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Optimization of Water Quality in River Basin
Optimization of Water Quality in River Basin I. Dimitrova and J. Kosturkov Institute of Water Problems, Bulgarian Academy of Sciences, Sofia 1113, Bulgaria
SUHHARY
An a l t e r n a t i v e management scheme f o r water q u a l i t y maintenance i n r i v e r basin i s presented.The t w o f o l d basic planning problems u s u a l l y a r e t o determine t h e d e s i r e d l e v e l o f water q u a l i t y and t o develop a waste management program.ln t h i s paper t h e o p t i m i z a t i o n problem i s formulated.The o b j e c t i v e i s t o minimize t h e sum o f t h e waste removal c o s t s f o r some dischargers.This i s carr i e d o u t i n terms o f determining an optimal design procedure f o r t h e i n d i v i d u a l p l a n t s and then o p t i m i z i n g t h e o v e r a l l treatment costs w i t h c o n s t r a i n t o f stream q u a l i t y preservation.Because o f water d e f i c i t i n t h e experimental r i v e r basin i n low water per i o d , t h e model g i v e s t h e p o s s i b i l i t y t o Control t h e r i v e r d i s charge.The separable programming f o r s o l v i n g t h e o p t i m i z a t i o n problem i s used.The r e s u l t s from t h e o p t i m i z a t i o n are given. INTRODUCTION The p o l l u t i o n o f r i v e r s has sharply increased d u r i n g t h e l a s t several decades under t h e i n f l u e n c e o f anthropogenous and technogenous factors.The maintenance o f t h e i r water q u a l i t y w i t h i n t h e standard i s c a r r i e d o u t by r e g u l a t i n g waste water q u a l i t y and q u a n t i t y discharged in.This may be achieved i n d i f f e r e n t ways,and i n t h e f i r s t p l a c e b y waste water treatment,improvement o f treatment methods,implementation o f water r e c y c l i n g i n water supply and wasteless technologies,use o f waste water,etc.In add i t i o n , maintenance o f water q u a l i t y w i t h i n t h e standard may be c a r r i e d o u t by increasing r i v e r s e l f p u r i f i c a t i o n capacitY,name l y by increasing water q u a n t i t y i n low water periods,dam b u i l d i n g , a r t i f i c i a l a e r a t ion,water t r a n s f e r , etc.R i v e r p o l l u t i o n i s mostly reduced by waste water treatment i n waste water t r e a t ment plants.Thus t h e problem r e l a t e d t o f i n d i n g o u t a combinat i o n o f stages i n treatment o f waste water by d i f f e r e n t d i s chargers.Such a combination i s t o ensure a water q u a l i t y r e q u i r e d b y t h e standard i n t h e r i v e r a t minimum t o t a l c o s t s i n p a r t
405
406 of or t h e whole r i v e r basin. FORMULATION OF THE PROBLEM According t o f i g u r e 1 t h e p a r t o f t h e r i v e r b a s i n considered i s t h e following:ql=0.53m3/s a r e discharged f o r f l o w i n g in t h e r i v e r from a dam b u i l t f o r i n d u s t r i a l water supply, i r r i g a t i o n and r e c r e a t i o n purposes.The r i v e r considered i s small, f l o w i n g i n a densely populated i n d u s t r i a l area and s u b j e c t t o i n t e n s i v e p o l l u t i o n . D u r i n g t h e low water-level b e r i o d r i v e r f l o w is cons i d e r e d t o t a l l y formed by waste water and a r u n - o f f from t h e dam provided f o r f l o w i n g i n t h e r i v e r . T h e r e a r e f i v e waste d i s charges downstream's o f t h e dam:qp=4.64m3/s, q3=3.50m3/s ~4=2.31m3/s, qg=0.70mJ/s and ~6=0.48mJ/s.~astewater qua1 i t y o f each waste discharger i s shown i n t a b l e 1.The s i x parameters i.e. solubles,chemical oxygen demand (COD),biological oxygen demand (BODg),nitrogen,phosphorus and o i l products a r e exceed i n g t h e standard s p e c i f i e d f o r t h e r i v e r under consideration. The f o l l o w i n g t e c h n o l o g i c a l processes a r e s e l e c t e d f o r t r e a t i n g t h e waste water o f dischargers:filtration,precipitation,flotation,biochemical treatment,coagulation,active carbon adsorption, chlorination.The r e s i d u a l concentrations obtained f o r t h e d i f f e r e n t parameters o f p o l l u t i o n ( i = l . . 6 ) a f t e r u s i n g d i f f e r e n t t e c h n o l o g i c a l combinations o f treatment as per t h e treatment methods mentioned above a r e shown i n t a b l e 1 f o r each waste discharger (j=1..6).This t a b l e a l s o shows t h e c o s t data (tot a l costs S j ) o f each technological combination o f t r e a t ment
.
