UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Development of an activated sludge process control strategy using Bayesian and Markovian decision theory Vassos, Troy David 1986

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1986_A1 V37.pdf [ 16MB ]
Metadata
JSON: 831-1.0062699.json
JSON-LD: 831-1.0062699-ld.json
RDF/XML (Pretty): 831-1.0062699-rdf.xml
RDF/JSON: 831-1.0062699-rdf.json
Turtle: 831-1.0062699-turtle.txt
N-Triples: 831-1.0062699-rdf-ntriples.txt
Original Record: 831-1.0062699-source.json
Full Text
831-1.0062699-fulltext.txt
Citation
831-1.0062699.ris

Full Text

DEVELOPMENT OF AN ACTIVATED SLUDGE PROCESS CONTROL STRATEGY USING BAYESIAN AND MARKOVIAN DECISION THEORY by TROY DAVID VASSOS M.Eng., U n i v e r s i t y of B r i t i s h Columbia, 1983 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES Department of C i v i l E n g i n e e r i n g We accept t h i s t h e s i s as conforming to the r e q u i r e d standard THE UNIVERSITY OF JULY (c) Troy David BRITISH COLUMBIA 1986 Vassos, 1986 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and study. I f u r t h e r agree t h a t permission f o r e x t e n s i v e copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s or her r e p r e s e n t a t i v e s . I t i s understood that copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l gain s h a l l not be allowed without my w r i t t e n p e r m i s s i o n . Department of C i v i l E n g i n e e r i n g The U n i v e r s i t y of B r i t i s h Columbia 2324 Main M a l l Vancouver, B r i t i s h Columbia V6T 1 W 5 Date: A b s t r a c t L i t t l e has been done i n the past to u t i l i z e a c t i v a t e d sludge wastewater treatment p l a n t m o nitoring data to a s s i s t i n process c o n t r o l . T h i s data c o n s i s t s of d i s c r e t e measurements of process v a r i a b l e s and c o n t i n u o u s l y monitored parameters with s p e c i f i c c h a r a c t e r i s t i c s which make s t a t i s t i c a l a n a l y s i s d i f f i c u l t . The use of t h i s data i n the development of c o n t r o l s t r a t e g i e s has a l s o been r e s t r i c t e d by the inadequacy of process models and the non-steady-state c h a r a c t e r i s t i c s of most treatment f a c i l i t i e s . Consequently, most s u c c e s s f u l process models are s t o c h a s t i c i n nature and p l a n t s p e c i f i c . The recent use of computers has r e s u l t e d i n i n c r e a s e d m o n i t o r i n g data, due to the c a p a b i l i t y of monitoring parameters on a c o n t i -nuous b a s i s . Although computers can be used to analyze the data, there i s l i t t l e i n c e n t i v e on the p a r t of o p e r a t o r s to improve the data q u a l i t y , due to a l a c k of process c o n t r o l techniques to u t i l i z e the i n f o r m a t i o n gathered. T h i s r e s e a r c h focuses on techniques f o r i n c o r p o r a t i n g d e c i s i o n theory concepts, i n v o l v i n g p r o b a b i l i t y and u t i l i t y e s t i m a t i o n s , a p p l i e d t o the problem of a c t i v a t e d sludge b u l k i n g due to f i l a -mentous microorganisms. Both s i n g l e - s t a t e Bayesian and m u l t i -s t a t e Markov P o l i c y - I t e r a t i o n techniques are h e u r i s t i c a l l y a p p l i e d to o p e r a t i o n s data obtained from a c o n v e n t i o n a l a c t i v a t e d sludge p l a n t with c h r o n i c sludge b u l k i n g . Six years of monitoring data were used to e s t a b l i s h an o p t i m a l sludge b u l k i n g c o n t r o l s t r a t e g y i i using a combination of a e r a t i o n b a s i n d i s s o l v e d oxygen c o n c e n t r a t i o n and food-to-microorganism r a t i o s e t t i n g s . S i n g l e s t a t e Bayesian d e c i s i o n a n a l y s i s techniques were f i r s t a p p l i e d to e s t a b l i s h outcome p r o b a b i l i t i e s i n terms of sludge volume index (SVI) l e v e l s and e f f l u e n t suspended s o l i d s (SS) c o n c e n t r a t i o n s fo r the two c o n t r o l a l t e r n a t i v e s . Based on u t i l i t y m a t r i c e s obtained from three p l a n t o p e r a t o r s and t h e o r e t i c a l c o n s i d e r a -t i o n s , four o p t i m a l c o n t r o l p o l i c i e s were c a l c u l a t e d . To o b t a i n c o n t r o l p o l i c i e s which were dependent upon the c u r r e n t b u l k i n g s t a t e , or c o n d i t i o n , a Markov technique was a p p l i e d to the same data base but using u t i l i t i e s d e f i n e d by the SVI l e v e l and c o n t r o l a l t e r n a t i v e s . T h i s technique r e s u l t e d i n o p t i m a l p o l i c y recommendations which were more c o n s i s t e n t with b u l k i n g theory than the former s i n g l e - s t a t e Bayesian approach. The Markov P o l i c y - I t e r a t i o n technique was adapted to a process c o n t r o l s t r a t e g y to allow the p r o b a b i l i t y or t r a n s i t i o n matrix to be m o d i f i e d by experimental f i n d i n g s , r e s u l t i n g i n a dynamic c o n t r o l s t r a t e g y . The model was then a p p l i e d to a simulated low d i s s o l v e d oxygen b u l k i n g process c o n d i t i o n and p o l i c y adjustments were examined to i n c r e a s e the r a t e of convergence of the model. Although the optimal p o l i c y v e c t o r was found to be r e l a t i v e l y i n s e n s i t i v e to the u t i l i t y matrix s t r u c t u r e , the r a t e of conver-gence was a f f e c t e d . Use of a p o l i c y adjustment technique, which all o w s the d e c i s i o n maker to provide input to the model, can e l i m i n a t e the convergence problem. D i f f i c u l t i e s i n convergence can occur when the u t i l i t y m atrix, d e f i n e d by the o p e r a t o r , i s i n c o n f l i c t with the optimal d e c i s i o n p o l i c y . i i i TABLE OF CONTENTS Chapter Page ABSTRACT i i LIST OF TABLES v i i LIST OF FIGURES x LIST OF ABBREVIATIONS x i i i ACKNOWLEDGEMENTS x i v 1.0 INTRODUCTION 1 1.1 Problem D e f i n i t i o n 1 1.2 T h e s i s O b j e c t i v e s 2 1.3 T h e s i s O u t l i n e 4 2.0 LITERATURE REVIEW 7 2.1 M o n i t o r i n g Data C h a r a c t e r i s t i c s 7 2.1.1 Process V a r i a b l e s 9 2.1.2 Flow and Co n c e n t r a t i o n F l u c t u a t i o n s 12 2.1.3 Sampling C o n s i d e r a t i o n s 13 2.1.4 Data Accuracy and P r e c i s i o n 15 2.1.5 S t a t i s t i c a l Summary Techniques 17 2.1.6 Summary 21 2.2 Process M o d e l l i n g and C o n t r o l 22 2.2.1 M e c h a n i s t i c M o d e l l i n g 22 2.2.2 S t o c h a s t i c M o d e l l i n g 27 2.2.3 C o r r e l a t i o n A n a l y s i s 28 2.2.4 Summary 29 2.3 D e c i s i o n Theory Approach to Process C o n t r o l 30 2.3.1 Bayesian D e c i s i o n Theory 32 2.3.2 Markov P r o b a b i l i t y Theory 34 2.3.3 Summary 39 2.4 Sludge B u l k i n g 40 2.4.1 D e f i n i t i o n of Bu l k i n g Sludge 42 2.4.2 Sludge Volume Index as a Measure of Bu l k i n g Sludge 44 i v Chapter TABLE OF CONTENTS (cont'd) Page 2.4.3 I n f l u e n c e of Bu l k i n g Sludge on E f f l u e n t Suspended S o l i d s 46 2.4.4 Filamentous Microorganisms 47 2.4.5 Filamentous B u l k i n g C o n t r o l 49 2.4.5.1 DO E f f e c t s on Bulking 51 2.4.5.2 Organic Loading E f f e c t s on B u l k i n g 56 2.4.5.3 N u t r i e n t E f f e c t s on Bulking 59 2.4.5.4 Temperature E f f e c t s on Bu l k i n g 61 2.4.5.5 Other Causes of Bul k i n g 61 2.4.5.6 Toxic Chemical E f f e c t s on B u l k i n g 62 2.4.6 Summary 64 3.0 APPLICATION OF BAYESIAN DECISION THEORY TO ACTIVATED SLUDGE BULKING CONTROL 66 3.1 French Creek P o l l u t i o n C o n t r o l Centre 66 3.1.1 Process D e s c r i p t i o n 67 3.1.2 M o n i t o r i n g Data C h a r a c t e r i s t i c s 69 3.2 C o n t r o l Parameters and Operating Ranges 80 3.2.1 D i s s o l v e d Oxygen C o n t r o l 80 3.2.2 Food-to-Microorganism R a t i o C o n t r o l 81 3.2.3 C h l o r i n e Treatment 82 3.2.4 Process C o n f i g u r a t i o n M o d i f i c a t i o n s 82 3.2.5 Sludge Volume Index Operating Ranges 83 3.2.6 E f f l u e n t S o l i d s Concentration Ranges 83 3.3 D e c i s i o n A n a l y s i s C o n t r o l Approach 84 3.3.1 Case D e f i n i t i o n s 86 3.3.2 Assumptions 88 3.3.3 St a t e D e f i n i t i o n s 89 3.3.4 Establishment of P r o b a b i l i t i e s 90 3.3.5 Establishment of D e c i s i o n A n a l y s i s U t i l i t i e s 104 3.3.6 Markov P o l i c y - I t e r a t i o n U t i l i t i e s 106 4.0 RESULTS OF DECISION THEORY CONTROL APPROACHES 119 4.1 Case A - S t a t i c S o l u t i o n f o r Combined B u l k i n g and E f f l u e n t Suspended S o l i d s U t i l i t i e s 120 4.1.1 P r o b a b i l i t y Determinations From H i s t o r i c a l Data 121 4.1.2 U t i l i t y Determinations 122 4.1.3 Expected U t i l i t i e s 123 4.1.4 Summary 128 v TABLE OF CONTENTS (cont'd) Chapter Page 4.2 Case B - Markov P o l i c y - I t e r a t i o n Approach 130 4.2.1 U t i l i t y Determinations 130 4.2.2 I n f l u e n c e of B a s e l i n e Frequency M a t r i c e s 131 4.2.3 H i s t o r i c a l Data C o n t r o l P o l i c i e s 132 4.2.4 Temperature E f f e c t s on H i s t o r i c a l Data P o l i c y V e c t o r s 138 4.2.5 P o l i c y S e l e c t i o n For a Simulated Low DO Bu l k i n g Process 141 4.3 Case C - Dynamic Markov P o l i c y - I t e r a t i o n Approach To Sludge B u l k i n g C o n t r o l 146 4.3.1 U t i l i t y M a trix S t r u c t u r e E f f e c t s 147 4.3.2 Adap t a t i o n to S i n g l e C o n t r o l DO S t r a t e g y 178 4.3.3 Manual P o l i c y Adjustments 178 4.3.4 A p p l i c a t i o n of H i s t o r i c a l Data 188 5.0 DISCUSSION 195 5.1 D e c i s i o n Theory C o n t r o l S t r a t e g y Without 196 H i s t o r i c a l Data 5.2 Adaptation of H i s t o r i c a l Data Base Information 198 5.3 Comparison of Expected U t i l i t i e s With Operator Judgement 203 5.4 S e n s i t i v i t y C o n s i d e r a t i o n s 207 5.5 F/M C o n t r o l 208 6.0 SUMMARY AND CONCLUSIONS 212 7.0 FUTURE RESEARCH DIRECTIONS 220 REFERENCES 222 APPENDICES A - DATA PLOTS 239 B - FREQUENCY CURVES 270 v i L i s t o f F i g u r e s Page 1. Relationship Between Substrate Removal Rate and Aeration Basin Dissolved Oxygen for an MLSS of 1100 mg/L 55 2. Example of SVI Bulking and Recovery Periods Using Aeration Basin Dissolved Oxygen Control 60 3. French Creek Pollution Control Centre Process Diagram 68 4. Aeration Reactor #1 SVI Fluctations 73 5. Aeration Reactor #2 SVI Fluctations 73 6. Influent Flow 75 7. Aeration Basin BOD Removal E f f i c i e n c y 75 8. Primary and Secondary C l a r i f i e r Effluent BOD 76 9. Total BOD Removal E f f i c i e n c y 77 10. Aeration #1 DO Fluctuations 78 11. Aeration #2 DO Fluctuations 78 12. Aeration #1 F/M Fluctuations 79 13. Aeration #2 F/M Fluctuations 79 14. 3-D Plot of U t i l i t y Matrix #1 112 15. 3-D Plot of U t i l i t y Matrix #2 113 16. 3-D Plot of U t i l i t y Matrix #3 114 17. 3-D Plot of U t i l i t y Matrix #4 115 18. 3-D Plot of U t i l i t y Matrix #5 116 19. 3-D Plot of U t i l i t y Matrix #6 117 20. 3-D Plot of U t i l i t y Matrix #7 118 21. Simulation #1 - U t i l i t y #1 Matrix Average U t i l i t y and State Plots 150 v i i L i s t of F i g u r e s (cont ' d ) Page 2 2 . S i m u l a t i o n #2 - U t i l i t y #3 M a t r i x A v e r a g e U t i l i t y a n d S t a t e P l o t s 155 2 3 . S i m u l a t i o n #3 - U t i l i t y #4 M a t r i x A v e r a g e U t i l i t y a n d S t a t e P l o t s 161 2 4 . S i m u l a t i o n #4 - U t i l i t y #6 M a t r i x A v e r a g e U t i l i t y a n d S t a t e P l o t s 167 2 5 . S i m u l a t i o n #5 - U t i l i t y #7 M a t r i x A v e r a g e U t i l i t y a n d S t a t e P l o t s 173 2 6 . S i m u l a t i o n #6 - U t i l i t y #1 M a t r i x - P o l i c y A d j u s t e d A v e r a g e U t i l i t y a n d S t a t e P l o t s 180 2 7 . S i m u l a t i o n #7 - U t i l i t y #1 M a t r i x - No F / M C o n t r o l A v e r a g e U t i l i t y a n d S t a t e P l o t s 186 2 8 . S i m u l a t i o n #8 - U t i l i t y #1 M a t r i x - H i s t o r i c a l B a s e l i n e A v e r a g e U t i l i t y a n d S t a t e P l o t s 190 v i i i L i s t o f Tables P a g e 1. Monitored Parameters and Sampling Frequencies 70 2. Operation and Performance Data f o r the French Creek P o l u u t i o n C o n t r o l Centre 71 3. Case "A" Sludge Volume Index P r o b a b i l i t y D i s t r i -b u t i o n s f o r S e l e c t A e a r t i o n Basin D i s s o l v e d Oxygen Co n c e n t r a t i o n s and Food-to-Microorganism R a t i o Ranges 92 4. Case "A" F i n a l E f f l u e n t Susupended S o l i d s Proba-b i l i t y D i s t r i b u t i o n s f o r S e l e c t A e a r t i o n Basin D i s s o l v e d Oxygen Concen t r a t i o n s and Food-to-Microorganism R a t i o Ranges 94 5. Case "B" S t a t e / C o n t r o l Outcome Frequency and Proba-b i l i t y D i s t r i b u t i o n s Based on A l l H i s t o r i c a l Data 97 6. Case "B" S t a t e / C o n t r o l Outcome Frequency and Proba-b i l i t y D i s t r i b u t i o n s Based on H i s t o r i c a l Data With Temperatures <= 12 Degrees C e l c i u s 98 7. Case "B" S t a t e / C o n t r o l Outcome Frequency and Proba-b i l i t y D i s t r i b u t i o n s Based on H i s t o r i c a l Data With Temperatures 12 < T < 16 Degrees C e l c i u s 99 8. Case "B" S t a t e / C o n t r o l Outcome Frequency and Proba-b i l i t y D i s t r i b u t i o n s Based on H i s t o r i c a l Data With Temperatures >= 16 Degrees C e l c i u s 100 9. B a s e l i n e S t a t e / S t a t e Frequency Matrix 101 10. Case " C Simulated (Known) P r o b a b i l i t y M a t r i x 102 11. Operator "A" U t i l i t y Matrix 105 12. Operator "B" U t i l i t y Matrix 105 13. Operator "C" U t i l i t y Matrix 105 14. Operator "D" U t i l i t y Matrix 106 15. C o n t r o l and S t a t e D e s c r i p t i o n s and D e f i n i t i o n s 108 16. U t i l i t y M a trix #1 112 17. U t i l i t y M a trix #2 113 18. U t i l i t y M a t r i x #3 114 19. U t i l i t y Matrix #4 115 ix L i s t of Tables (cont'd) Page 20. U t i l i t y M a trix #5 116 21. U t i l i t y M a trix #6 1 17 22. U t i l i t y M a t r i x #7 118 23. Operator "A" U t i l i t y Matrix and R e s u l t i n g C o n t r o l A l t e r n a t i v e Expected U t i l i t i e s 124 24. Operator "B" U t i l i t y Matrix and R e s u l t i n g C o n t r o l A l t e r n a t i v e Expected U t i l i t i e s 125 25. Operator "C" U t i l i t y Matrix and R e s u l t i n g C o n t r o l A l t e r n a t i v e Expected U t i l i t i e s 126 26. Operator "D" U t i l i t y M a trix and R e s u l t i n g C o n t r o l A l t e r n a t i v e Expected U t i l i t i e s 127 27. B a s e l i n e Frequency P o l i c y Vector and Average Expected U t i l i t i e s 131 28. U t i l t i t y #1 Matrix P o l i c y Vector and Average Expected U t i l i t i e s f o r the H i s t o r i c a l Data T r a n s -i t i o n M a t r i x I n c l u d i n g B a s e l i n e Frequencies 133 29. U t i l t i t y #2 Matrix P o l i c y Vector and Average Expected U t i l i t i e s f o r the H i s t o r i c a l Data T r a n s -i t i o n M a trix I n c l u d i n g B a s e l i n e F r e q u e n c i e s 133 30. U t i l t i t y #3 Matrix P o l i c y Vector and Average Expected U t i l i t i e s f o r the H i s t o r i c a l Data T r a n s -i t i o n M a t r i x I n c l u d i n g B a s e l i n e Frequencies 134 31. U t i l t i t y #4 Matrix P o l i c y Vector and Average Expected U t i l i t i e s f o r the H i s t o r i c a l Data T r a n s -i t i o n M a t r i x I n c l u d i n g B a s e l i n e Frequencies 135 32. U t i l t i t y #5 Matrix P o l i c y Vector and Average Expected U t i l i t i e s f o r the H i s t o r i c a l Data T r a n s -i t i o n M a t r i x I n c l u d i n g B a s e l i n e Frequencies 135 33. U t i l t i t y #6 Matrix P o l i c y Vector and Average Expected U t i l i t i e s f o r the H i s t o r i c a l Data T r a n s -i t i o n M a t r i x I n c l u d i n g B a s e l i n e Frequencies 136 34. U t i l t i t y #7 Matrix P o l i c y Vector and Average Expected U t i l i t i e s f o r the H i s t o r i c a l Data T r a n s -i t i o n M a t r i x I n c l u d i n g B a s e l i n e Frequencies 137 x L i s t of Tables (cont'd) Page 35. U t i l i t y #1 Ma t r i x P o l i c y Vector and Average Expected U t i l i t i e s f o r H i s t o r i c a l Data Temperatures (Temp <= 12 deg C) I n c l u d i n g B a s e l i n e F r e q u e n c i e s 139 36. U t i l i t y #1 Ma t r i x P o l i c y Vector and Average Expected U t i l i t i e s f o r H i s t o r i c a l Data Temperatures (12 deg C < Temp < 16 deg C) I n c l u d i n g B a s e l i n e F r e q u e n c i e s 139 37. U t i l i t y #1 Ma t r i x P o l i c y Vector and Average Expected U t i l i t i e s f o r H i s t o r i c a l Data Temperatures (16 deg C <= Temp) I n c l u d i n g B a s e l i n e F r e q u e n c i e s 140 38. U t i l i t y #1 M a t r i x P o l i c y Vector and Average Expected U t i l i t i e s f o r a Simulated Low DO B u l k i n g Process 142 39. U t i l i t y #2 Ma t r i x P o l i c y Vector and Average Expected U t i l i t i e s f o r a Simulated Low DO B u l k i n g Process 142 40. U t i l i t y #3 Ma t r i x P o l i c y Vector and Average Expected U t i l i t i e s f o r a Simulated Low DO B u l k i n g Process 143 41. U t i l i t y #4 Ma t r i x P o l i c y Vector and Average Expected U t i l i t i e s f o r a Simulated Low DO B u l k i n g Process 143 42. U t i l i t y #5 Ma t r i x P o l i c y Vector and Average Expected U t i l i t i e s f o r a Simulated Low DO B u l k i n g Process 144 43. U t i l i t y #6 M a t r i x P o l i c y Vector and Average Expected U t i l i t i e s f o r a Simulated Low DO B u l k i n g Process 144 44. U t i l i t y #7 Ma t r i x P o l i c y Vector and Average Expected U t i l i t i e s f o r a Simulated Low DO B u l k i n g Process 145 45. S i m u l a t i o n #1 - U t i l i t y #1 Ma t r i x - Recorded S t a t e and P o l i c y V e c t o r Changes For Low DO B u l k i n g 151 46. S i m u l a t i o n #2 - U t i l i t y #3 Ma t r i x - Recorded S t a t e and P o l i c y V e c t o r Changes For Low DO B u l k i n g 156 47. S i m u l a t i o n #3 - U t i l i t y #4 M a t r i x - Recorded S t a t e and P o l i c y V e c t o r Changes For Low DO B u l k i n g 162 48. S i m u l a t i o n #4 - U t i l i t y #6 Matrix - Recorded S t a t e and P o l i c y V e c t o r Changes For Low DO B u l k i n g 168 49. S i m u l a t i o n #5 - U t i l i t y #7 M a t r i x - Recorded S t a t e and P o l i c y V e c tor Changes For Low DO B u l k i n g 174 x i L i s t of Tables (cont'd) Page 50. S i m u l a t i o n #6 - U t i l i t y #1 Ma t r i x - State and P o l i c y Vector Changes For Simulated (Known) Low DO B u l k i n g Under Manual P o l i c y Adjustments 181 51. S i m u l a t i o n #7 - U t i l i t y #1 Ma t r i x - State and P o l i c y Vector Changes For Simulated (Known) Low DO B u l k i n g Under Manual P o l i c y Adjustments Without F/M Adjustments 187 52. S i m u l a t i o n #8 - U t i l i t y #1 Ma t r i x - State and P o l i c y V e c t or Changes For Simulated (Known) Low DO B u l k i n g Under Manual P o l i c y Adjustments Using H i s t o r i c a l Data 191 x i i L i s t o f A b b r e v i a t i o n s A/S A c t i v a t e d Sludge ATP - Adenosine Tri-Phosphate AVG Average ( A r i t h m e t i c Mean) BOD Biochemical Oxygen Demand C C e l c i u s COD Chemical Oxygen Demand d - Day DO D i s s o l v e d Oxygen deg degree BOD/Kg MLVSS day) F/M Food to Microorganism R a t i o (Kg FESS F i n a l E f f l u e n t Suspended S o l i d s g - Grams kg Kilograms hrs - Hours I g a l I m p e r i a l G a l l o n s Igpd Imperial G a l l o n s per Day ITER. I t e r a t i o n m - Metre MAX Maximum MCRT - Mean C e l l R e t e n t i o n Time MED - Medium mg/L - M i l l i g r a m s per L i t r e MIN Minimum mL - M i l l i l i t r e s mL/g - M i l l i l i t r e s per gram MLSS Mixed L i q u o r Suspended S o l i d s MLVSS • - Mixed L i q u o r V o l a t i l e Suspended S o l i d s mm - M i l l i m e t r e SRT S o l i d s R e t e n t i o n Time SS Suspended S o l i d s SSVI S t i r r e d Sludge Volume Index STD Standard D e v i a t i o n SVI Sludge Volume Index (ml/g) TSS - T o t a l Suspended S o l i d s Temp - Temperature (degrees C) WPCC - Water P o l l u t i o n C o n t r o l Centre x i i i Acknowledgement The author s i n c e r e l y thanks h i s s u p e r v i s o r s , Dr. W. K. Oldham and Dr. S. 0 . R u s s e l l , f o r t h e i r constant encouragement, i n t e r e s t and i n s i g h t d u r i n g t h i s study. I am p a r t i c u l a r l y t h a n k f u l to Dr. R u s s e l l f o r s u g g e s t i n g the use of the Markov P o l i c y - I t e r a t i o n technique, and f o r the many l e n g t h l y d i s c u s s i o n s h e l d over the course of t h i s i n v e s t i g a t i o n . The f i n a n c i a l support p r o v i d e d by the N a t u r a l Sciences and E n g i n e e r i n g Research C o u n c i l of Canada i s g r a t e f u l l y acknowledged. I would a l s o l i k e to take t h i s o p p o r t u n i t y to thank my wife, L e s l e y , who completed a Masters degree i n E d u c a t i o n and a two year I n t e r i o r Design program in a v a l i a n t e f f o r t t o keep occupied while I completed my r e s e a r c h . x i v 1.0 INTRODUCTION 1.1 Problem D e f i n i t i o n Although a c t i v a t e d sludge processes have a r e p u t a t i o n f o r being capable of a t t a i n i n g a high l e v e l of organic carbon removal from sewage, i n c o n s i s t e n t e f f l u e n t q u a l i t y and sub-optimal o p e r a t i o n have been the s u b j e c t of c o n s i d e r a b l e review i n the p a s t . C o n s i d e r i n g the l a c k of knowledge about the b i o - k i n e t i c s of the process, v a r y i n g growth and uptake r a t e s , and d i v e r s e m i c r o b i a l composition, the p o s i t i v e r e p u t a t i o n of a c t i v a t e d sludge processes p o s s i b l y owes more to the e f f o r t s of t h e i r o p e r a t o r s than those of the p l a n t d e s i g n e r s . Once a p l a n t i s c o n s t r u c t e d , the operator i s u s u a l l y l e f t to manipulate the p r o c e s s to achieve the r e q u i r e d e f f l u e n t standard with l i t t l e h e l p or c o n t a c t with the d e s i g n e r . As noted by Vasicek (1982), a c t i v a t e d sludge systems tend to be overdesigned f o r f e a r of system inadequacy, o f t e n r e s u l t i n g i n o v e r s i z e d r e a c t o r s . M u n i c i p a l wastewater treatment p l a n t o p e r a t o r s and t e c h n i c i a n s are f o r c e d to operate these overdesigned p l a n t s i n modes d i f f e r e n t from those envisaged i n the o r i g i n a l d e s i g n . The r e l a t i o n s h i p s between process v a r i a b l e s and performance v a r i e s from s i t e t o s i t e and are h e a v i l y i n f l u e n c e d by the o p e r a t i n g s t r a t e g i e s used to overcome the problems c r e a t e d by overdesign. The development and implementation of c o n t r o l s t r a t e g i e s i s d i f f i c u l t , due to inadequate process models and c o n f l i c t i n g i n t e r p r e t a t i o n r e g a r d i n g the s i g n i f i c a n c e of monitored v a r i a b l e s . The use of computers f o r process monitoring to measure and r e c o r d process data holds promise f o r improved process performance. However, 1 l i t t l e work has been done in o r g a n i z i n g the c o l l e c t i o n , storage and u t i l i z a t i o n of these p o t e n t i a l l y l a r g e data bases f o r improving p l a n t performance. Designers have r e c e n t l y begun i n c o r p o r a t i n g computers i n t o sewage treatment p l a n t s to h e l p monitor process parameters, and to provide feedback c o n t r o l f o r the p r o c e s s . Such use has r e s u l t e d i n an e x p l o s i o n of data. T h i s l a r g e data base should be usable f o r process o p t i m i z a t i o n , e i t h e r through r e a l - t i m e process c o n t r o l or i n a step-by-step process f o l l o w i n g a n a l y s i s of the data gathered. However, the necessary methodologies have not yet been developed. Although i t i s known that p e r i o d i c o p e r a t i o n c o n t r o l , such as proposed by Yeung et a l . (1980), can s u b s t a n t i a l l y reduce the average e f f l u e n t BOD and/or i t ' s v a r i a b i l i t y r e l a t i v e to c o n v e n t i o n a l c o n t r o l t e c h n i q u e s , i n p r a c t i c e the i n t e r p r e t a t i o n of l a r g e amounts of data i s beyond the c a p a c i t y of most p l a n t o p e r a t o r s . As a r e s u l t , most monitoring data i s simply c o l l e c t e d and s t o r e d , to be r e f e r e n c e d only i n the assessment of i n f l u e n t c h a r a c t e r i s t i c s i n the event that p l a n t expansion i s planned. 1.2 T h e s i s O b j e c t i v e s T h i s r e s e a r c h i s concerned with the problem of u t i l i z i n g m o n i toring data c o l l e c t e d at a c t i v a t e d sludge treatment f a c i l i t i e s f o r the purpose of improving p r o c e s s c o n t r o l d e c i s i o n s . The o v e r a l l o b j e c t i v e i s to develop a methodology f o r o p t i m i z i n g the o p e r a t i o n of an a c t i v a t e d sludge sewage treatment 2 p l a n t . T h i s can be accomplished by making the most of the a v a i l a b l e i n f o r m a t i o n i n c l u d i n g recorded data, and operator experience and judgement, and by r e c o g n i z i n g knowledge gaps and the inherent v a r i a b i l i t y of c o n d i t i o n s i n an o p e r a t i n g p l a n t . D e c i s i o n a n a l y s i s techniques o f f e r the promise of u t i l i z i n g the i n f o r m a t i o n c o n t a i n e d i n the data, and i n t e g r a t i n g i t with the experience and judgement of the treatment p l a n t o p e r a t o r , to improve process performance or to c o r r e c t process problems. In t h i s t h e s i s , d e c i s i o n theory concepts i n v o l v i n g p r o b a b i l i t y and u t i l i t y e s t i m a t i o n s are a p p l i e d to the problem of filamentous sludge b u l k i n g at the French Creek Water P o l l u t i o n C o n t r o l Centre (WPCC), l o c a t e d i n the Nanaimo Regional D i s t r i c t on Vancouver I s l a n d , i n B r i t i s h Columbia. Both s i n g l e - s t a t e Bayesian and m u l t i - s t a t e Markov P o l i c y - I t e r a t i o n techniques are a p p l i e d to t h i s data base to e s t a b l i s h the o p t i m a l o p e r a t i n g s t r a t e g y to c o n t r o l sludge b u l k i n g using combinations of d i s s o l v e d oxygen (DO) c o n c e n t r a t i o n and food-to-microorganism (F/M) r a t i o s e t t i n g s . S t a t e s are d e f i n e d i n terms of d i s c r e t e ranges of sludge volume index (SVI) values, and, f o r the s t a t i c model, in terms of e f f l u e n t suspended s o l i d s (SS) c o n c e n t r a t i o n s . S t a t e to s t a t e outcomes are determined f o r each DO and F/M combination, r e s u l t i n g i n a s t a t e frequency and p r o b a b i l i t y m a t r i x . U t i l i t y v a l u e s are then a s s i g n e d to each outcome or control/outcome combination based on the personal judgement and e x p e r i e n c e of the d e c i s i o n maker. 3 Before d e c i s i o n theory concepts can be a p p l i e d to a c t i v a t e d sludge process c o n t r o l , an assessment of the e f f e c t i v e n e s s of the technique i n p r o v i d i n g reasonable c o n t r o l s t r a t e g i e s must be undertaken. In t h i s regard, the s p e c i f i c o b j e c t i v e s of the t h e s i s a r e : 1. to u t i l i z e h i s t o r i c a l data obtained from the French Creek WPCC to e s t a b l i s h outcome p r o b a b i l i t i e s i n terms of SVI l e v e l s and e f f l u e n t SS c o n c e n t r a t i o n s f o r d i s c r e t e combinations of DO c o n c e n t r a t i o n and F/M r a t i o ranges. 2. to ev a l u a t e the optimal s i n g l e - s t a t e p o l i c y d e c i s i o n based on p r o b a b i l i t i e s generated i n item (1), and on u t i l i t y estima-t i o n s f o r SVI and e f f l u e n t SS c o n c e n t r a t i o n outcomes. 3 . to examine the s e n s i t i v i t y of maximum expected u t i l i t i e s , and corr e s p o n d i n g p o l i c y d e c i s i o n s , to v a r i a t i o n s i n the d e f i n i -t i o n of outcome u t i l i t i e s made by p l a n t o p e r a t o r s and theore-t i c a l c o n s i d e r a t i o n s . 4. to develop a m u l t i - s t a t e a p p l i c a t i o n of the Markov P o l i c y -I t e r a t i o n technique f o r filamentous sludge b u l k i n g c o n t r o l based on h i s t o r i c a l data from the French Creek WPCC. 5. to develop a dynamic Markov P o l i c y - I t e r a t i o n procedure f o r filamen t o u s sludge b u l k i n g c o n t r o l based on a simulated a c t i -vated sludge treatment f a c i l i t y with low DO b u l k i n g , with and without h i s t o r i c a l data. 6. to examine the i n f l u e n c e of u t i l i t y matrix s t r u c t u r e s on the Markov P o l i c y - I t e r a t i o n procedure developed i n (5) above. 1.3 T h e s i s O u t l i n e Chapter 2 reviews the l i t e r a t u r e p e r t a i n i n g t o the c h a r a c t e r -i s t i c s of mo n i t o r i n g data c o l l e c t e d at a c t i v a t e d sludge treatment f a c i l i t i e s and examines pr e v i o u s r e s e a r c h attempts at mo d e l l i n g the treatment p r o c e s s . D e c i s i o n theory models are in t r o d u c e d as an a l t e r n a t i v e to mo d e l l i n g f o r process c o n t r o l and filamentous sludge b u l k i n g theory i s in t r o d u c e d . 4 Chapter 3 d e s c r i b e s the French Creek WPCC i n terms of the process c o n f i g u r a t i o n and monitoring parameters. P o t e n t i a l b u l k i n g c o n t r o l o p t i o n s are examined and d e f i n i t i o n s of the p o s s i b l e b u l k i n g " s t a t e s " are e s t a b l i s h e d . Assumptions used i n the d e c i s i o n theory approach are then e x p l a i n e d and the r e q u i r e d p r o b a b i l i t i e s and u t i l i t i e s are d e f i n e d f o r use i n Chapter 4. Chapter 4 examines the use of h i s t o r i c a l d ata, f i r s t i n a " s t a t i c " s i n g l e - s t a t e Bayesian D e c i s i o n theory model and then in a m u l t i - s t a t e Markov P o l i c y - I t e r a t i o n e x t e n s i o n of the method, to take i n t o account v a r i a t i o n s i n the p l a n t over time. The i n f l u e n c e of the s u b j e c t i v e u t i l i t y m a t r i c e s , which are r e q u i r e d i n the a n a l y s i s , are examined i n terms of the maximum expected u t i l i t y p o l i c y and the r a t e of convergence of the P o l i c y -I t e r a t i o n technique. A dynamic Markov P o l i c y - I t e r a t i o n technique i s developed a l l o w i n g f o r the i n c o r p o r a t i o n of h i s t o r i c a l data, and a d a p t a t i o n of new i n f o r m a t i o n o btained. Chapter 5 examines four key c o n s i d e r a t i o n s i n the a p p l i c a t i o n of a dynamic P o l i c y - I t e r a t i o n technique. A l t e r n a t i v e s f o r the establishment of the technique without a v a i l a b l e h i s t o r i c a l data are examined as are techniques f o r the a d a p t a t i o n of h i s t o r i c a l d ata. The c h a r a c t e r i s t i c s and i n f l u e n c e of the o perator " u t i l i t y f u n c t i o n " are then examined. L a s t l y , s e n s i t i v i t y c o n s i d e r a t i o n s are d i s c u s s e d and p o t e n t i a l F/M c o n t r o l s t r a t e g i e s are reviewed. 5 Chapter 6 and 7 summarize the f i n d i n g s of the r e s e a r c h and explore p o s s i b l e d i r e c t i o n s f o r f u r t h e r r e s e a r c h . 6 2. LITERATURE REVIEW In the p r e v i o u s chapter, the a c t i v a t e d sludge process was d e s c r i b e d as having an i n c o n s i s t e n t e f f l u e n t q u a l i t y and sub-optimal performance h i s t o r y . The r e l a t i o n s h i p s between process v a r i a b l e s and performance are a f f e c t e d by many s i t e s p e c i f i c f a c t o r s and o p e r a t i n g s t r a t e g i e s . The use of computers for process monitoring to measure and r e c o r d p r o c e s s data holds promise f o r improved process performance, i f the i n f o r m a t i o n can be used f o r process c o n t r o l d e c i s i o n s . In t h i s chapter the s t a t i s t i c a l techniques which are a v a i l a b l e f o r a n a l y s i n g treatment process monitoring data are examined. Previo u s r e s e a r c h i n a c t i v a t e d sludge m o d e l l i n g i s reviewed, i n c l u d i n g m e c h a n i s t i c or k i n e t i c , s t o c h a s t i c , and t r a n s f e r f u n c t i o n model r e s e a r c h and a p p l i c a t i o n s . Two d e c i s i o n a n a l y s i s techniques are reviewed f o r a p p l i c a t i o n t o p r o c e s s c o n t r o l . F i n a l l y , a c t i v a t e d sludge filamentous b u l k i n g i s reviewed as an example f o r use i n the development of a dynamic d e c i s i o n a n a l y s i s process c o n t r o l s t r a t e g y . 2.1 Monitoring Data Characteristics Routine measurements of process v a r i a b l e s from over 20,000 sewage treatment f a c i l i t i e s i n Canada and the U n i t e d S t a t e s r e p r e s e n t s a s u b s t a n t i a l data base from which performance a n a l y s i s can be undertaken. The data c o n s i s t s of d i s c r e t e and continuous process v a r i a b l e measurements. As d i s c u s s e d by Berthouex et a l . (1981), 7 the data bases c o n t a i n some or a l l of the f o l l o w i n g c h a r a c t e r i s t i c s which i n f l u e n c e the s t a t i s t i c a l a n a l y s e s : 1. Large q u a n t i t i e s of data c o n t a i n i n g : a) aberrant v a l u e s ( e i t h e r bad data or unusual o c c u r r e n c e s ) ; b) l a r g e measurement e r r o r s , both random and s y s t e m a t i c ; c) d i s c r e t e and c o n t i n u o u s l y monitored v a r i a b l e s ; d) m i s s i n g d a t a . 2. Data v a r i a b i l i t y i n f l u e n c e d by: a) v a r i a b l e s which e x e r t an i n f l u e n c e but are not measured; b) complex cause and e f f e c t r e l a t i o n s h i p s ; c) s e r i a l c o r r e l a t i o n (auto c o r r e l a t i o n ) ; d) skewed o b s e r v a t i o n d i s t r i b u t i o n s ; e) seasonal f l u c t u a t i o n s . 3. O b s e r v a t i o n a l data as opposed to data o b t a i n e d from d e s i g n a t e d experiments. Many of the r e g u l a t o r y agencies i n North America do not have an orga n i z e d method of h a n d l i n g wastewater process d a t a , (Berthouex et a l . , 1981), and o f t e n are only i n t e r e s t e d i n d i s c h a r g e q u a n t i t y and q u a l i t y c h a r a c t e r i s t i c s . T h i s s e c t i o n reviews the s t a t i s t i c a l methods which can be u t i l i z e d to examine wastewater mo n i t o r i n g d a t a . Beginning with a fundamental d e s c r i p t i o n of process v a r i a b l e s and t h e i r s i g n i f i c a n c e , the f l u c t u a t i n g c h a r a c t e r i s t i c s of flows and c o n c e n t r a t i o n s i s examined and sampling s t r a t e g i e s are reviewed. T h i s i s f o l l o w e d by an examination of m o d e l l i n g and d e c i s i o n a n a l y s i s techniques f o r a c t i v a t e d sludge p r o c e s s c o n t r o l . The problem of sludge b u l k i n g i s examined f o r use i n the development of a d e c i s i o n a n a l y s i s process c o n t r o l s t r a t e g y . 