ION

The above section has pointed out many problems due to not d e s i g n i n g a m o n i t o r i n g system that

all

accuracy. on

aspects

in a

of

For example,

nonrepresentative,

excessive segment

a

accuracy

systems

context.

monitoring

Perhaps

program

i t would not be wise to

grab

i n one

sample d a t a . segment

The

compared

the major

should

match

use

time

system to

concern

in

terms

series

would

be

the accuracy

is of

analysis providing another

in

.

I n a s i m i l a r manner, sophisticated

i t may be u n r e a l i s t i c to encourage use of

sample collection

and

laboratory

a n a l y s i s techniques

more

if

the

d a t a i s not to receive a thorough s t a t i s t i c a l a n a l y s i s . It

i s difficult

to

test

hypotheses,

make decisions

flow

weighted,

several

times

a

year,

from

and

i n i t i a t e action

in the daytime a n d not

u s i n g water q u a l i t y d a t a which a r e collected o n l y

locations

which

are

not

completely mixed a n d u s i n g l a b analyses procedures which may h a v e more variation

in

their

results

when

analyzing

the

same

sample

than

the

ambiant v a r i a t i o n of the water q u a l i t y v a r i a b l e in the r i v e r . Perhaps an even l a r g e r concern to those in m o n i t o r i n g network i s the

use of

water

quality

T h i s lowers the v a l u e of a n y t h a t of spot checks. standards

would

standards information

that

generally

ignore

design

statistics.

from a compliance v i e w p o i n t ,

I n c o r p o r a t i n g water q u a l i t y means a n d v a r i a t i o n

greatly

facilitate

incorporating

more

statistics

to into into

216 m o n i t o r i n g . T h i s would h a v e t h e effect of t y i n g network design to d a t a use in a much more concrete,

a l s o encourage use of would

be

a

s t a t i s t i c a l manner t h a n i s now possible.

the

statistical

system

thread

approach moving

to

network

through

the

design entire

I t would as

there

monitoring

operat ion.

REFERENCES

Lettenmaier, D.P., 1975. Design of M o n i t o r i n g Systems f o r Detection of Trends i n Stream Q u a l i t y . Technical Report No. 39, Charles W. H a r r i s H y d r a u l i c s L a b o r a t o r y , U n i v e r s i t y of Washington, Seattle. L o f t i s , J.C. a n d Ward, R.C., 1978. S t a t i s t i c a l Tradeoffs i n M o n i t o r i n g Network Design, presented a t AWRA Symposium Establishment of Water Q u a l i t y M o n i t o r i n g Programs. San Francisco, C a l i f o r n i a . Pomeroy, R.D. a n d Orlob, G.T., 1967. Problems of S e t t i n g S t a n d a r d s o f S u r v e i l l a n c e f o r Water Q u a l i t y Control. C a l i f o r n i a State Water Q u a l i t y Control Board P u b l i c a t i o n No. 65, Sacramento, C a l i f o r n i a . Quimpo, R.G., 1968. Stochastic A n a l y s i s of D a i l y R i v e r Flows. Journal o f H y d r a u l i c s , ASCE. 94(HY1) p43-47. Sanders, T.G., A d r i a n , D.D. a n d Joyce, J.M., 1977. M i x i n g L e n g t h f o r Representative Water Q u a l i t y Sampling. Journal Water P o l l u t i o n Control Federation. 49 p2467-2478. T.G. a n d Ward, R.C., 1978. R e l a t i n g Stream Standards to Sanders. Regulatory Water Q u a l i t y M o n i t o r i n g Practices. Presented a t the AWRA Symposium “Establishment of Water Q u a l i t y M o n i t o r i n g Programs, San Francisco, Ca I i f o r n i a . Sanders, T.G. and Adrian, D.D., 1978. Sampling Frequency f o r R i v e r Q u a l i t y M o n i t o r i n g . Water Resources Research. 1 4 ( 4 ) p 569-576. Ward, R.L. L o f t i s , J.G. Steel, T.D, Adrian, D.D. and Sanders, T.G., Yevjevich, V., 1986. Design of Networks f o r M o n i t o r i n g Water Q u a l i t y , 2nd E d i t i o n , Water Resources P u b l i c a t i o n s , Colorado. Sharp, W.E., 1973. A T o p o l o g i c a l l y Optimum R i v e r Sampling P l a n f o r South C a r o l i n a . Water Resources Research I n s t i t u t e Report No. 36, Clemson U n i v e r s i t y , Clemson , South Carol i n a . Ward, R.C., Neilsen, K.S. a n d Bundgaard-Nielsen, M., 1976. Design of M o n i t o r i n g Systems f o r Water Q u a l i t y Management. C o n t r i b u t i o n f o r the Water Q u a l i t y I n s t i t u t e , Danish Academy of Technical Science, No. 3, Horshdm, Denmark.