F i g u r e 1.Waste loading s i t u a t i o n The mathematical f o r m u l a t i o n o f t h e problem r e l a t e d t o l o o k i n g f o r an optimum combination o f stages f o r waste water treatment o f dischargers i n a r i v e r basin i s as follows.Water q u a l i t y i n a r i v e r may be c h a r a c t e r i z e d by t h e values o f parameters i n s i x c o n t r o l s t a t i o n s , t h e p l a c e o f which i n a s e c t i o n between two. waste dischargers i s s e l e c t e d i n such a way t h a t concentration (Dki,k=1..6) per parameter should be t h e maximum one. River water q u a l i t y meets t h e s a n i t a r y standard (Dsi) per parameter (or group o f Parameters) o f p o l l u t i o n i n case t h e i r values (Dki) do n o t exceed the.stanQard f o r each parameter. O K 1 1 Dsl (1)
407 This concentr a ti o n (Dki) i s t h e r e s u l t o f a superposition o f mixed q u a n t i t i e s o f i-parameter o f p o l l u t i o n o f a l l waste dischargers " j " located upstream. The t r a n s f e r , c o e f f i c i e n t i s equal t o t h e r a t i o between concent r a t i o n (Dkj ' i n k - s t a t i o n o f i-parameter as discharged by j waste dischargers and i t s co n ce n tr a ti o n i n t h e discharger (C.ii)
Ignoring d i f f u s i o n p a r t i c u l i r i t i e s o f each parameter o f water Q u a l i t y we accept t h a t t h e c o e f f i c i e n t s o f t r a n s f e r a r e i d e n t i c a l f o r each o f them,i.e. Tk.'=Tk..Each c o e f f i c i e n t ' s values T k j i s inversely p r o p o r t i o n a l t o t h e waste discharge d i l u t i o n . Table 1.Waste loading,version o f treatment and c o s t data
fer ion of :reitment I
-
Tota 1 cost mill. 1 eva/ year
Insolubles
-
15.5
I 2 3 4 5 6
0.0 15.0 16.1 17.4 25.4 33.7
t 2 3 4
0.0 0.8 9.7 10.3
1 2 3 4
0.0 0.6 10.9 14.5
1 2 3 4 5
0.0 5.4 8.6 15.8 18.7
1 2 3 4 5
0.0 2.4 8.6 10.7 12.3
-
COD
BOD5
Nitrogen
Phosphopus
0i Is
j = 1
1073 13.7 8.8 5.1 4.0 I. 8 j 7.7 3.4 0.4 0.3 j 40.0 3.6 1.6 0.8 j 68.0 13.4 6.4 3.4 2.2 j 41.0 12.1 8.1 3.3 2.1
14.8
2.0
0.4
0.1
0.0
294.4 24.2 19.4 15.9 5sQ 2.9 = 3 92.5 60.1 9.6 4.6 = 4 56.4 36.7 2.8 1.8 = 5 164.0 14.1 9.4 4.9 2.9 = 6 37.6 28.6 10.8 6.5 3.8
211.5 10.6 9.2 5.3 3.1 1.1
34.8 17.4 17.4 17.4 8.4 3.0
5.0 3.5 3.5 3.5 1-5 0.3
52.4 10.5 8.1 3.2 1.1 0.3
17.4 10.5 3.7 1.7
10.2 10.2 7.7 3.0
0.5 0.5 0.2 0.1
15.9 6.5 0.8 0.2
14,3 3.6 1.4 1.4
12.5 12.5 8. I 3.5
0.9 0.9 0.3 0.1
25.0 7.3 0.3 0.1
73.8 3.7 2.8 2.0 I.8
14.6 7.3 7.3 7.3 3.1
2.4. 1.5 1.5 0.8 0.2
3.0 1.6 0.9 0.5 0.2
16.7 12.8 5.0 2.5 1.0
0.8 0.5 0.4 0.4 0.3
1.4 1.0 1.0 0.5 0.3
0.0 0.0 0.0 0.0 0.0
j = 2
408 Determination o f these c o e f f i c i e n t s i n p r a c t i c e i s made by t h e theory o f mixing.When t h e information needed i s m i s s i n g , t h e c o n t r o l s t a t i o n s accept waste i n t o waste outlet,where t h e i r f u l l mixin g is, o r :
Thus,these c o e f f i c i e n t s depend on r i v e r Water Q u a n t i t y and waste water o u t l e t d i f f u s o r s design.Therefore,rivet water q u a l i t y i n t h e d i f f e r e n t c o n t r o l s t a t i o n s may be expressed by means o f t h e f o l l o w i n g matr i x equation:
TI 1
12 1 T3 1 T41 T5 1 T6 1 or
0 T22
T32
T42
T52
T62
0 0
0 0 T33 0 T43 T44 T53 T54 T63 T64
0 0 0 0 T55
T65
TxC=D
(3)