8 2.1.1 Process V a r i a b l e s C h i n g ( 1 9 8 1 ) c l a s s i f i e s p r o c e s s v a r i a b l e s i n t o f o u r c a t e g o r i e s : 1 ) m a n i p u l a t e d ; 2) d i s t u r b a n c e ; 3) p e r f o r m a n c e ; a n d 4) i n t e r m e -d i a t e . M a n i p u l a t e d v a r i a b l e s c o n s i s t o f c o n t r o l l a b l e v a r i a b l e s s u c h a s s o l i d s r e t e n t i o n t i m e ( S R T ) , m i x e d l i q u o r s u s p e n d e d s o l i d s (MLSS) a n d d i s s o l v e d o x y g e n (DO) c o n c e n t r a t i o n s , a n d r e c y c l e r a t i o s . Low SRT v a l u e s a r e a s s o c i a t e d w i t h h i g h e r m i c r o b i a l a c t i v i t i e s (Roe a n d B h a g a t , 1 9 8 2 , K u c n e r o w i c z a n d V e r s t r a e t e , 1 9 7 9 ) , w h i l e a h i g h SRT i s a s s o c i a t e d w i t h g o o d c l a r i f i e r s e t t l i n g c h a r a c t e r -i s t i c s ( W i l s o n a n d L e e , 1 9 8 2 , C a s h i o n a n d K e i n a t h , 1 9 8 3 ) . V a r i a t i o n i n MLSS l e v e l s a r e g e n e r a l l y c o n t r o l l e d t o m a i n t a i n a c o n s t a n t f o o d - t o - m i c r o o r g a n i s m ( F / M ) r a t i o , a l t h o u g h r e s e a r c h h a s i n d i c a t e d t h a t MLSS l e v e l s c a n a l s o be u s e d t o c o n t r o l s l u d g e t h i c k e n i n g c h a r a c t e r i s t i c s ( T u n t o o l a v e s t e t a l . , 1 9 8 2 ) . I n c r e a s e d r e c y c l e r a t e s c a n be u s e d t o r e d u c e t h e a c t u a l h y d r a u l i c r e t e n t i o n t i m e w i t h i n i n d i v i d u a l r e a c t o r s a n d c a n r e s u l t i n i n c r e a s e d s u s p e n d e d s o l i d s l o a d i n g t o t h e s e c o n d a r y c l a r i f i e r s ( L a w l e r a n d S i n g e r , 1 9 8 4 ) . D i s s o l v e d o x y g e n l e v e l s c a n be u s e d t o c o n t r o l e f f l u e n t t u r b i d i t y ( S t a r k e y a n d K a r r , 1 9 8 4 ) a n d f i l a m e n t o u s b u l k i n g ( P a l m e t a l . , 1 9 8 2 , S t r o m a n d J e n k i n s , 1 9 8 4 ) , L a u a n d J e n k i n s , 1 9 8 4 a , 1 9 8 4 b ) . D i s t u r b a n c e v a r i a b l e s c o n s i s t o f u n c o n t r o l l a b l e p a r a m e t e r s s u c h a s i n f l u e n t f l o w r a t e s , a n d i n f l u e n t c o n c e n t r a t i o n s o f s u b s t r a t e s , s o l i d s a n d n u t r i e n t s . P a r a m e t e r s o f i n t e r e s t i n 9 monitoring include: substrate parameters, such as Chemical Oxygen Demand (COD) and Biochemical Oxygen Demand (BOD); nutrient l e v e l s , such as Total Phosphorus (TP) and Total Kjeldahl Nitrogen (TKN); and other influent conditions such as temperature, pH and flow rates. Process design can be u t i l i z e d to modify these variables to some extent. For instance, equalization basins can be used to reduce hydraulic and organic loading. Adjustment of manipulative variables i s also used to adapt a process to variable influent c h a r a c t e r i s t i c s and achieve a desired performance e f f e c t (Nelson and Mishra, 1980, Grinker and Meagher, 1984). E f f o r t s have been made to co r r e l a t e disturbance and performance variables with limited success (Niku and Schroeder, 1981). Performance variables are output parameters which are used to assess the performance of a waste treatment process. The objec-t i v e of the waste treatment process i s to reduce the nutrient and substrate concentrations in the e f f l u e n t . This i s accomplished through control and adjustment of manipulated v a r i a b l e s . The desired performance variable l e v e l can sometimes be achieved by co n t r o l l i n g one or more of the manipulated v a r i a b l e s . (Schroeder and Irvine, 1979). Intermediate variables are effluent or state parameters which are not considered process variables, such as pH and the sludge volume index (SVI). These variables can be used to assess general activated sludge conditions, such as sludge s e t t l e a b i l i t y and n i t r i f i c a t i o n c h a r a c t e r i s t i c s , but their l e v e l s are generally not 1 0 c o n t r o l l e d i n a c t i v a t e d s l u d g e t r e a t m e n t p l a n t s . A c t i v e b i o m a s s v a r i a b l e s , s u c h a s O x y g e n U p t a k e R a t e ( O U R ) , A d e n o s i n e T r i - P h o s p h a t e (ATP) l e v e l s a n d d e h y d r o g e n a s e e n z y m e a c t i v i t y , c a n be i n d i r e c t l y a d j u s t e d by m a n i p u l a t e d v a r i a b l e s s u c h a s t h e F o o d - t o - m i c r o o r g a n i s m r a t i o ( F / M ) . A c o n s i d e r a b l e amount o f r e s e a r c h h a s b e e n u n d e r t a k e n t o d e v e l o p t h e s e v a r i a b l e s i n t o e f f e c t i v e c o n t r o l p a r a m e t e r s . T h e o x y g e n u p t a k e (OUR) h a s b e e n e v a l u a t e d a s c o n t r o l p a r a m e t e r s by many r e s e a r c h e r s i n r e c e n t y e a r s ( B l o k , 1 9 7 4 , 1 9 7 6 , B e n e f i e l d e t a l . , 1 9 7 5 , W a l k e r a n d D a v i e s , 1 9 7 7 , A n d r e w s , 1 9 7 7 , Ekama a n d M a r a i s , 1 9 7 9 , G i o n a a n d A n n e s i n i , 1 9 7 9 , Mona e t a l . , 1 9 7 9 Y o u n g , 1 9 8 1 , E d w a r d s a n d S h e r r a r d , 1 9 8 2 , R o y e t a l . , 1 9 8 3 , Huang a n d C h e n g , 1 9 8 4 , H u a n g e t a l . , 1 9 8 5 ) . T h e t h r u s t o f t h i s r e s e a r c h was t o f i n d a n a l t e r n a t i v e v i a b i l i t y p a r a m e t e r f o r u s e i n t h e F / M r a t i o , a s t h e MLVSS was j u d g e d t o be a n i n a d e q u a t e a s s e s s m e n t o f l i v i n g c e l l s o r a c t i v e c e l l s ( G r e e n e a n d S h e l e f , " 1 9 8 1 , J o r g e n s e n , 1984 ) . A m e a s u r e o f r e s p i r a t i o n r a t e , t h e OUR was o r i g i n a l l y n o t e d t o i n c r e a s e d i r e c t l y w i t h i n f l u e n t BOD ( F o r d a n d E c k e n f e l d e r , 1 9 6 7 , D u g g a n a n d C l e a s b y , 1 9 7 6 ) . D e s p i t e i n i t i a l d i f f i c u l t i e s ( O l s s o n a n d A n d r e w s , 1 9 7 8 , H a a s , 1 9 7 9 , Chen e t a l . , 1 9 8 0 ) , OUR h a s r e c e n t l y f o u n d u s e i n r e a l t i m e F / M p r o c e s s c o n t r o l s t r a t e g i e s ( S t e n s t r o m a n d A n d r e w s , 1 9 7 9 , H o w e l l e t a l . , 1 9 8 4 ) . B o t h A T P a n d d e h y d r o g e n a s e enzyme a c t i v i t y h a v e b e e n s u c c e s s f u l l y u t i l i z e d a t t h e l a b o r a t o r y l e v e l f o r t h e a s s e s s m e n t o f c e l l m a s s v i a b i l i t y ( P a t t e r s o n e t a l . , 1 9 6 9 , J o n e s a n d P r a s a d , 1 9 6 9 , 1 1 Klapwijk et a l . , 1974, Ryssov & N e i l s e n , 1975, Droste & Sanchez, 1983). However, at present no a p p r o p r i a t e method of t e s t i n g has been developed f o r use at c o n v e n t i o n a l sewage treatment f a c i l i t i e s . 2.1.2 Flow and C o n c e n t r a t i o n F l u c t u a t i o n s F l u c t u a t i o n s i n d i s t u r b a n c e v a r i a b l e s present one of the key d i f f i c u l t i e s i n process c o n t r o l . I n f l u e n t wastewater flows and c o n c e n t r a t i o n s vary c y c l i c a l l y on d i u r n a l , weekly, monthly, seasonal and on an annual b a s i s . G e n e r a l l y , d i u r n a l v a r i a t i o n s are the r e s u l t of m u n i c i p a l and i n d u s t r i a l water use h a b i t s and, with the e x c e p t i o n of flow r a t e s , are not monitored at conven-t i o n a l treatment f a c i l i t i e s . D i u r n a l v a r i a t i o n s are not u s u a l l y assessed except i n short term i n t e n s i v e surveys, although they a f f e c t the d a i l y performance and e f f i c i e n t o p e r a t i o n of the treatment p r o c e s s . Instead, a sampling frequency ranging from d a i l y to weekly i s the usual p r a c t i c e , l a r g e l y due to i n s u f f i c i e n t s t a f f i n g l e v e l s f o r more frequent l a b o r a t o r y a n a l y s e s , and l a c k of automated or o n - l i n e a n a l y t i c a l equipment. The implementation of r e a l - t i m e c o n t r o l s t r a t e g i e s and o n - l i n e i n s t r u m e n t a t i o n has been l i m i t e d due to the l a c k of r e l i a b l e sensors (Busch, 1984) and the i n a b i l i t y to e s t a b l i s h an e f f e c t i v e process model f o r c o n t r o l of the manipulated v a r i a b l e s based on c a u s a l r e l a t i o n s h i p s (Hahn, 1974, Niku and Schroeder, 1981). Although flows g e n e r a l l y f o l l o w a p r e d i c t a b l e p a t t e r n , the s t r e n g t h of the wastewater may be h i g h l y v a r i a b l e , r e s u l t i n g i n an extremely v a r i a b l e mass l o a d i n g r a t e (Berthouex et a l . , 1981). Such an i n f l o w c h a r a c t e r i s t i c can r e s u l t i n i n c o r r e c t p l a n t 12 l o a d i n g c a l c u l a t i o n s , i f i n a p p r o p r i a t e sampling techniques are used ( S c h a e f f e r , 1983). T h i s w i l l be d i s c u s s e d f u r t h e r i n S e c t i o n 2.1.3. Wastewater q u a l i t y and q u a n t i t y from m u n i c i p a l , commercial and i n d u s t r i a l sources f l u c t u a t e i n a s t o c h a s t i c manner. S p e c t r a l a n a l y s i s has been a p p l i e d to treatment p l a n t data to account f o r the d i f f e r e n t c y c l i c components by a s s e s s i n g the frequency of recurrence (Thomann, 1970). However, t h i s technique r e q u i r e s a monitoring frequency g r e a t e r than the p e r i o d i c i t y of the d i s t u r -bance v a r i a b l e and, t h e r e f o r e , i s of l i m i t e d use to assess i n f l u e n c e s with l e s s than weekly p e r i o d s ( most p l a n t s do not sample on a d a i l y b a s i s ) . The major b e n e f i t of r e c o g n i z i n g c y c l i c a l p a t t e r n s i s to i d e n t i f y p e r i o d i c l o a d i n g to the p l a n t from commercial d i s c h a r g e s which may be a d v e r s e l y i n f l u e n c i n g p l a n t performance. R e c o g n i t i o n of these p a t t e r n s c o u l d be used to i d e n t i f y the r e s p o n s i b l e d i s c h a r g e r s f o r source c o n t r o l measures or to modify the p l a n t o p e r a t i o n and to a d j u s t f o r the i n c r e a s e d l o a d i n g , i f p o s s i b l e . 2.1.3 Sampling C o n s i d e r a t i o n s With the e x c e p t i o n of o n - l i n e a n a l y t i c a l t echniques, there are b a s i c a l l y three techniques of sampling used i n waste treatment f a c i l i t i e s : 1) grab; 2) time p r o p o r t i o n e d composite; and 3) flow p r o p o r t i o n e d composite. 13 Grab samples, c o l l e c t e d at d i s c r e t e i n t e r v a l s and analysed i n d i -v i d u a l l y , are the most common form of sampling due l a r g e l y to the expense of composite samplers and the changes which may occur d u r i n g the c o l l e c t i o n of a composite sample. Grab samples do not r e f l e c t the f l u c t u a t i o n s i n wastewater q u a l i t y inbetween sampling i n t e r v a l s . F u r t h e r , with the random and c y c l i c a l f l u c t u a t i o n s , a d a i l y grab sample i s not l i k e l y t o be r e p r e s e n t a t i v e of average d a i l y c o n d i t i o n s , nor i s the r a t i o of d i s c r e t e c o n c e n t r a t i o n to average d a i l y c o n c e n t r a t i o n or mass l o a d i n g l i k e l y to be constant from day to day. Time p r o p o r t i o n e d samples i n v o l v e c o l l e c t i n g equal volumes at r e g u l a r time i n t e r v a l s and d e p o s i t i n g them i n a common c o n t a i n e r to be analyzed c o l l e c t i v e l y . Flow p r o p o r t i o n e d composites are c o l l e c t e d as a f u n c t i o n of i n f l u e n t flow r a t e r a t h e r than time and are o f t e n c o l l e c t e d c o n t i n u o u s l y but with v a r y i n g sample r a t e s . G e n e r a l l y composites are thought to be more r e p r e s e n t a -t i v e than grab samples of average process stream performance. However, r e s e a r c h undertaken by S c h a e f f e r et a l . (1983) i n d i c a t e s that i f flows and c o n c e n t r a t i o n s a re h i g h l y c o r r e l a t e d , both time and volume p r o p o r t i o n e d samples are bi a s e d and tend to over estimate the mass l o a d i n g . Time p r o p o r t i o n e d composite samples may d i f f e r from flow p r o p o r t i o n e d samples by more than 10% (Ouano, 1981). Although the frequency of sampling should be based on process v a r i a b i l i t y , small treatment p l a n t s are g e n e r a l l y sampled l e s s 14 f r e q u e n t l y than l a r g e treatment f a c i l i t i e s , d e s p i t e having t y p i c a l l y much gr e a t e r e f f l u e n t v a r i a b i l i t y . T h i s has g e n e r a l l y been a t t r i b u t e d to a lack of manpower and money, and the g r e a t e r p o t e n t i a l d i s c h a r g e mass l o a d i n g from l a r g e p l a n t s to the environment (Berthouex et a l , 1981). I t has been suggested by some r e s e a r c h e r s that d a i l y sampling i s too frequent (Berthouex and Hunter, 1975, Berthouex et a l . , 1981) and t h a t bi-weekly to monthly sampling may be s u f f i c i e n t f o r tr e n d d e t e c t i o n (Lettenmaier, 1978). The sampling i n t e r v a l should be t a r g e t t e d at a process c o n t r o l o b j e c t i v e . For i n s t a n c e , h o u r l y sampling or d a i l y sampling may be only of academic r e s e a r c h i n t e r e s t i f the p l a n t i s in c a p a b l e of modifying the o p e r a t i n g c h a r a c t e r i s t i c s on the same r e a l - t i m e i n t e r v a l b a s i s . There i s l i t t l e v a lue i n knowing t h a t the i n f l u e n t s u b s t r a t e l e v e l i s i n c r e a s i n g i f the a b i l i t y of the process t o adapt t o the i n c r e a s e l o a d i n g i s slower than the sampling i n t e r v a l . Berthouex (1981) suggests t h a t f o r d e t e c t i n g t r e n d s i n a c t i v a t e d sludge systems, " d a i l y sampling i s not s u b s t a n t i a l l y more e f f e c t i v e than sampling every three or four days". 2.1 .4 Data Accuracy and P r e c i s i o n The f i r s t s t e p i n i n t e r p r e t i n g data i s to review the r e l i a b i l i t y of the da t a . In a d d i t i o n t o c r i t i c a l l y reviewing the data from the l a b o r a t o r y f o r ac c u r a t e t r a n s p o s i t i o n and reasonableness, the s i g n i f i c a n c e of the data, i n r e l a t i o n to o p e r a t i o n or r e c e i v i n g water impact, must be asse s s e d and a p p r o p r i a t e adjustments made to check or c o n f i r m a p p a r e n t l y s p u r i o u s data or to a l t e r the 15 p r o c e s s . T h i s can o f t e n be accomplished with simple g r a p h i c a l r e p r e s e n t a t i o n s . Q u a l i t y c o n t r o l programs are e s s e n t i a l to ensure that the r e s u l t s are v a l i d , r e p r e s e n t a t i v e , comparable and of known p r e c i s i o n and accuracy. The process has been d e s c r i b e d by Lee and Jones (1983) as an " a c t i v e " m o n i t o r i n g program. Most process and e f f l u e n t m o n i t o r i n g programs are " p a s s i v e " i n nature, with samples c o l l e c -ted at f i x e d and o f t e n a r b i t r a r y l o c a t i o n s and f r e q u e n c i e s , and the a n a l y t i c a l r e s u l t s are u s u a l l y s t o r e d i n a f i l i n g c a b i n e t or computer without c r i t i c a l review. P r o d u c t i v e and c o s t e f f e c t i v e m o n i t o r i n g programs should e v a l u a t e the value of sampling s i t e s and f r e q u e n c i e s and parameter s e l e c t i o n on a r o u t i n e b a s i s . F l e x i b i l i t y t o a d j u s t the program, based on f i n d i n g s and a quick data-to-review time, are d e s c r i b e d by Lee and Jones (1983) as being key elements i n a u s e f u l program. Two key elements i n q u a l i t y c o n t r o l are the assessment of ac c u r a -cy and p r e c i s i o n of a n a l y s e s . As d i s c u s s e d by Aldenhoff and Ern e s t (1983), q u a l i t y c o n t r o l i s the r o u t i n e a p p l i c a t i o n of a c t i v i t i e s and procedures designed and used to ensure the q u a l i t y and r e l i a b i l i t y of l a b o r a t o r y r e s u l t s . T h i s c o n s i s t s of adequate t r a i n i n g , p r e c i s i o n , accuracy and a v i s u a l review of the r e s u l t s to assure that they are c o n s i s t e n t with expected performance. Q u a l i t y assurance i s the sum of a c t i v i t i e s t h a t document and maintain the q u a l i t y of the d a t a . I t i s the means of a s s u r i n g t h a t o n l y approved a n a l y t i c a l methods are used, the procedures 1 6 are f o l l o w e d c o r r e c t l y , the instruments are c a l i b r a t e d and maintained, uniform sampling and a n a l y t i c a l procedures are f o l l o w e d , and the r e s u l t s and performances are p r o p e r l y documented and a u d i t e d . 2.1.5 S t a t i s t i c a l Data Summary Techniques Wastewater q u a l i t y and q u a n t i t y v a r i e s c o n t i n u o u s l y with time, f o l l o w i n g an o v e r a l l c y c l i c p a t t e r n but with a randomized appear-ance. As noted by Berthouex et a l . (1981), wastewater v a r i a b l e f l u c t u a t i o n s are h i g h l y s e r i a l l y c o r r e l a t e d (auto c o r r e l a t e d ) , with c u r r e n t values being dependent upon previous v a l u e s as opposed to being independent. For i n s t a n c e , sewage temperatures are not r a p i d l y i n f l u e n c e d by the surrounding a i r temperature; consequently, the l i q u i d temperatures g r a d u a l l y change with seasonal changes, r e s u l t i n g i n a smooth c y c l i c a l appearance. Water and wastewater q u a l i t y v a r i a b l e s g e n e r a l l y have a normal, lognormal or gamma d i s t r i b u t i o n (Shereani and Moreau, 1975, Ward et a l . , 1981). V a r i a b l e s modelled w e l l by one d i s t r i b u t i o n at a p a r t i c u l a r l o c a t i o n or p l a n t might be b e t t e r modelled by another d i s t r i b u t i o n at another l o c a t i o n (Ward et a l . , 1981). One of the key assumptions to the use of standard parametric s t a t i s t i c s , such as the F or T t e s t s f o r comparing two s e t s of data, i s that the data i s normally d i s t r i b u t e d . Although data may be t r a n s -formed to approximate the normal d i s t r i b u t i o n , these transforma-t i o n s do not n e c e s s a r i l y s a t i s f y other parametric assumptions, such as homogeniety of v a r i a n c e s . Rather than undertaking 17 e x t e n s i v e data t r a n s f o r m a t i o n s , Ames and Szonyi, 1982 suggest the use of non-parametric or d i s t r i b u t i o n - f r e e s t a t i s t i c s f o r the a n a l y s i s of wastewater treatment p l a n t process data. Skewed d i s t r i b u t i o n s tend to occur because of e i t h e r a constant percentage e r r o r v a r i a n c e over a wide response range or because there i s some p h y s i c a l l i m i t at one end of the range of o b s e r v a t i o n s . For example, where e f f l u e n t ortho-phosphate or b i o c h e m i c a l oxygen demand c o n c e n t r a t i o n s are a t or near the d e t e c t i o n l i m i t most of the time, o c c a s i o n a l high c o n c e n t r a t i o n s due to p r o c e s s upsets or a n a l y t i c a l e r r o r w i l l tend to skew the frequency histogram of such data towards the higher c o n c e n t r a -t i o n s . Often these skewed d i s t r i b u t i o n s are normalized through a t r a n s f o r m a t i o n (log-normal). Histograms can be used to s e l e c t the a p p r o p r i a t e p r o b a b i l i t y d e n s i t y f u n c t i o n and to determine i f a t r a n s f o r m a t i o n i s r e q u i r e d through the use of the c h i - s q u a r e t e s t (Ouano, 1981). One non-parametric t e s t which can be used to compare whether two data s e t s belong to the same p o p u l a t i o n i s the Kolmogorov-Smirnov Two-Sample T e s t , a l s o c a l l e d the "Two-Sample Smirnov T e s t s " (Ames and S z o n y i , 1982). The t e s t e v a l u a t e s whether two data s e t s are s t a t i s t i c a l l y d i f f e r e n t , but without r e l y i n g on t h e i r u n d e r l y i n g d i s t r i b u t i o n s . S p e c t r a l a n a l y s i s can be used to d e f i n e the u n d e r l y i n g c y c l i c p a t t e r n s of monitored v a r i a b l e s . In a d d i t i o n i t can be used to 18 determine the a p p r o p r i a t e sampling i n t e r v a l based on short term i n t e n s i v e m o nitoring programs (Ouano, 1981). Moving averages, as i l l u s t r a t e d by Berthouex and Hunter (1979), can a l s o be used to p r o v i d e an assessment of the c y c l i c nature of a waste stream. G e n e r a l l y , the moving average i s c a l c u l a t e d by e q u a l l y weighting the present value and a set of previous v a l u e s , • thereby damping the e f f e c t s of random v a r i a t i o n such as a n a l y t i c a l e r r o r or sampling e r r o r . A major disadvantage of t h i s technique l i e s i n the equal weighting of past and present v a l u e s such that long past events, which may have l i t t l e s i g n i f i c a n c e t o present v a l u e s are weighted e q u a l l y with recent v a l u e s . A m o d i f i c a t i o n i s to apply a weighting f a c t o r , such that c u r r e n t v a l u e s have a l a r g e r i n f l u e n c e on the c a l c u l a t e d average. The purpose of the moving average i s to smooth out noise and h i g h -l i g h t long term t r e n d changes of components with low frequences. F u r t h e r m o d i f i c a t i o n s of t h i s technique are d i s c u s s e d i n Gelb (1974). By r e c o g n i z i n g the assumptions r e q u i r e d f o r the v a r i o u s s t a t -i s t i c a l techniques and c h a r a c t e r i s t i c s of the data to be ana-l y z e d , j u d i c i o u s s e l e c t i o n of a p p r o p r i a t e techniques can be made. Often t h i s can be accomplished by f i r s t simply graphing the data and then a p p l y i n g a p p r o p r i a t e s t a t i s t i c a l procedures to address s p e c i f i c q u e s t i o n s . 19 Some data a n a l y s i s techniques which could be a p p l i e d to waste-water treatment p l a n t data i n c l u d e : 1. Time S e r i e s P l o t s Simple time s e r i e s p l o t s of the data can r e v e a l a great deal of i n f o r m a t i o n concerning c y c l i c p a t t e r n s , s h i f t s i n performance l e v e l and a u t o c o r r e l a t i o n , and can serve as a s t a r t i n g p o i n t f o r s t a t i s t i c a l a n a l y s i s . F u r t h e r , a q u a l i t a t i v e assessment of sampling frequency adequacy can be made by removing data and observing whether the o v e r a l l " t r e n d s " are s u b s t a n t i a l l y a l t e r e d . a) d a i l y values - simple " p l o t the data" approach b) data smoothing - weekly, monthly, moving and e x p o n e n t i a l l y weighted moving average. 2. P o p u l a t i o n D i s t r i b u t i o n C h a r a c t e r i s t i c s P o p u l a t i o n d i s t r i b u t i o n c h a r a c t e r i s t i c s can be u t i l i z e d i n design ( i . e . 95% confidence boundary) and i n v e r i f y i n g whether the p o p u l a t i o n s are normal or of s i m i l a r d i s t r i b u t i o n s . a) frequency histograms - to determine the data d i s t r i b u t i o n f o r design purposes, ( i . e . normal, log-normal) b) cumulative frequency p lo ts - to d e s c r i b e performance c h a r a c t e r i s t i c s i n terms of p r o b a b i l i t y of occurence. 3. I n t e r v e n t i o n A n a l y s i s A technique o r i g i n a l l y proposed by Box and T i a o (1965) to estimate the e f f e c t of a known change i n c o n d i t i o n s a f f e c t i n g a time s e r i e s of s e r i a l l y c o r r e l a t e d data. 4. Kolmogorov-Smirnov Two Sample Test A nonparametric ( d i s t r i b u t i o n independent) technique to determine i f two samples are s i g n i f i c a n t l y d i f f e r e n t . T h i s c o u l d be used t o check i f the p a r a l l e l r e a c t o r s are o p e r a t i n g i d e n t i c a l l y , and whether a c o n t r o l r e a c t o r i s s i g n i f i c a n t l y d i f f e r e n t from an experimental r e a c t o r . 20 2.1.6 Summary H i s t o r i c a l data records are maintained by most treatment f a c i l i -t i e s but are g e n e r a l l y not analyzed m e a n i n g f u l l y , i f at a l l . The data c o n s i s t s of manipulated, d i s t u r b a n c e , performance and i n t e r -mediate v a r i a b l e s with i r r e g u l a r c y c l i c p a t t e r n s . Much of the data has been c o l l e c t e d using grab sampling techniques with i n t e r v a l s ranging from d a i l y to weekly, with the exce p t i o n of continuous flow m o n i t o r i n g . S e v e r a l of the data c h a r a c t e r i s t i c s i d e n t i f i e d i n t h i s s e c t i o n present s e r i o u s problems f o r c o n v e n t i o n a l s t a t i s t i c a l a n a l y s i s . Bad data, l a r g e random and systematic e r r o r s , s e r i a l c o r r e l a t i o n and non-normal p o p u l a t i o n d i s t r i b u t i o n s v i o l a t e key assumptions of p arametric s t a t i s t i c s . Nonparametric s t a t i s t i c s do not r e q u i r e normal p o p u l a t i o n d i s t r i b u t i o n s ; however, the key assumption of randomness i s u s u a l l y not met, s i n c e the monitoring data i s t y p i c a l l y s e r i a l l y c o r r e l a t e d . Time s e r i e s a n a l y t i c a l techniques, while designed t o evaluate s e r i a l l y c o r r e l a t e d data, are s e r i o u s l y a f f e c t e d by mis s i n g data, and i r r e g u l a r sampling i n t e r -v a l s . Techniques to a d j u s t f o r m i s s i n g data and non-uniform sampling i n t e r v a l s are complex and not w e l l d e f i n e d i n the l i t e r -a t u r e . However, d e s p i t e obvious d i f f i c u l t i e s with the data chara-c t e r i s t i c s , j u d i c i o u s a p p l i c a t i o n of parametric, nonparametric and time s e r i e s techniques, combined with g r a p h i c a l r e p r e s e n t a -t i o n s of the data, can r e v e a l much about the data, p r o v i d i n g the c o n c l u s i o n s acknowledge the s t a t i s t i c a l assumptions which have been made and the shortcomings of the data. 21 2.2 Process M o d e l l i n g and C o n t r o l A v a r i e t y of techniques have been u t i l i z e d i n the past to des-c r i b e the a c t i v a t e d sludge process in terms of e s t a b l i s h e d t h e o r i e s and o b s e r v a t i o n s of process v a r i a b l e i n t e r a c t i o n s . T h i s p r o c e s s has r e s u l t e d i n e s s e n t i a l l y two types of models: 1) k i n e t i c or me c h a n i s t i c models; and 2) s t o c h a s t i c or time s e r i e s models. 2.2.1 M e c h a n i s t i c M o d e l l i n g S e v e r a l k i n e t i c models have been proposed f o r a c t i v a t e d sludge treatment design and o p e r a t i o n . Vasicek (1982) r e p o r t e d on the s u c c e s s f u l l a p p l i c a t i o n of k i n e t i c m odelling to an a c t i v a t e d sludge f a c i l i t y i n Hawaii based on the F/M r a t i o . M e c h a n i s t i c models have found p a r t i c u l a r use i n the assessment of the c o m p e t i t i v e growth k i n e t i c s of f l o c - f o r m i n g and filamentous b a c t e r i a as d i s c u s s e d by Lau et a l . (1984a, 1984b) . T y p i c a l of most k i n e t i c s t u d i e s , B l a c k w e l l (1971), Busby and Andrews (1975), Ekama and Marais (1979) and C l i f f and Andrews (1981), have deve-loped s u b s t r a t e u t i l i z a t i o n equations t o account f o r the p a r t i c u -l a t e and s t o r e d s u b s t r a t e , and the r a p i d l y biodegradable sub-s t r a t e f r a c t i o n s i n the i n f l u e n t wastewater. Tyteca (1981) d e s c r i b e d the development of a n o n l i n e a r programming model as e s s e n t i a l to the optimal design and the development of a process o p t i m i z a t i o n technique, t h i s was expanded f u r t h e r by Tyteca and Smeers (1981) to i l l u s t r a t e p o t e n t i a l process c o s t savings u t i l i z i n g such a model. An extended model, proposed by van 22 Haandel, Ekama and Marais (1981), for the simulation of a multi-reactor n i t r i f i c a t i o n - d e n i t r i f i c a t i o n process under conditions of constant and c y c l i c flow and load, appears to be in agreement with experimental and f u l l - s c a l e processes. Nicholls (1982) reported that t h i s extended model had been used successfully to predict, within 10 percent, the COD, TKN, ammonia and n i t r a t e concentrations in the effluent of two 50,000 cubic meters per day five-stage activated sludge plants. In applying the model ar b i t r a r y assumptions were made for the n i t r i f i c a t i o n growth rate, as well as soluble and particulate nonbiodegradable fractions of the incoming sewage COD. Stenstrom and Andrews (1979) suggested that F/M ratios and mean c e l l retention time (MCRT) control strategies are of limited use under non-steady state conditions, p a r t i c u l a r l y for organism growth rate assessment. Research studies which produce refined design models, often based on the Monod equation, are suggested to be of l i t t l e use and lead to skepticism among design engineers (Lawrence and McCarty, 1980). Many researchers have attempted to refine activated sludge kine-t i c models for the purpose of optimization, with limited success. Studies by Vasicek (1982) and Yueng et a l . (1980) have concluded that mathematical modeling i s possible, but that each plant must be studied and optimized i n d i v i d u a l l y . 23 The most promising conclusion regarding the development of these models are the observations made by Yeung et a l . (1980), Niku and Schroeder (1981) and Vasicek (1982), that a s p e c i f i c plant can be modelled and optimized as a separate individual process. I n t u i t i v e l y , a universal model could not be expected to accommodate the wide fluctuations in influent conditions experienced at many plants. The reaction of the biomass to influent conditions w i l l depend upon the types and proportions of organisms present in the biomass and the r e l a t i v e degree of stress. Further, differences in operating mode and process configuration with d i f f e r i n g hydraulic retention times (HRT), mean c e l l retention times (MCRT) and active biomass concentra-tions decrease the prob a b i l i t y that a general model w i l l be of use. There i s doubt that the process ever reaches steady-state in situations other than laboratory conditions. Kucnerowicz and Verstraete (1983) found that, beginning with a n i t r i f y i n g bio-mass, periods of up to 10 mean c e l l retention times were necessary before f u l l n i t r i f i c a t i o n rates were reached, under fixed influent and operational conditions. A further d i f f i c u l t y in modelling the activated sludge process l i e s in c o n f l i c t i n g interpretations as to the meaning of certain f i e l d measurements. H i s t o r i c a l l y , v o l a t i l e suspended solids (VSS) tests have been used to approximate the proportion of active biomass in a reactor. Researchers such as Green and Shelef (1981) dispute t h i s interpretation, noting that the viable organism content in the VSS i s not constant, as measured by changes in the maximum substrate u t i l i z a t i o n rate and the oxygen uptake r a t e . U t i l i z i n g ATP measurements, Nelson and Lawrence (1980) determined that the MLVSS can be d i v i d e d i n t o three f r a c -t i o n s : 1) a c t i v e or v i a b l e m i c r o b i a l s o l i d s ; 2) i n e r t m i c r o b i a l d e b r i s s o l i d s and; 3) nonviable biodegradable m i c r o b i a l s o l i d s . U n f o r t u n a t e l y , v i a b i l i t y t e s t s at most treatment p l a n t s are l i k e -l y to be r e s t r i c t e d to VSS a n a l y s e s , s i n c e ATP measurement techniques are s t i l l i n the development stage f o r use in waste-water a n a l y s i s . Even the e f f e c t s of temperature and pH on m i c r o b i a l growth are not c l e a r l y understood. Although the e f f e c t s of temperature and pH on n i t r i f y i n g organisms has been e x t e n s i v e l y s t u d i e d , r e s e a r c h such as that undertaken by P a i n t e r and L o v e l e s s (1983) conti n u e s to encounter circumstances i n which the e s t a b l i s h e d r e l a t i o n s h i p s do not h o l d . These unexpected e f f e c t s are g e n e r a l l y a t t r i b u t e d to unknown d i f f e r e n c e s i n compo-s i t i o n and s t r e n g t h of the i n f l u e n t sewage. D e s p i t e the c u r r e n t i n t e r e s t i n computerized monitoring and con-t r o l of wastewater treatment p r o c e s s e s , most e x i s t i n g p l a n t s have only manual methods of measurement and a n a l y s i s , o f t e n taken on a d a i l y or weekly b a s i s . The v a r y i n g s t r e n g t h of the i n f l u e n t sewage d u r i n g the day may g r e a t l y a l t e r the d i s s o l v e d oxygen c o n c e n t r a t i o n i n the r e a c t o r , a f f e c t i n g growth r a t e s and r e l a t i v e a c t i v i t y of the biomass. I t i s c l e a r t h a t , under such c i r c u m s t a n c e s , the u t i l i z a t i o n of s t e a d y - s t a t e k i n e t i c equations w i l l l e a d to erroneous models. As d e s c r i b e d by Manickam and Gaudy (1985), the unique d i f f e r e n c e s 25 in b i o l o g i c a l response to quantitative and hydraulic shocks m i t i -gate against lumping the response for predictive modelling using ki n e t i c equations. It i s the d i f f i c u l t y in adapting these kine-t i c equations to p a r t i c u l a r waste treatment processes which have encouraged research into dynamic or stochastic modelling. As noted by Lawrence and McCarty (1980) that "only under rare c i r -cumstances can the models accurately predict either effluent suspended so l i d s and effluent t o t a l BOD because these factors do not vary in a predictable fashion in the sludge age ranges used in actual operation". Sykes (1984) concluded that the bulking, residual substrate, and e f f l u e n t v a r i a b i l i t y phenomena are a result of competition and predation. Therefore, i f mechanistics models are to be used, they should be ecosystem models. Unfor-tunately, these mechanistic ecosystem models cannot be v e r i f i e d , and the pattern responses are predicted, by Sykes (1984), to be unique to each plant, with generalizations not being possible due to the complexities of the ecosystem. Vasicek (1982) noted that as a result of changes in wastewater composition, major changes in predominant b a c t e r i a l species or forms of s p e c i f i c strains (such as filamentous) bacteria could occur. Chronic operational problems can a l t e r the microorganism composition so extensively that, once the problems are corrected, i t could take months for the biomass to recover. Although these factors could cause the ki n e t i c relationships for the activated sludge process to vary s i g n i f i c a n t l y , i t i s not possible to monitor the changes from a microbiological perspective. 26 2.2.2 S t o c h a s t i c M o d e l l i n g S t o c h a s t i c m o d e l l i n g techniques have found moderate success i n p r e d i c t i n g the performance of a c t i v a t e d sludge processes on a s i t e s p e c i f i c b a s i s . Although the s t o c h a s t i c modelling of an i n d u s t r i a l a c t i v a t e d sludge process by Debelak and Sims (1981) concluded that a model based on i n f l u e n t and e f f l u e n t BOD or COD data alone i s not adequate to a c c u r a t e l y p r e d i c t process performance, they suggested t h a t the i n c l u s i o n of other para-meters such as flow, temperature and l o a d i n g would improve the model performance. Dynamic models, such as proposed by Berthouex et a l . (1976), and Hansen et a l . (1979, 1980) are r e p o r t e d to s u c c e s s f u l l y d e s c r i b e dynamic c o n d i t i o n s i n a c t i v a t e d sludge p l a n t s . Although s t r i c t l y s i t e or p l a n t s p e c i f i c , computer a l o g r i t h m s can be c o n s t r u c t e d to update such models as the process v a r i a b l e s change. V a r i o u s s t o c h a s t i c t i m e - s e r i e s a n a l y s i s techniques are d e s c r i b e d i n d e t a i l by Gelb (1974) and Box and Jenkins (1970). The t e c h n i -ques do not appear to have been widely a p p l i e d to wastewater m o d e l l i n g , l i k e l y due to the f a c t t h a t the r e s u l t i n g model i s s p e c i f i c t o the p l a n t s t u d i e d . As noted by Berthouex et a l . (1981) "model b u i l d e r s seem to c l i n g f o n d l y to mechanistic models even i f no data e x i s t to support them". He suggests that a more f r u i t f u l approach to a n a l y z i n g a wastewater treatment process data base would be by the use of time s e r i e s models and simple c h a r t s and s t a t i s t i c s . 27 2.2.3 Correlation Analyses Recognizing the lack of steady-state conditions in some waste-water treatment plants, some researchers have investigated the u t i l i z a t i o n of effluent v a r i a b i l i t y to i d e n t i f y probable causes in the plant operation. Guo et a l . (1981) and Niku and Schroeder (1981) applied some fundamental c o r r e l a t i o n and multi-variate regression techniques to activated sludge operating data obtained from f u l l scale processes of varying configurations and operating modes. By comparing monitored parameters with common levels of variance, the researchers were able to i d e n t i f y probable causes of effluent v a r i a b i l i t y . Of p a r t i c u l a r importance was the conclusion by both groups that a single variable or group of variables could not be used to explain the d i v e r s i t y in performance in a l l plants. U t i l i z i n g multi-variate analysis techniques, Niku and Schroeder (1981) found that often greater than f i f t y percent of the process v a r i a t i o n could not be explained by the parameters which were monitored. Although a follow-up study was not undertaken to determine i f the s t a t i s -t i c a l study could be u t i l i z e d to reduce the process v a r i a b i l i t y , i t i s believed that the methodology has promise for the i d e n t i f i -cation of major operational problems. Noting the comments made by Gray et a l . (1980), that improper operations and maintenance procedures were responsible for 85 to 95 percent of the plants surveyed, not meeting the NPDES permit requirements in the United States, i t i s apparent that operations variables must also be included in an assessment of wastewater 28 data. T h i s i s supported by Guo et a l . (1981), who observed that o p e r a t i o n a l problems are l a r g e l y r e s p o n s i b l e f o r process v a r i a b i l i t y . Niku and Schroeder (1981) noted that o p e r a t i o n s changes can be r e s p o n s i b l e f o r more than 50 percent of the observed e f f l u e n t v a r i a t i o n . Many of these o p e r a t i o n a l d i f f i c u l t i e s , such as clogged a i r l i n e s , power outages and pump f a i l u r e s are extremely d i f f i c u l t to i n c o r p o r a t e i n t o a numerical data base. 2.2.4 Summary L i m i t a t i o n s i n the accuracy of b i o k i n e t i c data, and the presence of non-steady s t a t e c o n d i t i o n s ( r e s u l t i n g from v a r i a b l e h y d r a u l i c and o r g a n i c l o a d i n g , temperature f l u c t u a t i o n s and other f a c t o r s ) , have been suggested as reasons why the exact p r e d i c t i o n of e f f l u e n t q u a l i t y i s i m p o s s i b l e . I n t e r a c t i o n between the v a r i o u s a c t i v a t e d sludge organisms makes the v e r i f i c a t i o n of an ecosystem model i m p o s s i b l e , and hence p r e c l u d e s the development of a g e n e r a l k i n e t i c model which can be used to a c c u r a t e l y p r e d i c t the performance of the a c t i v a t e d sludge p r o c e s s . Although s t o c h a s t i c models are s i t e s p e c i f i c , there are no key u n d e r l y i n g assumptions, such as steady s t a t e o p e r a t i o n . Although widely used i n other f i e l d s such as commerce, these time s e r i e s and techniques have not been widely a p p l i e d t o waste treatment d a t a . 