21 7

AUTHOR INDEX Abulnour, A.M. 116 Adarns, B.J. 190 Adarnson, P.T. 76 A d r i a n , D.D. 209,212 A g a r d y , F.J. 66 American Water Works Association 37 A r n o l d , R.W. 36 Baker-Duly, H.L.G. 123 B a l l , J.M. 70, 77 B a r e n b r u g , A.W.T. 2 Bauer, C.S. 143, 146, 149 Beck, M.B. 202 Bedient, P.B. 66 Betz, 3 Bishop, A.B. 165 Boyd, G.B. 66 B r a d f o r d , W. J 64 B r e b b i a , C.A. 62 Brownlow, A.H. 1 Bungaard-Nielsen, M. 210 Chan, W.Y.W. 167 Chiang, C.H. 165 CIRIA. 164 C o l w i l l , D.M. 66 Connor, J.J. 62 Corbetis, S. 116 Cordery, I. 70 Crabtree, P.R. 167

.

D e i n i n g e r , R.A. 36, 39, 51 D a n t z i g , G.B. 82, 163 F r i e d , J.J. 55 Fuchs, L. 190 G i l b e r t , R.G. 143 Goodier, J.M. 63 Green , I. R.A. 64 G r i z z a r d , T.J. 70 Grosman, D.D. 86 H a d l e y , G. 162 H a l l , G.C. 160 Helsel, D.R. 70 Henderson-Sel l e r s , B. 24 H i l t o n , E. 27, 119 Hine, A.E. 197 Hinton, E. 149 Ho, G.E. 143 Hoehn, R.C. 70 Holton, M.C. 75 Hunter, J.V.I. 66 IBM 162 Idelovitch,

E.

Joyce, J.M.

210

143

Kemp, P.H. 64 Kim, J.I. 70 Kleinecke, D. 41 Lance, J.C. 143 Larnbert, J.L. 66 Larnbourne, J.J. 66 L a n g e l i e r , W.F. 3, 5, 6 L a n y o n , R. 75 L a r s o n , T.J. 104 L a u r i a , D.T. 165 L e i g h t o n , J.P. 146, 149 Lettenmaier, D.P. 212 Lewis, R.W. 119, 149 L l o y d , P.J. 1 L o f t i s , J.C. 209, 212 Loucks, D.P. 116 L u d w i g , L. 9 L y n n , W.R. 116 M a d i s h a , J.L. 75 Mathew, K. 143 McDonell, D.M. 56 McPherson, D.R. 41, 45 M i c h a i l , M. 143 M i k a l s e n , K.T. 75 Mrost, M. 1 MOller, D. 190 Neilsen, K.5. 210 Neurnann, A. 190 Newrnan, P.W.G. 143 O'Conner, B.A. 56 Orlob, G.T. 212 P a l i n g , W.A.J. 141, 143, P e l l e t i e r , R.A. 1 P e r r y , R. 66 Peters, C.J. 66 Petersen, 5.0. 190 P o l l s , I. 75 Pomeroy, R.D. 212 Porges, J. 2 P r a t i s h t h a n a n d a , S. 165 Quimpo,

R.G.

145

211

R a n d a l l , C.W. 70 Rand Water B o a r d 155 Revelle, C.S. 116 Rice, R.C. 143 Rinaldi, S. 116 Ryzner, J.W. 36 Sanders, T.G. 24, 209, S a r t o r , J.D. 66 S c h i l l i n g , W. 190 S h a r l a n d , P.J. 41, 45 Sharp, W.E. 210

210,

212

21 8

S h a w , V.A. 167 Shoemaker, C.A. 146, 149 Simpson, D.E. 64 Smeers, Y. 116 Smith, A.A. 119, 149 Soncini-Sessa, R. 127 South A f r i c a n Bureau of S t a n d a r d s 72 S p r i n g e r , N.K. 66 Steel, T.D. 209, 212 Stehfest, H. 127 Stephenson, D. 27, 66, 80, 81, 82, 115, 116, 117, 163, 175, 197, 200