T k j f o r k=1..6 and j=1..6 a r e t h e t r a n s f e r c o e f f i c i e n t s ac cepted as i d e n t i c a l f o r each q u a l i t y parameter "C"; c k ' f o r k = l . . 6 a r e t h e concentrations.which a r e d i f f e r e n t f o r t h e d i f f e r e n t parameters i=1..6; Dk' f o r k = l . . 6 a r e c o n c e n t r a t i o n s i n t h e c o n t r o l s t a t i o n s which a r e d i f f e r e n t f o r t h e d i f f e r e n t parameters i.1. .6. I n t h i s way t h e l e f t p a r t o f a l l l i m i t a t i o n s (1) c h a r a c t e r i z i n g r i v e r water q u a l i t i e s w i l l be o f k i n d (3) where t h e values o f c k ' represent a f u n c t i o n o f t o t a l costs ( S j ) f o r waste water treatment o f a l l waste dischargers. c j = c j( S j ) (4) These f u n c t i o n s are shown i n t a b l e 1 Where S j a r e t h e c o s t s f o r waste water treatment o f j-discharger. The optimum i s looked f o r by s e l e c t i n g such a vector C a t which t h e system o f l i m i t a t i o n (1) i s f u l f i l l e d and t h e f u n c t i o n o f t h e c o s t s i s minimized: (S.)---> min Such a s o l u t i o n o f t h e probfem r e l a t e d t o l o o k i n g f o r an optimum combination o f stages f o r waste water t r e a t m e n t o f d i f f e r e n t waste dischargers i n a r i v e r basin i s presented by Gordin (1987) / f /. The problem formulated i n t h i s way i s a n o n - l i n e a r programmed one. I t i s solved by means o f separable f u n c t i o n s as per t h e method e s t a b l i s h e d by Hadley(1964)/2/.The problem mentioned above may be Solved i n two stages:the f i r s t one i s t o look f o r an optimum combination o f stages o f waste water treatment w i t h a view t o a chieving one parameter o f water q u a l i t y i n t h e r i v e r w i t h i n t h e standardland t h e second one i s , t o s e l e c t from t h e degrees of treatment obtained i n t h e f i r s t stage,a combination which
409 w i l l meet a l l parameters. The problem a l l o w s t o o b t a i n optimum
s o l u t i o n i n case o f increasing water q u a n t i t y discharged from t h e dam and f l o w i n g i n t h e r i v e r d u r i n g low w a t e r - l e v e l periods. I n t h i s s p e c i f i c case t h e value o f t h e water l e t f l o w i n t h e r i v e r i s n o t included i n t h e t o t a l co s t s because o f l a c k o f information,although t h e o p t i m i z a t i o n model a l l o w s t h e i r estirnation.The problem i s solved by means o f a computer programne,the s o l u t i o n being: 1-2,2-1,3-1,4-1,5-1 15.0 This r e c o r d i n g means t h a t t h e optimum combination o f t r e a t m e n t stages f o r t h i s area o f t h e r i v e r bas i n i s t h e fo1lowing:the second v e r s i o n f o r t h e f i r s t waste discharger,the f i r s t v e r s i o n f o r t h e second discharger,the f i r s t ver s i o n f o r t h e t h i r d d i s charger,the f i r s t version f o r t h e f o u r t h discharger and t h e f i r s t v e r s i o n f o r t h e f i f t h waste discharger.This being t h e d i s t r i b u t i o n and t h e standard o f r i v e r water q u a l i t y w i l l be a c h i eved a t minimum costs o f 15,000,000 leva/year.The r e s u l t s a r e shown i n t a b l e 2. Table 2.Computational Resul t s by Present Study Parameters
Standard VP!