29 Attempts made to c o r r e l a t e d i s t u r b a n c e v a r i a b l e s with manipulated v a r i a b l e s has achieved l i m i t e d success, a t t r i b u t e d to the absence of s u f f i c i e n t o p e r a t i o n a l data. 2.3 D e c i s i o n Theory Approach to Process C o n t r o l The u l t i m a t e o b j e c t i v e of wastewater treatment mod e l l i n g i s to optim i z e and s t a b i l i z e the treatment pr o c e s s . P e r i o d i c o p e r a t i o n c o n t r o l , such as proposed by Yeung et a l . (1980), can substan-t i a l l y reduce e f f l u e n t BOD and/or i t ' s v a r i a b i l i t y , r e l a t i v e to c o n v e n t i o n a l computer c o n t r o l techniques. Once a s i g n i f i c a n t change has been d e t e c t e d or there i s evidence t h a t the performance of the p l a n t i s d e t e r i o r a t i n g , a d e c i s i o n has to be made as to how to c o r r e c t the problem. C o r r e c t i v e a c t i o n i s based on o p e r a t i n g experience and q u a l i t a t i v e observa-t i o n s , such as sludge c o l o u r and odour. As p r e v i o u s l y noted, each p l a n t i s unique i n terms of design and o p e r a t i n g c h a r a c t e r i s t i c s . S i m i l a r l y , the causes of performance f a i l u r e and necessary remedial a c t i o n are g e n e r a l l y s p e c i f i c t o each p l a n t . S u c c e s s f u l process c o n t r o l d e c i s i o n s at one p l a n t may not be e f f e c t i v e at another p l a n t . P r e v i o u s l y s u c c e s s f u l process c o n t r o l d e c i s i o n s , made at the same p l a n t , does not guarantee that the same response w i l l be observed f o r the same process adjustments i n the f u t u r e , p a r t i c u l a r l y where the biomass has adapted t o the changing c o n d i t i o n s . T h i s r e s u l t s i n making o p e r a t i n g d e c i s i o n s under c o n d i t i o n s of c o n s i d e r a b l e u n c e r t a i n t y . 30 Due to the l a c k of data a n a l y s i s techniques, c u r r e n t o p e r a t i o n a l p r a c t i c e s o f t e n r e l y h e a v i l y on q u a l i t a t i v e o b s e r v a t i o n s , supple-mented by recent monitoring data. The c o l o u r of the mixed l i q u o r and the degree of s u r f a c e foaming are examples of such q u a l i t a -t i v e o b s e r v a t i o n s . As these types of o b s e r v a t i o n s are not e a s i l y recorded, and the i n t e r p r e t a t i o n i s s u b j e c t i v e , the i n f o r m a t i o n base i s g e n e r a l l y accumulated as "operator e x p e r i e n c e " . Consequently the q u a l i t a t i v e i n f o r m a t i o n i s d i f f i c u l t to i n c o r p o r a t e i n t o the e v a l u a t i o n of q u a n t i t a t i v e data, u n l e s s the e v a l u a t i o n i s undertaken by the o p e r a t o r . By comparing o p e r a t i n g c h a r a c t e r i s t i c s with r e p o r t e d data from other p l a n t s and re s e a r c h s t u d i e s , concerning a s p e c i f i c problem, the experience of ot h e r s can be used to a s s i s t i n the process change d e c i s i o n . For example, the presence of sludge f l o a t i n g i n a c l a r i f i e r c o u l d have a number of p o t e n t i a l causes. However, combined with the i n f o r m a t i o n that the c o n d i t i o n i s c o i n c i d e n t a l with i n c r e a s e d l i q u i d temperature and pH, and that the sludge age i s i n excess of ten days, i n c r e a s e s the l i k e l i h o o d that d e n i t r i -f i c a t i o n i s r e s p o n s i b l e . V i s u a l o b s e r v a t i o n s of gas bubbles i n the c l a r i f i e r would support t h i s h y p o t h e s i s . With s u c c e s s f u l c o r r e c t i v e a c t i o n , subsequent o b s e r v a t i o n s of i n c r e a s i n g pH and high temperatures, with f l o a t i n g s o l i d s , c o u l d be more r e a d i l y i n t e r p r e t e d as signs of d e n i t r i f i c a t i o n , i n t r o d u c i n g .a memory component to the data i n t e r p r e t a t i o n and d e c i s i o n making p r o c e s s . 31 Bayesian d e c i s i o n theory c o u l d be used to e v a l u a t e o p e r a t i o n s changes under c o n d i t i o n s of u n c e r t a i n t y . For each p o s s i b l e d e c i -s i o n a l t e r n a t i v e , a l i k e l i h o o d of success can be estimated from i n f o r m a t i o n such as h i s t o r i c a l m o n i t o r i n g data, r e s e a r c h , r e p o r t s of s t u d i e s on s i m i l a r p rocess problems, and operator e x p e r i e n c e . The r e s u l t s of d e c i s i o n s can be used to modify the estimates of f u t u r e s u ccess, e s t a b l i s h i n g a pr o c e s s memory mechanism. The f o l l o w i n g s e c t i o n s d e s c r i b e two d e c i s i o n a n a l y s i s techniques which have found widespread use i n economic a n a l y s i s . Although there are no r e p o r t e d a p p l i c a t i o n s of these techniques t o a c t i v a t e d sludge process c o n t r o l , they are w e l l s u i t e d to making d e c i s i o n s under c o n d i t i o n s of u n c e r t a i n t y . 2.3.1 Bayesian D e c i s i o n Theory Bayesian s t a t i s t i c a l i n f e r e n c e d i f f e r s from " c l a s s i c a l " s t a t i s -t i c s , p r i m a r i l y i n i t s use of s u b j e c t i v e i n f o r m a t i o n or b e l i e f s i n a d d i t i o n t o o b j e c t i v e d a t a . Bayes' Theorem i s an a l g e b r a i c r e l a t i o n s h i p which al l o w s p r i o r p r o b a b i l i t i e s to be reused i n the l i g h t of new i n f o r m a t i o n t o o b t a i n p o s t e r i o r p r o b a b i l i t i e s . These p r i o r p r o b a b i l i t i e s can e i t h e r be o b j e c t i v e or s u b j e c t i v e . Bayesian Bayes' Theorem can be d e s c r i b e d as f o l l o w s : P(H/D) = P(D/H) x P(H) P(D) where; P(H/D) = p r o b a b i l i t y of hy p o t h e s i s (H) given p o s t e r i o r datum (D) 32 P(D/H) = p r o b a b i l i t y of datum (D) given p r i o r h y p o thesis (H) P(H) = p r o b a b i l i t y of h y p othesis P(D) = p r o b a b i l i t y of datum U s u a l l y P(D/H) i s r e l a t i v e l y o b j e c t i v e , whereas the p r i o r p r o b a b i l i t y P(H), f o r l a c k of b e t t e r i n f o r m a t i o n , o f t e n tends to be based on p e r s o n a l e x p e r i e n c e . P(D) i s c a l c u l a t e d as the nor-m a l i z e d sum of the product of p r i o r p r o b a b i l i t i e s and sample l i k e l i h o o d s . Where s u f f i c i e n t l y p r e c i s e i n f o r m a t i o n e x i s t s , i t tends to overwhelm the i n i t i a l o p i n i o n P(H); i n t h i s case, the p r i o r p r o b a b i l i t y assessment becomes l a r g e l y i r r e l e v e n t (Webber, 1973). Although Bayes' Theorem i s not used d i r e c t l y i n t h i s t h e s i s , the d e c i s i o n theory concepts i n v o l v i n g s u b j e c t i v e p r o b a b i l i t y and u t i l i t y e s t i m a t e s , which are o f t e n grouped under Bayesian d e c i s i o n theory, are used. Bayesian d e c i s i o n theory i s w e l l s u i t e d to a s s i s t i n making d e c i s i o n s under c o n d i t i o n s of u n c e r t a i n t y , with the c r i t e r i o n of s e l e c t i n g the d e c i s i o n which maximizes expected u t i l i t y . The expected u t i l i t y i s the sum of the products of estimated u t i l i t y v a l u e s of p o t e n t i a l outcomes or events and t h e i r p r o b a b i l i t i e s . In terms of a c t i v a t e d sludge process c o n t r o l , t h e r e are s e v e r a l components which must be d e f i n e d . A p r o b a b i l i s t i c r e l a t i o n s h i p between c o n t r o l and outcomes must be f i r s t determined through e i t h e r h i s t o r i c a l data or s u b j e c t i v e assessment. The u t i l i t y or v a l u e of each p o s s i b l e outcome must then be estimated. These u t i l i t y e s timates can be h i g h l y s u b j e c t i v e , r e f l e c t i n g the judge-33 merit or values of the operator, o p e r a t i o n s s u p e r v i s o r or design engineer making the estimate. For example, m a i n t a i n i n g e f f l u e n t suspended s o l i d s or biochemical oxygen demand c o n c e n t r a t i o n s w e l l below the permit requirements w i l l have a hig h e r energy c o s t than j u s t meeting the permit requirements. Although the lower e f f l u e n t c o n c e n t r a t i o n s may have a hi g h u t i l i t y to the p l a n t operator, the a s s o c i a t e d excess energy c o s t s may r e s u l t in a low u t i l i t y r a t i n g by the a d m i n i s t r a t o r . 2.3.2 Markov P r o b a b i l i t y Theory The Markov process i s a mathematical model which can be used to d e s c r i b e a process which can be c h a r a c t e r i z e d by a number of d i s c r e t e " s t a t e s " , with d e f i n e d p r o b a b i l i t i e s of changing from one s t a t e to another between s e q u e n t i a l time p e r i o d s . In a simple Markov process the p r o b a b i l i t y of a t r a n s i t i o n from s t a t e i to s t a t e j over the next time p e r i o d i s independent of p r e v i o u s s t a t e s . Consequently, a set of c o n d i t i o n a l p r o b a b i l i t i e s ( P^j) can be s p e c i f i e d , such that f o r the t r a n s i t i o n from s t a t e i i n one time p e r i o d to s t a t e j i n the next, N = 1 j = l as the system must be i n some s t a t e a f t e r the t r a n s i t i o n . 34 Formally, Lee et a l . (1977) suggest that a f i r s t order Markov p r o b a b i l i t y model can be a p p l i e d to s t o c h a s t i c processes with the f o l l o w i n g c h a r a c t e r i s t i c s : 1) a f i n i t e number of p o s s i b l e outcomes or s t a t e s e x i s t S. ( i = l , 2 , . . . r ) which a d i s c r e t e random v a r i a b l e X may take at a f i n i t e number of time p o i n t s (t=0,1,2...T). 2) the p r o b a b i l i t y d i s t r i b u t i o n of a t r i a l outcome i s dependent only upon the outcome of the immediately preceding t r i a l Pr (X /X , X 2,...) = Pr (X /X ) and t h i s f i r s t order dependence i s the same at a l l s t a ges. Pr (X f c|...) denotes the c o n d i t i o n a l p r o b a b i l i t y d e n s i t y f u n c t i o n f o r Xfc, and the p r o b a b i l i t y of an ordered set of sequences can be expressed as: P r ( X Q , X 1 ... ,X T) = P r ( X Q ) P r ^ | X Q) P r ( X 2 | X ) ( X 0 ) . . . which i n terms of the Markov process i s u s u a l l y given as: T P r ( X Q , X l f . . . , X T ) = P r ( X n ) Pr(X f c | X f c_ 1) t=1 in which the system i s d e s c r i b e d by the i n i t i a l p r o b a b i l i t y d i s t r i b u t i o n Pr(Xg) and the c o n d i t i o n a l p r o b a b i l i t i e s Pr(X f c | X f c _ 1 ) . By s u b s t i t u t i n g s t a t e c o n d i t i o n s f o r the random v a r i a b l e s , such that X t - 1 = and Xfc = S y then: N Pr(X f c = S j | V , = s i > = P i j ( t ) " Y> P i 3 f ° r 3 1 1 j = 1 P^j i s r e f e r r e d to as the constant t r a n s i t i o n p r o b a b i l i t y , which d e s c r i b e s changes between p a i r s of s t a t e s and has the f o l l o w i n g p r o p e r t i e s : 35 a) 0 <= P. . <= 1 1D b) Y] p i j = 1 for a l l i = 1,2. . . r By a r r a n g i n g the t r a n s i t i o n p r o b a b i l i t i e s i n t o a s e r i e s of m a t r i c e s , r e l a t i n g a l t e r n a t i v e a c t i o n s to s t a t e s , a t r a n s i t i o n p r o b a b i l i t y matr ix P i s formed. T h i s m a t r i x can be used to d e t e r m i n i n g the p r o b a b i l i t y d i s t r i b u t i o n for each random v a r i a b l e ( X f c ) , g iven the present s t a t e , or to determine the l i m i t i n g d i s t r i b u t i o n of X f c as t goes to i n f i n i t y , where such l i m i t s e x i s t . The t r a n s i t i o n m a t r i x p r o b a b i l i t i e s cannot be n e g a t i v e , cannot be g r e a t e r than the u n i t y , and the sum of the p r o b a b i l i t i e s in each row must be u n i t y . A s imple example of the Markov p r o c e s s i s where there are o n l y two s t a t e s , such as c o n d i t i o n s of n o n - b u l k i n g s ludge ( s t a t e 1) and b u l k i n g s ludge ( s t a t e 2 ) . G i v e n t h a t the proces s i s not b u l k i n g and i s i n the f i r s t s t a t e , the p r o b a b i l i t y tha t a f t e r one week the s ludge w i l l remain n o n - b u l k i n g might be 70 p e r c e n t , w i th the p r o b a b i l i t y of b u l k i n g b e i n g 30 p e r c e n t . When the system i s i n the second s t a t e , and i s b u l k i n g , the l i k e l i h o o d of c o r r e c t i n g i t to s t a t e 1 over the next week might be 10 p e r c e n t , w i th a consequent p r o b a b i l i t y of r emain ing i n s t a t e 2 of 90 p e r c e n t . The c o n d i t i o n a l p r o b a b i l i t i e s ( p j , j ) and the r e s u l t i n g t r a n s i t i o n a l m a t r i x are as f o l l o w s : 0.70 0.30 0.10 0.90 p l l • = 0. 70 P 12 = = 0. 30 P 21 ' = 0. 10 P _ = = 0. 90 36 T h i s matrix can now be used to estimate the p r o b a b i l i t y that the sludge w i l l be i n a non-bulking c o n d i t i o n a f t e r an n-week p e r i o d . A s t a t e p r o b a b i l i t y 7T^(n) can be d e f i n e d , d e s c r i b i n g the proba-b i l i t y that the s t a t e w i l l be i n c o n d i t i o n i a f t e r n weeks such t h a t : 7T(n) = 7T(0) P n n = 0,1,2 Using the t r a n s i t i o n a l matrix d e f i n e d above, the p r o b a b i l i t y that a non-bulking sludge w i l l remain non-bulking i n one week i s : T T U ) = 7T(0) P = [ 1 0 ] 0.7 0.3 0.1 0.9 = [ 0.7 0.3 ] A f t e r two weeks: TT(2) = 7T(1) P = [ 0.7 0.3 ] 0.7 0.1 0.3 0.9 = [ 0.52 0.48 ] or; 7T(n) = 7r(0) P l As n becomes very l a r g e , the long term p r o b a b i l i t y v e c t o r conver-ges to 26 percent p r o b a b i l i t y of non-bulking and 74 percent p r o b a b i l i t y of b u l k i n g , r e g a r d l e s s of the i n i t i a l s t a t e . When a process converges to a long term s t e a d y - s t a t e p r o b a b i l i t y , independent of the i n i t i a l c o n d i t i o n , i t i s r e f e r e d to as a completely e r g o d i c process (Howard, 1960). 37 For e r g o d i c Markov processes with rewards ( i . e . where there i s a "reward" a s s o c i a t e d with a t r a n s f e r from one s t a t e to another), the expected t o t a l reward depends upon the t o t a l number of t r a n s i t i o n s or i t e r a t i o n s that the system i s s u b j e c t e d t o , and the average gain per t r a n s i t i o n . The average gain i s (Howard, 1960): where: g = system gain or average r e t u r n per i t e r a t i o n TT i = l i m i t i n g s t a t e p r o b a b i l i t i e s q. = expected immediate r e t u r n i n s t a t e i P.. = t r a n s i t i o n p r o b a b i l i t i e s ( i e . p r o b a b i l i t y of ] going from s t a t e i to s t a t e j ) R. . = reward elements (reward or g a i n a s s o c i a t e d with •* going from s t a t e i to s t a t e j ) If i t i s p o s s i b l e to a f f e c t the p r o b a b i l i t i e s of t r a n s f e r i n g from one s t a t e to the next by t a k i n g some a c t i o n , then a " p o l i c y v e c t o r " can be determined which d e f i n e s an a c t i o n ( p o l i c y ) f o r each s t a t e which maximizes the g a i n . The o p t i m a l p o l i c y v e c t o r s p e c i f i e s the p o l i c y which r e s u l t s i n the l a r g e s t long-term average gain f o r the whole process. As noted by Howard ( i 9 6 0 ) , where a l a r g e number of p o t e n t i a l s t a t e s and p o l i c i e s e x i s t e d , i t would not be p r a c t i c a l to c a l c u l a t e the gain f o r each s t a t e / p o l i c y combination. F o r t u n a t e l y , he developed a p o l i c y -i t e r a t i o n method f o r c a l c u l a t i n g the o p t i m a l p o l i c y i n a small number of i t e r a t i o n s . The reader i s r e f e r r e d t o Howard's book f o r N i = 1 N j = 1 38 a d e t a i l e d d e s c r i p t i o n of the technique. 2.3.3 Summary D e c i s i o n a n a l y s i s techniques e x i s t which appear w e l l s u i t e d to s e l e c t i n g optimal c o n t r o l s t r a t e g i e s under c o n d i t i o n s of u n c e r t a i n t y . Although these techniques have not been p r e v i o u s l y a p p l i e d to the c o n t r o l of a c t i v a t e d sludge systems, they have been a p p l i e d to economic data a n a l y s i s with reasonable s u c c e s s . Economic data have many s i m i l a r c h a r a c t e r i s t i c s t o m o n i t o r i n g data, such as being i n f l u e n c e d by many unmonitored e x t e r n a l and i n t e r n a l parameters, and o f t e n being h i g h l y a u t o c o r r e l a t e d . The a b i l i t y of the Markov P o l i c y - I t e r a t i o n technique to f i n d an optimal p o l i c y , i n a small number of i t e r a t i o n s , i s an a p p e a l i n g f e a t u r e f o r an experimental c o n t r o l s t r a t e g y . The problem of c o n t r o l l i n g b u l k i n g i n a c t i v a t e d sludge wastewater treatment f a c i l i t i e s i s an good example of having to make d e c i -s i o n s under c o n d i t i o n s of u n c e r t a i n t y . D e s p i t e the i n t e n s i v e amount of a t t e n t i o n and r e s e a r c h that sludge b u l k i n g has r e c e i v e d i n recent y e a r s , r e l a t i v e l y l i t t l e i s known about the phenomena. The f o l l o w i n g s e c t i o n d e f i n e s the p r a c t i c a l problem and reviews p o s s i b l e c o n t r o l a l t e r n a t i v e s which have been r e p o r t e d i n the l i t e r a t u r e . 39 2.4 Sludge B u l k i n g Sludge b u l k i n g i s a c o n d i t i o n which a f f e c t s most a c t i v a t e d sludge treatment p l a n t s , r e s u l t i n g i n i t i a l l y i n good e f f l u e n t q u a l i t y , but g r a d u a l l y p r o g r e s s i n g to severe s o l i d s l o s s e s i n the p l a n t e f f l u e n t . There are two p r i n c i p a l causes of b u l k i n g sludge: (1) f i l a m e n t o u s b u l k i n g ; and (2) bound water i n the b a c t e r i a l f l o e , which reduces the f l o e d e n s i t y (Gaudy and Gaudy, 1980). Non-f i l a m e n t o u s b u l k i n g i s c o n s i d e r e d to be r a r e and a r e s u l t of d e f l o c c u l a t i o n , p i n - p o i n t f l o e or other s e t t l i n g problems (Tomlinson and Chambers, 1982). Filamentous b u l k i n g micro-organisms can be b a c t e r i a , algae or fungi (Sykes, 1979, Gaudy & Gaudy, 1980). Depending upon the environmental c o n d i t i o n s , bac-t e r i a l micro-organisms r e s p o n s i b l e f o r b u l k i n g sludge may have a f i l a m e n t o u s , p e l l e t or p i n - p o i n t f l o e form (Tanaka et a l . [1985). B u l k i n g sludge c o n d i t i o n s can be c r e a t e d by p h y s i c a l and chemical wastewater c h a r a c t e r i s t i c s , and i n c o r r e c t p l a n t o p e r a t i o n . P l a n t design l i m i t a t i o n s may a l s o r e s t r i c t the a b i l i t y to a d j u s t b u l k i n g c o n d i t i o n s (Sykes, 1979, Tomlinson & Chambers, 1984, G a r r e t J r . et a l . , 1984, Chudoba, 1985). G e n e r a l l y , sludge b u l k i n g c o n d i t i o n s are i d e n t i f i e d i n a t r e a t -ment p l a n t when the sludge volume index (SVI) v a l u e s exceed 150 mL/g, and i s most f r e q u e n t l y a s s o c i a t e d with an overgrowth of f i l a m e n t o u s microorganisms. There are over 30 v a r i e t i e s of algae, b a c t e r i a and f u n g i which can grow as f i l a m e n t s i n a c t i v a t e d sludge, and l i t t l e i n f o r m a t i o n i s a v a i l a b l e on the p l a n t charac-t e r i s t i c s l e a d i n g to overgrowth (Strom, 1984). Consequently, the 40 b u l k i n g c o n d i t i o n worsens u n t i l the p l a n t i s at r i s k of d i s c h a r -ging s o l i d s with the secondary e f f l u e n t ; at t h i s time the operator g e n e r a l l y t r e a t s the sludge with c h l o r i n e , or hydrogen per o x i d e , t o k i l l the filamentous micro-organisms and allow s e t t l i n g to resume. T h i s a c t i o n c o s t s money, r e s u l t s i n a t u r b i d e f f l u e n t and the d e s t r u c t i o n of n i t r i f y i n g organisms, and does nothing to e l i m i n a t e the problem or i d e n t i f y i t s cause. The f o l l o w i n g f i v e f i lamentous b u l k i n g c h a r a c t e r i s t i c s i n f l u e n c e the c o n t r o l s t r a t e g i e s (Chudoba, 1985, Chambers & Tomlinson, 1982, Tomlinson & Chambers, 1984): 1. Filamentous micro-organisms are present i n any a c t i v a t e d sludge. B u l k i n g problems appear when the f i l a m e n t s overgrow the f l o c - f o r m e r s . 2. Overgrowing of filamentous micro-organisms i n a c t i v a t e d sludge i s a f f e c t e d by a number of process c h a r a c t e r i s t i c s . 3. The micro-organism which accumulates most of the a v a i l a b l e s u b s t r a t e at the i n l e t of the a e r a t i o n system w i l l domi-nate, p r o v i d i n g the r e g e n e r a t i o n p e r i o d f o r the exhaustion of the accumulated s u b s t r a t e i s s u f f i c i e n t l y l o n g . 4. Filamentous micro-organisms i n a c t i v a t e d sludge are slow-growers. 5. F l o c - f o r m i n g micro-organisms i n a c t i v a t e d sludge are f a s t -growers . The problem of f i l a m e n t o u s sludge b u l k i n g has r e c e i v e d a con-s i d e r a b l e amount of i n t e r e s t i n recent y e a r s . Due to the exten-s i v e number of f i l a m e n t o u s organisms which have been i d e n t i f i e d as being r e s p o n s i b l e f o r filamentous b u l k i n g , the cause and remedial a c t i o n i s s i t e s p e c i f i c . Furthermore, i n s u f f i c i e n t r e s e a r c h has been undertaken to determine the c r i t i c a l c o n d i t i o n s 41 which c o n s i s t e n t l y promote the p r o l i f e r a t i o n of even the most common filamentous microorganism i n a mixed c u l t u r e s i t u a t i o n . Consequently, attempts to c o n t r o l filamentous b u l k i n g have r e c e n t l y been d i r e c t e d at i d e n t i f y i n g the dominant fil a m e n t present and c o r r e l a t i n g the process c o n d i t i o n s with other processes which have had problems with the same organism. While u s e f u l i n suggesting a probable cause, the l i t e r a t u r e i n d i c a t e s that the c o r r e l a t i o n s are not c o n s i s t e n t and process experimenta-t i o n must be undertaken to c o n t r o l the b u l k i n g . The f o l l o w i n g s e c t i o n s d e s c r i b e the method i n which filamentous sludge b u l k i n g i s most o f t e n monitored at a c t i v a t e d sludge p l a n t s , the c u r r e n t theory concerning the causes of b u l k i n g and c o n t r o l o p t i o n s based on that theory and e m p i r i c a l o b s e r v a t i o n s of b u l k i n g p l a n t s . 2.4.1 D e f i n i t i o n of B u l k i n g Sludge A " h e a l t h y " a c t i v a t e d sludge biomass r e q u i r e s the c o e x i s t e n c e of both f i l a m e n t o u s and f l o c - f o r m i n g microorganisms, r e s u l t i n g i n s t r o n g f l o e s with good s e t t l i n g and compaction c h a r a c t e r i s t i c s and a c l e a r e f f l u e n t . As these organisms have d i f f e r e n t growth r a t e s f o r given s u b s t r a t e and d i s s o l v e d oxygen c o n c e n t r a t i o n s , t h e i r s t a b l e c o e x i s t e n c e r e q u i r e s that t h e i r average net growth r a t e be e q u a l . Sezgin et a l . (1978) and Lau et a l . (1984 a,b) have proposed that t h i s balance i s maintained by the s i z e of the z o o g l e a l mass and the d i f f u s i o n c h a r a c t e r i s t i c s f o r the t r a n s p o r t of s u b s t r a t e and oxygen to the c e n t e r of the f l o e . While the f i l a m e n t s may have an advantage and higher growth r a t e s i n the 42 b u l k s o l u t i o n , c o m p a r e d t o t h e f l o c - f o r m e r s , t h e l o w e r c o n c e n t r a -t i o n s w i t h i n t h e b i o m a s s r e d u c e s t h e i r n e t g r o w t h r a t e s . F u r -t h e r , t h e r e i s e v i d e n c e t h a t t h e b u l k s o l u t i o n s u b s t r a t e c o n c e n -t r a t i o n may a l t e r t h e s p e c i f i c g r o w t h r a t e , s u c h t h a t t h e f i l a -m e n t o u s m i c r o o r g a n i s m s may e x c e e d t h e f l o c - f o r m e r s g r o w t h r a t e f o r l o w s u b s t r a t e c o n c e n t r a t i o n s ( P a l m e t a l . , 1 9 8 0 ) . I t s h o u l d be n o t e d t h a t t h e m a j o r i t y o f p u r e a n d d u a l c u l t u r e w o r k s u p p o r t i n g t h i s h y p o t h e s i s ( S e z g i n e t a l . , 1 9 7 8 , P a l m e t a l . , 1980 a n d L a u e t a l . , 1 9 8 4 ) , h a v e e x a m i n e d o n l y one f i l a m e n t , S p h a e r o t i l u s n a t a n s . E i k e l b o o m ( 1 9 8 2 ) , a n d S t r o m a n d J e n k i n s ( 1 9 8 4 ) n o t e t h a t t h e r e a r e o v e r 30 d i f f e r e n t t y p e s o f f i l a m e n t o u s m i c r o o r g a n i s m s w h i c h h a v e b e e n i s o l a t e d i n b u l k i n g s l u d g e . C o n s e q u e n t l y , i t i s n o t s u p r i s i n g t h a t f i l a m e n t o u s o v e r g r o w t h c a n o c c u r a t a v a r i e t y o f d i s s o l v e d o x y g e n c o n c e n t r a t i o n s a n d s u b s t r a t e l o a d i n g r a t e s . R e s e a r c h u n d e r t a k e n b y S e z g i n e t a l . ( 1 9 7 8 ) , P i p e s ( 1 9 7 9 ) a n d P a l m e t a l . ( 1 9 8 0 ) , e s t a b l i s h i n g t h e r o l e o f f i l a m e n t o u s m i c r o -o r g a n i s m s i n s l u d g e b u l k i n g , s u g g e s t s t h a t t h e p r o p o r t i o n o f f i l a m e n t o u s v e r s u s f l o c - f o r m i n g m i c r o o r g a n i s m s c o u l d be d e t e r -m i n e d by t h e c o n c e n t r a t i o n o f d i s s o l v e d o x y g e n a n d t h e s u b s t r a t e l o a d i n g r a t e . S u b s e q u e n t w o r k b y E i k e l b o o m ( 1 9 7 5 ) , ( 1 9 7 7 ) a n d R i c h a r d e t a l . ( 1 9 8 2 ) i d e n t i f i e d a p p r o x i m a t e l y 26 m o r p h o l o g i c a l t y p e s o f f i l a m e n t o u s o r g a n i s m s i n v a r i o u s b u l k i n g s l u d g e , a l a r g e p r o p o r t i o n o f w h i c h r e m a i n unnamed a n d a r e r e f e r r e d t o by t y p e n u m b e r s . 43 With the e x c e p t i o n of a few f i l a m e n t s such as Type 1701 (Richard et a l . , 1985, Lau et a l . , 1980 and Hao et a l . , 1982), the growth c h a r a c t e r i s t i c s of most i d e n t i f i e d f i l a m e n t s remain l a r g e l y undetermined. Research i n t o growth c h a r a c t e r i s t i c s has been l i m i t e d to chemostatic experiments of s i n g l e or dual ( f i l a m e n t and f l o c - f o r m i n g ) c u l t u r e s of a very few microorganisms. The r e s u l t s of these pure c u l t u r e t e s t s are d i f f i c u l t to apply to a c t i v a t e d sludge b u l k i n g c o n t r o l , due to the complex micro-organism and s u b s t r a t e composition of wastewater treatment f a c i l i t i e s . Consequently, r e s e a r c h on b u l k i n g c o n t r o l has attempted to c o r r e l a t e the e x c e s s i v e f i l a m e n t o u s organism growth with a s s o c i a t e d wastewater c h a r a c t e r i s t i c s and o p e r a t i n g c o n d i t i o n s (Tomlinson and Chambers, 1982, Strom and J e n k i n s , 1984, R i c h a r d et a l . [1985). 2.4.2 Sludge Volume Index (SVI) as a Measure of B u l k i n g Sludge A c t i v a t e d sludge which s e t t l e s and compacts p o o r l y i s g e n e r a l l y r e f e r r e d t o as a " b u l k i n g sludge". C o n v e n t i o n a l l y , the s e t t l e -a b i l i t y and c o m p a c t a b i l i t y of the sludge i s determined through use of the SVI c a l c u l a t i o n , with SVI v a l u e s g r e a t e r than 150 mL/g g e n e r a l l y c o n s i d e r e d to be a b u l k i n g sludge (Palm et a l . , 1980, Strom and J e n k i n s , 1984). Conversely, SVI v a l u e s l e s s than 70 mL/g can produce a " p i n - p o i n t " f l o e which may r e s u l t i n high e f f l u e n t t u r b i d i t y . As the SVI c a l c u l a t i o n i s based on both the mixed l i q u o r suspended s o l i d s c o n c e n t r a t i o n and the r a t e of s e t t l i n g the " i d e a l " SVI to produce a c l e a r e f f l u e n t may vary from p l a n t t o p l a n t . 44 The sludge volume index (SVI) was o r i g i n a l l y proposed as a quan-t i t a t i v e measure of b u l k i n g by Pearse (1937). I t i s a measure of how w e l l the aerated mixed l i q u o r sludge s e t t l e s and compacts; c a l c u l a t e d as the volume occupied by one l i t r e of sludge a f t e r 30 minutes of s e t t l i n g (SV30), d i v i d e d by the mixed l i q u o r suspended s o l i d s c o n c e n t r a t i o n (MLSS). SVI (mL/g) = SV30 (mL/L) MLSS (g/L) SVI v a l u e s are d i f f i c u l t to compare between p l a n t s , as they are dependent upon the i n i t i a l MLSS c o n c e n t r a t i o n s and the c o n d i t i o n s of the t e s t (Dick and V e s i l i n d (1969), with higher mixed l i q u o r s o l i d s c o n c e n t r a t i o n s g e n e r a l l y r e s u l t i n g i n lower SVI v a l u e s . Pipes (1979) has d e s c r i b e d the SVI measurement as an o p e r a t i o n a l parameter, as opposed to a s c i e n t i f i c parameter which has the requirement of v a l i d i t y and r e p r o d u c i b i l i t y . D e s p i t e these d i f f i -c u l t i e s , i t i s the most common measure of sludge s e t t l e a b i l i t y , due to i t s s i m p l i c i t y and u t i l i t y i n monitoring changes i n the biomass w i t h i n a given p l a n t . Although MLSS c o n c e n t r a t i o n s may vary between treatment p l a n t s , u n l e s s severe s o l i d s l o s s e s occur, the MLSS c o n c e n t r a t i o n w i t h i n a given p l a n t does not vary g r e a t l y between sampling p e r i o d s . Sezgin et a l . (1978), Palm et a l . (1980) and Lau et a l . (1984a, 1984b) have demonstrated that the SVI measurement i s r e l a t e d to f i l a m e n t l e n g t h i n the a c t i v a t e d sludge. Chudoba et a l . (1973) 45 found that the number of f i l a m e n t s present was d i r e c t l y r e l a t e d to SVI. These f i l a m e n t s , when extended beyond the f l o e mass, enmesh and prevent the f l o e p a r t i c l e s from compacting and i n c r e a -s i n g d e n s i t y . 2.4.3 Inf l u e n c e of Sludge B u l k i n g on E f f l u e n t Suspended S o l i d s Although b u l k i n g sludge s e t t l e s s l o w l y and has poor t h i c k e n i n g c h a r a c t e r i s t i c s , the e f f l u e n t suspended s o l i d s q u a l i t y i s u s u a l l y high, as long as the sludge mass or blanket i s not escaping over the secondary c l a r i f i e r w e i r s . The extent of sludge b u l k i n g and the design of the secondary c l a r i f i e r s determines the e f f e c t s of b u l k i n g on secondary e f f l u e n t suspended s o l i d s q u a l i t y . Where the secondary c l a r i f i e r s are over designed or o p e r a t i n g below design c a p a c i t y , a b u l k i n g sludge may be t o l e r a t e d f o r extended p e r i o d s of time. As noted by Tomlinson (1982), the b u l k i n g sludge can a c t as blanket c l a r i -f i e r , f i l t e r i n g the e f f l u e n t before d i s c h a r g e . However, i f such c o n d i t i o n s are allowed to c o n t i n u e and the s o l i d s h a n d l i n g c a p a c i t y i s exceeded, the b u l k i n g sludge w i l l r i s e i n the c l a r i -f i e r u n t i l i t passes over the weirs and i s d i s c h a r g e d . As most small treatment p l a n t s are not monitored f o r e x t e n s i v e p e r i o d s of time, such as long weekends, e x t e n s i v e l o s s e s of a c t i v a t e d sludge may occur, l e a d i n g to a r e d u c t i o n i n sludge age and e f f l u e n t q u a l i t y . A study of 65 p l a n t s i n the U.K. noted t h a t 27 p l a n t s with h i g h SVI v a l u e s were not e x h i b i t i n g s o l i d s l o s s e s (Tomlinson, 1982). An examination of these p l a n t s r e v e a l e d that 46 the s o l i d s l o s s e s were avoided because of an abnormally high s e t t l i n g tank c a p a c i t y or because the p l a n t s were operated at very low c o n c e n t r a t i o n s of mixed l i q u o r suspended s o l i d s . 2.4.4 Filamentous Microorganisms Eikelboom (1975, 1977) has developed a method f o r c l a s s i f y i n g the types of filamentous b a c t e r i a found i n a c t i v a t e d sludges, based on s i z e , morphology, and s t a i n i n g t e c hniques. I d e n t i f i c a t i o n of filamentous types, and r e s e a r c h i n t o growth c h a r a c t e r i s t i c s and environmental c o n d i t i o n s promoting growth of f i l a m e n t s , has the p o t e n t i a l to i d e n t i f y i n g s o l u t i o n s to b u l k i n g problems through the i d e n t i f i c a t i o n of the filamentous microorganism r e s p o n s i b l e (Eikelboom 1977, Strom and J e n k i n s 1981). As some filam e n t o u s s t r u c t u r e i s r e q u i r e d to maintain a w e l l s t r u c t u r e d b i o l o g i c a l f l o e (Sezgin et a l . , 1978, Lau et a l . , 1984), i t i s not s u p r i s i n g t h at f i l a m e n t s have been observed f o r a wide range of e n v i -ronmental c o n d i t i o n s and a c t i v a t e d sludge p r o c e s s c o n f i g u r a t i o n s . R i c h a r d et a l . (1982) examined b u l k i n g sludge from 90 a c t i v a t e d sludge f a c i l i t i e s i n the U.S. and i d e n t i f i e d the c a u s a t i v e f i l a -mentous organism and a s s o c i a t e d process c o n d i t i o n s . Of p a r t i c u l a r i n t e r e s t i s the l a r g e percentage of organisms a s s o c i a t e d with e i t h e r low F/M or low DO c a u s a t i v e c o n d i t i o n s . The organism S p h a e r o t i l u s natans, which has been the s u b j e c t of most of the pure c u l t u r e r e s e a r c h work on filamentous microorganism growth, was the predominant f i l a m e n t i n only 7% of the cases and ranked 47 7th i n terms of frequency of occurrence. Type 1701 was the most frequent cause of sludge b u l k i n g (33%) i n the 1982 survey. Chemostat s t u d i e s of Type 1701 and a f l o c - f o r m e r r e s u l t e d i n balanced growth at a DO of 0.06 mg/L and d i l u t i o n r a t e of 1.5 day 1 , with dominant f l o c - f o r m e r growth and f i l a m e n t o u s growth at higher and lower DO c o n c e n t r a t i o n s r e s p e c t i v e l y . I t was suggested that Type 1701 may undergo e x c e s s i v e growth under more severe DO d e f i c i e n c y c o n d i t i o n s than S p h a e r o t i l u s natans. Dominance of e i t h e r Type 1701 or the f l o c - f o r m e r w i t h i n one to two mean c e l l r e t e n t i o n times c o u l d be achieved by changes i n DO c o n c e n t r a t i o n . In comparison, Lau et a l . (1980) noted that dominance took from two to seven mean c e l l r e t e n t i o n times f o r a dual c u l t u r e of S p h a e r o t i l u s natans and a f l o c - f o r m e r . Of 315 a c t i v a t e d sludge p l a n t s examined i n Germany, 45 percent e x h i b i t e d e x t e n s i v e filamentous growth (Wagner, 1982). U n l i k e the f i n d i n g s of Strom and J e n k i n s (1984), Type 1701 was not the most f r e q u e n t l y o c c u r r i n g f i l a m e n t , o c c u r r i n g i n only 3.4 percent of the cases and ranking e i g h t h . S p h a e r o t i l u s natans, which has been e x t e n s i v e l y s t u d i e d i n North America, o c c u r r e d i n only 9 percent of the cases. However, most of the b u l k i n g cases o c c u r r e d with a c t i v a t e d sludge p l a n t s t r e a t i n g i n d u s t r i a l waste such as paper, milk, v e g e t a b l e and f r u i t p r o c e s s i n g , l e a t h e r and glue, wine making and d i s t i l l e r i e s . The s p e c i f i c m o r p h o l o g i c a l c h a r a c t e r i s t i c s and i d e n t i f i c a t i o n c h a r a c t e r i s t i c s are beyond the scope of t h i s t h e s i s . The t e c h -niques, as presented i n Eikelboom (1975)(1978) and Strom and 48 J e n k i n s (1984), are too complicated f o r most a c t i v a t e d sludge f a c i l i t y o p e r a t o r s . S e v e r a l of the filamentous types i d e n t i f i e d may have more than one s p e c i e s , and may have more than one growth form (Lau et a l . , 1984). Although gram s t a i n i n g i s one of the m o r p h o l o g i c a l i d e n t i f i c a t i o n procedures used by Eikelboom (1975, 1978) i t has been found that a given f i l a m e n t can be i d e n t i f i e d as e i t h e r gram p o s i t i v e or n e g a t i v e , depending on the age and the form of the f i l a m e n t (Tomlinson and Chambers, 1982). T h i s i n c o n s i s t e n c y makes i d e n t i f i c a t i o n much more s u b j e c t i v e and dependent upon the experience of the t e c h n i c i a n performing the t e s t s . Consequently, the i d e n t i f i c a t i o n procedures would not l i k e l y be s u i t a b l e f o r most wastewater treatment p l a n t o p e r a t o r s . 