T e r s t r i e p , 66 Thomann, R.V. 39 Timoshenko, 5 . 55 Tyteca, D. 116 U h l i g , H.H. 13 Van Staden, C.M.V.H. Velz, C.J. 41

2

W a n i e l i s t a , M.P. 64, 146, 149 Ward, R.C. 209, 210, 212 Whipple, W. 66 Wang, L.K., 167 Yen, B.C., 190 Yevjevich, V . 209 Y u , S.L. 66 Zukovs, G.

190

21 9

SUBJECT INDEX Acid 1 Additives 6 Advection 21, 52 Aerobic 9 A g r i c u l t u r e 17 Antecedent moisture 66 Air 1 Alkalinity 3 A l l o c a t i o n 79 A l l o y 13 Ammonia 9 Anaerobic 9 Analyses 195 A n a l y t i c a l 39 Apartments 167 A q u i f e r 141 Arsenic 17 A r t i f i c i a l r e c h a r g e 141 Backwater 193 B a c t e r i a 9, 206, 207 B a r i u m 16 B a s i n 209 Benefits 126 Bicarbonate 67 Biocide 9 Blend 89 Blowdown 2 BOD (biochemical oxygen demand) 37 Booster 152 Bottleneck 173 Boundaries 62 Bremen 193 B r i n e 104, 122 Calcium carbonate 4 C a l i b r a t i o n 40 C a p i t a l 107, 157 Carbonaceous 38 Cathode 10 Catchment 64 Cellulose acetate 104 C h a r a c t e r i s t i c 39 Chelant 7 Chemical 67 C h l o r i d e 2, 67 Chlorine 9 C i v i l e n g i n e e r i n g 107 Commerci a I 1 70 Cleaning 115 Computer 20, 115, 128 Concentration 2, 71, 159, 212 C o n d u c t i v i t y 18 Conduit 175 Confidence 214 C o n s t r a i n t s 41, 86 Conveyance 141 Cooling 20

C o r r e l a t i o n 66 Corrosion 3, 13 Cost 79, 107, 146 C r i t e r i a 211 Crop 17 Crump w e i r 65 Crystal 7 C y a n i d e 16 Cycle 214 D a t a 177, 204 Dead water 24 Decomposition p r i n c i p l e 163 D e s a l i n a t i o n 99, 115 D e t e r i o r a t i o n 116 D i f f u s i o n 36 Disc 128 Dispersants 7 Dispersion 21, 166 D i s t i l l a t i o n 101 DO ( d i s s o l v e d o x y g e n ) 37, 206 Dissolved s o l i d s 206 Downstream 193 D r y d a y s 66 D r y weather 77 Economics 99 E l e c t r i c a l corrosion 14 E Iect r o d ia I v s i s 105 Emulsion 10 Env ironmenta I 193 Equipment 107 E r r o r 91 E s t u a r i e s 37 E u l e r 57, 59 Evaporation 2 E x p l i c i t 39, 51 F a l l o u t 66 F a r a d a y s l a w 14 Feedback 205 F i e l d 45 F i n i t e d i f f e r e n c e 55 F i n i t e elements 62 F i r s t f l u s h 70 F l o o d i n g 193 Flow 166 Foam 8 F o r m u l a t i o n 88 Fouling 9 Four p o i n t 51 F o u r i e r series 54, 169 Freezing 103 Frequency 21 1 Gain 23 G a l v a n i c corrosion 13 Geochemical 1 Geohydrology 41

220

G r a p h i c s 118, 177 Groundwater 98, 112, 143 Gypsum 6 H i e r a r c h y 209 H i l l b r o w 68 H y d r a u l i c 51, 167 Hydrodynamic 56 H y d r o g r a p h 166 IBM 150 I m p l i c i t 55 I n d u s t r i a l 1, 104, 112, 172 I n f i l t r a t i o n 143, 176 I n f l o w 177 I n a c c u r a c y 52 I n s t a b i l i t y 55 I n t e g e r Programming 141, 149 I n t e r e s t r a t e 107 I o n exchange 105 I r o n 3, 16 I r r i g a t i o n 17 I t e r a t i o n 165 Johannesburg 167 K l i p r i v e r 40 L a b o r a t o r y 205 L a b o u r 108 L a n g e l i e r index 5 L a x a t i v e 16 Leach 1 , 26, 75 L e a d 17 L e a k 166, 176 L e a p f r o g 51 Least squares 42 L e g i s l a t i o n 204 L i n e a r p r o g r a m m i n g 43, L o a d f a c t o r 107 Loops 119