Q1
m3/s
Optimal versionm i l l i o n leva/year
DS'
In sol u b l es
80.0
0.53
COD
70.0
0.53
BOD5
25.0
0.53
3.0
0.53
0.5
0.53
1-2,2-1,3-1,4-1,5-t 15.0 1-2,2-1,3-1,4-f,5-1 15.0 1-2,2-1,3-1,4-1,5-4 15.0 1 -6,2-4,3-4,4-5,577.2 1-6,2-4,3-1,4-1,5-1
0.3
0.53
1 - 6,2-4,3-3,4-3
Inso I u b l es ,COD, 8005, n itr ogen, phosphorus,oils
-
0.53
1-6,2-4,3-4,4-5,577.2
I nso 1 ub 1 es ,COD, BODS, phosphoru s,oi Is
-
13.48
I nso I u b l es ,COD, BOD5,phosphor us
1-6,2-3,3-3,4-1,5-1 54.3
-
4.65
1-6,2-1,3-1,4-1,5-1 33.7
Nitrogen /ammon i a/ Phosphorus /so I u b l e/ O i l p roducts
44.0
63-5
1
,5- 1 1
410 CONCLUS ION The method proposed f o r e s t a b l i s h i n g an optimum combination o f stages o f waste water treatment o f d i f f e r e n t waste dischargers i n a r i v e r basin enables t o s o l v e t h e basic problems r e l a t e d t o maintenance o f water standard q u a l i t y r e q u i r e d i n a r i v e r b a s i n a t minimum sum o f t h e waste removal costs.An optimum management programme f o r waste water treatment may be obtained f o r d i f f e r e n t r i v e r water standard q u a l i t i e s r e q u i r e d . REFERENCES
Chapter i n a book 1. Gordin, I . V . (1987),Tehnologicheskie s i s t e m i vodoobrabotki,Dinamicheskaja optimizaczija,Leningrad,Himia. 2. Hadley,G.,(l964),Nonlinear and dynamic programming,Addison Wesley P u b l i s h i n g company,Mass.,London.
SUHHARY
An a l t e r n a t i v e management scheme f o r water q u a l i t y maintenance i n r i v e r basin i s presented.The t w o f o l d basic planning problems u s u a l l y a r e t o determine t h e d e s i r e d l e v e l o f water q u a l i t y and t o develop a waste management program.ln t h i s paper t h e o p t i m i z a t i o n problem i s formulated.The o b j e c t i v e i s t o minimize t h e sum o f t h e waste removal c o s t s f o r some dischargers.This i s carr i e d o u t i n terms o f determining an optimal design procedure f o r t h e i n d i v i d u a l p l a n t s and then o p t i m i z i n g t h e o v e r a l l treatment costs w i t h c o n s t r a i n t o f stream q u a l i t y preservation.Because o f water d e f i c i t i n t h e experimental r i v e r basin i n low water per i o d , t h e model g i v e s t h e p o s s i b i l i t y t o Control t h e r i v e r d i s charge.The separable programming f o r s o l v i n g t h e o p t i m i z a t i o n problem i s used.The r e s u l t s from t h e o p t i m i z a t i o n are given. INTRODUCTION The p o l l u t i o n o f r i v e r s has sharply increased d u r i n g t h e l a s t several decades under t h e i n f l u e n c e o f anthropogenous and technogenous factors.The maintenance o f t h e i r water q u a l i t y w i t h i n t h e standard i s c a r r i e d o u t by r e g u l a t i n g waste water q u a l i t y and q u a n t i t y discharged in.This may be achieved i n d i f f e r e n t ways,and i n t h e f i r s t p l a c e b y waste water treatment,improvement o f treatment methods,implementation o f water r e c y c l i n g i n water supply and wasteless technologies,use o f waste water,etc.In add i t i o n , maintenance o f water q u a l i t y w i t h i n t h e standard may be c a r r i e d o u t by increasing r i v e r s e l f p u r i f i c a t i o n capacitY,name l y by increasing water q u a n t i t y i n low water periods,dam b u i l d i n g , a r t i f i c i a l a e r a t ion,water t r a n s f e r , etc.R i v e r p o l l u t i o n i s mostly reduced by waste water treatment i n waste water t r e a t ment plants.Thus t h e problem r e l a t e d t o f i n d i n g o u t a combinat i o n o f stages i n treatment o f waste water by d i f f e r e n t d i s chargers.Such a combination i s t o ensure a water q u a l i t y r e q u i r e d b y t h e standard i n t h e r i v e r a t minimum t o t a l c o s t s i n p a r t