2.4.5 Filamentous B u l k i n g C o n t r o l S t r a t e g i e s The c o n t r o l of sludge b u l k i n g has been l a r g e l y undertaken, i n the past, by o p e r a t i o n s personnel on a t r i a l and e r r o r b a s i s . V a r i o u s p l a n t c o n d i t i o n s i n c l u d i n g low and high DO c o n c e n t r a t i o n s and s u b s t r a t e l o a d i n g s , s e p t i c wastewater, n u t r i e n t d e f i c i e n c i e s , metal l o a d i n g s , process c o n f i g u r a t i o n s and wastewater types have been i m p l i c a t e d as causes f o r sludge b u l k i n g . Operators o f t e n r e v e r t to a p p l y i n g a t o x i c c h e m i c a l , such as c h l o r i n e or hydrogen perox i d e , which reduces the filamentous p o p u l a t i o n at the c o s t of a l s o d e s t r o y i n g the n i t r i f y i n g microorganisms present and r e s u l t i n g i n a t u r b i d e f f l u e n t f o r a p e r i o d of time. Where c h r o n i c b u l k i n g occurs and the h y d r a u l i c c a p a c i t y of the secondary c l a r i f i e r s i s near i t s design v a l u e , c h l o r i n e a d d i t i o n 4 9 may be p r a c t i s e d on a c o n t i n u a l b a s i s t o c o n t r o l f i l a m e n t s . T h i s may r e s u l t i n r e d u c e d p r o c e s s e f f i c i e n c y a n d c o n s i d e r a b l e c h l o r i n e c o s t . A s s u m m a r i z e d by C h i e s a a n d I r v i n e ( 1 9 8 5 ) t h e r e a r e a v a r i e t y o f r e p o r t e d c a u s e s f o r f i l a m e n t o u s b u l k i n g : 1 . l o w a e r a t i o n b a s i n DO c o n c e n t r a t i o n s 2 . h i g h a e r a t i o n b a s i n DO c o n c e n t r a t i o n s 3 . l o w o r g a n i c l o a d i n g r a t e s 4 . h i g h o r g a n i c l o a d i n g r a t e s 5 . c o m p l e t l y m i x e d r e a c t o r c o n f i g u r a t i o n s 6 . c o n v e n t i o n a l p l u g f l o w r e a c t o r c o n f i g u r a t i o n s 7 . i n s u f f i c i e n t m i c r o n u t r i e n t c o n c e n t r a t i o n s 8 . h i g h m e t a l c o n c e n t r a t i o n s 9 . l o w pH 1 0 . e l e v a t e d s u l p h i d e c o n c e n t r a t i o n s 1 1 . l o w n i t r o g e n o r p h o s p h o r u s c o n c e n t r a t i o n s 1 2 . o v e r g r a z i n g by p r o t o z o a T h e t w o m o s t c o m m o n l y a s s o c i a t e d c a u s e s o f f i l a m e n t o u s b u l k i n g a r e l o w / h i g h d i s s o l v e d o x y g e n c o n c e n t r a t i o n s a n d l o w / h i g h o r g a n i c l o a d i n g r a t e s ( S t r o m a n d J e n k i n s , 1 9 8 4 ) . T h e o b v i o u s l y w i d e r a n g e o f c o n d i t o n s u n d e r w h i c h b u l k i n g h a s b e e n o b s e r v e d h a s b e e n a t t r i b u t e d t o t h e o v e r 30 d i f f e r e n t t y p e s o f f i l a m e n t o u s m i c r o -o r g a n i s m s i s o l a t e d i n b u l k i n g s l u d g e s u n d e r v a r y i n g c o n d i t i o n s ( E i k e l b o o m 1 9 8 2 , S t r o m a n d J e n k i n s 1 9 8 4 ) . H o w e v e r , t h e r e i s e v i d e n c e t h a t a s i n g l e e n v i r o n m e n t a l c h a r a c t e r i s t i c o r p a r a m e t e r 50 may be r e s p o n s i b l e f o r the p r o l i f e r a t i o n of a p a r t i c u l a r f i l a m e n -tous organism. As expressed by Chiesa and I r v i n e (1985), filam e n t o u s organisms can t h r i v e on the su b s t r a t e a v a i l a b l e at almost any treatment p l a n t , and unless c o n d i t i o n s favour f l o c -forming microorganisms over the f i l a m e n t s , b u l k i n g w i l l e v e n t u a l l y occur. For example, Pipes (1979) repo r t e d that the same f i v e f i l a m e n t s were noted f o r both high and low F/M b u l k i n g c o n d i t i o n s , i n c l u d i n g the common filam e n t S p h a e r o t i l u s natans. Palm et a l . (1980) induced the p r o l i f e r a t i o n of S p h a e r o t i l u s  natans by v a r y i n g the s u b s t r a t e l o a d i n g r a t e at a f i x e d DO c o n c e n t r a t i o n . I t has been proposed by s e v e r a l r e s e a r c h e r s (Eikelboom, 1982, Je n k i n s , 1982, Strom and J e n k i n s , 1984) that the i d e n t i f i c a t i o n and i s o l a t i o n of the predominant fil a m e n t be used to determine the cause of b u l k i n g . However, the c o r r e l a t i o n s between f i l a m e n t types and c a u s a l c o n d i t i o n s are too few and too c o n t r a d i c t a r y t o be r e l i e d upon a t t h i s time. What i s r e q u i r e d i s a method of experimentation t o determine the c o n t r o l s t r a t e g y which u t i l i z e s o p e rator experience and p l a n t o p e r a t i o n data ( h i s t o r y ) , and can i n c o r p o r a t e incomplete expert knowledge of c a u s a l i t i e s . 2 .4.5.1 DO E f f e c t s on B u l k i n g Sezgin et a l . (1978) p o s t u l a t e d that the growth l i m i t i n g c o n d i -t i o n s of filam e n t o u s and f l o c - f o r m i n g b a c t e r i a are s u f f i c i e n t l y d i f f e r e n t t h a t , for. low bulk DO c o n c e n t r a t i o n s , the filamentous 51 microorganisms grow more rapidly. Conversely, at high DO concen-trations the reverse i s true. B a s i c a l l y , low DO concentrations were hypothesized to result in comparatively advantageous growth conditions for the filamentous organisms, res u l t i n g in large sludge floes and consequently lower dissolved oxygen concentra-tions within the floe mass. These lower DO concentrations would then reinforce the filamentous bulking condition. Conversely, high DO concentrations were believed to be of advantage to the floc-forming bacteria, r e s u l t i n g in fewer filaments and conse-quently, smaller floes and higher DO concentrations within the f l o e . Taken to an extreme, i t was believed by the authors that extremely high DO concentrations would eventually lead to "pin-point" f l o e , with no filaments. To support their hypothesis Sezgin et a l . (1978) referenced several studies on Sphaerotilus  natans, which indicated that the organism grew better than the remaining mixed cultures at low DO concentrations. With the exception of two references for Arthobacter globiformis, a l l supporting l i t e r a t u r e was for Sphaerotilus natans studies. The experimental results reported by Sezgin et a l . (1978), which confirmed the low DO bulking phenomena, tentatively i d e n t i f i e d the filamentous organisms as Sphaerotilus natans, although no de t a i l e d microbiological examination and i d e n t i f i c a t i o n was reported. Filamentous organisms were reported present over the entire range of DO l e v e l s tested (0.7 to > 20 mg/L). The experi-ments undertaken by Sezgin et a l . (1978) were at a low substrate uptake rate of 0.33 to 0.37 g COD/g VSS day and they compared bulk DO concentrations of 6.3 to 1.8 mg/L and 6.7 to 8.0 mg/L. Increased substrate lev e l s were suggested by the authors to 52 l i k e l y i n c r e a s e the DO consumption and consequently lower the DO c o n c e n t r a t i o n s w i t h i n the f l o e , r e s u l t i n g i n favourable c o n d i t i o n s f o r filamentous p r o l i f e r a t i o n . Lau et a l . (1984 b) noted that under c o n d i t i o n s of low DO and s u b s t r a t e c o n c e n t r a t i o n s c e r t a i n f i l a m e n t s , such as S. natans, may have growth r a t e s which exceed those of the f l o e forming b a c t e r i a . Once the f i l a m e n t has grown beyond the c o n f i n e s of the f l o e , the much higher s u b s t r a t e and DO c o n d i t i o n s i n the bulk s o l u t i o n would r e s u l t i n an even higher growth r a t e than the f l o e volume-averaged r a t e . The authors s p e c u l a t e d that t h i s may be a p a r t i a l reason f o r the o b s e r v a t i o n that much higher DO con c e n t r a -t i o n s were r e q u i r e d to cure low DO b u l k i n g than to prevent i t . Lau et a l . , 1984) determined the h a l f s a t u r a t i o n c o e f f i c i e n t f o r S p h a e r o t i l u s natans and C i t r o b a c t e r ( f l o e former) grown i n pure c u l t u r e s under s i m i l a r continuous feed c o n d i t i o n s as shown below: S p h a e r o t i l u s natans K l (glucose) = 10 mg/L K2 (DO) = 0.0. mg/L C i t r o b a c t e r K l (glucose) = 5 mg/L K2 (DO) = 0.15 mg/L u = 6.5 day -1 u = 9.2 day -1 Dual c u l t u r e experiments confirmed that S. natans predominated at low DO with low moderate organic l o a d i n g , while C i t r o b a c t e r dominated at high DO or hig h organic l o a d i n g . However, t h i s r e l a t i o n s h i p was not c o n s i s t e n t f o r a l l experiments. The authors suggest t h a t once an organism i s w e l l e s t a b l i s h e d , i t m o d i f i e s 53 the environmental c o n d i t i o n s to favour i t s e l f over other organisms. S i m i l a r l y , Hao (1983) eva l u a t e d the h a l f - s a t u r a t i o n c o e f f i c i e n t s f o r S p h a e r o t i l u s natans and a f l o c - f o r m i n g organism, e s t a b l i s h i n g that the f i l a m e n t s can outgrow the f l o e formers at low DO c o n c e n t r a t i o n s . Palm et a l . (1980) i n v e s t i g a t e d the r e l a t i o n s h i p between sub-s t r a t e removal r a t e s , d i s s o l v e d oxygen c o n c e n t r a t i o n and the sludge volume index. The authors demonstrated t h a t f o r Sphaero- t i l u s sp., i n c r e a s e d s u b s t r a t e removal r a t e s r e q u i r e i n c r e a s e d bulk oxygen l e v e l s to maintain a non-bulking sludge. The r e l a t i o n s h i p between DO and s u b s t r a t e removal r a t e s , f o r b u l k i n g and non-bulking sludge e s t a b l i s h e d i n t h i s study, i s i l l u s t r a t e d i n F i g u r e 1. The l i n e shown i n F i g u r e 1 has been s h i f t e d 0.5 mg/L DO to the r i g h t from the r e s e a r c h f i n d i n g s , as a f a c t o r of s a f e t y f o r o p e r a t i o n s . I f the s u b s t r a t e l o a d i n g r e s u l t s i n a b u l k i n g c o n d i t i o n , the DO can be i n c r e a s e d to "cure" the b u l k i n g . Reduc-t i o n s of as l i t t l e as 0.5 mg/L d i s s o l v e d oxygen were s u f f i c i e n t to induce b u l k i n g as compared t o a c o n t r o l r e a c t o r . The f i l a m e n -tous p o p u l a t i o n c o u l d be reduced by i n c r e a s i n g the d i s s o l v e d oxygen c o n c e n t r a t i o n by a s i m i l a r amount. S l i g h t r e d u c t i o n s i n d i s s o l v e d oxygen ( i n the order of 0.5 mg/L) were observed to take up t o ten mean c e l l r e t e n t i o n s to f u l l y e s t a b l i s h a s t a b l e f i l a m e n t o u s p o p u l a t i o n and a b u l k i n g sludge. Where a l a r g e i n c r e a s e i n DO was made ( i n the order of 2 mg/L), the time f o r recovery ranged from one t o three mean c e l l r e t e n -t i o n times. 54 F i g u r e 1. R e l a t i o n s h i p Between Substrate Removal Rate and  A e r a t i o n Basin D i s s o l v e d Oxygen f o r an MLSS of 1100  mg/L ( A f t e r Palm et a l . , 1980) i I 1 1 1 1 1 0 10 2.0 3.0 4.0 5.0 6J0 AERATION BASIN DO, mg/1 In s t u d i e s with a dual mixed c u l t u r e system of Pseudomonas sp. and S p h a e r o t i l u s sp., Tanaka et a l . (1985) noted that changes i n DO l e v e l s can r e s u l t i n t r a n s f o r m a t i o n s i n growth form. The filamentous b a c t e r i a are r e p o r t e d to have three growth form types: filamentous, p e l l e t and d i s p e r s e d form. The f l o e former has two growth forms: f l o c c u l a n t and d i s p e r s e d . The types of growth forms f o r both organisms were observed to be r e v e r s i b l e by a l t e r i n g the DO l e v e l . S l i g h t r e d u c t i o n s i n DO l e v e l induced filamentous b u l k i n g on a gradual b a s i s , whereas more r a p i d reduc-t i o n s i n DO induced sludge b u l k i n g more r a p i d l y . Of p a r t i c u l a r note i s that the mixed c u l t u r e s had b e t t e r s e t t l i n g c h a r a c t e r -i s t i c s than pure c u l t u r e s f o r the same environmental c o n d i t i o n s . 55 D i s s o l v e d oxygen c o n c e n t r a t i o n s w i t h i n the a e r a t i o n basin have a l s o been a s s o c i a t e d with e f f l u e n t suspended s o l i d s . Using a food-to-microorganism r a t i o of 0.3 kg BOD/mg MLVSS day, i n f l u e n t s u b s t r a t e and suspended s o l i d s c o n c e n t r a t i o n s of 150 mg/L and a s i x hour h y d r a u l i c r e t e n t i o n time, Starkey and Karr (1984) were abl e to demontrate a r e l a t i o n s h i p between DO c o n c e n t r a t i o n and e f f l u e n t t u r b i d i t y . By d e c r e a s i n g DO c o n c e n t r a t i o n s from 5 to 0.4 mg/L, the authors were able to i n c r e a s e the e f f l u e n t t u r b i d i t y from 7 to 130 NTU over a p e r i o d of 50 hours. Subse-q u e n t l y , i n c r e a s i n g the DO r e s u l t e d i n a r e d u c t i o n to c o n t r o l t u r b i d i t y l e v e l s w i t h i n 20 hours. No changes i n SVI or i n c r e a s e d f i l a m e n t o u s p o p u l a t i o n s were noted d u r i n g any of the low DO experiments, p o s s i b l y due to the short d u r a t i o n of the t e s t s ( l e s s than 90 h o u r s ) . The changes i n t u r b i d i t y l e v e l were a t t r i b u t e d to a l t e r e d e x o c e l l u l a r polymer p r o d u c t i o n . 2.4.5.2 Organic Loading E f f e c t s on B u l k i n g The r e l a t i o n s h i p between SVI and organic l o a d i n g has long been in d i s p u t e . Logun and Budd (1956) reported that the F/M r a t i o s above or below the range of 0.22 to 0.48 kg BOD/kg MLVSS day tended to r e s u l t i n i n c r e a s e d SVI v a l u e s . S i m i l a r r e s u l t s were subsequently r e p o r t e d by Ford and Eckenfelder (1967), based on l a b o r a t o r y and p i l o t s c a l e r e s e a r c h . F o l l o w i n g t h i s work G a n c z a r c z i j k (1970) and Rensink (1974) r e p o r t e d r e s u l t s which i n d i c a t e d t h a t sludge b u l k i n g c o u l d occur f o r a l l F/M r a t i o s . 56 Some authors (Tomlinson, 1976, Chudoba et a l . , 1973a, 1973b, 1974) suggest that b u l k i n g at low F/M r a t i o s i s caused by low s u b s t r a t e c o n c e n t r a t i o n s , whereas b u l k i n g at higher F/M r a t i o s i s due to low bulk d i s s o l v e d oxygen c o n c e n t r a t i o n s . They a l s o suggest t h a t the type of f i l a m e n t o u s organisms r e s p o n s i b l e f o r b u l k i n g are d i f f e r e n t f o r s p e c i f i c F/M r a t i o s . Other r e s e a r c h e r s , such as Pipes (1979) maintain that b u l k i n g i s p r i m a r i l y a phenomena of low o r g a n i c l o a d i n g . Sezgin et a l . (1978) attempted t o e x p l a i n the r e l a t i o n s h i p between s u b s t r a t e l o a d i n g and i n c r e a s e d SVI i n terms of the sludge s t r u c t u r e and microorganism composition. They noted that the d i f f u s i o n of DO and s u b s t r a t e t o the c e n t e r of the f l o e r e s u l t e d i n c o n c e n t r a t i o n s w i t h i n the f l o e being lower than i n the bulk media. Examining the SVI and F/M r a t i o s from 29 p l a n t s i n the U.S., Pipes (1979) noted that there appeared to be lower SVI values f o r p l a n t s o p e r a t i n g i n the 0.25 to 0.4 kg BOD/kg MLVSS day, F/M range. However, the few p l a n t s with F/M r a t i o s i n t h i s range were l a r g e r and were operated by more experienced p e r s o n n e l . As l a r g e r f a c i l i t i e s tend to be more s t a b l e and experienced o p e r a t i n g personnel are more l i k e l y t o be a b l e to c o n t r o l the p r o c e s s , the data i n t h i s F/M range may have been b i a s e d . The h i g h e s t SVI v a l u e s o c c u r r e d at the lowest F/M range of 0.01 t o 0.1 kg BOD/kg MLVSS day. Processes which produced sludge with a p i n - p o i n t f l o e had the lowest SVI v a l u e s (<100), while processes which had a tendency to bulk d i d not produce a p i n - p o i n t f l o e . 57 Pipes (1979) a l s o noted that a v a r i e t y of filamentous organisms, such as B a c i l l u s Sp., S p h a e r o t i l u s Sp., Beqqiatoa Sp., A r t h r o b a c t e r Sp. and B r e v i b a c t e r i a Sp., were present i n both h i g h and low F/M b u l k i n g sludges. In support of the hypothesis that i n d i v i d u a l filamentous s p e c i e s have s p e c i f i c F/M r a t i o s growth ranges, Pipes suggested that the presence of low F/M f i l a m e n t s , under high F/M c o n d i t i o n s , were l i k e l y due to e x c e s s i v e s o l i d s l o s s d u r i n g low F/M b u l k i n g . Subsequent work by Palm et a l . (1980) proposed t h a t the s u b s t r a t e t r a n s p o r t i n t o the f l o e c o n t r o l l e d the c o n c e n t r a t i o n of s u b s t r a t e w i t h i n the f l o e , and consequently a l t e r e d the growth r a t e of the filamentous and f l o c - f o r m i n g microorganisms. The authors noted t h a t , f o r a dual c u l t u r e sludge, the filamentous microorganism had a higher growth r a t e than the f l o c - f o r m e r at low F/M r a t i o s , and that the re v e r s e was tr u e f o r hig h F/M r a t i o s . Barahona and E c k e n f e l d e r (1984) noted that the s e t t l i n g v e l o c i t y of the sludge was dependent upon the p r o p o r t i o n of fi l a m e n t o u s b a c t e r i a present and that zone s e t t l i n g v e l o c i t y i n c r e a s e d with i n c r e a s e d o r g a n i c l o a d i n g due to i n c r e a s e d f l o e s i z e . However, a review of p u b l i s h e d r e l a t i o n s h i p s between SVI and organic l o a d i n g undertaken by Chambers and Tomlinson (1982) shows that there i s no c o n s i s t e n t r e l a t i o n s h i p and t h a t b u l k i n g has been r e p o r t e d to occur under F/M r a t i o c o n d i t i o n s ranging from 0.01 to 2.0 kg BOD/kg MLSS day. 58 2.4.5.3 N u t r i e n t E f f e c t s on B u l k i n g Although they are not normally a c o n s i d e r a t i o n f o r c o n v e n t i o n a l a c t i v a t e d sludge processes t r e a t i n g predominantly domestic waste-waters, n u t r i e n t balances may be a s i g n i f i c a n t b u l k i n g f a c t o r f o r " s p e c i a l " or high s t r e n g t h wastewaters. Although a BODrnitrogenrphosphorus r a t i o of about 100:5:1 i s g e n e r a l l y c o n s i d e r e d to be the r e q u i r e d composition f o r a c t i v a t e d sludge treatment, l i t t l e i n f o r m a t i o n i s a v a i l a b l e on the i n f l u e n c e of v a r i a t i o n s i n n u t r i e n t : s u b s t r a t e r a t i o s on sludge s e t t l e a b i l i t y . V a r i o u s r e s e a r c h e r s have suggested that sludge b u l k i n g may be due to a d e f i c i e n c y i n n u t r i e n t c o n c e n t r a t i o n s (Jones, 1965, Wagner, 1982, Yeung et a l . , 1984). Jones (1965) repo r t e d that sludge b u l k i n g c o u l d be induced under n i t r o g e n and phosphorus l i m i t i n g c o n d i t i o n s i n batch systems. As n u t r i e n t c o n d i t i o n s have been shown to be capable of promoting and s u p p r e s s i n g filamentous b a c t e r i a i n pure c u l t u r e s , i t i s reasonable t o assume t h a t n u t r i e n t l e v e l s c o u l d i n f l u e n c e a c t i -v ated sludge s e t t l i n g , c o n s i d e r i n g the important r o l e f i l a m e n t s p l a y i n the formation of str o n g g o o d - s e t t l i n g f l o e s and b u l k i n g sludges (Sezgin et a l , 1978). Yueng et a l . (1984) i n v e s t i g a t e d the i n f l u e n c e of n i t r o g e n d e f i -c i e n c y on sludge b u l k i n g , over a wide range of F/M r a t i o s (0.2 to 3.0 kg COD/kg MLSS day). N i t r o g e n - r i c h c o n d i t i o n s (COD:N of 5.3:1) r e s u l t e d i n s u b s t a n t i a l l y lower SVI va l u e s than n i t r o g e n 59. d e f i c i e n t c o n d i t i o n s (COD:N of 106:1), based on a s y n t h e t i c feed. F i g u r e 2 i l l u s t r a t e s that n i t r o g e n - r i c h systems tend to bulk at both low and high F/M r a t i o c o n d i t i o n s , while mid-range F/M c o n d i t i o n s are l i k e l y to r e s u l t i n a b e t t e r conditoned sludge and lower SVI v a l u e s . The opposite occurs f o r nitrogen-poor systems. Microorganisms noted during the study i n c l u d e d S p h a e r o t i l u s  natans, type 0581, Type 1701, M i c r o t h r i x p a r v i c e l l a and Nostocodia l i m i c o l a . S. natans was observed d u r i n g both n u t r i e n t -r i c h and n u t r i e n t - d e f i c i e n t c o n d i t i o n s . F i g u r e 2. Example of the E f f e c t s of Nitrogen on the R e l a t i o n - ship Between SVI and Substrate Loading ( A f t e r Yeung et a l . 1984T 6 0 F o r e s t e r (1985) has suggested that f u r t h e r r e s e a r c h , to determine the p r e c i s e nature of the i n f l u e n c e of n u t r i e n t d e f i c i e n c i e s on sludge b u l k i n g , may not be p r o d u c t i v e . He notes that the re s e a r c h to date has f a i l e d to d i f f e r e n t i a t e between the r o l e s of filame n t o u s and f l o c - f o r m i n g organisms i n s e t t l e a b i l i t y f l u c t u a t i o n s , due to n u t r i e n t balance changes. 2.4.5.4 Temperature E f f e c t s on B u l k i n g R i c h a r d et a l . (1985) r e p o r t e d that the s p e c i f i c growth r a t e of Type 1701 f i l a m e n t doubles f o r approximately every 7 °C r i s e i n temperature over the range of 16 to 28 °C. The organism was f u r t h e r found to have an a c t i v a t i o n energy of 19 Kcal/mole. T h i s h i g h a c t i v a t i o n energy, as compared to 10 to 12 Kcal/mole f o r most b a c t e r i a (Mohr and Kraweic, 1980), was suggested to p a r t l y e x p l a i n the a s s o c i a t e d warm weather b u l k i n g phenomena noted at many p l a n t s . Increased DO was r e q u i r e d t o prevent Type 1701 b u l k i n g as the l i q u i d temperature i n c r e a s e d . Increased b u l k i n g occurrences at high temperatures was a l s o noted by Tomlinson (1982). Problems of poor s e t t l e a b i l i t y have a l s o been observed with low temperatures d u r i n g batch and f i l l - a n d - d r a w l a n d f i l l l e a c h a t e t r e a t a b i l i t y s t u d i e s ( Z a p f e - G i l j e and M a v i n i c , 1981, Wong and Mavinic 1982). Subsequent low temperature l e a c h a t e t r e a t a b i l i t y work u s i n g both f i l l - a n d - d r a w and continuous-flow r e a c t o r s by Raina (1984) noted high SVI v a l u e s f o r the f i l l - a n d - d r a w r e a c t o r s but low SVI valu e s f o r the continuous-flow p r o c e s s . 6 1 2.4.5.5 Other Causes of B u l k i n g Sewage which reaches a treatment p l a n t a f t e r passage through long sewer mains or a f t e r e x t e n s i v e storage before being pumped i s o f t e n anaerobic and s e p t i c . Research undertaken by Chambers (1982) demonstrated that a c t i v a t e d sludge processes t r e a t i n g s e p t i c sewage c o n s i s t e n t l y had poorer s e t t l i n g sludge than d i d systems t r e a t i n g f r e s h sewage. Si x a c t i v a t e d sludge p i l o t p l a n t s were operated i n s i x d i f f e r e n t c ompartmentalization c o n f i g u r a -t i o n s of 1,2,4,8,12 and 24 c e l l s , s i m u l a t i n g complete mix to plug flow c o n f i g u r a t i o n s . A f t e r 3 months of f r e s h sewage feed, the feed was changed to s e p t i c sewage, which had been s t o r e d f o r s e v e r a l days before use. The s e p t i c sewage c o n s i s t e n t l y r e s u l t e d i n a b u l k i n g sludge, r e g a r d l e s s of the process c o n f i g u r a t i o n , with g e n e r a l improvement f o r both systems as compartmentalization i n c r e a s e d . P r i n c i p a l d i f f e r e n c e s noted f o r the f r e s h and s e p t i c feeds i n c l u d e d an i n c r e a s e i n s u l p h i d e s , from l e s s than 0.5 mg/L to 15 mg/L, and i n c r e a s e s i n v o l a t i l e o r g a n i c a c i d s , from 45 - 50 mg/L to 100 - 150 mg/L as a c e t i c a c i d . Sludge b u l k i n g l e v e l was a l s o r e p o r t e d to decrease w i t h i n c r e a s e d h y d r a u l i c r e t e n t i o n time from 3.3 to 8.0 hours. 2.4.5.6 T o x i c Chemical E f f e c t s on B u l k i n g C h l o r i n e and hydrogen peroxide are the most common chemicals used to k i l l f i lamentous organisms pres e n t i n a c t i v a t e d s l udge. High dosages or shock loads of t o x i c chemicals w i l l k i l l f i l a m e n t s and other microorganisms, producing a h i g h l y t u r b i d e f f l u e n t . Lower 62 c o n c e n t r a t i o n s a p p l i e d over a p e r i o d of up to a week have a l s o been found to be e f f e c t i v e i n s u b s t a n t i a l l y reducing the number of f i l a m e n t s present (Sezgin et a l , 1978). C h l o r i n a t i o n of the r e t u r n sludge i s r e p o r t e d to e f f e c t i v e l y "cure" sludge b u l k i n g , i n doses ranging from 4 to 20 grams of c h l o r i n e per c u b i c meter of r e t u r n sludge (Eikelboom, 1982, J e n k i n s , 1982). P r e l i m i n a r y r e s u l t s r e p o r t e d by Jenkins i n d i c a t e t h a t c h l o r i n e c o n c e n t r a t i o n s of 12 mg/L, a p p l i e d f i v e to ten times a day with o v e r a l l d a i l y dosages of approximately 40 g C^/Kg SS, e f f e c t i v e l y c o n t r o l l e d b u l k i n g sludge i n one study. The p r i n c i p a l concern i n a p p l y i n g c h l o r i n e i s that overdoses w i l l r e s u l t i n f l o e d e s t r u c t i o n and i n c r e a s e d e f f l u e n t t u r b i d i t y . C h l o r i n e overdosing can r e s u l t i n a complete d e s t r u c t i o n of f i l a m e n t s , with the c o n s e q u e n t i a l appearance of a " p i n - p o i n t " f l o e and i n c r e a s e d e f f l u e n t suspended s o l i d s , i n a d d i t i o n to the d e s t r u c t i o n of n i t r i f y i n g b a c t e r i a present i n the biomass. Eisenhauser et a l . (1976) found t h a t small c h l o r i n e dosages of from 2 to 3 lb/1000 l b MLVSS per day would reduce the SVI from approximately 180 to 60 mL/g without reducing n i t r i f i c a t i o n . I t was found t h a t , to achieve a s i g n i f i c a n t r e d u c t i o n i n SVI at these dosage l e v e l s , i t was necessary to apply the c h l o r i n e c o n t i n u o u s l y to the a e r a t i o n b a s i n over a one week p e r i o d . C h l o r i n e dosages of from 5 to 7 lb/1000 l b MLVSS day were found to reduce n i t r i f i c a t i o n . 63 H y d r o g e n p e r o x i d e c o n t r o l o f f i l a m e n t o u s b a c t e r i a i n a c t i v a t e d s l u d g e w a s r e p o r t e d b y C o l e e t a l . ( 1 9 7 3 ) t o b e e f f e c t i v e i n r e d u c i n g S V I v a l u e s . A g a i n , o v e r d o s e c o n c e n t r a t i o n s w e r e f o u n d t o r e s u l t i n d e s t r u c t i o n o f t h e f l o e a n d i n c r e a s e d e f f l u e n t t u r b i d i t y . T h e u s e o f h y d r o g e n p e r o x i d e i s n o t common d u e t o i t s h i g h c o s t c o m p a r e d t o t h a t o f c h l o r i n e . 2.4.6 Summary S l u d g e b u l k i n g i s a c o n d i t i o n w h i c h a f f e c t s m o s t a c t i v a t e d t r e a t m e n t p l a n t s a t some t i m e i n t h e i r h i s t o r y . C o m m o n l y i d e n t i f i e d b y t h e s l u d g e v o l u m e i n d e x v a l u e s i n e x c e s s o f 150 m L / g , t h e c o n d i t i o n i s c h a r a c t e r i z e d b y a p o o r l y s e t t l i n g s l u d g e . I n t h e e a r l y s t a g e s o f b u l k i n g a n i m p r o v e m e n t i n e f f l u e n t q u a l i t y i s u s u a l l y o b s e r v e d . I f t h e c o n d i t i o n i s l e f t u n c h e c k e d i t c a n r e s u l t i n m a s s i v e s l u d g e l o s s e s . S l u d g e b u l k i n g i s m o s t c o m m o n l y a s s o c i a t e d w i t h e x c e s s i v e f i l a m e n t o u s m i c r o o r g a n i s m g r o w t h . T h e c o n d i t i o n s w h i c h s u p p o r t f i l a m e n t g r o w t h a r e d i v e r s e , a s t h e r e a r e m o r e t h a n 30 v a r i e t i e s o f a l g a e , b a c t e r i a a n d f u n g i w h i c h c a n g r o w i n a f i l a m e n t o u s f o r m . Some r e s e a r c h e r s h a v e s u g g e s t e d t h a t o n c e t h e p r e d o m i n a n t f i l a m e n t o u s m i c r o o r g a n i s m h a s b e e n i d e n t i f i e d , b u l k i n g c o n t r o l c o u l d b e a c c o m p l i s h e d b y a l t e r i n g t h e c o n d i t i o n s w h i c h p r o m o t e t h e g r o w t h o f t h i s p r e d o m i n a n t f i l a m e n t . H o w e v e r , t h e r e i s n o t y e t s u f f i c i e n t i n f o r m a t i o n a v a i l a b l e o n t h e g r o w t h c h a r a c t e r i s t i c s o f e a c h f i l a m e n t t y p e t o u s e t h i s a p p r o a c h . A t 64 p r e s e n t , the most promising method of b u l k i n g c o n t r o l i s to a l t e r the process c o n d i t i o n s to i n h i b i t b u l k i n g . S e v e r a l r e s e a r c h e r s have demonstrated that b u l k i n g c o n t r o l can be a c h i e v e d through c o n t r o l of the d i s s o l v e d oxygen c o n c e n t r a t i o n s w i t h i n the a e r a t i o n basin and c o n t r o l of the a p p l i e d s u b s t r a t e l o a d i n g r a t e ( f o r example, Palm et a l . , 1980). P r a c t i c a l mechanisms f o r c o n t r o l l i n g these parameters i n c l u d e c o n t r o l of the d i s s o l v e d oxygen c o n c e n t r a t i o n i n the a e r a t i o n tank and c o n t r o l of the mixed l i q u o r suspended s o l i d s c o n c e n t r a t i o n . The d i s s o l v e d oxygen c o n t r o l can only be e f f e c t e d by i n c r e a s i n g or d e c r e a s i n g the a i r supply, i n response to d i s s o l v e d oxygen changes i n the a e r a t i o n b a s i n . Mixed l i q u o r suspended s o l i d s c o n c e n t r a t i o n s can be c o n t r o l l e d by i n c r e a s i n g or d e c r e a s i n g the amount of a c t i v a t e d sludge wasted d a i l y . A l t e r n a t i v e l y , sludge h o l d i n g tanks c o u l d be used to h o l d wasted sludge d u r i n g low l o a d i n g p e r i o d s , and as a supply of microorganisms d u r i n g high o r g a n i c l o a d i n g p e r i o d s . 65 3.0 APPLICATION OF DECISION THEORY TO SLUDGE BULKING CONTROL 3.1 French Creek Water P o l l u t i o n C o n t r o l Centre The French Creek Water P o l l u t i o n C o n t r o l Centre (WPCC) a c t i v a t e d sludge wastewater treatment f a c i l i t y has been s e l e c t e d f o r the development of a dynamic d e c i s i o n a n a l y s i s technique to c o n t r o l c h r o n i c sludge b u l k i n g . The treatment f a c i l i t y i s l o c a t e d near the town of P a r k s v i l l e , on Vancouver I s l a n d , and serves the northern p o r t i o n of the Nanaimo Regiona l D i s t r i c t . P l a c e d i n t o s e r v i c e i n e a r l y 1978, the 1.2 m i l l i o n I m p e r i a l g a l l o n s per day (IGPD) (5455 m /d) p l a n t i s designed to serve a p o p u l a t i o n of 12,000 people. The French Creek WPCC i s t y p i c a l of small a c t i v a t e d sludge treatment f a c i l i t i e s designed p r i m a r i l y f o r orga n i c carbon removal. The process c o n s i s t s of p a r a l l e l r e c t a n g u l a r primary and secondary c l a r i f i e r s , connected by two p a r a l l e l coarse-bubble s p i r a l - f l o w a e r a t i o n tanks. The process i s s u b j e c t to extreme and c h r o n i c b u l k i n g c o n d i t i o n s , which have not yet s e r i o u s l y a f f e c t e d the e f f l u e n t q u a l i t y due to c u r r e n t secondary c l a r i f i e r h y d r a u l i c u n d e r l o a d i n g . The SVI va l u e s over the past s i x years at t h i s p l a n t have been i n excess 150 mL/g f o r more than 60 percent of the time, with recorded v a l u e s as h i g h as 1100 mL/g. M i c r o s c o p i c examination undertaken by o p e r a t i o n s s t a f f has confirmed the presence of filamentous microorganisms i n the b u l k i n g sludge. No morphological i d e n t i f i c a t i o n has been undertaken to determine the type of 66 f i l a m e n t o u s microorganisms present or whether the predominant s p e c i e s changes from one p e r i o d to the next. D e s p i t e the high SVI va l u e s , the p l a n t g e n e r a l l y achieves a low e f f l u e n t suspended s o l i d s c o n c e n t r a t i o n below 20 mg/L. T h i s i s l a r g e l y due to the excess h y d r a u l i c c a p a c i t y i n the secondary c l a r i f i e r s which are o p e r a t i n g at approximately h a l f c a p a c i t y . B u l k i n g c o n t r o l i s achieved by c h l o r i n e a d d i t i o n , once the c o n d i -t i o n p r o g r e s s e s to the p o i n t that e f f l u e n t q u a l i t y i s threatened. O p e r a t i n g s t a f f i n d i c a t e that the a d d i t i o n of c h l o r i n e r e s u l t s i n a t u r b i d e f f l u e n t f o r p e r i o d s of up to a day. T h i s i n c r e a s e d t u r b i d i t y i s not r e f l e c t e d i n the secondary c l a r i f i e r t o t a l suspended s o l i d s (TSS) monitoring data, as the c l a r i f i e r s are grab sampled only once per week f o r TSS a n a l y s e s . The use of c h l o r i n e i s not a d e s i r a b l e c o n t r o l s t r a t e g y as i t i s expensive, a f f e c t s other microorganisms, and r e s u l t s i n a t u r b i d e f f l u e n t . F u r t h e r , as the p l a n t nears design c a p a c i t y , more frequent c h l o r i n e doses w i l l be r e q u i r e d to prevent s o l i d s l o s s . The estab l i s h m e n t of a process c o n t r o l s t r a t e g y to e l i m i n a t e the b u l k i n g c o n d i t i o n s w i l l r e s u l t i n a more s t a b l e biomass, and a c o n s i s t e n t e f f l u e n t q u a l i t y , as the p l a n t nears c a p a c i t y . 3 . 1 . 1 P r o c e s s D e s c r i p t i o n F i g u r e 3 i l l u s t r a t e s the French Creek WPCC process diagram. Sewage e n t e r s the p l a n t headworks, where i t passes through coarse screens and a curved bar screen, before e n t e r i n g a 5,000 Imperial g a l l o n ( I g a l ) (23 m ) aerated g r i t chamber. The wastewater i s 67 F i g u r e 3 . French Creek P o l l u t i o n C o n t r o l Centre Process  Diagram 68 then s p l i t i n t o two 60,000 I g a l (273 m ) p a r a l l e l r e c t a n g u l a r primary c l a r i f i e r s , a f t e r which the waste streams are recombined, before being s p l i t again i n t o two 140,000 I g a l (636 m ) a c t i v a t e d sludge b a s i n s i n a step feed c o n f i g u r a t i o n . The mixed l i q u o r i s then recombined, before being s p l i t i n t o two p a r a l l e l 60,000 I g a l (273 m ), r e c t a n g u l a r secondary c l a r i f i e r s . The e f f l u e n t from the secondary c l a r i f i e r s i s then d i s c h a r g e d by g r a v i t y through a 7,300 fo o t (2225 m), 20 i n c h (500 mm) diameter, marine o u t f a l l . Although the p l a n t was designed to waste s o l i d s from the mixed l i q u o r channel l e a d i n g t o the secondary c l a r i f i e r , the wastage p o i n t has been moved to the a c t i v a t e d sludge r e t u r n l i n e . A p o r t i o n of the r e t u r n sludge i s manually wasted i n t o the primary c l a r i f i e r , where f u r t h e r s e t t l i n g o c c u r s . I t i s then removed with the primary s o l i d s i n t o a 220,000 I g a l (1000 m ) a e r o b i c d i g e s t e r . By the time the waste s o l i d s are pumped to the a e r o b i c d i g e s t e r s , they may have been r e t a i n e d i n an anaerobic or anoxic c o n d i t i o n f o r up t o ten hours. 3.1.2 M o n i t o r i n g Data C h a r a c t e r i s t i c s Sample c o l l e c t i o n and a n a l y s i s i s done by the o p e r a t i o n s s t a f f . Grab samples are c o l l e c t e d at the d i s c h a r g e end of each of the process modules, and at the flow meter chamber p r i o r to d i s c h a r g e through the o u t f a l l . The parameters and t h e i r sampling f r e q u e n c i e s are p r e s e n t e d i n Table 1. 69 T a b l e 1. Monitored Parameters and Sampling Frequencies MODULE PARAMETER SAMPLING FREQUENCY ( per week ) INFLUENT BOD 1 PH 3 TEMPERATURE 3 TSS 1 VSS 1 PRIMARY BOD 1 CLARIFIER TSS 1 VSS 1 AERATION BOD 1 BASINS DO 3 (#1 & #2) MLSS 1 MLVSS 1 PH 3 SVI 3 TEMPERATURE 3 SECONDARY TSS 1 CLARIFIER (#1 & #2) FINAL BOD 1 EFFLUENT PH 3 TEMPERATURE 3 DO 1 FLOWS INFLUENT 7 RETURN A/S 7 WASTE A/S not metered a f t e r 1979 Time s e r i e s and cumulative frequency p l o t s f o r the above para-meters are presented i n Appendices A and B. Although s o l i d s a n a l y s e s are undertaken on a once per week b a s i s , a c e n t r i f u g e i s used t o estimate the MLSS c o n c e n t r a t i o n f o r SVI c a l c u l a t i o n s which are made three times per week. Operation and performance data f o r the French Creek WPCC are summarized i n Table 2. 