85

Maintenance 116 Make-up 26, 33 Manhole 167 Mass b a l a n c e 20, 35, 64, 72, 161 Master programme 163 Mathematical models 20, 149, 158 Measurement 167 Membranes 105, 108 Meta p r o d u c t i o n 191 M i n e water 26, 117, 123 M i n i m i z e 41 M i x e d f l o w 21 M o n i t o r i n g 204 M u l t i - s t a g e f l a s h d i s t i l l a t i o n 103 M u l t i step 61 Network 146, 205 N i t r a t e 17, 72

Nodes 119, 128, 160 Non c o n s e r v a t i v e 35 Numerical 23, 51 d i f f u s i o n 35 O b j e c t i v e 41 O i l 10 O p e r a t i n g 157 Optimum 79 O p t i m i z a t i o n 116, 152, 162 Ore 30 Oxygen 10, 37, 40 Peak 146, 174 PH 3 Phenol 16 Phosphate 7 Photosynthesis 46 P i p i n g 2, 146 P l a n n i n g 149 P l a n t 122 P l u g f l o w 21 P o l l u t i o n 1 , 64 Pol l u t o g r a p h 23 Polymer 7 Polyphosphate 7 P o p u l a t i o n 166 P o t a b l e 15 P o u r b a i x d i a g r a m 12 P r o b a b i l i t y 167 P r o d u c t i o n system 190 P r o g r a m 122, 128, 136, 174, 179 P u r i f i c a t i o n 143 Rand Water Board 157 Random 212 Raw water 122 Reaction 14 Recharge 144 Recovery r a t i o 1 1 1 Reed beds 40 Regional 155 Regression 67 R e l i a b i l i t y 211 Reservoir 23 R e s i d e n t i a l 167 Re-use 99 Reverse osmosis 81, 104 R i v e r s 37, 214 R o u t i n g 166, 175 R u l e base 191 Runge Cutte 61 R u n n i n g 108 Runoff 67 Ryzner i n d e x 3 S a l t s 102 S a n i t a t i o n 195 S a n i t a r y e n g i n e e r i n g 206 Sample 68, 204, 205

221

Sampling frequency 206 Scale 102 Scaling 3 Sea water 101 Sediment 8 S e n s i t i v i t y 195 Separable programming 81, 95 S e n s i t i v i t y 95, 165 Sewage 144, 176 Sewer 72, 166, 190, 196, 198 Shadow v a l u e 165 Shops 169 Simulation 31, 51, 166 Simplex method 89 S i n k 42 Slack 82, 160 Software 195 Solution 82, 160 Source 43 Standards 15, 141 Station 210 S t a t i s t i c a l 205 S t a t i s t i c s 215 Steady s t a t e 20 Stormwater 64, 77, 166, 176 Stream 159, 204 Stream gauge 66 Streeter Phelps e q u a t i o n 37 Sub-programme 165 Sub-division 173 Sulphate 5, 16, 30, 67 Surcharge 168 Suspended 206 System 80 Systems a n a l y s i s 24, 118 Tape 128 Taste 16 T a y l o r series 53 TDS ( t o t a l d i s s o l v e d s o l i d s ) 2, 95 Temperature 3, 206, 107 Terminal concentration 24 Time l a g 166 Topography 1% Toxic 16 T r a f f i c 69 T r a n s p o r t a t i o n p r o g r a m m i n g 80 Treatment 141, 155, 157 T u r b i d i t y 206 Turbulence 8 Two step 39, 52 U n p r e d i c t a b l e 64 Upstream 193 V a a l r i v e r 155 Vapour compression 102 Vegetables 18 Ventilation 2

Washoff 67 Waste t i p 65 Waste water 99, 155 Water resources 79 Water s u p p l y 116 Waterways 190 Water v a p o u r 2 Welding 13 W i t w a t e r s r a n d 155 Zeolites 107 Z i n c 16 Zooming 56

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