405
406 of or t h e whole r i v e r basin. FORMULATION OF THE PROBLEM According t o f i g u r e 1 t h e p a r t o f t h e r i v e r b a s i n considered i s t h e following:ql=0.53m3/s a r e discharged f o r f l o w i n g in t h e r i v e r from a dam b u i l t f o r i n d u s t r i a l water supply, i r r i g a t i o n and r e c r e a t i o n purposes.The r i v e r considered i s small, f l o w i n g i n a densely populated i n d u s t r i a l area and s u b j e c t t o i n t e n s i v e p o l l u t i o n . D u r i n g t h e low water-level b e r i o d r i v e r f l o w is cons i d e r e d t o t a l l y formed by waste water and a r u n - o f f from t h e dam provided f o r f l o w i n g i n t h e r i v e r . T h e r e a r e f i v e waste d i s charges downstream's o f t h e dam:qp=4.64m3/s, q3=3.50m3/s ~4=2.31m3/s, qg=0.70mJ/s and ~6=0.48mJ/s.~astewater qua1 i t y o f each waste discharger i s shown i n t a b l e 1.The s i x parameters i.e. solubles,chemical oxygen demand (COD),biological oxygen demand (BODg),nitrogen,phosphorus and o i l products a r e exceed i n g t h e standard s p e c i f i e d f o r t h e r i v e r under consideration. The f o l l o w i n g t e c h n o l o g i c a l processes a r e s e l e c t e d f o r t r e a t i n g t h e waste water o f dischargers:filtration,precipitation,flotation,biochemical treatment,coagulation,active carbon adsorption, chlorination.The r e s i d u a l concentrations obtained f o r t h e d i f f e r e n t parameters o f p o l l u t i o n ( i = l . . 6 ) a f t e r u s i n g d i f f e r e n t t e c h n o l o g i c a l combinations o f treatment as per t h e treatment methods mentioned above a r e shown i n t a b l e 1 f o r each waste discharger (j=1..6).This t a b l e a l s o shows t h e c o s t data (tot a l costs S j ) o f each technological combination o f t r e a t ment
.
F i g u r e 1.Waste loading s i t u a t i o n The mathematical f o r m u l a t i o n o f t h e problem r e l a t e d t o l o o k i n g f o r an optimum combination o f stages f o r waste water treatment o f dischargers i n a r i v e r basin i s as follows.Water q u a l i t y i n a r i v e r may be c h a r a c t e r i z e d by t h e values o f parameters i n s i x c o n t r o l s t a t i o n s , t h e p l a c e o f which i n a s e c t i o n between two. waste dischargers i s s e l e c t e d i n such a way t h a t concentration (Dki,k=1..6) per parameter should be t h e maximum one. River water q u a l i t y meets t h e s a n i t a r y standard (Dsi) per parameter (or group o f Parameters) o f p o l l u t i o n i n case t h e i r values (Dki) do n o t exceed the.stanQard f o r each parameter. O K 1 1 Dsl (1)
407 This concentr a ti o n (Dki) i s t h e r e s u l t o f a superposition o f mixed q u a n t i t i e s o f i-parameter o f p o l l u t i o n o f a l l waste dischargers " j " located upstream. The t r a n s f e r , c o e f f i c i e n t i s equal t o t h e r a t i o between concent r a t i o n (Dkj ' i n k - s t a t i o n o f i-parameter as discharged by j waste dischargers and i t s co n ce n tr a ti o n i n t h e discharger (C.ii)