70 T a b l e 2. O p e r a t i o n and Performance Data f o r the F r e n c h Creek Water P o l l u t i o n C o n t r o l Centre (1979-1984) PARAMETER n AVG STD MIN MAX INFLUENT BOD 295 182 79 60 660 PH 855 7.3 0.19 6.7 8.3 TEMP 855 14.1 3.14 8 20 TSS 294 139 119 28 998 VSS 285 117 103 18 879 PRIMARY CLAR. BOD 291 112 41 .8 35 280 TSS 287 55 31 .5 20 366 VSS 282 46 26.1 17 296 AERATION #1 DO 849 2.9 1 .58 0.3 9 F / M 280 0.286 0.141 0.031 1 .52 MLSS 291 878 334 410 3500 MLVSS 291 725 264 130 2833 PH 849 6.9 0.25 6 7.4 SVI 848 228 162 34 1 168 TEMP 855 14.3 3.18 8 21 AERATION #2 DO 850 2 .9 1 .62 0.4 8.8 F / M 280 0.282 0. 149 0.035 1 .54 MLSS 290 894 307 380 31 00 MLVSS 291 741 241 128 2533 PH 848 6.9 0.25 6.2 7 .5 SVI 849 228 159 34 1 180 TEMP 855 14.3 3.18 8 21 FINAL CLAR. BOD 292 19 1 1 .7 3 95 PH 846 7 0.2 6 7 .5 SS #1 293 14 8.88 2 108 SS #2 269 1 1 7.43 2 88 TEMP 855 14. 1 3.1 8 20 FLOWS FLOW 2030 484000 73500 187200 835100 WASTE A / S 564 48424 22764 100 127500 RETURN A / S 1969 115860 31617 52833 379600 71 Table 2 . (cont'd) CALCULATED VALUES n AVG STD RANGE F/M RATIO, (1/day) (#1) 274 0.28 0. 140 0.03 - 1.52 (#2) 274 0.28 0. 148 0.04 - 1.54 PLANT BOD REMOVAL, % 292 89 12.8 1 0 - 9 8 AERATION BOD REMOVAL, % 284 82 10.7 33 - 97 HRT (PLANT), hrs 1985 24 3.25 14 - 61 HRT (CLARIFIERS), hrs 1985 12 1 .63 7 - 3 0 In a d d i t i o n to the parameters l i s t e d i n T a b l e s 1 and 2, a n a l y ses are undertaken of samples from the a e r o b i c d i g e s t e r s . In 1980, the method of sludge wastage was a l t e r e d from a metered mixed-l i q u o r wastage method to an unmetered manually c o n t r o l l e d (valved) r e t u r n - s l u d g e p o i n t . Based on an average MLVSS c o n c e n t r a t i o n of 700 mg/L, a BOD r e d u c t i o n of 95 mg/L, an i n f l u e n t flow of 500,000 IGPD (2273 m3/d) and a 2/3 biomass-to-s u b s t r a t e r a t i o , the sludge age i s e s timated at approximately 5.5 days. F i g u r e s 4 and 5 i l l u s t r a t e the wide f l u c t u a t i o n s i n SVI l e v e l s i n a e r a t i o n r e a c t o r s #1 and #2, over the p e r i o d from 1979 to 1984. Although extremely h i g h SVI l e v e l s appear to occur p r i m a r i l y d u r i n g the warmer summer months, i t i s c l e a r that b u l k i n g a l s o o ccurs d u r i n g the winter months. Operations s t a f f i n d i c a t e t h a t , d u r i n g the e a r l y y e a r s , extreme b u l k i n g was c o n t r o l l e d by a p p l y i n g doses of c h l o r i n e on an i n t e r m i t t e n t b a s i s . Unfortuna-t e l y , no o p e r a t i o n s l o g has been kept to i n d i c a t e when c h l o r i n e has been a p p l i e d . The p r a c t i c e of shocking the system with high 72 F i g u r e 4. A e r a t i o n Reactor 1.2 1 SVI F l u c t u a t i o n s T — i — i — i — I — i — i — i — i — i — i — i — i — i — i — i — r 0.2 0 .4 0.6 0.8 1 1.2 1.4 1.6 ( T h o u s a n d s ) DAYS (beginning J a n u a r y 1, 1 9 7 9 ) F i g u r e 5. A e r a t i o n Reactor 2 SVI F l u c t u a t i o n s Ul h ~i—i—i—i—I—i—i—i—i—i—i—i—i—r 0.4 0.6 0 .8 1 1.2 1.4 1.6 1.8 ( T h o u s a n d s ) DAYS (beginn ing J a n u a r y 1. 1 9 7 9 ) 73 c h l o r i n e dosages was a l t e r e d by o p e r a t i o n s s t a f f i n 1982. Perma-nent c h l o r i n e a p p l i c a t i o n l i n e s were i n s t a l l e d at the head end of the a e r a t i o n basins so that a lower c h l o r i n e dose c o u l d be a p p l i e d c o n t i n u o u s l y over the p e r i o d of a day when extreme b u l k i n g o c c u r r e d . Over the past year the c h l o r i n e has been a p p l i e d on a once per week b a s i s to maintain SVI l e v e l s below 200 mL/g. As i l l u s t r a t e d i n F i g u r e 6, the flow i n t o the treatment p l a n t has been s t e a d i l y i n c r e a s i n g from 1979 to 1984. The treatment p l a n t i s c u r r e n t l y o p e r a t i n g at approximately h a l f of the design flow ; of 1.2 m i l l i o n IGPD (5455 m / d ) . The p l a n t appears to have been s e v e r e l y a f f e c t e d by storm water i n f i l t r a t i o n d u r i n g c e r t a i n p e r i o d s , w i t h t o t a l d a i l y flows of up to 800,000 IGPD (3637 m / d ) , approximately 60% g r e a t e r than average d a i l y flows over the p e r i o d of data c o l l e c t i o n . F i g u r e 7 i n d i c a t e s t h a t the percent BOD removal a c r o s s the a e r a t i o n basin has improved s i n c e 1979, with the e x c e p t i o n of two minor r e d u c t i o n s i n performance. C o n c u r r e n t l y , the f l u c t u a t i o n s i n primary c l a r i f i e r BOD c o n c e n t r a t i o n s are l e s s prominent i n the p e r i o d 1982 to 1984, than i n the p r e v i o u s three y e a r s . T h i s i s i l l u s t r a t e d by the narrower BOD c o n c e n t r a t i o n ranges f o r that p e r i o d i n F i g u r e 8. Although the primary and secondary c l a r i f i e r BOD c o n c e n t r a t i o n s do not appear to be w e l l c o r r e l a t e d , the decreased r e d u c t i o n i n primary BOD f l u c t u a t i o n s c o i n c i d e s with improved e f f l u e n t BOD q u a l i t y . 74 I n f l u e n t Flows ~i i i — i — i — i — i — i — i — i — i — i — i — i— i— i — i — i — i — r 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 ( T h o u s a n d s ) DAYS (beginning J a n u a r y 1, 1 9 7 9 ) F i g u r e 7. A e r a t i o n Basin BOD Removal E f f i c i e n c y 100 2 a: a o ID - i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — r 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 ( T h o u s a n d s ) DAYS (beginning J a n u a r y 1, 1 9 7 9 ) 75 F i g u r e 8. Comparison of P r i m a r y and Secondary C l a r i f i e r E f f l u e n t BOD C o n c e n t r a t i o n s _ J \ CO 8 O E— c n cn L J o 2: o o a o • • 4 0 0 3 5 0 3 0 0 180 3 6 0 5 4 0 7 2 0 9 0 0 1 0 8 0 1 2 6 0 DATE ( d a y s from J a n u a r y 1 1979) H i o 76 F i g u r e 9. T o t a l ( P l a n t ) BOD Removal E f f i c i e n c y ioo 2 0 -10 -o - \ — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 (Thousands) DAYS (beginning January 1, 1979) BOD removal e f f i c i e n c y a c r o s s the e n t i r e p l a n t does not appear t o have changed a p p r e c i a b l y , g e n e r a l l y a c h i e v i n g a 90 percent removal e f f i c i e n c y as i n d i c a t e d i n F i g u r e 9. An examination of F i g u r e s 10 and 11 i n d i c a t e s that higher DO c o n c e n t r a t i o n s were a t t a i n e d i n both a e r a t i o n basins d u r i n g the p e r i o d of 1982 to 1984 than i n p r e v i o u s y e a r s . As the i n f l u e n t mass BOD l o a d i n g has i n c r e a s e d over the s i x yea r s , the F/M r a t i o has i n c r e a s e d c o r r e s p o n d i n g l y from approximately 0.15 to 0.25 as shown i n F i g u r e s 12 and 13. 77 F i g u r e 10. A e r a t i o n Basin 1 DO C o n c e n t r a t i o n F l u c t u a t i o n s 78 F i g u r e 12. A e r a t i o n Basin 1 F/M R a t i o F l u c t u a t i o n s 0.7 -i 0.8 H 0 H — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — r 0 0.2 0 .4 0 .6 0.8 1 1.2 1.4 1.6 1.8 2 ( T h o u s a n d s ) DAYS (beginning J a n u a r y 1, 1 9 7 3 ) F i g u r e 13. A e r a t i o n Basin 2 F/M R a t i o F l u c t u a t i o n s 0.8 -j 0 .7 H 0 H — j 1 1 1 1 1 1 1 1 1 1 1 1 1 1—i 1 1 1 i 0 0.2 0 .4 0 .6 0.8 1 1.2 1.4 1.6 1.8 2 ( T h o u s o n d s ) DAYS (beginning J a n u a r y 1. 1 9 7 9 ) 79 3.2 S e l e c t i o n of C o n t r o l Parameters and O p e r a t i n g Ranges There are four b a s i c o p e r a t i n g c o n t r o l s which c o u l d be a d j u s t e d to c o n t r o l b u l k i n g sludge at the French Creek p l a n t : 1. D i s s o l v e d Oxygen C o n t r o l 2. Food-to-Microorganism R a t i o (F/M) C o n t r o l 3. C h l o r i n e Treatment 4. Process C o n f i g u r a t i o n M o d i f i c a t i o n s 3.2.1 D i s s o l v e d Oxygen C o n t r o l Without r e a l - t i m e process c o n t r o l equipment and v a r i a b l e speed blowers, i t i s not p o s s i b l e to maintain d i s s o l v e d oxygen concen-t r a t i o n s at a s p e c i f i c l e v e l throughout the day. Consequently, c o n v e n t i o n a l treatment f a c i l i t i e s can only be expected to main-t a i n the d i s s o l v e d oxygen c o n c e n t r a t i o n w i t h i n a general range. The p r a c t i c a l d i s s o l v e d oxygen o p e r a t i n g range, with compressed a i r systems, i s approximately 0.5 mg/L to 6.5 mg/L. Lower than 0.5 mg/L r i s k s c r e a t i n g anaerobic c o n d i t i o n s and g r e a t e r than 6.5 mg/L i s d i f f i c u l t , due to oxygen t r a n s f e r l i m i t a t i o n s . S u b s t r a t e l o a d i n g to the p l a n t i s expected to vary c o n s i d e r a b l y d u r i n g the day with the i n f l u e n t flow. Oxygen demand w i l l be higher d u r i n g p e r i o d s of h i g h s u b s t r a t e l o a d i n g . As the a i r supply to the a e r a t i o n tanks i s not a d j u s t e d d u r i n g the day, the d i s s o l v e d oxygen c o n c e n t r a t i o n w i t h i n the a e r a t i o n tanks can be expected to vary i n v e r s e l y with i n c r e a s e d s u b s t r a t e l o a d i n g . D i s s o l v e d oxygen 80 c o n c e n t r a t i o n s can be expected to vary approximately 0.5 mg/L higher or lower than the d e s i r e d DO c o n c e n t r a t i o n . 3.2.2 Food-to-Microorganism R a t i o C o n t r o l By v a r y i n g the sludge wastage r a t e s , s e v e r a l process parameters are a f f e c t e d , i n c l u d i n g the sludge age, s o l i d s c o n c e n t r a t i o n and, consequently, the Food-to-Microorganism (F/M) r a t i o . Low F/M r a t i o s are i n d i c a t i v e of extended a e r a t i o n systems, with long sludge ages, high biomass c o n c e n t r a t i o n s and low sludge volume p r o d u c t i o n s , while the converse i s true f o r high F/M r a t i o s . (Metcalf and Eddy, 1979). V a r i a t i o n s i n the F/M r a t i o at p l a n t s g e n e r a l l y occur as a r e s u l t of s o l i d s wastage p r a c t i c e s . I f sludge i s not wasted on a r e g u l a r and c o n t r o l l e d b a s i s , the c o n c e n t r a t i o n of biomass i n the a e r a t i o n tank w i l l vary and consequently change the F/M r a t i o . S i m i l a r l y , i f the p l a n t i s su b j e c t t o v a r y i n g s u b s t r a t e c o n c e n t r a t i o n s throughout the day, or from day to day, the F/M r a t i o w i l l change. For example, although the French Creek WPCC was designed to operate at an F/M r a t i o of from 0.2 to 0.5 kg BOD/kg MLVSS day. Table 2 shows that the o p e r a t i n g range has v a r i e d from 0.03 to 1.54 kg BOD/kg MLVSS day. Since t h e r e i s no c o n t r o l on BOD l o a d i n g s , a d j u s t i n g the MLVSS by changing the sludge wasting r a t e i s the only means of c o n t r o l l i n g the F/M r a t i o . While F/M i n c r e a s e s can be accomplished f a i r l y q u i c k l y through i n c r e a s e d sludge wasting, F/M decreases are more 81 d i f f i c u l t t o o b t a i n , as they r e q u i r e growth of biomass to occur. Should a r a p i d i n c r e a s e i n BOD occur, the o n l y method of i n c r e a s i n g the biomass at most c o n v e n t i o n a l treatment f a c i l i t i e s would be to wait u n t i l the sludge c o n c e n t r a t i o n i n c r e a s e d i n response to i n c r e a s e d food. 3.2.3 C h l o r i n e Treatment Adding c h l o r i n e i s a f a s t , but temporary, method of c o n t r o l l i n g b u l k i n g , through the incomplete d e s t r u c t i o n of filamentous microorganism. T h i s works w e l l f o r s p o r a d i c b u l k i n g episodes but does nothing to a l t e r the c o n d i t i o n s f a v o u r i n g the f i l a m e n t s . If these c o n d i t i o n s remain u n a l t e r e d , e x c e s s i v e f i l a m e n t o u s growth w i l l g e n e r a l l y r e o c c u r . As the p l a n t nears design flow c a p a c i t y , the c l a r i f i e r ' s c a p a c i t y to t o l e r a t e b u l k i n g i s d i m i n i s h e d and more frequent c h l o r i n a t i o n i s r e q u i r e d . For the purposes of e s t a b l i s h i n g a d e c i s i o n - a n a l y s i s c o n t r o l s t r u c t u r e f o r b u l k i n g c o n t r o l , c h l o r i n e a d d i t i o n w i l l be c o n s i d e r e d to be a l a s t r e s o r t which should be implemented only i f the s e l e c t e d c o n t r o l parameters f a i l to c o n t r o l the b u l k i n g and the c l a r i f i e r i s a t r i s k of d i s c h a r g i n g s o l i d s . 3.2.4 Process C o n f i g u r a t i o n M o d i f i c a t i o n s Process m o d i f i c a t i o n i s the most c o s t l y c o n t r o l a l t e r n a t i v e and may not be e c o n o m i c a l l y p r a c t i c a l . Although the l i t e r a t u r e i n d i -c a t e s t h a t plug flow c o n f i g u r a t i o n s are l e s s s u s c e p t a b l e to 82 filamentous bulking (Chambers & Tomlinson, 1982, Tomlinson & Chambers, 1984), bulking condit ions in a completely mixed system may not necessar i ly be improved by modifying the flow conf igura t ion . Due to the expense involved in a l t e r i n g the process conf igurat ion (plug versus completely mixed) at the French Creek WPCC, and the lack of a guarantee that changes w i l l be e f f ec t ive in c o n t r o l l i n g bu lk ing , process modif icat ions should only be considered i f the DO and F/M contro l strategy f a i l s . 3.2.5 Sludge Volume Index O p e r a t i n g Ranges SVI values for French Creek range from approximately 35 to 1200 mL/g. I d e a l l y , the SVI value should be between approximately 60 and 100 mL/g, with values in excess of 150 mL/g ind ica t ive of bulking sludge (Sezgin, 1981). The operators at French Creek have indicated that they prefer to have the SVI l e v e l near 150 mL/g, as i t r e s u l t s in an extremely c lear e f f luent . 3.2.6 E f f l u e n t S o l i d s C o n c e n t r a t i o n Ranges Although conventional ac t ivated sludge f a c i l i t i e s can be expected to achieve an ef f luent suspended so l id s l e v e l of approximately 20 mg/L, plant upsets may resu l t in ef f luent so l ids concentrations exceeding 100 mg/L. As noted prev ious ly , large f luctuat ions in the d i s so lved oxygen concentration or F/M r a t i o can resu l t in a • 8 3 t u r b i d e f f l u e n t . A l t h o u g h the average e f f l u e n t suspended s o l i d s c o n c e n t r a t i o n s at the F r e n c h Creek f a c i l i t y i s below 15 mg/L , c o n c e n t r a t i o n s as h i g h as 108 mg/L have been r e c o r d e d . 3.3 D e c i s i o n A n a l y s i s C o n t r o l Approach F o r each p r o c e s s c o n t r o l d e c i s i o n t h e r e i s a set of p o t e n t i a l outcomes, each wi th a s p e c i f i c p r o b a b i l i t y of o c c u r r i n g . As a g i v e n a c t i o n must r e s u l t i n some subsequent o p e r a t i n g s t a t e , the sum of the p r o b a b i l i t i e s of a l l p o t e n t i a l outcomes ( i n c l u d i n g no change) must e q u a l 1.0 (100%). A c t i o n s and outcomes have a s s o c i a t e d c o s t s and rewards , some of which a r e measurable and some i n t a n g i b l e . For i n s t a n c e , t h e r e may be f i n e s f o r exceed ing e f f l u e n t d i s c h a r g e permi t r e q u i r e m e n t s ; these p r o v i d e a d i r e c t economic i n c e n t i v e (measurable) f or m a i n t a i n i n g e f f l u e n t q u a l i t y . However, t h e r e i s a l s o job s a t i s f a c t i o n f o r the o p e r a t o r in m a i n t a i n i n g a h i g h q u a l i t y e f f l u e n t and a v o i d i n g n e g a t i v e p o l i t i c a l consequences of even temporary p l a n t f a i l u r e . To a p p l y d e c i s i o n t h e o r y , i t i s n e c e s s a r y to be a b l e to a s se s s the comparat ive u t i l i t i e s f o r the v a r i o u s p o s s i b l e outcomes which r e f l e c t s both d i r e c t l y measurable and a l s o i n t a n g i b l e v a l u e s . Such a u t i l i t y s c a l e may range from 0, f o r u n a c c e p t a b l e outcomes, to 100, f o r " i d e a l " outcomes. The expec ted u t i l i t y of a c o n t r o l a l t e r n a t i v e i s d e f i n e d as the a l g e b r a i c sum of the u t i l i t y , a s s o c i a t e d w i t h each p o t e n t i a l outcome, m u l t i p l i e d by the p r o b a b i l i t y of a c h i e v i n g t h a t outcome 84 given the c o n t r o l d e c i s i o n . T h i s i s i l l u s t r a t e d below: CONTROL (1) POTENTIAL OUTCOMES (A) (B) (C) PROBABILITY OF OUTCOME GIVEN CONTROL (1) P(1A)=0.2 P(1B)=0.5 P(1C)=0.3 RELATIVE UTILITY OF OUTCOME U(A)=80 U(B)=100 U(C)=40 EXPECTED UTILITY OF CONTROL ALTERNATIVE [P(1A) x U(A)] + [P(1B) x U(B)] + [P(1C) x U(C)] [.2 x 80] + [.5 x 100] + [.3 x 40] = 78 The s e l e c t e d c o n t r o l a l t e r n a t i v e should be the a l t e r n a t i v e with the h i g h e s t expected u t i l i t y . Where the r e l a t i v e u t i l i t y i n v o l v e s two or more r e l a t i v e l y independent measures of the outcomes, such as SVI and e f f l u e n t SS, the p r o b a b i l i t y of a c h i e v i n g that outcome i s the product of p r o b a b i l i t i e s of a c h i e v i n g each of the measures of that outcome. CONTROL (1) POTENTIAL OUTCOMES DEFINED BY TWO INDEPENDENT MEASURES (Aa) (Ba) (Ca) (Ab) (Bb) (Cb) (Ac) (Be) (Cc) PROBABILITY OF INDEPENDENT MEASURES GIVEN CONTROL (1) P(1A)=0.2 P(1B)=0.5 P(1C)=0.3 P(1a)»0.6 P(!b)=0.1 P(1c)=0.3 85 RELATIVE UTILITY OF OUTCOME U(Aa)=80 U(Ba)=lOO U(Ca)=40 U(Ab)=60 U(Bb)=85 U(Cb)=25 U(Ac)=20 U(Bc)=30 U(Cc)=5 EXPECTED UTILITY OF CONTROL ALTERNATIVE ((P(1A) x P(1a)) x U(Aa) ((P(1A) x P(1c)) x U(Ac) ((P(1B) x P(1b)) x U(Bb) ((P(1C) x P(1a)) x U(Ca) ((P(1C) x P(1c)) x U(Cc) (.2 x .6 x 80) + (.2 x . ( . 5 x . 6 x 6 0 ) + ( . 5 x . ( .3 x .6 x 20) + (.3 x . + ((P(1A) x P(1b)) x U(Ab)) + + ((P(1B) x P(1a)) x U(Ba)) + + ((P(1B) x P(1c)) x U(Bc)) + + ((P(1C) x P(1b)) x U(Cb)) + x 100) + (.2 x .3 x 40) + x 85) + (.5 x .3 x 25) + x 30) + (.3 x .3 x 5) = 44.95 T h i s procedure i s used t o c a l c u l a t e the expected u t i l i t i e s f o r S e c t i o n 4.1. 3.3.1 Case D e f i n i t i o n s Case A Case A i s d e f i n e d as a " s t a t i c " s i n g l e - s t a t e Bayesian d e c i s i o n model, i n which p r o b a b i l i t y e stimates are not a d j u s t e d i n l i g h t of new i n f o r m a t i o n . The outcomes are assumed to depend on the c o n t r o l a l t e r n a t i v e adopted, but not on the s t a t e , ( i . e . i t i s assumed t h a t t h e r e i s a s i n g l e "best" c o n t r o l a l t e r n a t i v e , f o r a l l s t a t e s , and the purpose of of the a n a l y s i s i s t o f i n d t h i s 86 a l t e r n a t i v e ) . The assumption of a s i n g l e "best" a l t e r n a t i v e i s c o n s i s t e n t w i t h o p e r a t i n g p o l i c i e s at most treatment f a c i l i t i e s , which t y p i c a l l y attempt to m a i n t a i n a s e l e c t e d DO c o n c e n t r a t i o n and F / M r a t i o . Outcomes are d e f i n e d i n terms of both SVI l e v e l and e f f l u e n t SS c o n c e n t r a t i o n s as d e s c r i b e d i n S e c t i o n 3 . 3 . 3 . H i s t o r i c a l da ta from F r e n c h Creek i s used to c o n s t r u c t the s t a t i c p r o b a b i l i t y e s t i m a t e s used i n Case A , d e s c r i b e d i n S e c t i o n 3 . 3 . 4 . Case B Case B i s d e f i n e d as a " s t a t i c " Markov ian d e c i s i o n model i n which p r o b a b i l i t y e s t i m a t e s are dependent upon s t a t e c o n d i t i o n s , - a s w e l l as the c o n t r o l s t r a t e g y , and are not updated i n l i g h t of new i n f o r m a t i o n . P r o b a b i l i t y e s t i m a t e s are made f o r each c o n t r o l / s t a t e c o m b i n a t i o n . As d i s c u s s e d i n S e c t i o n 3 . 3 . 3 , outcomes f o r Case B are d e f i n e d in terms of SVI ranges o n l y . P r o b a b i l i t i e s are based s o l e l y on h i s t o r i c a l da ta as d e s c r i b e d i n S e c t i o n 3 . 3 . 5 . U t i l i t i e s are d e f i n e d i n terms of both the outcome s t a t e and c o n t r o l p o l i c y , as d e s c r i b e d i n S e c t i o n 3 . 3 . 6 . Markov P o l i c y - I t e r a t i o n c a l c u l a t i o n s are then made based on these p r o b a b i l i t y and u t i l i t y e s t i m a t e s . Case C Case C i s d e f i n e d as a "dynamic" Markov ian d e c i s i o n model i n which the p r o b a b i l i t y e s t i m a t e s , made from h i s t o r i c a l d a t a , are c o n t i n u a l l y m o d i f i e d by the outcome of each d e c i s i o n . P r o b a b i l i t y e s t i m a t e s used i n Case B serve as the s t a r t i n g p o i n t for the Markov P o l i c y - I t e r a t i o n c a l c u l a t i o n s . The u t i l i t y s t r u c t u r e s used 87 i n Case B are a l s o used f o r Case C. The outcome of s p e c i f i c c o n t r o l d e c i s i o n s are used to improve the i n i t i a l p r o b a b i l i t y e s t i m a t e s . 3.3.2 Assumptions Some s i m p l i f y i n g assumptions have been made re g a r d i n g the c o n t r o l of b u l k i n g sludge. These i n c l u d e the s e l e c t i o n of a " d e c i s i o n p e r i o d " which takes i n t o account the delay between process c o n t r o l adjustments and system response, and the s e l e c t i o n of process c o n t r o l parameters and o p e r a t i n g c o n d i t i o n s a f f e c t i n g sludge b u l k i n g . A time l a g i s expected between a process adjustment and a measurable response f o r b i o l o g i c a l systems. As noted by Palm (1982), a c t i v a t e d sludge b u l k i n g , which i s due to low a e r a t i o n b a s i n DO, can be "cured" by r a i s i n g the DO c o n c e n t r a t i o n , but i t may take up t o three mean c e l l r e s i d e n c e times to produce a non-b u l k i n g sludge, depending upon the degree of b u l k i n g . For the French Creek WPCC, with a mean c e l l r e s i d e n c e time of about 5 to 6 days, i t may take two to t h r e e weeks to completely recover from such h i g h b u l k i n g c o n d i t i o n s . F/M c o n t r o l s t r a t e g i e s at a c o n v e n t i o n a l a c t i v a t e d sludge f a c i l i t y can a chieve r a p i d F/M i n c r e a s e s by i n c r e a s e d sludge wasting. However, decreases i n F/M r a t i o s can o n l y be e f f e c t i v e l y undertaken through the r e d u c t i o n i n wasting and consequent i n c r e a s e s i n sludge mass through growth over time. C o n s i d e r i n g the 5 day time requirement f o r the BOD t e s t and l i m i t a t i o n s i n o p e r a t i o n s personnel time f o r l a b o r a t o r y 88 a n a l y s i s , a weekly adjustment frequency would be reasonable. P l a n t personnel i n d i c a t e that process pumping and a i r flow adjustments are made about once a week. Based on these c o n s i d e r -a t i o n s , a time l a g of one week was s e l e c t e d f o r c o n s t r u c t i n g the p r o b a b i l i t y m a t r i c e s . I t i s a l s o assumed that the process c o n t r o l parameters are maintained w i t h i n a set range throughout the e n t i r e d e c i s i o n p e r i o d . DO c o n c e n t r a t i o n s and F/M r a t i o s are expected to vary s l i g h t l y on a d i u r n a l b a s i s , due to s u b s t r a t e c o n c e n t r a t i o n and mass l o a d changes throughout the day. T h i s v a r i a t i o n has been allowed f o r i n the s e l e c t i o n of o p e r a t i n g ranges f o r both DO and F/M r a t i o c o n t r o l s , as d i s c u s s e d i n S e c t i o n 3 . 3 . 3 . 3.3.3 S t a t e D e f i n i t i o n s For Case A, both the SVI and e f f l u e n t SS c o n c e n t r a t i o n s are c o n s i d e r e d as s t a t e d e f i n i t i o n parameters. Outcome s t a t e s f o r use i n t h i s study are d e f i n e d i n terms of d i s c r e t e SVI and e f f l u e n t SS ranges as f o l l o w s : SVI RANGES EFFLUENT SS SVI < = 60 mL/g 60 mL/g < SVI < = 100 mL/g 100 mL/g < SVI < = 200 mL/g 200 mL/g < SVI <= 300 mL/g 300 mL/g < SVI <= 500 mL/g 500 mL/g < SVI SS 5 mg/L 5 mg/L < ss < = 10 mg/L 10 mg/L < ss <= 15 mg/L 15 mg/L < ss < = 20 mg/L 20 mg/L < ss 60 mg/L 60 mg/L < ss 89 For the Markov P o l i c y - I t e r a t i o n a p p l i c a t i o n s , Cases B and C, the e f f l u e n t suspended s o l i d s c r i t e r i a was removed. T h i s was done f o r ease of e x p l a n a t i o n and to f a c i l i t a t e the adoption of an energy p o l i c y u t i l i t y s t r u c t u r e as d e s c r i b e d i n S e c t i o n 3.3.5. The French Creek WPCC e f f l u e n t d i s c h a r g e permit r e q u i r e s the suspended s o l i d s to be below 60 mg/L. As the average f i n a l c l a r i -f i e r suspended s o l i d s c o n c e n t r a t i o n i s approximately 8 mg/L (95 percent below 30 mg/L), there i s l i t t l e v a r i a t i o n i n the u t i l i t y e s t i m a t e s . Decreasing the number of outcome s t a t e s from 36 to 5 r e s u l t s i n a l a r g e r number of samples per s t a t e d e f i n i t i o n and l e s s " n o i s e " i n the o f f d i a g o n a l s of the t r a n s i t i o n matrix ( C o l l i n s , 1975). The s p e c i f i c ranges were a l s o a d j u s t e d , as shown below, t o achieve a more even d i s t r i b u t i o n of sample p o i n t s i n each range: STATE 1 STATE 2 STATE 3 STATE 4 STATE 5 100 mL/g < 200 mL/g < 300 mL/g < 500 mL/g < SVI <= SVI <= SVI <= SVI <= SVI 100 mL/g 200 mL/g 300 mL/g 500 mL/g 3.3.4 E s t a b l i s h m e n t of P r o b a b i l i t i e s The d e t e r m i n a t i o n of process c o n t r o l response p r o b a b i l i t i e s r e -q u i r e s some knowledge of the s p e c i f i c a c t i v a t e d sludge process being c o n s i d e r e d . T h i s knowledge can be i n the form of measured responses to process changes made i n the past or i n the form of q u a l i t a t i v e o b s e r v a t i o n s ; the l a t t e r can be made by the p l a n t 90 operator or process design p r o f e s s i o n a l s of the p l a n t i n q u e s t i o n or of s i m i l a r p l a n t s , or some combination of both. For each DO and F/M combination which has occurred i n the past a t the treatment f a c i l i t y , the co r r e s p o n d i n g SVI and e f f l u e n t SS l e v e l a f t e r a one week l a g was noted. By examining s i x years of data from the French Creek f a c i l i t y , a frequency matrix was con-s t r u c t e d of the r e s u l t i n g outcome f o r each DO and F/M c o n t r o l combination o c c u r r i n g i n that time p e r i o d . P r o b a b i l i t i e s were determined by n o r m a l i z i n g the SVI/SS outcome f r e q u e n c i e s f o r each DO and F/M combination. The r e s u l t i n g p r o b a b i l i t y m a t r i c e s are presented i n Tables 3 and 4 f o r the s e l e c t e d SVI and e f f l u e n t SS range combinations d i s c u s s e d i n S e c t i o n 3.3.3, and used f o r the Case A " s t a t i c " Bayesian d e c i s i o n a n a l y s i s approach. A s i m i l a r technique was used to generate an SVI s t a t e outcome frequency and t r a n s i t i o n or p r o b a b i l i t y matrix f o r use i n the Markov P o l i c y - I t e r a t i o n a p p l i c a t i o n s f o r Cases B and C, S e c t i o n 4.2. Tables 5 t o 8 i l l u s t r a t e the r e s u l t i n g frequency and t r a n s i t i o n m a t r i c e s , based on a l l of the h i s t o r i c a l data and f o r three temperature range groupings ( T <= 12, 1 2 < T < 16, & 16 <= T ). These temperature ranges were s e l e c t e d on the b a s i s of an approximately equal number of data p o i n t s per range. S e v e r a l c o n t r o l o p t i o n s have not oc c u r r e d i n the past and consequently have no p r o b a b i l i t y d i s t r i b u t i o n s . As the Markov P o l i c y - I t e r a t i o n technique r e q u i r e s that some p r o b a b i l i t y estimate be made f o r a l l c o n t r o l a l t e r n a t i v e s , a b a s e l i n e frequency matrix concept was developed to p r o v i d e some i n i t i a l p r o b a b i l i t y e s t i m a t e , while 91 Table 3. Case "A" Sludge Volume Index P r o b a b i l i t y D i s t r i b u t i o n s  f o r S e l e c t A e r a t i o n Basin D i s s o l v e d Oxygen Co n c e n t r a t i o n  and Food-to-Microorganism R a t i o Ranges SVI PROBABILITY TABLE FOR ( DO <= 1.50 ) SVI FM<0.18 . 18- .25 . 2 5 - . 3 0 . 3 0 - . 4 0 .40<FM (mL/g) (1 /day) (1 /day) (1 /day) (1 /day) (1 /day) <= 60 0.14 0.14 0.07 0.16 0.19 6 0 - 1 0 0 0.22 0.14 0.14 0.16 0.13 100 - 200 0.31 0.32 0.36 0.37 0.31 200 - 300 0.1 4 0.18 0.29 0.21 0.25 300 - 500 0.06 0.04 0.00 0.00 0.00 500 <= 0.14 0.18 0.14 0.11 0.13 n 36 28 14 19 16 AVG 239 238 327 239 305 STD 246 197 267 142 207 SVI PROBABILITY TABLE FOR ( 1.50 < DO <= 2.50 ) SVI FM<0.18 . 1 8 - . 2 5 . 25 - . 30 . 3 0 - . 4 0 .40<FM (mL/g) (1 /day) (1 /day) (1 /day) (1 /day) (1 /day) <= 60 0.14 0.13 0.14 0.14 0.13 60 - 100 0.14 0.13 0.14 0.23 0.13 100 - 200 0.36 0.39 0.38 0.29 0.33 200 - 300 0.23 0.22 0.24 0.14 0.27 300 - 500 0.00 0.00 0.00 0.06 0.00 500 <= 0.14 0.13 0.10 0.14 0.13 n 22 23 21 35 15 AVG 244 340 253 277 243 STD 263 273 195 201 99 92 T a b l e 3. ( c o n t ' d ) SVI PROBABILITY TABLE FOR ( 2.50 < DO <= 3.50 ) SVI FM<0.18 . 18-.25 . 2 5 - . 3 0 . 3 0 - . 4 0 . 40<FM (mL/g) (1 /day) (1 /day) (1 /day) (1 /day) (1 /day) <= 60 0.15 0.14 0.18 0.07 0.00 60 - 100 0.15 0.14 0.18 0.14 0.00 100 - 200 0.40 0.38 0.29 0.36 0.50 200 - 300 0.20 0.24 0.24 0.29 0.38 300 - 500 0.00 0.00 0.00 0.00 0.00 500 <= 0.10 0.10 0.12 0.14 0.13 n 20 21 1 7 14 8 AVG 248 239 272 265 315 STD 199 177 134 148 162 SVI PROBABILITY TABLE FOR ( 3.50 < DO <= 4.50 ) SVI FM<0.18 . 18- .25 . 2 5 - . 3 0 . 3 0 - . 4 0 .4 0<FM (mL/g) (1 /day) (1 /day) (1 /day) (1 /day) (1 /day) <= 60 0.13 0.18 0.1 6 0. 13 0.10 6 0 - 1 0 0 0.13 0.18 0.16 0.13 0.00 100 - 200 0.33 0.29 0.37 0.33 0.40 200 - 300 0.27 0.24 0.21 0.27 0.30 300 - 500 0.00 0.00 0.00 0.00 0.00 500 <= 0.13 0.12 0.11 0.13 0.20 n 15 17 19 15 10 AVG 1 13 174 244 1 93 331 STD 55 71 197 82 180 93 Table 3. (cont'd) SVI PROBABILITY TABLE FOR ( 4.50 < DO ) SVI FM<0.18 . 18- .25 . 2 5 - . 3 0 . 3 0 - . 4 0 .40<FM (mL/g) (1/day) (1/day) (1/day) (1/day) (1/day) <= 60 0.09 0.12 0.13 0.14 0.08 6 0 - 1 0 0 0.09 0.12 0.13 0.14 0.17 100 - 200 0.36 0.36 0.39 0.36 0.33 200 - 300 0.27 0.20 0.22 0.23 0.25 300 - 500 0.00 0.04 0.00 0.00 0.00 500 <= 0.18 0.16 0.13 0.14 0.17 n 1 1 25 23 22 12 AVG 309 219 183 201 263 STD 234 196 91 97 97 Table 4. Case "A" F i n a l E f f l u e n t Suspended S o l i d s P r o b a b i l i t y  D i s t r i b u t i o n s f o r S e l e c t A e r a t i o n Basin D i s s o l v e d  Oxygen C o n c e n t r a t i o n and Food-to-Microorganism R a t i o  Ranges FESS PROBABILITY TABLE FOR ( DO <= 1.50 ) FESS FM<0.18 . 18- .25 . 2 5 - . 3 0 . 3 0 - . 4 0 .40<FM (mg/L) (1/day) (1/day) (1/day) (1/day) (1/day) <= 5 0.18 0.12 0.17 0.12 0.1 3 5 - 10 0.56 0.32 0.58 0.47 0.25 10 - 15 0.21 0.28 0.08 0.18 0.50 15 - 20 0.05 0.20 0.08 0.18 0.13 20 - 60 0.00 0.08 0.08 0.06 0.00 60 <= 0.00 0.00 0.00 0.00 0.00 n 39 25 12 17 16 AVG 9.0 13.4 9.3 10.8 10.4 STD 3.67 7.03 6.00 5.40 4.92 94 Table 4. (cont ' d ) FESS PROBABILITY TABLE FOR ( 1.50 < DO <= 2.50 ) FESS FM<0.18 . 1 8 - . 2 5 . 2 5 - . 3 0 . 3 0 - . 4 0 .40<FM (mg/L) (1 /day) (1 /day) (1 /day) (1 /day) (1 /day) <= 5 0.09 0.09 0.05 0.12 0.07 5 - 10 0.32 0.18 0.26 0.35 0.07 10 - 15 0.50 0.55 0.37 0.15 0.36 1 5 - 2 0 0.09 0.09 0.26 0.24 0.36 20 - 60 0.00 0.09 0.05 0.15 0.14 60 <= 0.00 0.00 0.00 0.00 0.00 n 22 22 19 34 14 AVG 11.1 12.8 13.2 12.7 15.0 STD 3.64 6.43 5.73 6.14 4.39 FESS PROBABILITY TABLE FOR ( 2.50 < DO <= 3.50 ) FESS FM<0.18 . 1 8 - . 2 5 . 2 5 - . 3 0 . 3 0 - . 4 0 .40<FM (mg/L) (1 /day) (1 /day) (1 /day) (1 /day) (1 /day) <= 5 0.05 0.05 0.06 0.06 0.25 5 - 10 0.37 0.53 0.18 0.24 0.00 10 - 15 0.47 0.21 0.47 0.35 0.50 15 - 20 0.11 0.11 0.29 0.24 0.00 20 - 60 0.00 0.11 0.00 0.12 0.25 60 <= 0.00 0.00 0.00 0.00 0.00 n 19 19 17 17 8 AVG 11.3 11.4 1 1.9 14.1 13.4 STD 3.05 6.34 5.30 5.84 8.23 95 Table 4. (cont'd) FESS PROBABILITY TABLE FOR ( 3.50 < DO <= 4.50 ) FESS FM<0.18 . 18-.25 .25-.30 .30-.40 .40<FM (mg/L) (1/day) (1/day) (1/day) (1/day) (1/day) <= 5 0.06 0.06 0.00 0.00 0.00 5 - 10 0.31 0.29 0.26 0.40 0.22 10 - 15 0.44 0.18 0.42 0.33 0.44 15 - 20 0.19 0.35 0.16 0.07 0.11 20 - 60 0.00 0.12 0.16 0.20 0.22 60 <= 0.00 0.00 0.00 0.00 0.00 n 16 17 19 15 9 AVG 11.6 14.2 15. 1 13.5 16.2 STD 3.66 6.10 7.36 6.59 6.46 FESS PROBABILITY TABLE FOR ( 4.50 < DO ) FESS FM<0.18 . 18-.25 .25-.30 .30-.40 .40<FM (mg/L) (1/day) (1/day) (1/day) (1/day) (1/day) <= 5 0.14 0.04 0.00 0.18 0.00 5 - 10 0.43 0.29 0.32 0.36 0.50 10 - 15 0.43 0.42 0.36 0.14 0.31 1 5 - 2 0 0.00 0.13 0.09 0.18 0.06 20 - 60 0.00 0.13 0.23 0.14 0.13 60 <= 0.00 0.00 0.00 0.00 0.00 n 7 24 22 22 16 AVG 9.7 13.9 15.4 12.3 12.5 STD 3.28 7.09 8.53 7.20 5.94 minimizing any b i a s to the t r a n s i t i o n m a t r i x . The p r o b a b i l i t y m a t r i c e s i l l u s t r a t e d i n Ta b l e s 5 t o 8 shows that there i s a st r o n g d i a g o n a l s t a t e - t o - s t a t e c h a r a c t e r i s t i c . T h i s i n d i c a t e s Table 5. Case "B" S t a t e / C o n t r o l Outcome Frequency and Pr o b a b i - l i t y D i s t r i b u t i o n s Based on a l l H i s t o r i c a l Data F R E Q U E N C Y P R O B A B I L I T Y (%) STATE (J) STATE (J) STATE (1) CONTROL 1 2 3 4 5 STATE (1) CONTROL 1 2 3 4 5 1 1 10 5 0 0 0 1 1 67 33 0 0 0 2 2 0 0 0 0 2 100 0 0 0 0 3 0 0 0 0 0 3 0 0 0 0 0 4 13 5 0 0 0 4 72 28 0 0 0 5 14 7 0 2 0 5 61 30 0 9 0 6 0 0 0 1 0 6 0 0 0 100 0 7 3 4 0 0 0 7 43 57 0 0 0 8 1 1 6 0 0 0 8 65 35 0 0 0 9 0 0 0 0 0 9 0 0 0 0 0 2 1 0 12 1 0 1 2 1 0 86 7 0 7 2 2 16 3 1 0 2 9 73 14 5 0 3 1 3 0 0 0 3 25 75 0 0 0 4 4 17 4 2 0 4 15 63 15 7 0 5 10 37 10 6 0 5 16 59 16 10 0 6 0 8 2 0 0 6 0 80 20 0 0 7 0 4 1 2 0 7 0 57 14 29 0 8 3 18 4 5 0 8 10 60 13 17 0 9 0 3 5 1 0 9 0 33 56 1 1 0 3 1 0 1 2 0 1 3 1 0 25 50 0 25 2 0 1 8 2 0 2 0 9 73 18 0 3 1 0 1 4 0 3 17 0 17 67 0 4 0 6 2 1 1 4 0 60 20 10 10' 5 1 1 1 4 3 0 5 5 58 2 1 16 0 6 0 2 0 4 1 6 0 29 0 57 14 7 0 1 0 3 1 7 0 20 0 60 20 8 1 6 6 4 0 8 6 35 35 24 0 9 0 1 1 3 0 9 0 20 20 60 0 4 1 0 1 3 1 3 4 1 0 13 38 13 38 2 1 1 0 3 3 2 13 13 0 38 38 3 0 0 3 1 1 3 0 0 60 20 20 4 0 0 0 0 0 4 0 0 0 0 0 5 2 4 9 9 4 5 7 14 32 32 14 6 0 . 0 4 3 0 6 0 0 57 43 0 7 0 4 0 0 1 7 0 80 0 0 20 8 1 3 3 4 1 8 8 25 25 33 8 9 0 0 1 2 1 9 0 0 25 50 25 5 1 0 0 1 0 6 5 1 0 0 14 0 86 2 0 0 0 2 5 2 0 0 O 29 71 3 o O 1 0 0 3 0 0 100 0 0 4 0 0 1 1 5 4 0 0 14 14 71 5 0 0 2 4 10 5 0 0 13 25 63 6 0 0 0 2 2 6 0 0 0 50 50 7 0 0 0 0 1 7 0 0 0 0 100 8 0 0 0 0 1 8 0 0 0 0 100 9 0 0 0 0 0 9 0 0 0 0 0 97 Table 6. Case "B" S t a t e / C o n t r o l Outcome Frequency and P r o b a b i l i t y D i s t r i b u t i o n s f o r Case B Based on H i s t - o r i c a l Data With Temperatures <- 12 Degrees C e l c i u s F R E Q U E N C Y P R O B A B I L I T Y (%) STATE (J) STATE (1) CONTROL 1 2 3 4 5 1 1 0 0 0 0 0 2 0 0 0 0 0 3 0 0 0 0 0 4 0 2 0 0 0 5 1 3 0 0 0 6 0 0 0 0 0 7 0 3 0 0 o 8 5 3 0 0 0 g 0 0 0 0 0 2 1 : 0 6 0 0 1 2 0 2 2 0 0 3 • 0 1 0 0 0 4 2 13 1 2 0 : 5 2 13 2 2 0 G 0 3 0 0 0 7 0 4 1 2 0 8 1 6 2 2 0 9 • 0 0 5 0 0 3 1 0 1 0 0 1 2 0 0 0 1 0 3 0 0 0 1 0 4 0 4 1 1 1 5 1 1 2 1 0 6 0 0 0 0 0 7 0 1 0 3 0 8 1 3 2 4 0 9 0 0 1 2 0 4 1 0 0 2 1 1 2 0 0 0 0 0 3 0 0 0 0 0 4 0 0 0 0 0 5 0 1 5 2 0 6 0 0 0 0 0 7 0 2 0 0 0 8 1 2 3 4 0 9 0 0 1 1 1 5- 1 0 0 1 0 2 2 0 O 0 0 o 3 0 0 0 0 0 4 0 0 1 0 1 5 0 0 0 0 0 6 o 0 0 0 0 7 0 0 0 0 1 8 0 0 0 0 0 9 0 0 0 0 0 STATE (J) STATE (i ) CONTROL 1 2 3 4 5 1 1 0 0 0 0 0 2 0 0 0 0 0 3 0 0 0 0 0 4 O 100 0 0 0 5 25 75 0 0 0 6 0 0 0 0 0 7 0 100 0 0 0 8 63 38 0 0 0 9 0 0 0 0 0 2 1 0 86 0 0 14 2 0 50 50 0 0 3 0 100 0 0 0 4 11 72 6 11 0 5 11 68 11 11 0 6 0 100 0 0 0 7 0 57 14 29 0 8 9 55 18 18 0 9 0 0 100 0 0 3 1 0 50 0 0 50 2 0 0 0 100 0 3 0 0 0 100 0 4 0 57 14 14 14 5 20 20 40 20 0 6 0 0 0 0 0 7 0 25 0 75 0 8 10 30 20 40 0 9 0 0 33 67 0 4 1 0 0 50 25 25 2 0 0 0 0 0 3 0 0 0 0 0 4 0 0 0 0 0 5 0 13 63 25 0 6 0 0 0 0 0 7 0 100 0 0 0 8 10 20 30 40 0 9 0 0 33 33 33 5 1 0 0 33 0 67 2 0 0 0 0 0 3 0 0 0 0 0 4 0 0 50 0 50 5 0 0 0 0 0 6 0 0 0 0 0 7 0 0 0 0 100 8 0 0 0 0 0 9 0 0 0 0 0 98 Table 7. Case "B" S t a t e / C o n t r o l Outcome Frequency and Prob- a b i l i t y D i s t r i b u t i o n s f o r Case B Based on H i s t o r i c a l  Data With Temperatures 12 > T <16 Degrees C e l c i u s F R E Q U E N C Y P R O B A B I L I T Y (%) STATE ( j ) STATE ( j ) STATE (1) CONTROL 1 2 3 4 5 STATE (O CONTROL 1 2 3 4 5 1 1 7 5 0 0 0 1 1 58 42 0 0 0 2 0 0 0 0 0 2 0 C 0 0 0 3 0 0 0 0 0 3 0 0 0 0 0 4 8 2 0 0 0 4 80 20 0 0 0 5 6 1 0 0 0 5 86 14 0 0 0 6 0 0 0 0 0 S 0 0 0 0 0 7 1 1 0 0 0 7 50 50 0 0 0 8 5 3 0 0 0 8 63 38 0 0 0 9 0 0 0 0 0 9 : 0 0 0 0 0 2 1 0 5 1 0 0 2 1 0 83 17 0 0 2 0 5 1 0 0 2 : 0 83 17 0 0 3 0 1 0 0 0 3 0 100 0 0 0 4 0 3 0 0 0 4 0 100 0 0 0 5 5 9 5 2 0 5 24 43 24 10 0 6 0 2 0 0 0 6 0 100 0 0 0 7 0 0 0 0 0 7 0 0 0 0 0 8 2 1 1 2 3 0 8 11 61 1 1 17 0 9 0 1 0 0 0 9 0 100 0 0 0 3 1 0 0 O 0 0 3 1 0 0 0 o 0 2 0 1 1 1 0 2 : 0 33 33 33 0 3 0 0 0 0 0 3 0 0 0 0 0 4 0 2 1 0 0 4 0 67 33 0 0 5 0 4 1 1 0 5 0 67 17 17 0 6 0 0 0 0 0 6 0 0 0 0 0 7 0 0 0 0 1 7 0 0 0 0 100 8 0 2 4 0 0 8 0 33 67 0 0 9 0 0 0 1 0 9 0 0 0 100 0 4 1 0 1 1 0 0 4 1 0 50 50 0 0 2 0 0 0 2 0 2 0 0 0 100 0 3 0 0 0 0 0 3 0 0 0 0 0 4 0 0 0 0 0 4 0 0 0 0 0 5 2 2 2 5 2 5 15 15 15 38 15 6 0 0 0 1 0 6 0 0 0 100 0 7 0 2 0 0 1 7 0 67 0 0 33 8 0 - 0 0 0 0 8 0 0 0 0 0 9 0 0 0 0 0 9 0 0 0 0 0 5 1 0 0 0 0 0 5 1 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 3 0 0 0 0 0 3 0 0 0 0 0 4 0 0 0 0 1 4 0 0 0 0 100 5 0 0 1 2 2 5 0 0 20 40 40 6 0 0 0 0 0 6 0 0 0 ' 0 0 7 0 0 0 0 0 : 7 0 0 0 0 0 8 0 0 0 0 0 8 0 0 0 0 0 9 0 0 0 0 0 : 9 : 0 0 0 0 0 99 Table 8, Case "B" S t a t e / C o n t r o l Outcome Frequency and Prob- a b i l i t y D i s t r i b u t i o n s f o r Case B Based on H i s t o r i c a l  Data With Temperatures >= 16 Degrees C e l c i u s F R E Q U E N C Y P R O B A B I L I T Y (%) STATE ( j ) STATE ( j ) STATE (1) : CONTROL 1 2 3 4 5 STATE (1) CONTROL • 1 2 3 4 5 1 : 1 3 0 0 0 0 1 1 100 0 0 0 0 2 2 0 0 0 0 2 100 0 0 0 0 3 0 0 0 0 0 3 0 0 0 0 0 4 5 1 0 0 0 4 83 17 0 0 0 5 7 3 0 2 0 5 58 25 0 17 0 6 0 0 0 1 0 6 0 0 0 100 0 : 7 2 0 0 0 0 7 100 0 0 0 0 8 0 0 0 0 0 8 0 0 0 0 0 9 9 0 0 0 0 0 2 1 0 1 0 0 0 2 1 0 100 0 0 0 2 2 9 0 1 0 2 17 75 0 8 0 3 1 1 0 0 0 3 50 50 0 0 0 4 2 1 3 0 0 4 33 17 50 0 0 5 3 15 3 2 0 5 13 65 13 9 0 6 0 3 2 0 0 6 0 60 40 0 0 7 0 0 0 0 0 7 0 0 0 0 0 8 0 1 0 0 0 8 0 100 0 0 0 9 0 2 0 1 0 9* 0 67 0 33 0 3 1 0 0 2 0 0 3 1 0 0 100 0 0 2 0 0 7 0 0 2 0 0 100 0 0 3 1 0 1 3 0 3 20 0 20 60 0 4 0 0 0 0 0 4 0 0 0 0 0 5 0 6 1 1 0 5 0 75 13 13 0 6 : 0 2 0 4 1 6 0 29 0 57 14 7 0 0 0 0 0 7 0 0 0 0 0 8 0 1 0 0 0 8 0 100 0 0 0 9 0 1 0 0 0 9 0 100 0 0 0 4 1 0 0 0 0 2 4 1 0 0 0 0 100 2 1 1 0 1 3 2 17 17 0 17 50 3 0 0 3 1 1 3 0 0 60 20 20 4 0 0 0 0 0 4 0 0 0 0 0 5 0 1 2 2 2 5 0 14 29 29 29 6 0 0 4 2 0 6 0 0 67 33 0 7 0 0 0 0 0 7 0 0 0 0 0 8 0 1 0 0 1 8 0 50 0 0 50 9 0 0 0 1 0 9 0 0 0 100 0 5 1 0 0 0 0 4 5 1 0 0 0 0 100 2 0 0 0 2 5 2 • 0 0 0 29 7 1 3 0 0 1 0 0 3 • 0 0 100 0 0 4 0 0 0 1 3 4 0 0 0 25 75 5 0 0 1 2 8 5 : 0 0 9 18 73 6 0 0 0 2 2 6 : 0 0 0 50 50 7 0 0 0 0 0 7 0 0 0 0 0 8 0 0 0 0 1 8 0 0 0 0 100 9 0 0 0 0 0 9 : 0 0 0 0 0 100 that there i s a str o n g tendency to e i t h e r remain i n the same s t a t e , or move e i t h e r a s i n g l e s t a t e up or down, over the d e c i s i o n p e r i o d . For example, i n Table 5, given a c u r r e n t s t a t e 2 and a c o n t r o l d e c i s i o n #5, there i s a 59 percent p r o b a b i l i t y of remaining i n s t a t e 2 and a 16 percent p r o b a b i l i t y of moving to e i t h e r s t a t e 1 or 3 over the next time p e r i o d . T h i s tendency to remain i n the same s t a t e or move e i t h e r one s t a t e up or down i s i l l u s t r a t e d i n the S t a t e : S t a t e b a s e l i n e frequency matrix given i n Table 9 below. Tab l e 9. B a s e l i n e S t a t e / S t a t e Frequency M a t r i x BASELINE FREQUENCY MATRIX INITIAL NEXT STATE ( j ) STATE ( i ) 1 2 3 4 5 1 1 1 0 0 0 2 1 1 1 0 0 3 0 1 1 1 0 4 0 0 1 1 1 5 0 0 0 1 1 The b a s e l i n e frequency matrix was added to the h i s t o r i c a l frequency m a t r i c e s i n Tab l e 5 t o 8 before the p r o b a b i l i t i e s were c a l c u l a t e d . Where no data e x i s t e d f o r a c o n t r o l a l t e r n a t i v e the r e s u l t i n g p r o b a b i l i t y f o r a p a r t i c u l a r s t a t e outcome i s e i t h e r 0.33 or 0.50. The impact of adding the b a s e l i n e matrix t o f r e -quency m a t r i c e s generated from h i s t o r i c a l data records f o r use i n a Markov P o l i c y - I t e r a t i o n a p p l i c a t i o n i s examined i n S e c t i o n 4.2. 101 A simulated or known t r a n s i t i o n matrix was c o n s t r u c t e d f o r use in deve l o p i n g a dynamic Markov P o l i c y - I t e r a t i o n procedure c o n s i s t e n t with low DO b u l k i n g c o n d i t i o n s . The t r a n s i t i o n matrix, i l l u s -t r a t e d i n Table 10 below, i s c o n s i s t e n t with the p o l i c y that the higher the DO c o n c e n t r a t i o n , and the lower the F/M r a t i o , the gr e a t e r the p r o b a b i l i t y that the f o l l o w i n g s t a t e w i l l be lower (lower SVI). R e f l e c t i n g e r r o r s i n determining the c u r r e n t s t a t e and random f l u c t u a t i o n s i n p l a n t performance, a r e l a t i v e l y broad range of p o s s i b l e s t a t e outcomes was i n c o r p o r a t e d i n t o the proba-b i l i t y d i s t r i b u t i o n of most c o n t r o l o p t i o n s . The c l o s e r the p o l i c y i s t o the h i g h DO and low F/M c o n t r o l a l t e r n a t i v e , the gr e a t e r the p r o b a b i l i t y t h a t the next s t a t e w i l l be lower. Table 10. Case "C" Simulated (Known) P r o b a b i l i t y M a t r i x CONTROL INITIAL NEXT STATE ( j ) ALTERNATIVE STATE DESCRIPTION ( i ) 1 2 3 4 5 LOW DO 1 0.4 0.5 0.1 0 0 LOW F/M 2 0.15 0.45 0.25 0.1 0.05 3 0 0.15 0.5 0.25 0.1 (#1) 4 0 0.05 0.15 0.6 0.2 5 0 0 0.05 0.25 0.7 LOW DO 1 0.35 0.45 0.1 5 0.05 0 MEDIUM F/M 2 0.1 0.35 0.3 0.15 0.1 3 0 0.05 0.3 0.3 0.35 (#2) 4 0 0 0.1 0.3 0.6 5 0 0 0 0.1 0.9 LOW DO 1 0.3 0.4 0.15 0.1 0.05 HIGH F/M 2 0 0.25 0.3 0.25 0.2 3 0 0 0.1 0.3 0.6 (#3) 4 0 0 0 0.05 0.95 5 0 0 0 0 1 102 S t a t e 10. (cont'd) CONTROL INITIAL NEXT STATE ( j ) ALTERNATIVE STATE DESCRIPTION ( i ) 1 2 3 4 5 MEDIUM DO 1 0.45 0.5 0.05 0 0 LOW F / M 2 0.35 0.5 0.15 0 0 3 0.1 0.3 0.4 0.15 0.05 (#4) 4 0 0.1 0.4 0.4 0.1 5 0 0 0.15 0.45 0.4 MEDIUM DO 1 0.4 0.5 0.05 0.05 0 MEDIUM F / M 2 0.2 0.45 0.2 0.1 0.05 3 0.05 0.2 0.35 0.25 0.15 (#5) 4 0 0.05 0.3 0.35 0.3 5 0 0 0.1 0.3 0.6 MEDIUM DO 1 0.35 0.5 0.1 0.05 0 HIGH F / M 2 0.1 0.4 0.25 0.15 0.1 3 0.05 0.1 0.35 0.25 0.25 (#6) 4 0 0.05 0.2 0.25 0.5 5 0 0 0.05 0.2 0.75 HIGH DO 1 0.5 0.5 0 0 0 LOW F / M 2 0.4 0.55 0.05 0 0 3 0.2 0.5 0.3 0 0 (#7) 4 0.05 0.2 0.6 0.15 0 5 0 0.05 0.25 0.65 0.05 HIGH DO 1 0.45 0.55 0 0 0 MEDIUM F / M 2 0.3 0.6 0.1 0 0 3 0.1 5 0.35 0.45 0.05 0 (#8) 4 0 0.15 0.5 0.3 0.05 5 0 0 0.2 0.55 0.25 HIGH DO 1 0.4 0.6 0 0 0 HIGH F / M 2 0.2 0.6 0.2 0 0 3 0.1 0.25 0.55 0.1 0 (#9) 4 0 0.1 0.35 0.45 0.1 5 0 0 0.15 0.5 0.35 103 3 . 3 . 5 E s t a b l i s h m e n t of D e c i s i o n A n a l y s i s U t i l i t i e s The concept of u t i l i t y combines both t a n g i b l e and i n t a n g i b l e c o n s i d e r a t i o n s . For example , the o p e r a t i o n of a p l a n t at h i g h DO c o n c e n t r a t i o n s i s more expens ive than o p e r a t i o n at low DO concen-t r a t i o n s a n d , by t h i s c r i t e r i o n a l o n e , h igh DO o p e r a t i o n has a lower "va lue" . However, i f the p l a n t i s b u l k i n g due to low DO c o n d i t i o n s , the low v a l u e a s s o c i a t e d w i t h h igh energy c o s t i s o f f s e t by improved p l a n t per formance . The concept of u t i l i t y i n c l u d e s both the o b j e c t i v e c o s t s of energy and the i n t r i n s i c v a l u e s of p r o c e s s p e r f o r m a n c e . As r e l a t i v e u t i l i t y l e v e l s a r e s u b j e c t i v e , i t i s e a s i e s t to beg in by a s s i g n i n g to the most d e s i r a b l e outcome a maximum u t i l i t y of 100, and to the l e a s t d e s i r a b l e outcome a minimum u t i l i t y not l e s s than 0. Note t h a t t h e r e may be more than one p o t e n t i a l outcome w i t h the same u t i l i t y , when s e v e r a l outcomes are a l l e q u a l l y d e s i r a b l e or u n d e s i r a b l e . U t i l i t i e s were a s s i g n e d i n d e p e n d e n t l y by three o p e r a t o r s and the author f o r each of the p o s s i b l e 36 SVI /SS combinat ions d e s c r i b e d i n S e c t i o n 3 . 3 . 3 . The t h r e e u t i l i t i e s presented i n T a b l e s 11 to 13 and i d e n t i f i e d as o p e r a t o r " A " , " B " , and " C " u t i l i t i e s , were de termined by h a v i n g each of the p l a n t o p e r a t o r s f i r s t s e l e c t the most d e s i r a b l e outcome and the l e a s t d e s i r a b l e outcome, and a s s i g n i n g to these outcomes the u t i l i t y va lues of 100 and 0, r e s p e c t i v e l y . The o p e r a t o r s were then i n s t r u c t e d to a s s i g n c o m p a r a t i v e u t i l i t i e s t o the remain ing SVI and e f f l u e n t SS 104 Table 11. Operator "A" U t i l i t y M a t r i x EFFLUENT SOLIDS SLUDGE VOLUME INDEX (mL/g) (mg/L) 20 60 100 150 500 1000 5 60 80 100 100 50 30 10 50 70 90 90 40 15 15 40 50 80 80 30 10 20 30 30 50 50 20 5 60 5 5 5 5 5 0 100 0 0 0 0 0 0 Table 12. Operator "B" U t i l i t y M a t r i x EFFLUENT SOLIDS SLUDGE VOLUME INDEX (mL/g) (mg/L) 20 60 100 150 500 1000 5 20 60 100 100 60 20 10 20 60 100 100 50 15 15 20 60 100 100 40 10 20 10 50 90 90 30 5 60 5 30 20 20 10 0 100 0 0 0 0 0 0 Table 13. Operator "C" U t i l i t y M a t r i x EFFLUENT SOLIDS SLUDGE VOLUME INDEX (mL/g) (mg/L) 20 60 100 150 500 1000 5 60 80 100 90 60 20 10 80 90 100 80 60 20 15 70 90 100 80 60 20 20 70 80 100 80 50 40 60 20 60 60 60 30 20 100 0 5 5 5 5 0 105 combinations w i t h i n the range of 0 to 100. U t i l i t y "D", i l l u s -t r a t e d i n Table 14, was c o n s t r u c t e d i n a s i m i l a r manner, based on g e n e r a l management c o n s i d e r a t i o n s . I t was assumed that the i d e a l c o n d i t i o n ( u t i l i t y of 100) would be an SVI of 60 and the lowest e f f l u e n t SS c o n c e n t r a t i o n . S i m i l a r l y , the worst combination was a s s i g n e d to the h i g h e s t SVI and e f f l u e n t SS combination. In a s s i g n i n g the remaining outcome u t i l i t i e s , i t was assumed that p r o g r e s s i v e l y i n c r e a s i n g or d e c r e a s i n g SVI values would be a s s i g n e d d e c r e a s i n g u t i l i t i e s f o r a given e f f l u e n t SS concentra-t i o n . F u r t h e r , f o r a given SVI v a l u e , i n c r e a s i n g e f f l u e n t SS c o n c e n t r a t i o n s were a s s i g n e d d e c r e a s i n g u t i l i t y v a l u e s . Table 14. Operator "D" U t i l i t y M a t r i x EFFLUENT SOLIDS SLUDGE VOLUME INDEX (mL/g) (mg/L) 20 60 100 150 500 1000 5 95 100 97 88 76 69 10 94 98 94 84 72 65 15 84 92 85 73 60 52 20 64 78 65 53 39 29 60 22 27 23 17 1 1 8 100 6 10 7 5 2 0 3.3.6 Markov P o l i c y - I t e r a t i o n U t i l i t i e s For the Markov P o l i c y - I t e r a t i o n techniques, the f i n a l e f f l u e n t suspended s o l i d s c r i t e r i a was dropped and the SVI l e v e l s reduced to 5 ranges d e s c r i b e d i n S e c t i o n 3.3.2. A second u t i l i t y c r i t e r i a 106 of c o n t r o l a l t e r n a t i v e was then added to introduce the element of c o s t to the u t i l i t y matrix s t r u c t u r e . Three DO and F/M c o n t r o l l e v e l s , forming 9 p o t e n t i a l combinations, were combined with 5 p o t e n t i a l SVI outcomes or s t a t e s , r e s u l t i n g i n a 45 element u t i l i t y m a t r i x . Increased F/M r a t i o and DO c o n c e n t r a t i o n l e v e l s r e s u l t i n higher o p e r a t i n g c o s t s , because of the i n c r e a s e d sludge generated and the i n c r e a s e d energy c o s t s . As the Markov u t i l i t y matrix r e f l e c t s both process c o n d i t i o n and c o s t , two d i s t i n c t u t i l i t y c h a r a c t e r i s t i c s can be d e f i n e d f o r each parameter. U t i l i t i e s were d e f i n e d based on the f o l l o w i n g c o n t r o l and s t a t e d e f i n i t i o n s given i n Table 15. Assuming that S t a t e 2 i s the " i d e a l " SVI range, under c o n d i t i o n s of low energy (low DO and F/M) a r e l a t i v e u t i l i t y of 100 c o u l d be a s s i g n e d . For the same energy l e v e l , States 1 and 3 would be somewhat lower than State 2. State 2 might be a s s i g n e d a s l i g h t l y lower u t i l i t y than State 1 because S t a t e 1 i s w i t h i n the range of b u l k i n g . S t a t e s 4 and 5 represent extreme b u l k i n g with a s s o c i a t e d low u t i l i t i e s . The r e s u l t a n t r e l a t i o n s h i p between SVI range and u t i l i t y i s somewhat p a r a b o l i c i n shape. 107 Table 1 5 . C o n t r o l and State D e s c r i p t i o n s D e f i n i t i o n s CONTROL ALTERNATIVE CONTROL DESCRIPTION 1 LOW DO LOW F/M 2 LOW DO MEDIUM F/M 3 LOW DO HIGH F/M 4 MEDIUM DO LOW F/M 5 MEDIUM DO MEDIUM F/M 6 MEDIUM DO HIGH F/M 7 HIGH DO LOW F/M 8 HIGH DO MEDIUM F/M 9 HIGH DO HIGH F/M CONTROL ] DEFINITIONS LOW DO DO <= 2.0 (mg/L) MEDIUM DO 2.0 (mg/L) < DO < 4.0 (mg/L) HIGH DO 4.0 (mg/L) <= DO LOW F/M F/M <= 0.2 (1/day) MEDIUM F/M 0.2 (1/day) < F/M < 0.4 (1/day) HIGH F/M 0.4 (1/day) <= F/M STATE STATE DEFINITIONS 1 SVI <= 100 (mL/g) 2 100 (mL/g) < SVI <= 200 (mL/g) 3 200 (mL/g) < SVI <= 300 (mL/g) 4 300 (mL/g) < SVI <= 500 (mL/g) 5 500 (mL/g) < SVI The lowest c o s t a l t e r n a t i v e would be the combination of low DO and low F/M. For the " i d e a l " S t a t e 2 SVI range, the u t i l i t y i s as s i g n e d 100. Assuming that incremental i n c r e a s e s i n F/M have lower energy c o s t s than i n c r e a s e s i n DO, the f o l l o w i n g a l t e r n a -t i v e combinations represent a reasonable ranking of c o n t r o l a l t e r n a t i v e s , i n terms of energy c o s t and u t i l i t y : 108 DO F/M COST UTILITY low low low low medium low h i g h medium medium medium high low medium high h i g h h i g h h i g h low v v medium hi g h h i g h low Depending upon whether the energy increments between each of the DO and F/M combinations i s r e l a t i v e l y continuous, or whether the DO increments exceed the F/M u t i l i t y range, the r e s u l t i n g u t i l i t y curve w i l l be " e x p o n e n t i a l " or " p l a t e a u - l i k e " i n shape. The r e l a t i v e s lope of the u t i l i t y curve depends upon whether the operator i s r e l u c t a n t to expend energy. I f the p l a n t performance i n terms of b u l k i n g i s more c r i t i c a l than energy c o s t s , the u t i l i t y curve w i l l have a shallower s l o p e . On the other hand, an extreme r e l u c t a n c e to expend energy, even a t the expense of sludge b u l k i n g , w i l l r e s u l t i n a steep s l o p e . A u t i l i t y value of 100 was a s s i g n e d the most d e s i r a b l e s t a t e and c o n t r o l combination. Next a r e l a t i v e u t i l i t y v a lue of 80 was s e l e c t e d as being a comparable v a l u e f o r the combination of most d e s i r a b l e s t a t e , and l e a s t d e s i r a b l e c o n t r o l a l t e r n a t i v e as shown i n the f o l l o w i n g : 109 CONTROL STATE 1 STATE 2 STATE 3 STATE 4 STATE 5 LOW DO LOW DO LOW DO MED DO MED DO MED DO HIGH DO HIGH DO HIGH DO LOW F/M MED F/M HIGH F/M LOW F/M MED F/M HIGH F/M : LOW F/M : MED F/M : HIGH F/M 100 80 By i n t e r p o l a t i n g between these two extreme values, u t i l i t i e s are estimated f o r a l l c o n t r o l a l t e r n a t i v e s w i t h i n the most d e s i r a b l e s t a t e (STATE 2) : CONTROL STATE 1 STATE 2 STATE 3 STATE 4 STATE 5 LOW DO . . LOW F/M 100 LOW DO : MED F/M 97 LOW DO : HIGH F/M 95 MED DO ' LOW F/M 90 MED DO : MED F/M 87 MED DO : HIGH F/M 86 HIGH DO : LOW F/M 85 HIGH DO : MED F/M 82 HIGH DO : HIGH F/M 80 To e s t a b l i s h r e l a t i v e u t i l i t i e s f o r s t a t e v a r i a t i o n s , a range of u t i l i t i e s are estimated f o r the most d e s i r a b l e or lowest c o s t c o n t r o l a l t e r n a t i v e (LOW DO : LOW F/M), based on a comparison with the most d e s i r a b l e and l e a s t d e s i r a b l e u t i l i t i e s a l r e a d y def i n e d . CONTROL STATE 1 STATE LOW DO : LOW F/M 90 100 LOW DO • MED F/M 97 LOW DO ' • HIGH F/M 95 MED DO : LOW F/M 90 MED DO t MED F/M 87 MED DO : HIGH F/M 86 HIGH DO : LOW F/M 85 HIGH DO : MED F/M 82 HIGH DO : HIGH F/M 80 STATE 3 STATE 4 STATE 5 80 30 10 110 The above procedure r e s u l t e d i n a general p a r a b o l i c u t i l i t y shape fo r s t a t e v a r i a t i o n , while the c o n t r o l v a r i a t i o n has a more e x p o n e n t i a l shape. Based on t h i s g r a p h i c a l r e l a t i o n s h i p , the remaining u t i l i t i e s were d e f i n e d as shown i n T a b l e 16, forming u t i l i t y matrix #1. Seven u t i l i t y m a t r i c e s were c o n s t r u c t e d with the above c o n s i d e r a -t i o n s i n mind. U t i l i t y m a t r i c e s #1, #2 and #3, i l l u s t r a t e d i n Tables 16, 17, and 18, and i n F i g u r e s 14, 15 and 16, represent incremental u t i l i t y r e d u c t i o n s f o r p o l i c i e s of low, medium and high r e l a t i v e energy c o s t s . U t i l i t y m a t r i c e s #4, #5, and #6, i l l u s t r a t e d i n Tables 19, 20 and 21, and i n F i g u r e s 17, 18 and 19, represent p l a t e a u u t i l i t y r e d u c t i o n s f o r p o l i c i e s of low, medium and high energy c o s t s . U t i l i t y matrix #7, i l l u s t r a t e d i n Table 22 and i n F i g u r e 20, r e p r e s e n t s a p o l i c y of no energy c o s t (or c o n s i d e r a t i o n ) and r e f l e c t s only b u l k i n g c o n s i d e r a t i o n s . These u t i l i t i e s are used i n the a n a l y s i s of Case B and Case C i n S e c t i o n 4.2 and 4.3 r e s p e c t i v e l y . 11 1 Table 16. U t i l i t y Matrix 1 UTILITY #1 MATRIX CONTROL ALTERNATIVE 1 STATE 2 U T I L I T I E S 3 4 5 1 90 100 80 30 10 2 86 97 76 27 7 3 84 95 74 25 6 4 78 90 68 23 3 5 74 87 65 20 2 6 73 86 64 19 1 7 72 85 63 18 0 8 69 82 60 13 0 9 67 80 55 12 0 Figure 14. 3-D Plot of U t i l i t y Matrix 1 112 Table 17. U t i l i t y M a t r i x 2 UTILITY #2 MATRIX CONTROL ALTERNATIVE 1 STATE 2 U T I L I T I E S 3 4 5 1 90 100 80 35 12 2 84 93 76 32 1 1 3 78 85 71 29 10 4 67 74 61 21 6 5 63 70 58 18 5 6 59 65 55 16 4 7 51 55 46 10 2 8 48 53 43 9 1 9 45 50 40 8 0 F i g u r e 15. 3-D P l o t of U t i l i t y M a t r i x 2 9 8 7 6 5 4 3 2 ALTERNATIVE 1 1 3 T a b l e 18. U t i l i t y M a t r i x 3 UTILITY #3 MATRIX CONTROL STATE U T I L I T I E S ALTERNATIVE 1 2 3 4 5 1 90 100 80 35 12 2 74 83 64 27 8 3 62 70 52 21 5 4 53 60 43 16 3 5 45 52 36 13 2 6 39 45 31 10 1 7 33 39 27 8 1 8 29 34 23 6 0 9 25 30 20 5 0 F i g u r e 16. 3-D P l o t of U t i l i t y M a t r i x 3 9 8 7 6 5 4 3 2 I ALTERNATIVE 114 Table 19. U t i l i t y M a t r i x 4 UTILITY #4 MATRIX CONTROL ALTERNATIVE 1 STATE 2 U T I L I T I E S 3 4 5 1 90 100 80 30 10 2 90 100 80 30 10 3 90 100 80 30 10 4 75 85 70 25 8 5 75 85 70 25 8 6 75 85 70 25 8 7 65 75 60 20 7 8 65 75 60 20 7 9 65 75 60 20 7 F i g u r e 17. 3-D P l o t of U t i l i t y M a t r i x 4 9 8 7 6 5 4 3 2 I ALTERNATIVE 115 Table 20. U t i l i t y M a t r i x 5 UTILITY #5 MATRIX CONTROL ALTERNATIVE 1 STATE 2 UTILITIES 3 4 5 1 90 100 80 30 10 2 90 100 80 30 10 3 90 100 80 30 10 4 65 70 55 20 7 5 65 70 55 20 7 6 65 70 55 20 7 7 45 50 40 15 5 8 45 50 40 15 5 9 45 50 40 15 5 Figure 18. 3-D P l o t of U t i l i t y M a t r i x 5 9 8 7 6 5 4 3 2 I ALTERNATIVE 116 Table 21. U t i l i t y M a t r i x 6 UTILITY #6 MATRIX CONTROL ALTERNATIVE 1 STATE 2 U T I L I T I E S 3 4 5 1 90 100 80 30 10 2 90 100 80 30 10 3 90 100 80 30 10 4 45 50 40 15 4 5 45 50 40 15 4 6 45 50 40 15 4 7 22 25 20 8 2 8 22 25 20 8 2 9 22 25 20 8 2 F i g u r e 19. 3-D P l o t of U t i l i t y M a t r i x 6 9 8 7 6 5 4 3 2 I ALTERNATIVE 1 1 7 Table 2 2 . U t i l i t y M a t r i x 7 UTILITY #7 MATRIX CONTROL STATE U T I L I T I E S ALTERNATIVE 1 2 3 4 5 1 90 100 80 30 10 2 90 100 80 30 10 3 90 100 80 30 10 4 90 100 80 30 10 5 90 100 80 30 10 6 90 100 80 30 10 7 90 100 80 30 10 8 90 100 80 30 10 9 90 100 80 30 10 F i g u r e 2 0 . 3-D P l o t of U t i l i t y M a t r i x 7 ALTERNATIVE 118 4.0 RESULTS OF DECISION THEORY APPLICATIONS TO SLUDGE BULKING CONTROL As e x p l a i n e d p r e v i o u s l y , v a r i o u s combinations of SVI and e f f l u e n t SS are p o s s i b l e at the French Creek p l a n t , depending p a r t l y on the c o n t r o l s t r a t e g y adopted and p a r t l y on i n f l u e n t and other c o n d i t i o n s which cannot be c o n t r o l l e d . In the p r e v i o u s chapter the v a r i o u s p o s s i b l e s t a t e s were c a t e g o r i z e d and assigned u t i l i t y v a l u e s ; the v a r i o u s p o s s i b l e c o n t r o l s t r a t e g i e s were d e f i n e d ; and the p r o b a b i l i t i e s of moving from one s t a t e to another (given any p a r t i c u l a r c o n t r o l s t r a t e g y ) were assessed. In t h i s c hapter, three approaches to a p p l y i n g d e c i s i o n a n a l y s i s to a c t i v a t e d sludge b u l k i n g c o n t r o l are undertaken. Defined as Case A, B and C, the o b j e c t i v e s of the three approaches are as f o l l o w s : (1) An a p p l i c a t i o n of Bayesian d e c i s i o n theory to determine a s i n g l e "best" c o n t r o l s t r a t e g y , independent of the i n i t i a l s t a t e , and t a k i n g i n t o account 36 p o s s i b l e SVI and e f f l u e n t SS combinations or s t a t e s . T h i s i s the s t r a t e g y which would maximize the expected u t i l i t y at the end of the d e c i s i o n p e r i o d . (2) An e x t e n s i o n of (1) to take i n t o account the f a c t t h at the l i k e l i h o o d of success of a p a r t i c u l a r c o n t r o l i s p a r t l y dependent upon the c u r r e n t s t a t e or c o n d i t i o n of the p l a n t , and t h a t , s e v e r a l stages i n the f u t u r e , the p l a n t may end up i n a very u n d e s i r a b l e s t a t e (with low u t i l i t y ) . T h i s concern can be handled e l e g a n t l y by Howard's (1960) Markov P o l i c y -I t e r a t i o n approach. (3) An e x t e n s i o n of (2) to allow p r o b a b i l i t i e s to be updated as o p e r a t i n g c o n d i t i o n s change. 119 4 . 1 Case "A" - S t a t i c Solution For Combined Bulking and Effluent Suspended Solids C r i t e r i a As previously described in Chapter 2, sludge bulking can result in either low or high s o l i d s losses, depending upon the degree of bulking and the capacity of the secondary c l a r i f i e r . A bulking sludge can result in an extremely clear e f f l u e n t , as long as the c l a r i f i e r hydraulic c h a r a c t e r i s t i c s are s u f f i c i e n t to prevent the sludge mass from r i s i n g and being discharged over the weirs. Depending upon the plant design, and influent and biomass charac-t e r i s t i c s , various combinations of bulking, as measured by SVI, and e f f l u e n t suspended s o l i d s concentrations are possible. Each combination has a value or u t i l i t y to the plant operator. As plant performance i s generally rated by the effluent BOD (or COD) and suspended so l i d s q u a l i t y , the lower the suspended s o l i d s l e v e l , the higher the u t i l i t y . On the other hand, the degree of sludge bulking only adversely a f f e c t s the effluent when so l i d s are not trapped in the sludge (low SVI) or when bulking i s so severe that sludge i s discharged (high SVI). As bulking can resul t in lower effluent s o l i d s l e v e l s , the u t i l i t y of bulking l e v e l s r e f l e c t s the anticipated effluent q u a l i t y and the pote n t i a l for extensive bulking and biomass l o s s . Based on the assumption that sludge bulking at the French Creek WPCC i s a function of DO and F/M operating ranges, f i v e years of operating data were examined to determine SVI and effluent SS p r o b a b i l i t i e s for selected control operating ranges. By multiplying the u t i l i t y for each SVI/SS combination by the 120 p r o b a b i l i t y of that combination o c c u r r i n g f o r a s p e c i f i c DO/(F/M) c o n t r o l s e t t i n g , expected u t i l i t i e s f o r each c o n t r o l s e t t i n g are generated. The technique i s s t a t i c i n nature and independent of the i n i t i a l s t a t e , as i t i s based on a l a r g e data base ( s i x years) and assumes t h a t there i s one "best" average o p e r a t i n g s e t t i n g to maximize the expected u t i l i t y . Most a c t i v a t e d sludge f a c i l i t i e s attempt to operate at a s i n g l e DO and F/M l e v e l . 4 . 1 . 1 P r o b a b i l i t y Determinations From H i s t o r i c a l Data The d e t e r m i n a t i o n of p r o b a b i l i t i e s from the French Creek h i s t o r i c a l o p e r a t i n g data i s d e s c r i b e d i n S e c t i o n 3.3.4. From the cumulative frequency curves f o r the DO and F/M o p e r a t i n g ranges (Appendix B), f i v e c o n t r o l ranges were s e l e c t e d f o r each parameter. The ranges below were s e l e c t e d to achieve a r e l a t i v e l y uniform number of DO/(F/M) o p e r a t i n g c o n d i t i o n s . The c o n t r o l and s t a t e ranges d e s c r i b e d i n Chapter 3 are repeated here f o r ease of r e f e r e n c e . DO CONTROL RANGES DO <= 1.5 (mg/L) ... (1) 1.5 (mg/L) < DO <= 2.5 (mg/L) ... (2) 2.5 (mg/L) < DO <= 3.5 (mg/L) ... (3) 3.5 (mg/L) < DO <= 4.5 (mg/L) ... (4) 4.5 (mg/L) < DO (5) 121 F/M CONTROL RANGES . F/M <= 0.18 (day"]) ... (1) 0.18 (day_ ) < F/M <= 0.25 (day ) ... (2) 0.25 (day 1) < F/M <= 0.30 (day ) ... (3) 0.30 (day ) < F/M <= 0.40 (day ]) ... (4) 0.40 (day ) < F/M (5) SVI STATE RANGES SVI < = 60 (mL/g) . .. (1) 60 (mL/g) < SVI <= 100 (mL/g) . .. (2) 100 (mL/g) < SVI <= 200 (mL/g) . .. (3) 200 (mL/g) < SVI <= 300 (mL/g) . .. (4) 300 (mL/g) < SVI <= 500 (mL/g) . .. (5) 500 (mL/g) < SVI .. (6) EFFLUENT SS STATE RANGES SS <= 5 (mg/L) .. . (1) 5 (mg/L) < SS <= 10 (mg/L) . .. (2) 10 (mg/L) < SS <= 15 (mg/L) . .. (3) 15 (mg/L) < SS <= 20 (mg/L) . . (4) 20 (mg/L) < SS <= 60 (mg/L) . (5) 60 (mg/L) < SS . (6) The r e s u l t i n g p r o b a b i l i t y d i s t r i b u t i o n s are given i n Tables 3 and 4. 4.1.2 U t i l i t y Determinations The u t i l i t i e s used are d e s c r i b e d i n S e c t i o n 3.3.5. Four u t i l i -t i e s , r e f e r r e d to as Operator "A", "B", "C" and "D" are used to determine the maximum expected u t i l i t i e s f o r each of 25 DO c o n c e n t r a t i o n and F/M r a t i o c o n t r o l combinations. 122 4.1.3 Expected U t i l i t i e s Expected u t i l i t i e s , f o r each of the 25 c o n t r o l o p t i o n s , were gen-e r a t e d by m u l t i p l y i n g the p r o b a b i l i t y d i s t r i b u t i o n s f o r SVI and FESS range l e v e l s by the u t i l i t y a ssigned to each outcome. The sum of these p r o b a b i l i t y - u t i l i t y products forms the expected u t i l i t y f o r that c o n t r o l o p t i o n . The r e s u l t i n g expected u t i l i t i e s f o r the four operator u t i l i t i e s are presented i n Tables 23 t o 26. Despite the u t i l i t y matrix d i f f e r e n c e s , the r e s u l t i n g expected u t i l i t y outcomes f o r the 25 c o n t r o l o p t i o n s are s i m i l a r , although the o p t i o n with the maximum expected u t i l i t y d i f f e r s . The expected u t i l i t y matrix f o r operator "A" has a maximum expec-ted u t i l i t y of 62.4, f o r the combination of D0(1) and F/M(1). The matrix has a banded appearance, with higher expected u t i l i t i e s f o r low and hig h F/M extremes, i r r e s p e c t i v e of DO c o n c e n t r a t i o n s . The combinations of D0(5) and F/M(l) and D0(1) and F/M(4) have almost the same expected u t i l i t i e s (61.4 and 61.1 r e s p e c t i v e l y ) as the maximum u t i l i t y o p t i o n . However, the hig h F/M and low DO combination i s not c o n s i s t e n t with b u l k i n g c o n t r o l theory. T h i s may be due to the o p e r a t o r s ' p o l i c y of c h l o r i n a t i n g t o de s t r o y the f i l a m e n t o u s microorganisms and reduce the SVI l e v e l . Conse-q u e n t l y , c o n d i t i o n s which promote sludge b u l k i n g may be a s s o c i a t e d with low SVI c o n d i t i o n s , i f b u l k i n g c o n t r o l through c h l o r i n a t i o n i s p r a c t i c e d . 123 Table 23. Operator "A" U t i l i t y M a t r i x and R e s u l t i n g C o n t r o l  A l t e r n a t i v e Expected U t i l i t i e s UTILITY MATRIX ( OPERATOR "A" ) EFFLUENT SLUDGE VOLUME INDEX (mL/g) SOLIDS (mg/L) <= 60 60-100 100-200 200-300 300-500 500 < <= 5 60 100 100 80 50 30 5-10 50 90 90 70 40 15 10-15 40 80 80 50 30 10 15-20 30 50 50 30 20 5 20-60 5 5 5 5 5 0 60 < 0 0 0 0 0 0 EXPECTED UTILITIES ( OPERATOR "A" ) CONTROL FM<=.18 .18-.25 .25-.30 .30-.40 .40<FM DO<=1.5 62.4 56.9 44.5 61 .1 54.3 1.5-2.5 57.3 56.4 37.3 53.4 39.8 2.5-3.5 56.7 58.6 38.0 52.3 44.9 3.5-4.5 54.6 49.8 33.9 52.2 41 . 1 4.5 < DO 61 .4 54.0 33.0 56.8 50. 1 The expected u t i l i t y matrix f o r operator "B" has a maximum expec-ted u t i l i t y of 68.6 f o r the D0(1) and F/M(4) c o n t r o l o p t i o n . The expected u t i l i t y matrix has a s i m i l a r appearance t o the pr e v i o u s matrix, with h i g h expected u t i l i t i e s f o r extreme F/M c o n t r o l o p t i o n s . 124 Table 24. Operator "B" U t i l i t y M a trix and R e s u l t i n g C o n t r o l A l t e r n a t i v e Expected U t i l i t i e s UTILITY MATRIX ( OPERATOR "B" ) EFFLUENT SLUDGE VOLUME INDEX (mL/g) SOLIDS (mg/L) <= 60 60-100 100-200 200-300 300-500 500 < <= 5 20 100 100 60 60 20 5-10 20 100 100 60 50 15 10-15 20 100 100 60 40 10 15-20 10 90 90 50 30 5 20-60 5 20 20 30 10 0 60 < 0 0 0 0 0 0 EXPECTED UTILITIES ( OPERATOR ) CONTROL FM<=.18 .18-.25 .25-.30 .30-.40 .40<FM DO<=1.5 67.0 67.4 46.1 68.6 63.6 1.5-2.5 65.9 67.5 43.5 63.2 54.1 2.5-3.5 65.8 67.1 44.8 64.5 53.8 3.5-4.5 65.0 63.6 40.4 61 .7 53.0 4.5 < DO 67. 1 65.3 38.8 64.4 58.7 The operator "C" expected u t i l i t y matrix has a maximum expected u t i l i t y of 71.7 f o r the DO(l) and F/M(2) c o n t r o l o p t i o n . Once a g a i n , the matrix has a banded s t r u c t u r e , with low expected u t i l i t i e s f o r mid range F/M c o n t r o l l e v e l s and l i t t l e d i f f e r e n -t i a t i o n a c r o s s the DO c o n t r o l o p t i o n s . 125 Table 25. Operator "C" U t i l i t y M a t r i x and R e s u l t i n g C o n t r o l A l t e r n a t i v e Expected U t i l i t i e s UTILITY MATRIX ( OPERATOR "C" ) EFFLUENT SOLIDS SLUDGE VOLUME INDEX (mL/g) (mg/L) <= 60 60-100 100-200 200-300 300-500 500 < <= 5 60 100 90 80 60 20 5-10 80 100 80 70 60 20 10-15 70 100 80 70 60 20 15-20 70 "100 80 70 50 40 20-60 20 60 60 40 30 20 60 < 0 5 5 5 5 0 EXPECTED UTILITIES ( OPERATOR "C" ) CONTROL FM<=.18 . 18-.25 .25-.30 .30-.40 .40<FM DO<=1.5 65.9 71.6 54.2 69.5 69.8 1.5-2.5 65.6 71 . 1 54.9 67.6 65. 1 2.5-3.5 65.5 70.7 56.1 67.7 63.8 3.5-4.5 66.0 70.3 52.3 65.3 63 .1 4.5 < DO 65.4 70.0 50.7 68.2 65.8 L a s t l y , the operator "D" expected u t i l i t y matrix has a maximum expected u t i l i t y of 64.2 f o r the DO(1) and F/M(4) c o n t r o l o p t i o n . S i m i l a r to the operator "A" matrix, the ( low DO : low F/M ) and ( h i g h DO : low F/M ) c o n t r o l o p t i o n s have the next h i g h e s t expected u t i l i t i e s of 61.7 and 61.3 r e s p e c t i v e l y . Again, the 126 matrix i s banded i n appearance with the mid range F/M(3) c o n t r o l o p t i o n having the lowest expected u t i l i t i e s , i n comparison to other F/M s e t t i n g s , r e g a r d l e s s of the DO s e t t i n g . Table 26. Operator "D" U t i l i t y M a t r i x and R e s u l t i n g C o n t r o l  A l t e r n a t i v e Expected U t i l i t i e s UTILITY MATRIX ( OPERATOR "D" ) EFFLUENT SOLIDS SLUDGE VOLUME INDEX (mL/g) (mg/L) <= 60 60-100 100-200 200-300 300-500 500 < <= 5 85 100 95 75 30 10 5-10 80 95 90 65 25 8 10-15 75 90 85 55 20 6 15-20 60 80 70 30 10 4 20-60 30 50 45 15 3 1 60 < 0 5 3 1 0 0 EXPECTED UTILITIES ( OPERATOR "D" ) CONTROL FM<=.18 . 18-.25 .25-.30 .30-.40 .40<FM DO<=1.5 61 .7 60.8 41 .8 64.2 52.3 1.5-2.5 59.2 60.9 37.8 59.4 42.6 2.5-3.5 58.9 61.8 38.4 59.0 46.5 3.5-4.5 57.8 56.4 35.9 59.1 43.9 4.5 < DO 61 .3 59.3 35.3 61.5 49.4 127 4 .1.4 Summary De s p i t e d i f f e r e n c e s i n the outcome u t i l i t y s t r u c t u r e s , a l l four operator u t i l i t y m a t r i c e s r e s u l t e d i n b a s i c a l l y the same c o n t r o l -o p t i o n expected u t i l i t y s t r u c t u r e . A l l expected u t i l i t y m a t r i c e s were banded ac r o s s the F/M c o n t r o l range, with lower expected u t i l i t i e s f o r mid range F/M v a l u e s f o r a l l DO c o n t r o l combina-t i o n s . The maximum expected u t i l i t y c a l c u l a t e d was g e n e r a l l y f o r low DO and high F/M c o n t r o l o p t i o n s . T h i s c o n t r o l technique i s c o n t r a -d i c t o r y t o filamentous sludge b u l k i n g c o n t r o l theory, which sug-g e s t s that higher s u b s t r a t e c o n c e n t r a t i o n s r e q u i r e higher DO l e v e l s . As c h l o r i n e a p p l i c a t i o n s to c o n t r o l sludge b u l k i n g are not recorded, i t i s p o s s i b l e that the low SVI valu e s recorded f o r ( low DO : high F/M ) combinations are due to the a d d i t i o n of c h l o r i n e to a b u l k i n g sludge, and not due " to the c o n t r o l t e c h n ique. For each expected u t i l i t y matrix there are s e v e r a l c o n t r o l op-t i o n s with s i m i l a r l y h i g h v a l u e s , such that i t would be d i f f i c u l t t o j u s t i f y the s e l e c t i o n of one c o n t r o l o p t i o n over the other based on the expected u t i l i t y value a l o n e . The estimated p r o b a b i l i t i e s are based on a l a r g e but, as e x p l a i n e d e a r l i e r , not w e l l c o n t r o l l e d data base (6 years) and consequently would be d i f f i c u l t t o a l t e r through process experimentation. As the out-come p r o b a b i l i t y d i s t r i b u t i o n s f o r each c o n t r o l a l t e r n a t i v e may be based on t h i r t y or more data r e c o r d s , i t would take many 128 c o n t r a d i c t o r y experimental r e s u l t s to change a p r o b a b i l i t y d i s t r i b u t i o n . I t i s a l s o l i k e l y that the outcome from a p a r t i c u l a r c o n t r o l o p t i o n i s p a r t l y dependent on the s t a t e , i n which case a simple c o n t r o l s t r a t e g y c o u l d not be o p t i m a l f o r a l l s t a t e s . With 25 p o s s i b l e c o n t r o l o p t i o n s , and u n c e r t a i n t y about the e f f e c t of the s t a t e on the outcome from a c o n t r o l o p t i o n , i t appears that the technique i s not p r a c t i c a l f o r use i n c o n t r o l of t h i s p a r t i c u l a r p r o c e s s . 129 4 . 2 Case "B" - Markov P o l i c y - I t e r a t i o n Approach U n l i k e t h e C a s e "A" t e c h n i q u e , w h i c h e x a m i n e s o n l y t h e p r o b -a b i l i t y o f t h e n e x t s t a t e o u t c o m e , t h e M a r k o v P o l i c y - I t e r a t i o n t e c h n i q u e a s s e s s e s t h e a v e r a g e l o n g - t e r m e x p e c t e d s t a t e p r o b a b i l i t i e s , a n d t a k e s i n t o a c c o u n t t h a t t h e o u t c o m e d e p e n d s p a r t l y o n t h e s t a t e a n d p a r t l y o n t h e c o n t r o l o p t i o n . T h e p r o c e d u r e r e q u i r e s t h a t a p r o b a b i l i t y o r t r a n s i t i o n m a t r i x b e d e f i n e d f o r e a c h s p e c i f i c s t a t e , w h i c h t h e n g i v e s t h e p r o b a b i l i t y o f m o v i n g f r o m t h a t s t a t e , t o a n y o t h e r s t a t e , d u r i n g t h e n e x t t i m e p e r i o d f o r e a c h p r o c e s s c o n t r o l o p t i o n . W h e r e a s C a s e "A" e s t i m a t e d a " b e s t - g u e s s " p r o c e s s c o n t r o l o p t i o n ( w h i c h d i d n o t t a k e i n t o c o n s i d e r a t i o n t h e c u r r e n t p l a n t s t a t e ) , t h e M a r k o v P o l i c y - I t e r a t i o n t e c h n i q u e s e l e c t s t h e c o n t r o l o p t i o n w i t h t h e m a x i m u m o v e r a l l e x p e c t e d u t i l i t y f o r e a c h p o s s i b l e s t a r t i n g s t a t e . 4 . 2 . 1 U t i l i t y M a t r i c e s S e v e n u t i l i t y m a t r i c e s , a s d e s c r i b e d i n S e c t i o n 3 . 3 . 6 , w e r e a p p l i e d t o t r a n s i t i o n m a t r i c e s g e n e r a t e d f r o m h i s t o r i c a l p l a n t d a t a . U n l i k e t h e C a s e "A" o p e r a t o r u t i l i t y m a t r i c e s , w h i c h a s s e s s e d u t i l i t y o n t h e b a s i s o f c o m b i n a t i o n s o f S V I a n d F E S S , t h e u t i l i t i e s u s e d f o r C a s e " B " a r e b a s e d o n c o n s i d e r a t i o n o f b o t h t h e D O : F / M c o n t r o l a l t e r n a t i v e a n d t h e S V I s t a t e c o n d i t i o n , t a k i n g i n t o a c c o u n t b o t h b u l k i n g c o n d i t i o n s a n d t h e c o s t s o f t r e a t m e n t p l a n t o p e r a t i o n . 130 4.2.2 I n f l u e n c e of B a s e l i n e Frequency M a t r i c e s As e x p l a i n e d above, t r a n s i t i o n m a t r ices are r e q u i r e d f o r the P o l i c y - I t e r a t i o n technique. These give the p r o b a b i l i t i e s of moving from one s t a t e t o another, i n one time step, f o r each s p e c i f i c c o n t r o l o p t i o n . Where no h i s t o r i c a l data e x i s t s t o d e f i n e these p r o b a b i l i t i e s , as occurs where c e r t a i n c o n t r o l o p t i o n s have not been attempted i n the past, they must be e s t i m a t e d . As d i s c u s s e d i n S e c t i o n 3.3.6, i t i s proposed that a b a s e l i n e frequency matrix, which assumes that t h e r e i s an equal p r o b a b i l i t y of remaining i n the same s t a t e or moving to an adjacent s t a t e , p r o v i d e s a reasonable f i r s t - g u e s s e stimate. These t r a n s i t i o n m a t r i c e s are presented i n S e c t i o n 3.3.4 i n Tables 5 to 8. Using the simple b a s e l i n e frequency m a t r i c e s , a P o l i c y - I t e r a t i o n c a l c u l a t i o n was performed with each of the seven u t i l i t y mat-r i c e s , as d e s c r i b e d i n S e c t i o n 3.3.6. A l l seven u t i l i t y m a t r i c e s r e s u l t e d i n the same p o l i c y v e c t o r given below i n Table 27. Table 27. B a s e l i n e Frequency P o l i c y V e c t o r and Average  Expected U t i l i t i e s CURRENT FIRST FINAL STATE ITERATION ITERATION 1 2 ] ; 3 1 1 4 1 1 5 1 1 AVERAGE EXPECTED UTILITY 67.5 67.5 131 Both the f i r s t and f i n a l i t e r a t i o n p o l i c i e s , to maximize the expected u t i l i t y are the same, as are the average expected u t i l i -t i e s . The s e l e c t e d p o l i c y i s independent of s t a t e , and f o l l o w s the lowest energy (highest u t i l i t y ) c o n t r o l a l t e r n a t i v e . P o l i c y 1 i s d e s c r i b e d i n S e c t i o n 3.3.3 as low DO [ <= 2 (mg/L)] and low F/M [ <= 0.2 (day 1 ) ] . A d d i t i o n a l l y , the p o l i c y v e c t o r s and average expected u t i l i t i e s are independent of the u t i l i t y matrix shape. 