Ignoring d i f f u s i o n p a r t i c u l i r i t i e s o f each parameter o f water Q u a l i t y we accept t h a t t h e c o e f f i c i e n t s o f t r a n s f e r a r e i d e n t i c a l f o r each o f them,i.e. Tk.'=Tk..Each c o e f f i c i e n t ' s values T k j i s inversely p r o p o r t i o n a l t o t h e waste discharge d i l u t i o n . Table 1.Waste loading,version o f treatment and c o s t data
fer ion of :reitment I
-
Tota 1 cost mill. 1 eva/ year
Insolubles
-
15.5
I 2 3 4 5 6
0.0 15.0 16.1 17.4 25.4 33.7
t 2 3 4
0.0 0.8 9.7 10.3
1 2 3 4
0.0 0.6 10.9 14.5
1 2 3 4 5
0.0 5.4 8.6 15.8 18.7
1 2 3 4 5
0.0 2.4 8.6 10.7 12.3
-
COD
BOD5
Nitrogen
Phosphopus
0i Is
j = 1
1073 13.7 8.8 5.1 4.0 I. 8 j 7.7 3.4 0.4 0.3 j 40.0 3.6 1.6 0.8 j 68.0 13.4 6.4 3.4 2.2 j 41.0 12.1 8.1 3.3 2.1
14.8
2.0
0.4
0.1
0.0
294.4 24.2 19.4 15.9 5sQ 2.9 = 3 92.5 60.1 9.6 4.6 = 4 56.4 36.7 2.8 1.8 = 5 164.0 14.1 9.4 4.9 2.9 = 6 37.6 28.6 10.8 6.5 3.8
211.5 10.6 9.2 5.3 3.1 1.1
34.8 17.4 17.4 17.4 8.4 3.0
5.0 3.5 3.5 3.5 1-5 0.3
52.4 10.5 8.1 3.2 1.1 0.3
17.4 10.5 3.7 1.7
10.2 10.2 7.7 3.0
0.5 0.5 0.2 0.1
15.9 6.5 0.8 0.2
14,3 3.6 1.4 1.4
12.5 12.5 8. I 3.5
0.9 0.9 0.3 0.1
25.0 7.3 0.3 0.1
73.8 3.7 2.8 2.0 I.8
14.6 7.3 7.3 7.3 3.1
2.4. 1.5 1.5 0.8 0.2
3.0 1.6 0.9 0.5 0.2
16.7 12.8 5.0 2.5 1.0
0.8 0.5 0.4 0.4 0.3
1.4 1.0 1.0 0.5 0.3
0.0 0.0 0.0 0.0 0.0
j = 2
408 Determination o f these c o e f f i c i e n t s i n p r a c t i c e i s made by t h e theory o f mixing.When t h e information needed i s m i s s i n g , t h e c o n t r o l s t a t i o n s accept waste i n t o waste outlet,where t h e i r f u l l mixin g is, o r :
Thus,these c o e f f i c i e n t s depend on r i v e r Water Q u a n t i t y and waste water o u t l e t d i f f u s o r s design.Therefore,rivet water q u a l i t y i n t h e d i f f e r e n t c o n t r o l s t a t i o n s may be expressed by means o f t h e f o l l o w i n g matr i x equation:
TI 1
12 1 T3 1 T41 T5 1 T6 1 or
0 T22
T32
T42
T52
T62
0 0
0 0 T33 0 T43 T44 T53 T54 T63 T64
0 0 0 0 T55
T65
TxC=D
(3)
T k j f o r k=1..6 and j=1..6 a r e t h e t r a n s f e r c o e f f i c i e n t s ac cepted as i d e n t i c a l f o r each q u a l i t y parameter "C"; c k ' f o r k = l . . 6 a r e t h e concentrations.which a r e d i f f e r e n t f o r t h e d i f f e r e n t parameters i=1..6; Dk' f o r k = l . . 6 a r e c o n c e n t r a t i o n s i n t h e c o n t r o l s t a t i o n s which a r e d i f f e r e n t f o r t h e d i f f e r e n t parameters i.1. .6. I n t h i s way t h e l e f t p a r t o f a l l l i m i t a t i o n s (1) c h a r a c t e r i z i n g r i v e r water q u a l i t i e s w i l l be o f k i n d (3) where t h e values o f c k ' represent a f u n c t i o n o f t o t a l costs ( S j ) f o r waste water treatment o f a l l waste dischargers. c j = c j( S j ) (4) These f u n c t i o n s are shown i n t a b l e 1 Where S j a r e t h e c o s t s f o r waste water treatment o f j-discharger. The optimum i s looked f o r by s e l e c t i n g such a vector C a t which t h e system o f l i m i t a t i o n (1) i s f u l f i l l e d and t h e f u n c t i o n o f t h e c o s t s i s minimized: (S.)