4.2.3 H i s t o r i c a l Data C o n t r o l P o l i c i e s The b a s e l i n e frequency matrix was added to the h i s t o r i c a l . data frequency matrix presented i n Table 5, such that the cumulative sum of the f r e q u e n c i e s f o r each c o n t r o l a l t e r n a t i v e was i n c r e a s e d by 3. The combined f r e q u e n c i e s were then converted i n t o p r o b a b i l i t i e s , on the b a s i s of the sum of the f r e q u e n c i e s f o r a given c o n t r o l a l t e r n a t i v e . The r e s u l t i n g f i v e t r a n s i t i o n proba-b i l i t y m a t r i c e s were then a p p l i e d t o u t i l i t y m a t r i c e s #1 to #7. The r e s u l t i n g expected u t i l i t y p o l i c y v e c t o r s , f o r u t i l i t y m a t r i c e s #1, #2 and #3, are presented i n Tables 28 to 30. 132 Table 28. U t i l i t y 1 Matrix Policy Vector and Average Expected U t i l i t i e s for the H i s t o r i c a l Data Transition Matrix Including Baseline Frequencies CURRENT STATE 1 2 3 4 5 AVERAGE EXPECTED UTILITY FIRST ITERATION 83. 1 FINAL ITERATION 1 3 5 7 3 87.8 Table 29. U t i l i t y 2 Matrix Policy Vector and Average Expected  U t i l i t i e s for the H i s t o r i c a l Data Transition Matrix  Including Baseline Frequencies CURRENT STATE 1 2 3 4 5 AVERAGE EXPECTED UTILITY FIRST ITERATION 74.6 FINAL ITERATION 1 3 5 7 3 80.7 133 Table 30. U t i l i t y 3 M a t r i x P o l i c y Vector and Average Expected U t i l i t i e s f o r the H i s t o r i c a l Data T r a n s i t i o n Matrix I n c l u d i n g B a s e l i n e Frequencies CURRENT STATE 1 2 3 4 5 AVERAGE EXPECTED UTILITY FIRST ITERATION 72.5 FINAL ITERATION 1 1 5 7 3 77.1 There i s a n o t i c e a b l e d i f f e r e n c e between the f i r s t and f i n a l i t e r a t i o n s and u l t i m a t e average expected u t i l i t i e s f o r u t i l i t y m a t r i c e s #2 and #3. The u l t i m a t e p o l i c y v e c t o r i s s i m i l a r f o r a l l t h r e e u t i l i t y matrix shapes, and i n d i c a t e s t h a t there should be an i n c r e a s e d energy input and higher DO l e v e l s as the s t a t e c o n d i t i o n ( l e v e l of b u l k i n g ) i n c r e a s e s . The low energy c o n t r o l p o l i c y i n d i c a t e d f o r s t a t e 5 may r e f l e c t the p r a c t i c e of c h l o r i -n a t i n g under hi g h b u l k i n g c o n d i t i o n s . For example, i f b u l k i n g i s caused by low DO c o n d i t i o n s , and c h l o r i n e i s added once a s t a t e 5 c o n d i t i o n i s reached, a low DO c o n t r o l p o l i c y under s t a t e 5 c o n d i t i o n s w i l l be a s s o c i a t e d with an improvement i n b u l k i n g . G e n e r a l l y , the u l t i m a t e p o l i c y v e c t o r r e f l e c t s a low energy p o l i c y under c o n d i t i o n s of low SVI l e v e l s and a h i g h energy p o l i c y under hi g h SVI c o n d i t i o n s . T h i s p o l i c y i s c o n s i s t e n t with low DO b u l k i n g , as i n c r e a s e d DO c o n c e n t r a t i o n s (high energy) would be expected to "cure" a low DO b u l k i n g sludge. 134 The f i r s t u t i l i t i e s T a b l e s 31 and f i n a l i t e r a t i o n p o l i c y v e c t o r s and average expected f o r u t i l i t y m a t r ices #4, #5 and #6 are i l l u s t r a t e d i n to 33 below. Table 31. U t i l i t y 4 M a t r i x P o l i c y Vector and Average Expected  U t i l i t i e s f o r the H i s t o r i c a l Data T r a n s i t i o n M a t r i x  I n c l u d i n g B a s e l i n e Frequencies CURRENT STATE 1 2 3 4 5 AVERAGE EXPECTED UTILITY FIRST ITERATION 80. 1 FINAL ITERATION 3 3 5 7 3 90.5 Table 32. U t i l i t y 5 M a t r i x P o l i c y Vector and Average Expected  U t i l i t i e s f o r the H i s t o r i c a l Data T r a n s i t i o n M a t r i x  I n c l u d i n g B a s e l i n e Frequencies CURRENT STATE 1 2 3 4 5 AVERAGE EXPECTED UTILITY FIRST ITERATION 80.1 FINAL ITERATION 3 3 5 7 3 89.0 135 Table 33. U t i l i t y 6 M a t r i x P o l i c y V e c tor and Average Expected U t i l i t i e s f o r the H i s t o r i c a l Data T r a n s i t i o n M a t r i x I n c l u d i n g B a s e l i n e Frequencies CURRENT STATE FIRST ITERATION FINAL ITERATION 2 3 4 5 3 3 2 3 3 2 3 5 7 3 AVERAGE EXPECTED UTILITY 80. 1 87.3 There i s l e s s d i f f e r e n c e between the f i r s t and f i n a l i t e r a t i o n c o n t r o l p o l i c y v e c t o r s f o r u t i l i t y m a t r i c e s #4, #5 and #6, than f o r the p r e v i o u s three u t i l i t y m a t r i c e s . The f i n a l i t e r a t i o n p o l i c y v e c t o r i s the same f o r a l l three u t i l i t i e s , with a p o l i c y of i n c r e a s i n g DO as b u l k i n g c o n d i t i o n s worsen. As with u t i l i t y m a t r i c e s 1 t o 3, the lower energy c o n t r o l a l t e r n a t i v e f o r s t a t e 5 may r e f l e c t the p r a c t i c e of c h l o r i n a t i o n under high b u l k i n g c o n d i t i o n s . The average expected u t i l i t i e s f o r u t i l i t y m atrices #4 to #6 are higher than f o r u t i l i t y m a t r i c e s #1 to #3. T h i s i s a t t r i b u t a b l e to the d e f i n e d c o n t r o l / s t a t e u t i l i t i e s being only a f u n c t i o n of SVI l e v e l and DO c o n c e n t r a t i o n s . The complete absence of c o n t r o l u t i l i t i e s i s represented by u t i l i t y matrix #7. The r e s u l t i n g immediate and u l t i m a t e p o l i c y v e c t o r and average expected u t i l i t i e s are shown i n Table 34. 136 T a b l e 34. U t i l i t y 7 M a t r i x P o l i c y V e c t o r and Average Expected U t i l i t i e s f o r the H i s t o r i c a l Data T r a n s i t i o n M a t r i x I n c l u d i n g B a s e l i n e F r e q u e n c i e s CURRENT STATE FIRST ITERATION FINAL ITERATION 2 3 4 5 3 3 5 7 3 3 3 5 7 3 AVERAGE EXPECTED UTILITY 90.8 90.8 When energy i s not i n c l u d e d i n the d e t e r m i n a t i o n of u t i l i t y , the f i r s t and f i n a l p o l i c y v e c t o r s a r e i d e n t i c a l , as are t h e i r expec ted average u t i l i t i e s . The u l t i m a t e p o l i c y v e c t o r i s i d e n t i c a l t o the #4 u t i l i t y m a t r i x s o l u t i o n , and i t i s s i m i l a r to the p o l i c y v e c t o r s of the o t h e r u t i l i t i e s . The u l t i m a t e average expec ted u t i l i t y i s the h i g h e s t of the seven u t i l i t y m a t r i c e s , and the p o l i c y v e c t o r a g a i n r e f l e c t s an i n c r e a s e d energy e x p e n d i t u r e and h i g h e r DO c o n c e n t r a t i o n s , as b u l k i n g c o n d i t i o n s worsen. Wi th the e x c e p t i o n of the s t a t e 1 p o l i c y f o r u t i l i t y m a t r i c e s #1 to #3 and the s t a t e 4 p o l i c y f o r a l l seven u t i l i t y m a t r i c e s , t h e r e i s a tendency towards medium to h i g h F / M r a t i o l e v e l s . For s t a t e c o n d i t i o n s 3 to 5, r e p r e s e n t i n g moderate to h i g h b u l k i n g ( SVI g r e a t e r than 200 mL/g ) , the p o l i c y v e c t o r s f o r a l l seven u t i l i t y m a t r i c e s are i d e n t i c a l . 137 With an u l t i m a t e average expected u t i l i t y i n excess of 77 f o r a l l seven u t i l i t y m a t r i c e s , the average SVI l e v e l i s expected to be l e s s than 300 (mL/g) f o r the p o l i c y v e c t o r s i n d i c a t e d . A l l seven u t i l i t y m a t r i c e s converged r a p i d l y , w i t h i n three i t e r a t i o n s , on t h e i r r e s p e c t i v e u l t i m a t e p o l i c y v e c t o r s and average expected u t i l i t i e s . 4.2.4 Temperature E f f e c t s on H i s t o r i c a l Data P o l i c y V e c t o r s Based on the f i n d i n g s of S e c t i o n 4.2.3, which concluded that the u l t i m a t e p o l i c y v e c t o r was r e l a t i v e l y independent of the u t i l i t y matrix shape, u t i l i t y matrix #1 was used to examine the e f f e c t s of temperature on the p o l i c y v e c t o r s e l e c t i o n . As d e s c r i b e d i n S e c t i o n 3.3.5, the French Creek o p e r a t i n g data was d i v i d e d i n t o three temperature range groups: (1) l e s s than or equal to 12 °C, (2) g r e a t e r than 12 °C and l e s s than 16 °C, and (3) g r e a t e r than or equal to 16 °C. Frequency d i s t r i b u t i o n s were then c a l c u l a t e d (Tables 6 to 8 ) . These were combined with the b a s e l i n e frequency m a t r i c e s to o b t a i n the p r o b a b i l i t y or t r a n s i t i o n m a t r i c e s . Tables 35 to 37 summarize the r e s u l t i n g p o l i c y v e c t o r s and average expected u t i l i t i e s f o r the three temperature groups. 138 Table 35. U t i l i t y 1 M a t r i x P o l i c y Vector and Average Expected  U t i l i t i e s f o r H i s t o r i c a l Data Temperatures (Temp<=  12 deg C) I n c l u d i n g B a s e l i n e Frequencies CURRENT STATE 1 2 3 4 5 AVERAGE EXPECTED UTILITY FIRST ITERATION 6 9 . 6 FINAL ITERATION 1 3 5 7 4 80.1 Table 36. U t i l i t y 1 M a t r i x P o l i c y V e c t or and Average Expected  U t i l i t i e s f o r H i s t o r i c a l Data Temperatures (12 deg C  > Temp < 16 deg C) I n c l u d i n g B a s e l i n e Frequencies CURRENT STATE 1 2 3 4 5 AVERAGE EXPECTED UTILITY FIRST ITERATION 8 7 . 9 FINAL ITERATION 1 1 4 1 5 8 7 . 8 139 T a b l e 37. U t i l i t y 1 M a t r i x P o l i c y Vector and Average Expected  U t i l i t i e s f o r H i s t o r i c a l Data Temperatures (16 deg C  >=Temp) I n c l u d i n g B a s e l i n e Frequencies CURRENT STATE FIRST ITERATION FINAL ITERATION 2 3 4 5 3 3 3 5 6 3 AVERAGE EXPECTED UTILITY 80.0 87.0 Examining the p o l i c y v e c t o r s i n terms of DO c o n t r o l , i t appears that moderate to high DO c o n c e n t r a t i o n s are r e q u i r e d to c o n t r o l b u l k i n g i n both summer and w i n t e r . With the exception of the s t a t e 4 and 5 c o n t r o l a l t e r n a t i v e s , the p o l i c y v e c t o r s f o r extreme temperature c o n d i t i o n s are i d e n t i c a l . S l i g h t l y higher average expected u t i l i t i e s are p r o j e c t e d f o r the high temperature o p e r a t i n g c o n d i t i o n , than f o r the low temperature range, r e f l e c t i n g the lower u t i l i t y a s s o c i a t e d with having to p r o v i d e i n c r e a s e d DO c o n c e n t r a t i o n s . The p o l i c y v e c t o r f o r the midrange temperature group appears to be s u b s t a n t i a l l y d i f f e r e n t than f o r the extreme temperature ranges. However, from a DO c o n t r o l p e r s p e c t i v e , only the s t a t e 4 c o n t r o l a l t e r n a t i v e of low DO and low F/M i s anomalous. The average expected u t i l i t y , f o r the f i n a l i t e r a t i o n , i s i d e n t i c a l to the u t i l i t y curve #1 p o l i c y - i t e r a t i o n r e s u l t f o r the e n t i r e data base, d i s c u s s e d i n S e c t i o n 4.2.3, d e s p i t e a c o n s i d e r a b l y d i f f e r e n t p o l i c y v e c t o r . 140 The d i f f e r e n c e s i n p o l i c y v e c t o r s , f o r the three temperatures, c o u l d be due to i n s u f f i c i e n t data c o l l e c t i o n to determine the p r o b a b i l i t i e s on which the optimal ( o v e r a l l ) c o n t r o l p o l i c y i s based. For example, an examination of the DO time s e r i e s p l o t s i n Appendix A, f o r r e a c t o r s #1 and #2, i n d i c a t e s that a c y c l i c a l p a t t e r n e x i s t s , with higher DO c o n c e n t r a t i o n s o c c u r r i n g d u r i n g the winter than i n the summer. T h i s o b s e r v a t i o n i s c o n s i s t e n t with the lower b i o l o g i c a l a c t i v i t y expected d u r i n g the winter months and, consequently lower DO demand. Since DO c o n t r o l can only be achieved through manual adjustment of v a l v e s , the DO c o n c e n t r a t i o n w i l l f l u c t u a t e with b i o l o g i c a l a c t i v i t y . The o p e r a t i o n s s t a f f i s r e l u c t a n t to i n c r e a s e the number of blowers i n use to compensate f o r higher DO demand, because of a s s o c i a t e d high energy c o s t s ; as such, the DO c o n c e n t r a t i o n s are allowed to f l u c t u a t e w i t h i n a wide range. With fewer hi g h DO c o n c e n t r a t i o n s d u r i n g the summer, there i s i n s u f f i c i e n t data a v a i l a b l e to e v a l u a t e h i g h DO c o n t r o l e f f e c t s under warm weather c o n d i t i o n s . Consequently, l i t t l e or no o p e r a t i n g experience i s a v a i l a b l e f o r e i t h e r low DO c o n d i t i o n s d u r i n g the winter months, or f o r h i g h DO c o n d i t i o n s d u r i n g the summer months. 4 . 2 . 5 P o l i c y S e l e c t i o n f o r a Simulated Low DO B u l k i n g Process The f i r s t and f i n a l i t e r a t i o n p o l i c y v e c t o r s and average expected u t i l i t i e s were determined f o r a l l seven u t i l i t y m a t r ices f o r a s i m u l a t e d low-DO b u l k i n g a c t i v a t e d sludge t r a n s i t i o n matrix. 141 Table 38. U t i l i t y 1 M a t r i x P o l i c y V e c tor and Average Expected  U t i l i t i e s f o r a Simulated Low DO B u l k i n g Process CURRENT STATE 1 2 3 4 5 AVERAGE EXPECTED UTILITY FIRST ITERATION 85.4 FINAL ITERATION 1 4 7 7 7 85.4 Table 39. U t i l i t y 2 M a t r i x P o l i c y V e c tor and Average Expected U t i l i t i e s f o r a Simulated Low DO B u l k i n g Process CURRENT STATE 1 2 3 4 5 AVERAGE EXPECTED UTILITY FIRST ITERATION 78.7 FINAL ITERATION 1 4 7 7 7 75.2 142 T a b l e 40. U t i l i t y 3 M a t r i x P o l i c y V e c t o r and Average Expected  U t i l i t i e s f o r a S i m u l a t e d Low DO B u l k i n g Process CURRENT STATE 1 2 3 4 5 AVERAGE EXPECTED UTILITY FIRST ITERATION 39.7 FINAL ITERATION 1 1 7 7 7 68.9 T a b l e 41 . U t i l i t y 4 M a t r i x P o l i c y V e c t o r and Average Expec ted  U t i l i t i e s f o r a S i m u l a t e d Low DO B u l k i n g Process CURRENT STATE 1 2 3 4 5 AVERAGE EXPECTED UTILITY FIRST ITERATION 79.9 FINAL ITERATION 1 4 7 7 7 82.6 143 T a b l e 42. U t i l i t y 5 M a t r i x P o l i c y V e c t o r and Average Expected U t i l i t i e s f o r a S imula ted Low DO B u l k i n g Proces s CURRENT STATE 1 2 3 4 5 AVERAGE EXPECTED UTILITY FIRST ITERATION 68.4 FINAL ITERATION 1 1 7 7 7 72.5 T a b l e 43. U t i l i t y 6 M a t r i x P o l i c y V e c t o r and Average Expected  U t i l i t i e s f o r a S imula ted Low DO B u l k i n g P r o c e s s CURRENT STATE 1 2 3 4 5 AVERAGE EXPECTED UTILITY FIRST ITERATION 37.3 FINAL ITERATION 1 1 7 7 7 65.0 144 Table 44. U t i l i t y 7 M a t r i x P o l i c y Vector and Average Expected U t i l i t i e s f o r a Simulated Low DO B u l k i n g Process CURRENT STATE FIRST ITERATION FINAL ITERATION 2 3 4 5 4 7 7 7 4 7 7 7 AVERAGE EXPECTED UTILITY 85.4 85.4 As expected, the f i n a l i t e r a t i o n p o l i c y v e c t o r i n a l l cases r e f l e c t s a c o n t r o l p o l i c y of inc r e a s e d DO c o n c e n t r a t i o n , at low F/M r a t i o s , f o r a l l u t i l i t y m a t r i c e s . There i s l i t t l e d i f f e r e n c e between the f i r s t and f i n a l i t e r a t i o n p o l i c y v e c t o r s f o r u t i l i t i e s #1, #4 and #5. As the d i f f e r e n c e i n r e l a t i v e u t i l i t i e s between c o n t r o l a l t e r n a t i v e s i n c r e a s e s , the d i f f e r e n c e between the f i r s t and f i n a l i t e r a t i o n c o n t r o l p o l i c y becomes more pronounced. The d i f f e r e n c e i n r e l a t i v e u t i l i t i e s f o r inc r e a s e d energy u t i l i z a t i o n i s a l s o r e f l e c t e d i n the d e c r e a s i n g average expected u t i l i t i e s f o r the p o l i c y v e c t o r s . The number of i t e r a t i o n s r e q u i r e d to converge on the f i n a l p o l i c y v e c t o r i n c r e a s e s with i n c r e a s e d a l t e r n a t i v e c o n t r o l u t i l i t y g r a d i e n t s . For low DO b u l k i n g c o n d i t i o n s , the low u t i l i t y asso-c i a t e d w i t h the high e r DO c o n c e n t r a t i o n s r e q u i r e d t o cure the b u l k i n g i s i n c o n f l i c t with the s t a t e u t i l i t y s t r u c t u r e . Although the t r a n s i t i o n matrix d i c t a t e s that i n c r e a s e d DO i s r e q u i r e d , the o p e r a t o r ' s low u t i l i t y f o r h i g h DO l e v e l s i n c r e a s e s 145 the number of i t e r a t i o n s r e q u i r e d f o r convergence on the f i n a l p o l i c y which maximizes the average expected u t i l i t y . Consequently, u t i l i t i e s with steep g r a d i e n t s r e q u i r e more i t e r a t i o n s to converge than those with shallow g r a d i e n t s . 146 4.3 Case C - Dynamic Markov P o l i c y - I t e r a t i o n Approach to Sludge B u l k i n g C o n t r o l T h i s s e c t i o n e v a l u a t e s the u t i l i z a t i o n of the Markov p o l i c y -i t e r a t i o n technique in dynamic c o n t r o l of sludge b u l k i n g . Using a b a s e l i n e frequency t r a n s i t i o n matrix and a s e l e c t e d u t i l i t y s t r u c t u r e , the Markov P o l i c y - I t e r a t i o n i s used to c a l c u l a t e a f i n a l p o l i c y v e c t o r from which a c o n t r o l a l t e r n a t i v e i s s e l e c t e d f o r a s t a t e 1 c o n d i t i o n . The known p r o b a b i l i t y matrix used i n S e c t i o n 4.2 i s then used to determine the outcome of the s e l e c t e d c o n t r o l , through the use of a random number from 1 to 100. For example, assuming that the p o l i c y v e c t o r i n d i c a t e s t h a t , f o r a s t a t e 1 c o n d i t i o n , c o n t r o l a l t e r n a t i v e 1 should be s e l e c t e d , and that the random number generated i s 55, Table 10 i n d i c a t e s that the next s t a t e i s s t a t e 2. The b a s e l i n e t r a n s i t i o n frequency matrix i s then m o d i f i e d to r e f l e c t the r e s u l t of the p r e v i o u s c o n t r o l s e l e c t i o n , and a new u l t i m a t e p o l i c y v e c t o r i s c a l c u l a t e d . The process i s then repeated f o r the c u r r e n t s t a t e . 4.3.1 U t i l i t y M a t r i x S t r u c t u r e E f f e c t s U t i l i t y matrix #1, #3, #4, and #5 were examined to determine the e f f e c t of the u t i l i t y shape on the average expected u t i l i t y and process c o n d i t i o n , u s i n g a dynamic Markov P o l i c y - I t e r a t i o n approach, beginning with a b a s e l i n e frequency m a t r i x . The r e s u l t i n g changes in s t a t e and average u t i l i t y with i n c r e a s e d i t e r a t i o n s , or sampling p e r i o d s , i s i l l u s t r a t e d i n F i g u r e s 21 to 28 and i n c orresponding Tables 45 to 52. 147 R e c a l l i n g t h a t the s t a t e 1 to 5 f i n a l p o l i c y v e c t o r for u t i l i t y matrix #1 was [1, 4, 7, 7, 7] from S e c t i o n 4.2.5, Table 45 i l l u s t r a t e s t h a t 97 i t e r a t i o n s or t r i a l s were required to converge on the f i n a l p o l i c y v e c t o r from a p o s i t i o n of no s t a r t i n g i n f o r m a t i o n . The recommended c o n t r o l p o l i c y f o r each s t a t e i s r e l a t i v e l y s t a b l e . As a r e s u l t , non c r i t i c a l c o n t r o l o p t i o n s are avoided or q u i c k l y by-passed, to converge on a p o l i c y which w i l l improve expected u t i l i t y . The i n i t i a l i t e r a t i o n s r e s u l t i n a decrease i n expected u t i l i t y , as the i n i t i a l c o n t r o l s t r a t e g y , which i s based on the b a s e l i n e frequency matrix, causes the p l a n t to r a p i d l y b u l k . Once i n a s t a t e 5 c o n d i t i o n , i t takes seven i t e r a t i o n s to f i n d a c o n t r o l o p t i o n which w i l l decrease b u l k i n g ( i t e r a t i o n 10 - 17). Advancing to s t a t e 4 an a d d i t i o n a l 5 i t e r a t i o n s are r e q u i r e d to determine a c o n t r o l strategy to f u r t h e r reduce the b u l k i n g s t a t e . T h i s procedure continues u n t i l a l t e r n a t i v e s are found which w i l l have some expectation of d i m i n i s h i n g "the l e v e l of b u l k i n g to s t a t e 2. Once a c o n t r o l s t r a t e g y i s determined to reduce the b u l k i n g - s t a t e c o n d i t i o n s ( s t a t e 3 - 5) to non-bulking c o n d i t i o n s ( s t a t e s 1 and 2), the model attempts to maximize the average expected u t i l i t y by m i n i m i z i n g the energy e x p e n d i t u r e s , without c r e a t i n g a b u l k i n g c o n d i t i o n . A compromise i s reached between h i g h - u t i l i t y c o n t r o l o p t i o n s and high b u l k i n g p o t e n t i a l at lower s t a t e s , and low-u t i l i t y and low b u l k i n g p o t e n t i a l at higher s t a t e s . The o b j e c t i v e w i t h i n the " i d e a l " s t a t e i s to maximize u t i l i t y , while m a i n t a i n i n g the i d e a l s t a t e c o n d i t i o n . Conversely, the o b j e c t i v e at s t a t e s higher than the " i d e a l " s t a t e i s t o reduce the s t a t e 148 l e v e l by s e l e c t i n g c o n t r o l s with lower u t i l i t i e s but higher p o t e n t i a l to improve b u l k i n g . I n s t e a d of e v a l u a t i n g a l l p o s s i b l e c o n t r o l o p t i o n s , which would r e q u i r e an e x t e n s i v e number of i t e r a t i o n s to e s t a b l i s h t r a n s i t i o n p r o b a b i l i t i e s f o r each of the 45 p o s s i b l e s t a t e / c o n t r o l o p t i o n s , the model converges on the c r i t i c a l o p t i o n s . Continued i t e r a t i o n s , w i t h i n each s t a t e , are then c a r r i e d out to r e f i n e the t r a n s i t i o n p r o b a b i l i t i e s f o r the c r i t i c a l o p t i o n s . As the o b j e c t i v e of the c o n t r o l techniques i s to reduce b u l k i n g , l e s s time (fewer i t e r a t i o n s ) i s spent i n e v a l u a t i n g the higher s t a t e l e v e l o p t i o n s , to maximize the expected u t i l i t y at these higher s t a t e s and r e f i n i n g the t r a n s i t i o n p r o b a b i l i t y m a t r i c e s . Consequently, i t takes a c o n s i d e r a b l e amount of time (g r e a t e r than 100 i t e r a t i o n s ) f o r the u l t i m a t e average expected u t i l i t y to converge on the value determined i n S e c t i o n 4.2.5, f o r the si m u l a t e d t r a n s i t i o n m a t r i x . Note t h a t f o r the dynamic Markov P o l i c y - I t e r a t i o n process the term " i t e r a t i o n " r e f e r s to the number of process c o n t r o l p e r i o d s . T h i s d i f f e r s from Case B, where the number of i t e r a t i o n s r e f e r e d t o the number of c a l c u l a t i o n c y c l e s r e q u i r e d f o r the Markov P o l i c y - I t e r a t i o n technique to converge on a maximum average expected u t i l i t y . 149 F I G U R E 21 SIMULATION «1 - UTILITY *1 MATRIX AVERAGE UTILITY AND STATE PLOTS lOO-i — > -t—• ITERATION ( « ) T a b l e 45. S i m u l a t i o n 1 - U t i l i t y 1 M a t r i x - Recorded S t a t e  and P o l i c y V e c t o r Changes For Low DO B u l k i n g SIMULATION #1 - UTILITY MATRIX #1 I T E R . STATE STATE ALTERNATIVES AVERAGE # # 1 2 3 4 5 UTILITY 1 1 1 1 1 1 1 67.5 2 2 2 1 1 1 1 66.9 3 3 2 2 1 1 1 66.0 4 2 2 2 1 1 1 74. 1 5 2 1 2 1 1 1 76.4 6 1 1 2 1 1 1 79.8 7 2 2 2 1 1 1 79 .5 8 3 2 2 1 1 1 74. 1 9 3 2 2 1 1 1 74.4 10 5 2 2 2 1 1 65.2 1 1 5 2 2 2 1 2 61 .2 12 5 2 2 2 1 3 61 .0 1 3 5 2 2 2 1 4 60.6 1 4 5 2 2 2 1 5 60.3 15 5 2 2 2 1 6 60.2 1 6 5 2 2 2 1 7 60.0 17 4 2 2 2 1 7 62.4 18 4 2 2 2 2 7 61 .6 19 4 2 2 2 3 7 61 .2 20 4 2 2 2 4 7 60.3 21 4 2 2 2 5 7 59.8 22 3 2 2 2 5 7 69.0 23 4 2 2 3 5 7 68.4 24 5 2 2 3 5 7 63.0 25 5 2 2 3 5 7 63.2 26 4 2 2 3 5 7 62.4 27 3 2 2 3 5 7 67.7 28 5 2 2 4 5 7 66 .5 29 5 2 2 4 5 7 65.8 30 4 2 2 4 5 7 66.3 31 4 2 2 4 5 7 63.0 32 3 2 2 4 5 7 66.3 33 4 2 2 5 5 7 65.8 34 5 2 2 5 5 7 62.9 35 3 2 2 5 5 7 64.6 36 3 2 2 5 5 7 64.6 37 4 2 2 1 5 7 64.6 38 4 2 2 1 5 7 63. 1 39 3 2 2 1 5 7 65. 1 40 3 2 2 1 5 7 65.7 151 T a b l e 45. (cont'd) SIMULATION #1 - UTILITY MATRIX #1 ( c o n t ' d ) I T E R . STATE STATE ALTERNATIVES AVERAGE # # 1 2 3 4 5 UTILITY 41 3 2 2 1 5 7 66.3 42 3 2 2 1 5 7 66.8 43 3 2 2 1 5 7 67.3 44 4 2 2 6 5 7 64.9 45 5 2 2 6 5 7 63.2 46 3 2 2 6 5 7 64.5 47 5 2 2 7 5 7 64.2 48 4 2 2 7 5 7 64. 1 49 4 2 2 7 5 7 63.1 50 3 2 2 7 5 7 64.6 51 3 2 2 7 5 7 64.5 52 2 2 2 7 5 7 72.4 53 2 2 2 7 5 7 73.7 54 1 2 2 7 5 7 75.9 55 3 1 2 7 5 7 75.6 56 1 1 2 7 5 7 79.8 57 2 1 2 7 5 7 79.6 58 2 1 2 7 5 7 80 .5 59 2 1 2 7 5 7 81 .3 60 5 1 2 7 5 7 75.7 61 4 1 3 7 5 7 75.7 62 4 3 3 7 5 7 74.9 63 5 3 3 7 5 7 74.6 64 3 3 3 7 5 7 75.1 65 3 3 3 7 5 7 74.6 66 3 3 3 7 5 7 74.2 67 3 3 3 7 5 7. 73.8 68 1 1 3 7 5 7 76 .5 69 1 1 3 7 5 7 77. 1 70 2 1 3 7 5 7 76.8 71 5 1 4 7 5 7 74.8 72 4 1 4 7 5 7 74.7 73 5 1 4 7 5 7 74.7 74 4 1 4 7 5 7 74.3 75 5 1 4 7 6 7 74.0 76 4 1 4 7 6 7 73 .9 77 3 1 1 7 6 7 76.2 78 2 1 1 7 6 7 77.8 79 2 1 1 7 6 7 79 .5 80 2 1 1 7 6 7 81.0 152 T a b l e 45. ( c o n t ' d ) SIMULATION #1 - UTILITY MATRIX #1 ( c o n t ' d ) ITER. STATE STATE ALTERNATIVES AVERAGE # # 1 2 3 4 5 UTILITY 81 2 1 1 7 6 7 82.3 82 3 1 1 7 6 7 81 .6 83 2 1 1 7 6 7 80.9 84 3 1 1 7 6 7 79.2 85 2 1 1 7 6 7 80.2 86 2 1 1 7 6 7 81.1 87 2 1 1 7 6 7 82.0 88 2 1 1 7 6 7 82.7 89 2 1 1 7 6 7 83.4 90 2 1 1 7 6 7 84.1 91 2 1 1 7 6 7 84.7 92 2 1 1 7 6 7 85.2 93 3 1 1 7 6 7 83.8 94 1 1 1 7 6 7 84.6 95 2 1 1 7 6 7 84.6 96 2 1 1 7 6 7 84.6 97 5 1 4 7 6 7 79.6 98 4 1 4 7 6 7 79.6 99 5 1 4 7 6 7 78.7 100 4 1 4 7 6 7 78.7 101 5 1 4 7 1 7 77.7 102 4 1 4 7 1 7 77.6 103 1 1 4 7 7 7 80.6 1 04 1 1 4 7 7 7 81 .0 105 2 1 4 7 7 7 80.8 106 1 1 4 7 7 7 83.0 1 07 1 1 4 7 7 7 83.3 108 1 1 4 7 7 7 83.5 1 09 1 1 4 7 7 7 83.7 110 2 1 4 7 7 7 83.5 1 1 1 1 1 4 7 7 7 84.8 1 12 2 1 4 7 7 7 84.7 1 13 3 1 4 7 7 7 82.0 1 14 2 1 4 7 7 7 82.3 1 15 1 1 4 7 7 7 83.3 1 16 1 1 4 7 7 7 83.5 1 17 2 1 4 7 7 7 83.4 1 18 2 1 4 7 7 7 83.7 119 1 1 4 7 7 7 84.4 120 2 1 4 7 7 7 84.5 153 S i m u l a t i o n #2 i s s i m i l a r t o s i m u l a t i o n #1 but uses u t i l i t y matrix #3, r e f l e c t i n g lower u t i l i t i e s f o r increased F/M and DO l e v e l s . U n l i k e s i m u l a t i o n #1, F i g u r e 22 and Table 46 i l l u s t r a t e s that the model does not converge w i t h i n 160 i t e r a t i o n s and the average expected u t i l i t i e s d i m i n i s h c o n s i s t e n t l y with time. Instead of s t e a d i l y improving b u l k i n g c o n d i t i o n s , the process c o n d i t i o n o s c i l l a t e s between s t a t e s 3 and 5. Despite e x t e n s i v e i t e r a t i o n s under h i g h - b u l k i n g c o n d i t i o n s the model i s slow to attempt con-t r o l a l t e r n a t i v e s which w i l l d i m i n i s h f u r t h e r the expected u t i l i t y . The u l t i m a t e p o l i c y v e c t o r f o r i t e r a t i o n 156 d i d not change from i t e r a t i o n #113 to #156, remaining a t [2, 2, 1, 1, 4 ] ; t h i s i s c o n s i d e r a b l y d i f f e r e n t from the [1, 1, 7, 7, 7] p o l i c y v e c t o r determined i n S e c t i o n 4.2.5 f o r u t i l i t y matrix #3. Consequently, the average expected u t i l i t y , s lowly but s t e a d i l y , d i m i n i s h e s to 49.5. 154 FIGURE 22 cn cn 100 t—1 LxJ CD cn LxJ > cn o i—i a o o LJ t— cn E - < cn SIMULATION « 2 - UTILITY *3 MRTRIX RVERRGE UTILITY RND STRTE PLOTS 160 60 80 100 ITERATION in) T a b l e 46. S i m u l a t i o n 2 - U t i l i t y 3 M a t r i x - Recorded Sta te and P o l i c y V e c t o r Changes For Low DO B u l k i n g SIMULATION #2 - UTILITY MATRIX #3 ITER. STATE STATE ALTERNATIVES AVERAGE # # 1 2 3 4 5 UTILITY 1 1 1 1 1 1 1 68.6 2 3 2 I 1 1 1 66.0 3 3 2 1 1 1 1 67. 1 4 4 2 2 1 1 62.6 5 4 2 2 1 1 57.9 6 4 2 1 2 1 1 54.3 7 3 2 2 1 1 63.6 8 4 2 3 1 1 61.0 9 4 2 3 1 1 58.6 10 4 2 3 1 1 56.5 1 1 4 2 1 3 1 1 54.6 12 4 2 3 1 1 53. 1 13 5 2 3 2 1 57.7 14 5 2 3 1 2 46.6 15 5 2 3 2 3 53.5 16 5 2 3 2 4 52.9 17 3 2 3 2 4 59.7 18 5 2 1 2 4 58.1 19 4 2 1 1 2 4 57.2 20 4 2 4 3 4 55.5 21 5 2 4 1 4 54.4 22 5 2 4 1 4 52.6 23 4 2 4 1 4 52.1 24 3 2 1 4 1 4 55.2 25 2 2 4 1 4 63.6 26 2 2 4 1 4 63.6 27 2 2 4 1 4 67.1 28 2 2 1 4 1 4 70.0 29 2 2 1 4 1 4 72.4 30 2 2 4 1 4 74 .5 31 2 2 1 4 1 4 76.3 32 2 2 1 4 1 4 77 .9 33 3 2 1 4 1 4 69.7 34 3 2 1 4 1 4 68.4 35 2 2 1 4 1 4 73. 1 36 3 2 1 4 1 4 68.6 37 5 2 1 4 1 4 59.5 38 5 2 1 4 1 4 58.0 39 4 2 1 4 1 4 58.1 40 5 2 1 4 1 4 57.0 156 T a b l e 46. ( c o n t ' d ) SIMULATION #2 - UTILITY MATRIX #3 ( c o n t ' d ) I T E R . STATE STATE ALTERNATIVES AVERAGE # # 1 2 3 4 5 UTILITY 41 5 2 1 4 1 4 55.8 42 5 2 1 4 1 4 54.7 43 4 2 1 4 1 4 55.0 44 2 2 1 4 1 4 59.4 45 2 2 1 4 1 4 60.7 46 3 2 1 4 1 4 57.2 47 3 2 1 4 1 4 56.8 48 3 2 1 4 1 4 56.4 49 4 2 1 1 1 4 55.8 50 4 2 1 1 1 4 54.5 51 4 2 1 1 1 4 53.4 52 4 2 2 1 1 4 52.5 53 4 2 2 1 1 4 51 .7 54 4 2 2 1 1 4 51.0 55 3 2 1 1 1 4 53. 1 56 3 2 1 1 1 4 54.3 57 4 2 2 5 1 4 51.8 58 5 2 2 5 1 4 51.1 59 4 2 2 5 1 4 51 .3 60 3 2 2 5 1 4 52.7 61 4 2 2 4 1 4 52. 1 62 2 2 1 1 1 4 55. 1 63 4 2 2 1 1 4 54.8 64 4 2 2 1 1 4 54. 1 65 4 2 2 4 1 4 53.5 66 4 2 2 4 1 4 53. 1 67 4 2 2 4 1 4 52.7 68 4 2 2 4 1 4 52.7 69 5 2 2 4 1 4 52.2 70 3 2 2 4 1 4 53.7 71 3 2 2 4 1 4 54.3 72 1 2 2 4 1 4 56.9 73 2 2 2 4 1 4 56.0 74 2 2 2 4 1 4 58. 1 75 2 2 2 4 1 4 58.9 76 2 2 2 4 1 4 61 .5 77 3 2 2 4 1 4 54.7 78 3 2 2 4 1 4 54.5 79 3 2 2 1 1 4 51.8 80 3 2 2 1 1 1 55.9 157 Table 46. (cont'd) SIMULATION #2 - UTILITY MATRIX #3 ( cont 'd ) ITER. STATE STATE ALTERNATIVES AVERAGE # # ' 1 2 3 4 5 UTILITY 81 3 2 2 1 1 1 56.8 82 3 2 2 1 1 i 57.6 83 3 2 2 1 1 i 58.4 84 3 2 2 1 1 1 59. 1 85 2 2 2 1 1 1 62.7 86 3 2 1 1 1 1 62. 1 87 5 2 1 1 1 1 58.4 88 5 2 1 1 1 1 55.3 89 5 2 1 i 1 1 52.6 90 5 2 1 1 1 4 51.3 91 5 2 1 1 1 4 50.3 92 5 2 1 1 1 1 50. 1 93 5 2 1 1 1 4 49.2 94 3 2 1 1 1 4 51 .6 95 3 2 1 1 1 4 52.2 96 3 2 1 1 1 4 52.9 97 3 2 1 1 1 4 53.5 98 3 2 1 1 1 4 54.0 99 4 2 1 1 1 4 51 .7 100 4 2 1 1 1 4 51.4 101 4 2 1 1 1 4 51.0 102 4 2 1 1 1 4 50.7 103 4 2 1 1 1 4 50.4 104 4 2 1 i 1 4 50.2 105 3 2 1 1 1 4 51 .0 106 3 2 1 1 1 4 51 .5 107 4 2 1 1 1 4 49.7 108 5 2 1 1 1 4 49.2 109 4 2 1 1 1 4 49.2 110 3 2 1 1 1 4 50.0 1 1 1 3 2 1 1 1 4 50.5 1 12 2 2 1 1 1 4 52.7 113 4 2 2 1 1 4 52.3 1 14 4 2 2 1 1 4 52. 1 115 4 2 2 1 1 4 51 .8 116 4 2 2 1 1 4 51.6 117 4 2 2 1 1 4 51 .4 118 4 2 2 1 1 4 51.5 119 5 2 2 1 1 4 50.8 120 3 2 2 1 1 4 52.5 158 Table 46. (cont'd) SIMULATION #2 - UTILITY MATRIX #3 ( c o n t ' d ) ITER. STATE STATE ALTERNATIVES AVERAGE # # 1 2 3 4 5 UTILITY 121 3 2 2 1 1 4 53.0 1 22 2 2 2 1 1 4 54.9 1 23 3 2 3 1 1 4 53.7 124 3 2 2 1 1 4 54. 1 125 3 2 2 1 1 4 54.5 126 4 2 3 1 1 4 52.8 127 4 2 3 1 1 4 52.7 128 2 2 3 1 1 4 53.6 129 4 2 2 1 1 4 53.5 130 4 2 2 1 1 4 53.3 131 4 2 2 1 1 4 53.2 1 32 4 2 2 1 1 4 53.0 133 4 2 2 1 1 4 52.9 134 4 2 2 1 1 4 52.7 135 4 2 2 1 1 4 52.6 136 5 2 2 1 1 4 52.3 137 4 2 2 1 1 4 52.1 1 38 4 2 2 1 1 4 52.0 1 39 4 2 2 1 1 4 51 .8 140 3 2 2 1 1 4 52.4 141 2 2 2 1 1 4 53.8 142 2 2 2 1 1 4 54.3 143 3 2 2 1 1 4 53.5 144 4 2 2 1 1 4 51.9 145 4 2 2 1 1 ' 4 51.8 146 5 2 2 1 1 4 51.6 147 4 2 2 1 1 4 51 .4 1 48 3 2 2 1 1 4 51.9 1 49 3 2 2 1 1 4 52.2 150 5 2 2 1 1 4 50.4 151 4 2 2 1 1 4 50.3 1 52 4 2 2 1 1 4 50. 1 153 4 2 2 1 1 4 50.0 1 54 4 2 2 1 1 4 49.9 155 5 2 2 1 1 4 49.6 1 56 4 2 2 1 1 4 49.5 159 S i m u l a t i o n #3 uses u t i l i t y matrix #4, which i s s i m i l a r i n s t r u c t u r e t o u t i l i t y matrix #l,but without d i f f e r e n t i a t i n g between F/M c o n t r o l s i n terms of u t i l i t y . F i g u r e 23 and Table 47 i l l u s t r a t e t h a t the u l t i m a t e p o l i c y v e c t o r of [1, 4, 7, 7, 7] i s not converged upon w i t h i n 156 i t e r a t i o n s , remaining unchanged at [3, 4, 4, 4, 7] f o r i t e r a t i o n s 96 to 160. The average expected u t i l i t y of 77 to 80 i s lower than the value of 82.6 p r e d i c t e d i n S e c t i o n 4.2.5, and appears to o s c i l l a t e between the values without an appearance of convergence. As the s t a t e c o n d i t i o n i s g e n e r a l l y between 1 and 3, l i t t l e experimentation i s undertaken at higher s t a t e l e v e l s t o optimize the expected u t i l i t y at these b u l k i n g c o n d i t i o n s . 160 FIGURE 23 SIMULATION «3 - UTILITY *4 MATRIX AVERAGE UTILITY AND STATE PLOTS 160 20 40 60 80 100 ITERATION in) 120 140 160 Table 47. Sim u l a t i o n 3 - U t i l i t y 4 M a t r i x - Recorded State and P o l i c y Vector Changes For Low DO Bulking SIMULATION #3 - UTILITY MATRIX #4 :R. STATE STATE ALTERNATIVES AVERAGE # 1 2 3 4 5 UTILITY 1 1 1 1 1 67.5 2 2 2 1 1 1 1 67.5 3 3 2 2 1 1 1 67.5 4 3 2 2 1 1 1 68.5 5 4 2 2 2 1 1 67.5 6 4 2 2 2 2 1 67.5 7 4 2 2 2 3 1 67.5 8 5 2 2 2 4 1 66.1 9 3 2 2 2 4 1 70.6 10 4 2 2 3 4 1 70.6 1 1 3 2 2 3 4 1 75.7 12 5 2 2 4 4 1 -72.7 13 3 2 2 4 4 1 72.7 14 3 2 2 5 4 1 72.7 15 3 2 2 6 4 1 72.7 16 5 2 2 4 4 1 72.4 17 5 2 2 4 4 1 72.4 18 5 2 2 4 4 1 72.4 19 5 2 2 4 4 1 72.4 20 5 2 2 4 4 1 72.4 21 5 2 2 4 4 1 72.4 22 5 2 2 4 4 1 72.4 23 4 2 2 4 4 1 72.4 24 2 2 2 4 4 2 78.6 25 5 2 3 4 4 2 78.6 26 5 2 3 4 4 3 78.6 27 5 2 3 4 4 4 78.7 28 4 2 3 2 4 4 80.4 29 3 2 3 2 4 4 81.9 30 3 2 3 1 4 4 81.8 31 3 2 3 2 4 4 81 .8 32 3 2 3 1 4 4 81.7 33 3 2 3 2 4 4 81.7 34 4 2 3 1 4 4 81 .6 35 3 2 3 1 4 4 82.4 36 4 2 3 4 4 4 81.7 37 2 2 3 2 4 4 83.4 38 3 2 1 2 4 4 80.2 39 3 2 1 1 4 4 80.2 40 3 2 1 2 4 4 80.2 162 Table 4 7 . (cont'd) SIMULATION #3 - UTILITY MATRIX #4 ( c o n t ' d ) ITER. STATE STATE ALTERNATIVES AVERAGE # # 1 2 3 4 5 UTILITY 41 4 2 1 1 4 4 80.2 42 5 2 1 4 4 4 77.4 43 5 2 1 4 4 4 76.0 44 5 2 4 4 4 1 74.2 45 5 2 4 4 4 6 74.3 46 5 2 4 4 4 7 74.3 47 4 2 4 4 4 7 74.0 48 3 2 4 4 4 7 74.4 49 3 2 4 5 4 7 74.4 50 4 2 4 4 4 7 74. 1 51 4 2 4 4 4 7 73.0 52 3 2 4 4 4 7 73.4 53 2 2 1 4 4 7 77.5 54 2 2 1 4 4 7 79. 1 55 4 2 3 4 4 7 77.5 56 3 2 3 4 4 7 77.8 57 2 2 3 4 4 7 80.3 58 3 2 4 4 4 7 78 .9 59 2 2 4 4 4 7 79.9 60 3 2 5 4 4 7 79.9 61 5 2 5 4 4 7 74.6 62 3 2 5 4 4 7 75.2 63 3 2 5 4 4 7 75. 1 64 3 2 5 4 4 7 74.9 65 2 2 5 4 4 7 76.2 66 2 2 5 4 4 7 77.7 67 3 2 6 4 4 7. 76.2 68 1 2 6 4 4 7 77.7 69 1 2 6 4 4 7 79.3 70 1 2 6 4 4 7 80 .5 71 3 3 6 4 4 7 77.7 72 2 3 6 4 4 7 78.4 73 3 3 3 4 4 7 77.6 74 3 3 3 4 4 7 77.4 75 4 3 3 4 4 7 75.7 76 4 3 3 4 4 7 75.0 77 4 3 3 4 4 7 74.4 78 4 3 3 4 4 7 73.9 79 4 3 3 4 4 7 73.3 80 2 3 3 4 4 7 74.0 163 T a b l e 47. ( c o n t ' d ) SIMULATION #3 - UTILITY MATRIX #4 ( c o n t ' d ) ITER. STATE STATE ALTERNATIVES AVERAGE # # 1 2 3 4 5 UTILITY 81 4 3 5 4 4 7 73.2 82 3 3 5 4 4 7 73.4 83 3 3 5 4 4 7 73.3 84 3 3 5 4 4 7 73.3 85 3 3 5 4 4 7 73.2 86 2 3 5 4 4 7 74.0 87 4 3 4 4 4 7 73. 1 88 3 3 4 4 4 7 73.3 89 2 3 4 4 4 7 73.9 90 2 3 4 4 4 7 74.8 91 2 3 4 4 4 7 75.5 92 1 3 4 4 4 7 77.8 93 2 1 4 4 4 7 76.9 94 2 1 4 4 4 7 77.4 95 1 1 4 4 4 7 78.8 96 3 3 4 4 4 7 78.8 97 5 3 4 4 4 7 77. 1 98 5 3 4 4 4 7 76.6 99 4 3 4 4 4 7 76.8 100 3 3 4 4 4 7 76.9 101 3 3 4 4 4 7 76.8 102 2 3 4 4 4 7 77.4 103 2 3 4 4 4 7 77.8 104 2 3 4 4 4 7 78. 1 105 1 3 4 4 4 7 79. 1 106 1 3 4 4 4 7. 80.0 107 2 3 4 4 4 7 79.4 108 2 3 4 4 4 7 79.6 109 2 3 4 4 4 7 79.8 110 2 3 4 4 4 7 80.0 1 1 1 3 3 4 4 4 7 78.0 112 3 3 4 4 4 7 77.9 1 13 3 3 4 4 4 7 77.8 1 14 2 3 4 4 4 7 78.3 115 1 3 4 4 4 7 79.0 1 16 2 3 4 4 4 7 78.8 117 1 3 4 4 4 7 79.4 118 2 3 4 4 4 7 79.2 119 1 3 4 4 4 7 79.8 120 2 3 4 4 4 7 79.6 164 Table 47 . (cont'd) SIMULATION #3 - UTILITY MATRIX #4 ( c o n t ' d ) I T E R . STATE STATE ALTERNATIVES AVERAGE # # 1 2 3 4 5 UTILITY 121 1 3 4 4 4 7 80. 1 122 3 3 4 4 4 7 78.0 123 4 3 4 4 4 7 77.4 124 3 3 4 4 4 7 77.5 125 2 3 4 4 4 7 77.9 126 2 3 4 4 4 7 78. 1 127 2 3 4 4 4 7 78.2 128 2 3 4 4 4 7 78.4 129 2 3 4 4 4 7 78.5 130 2 3 4 4 4 7 78.7 131 2 3 4 4 4 7 78.8 132 2 3 4 4 4 7 76.4 133 3 3 4 4 4 7 76.6 134 3 3 4 4 4 7 76.5 135 2 3 4 4 4 7 76.9 136 1 3 4 4 4 7 77.2 137 2 3 4 4 4 7 77.3 138 1 3 4 4 4 7 77.6 139 1 3 4 4 4 7 77.8 140 1 3 4 4 4 7 78. 1 141 2 3 4 4 4 7 78. 1 142 2 3 4 4 4 7 78.2 143 1 3 4 4 4 7 78.5 144 3 3 4 4 4 7 77.4 145 2 3 4 4 4 7 77.7 146 2 3 4 4 4 7 77.8 147 2 3 4 4 4 7 77.9 148 1 3 4 4 4 7 78.1 149 2 3 4 4 4 7 78.2 150 2 3 4 4 4 7 78.3 151 1 3 4 4 4 7 78.5 152 2 3 4 4 4 7 78.6 153 2 3 4 4 4 7 78.7 154 2 3 4 4 4 7 78.8 155 3 3 4 4 4 7 78.1 156 3 3 4 4 4 7 78.1 157 5 3 4 4 4 7 77.2 158 5 3 4 4 4 7 76.8 159 3 3 4 4 4 7 77. 1 160 3 3 4 4 4 7 77. 