---> min Such a s o l u t i o n o f t h e probfem r e l a t e d t o l o o k i n g f o r an optimum combination o f stages f o r waste water t r e a t m e n t o f d i f f e r e n t waste dischargers i n a r i v e r basin i s presented by Gordin (1987) / f /. The problem formulated i n t h i s way i s a n o n - l i n e a r programmed one. I t i s solved by means o f separable f u n c t i o n s as per t h e method e s t a b l i s h e d by Hadley(1964)/2/.The problem mentioned above may be Solved i n two stages:the f i r s t one i s t o look f o r an optimum combination o f stages o f waste water treatment w i t h a view t o a chieving one parameter o f water q u a l i t y i n t h e r i v e r w i t h i n t h e standardland t h e second one i s , t o s e l e c t from t h e degrees of treatment obtained i n t h e f i r s t stage,a combination which
409 w i l l meet a l l parameters. The problem a l l o w s t o o b t a i n optimum
s o l u t i o n i n case o f increasing water q u a n t i t y discharged from t h e dam and f l o w i n g i n t h e r i v e r d u r i n g low w a t e r - l e v e l periods. I n t h i s s p e c i f i c case t h e value o f t h e water l e t f l o w i n t h e r i v e r i s n o t included i n t h e t o t a l co s t s because o f l a c k o f information,although t h e o p t i m i z a t i o n model a l l o w s t h e i r estirnation.The problem i s solved by means o f a computer programne,the s o l u t i o n being: 1-2,2-1,3-1,4-1,5-1 15.0 This r e c o r d i n g means t h a t t h e optimum combination o f t r e a t m e n t stages f o r t h i s area o f t h e r i v e r bas i n i s t h e fo1lowing:the second v e r s i o n f o r t h e f i r s t waste discharger,the f i r s t v e r s i o n f o r t h e second discharger,the f i r s t ver s i o n f o r t h e t h i r d d i s charger,the f i r s t version f o r t h e f o u r t h discharger and t h e f i r s t v e r s i o n f o r t h e f i f t h waste discharger.This being t h e d i s t r i b u t i o n and t h e standard o f r i v e r water q u a l i t y w i l l be a c h i eved a t minimum costs o f 15,000,000 leva/year.The r e s u l t s a r e shown i n t a b l e 2. Table 2.Computational Resul t s by Present Study Parameters
Standard VP!
Q1
m3/s
Optimal versionm i l l i o n leva/year
DS'
In sol u b l es
80.0
0.53
COD
70.0
0.53
BOD5
25.0
0.53
3.0
0.53
0.5
0.53
1-2,2-1,3-1,4-1,5-t 15.0 1-2,2-1,3-1,4-f,5-1 15.0 1-2,2-1,3-1,4-1,5-4 15.0 1 -6,2-4,3-4,4-5,577.2 1-6,2-4,3-1,4-1,5-1
0.3
0.53
1 - 6,2-4,3-3,4-3
Inso I u b l es ,COD, 8005, n itr ogen, phosphorus,oils
-
0.53
1-6,2-4,3-4,4-5,577.2
I nso 1 ub 1 es ,COD, BODS, phosphoru s,oi Is
-
13.48
I nso I u b l es ,COD, BOD5,phosphor us
1-6,2-3,3-3,4-1,5-1 54.3
-
4.65
1-6,2-1,3-1,4-1,5-1 33.7
Nitrogen /ammon i a/ Phosphorus /so I u b l e/ O i l p roducts
44.0
63-5
1
,5- 1 1
410 CONCLUS ION The method proposed f o r e s t a b l i s h i n g an optimum combination o f stages o f waste water treatment o f d i f f e r e n t waste dischargers i n a r i v e r basin enables t o s o l v e t h e basic problems r e l a t e d t o maintenance o f water standard q u a l i t y r e q u i r e d i n a r i v e r b a s i n a t minimum sum o f t h e waste removal costs.An optimum management programme f o r waste water treatment may be obtained f o r d i f f e r e n t r i v e r water standard q u a l i t i e s r e q u i r e d . REFERENCES
Chapter i n a book 1. Gordin, I . V . (1987),Tehnologicheskie s i s t e m i vodoobrabotki,Dinamicheskaja optimizaczija,Leningrad,Himia. 2. Hadley,G.,(l964),Nonlinear and dynamic programming,Addison Wesley P u b l i s h i n g company,Mass.,London.