1 165 S i m u l a t i o n #4 uses u t i l i t y matrix #6, which i s s i m i l a r to u t i l i t y matrix #4, but with an extremely steep DO c o n t r o l u t i l i t y g r a d i e n t . F i g u r e 24 and Table 48 i l l u s t r a t e s t h a t c o n t r o l u s i n g p o l i c y v e c t o r s generated with t h i s type of u t i l i t y shape does not improve the expected u t i l i t y . The average expected u t i l i t y i n F i g u r e 28 decreases with time and the model appears to r e s u l t i n a c o n s i s t e n t b u l k i n g c o n d i t i o n . The success as a process c o n t r o l mechanism i s the lowest of s i m u l a t i o n s #1 to #4. State a l t e r n a -t i v e s are u n s t a b l e . As an example, although s t a t e 4 has a recom-mended c o n t r o l p o l i c y of 6, from i t e r a t i o n 39 to 117, the p o l i c y suddenly changes to a l t e r n a t i v e 2 f o r i t e r a t i o n s 118 to 129, then to 3, f o r i t e r a t i o n s 130 to 133, and then back to p o l i c y 6, f o r i t e r a t i o n s 134 to 139, before changing to p o l i c y 1. Consequently, the average expected u t i l i t y d i m i n i s h e s from 67.5 f o r the f i r s t i t e r a t i o n , u s i n g b a s e l i n e f r e q u e n c i e s , to 54 f o r the i t e r a t i o n 160. Although h i g h DO c o n c e n t r a t i o n s are r e q u i r e d t o cure the low DO b u l k i n g c o n d i t i o n s , the extremely low u t i l i t i e s a s s i g n e d to h i g h DO c o n t r o l o p t i o n s causes the convergence problems. The c o r r e c t c o n t r o l p o l i c y i s i n c o n f l i c t with the u t i l i t y s t r u c t u r e . Consequently, the process i s predominantly i n a s t a t e 4 to 5 b u l k i n g c o n d i t i o n . 166 ITERATION in) Table 48. S i m u l a t i o n 4 - U t i l i t y 6 Matrix - Recorded State and P o l i c y Vector Changes For Low DO B u l k i n g SIMULATION #4 - UTILITY MATRIX #6 ITER. STATE STATE ALTERNATIVES AVERAGE # # 1 2 3 4 5 UTILITY 1 1 1 1 1 1 67.5 2 2 2 1 1 1 67.5 3 2 2 1 1 1 70.0 4 2 2 1 1 1 1 74.4 5 2 3 1 1 1 74.4 6 3 3 1 1 1 67.5 7 4 3 2 1 1 67.5 8 3 3 2 1 1 77.0 9 5 3 3 1 1 77.0 10 4 3 3 1 1 79.8 1 1 5 3 3 1 1 75.0 12 4 3 1 3 1 1 76.3 13 4 3 1 3 1 1 73.3 14 4 3 3 2 1 69.1 15 5 3 3 3 1 69. 1 16 5 3 1 3 3 1 68.3 17 5 3 1 3 3 1 67.5 18 5 3 3 3 67.5 19 5 3 3 3 67.5 20 5 3 1 3 3 1 62.5 21 4 3 1 3 3 1 63.8 22 5 3 3 1 1 64.2 23 5 3 1 3 1 1 62.0 24 5 3 1 3 1 4 60.3 25 4 3 1 3 1 4 62.6 26 3 3 1 3 1 4 68.9 27 5 3 1 4 1 4 59.8 28 4 3 1 4 1 4 60.3 29 4 3 1 4 1 4 58.4 30 4 3 1 4 1 4 56.7 31 4 3 1 4 1 4 55.1 32 5 3 1 4 1 4 53.2 33 4 3 1 4 1 4 53.6 34 4 3 1 4 1 4 52.4 35 4 3 1 4 1 4 51 .2 36 4 3 1 4 1 4 50. 1 37 4 3 1 4 4 4 58.8 38 4 3 1 4 5 4 56.2 39 4 3 1 4 6 4 54.4 40 2 3 1 1 6 4 70.5 168 Table 48. (cont'd) SIMULATION #4 - UTILITY MATRIX #6 (cont'd) ITER. STATE STATE ALTERNATIVES AVERAGE ' # # 1 2 3 4 5 UTILITY 41 3 3 2 1 6 4 70.5 42 3 3 2 1 6 4 71 .0 43 3 3 2 1 6 4 71.4 44 5 3 2 4 6 4 68.0 45 5 3 2 4 6 4 68.0 46 5 3 2 4 6 4 68.0 47 5 3 2 4 6 4 68.0 48 4 3 2 4 6 4 68.0 49 4 3 2 4 6 4 64.1 50 3 3 2 4 6 4 66.3 51 3 3 2 5 6 4 66.3 52 2 3 2 5 6 4 72.6 53 3 3 3 5 6 4 72.6 54 3 3 3 5 6 4 70.9 55 3 3 3 5 6 4 69.3 56 3 3 3 5 6 4 67.9 57 3 3 3 5 6 4 66.6 58 4 3 3 6 6 4 66.3 59 5 3 3 6 6 4 63.2 60 5 3 3 6 6 4 63.0 61 5 3 3 6 6 5 63.0 62 3 3 3 6 6 5 64.0 63 5 3 3 4 6 5 62. 1 64 3 3 3 2 6 5 63.0 65 4 3 3 3 6 5 63.0 66 3 3 3 3 6 5 63.8 67 5 3 3 4 6 5 63.0 68 3 3 3 4 6 5 63.0 69 3 3 3 1 6 5 62.3 70 5 3 3 5 6 5 62.1 71 4 3 3 5 6 5 62.1 72 3 3 3 5 6 5 60.9 73 3 3 3 5 6 5 60.9 74 3 3 3 4 6 5 60. 1 75 2 3 3 4 6 5 67.8 76 3 3 1 4 6 5 62.9 77 2 3 1 4 6 5 67.2 78 2 3 1 4 6 5 69.3 79 2 3 1 4 6 5 70.2 80 4 3 2 4 6 5 64.0 169 T a b l e 48. ( c o n t ' d ) SIMULATION #4 - UTILITY MATRIX #6 ( c o n t ' d ) ITER. STATE STATE ALTERNATIVES AVERAGE # # 1 2 3 4 5 UTILITY 81 5 3 2 4 6 5 63.4 82 5 3 2 4 6 5 63.2 83 3 3 2 4 6 5 63.3 84 2 3 2 4 6 5 66.2 85 2 3 2 4 6 5 69.1 86 3 3 3 4 6 5 66.2 87 3 3 3 4 6 5 65.1 88 3 3 3 4 6 5 64. 1 89 2 3 3 4 6 5 66.3 90 2 3 3 4 6 5 69.1 91 2 3 3 4 6 5 71.4 92 3 3 3 4 6 5 66.9 93 4 3 3 4 6 5 62.6 94 4 3 3 4 6 5 62.1 95 3 3 3 4 6 5 62.7 96 3 3 3 4 6 5 62.0 97 3 3 3 4 6 5 61 .4 98 3 3 3 4 6 5 60.8 99 1 3 3 4 6 5 64.2 100 2 1 3 4 6 5 63.2 101 3 1 2 4 6 5 61 .2 102 1 1 2 4 6 5 63.7 103 2 2 2 4 6 5 63.7 104 2 2 2 4 6 5 65.7 105 2 2 2 4 6 5 66.3 106 2 2 2 4 6 5 69.0 107 2 2 2 4 6 5 70.4 108 5 2 3 4 6 5 63.1 109 5 2 3 4 6 5 63.1 110 4 2 3 4 6 5 63.0 1 1 1 4 2 3 4 6 5 62.6 1 12 5 2 3 4 6 5 62.2 113 5 2 3 4 6 5 62.1 1 14 4 2 3 4 6 5 62.0 115 5 2 3 4 6 5 61 .6 1 16 5 2 3 4 6 5 61 .4 117 4 2 3 4 6 5 61 .4 118 5 2 3 4 2 5 61 .1 119 5 2 3 4 2 5 60.9 120 5 2 3 4 2 5 60.6 170 T a b l e 48. ( c o n t ' d ) SIMULATION #4 - UTILITY MATRIX #6 (cont 'd) I T E R . STATE STATE ALTERNATIVES AVERAGE # # 1 2 3 4 5 UTILITY 121 3 2 3 4 2 5 61.1 122 2 2 3 4 2 5 62.4 123 2 2 3 4 2 5 63.8 124 3 2 3 4 2 5 61 .9 125 2 2 3 4 2 5 63.0 126 3 2 3 4 2 5 61.6 127 2 2 3 4 2 5 62.5 128 5 2 1 4 2 5 61.8 129 4 2 1 4 2 5 61.6 130 5 2 1 4 3 5 61.6 131 5 2 1 4 3 5 61.3 132 5 2 1 4 3 5 61.0 133 4 2 1 4 3 5 60.9 134 5 2 1 4 6 5 61 .0 135 5 2 1 4 6 5 60.8 136 5 2 1 4 6 5 60.7 137 5 2 1 4 6 5 60.6 138 5 2 1 4 6 5 60.5 139 4 2 1 4 6 5 60.4 140 5 2 1 4 1 5 58.8 141 5 2 1 4 1 5 58.6 142 3 2 1 4 1 5 59.3 143 4 2 1 4 1 5 56.9 144 5 2 1 4 6 5 57.6 145 5 2 1 4 6 5 57.4 146 5 2 1 4 6 5 57.3 147 5 2 1 4 6 5 57.2 148 5 2 1 4 6 5 57.0 149 5 2 1 4 6 5 56.9 150 5 2 1 4 6 5 56.8 151 3 2 1 4 6 5 57. 1 152 3 2 1 4 6 5 56.9 153 2 2 1 4 6 5 57.6 154 2 2 1 4 6 5 56.5 155 5 2 2 4 6 5 55.8 156 5 2 2 4 6 5 55.6 157 4 2 2 4 6 5 55.6 158 5 2 2 4 1 5 54.3 159 5 2 2 4 1 5 54.1 160 4 2 2 4 1 5 54.0 171 S i m u l a t i o n #5 uses u t i l i t y matrix #7, which determines u t i l i t y s o l e l y as a f u n c t i o n of SVI l e v e l . F i g u r e 25 and Table 49 i l l u s -t r a t e s that the u l t i m a t e p o l i c y v e c t o r of [1, 4, 7, 7, 7] i s not converged on i n 160 i t e r a t i o n s . However, a f t e r i t e r a t i o n #67, the b u l k i n g s t a t e never exceeds s t a t e 3, and stays mainly w i t h i n s t a t e s 1 and 2 u n t i l i t e r a t i o n 160. The average expected u t i l i t y of 85.4, from S e c t i o n 4.2.5, i s exceeded a f t e r 40 i t e r a t i o n s . The p o l i c y v e c t o r of [4, 7, 8, 4, 4] r e f l e c t s a high energy u t i l i z a -t i o n t o maintain a b u l k i n g s t a t e of 2. The moderate energy c o n t r o l a l t e r n a t i v e s f o r s t a t e s 4 and 5 ( c o n t r o l 4) occur because these s t a t e s occur i n f r e q u e n t l y i n the simulated p r o c e s s . As d e s c r i b e d e a r l i e r , u n l e s s a p a r t i c u l a r s t a t e c o n d i t i o n o c c u r s , no experimentation or p o l i c y o p t i m i z a t i o n can be undertaken and the recommended p o l i c i e s w i l l not change. The simulated low-DO b u l k i n g model d i f f e r e n t i a t e s p r i m a r i l y between DO c o n t r o l l e v e l s and to a l e s s e r extent between F/M p o l i c i e s . Consequently, under h i g h b u l k i n g s t a t e s , a l l combinations of h i g h DO and F/M c o n t r o l s w i l l have a h i g h p r o b a b i l i t y of reducing b u l k i n g . I f high DO and low F/M does not immediately reduce the b u l k i n g , the next c o n t r o l of high DO and medium F/M w i l l be attempted. I f the second combination r e s u l t s i n reduced b u l k i n g i t w i l l be s e l e c t e d at the next s t a t e 5 b u l k i n g c o n d i t i o n . A f u r t h e r success i n reducing b u l k i n g w i l l r e s u l t i n an entrenchment of that p o l i c y , even i f a lower F/M s t r a t e g y may have a s l i g h t l y b e t t e r p r o b a b i l i t y of reducing the b u l k i n g . Without a u t i l i t y d i f f e r e n c e between c o n t r o l s , there i s no i n c e n t i v e t o change p o l i c i e s , p a r t i c u l a r l y a f t e r one has an e s t a b l i s h e d a " t r a c k r e c o r d " of success. 1 7 2 F IGURE 2 5 100 -1 —• 80 H L J CD cn L J > QZ 60 H 40 A 6-T o 5 -E— i—i 4 -Q O 3 -C J L J 2 -E—• QZ E— 1 -i cn 0 -SIMULRTION *5 - UTILITY * 7 MRTRIX AVERAGE UTILITY AND STATE PLOTS 160 60 80 100 ITERATION in) 160 T a b l e 49 . S i m u l a t i o n 5 - U t i l i t y 7 M a t r i x - Recorded S t a t e and P o l i c y V e c t o r Changes For Low DO B u l k i n g SIMULATION #5 - UTILITY MATRIX #7 ITER. STATE STATE ALTERNATIVES AVERAGE # # 1 2 3 4 5 UTILITY 1 1 1 1 1 1 1 67.5 2 2 2 1 1 1 1 67.5 3 3 2 2 1 1 1 67.5 4 3 2 2 1 1 1 68.5 5 3 2 2 1 1 1 69.3 6 4 2 2 2 1 1 67.5 7 4 2 2 2 2 1 67.5 8 4 2 2 2 3 1 67.5 9 5 2 2 2 4 1 67.5 10 5 2 2 2 4 2 67.5 1 1 5 2 2 2 4 3 67.5 12 5 2 2 2 4 4 67.5 13 4 2 2 2 4 4 71 .8 14 3 2 2 2 4 4 79.8 15 4 2 2 3 4 4 79.8 16 4 2 2 3 4 4 76.0 17 3 2 2 3 4 4 80.2 18 5 2 2 4 4 4 80.2 19 5 2 2 4 4 4 77.3 20 4 2 2 4 4 4 79.2 21 3 2 2 4 4 4 81.8 22 2 2 2 4 4 4 86.3 23 4 2 3 4 4 4 86.3 24 4 2 3 4 4 4 84.7 25 3 2 3 4 4 4 86.1 26 4 2 3 4 4 4 81.5 27 4 2 3 5 4 4 79.5 28 2 2 3 4 4 4 82.5 29 4 2 4 4 4 4 82.5 30 3 2 4 4 4 4 83.5 31 5 2 4 5 4 4 83.4 32 4 2 4 5 4 4 84.0 33 5 2 4 5 4 4 82.5 34 4 2 4 5 4 4 83.0 35 4 2 4 5 4 4 81.9 36 3 2 4 5 4 4 82.8 37 4 2 4 6 4 4 82.8 38 3 2 4 6 4 4 83.5 39 3 2 4 7 4 4 83.5 40 3 2 4 8 4 4 83.5 174 Table 49. ( c o n t ' d ) SIMULATION #5 - UTILITY MATRIX #7 ( cont 'd ) ITER. STATE STATE ALTERNATIVES AVERAGE # # 1 2 3 4 5 UTILITY 41 1 2 4 8 4 4 87.6 42 2 3 4 8 4 4 87.6 43 3 3 5 8 4 4 87.6 44 3 3 5 8 4 4 87.2 45 3 3 5 8 4 4 86.8 46 2 3 5 8 4 4 88.8 47 1 3 5 8 4 4 89.7 48 2 4 5 8 4 4 89.7 49 2 1 5 8 4 4 90.6 50 1 1 5 8 4 4 91.2 51 1 2 5 8 4 4 91 .2 52 1 3 5 8 4 4 91 .2 53 2 3 5 8 4 4 91 .3 54 2 3 5 8 4 4 91 .9 55 2 3 5 8 4 4 92.4 56 1 3 5 8 4 4 92.7 57 3 1 5 8 4 4 92.3 58 1 1 5 8 4 4 92.7 59 1 2 5 8 4 4 92.7 60 2 2 5 8 4 4 92.9 61 2 2 5 6 4 4 93.3 62 2 2 5 8 4 4 93.6 63 2 2 5 8 4 4 93.9 64 5 1 6 8 4 4 89.4 65 5 1 • 6 8 4 4 89.1 66 5 1 6 8 4 4 88.9 67 4 1 6 B 4 4 89. 1 68 3 1 6 8 4 4 89.3 69 3 1 6 8 4 4 89.0 70 3 1 6 8 4 4 88.8 71 3 1 6 8 4 4 88.6 72 3 1 6 8 4 4 88.4 73 3 1 6 8 4 4 88.2 74 2 1 6 8 4 4 88.8 75 3 1 7 8 4 4 88.8 76 2 1 7 8 4 4 89.3 77 1 2 7 8 4 4 90.4 78 1 2 7 8 4 4 90.4 79 2 2 7 8 4 4 90.4 80 2 2 7 8 4 4 91 .2 175 T a b l e 49. ( c o n t ' d ) SIMULATION #5 - UTILITY MATRIX #7 ( c o n t ' d ) ITER. STATE STATE ALTERNATIVES AVERAGE # # 1 2 3 4 5 UTILITY 81 2 2 7 8 4 4 91.9 82 2 2 7 8 4 4 92.5 83 2 2 7 8 4 4 93.0 84 2 2 7 8 4 4 93.4 85 3 2 7 8 4 4 91.4 86 3 2 7 8 4 4 91.2 87 1 2 7 8 4 4 91.6 88 2 2 7 8 4 4 91.7 89 2 2 7 8 4 4 92.1 90 2 2 7 8 4 4 92.4 91 2 2 7 8 4 4 92.8 92 2 2 7 8 4 4 93. 1 93 1 2 7 8 4 4 93.1 94 2 2 7 8 4 4 93.2 95 2 2 7 8 4 4 93.4 96 1 2 7 8 4 4 93.5 97 2 2 7 8 4 4 93.5 98 1 2 7 8 4 4 93.6 99 3 4 7 8 4 4 93.2 00 3 4 7 8 4 4 93.1 01 3 4 7 8 4 4 93.0 02 2 4 7 8 4 4 93.3 03 2 4 7 8 4 4 93.5 04 1 4 7 8 4 4 93.4 05 2 4 7 8 4 4 93.8 06 1 4 7 8 4 4 93.8 07 2 4 7 8 4 4 93.9 08 1 4 7 8 4 4 93.9 09 1 4 7 8 4 4 93.7 10 2 4 7 8 4 4 93.8 1 1 2 4 7 8 4 4 94.0 12 2 4 7 8 4 4 94. 1 13 1 4 7 8 4 4 94. 1 14 1 4 7 8 4 4 93.9 15 2 4 7 6 4 4 94.0 16 2 4 7 8 4 4 94.1 17 2 4 7 8 4 4 94.3 18 2 4 7 8 4 4 94.4 19 2 4 7 8 4 4 94.5 20 1 4 7 8 4 4 94.5 176 T a b l e 49. ( c o n t ' d ) SIMULATION #5 - UTILITY MATRIX #7 ( cont 'd ) ITER. STATE STATE ALTERNATIVES AVERAGE # # 1 2 3 4 5 UTILITY 121 1 4 7 8 4 4 94.3 122 2 4 7 8 4 4 94.4 123 2 4 7 8 4 4 94.5 1 24 1 4 7 8 4 4 94.5 125 2 4 7 8 4 4 94.6 126 2 4 7 8 4 4 94.6 127 2 4 7 8 4 4 94.7 128 1 4 7 8 4 4 94.7 129 2 4 7 8 4 4 94.8 130 1 4 7 8 4 4 94.7 131 1 4 7 8 4 4 94.6 132 2 4 7 8 4 4 94.7 133 1 4 7 8 4 4 94.7 134 2 4 7 8 4 4 94.7 135 1 4 7 8 4 4 94.7 136 2 4 7 8 4 4 94.7 137 2 4 7 8 4 4 94.8 138 2 4 7 8 4 4 94.9 139 2 4 7 8 4 4 95.0 140 2 4 7 8 4 4 95.0 141 2 4 7 8 4 4 95.1 142 2 4 7 8 4 4 95.2 143 3 4 7 8 4 4 94.6 144 3 4 7 8 4 4 94.5 145 3 4 7 8 4 4 94.4 146 2 4 7 8 4 4 94.6 147 2 4 7 8 4 4 94.7 148 1 4 7 8 4 4 94.7 149 2 4 7 8 4 4 94.7 150 1 4 7 8 4 4 94.7 151 2 4 7 8 4 4 94.7 152 2 4 7 8 4 4 94.8 153 2 4 7 8 4 4 94.8 154 2 4 7 8 4 4 94 .9 155 2 4 7 8 4 4 95.0 156 1 4 7 8 4 4 94.9 157 1 4 7 8 4 4 94.9 158 1 4 7 8 4 4 94.8 159 1 4 7 8 4 4 94.7 160 2 4 7 8 4 4 94.7 177 4.3.2 A daptation to S i n g l e C o n t r o l DO S t r a t e g y U t i l i t y matrix #1 was used to e v a l u a t e the impact of e s t a b l i s h i n g a c o n t r o l p o l i c y i n which low F/M c o n d i t i o n s are maintained r e g a r d l e s s of the p o l i c y v e c t o r recommendations. For example, a recommended c o n t r o l p o l i c y of 2 would be ignored i n favour of p o l i c y 1, and a recommendation of p o l i c y 6 would be ignored in favour of p o l i c y 4. I t e r a t i o n s 1 to 78, i l l u s t r a t e d i n F i g u r e 26 and Table 50, were undertaken using the above c o n t r o l p o l i c y . The r e s u l t i s a f i x e d p o l i c y v e c t o r of [2, 2, 2, 2, 2] and an average expected u t i l i t y of 64.1. No change occ u r r e d i n e i t h e r the expected u t i l i t y or v e c t o r p o l i c y from i t e r a t i o n 14 to 78, wherein the t e s t was t e r m i n a t e d . 4.3.3 Manual P o l i c y Adjustments Beginning with i t e r a t i o n 79, a new p o l i c y was undertaken. T h i s i n v o l v e d i n c r e a s i n g the c o n t r o l p o l i c y to the next h i g h e s t DO l e v e l , under b u l k i n g c o n d i t i o n s where the s t a t e had not improved i n 3 i t e r a t i o n s . The new p o l i c y can be d e f i n e d as: 1. Only p o l i c i e s 1, 4 and 7 are s e l e c t e d r e g a r d l e s s of the p o l i c y v e c t o r recommendation. 2. S e l e c t p o l i c y 1 where e i t h e r p o l i c y 1, 2 or 3 i s recommended. 3. S e l e c t p o l i c y 4 where e i t h e r p o l i c y 4, 5 or 6 i s recommended. 178 4. S e l e c t p o l i c y 7 where e i t h e r p o l i c y 7, 8 or 9 i s recommended. 5. Increase the p o l i c y DO l e v e l to the next highest where a s t a t e improvement has not been noted in 3 i t e r a t i o n s , and the b u l k i n g c o n d i t i o n i s s t a t e 3 to 5. 6. C o n t r o l p o l i c i e s f o r b u l k i n g s t a t e c o n d i t i o n s must be the same or g r e a t e r than lower b u l k i n g s t a t e p o l i c i e s . ( i . e . i f s t a t e 3 goes to p o l i c y 4, then s t a t e s 4 and 5 must a l s o f o l l o w p o l i c y 4). Item 5 above ensures that the u t i l i t y s t r u c t u r e does not r e s t r i c t e x perimentation with lower u t i l i t y c o n t r o l o p t i o n s , where b u l k i n g c o n d i t i o n s do not improve and the model does not a d j u s t the c o n t r o l p o l i c y . Item 6 i s r a t i o n a l i z e d by assuming that p o l i c i e s , which are r e q u i r e d to cure b u l k i n g a t lower s t a t e c o n d i t i o n s , w i l l a l s o be r e q u i r e d at higher s t a t e c o n d i t i o n s . T h i s p o l i c y a l s o reduces the amount of time that the system w i l l spend i n the higher s t a t e s , before converging on an a p p r o p r i a t e c o n t r o l p o l i c y . As i l l u s t r a t e d i n F i g u r e 26 and Table 50, the above p o l i c y r e s u l t s i n r a p i d convergence on the p o l i c y v e c t o r [1, 2, 4, 4, 4] and an average expected u t i l i t y i n excess of 80 w i t h i n 26 i t e r a t i o n s . Although the system does o c c a s i o n a l l y bulk i n t o s t a t e 4 and 5 c o n d i t i o n s , the p o l i c y v e c t o r r a p i d l y reduces the b u l k i n g . To improve the average expected u t i l i t y f u r t h e r w i l l r e q u i r e i n c r e a s i n g the DO l e v e l to p o l i c y 7, f o r s t a t e s 3 to 5, to minimize the amount of b u l k i n g . T h i s d e c i s i o n can be l e f t to the o p e r a t o r who can determine i f the o c c a s i o n a l b u l k i n g i s s e r i o u s enough to warrant the c o s t of the i n c r e a s e d energy necessary to c o n t r o l i t . 179 F IGURE 2 6 00 o 100 - i { -« » 1 _ J {—< ZD L J CD GC cn LxJ > 6 -o 5 -1—1 E—1 i—i 4 -O o 3 -o txJ 2 -r—• cn E— 1 -CO 0 -SIMULATION *6 - UTILITY «1 MATRIX - POLICY ADJUSTED AVERAGE UTILITY AND STATE PLOTS 60 80 100 ITERATION in) 120 140 160 Table 50. S i m u l a t i o n 6 - U t i l i t y 1 M a t r i x - State and P o l i c y  V e c t or Changes f o r Simulated (Known) Low DO B u l k i n g  Under Manual P o l i c y Adjustments SIMULATION #6 - UTILITY MATRIX #1 :R. STATE STATE ALTERNATIVES AVERAGE # 1 2 3 4 5 UTILITY 1 1 1 1 ! 67.5 2 2 2 1 1 1 1 66.9 3 3 2 2 1 1 1 66.0 4 2 2 2 1 1 1 74.1 5 2 2 2 1 1 1 74. 1 6 1 2 1 1 1 1 75.3 7 2 2 1 1 1 1 75.3 8 3 2 2 1 1 1 74. 1 9 3 2 2 1 1 1 74.4 10 5 2 2 2 1 1 65.2 1 1 5 2 2 2 1 2 61 .2 12 5 2 2 2 1 2 59.6 13 4 2 2 2 1 2 62.6 14 4 2 2 2 2 2 64. 1 15 4 2 2 2 2 2 64. 1 16 4 2 2 2 2 2 64. 1 17 5 2 2 2 2 2 64. 1 18 5 2 2 2 2 2 64. 1 19 4 2 2 2 2 2 64. 1 20 2 2 2 2 1 2 64. 1 21 3 2 2 2 1 2 64.1 22 3 2 2 2 1 2 64. 1 23 3 2 2 2 1 2 64.1 24 4 2 2 2 1 2 64.1 25 5 2 2 2 2 2 64. 1 26 5 2 2 2 2 2 64. 1 27 4 2 2 2 2 2 64. 1 28 5 2 2 2 2 2 64. 1 29 5 2 2 2 2 2 64. 1 30 5 2 2 2 2 2 64.1 31 5 2 2 2 2 2 64. 1 32 4 2 2 2 2 2 64.1 33 4 2 2 2 2 2 64. 1 34 5 2 2 2 2 2 64. 1 35 4 2 2 2 2 2 64. 1 36 5 2 2 2 2 2 64.1 37 5 2 2 2 2 2 64.1 38 5 2 2 2 2 2 64. 1 39 4 2 2 2 2 2 64. 1 40 4 2 2 2 2 2 64.1 181 Table 50. (cont'd) SIMULATION #6 - UTILITY MATRIX #1 ( c o n t ' d ) ITER. STATE STATE ALTERNATIVES AVERAGE # # 1 2 3 4 5 UTILITY 41 4 2 2 2 2 2 64. 1 42 3 2 2 2 2 2 64. 1 43 3 2 2 2 2 2 64. 1 44 4 2 2 2 2 2 64.1 45 5 2 2 2 2 2 64. 1 46 4 2 2 2 2 2 64. 1 47 5 2 2 2 2 2 64. 1 48 5 2 2 2 2 2 64. 1 49 5 2 2 2 2 2 64.1 50 5 2 2 2 2 2 64. 1 51 5 2 2 2 2 2 64. 1 52 5 2 2 2 2 2 64. 1 53 5- 2 2 2 2 2 64.1 54 4 2 2 2 2 2 64. 1 55 3 2 2 2 2 2 64.1 56 5 2 2 2 2 2 64. 1 57 4 2 2 2 2 2 64. 1 58 4 2 2 2 2 2 64. 1 59 4 2 2 2 2 2 64.1 60 3 2 2 2 2 2 64. 1 61 5 2 2 2 2 2 64. 1 62 5 2 2 2 2 2 64.1 63 5 2 2 2 2 2 64.1 64 5 2 2 2 2 2 64.1 65 4 2 2 2 2 2 64. 1 66 4 2 2 2 2 2 64. 1 67 4 2 2 2 2 2 64. 1 68 5 2 2 2 2 2 64. 1 69 4 2 2 2 2 2 64. 1 70 2 2 2 2 2 2 64.1 71 3 2 2 2 2 2 64. 1 72 5 2 2 2 2 2 64.1 73 5 2 2 2 2 2 64. 1 74 5 2 2 2 2 2 64.1 75 5 2 2 2 2 2 64. 1 76 5 2 2 2 2 2 64.1 77 5 2 2 2 2 2 64.1 78 5 2 2 2 2 2 64.1 79 4 2 2 2 2 2 64. 1 80 3 2 2 2 4 2 72.3 182 Table 50. (cont'd) SIMULATION #6 - UTILITY MATRIX #1 ( c o n t ' d ) ITER. STATE STATE ALTERNATIVES AVERAGE . # # 1 2 3 4 5 UTILITY 81 2 2 2 4 4 2 77.3 82 2 2 2 4 4 2 77.3 83 2 2 2 4 4 2 77.3 84 3 2 2 4 4 2 77.3 85 3 2 2 4 4 2 76.7 86 4 2 2 2 4 2 76.7 87 3 2 2 2 4 2 76.4 88 3 2 2 2 4 2 76.4 89 3 2 2 2 4 2 76.4 90 3 2 2 2 4 2 76.4 91 2 2 2 4 4 2 76.8 92 2 2 2 4 4 2 76.8 93 2 2 2 4 4 2 76.8 94 2 2 2 4 4 2 76.8 95 3 2 2 4 4 2 76.8 96 1 2 2 4 4 2 79.3 97 2 2 2 4 4 2 79.3 98 2 2 2 4 4 2 79.3 99 5 2 2 4 4 2 79.3 100 5 2 2 4 4 2 78.1 101 4 2 2 4 4 2 79.3 102 4 2 2 4 4 2 77.1 103 4 2 2 4 4 2 75.1 104 4 2 2 4 4 2 73.3 105 3 2 2 4 4 2 73.7 106 2 2 2 4 4 2 77.5 107 3 2 2 4 4 2 77.5 108 2 2 2 4 4 2 78.8 109 1 2 2 4 4 2 78.8 110 1 1 2 4 4 2 79.0 1 1 1 1 1 2 4 4 2 79.4 1 12 2 1 2 4 4 2 79.2 1 13 1 1 2 4 4 2 79.2 1 14 2 1 2 4 4 2 79.0 115 4 1 2 4 4 2 79.0 1 16 4 1 2 4 4 2 80 .9 1 17 2 1 2 4 4 2 80.9 118 2 1 2 4 4 2 80.9 119 4 1 2 4 4 2 80 .9 120 4 1 2 4 4 2 79.9 183 Table 50. (cont'd) SIMULATION #6 - UTILITY MATRIX #1 ( c o n t ' d ) ITER. STATE STATE ALTERNATIVES AVERAGE # # 1 2 3 4 5 UTILITY 121 3 ! 2 4 4 2 80.9 122 3 1 2 4 4 2 80.6 123 2 1 2 4 4 2 81.5 124 2 1 2 4 4 2 81.5 125 2 1 2 4 4 2 81 .5 126 1 1 2 4 4 2 81.5 127 2 1 2 4 4 2 81.4 128 3 1 2 4 4 2 81 .4 129 3 1 2 4 4 2 81.2 130 5 2 2 4 4 2 76.7 131 4 2 2 4 4 4 77.6 1 32 3 1 2 4 4 4 78.3 133 5 2 2 2 4 4 77. 1 134 4 1 2 2 4 4 77.9 135 3 1 2 2 4 4 78.9 136 3 1 2 4 4 4 78.9 137 2 1 2 4 4 4 78.9 138 2 1 2 4 4 4 78.9 139 2 1 2 4 4 4 78.9 140 5 1 2 4 4 4 78.9 141 3 2 4 4 4 77.2 142 2 1 2 4 4 4 77.9 143 2 1 2 4 4 4 77.9 144 3 1 2 4 4 4 77.9 145 2 1 2 4 4 4 78.8 146 3 1 2 4 4 4 78.8 147 3 1 2 4 4 4 78.6 148 3 1 2 4 4 4 78.5 149 2 1 2 4 4 4 79.2 150 2 1 2 4 4 4 79.2 151 2 1 2 4 4 4 79.2 152 2 1 2 4 4 4 79.2 153 1 1 2 4 4 4 79.2 154 3 1 2 4 4 4 79.1 155 3 1 2 4 4 4 79.0 156 2 1 2 4 4 4 79.6 157 4 1 2 4 4 4 79.6 158 3 1 2 4 4 4 79.9 159 2 1 2 4 4 4 80.4 160 4 1 2 4 4 4 80.4 184 S i m u l a t i o n #7 examines the e f f e c t of the above p o l i c y s t r u c t u r e u s i n g u t i l i t y matrix #7. Assuming again no F/M c o n t r o l , the average expected u t i l i t y r a p i d l y i n c r e a s e s , converging on a p o l i c y v e c t o r of [2, 4, 4, 7, 7] w i t h i n 63 i t e r a t i o n s , with an average expected u t i l i t y of 90.2. S i m i l a r to s i m u l a t i o n #6, the s t a t e c o n d i t i o n o c c a s i o n a l l y moves i n t o a s t a t e 4 or 5 b u l k i n g c o n d i t i o n , but the high DO c o n t r o l at these s t a t e s r a p i d l y reduces the b u l k i n g . The r e s u l t s of S i m u l a t i o n #7 are i l l u s t r a t e d i n F i g u r e 27 and Table 51. The use of the p r e v i o u s l y d e f i n e d c o n t r o l - a d j u s t m e n t p o l i c y enables the model to r a p i d l y converge, even with r e s t r i c t e d c o n t r o l s . In comparison, s i m u l a t i o n #6, with no F/M c o n t r o l s and no adjustment p o l i c y , r e s t r i c t e d the process convergence. 185 00 cn FIGURE 2 7 SIMULATION *7 - UTILITY «1 MATRIX - NO F/M CONTROL AVERAGE UTILITY AND STATE PLOTS 100 >-t—• _ j f— ZD LLJ CD az cn L J az o E—• a o CJ LLJ E—• az E—1 CO 80 H 60 H 40 H 160 60 80 100 ITERATION in) 120 140 160 T a b l e 51. S i m u l a t i o n 7 - U t i l i t y 1 M a t r i x - S ta te and P o l i c y  V e c t o r Changes f o r S i m u l a t e d (Known) Low DO B u l k i n g  Under Manual P o l i c y Adjustments Without F / M C o n t r o l SIMULATION #7 - UTILITY MATRIX #1 ITER. STATE STATE ALTERNATIVES AVERAGE # # 1 2 3 4 5 UTILITY 1 1 1 1 r 67.5 2 2 2 1 1 1 1 67.5 3 3 2 2 1 1 1 67.5 4 1 2 2 1 1 1 77.5 5 1 1 2 1 1 1 77.5 6 1 1 2 1 1 1 78.4 7 2 1 2 1 1 1 77.5 8 3 1 2 1 1 1 77.5 9 3 1 2 1 1 1 77.6 10 5 1 2 2 1 1 67.5 1 1 5 1 2 2 1 1 67.5 12 4 1 2 2 1 1 67.5 13 2 1 2 2 4 1 80.8 14 3 1 2 2 4 1 80.9 15 3 1 2 i . 4 1 80.9 16 4 1 2 2 4 1 76.7 17 5 1 2 2 4 1 75.9 18 5 1 2 2 4 1 73.9 19 4 1 2 2 4 1 75.9 20 2 1 2 2 4 1 81 .5 21 3 1 2 2 4 1 81 .5 22 3 1 2 2 4 1 81 .5 23 3 1 2 2 4 1 81 . 5 24 4 1 2 2 4 1 81 .5 25 5 1 2 2 4 1 78.3 26 4 1 2 2 4 4 79.8 27 3 1 2 2 4 4 81.6 28 5 1 2 2 4 4 81.6 29 5 1 2 2 4 4 80.4 30 5 1 2 2 4 7 79.3 31 4 1 2 2 4 7 79.6 32 2 1 2 2 7 7 83.2 33 2 1 2 2 7 7 83.2 34 4 1 2 2 7 7 83.2 35 3 1 2 2 7 7 85. 1 36 3 1 2 2 7 7 85. 1 37 3 1 2 2 7 7 85. 1 38 3 1 2 4 7 7 85.1 39 2 1 2 4 7 7 86.8 40 2 1 2 4 7 7 86.8 187 Table 51. (cont'd) SIMULATION #7 - UTILITY MATRIX #1 (cont'd) R. STATE STATE ALTERNATIVES AVERAGE # 1 2 3 4 5 UTILITY 41 2 ! 2 4 7 7 86.8 42 2 1 2 4 7 7 86.8 43 2 1 2 4 7 7 86.8 44 4 1 2 4 7 7 86.8 45 4 1 2 4 7 7 85.4 46 2 1 2 4 7 7 86.9 47 4 1 2 4 7 7 86.9 48 3 1 2 4 7 7 87.4 49 3 1 2 4 7 7 87. 1 50 2 1 2 4 7 7 88.5 51 5 1 2 4 7 7 88.5 52 4 1 2 4 7 7 88.7 53 3 1 2 4 7 7 88.9 54 3 1 2 4 7 7 88.6 55 4 1 2 4 7 7 87.4 56 2 1 2 4 7 7 88. 1 57 3 1 2 4 7 7 88.1 58 2 1 2 4 7 7 88.9 59 1 1 4 4 7 7 90.2 60 3 2 4 4 7 7 90.2 61 3 2 4 4 7 7 90.0 62 3 2 4 4 7 7 90.0 63 2 2 4 4 7 7 90.2 4.3.4 A p p l i c a t i o n of H i s t o r i c a l Data S i m u l a t i o n #8 e v a l u a t e s the convergence of c h a r a c t e r i s t i c s based on h i s t o r i c a l data obtained from the French Creek WPCC, i n s t e a d of a b a s e l i n e frequency s t a r t i n g p o i n t . Assuming that the si m u l a t e d p r o b a b i l i t y model r e p r e s e n t s the tr u e performance of the French Creek p l a n t , the convergence c h a r a c t e r i s t i c s u sing u t i l i t y matrix #1 are e v a l u a t e d . 188 F i g u r e 28 and Table 52 i l l u s t r a t e the r a p i d r a t e of convergence which was obtained. Although a s t a b l e o p t i m a l - c o n t r o l p o l i c y v e c t o r of [1, 4, 8, 7, 9] was not a r r i v e d at u n t i l i t e r a t i o n 81, a s i m i l a r c o n t r o l p o l i c y v e c t o r of [2, 4, 8, 7, 9] was obtained by the i t e r a t i o n 30. Over the e n t i r e c o n t r o l sequence, s t a t e 5 b u l k i n g occurs f o r o n l y 8 p e r i o d s . The average expected u t i l i t i e s are w e l l i n excess of the expected u t i l i t i e s of s i m u l a t i o n #1, which was based on a b a s e l i n e (no data) s t a r t i n g p o i n t . C o n s i d e r a b l y l e s s time i s spent i n high b u l k i n g c o n d i t i o n s f o r s i m u l a t i o n #8 than f o r s i m u l a t i o n #1. 189 F I G U R E 2 8 L J CD QZ cn L J > c n o i—i E— Q O C J L J f—1 c n E—1 C O SIMULATION « 8 - UTILITY *1 - HISTORICAL BASELINE AVERAGE UTILITY AND STATE PLOTS 60 80 100 ITERATION in) 120 140 Table 52. S i m u l a t i o n 8 - U t i l i t y 1 M a t r i x - State and P o l i c y  Vector Changes f o r Simulated (Known) Low DO B u l k i n g  Under Manual P o l i c y Adjustments Using H i s t o r i c a l Data SIMULATION #8 - UTILITY MATRIX #1 ITER. STATE STATE ALTERNATIVES AVERAGE # # 1 2 3 4 5 UTILITY 1 1 1 3 5 7 3 87.8 2 2 1 3 5 7 3 87.5 3 4 1 2 5 7 3 84.3 4 1 1 2 5 7 3 85.6 5 1 1 2 5 7 3 85.8 6 1 1 2 5 7 3 86.0 7 2 1 2 5 7 3 85.7 8 3 1 1 5 7 3 84.1 9 3 1 1 5 7 3 83.5 10 5 1 1 4 7 3 82.8 1 1 5 2 1 4 7 3 81 .2 12 5 2 1 4 7 6 80.0 1 3 4 2 1 4 7 6 81 .5 14 3 1 1 4 7 6 81.6 15 3 2 1 4 7 6 81.2 16 3 2 1 4 7 6 80.9 17 4 2 1 8 7 6 80.7 18 3 2 1 8 7 6 80.7 19 2 1 1 8 7 6 81.9 20 1 1 1 8 7 6 85.6 21 2 1 1 8 7 6 85.4 22 2 1 1 8 7 6 86.8 23 3 1 1 8 7 6 83.0 24 3 2 1 8 7 6 82.3 25 4 2 1 8 7 6 80.9 26 3 2 1 8 7 6 80.9 27 2 2 1 8 7 6 82.0 28 5 2 4 8 7 6 79.0 29 5 2 4 8 7 6 79 .5 30 5 2 4 8 7 9 79.6 31 4 2 4 8 7 9 79. 1 32 2 2 4 8 7 9 79.6 33 2 2 4 8 7 9 80.7 34 3 2 2 8 7 9 79.3 35 2 2 2 8 7 9 80.3 36 2 2 2 8 7 9 81.7 37 3 2 2 8 7 9 79.2 38 2 2 2 8 7 9 80.0 39 2 2 2 8 7 9 81.1 40 2 2 2 8 7 9 82.1 191 T a b l e 52. ( c o n t ' d ) SIMULATION #8 - UTILITY MATRIX #1 ( c o n t ' d ) ITER. STATE STATE ALTERNATIVES AVERAGE # # 1 2 3 4 5 UTILITY 41 2 1 2 8 7 9 82.9 42 2 1 2 8 7 9 83.7 43 3 2 2 8 7 9 81.9 44 3 2 2 8 7 9 81.3 45 3 2 2 8 7 9 80.8 46 1 2 2 8 7 9 81 .8 47 3 1 2 8 7 9 81.7 48 3 1 2 8 7 9 81 .2 49 3 1 2 8 7 9 80.8 50 2 1 2 8 7 9 81.4 51 5 1 6 8 7 9 77.8 52 4 1 6 8 7 9 77.7 53 3 1 6 8 7 9 77.7 54 1 1 6 8 7 9 78.4 55 3 6 8 7 9 77.6 56 1 6 8 7 9 78.0 57 2 1 6 8 7 9 78.0 58 2 1 6 8 7 9 79.3 59 2 1 6 8 7 9 80.2 60 5 1 4 8 7 9 77.7 61 4 1 4 8 7 9 77.7 62 3 1 4 8 7 9 77.7 63 3 1 4 8 7 9 77.4 64 1 1 4 8 7 9 77 .9 65 2 1 4 8 7 9 77.8 66 2 1 4 8 7 9 78.7 67 2 1 4 8 7 9 79.5 68 1 1 4 8 7 9 80.5 69 1 1 4 8 7 9 80.8 70 2 1 4 8 7 9 80.8 71 3 1 4 8 7 9 79.2 72 3 1 4 8 7 9 78.9 73 3 1 4 8 7 9 78.7 74 3 1 4 8 7 9 78.4 75 4 1 4 8 7 9 77.8 76 4 1 4 8 7 9 77.2 77 2 1 4 8 7 9 77.4 78 1 1 4 8 7 9 78.4 79 1 1 4 8 7 9 78.7 80 2 1 4 8 7 9 78.6 192 T a b l e 52. ( c o n t ' d ) SIMULATION #8 - UTILITY MATRIX #1 ( c o n t ' d ) I T E R . STATE STATE ALTERNATIVES AVERAGE # • # 1 2 3 4 5 UTILITY 81 2 1 4 8 7 9 79.1 82 2 1 4 8 7 9 79.5 83 2 1 4 8 7 9 79.8 84 2 1 4 8 7 9 80.2 85 1 1 4 8 7 9 80.7 86 2 1 4 8 7 9 80.7 87 2 1 4 8 7 9 81.0 88 2 1 4 8 7 9 81 .3 89 1 1 4 8 7 9 81 .7 90 1 1 4 8 7 9 81.8 91 1 1 4 8 7 9 82.0 92 2 1 4 8 7 9 82.0 93 2 1 4 8 7 9 82.2 94 1 1 4 8 7 9 82.5 95 2 1 4 8 7 9 82.5 96 2 1 4 8 7 9 82.7 97 3 1 4 8 7 9 81.5 98 3 1 4 8 7 9 81 .3 99 3 1 4 8 7 9 81 .2 100 3 1 4 8 7 9 81 .0 101 2 1 4 8 7 9 81.3 102 1 1 4 8 7 9 81 .6 1 03 2 1 4 8 7 9 81.6 104 1 1 4 8 7 9 81.9 105 1 1 4 8 7 9 82.0 106 1 1 4 8 7 9 82.2 107 1 1 4 8 7 9 82.3 108 2 1 4 8 7 9 82.3 109 1 1 4 8 7 9 82 .5 110 2 1 4 8 7 9 82.5 1 1 1 3 1 4 8 7 9 81 .6 1 12 2 1 4 8 7 9 81 .8 1 13 1 1 4 8 7 9 82. 1 1 14 1 1 4 8 7 9 82.2 1 15 2 1 4 8 7 9 82.2 1 16 2 1 4 8 7 9 82.3 1 17 1 1 4 8 7 9 82.5 118 2 1 4 8 7 9 82.5 119 2 1 4 8 7 9 82.6 120 2 1 4 8 7 9 82.8 193 T a b l e 52. ( c o n t ' d ) SIMULATION #8 - UTILITY MATRIX #1 (cont 'd) ITER. STATE STATE ALTERNATIVES AVERAGE # # 1 2 3 4 5 UTILITY 121 2 1 4 8 7 9 82.9 122 1 1 4 8 7 9 83. 1 123 2 1 4 8 7 9 83.0 124 2 1 4 8 7 9 83. 1 125 2 1 4 8 7 9 83.2 126 3 1 4 8 7 9 82.5 127 3 1 4 8 7 9 82.4 128 1 1 4 8 7 9 82.6 129 3 1 4 8 7 9 82.0 130 2 1 4 8 7 9 82.2 131 1 1 4 8 7 9 82.4 1 32 2 1 4 8 7 9 82.4 133 1 1 4 8 7 9 82.6 134 2 1 4 8 7 9 82.6 1 35 2 1 4 8 7 9 82.7 1 36 3 1 4 8 7 9 82. 1 137 1 1 4 8 7 9 82.3 1 38 1 1 4 8 7 9 82.4 139 1 1 4 8 7 9 82 .5 1 40 2 1 4 8 7 9 82.5 141 1 1 4 8 7 9 82.6 142 2 1 4 8 7 9 82.6 143 2 1 4 8 7 9 82.7 144 2 1 4 8 7 9 82.8 145 1 1 4 8 7 9 82.9 146 2 1 4 8 7 9 82 .9 147 2 1 4 8 7 9 83.0 148 1 1 4 8 7 9 83.1 149 1 1 4 8 7 9 83.2 1 50 3 1 4 8 7 9 82.7 151 3 1 4 8 7 9 82.6 1 52 1 1 4 8 7 9 82.8 1 53 3 1 4 8 7 9 82.3 1 54 2 1 4 8 7 9 82.5 155 1 1 4 8 7 9 82.6 156 2 1 4 8 7 9 82.6 157 1 1 4 8 7 9 82.7 158 1 1 4 8 7 9 82.8 159 1 1 4 8 7 9 82.8 160 1 1 4 8 7 9 82.9 194 5.0 DISCUSSION The a p p l i c a t i o n of d e c i s i o n theory to process c o n t r o l r e q u i r e s e s t i m a t e s of outcome p r o b a b i l i t i e s f o r s p e c i f i c c o n t r o l a l t e r n a t i v e s . As demonstrated, the i n i t i a l p r o b a b i l i t y estimates do not have to be a c c u r a t e , p r o v i d e d that the d e c i s i o n model i s a d a p t i v e and can take i n t o account new i n f o r m a t i o n gained through e x p e r i e n c e . However, estimates of p r o b a b i l i t y are r e q u i r e d f o r each combination of c o n t r o l a l t e r n a t i v e and p o s s i b l e outcome due to t h a t c o n t r o l . T h i s s e c t i o n reviews some areas of c o n s i d e r a t i o n f o r the prac-t i c a l use of d e c i s i o n theory i n p r o c e s s c o n t r o l s t r a t e g i e s . The techniques presented l e a d to an o p t i mal c o n t r o l s t r a t e g y based on a v a i l a b l e i n f o r m a t i o n , estimated p r o b a b i l i t i e s and the a s s o c i a t e d reward or u t i l i t y f o r each control/outcome combination. The p r o c e s s r e q u i r e s some s t a r t i n g p o i n t , and must be a d a p t i v e to changing c o n d i t i o n s and new i n f o r m a t i o n . The s e l e c t e d u t i l i t y s t r u c t u r e has been shown to i n f l u e n c e the r a t e of convergence of the model and the optimal p o l i c y i t s e l f . The u t i l i t y s t r u c t u r e i s a compromise between lowest-cost opera-t i o n and maximum p o t e n t i a l performance of the process, which r e f l e c t s the v a l u e s and experience of the p l a n t o p e r a t o r . As the f i e l d a p p l i c a t i o n of a d e c i s i o n theory model w i l l l i k e l y encounter unforeseen c i r c u m s t a n c e s , some assessment of s e n s i t i v i t y to the p r o b a b i l i t y and u t i l i t y s t r u c t u r e s i s r e q u i r e d . Although the sludge b u l k i n g c o n t r o l p o l i c y at the 195 French Creek WPCC does not appear to i n d i c a t e that temperature i s a s i g n i f i c a n t f a c t o r , other a c t i v a t e d sludge process c o n t r o l i n t e r e s t s may be more s e n s i t i v e to temperature v a r i a t i o n s . 5.1 D e c i s i o n Theory C o n t r o l S t r a t e g y Without H i s t o r i c a l Data D e c i s i o n theory techniques r e q u i r e some estimate of p r o b a b i l i t y and u t i l i t y f o r each control/outcome combination. While u t i l i -t i e s can be f a i r l y e a s i l y determined by the r e l a t i v e value proce-dure p r e v i o u s l y d i s c u s s e d i n S e c t i o n 3.3.5, the e s t i m a t i o n of p r o b a b i l i t i e s i s d i f f i c u l t f o r c o n t r o l o ptions which have not been t r i e d b e f o r e . However, some estimate i s r e q u i r e d . The b a s e l i n e frequency technique used i n the S e c t i o n 4.2 simula-t i o n s i s one simple technique which can be used as a s t a r t i n g p o i n t i n an a d a p t i v e , dynamic, d e c i s i o n model. The premise of the b a s e l i n e frequency technique i s that extreme s t a t e changes are u n l i k e l y t o occur due to a s p e c i f i c c o n t r o l adjustment, because a reasonable time l a g i s r e q u i r e d f o r the organisms to adapt to the change. Consequently, i t i s a n t i c i p a t e d that the subsequent s t a t e w i l l e i t h e r be the same s t a t e (no change), one s t a t e lower or one s t a t e h i g h e r . F u r t h e r , i t i s assumed that a l l three s t a t e s are of equal p r o b a b i l i t y . A frequency e n t r y of 1 i s p l a c e d i n the c u r r e n t s t a t e and the s t a t e above and below, r e s u l t i n g i n o v e r a l l p r o b a b i l i t i e s of 33.3% f o r each s t a t e . T h i s r e s u l t s i n the f o l l o w i n g STATE/STATE b a s e l i n e frequency matrix and p r o b a b i l i t y m a t r i c e s : 196 STATE ( j ) 1 2 3 4 5 BASELINE 1 1 1 0 0 0 FREQUENCY STATE 2 1 1 1 0 0 MATRIX ( i ) 3 0 1 1 1 0 4 0 0 1 1 1 5 0 0 0 1 1 STATE ( j ) 1 2 3 4 5 BASELINE 1 .50 .50 0 0 0 PROBABILITY STATE 2 .33 .33 .33 0 0 MATRIX ( i ) 3 0 .33 .33 .33 0 4 0 0 .33 .33 .33 5 0 0 0 .50 .50 Note that the extreme s t a t e p r o b a b i l i t i e s have only two p o s s i b l e a l t e r n a t i v e s , due to boundary r e s t r i c t i o n s . These STATE/STATE f r e q u e n c i e s are extended t o form CONTROL/STATE f r e q u e n c i e s and cor r e s p o n d i n g p r o b a b i l i t i e s , by assuming that each c o n t r o l o p t i o n has the same p r o b a b i l i t y s t r u c t u r e , that i s , equal p r o b a b i l i t y of remaining i n the same s t a t e or proceeding to the next h i g h e s t or lowest p o s s i b l e s t a t e . As the p r o b a b i l i t i e s are based on a u n i t frequency b a s e l i n e matrix, i t does not take many t r i a l s to e i t h e r v e r i f y the assumed s t r u c t u r e or t o e s t a b l i s h a new p r o b a b i l i t y s t r u c t u r e . T h i s technique c o u l d be f u r t h e r improved by c o n s t r u c t i n g a normalized frequency matrix, such that a c u r r e n t o b s e r v a t i o n would be equal i n weight to the sum of the assumed frequency s t r u c t u r e . A l t e r n a t i v e l y , the p r o b a b i l i t i e s c o u l d be updated using Bayes' Theorem, making the d e c i s i o n process t r u l y "Bayesian". 197 The f i n a l frequency matrices f o r s i m u l a t i o n s #1 to #4 c l e a r l y demonstrate that the Markov P o l i c y - i t e r a t i o n technique q u i c k l y converges on the c r i t i c a l or optimal p o l i c y frequency d i s t r i b u -t i o n s . C o n t r o l a l t e r n a t i v e s which are not c r i t i c a l c o n t a i n only the o r i g i n a l b a s e l i n e frequency e n t r i e s . As an a l t e r n a t i v e to b a s e l i n e f r e q u e n c i e s , p r o b a b i l i t i e s c o u l d be s y n t h e s i z e d from expert o p i n i o n or from data obtained from s i m i l a r treatment p l a n t s . For example, the observation that the predominant filamentous organism present i n the b u l k i n g sludge has been a s s o c i a t e d with a s p e c i f i c process c o n d i t i o n , such as low DO b u l k i n g , a p r o b a b i l i t y matrix can be c o n s t r u c t e d which i s c o n s i s t e n t with that h y p o t h e s i s . Concurrently, a s t a r t i n g frequency matrix would be c o n s t r u c t e d such that the sum of the f r e q u e n c i e s of each c o n t r o l a l t e r n a t i v e was equal to 3 (such as the b a s e l i n e frequency p r e v i o u s l y d i s c u s s e d ) or to s i n g l e u n i t value of 1. T h i s frequency matrix would then be m o d i f i e d as c o n t r o l changes are made to the p l a n t i n q u e s t i o n . I f the hypo t h e s i s i s c o r r e c t , the model w i l l r a p i d l y converge. On the other hand, i f the hypothesis i s i n c o r r e c t the convergence r a t e w i l l be s i m i l a r to using a b a s e l i n e frequency matrix s t a r t i n g p o i n t . 5.2 A d a p t a t i o n of H i s t o r i c a l Data Data Base Information H i s t o r i c a l CONTROL/STATE frequency data can be u t i l i z e d t o con-s t r u c t a s t a r t i n g p r o b a b i l i t y d i s t r i b u t i o n matrix. As changing 198 i n f l u e n t c h a r a c t e r i s t i c s may have a l t e r e d the p l a n t per formance , a d e c i s i o n must be made as to how much of the h i s t o r i c a l data r e f l e c t s c u r r e n t o p e r a t i n g c o n d i t i o n s . Causes of p r o c e s s c o n d i -t i o n s , such as s ludge b u l k i n g , may change over the l i f e of the treatment p l a n t , as the p r o c e s s p r o g r e s s e s from the i n i t i a l c h a r -a c t e r i s t i c a l l y o v e r d e s i g n e d , and h y d r a u l i c a l l y and o r g a n i c a l l y under loaded c o n d i t i o n , to the o t h e r extreme. A d d i t i o n a l l y , poor sampl ing or a n a l y t i c a l p r a c t i c e s may r e s u l t i n q u e s t i o n a b l e data and i n c o r r e c t f requency d i s t r i b u t i o n s . A l a r g e number of CONTROL/ALTERNATIVE f r e q u e n c i e s may c r e a t e d i f f i c u l t i e s i n p o l i c y convergence i f the h i s t o r i c a l data i s i n c o r r e c t . F u r t h e r , c e r t a i n p o t e n t i a l c o n t r o l a l t e r n a t i v e s may not have been at tempted i n the pas t and a p r o b a b i l i t y must be e s t i m a t e d . A s u i t a b l e s o l u t i o n , used in S i m u l a t i o n #8, i s t o n o r m a l i z e the h i s t o r i c a l f requency m a t r i x to a g i v e n u n i t v a l u e , a f t e r ad d ing a s i m i l a r l y n o r m a l i z e d b a s e l i n e f r e q u e n c y . The n o r m a l i z e d frequency m a t r i x w i l l supply a r e a s o n a b l e p r o b a b i l i t y e s t i m a t e f o r those c o n t r o l o p t i o n s wi thout h i s t o r i c a l d a t a . As the h i s t o r i c a l data c o u l d be argued to p r o v i d e more i n f o r m a t i o n than the b a s e l i n e f r e q u e n c i e s , the b a s e l i n e i s added to the h i s t o r i c a l data b e f o r e n o r m a l i z i n g . A g a i n , the assumpt ion i s t h a t new data which i s c o l l e c t e d under more c o n t r o l l e d c o n d i t i o n s s h o u l d be g i v e n g r e a t e r w e i g h t . An example of such a n o r m a l i z i n g p r o c e s s i s p r e s e n t e d below: 199 1. HISTORICAL AND BASELINE FREQUENCY MATRICES FOR STATE ( i ) 2 HISTORICAL FREQUENCY MATRIX STATE ( j ) 1 2 3 4 5 A 3 4 2 1 0 CONTROL B 3 5 7 2 1 OPTIONS C 0 0 0 0 0 D 1 3 0 0 0 E 1 2 1 0 0 NOTE: No data e x i s t s f o r cont r o l o p t i o n C BASELINE FREQUENCY MATRIX CONTROL OPTIONS A B C D E STATE ( j ) 2 3 4 0 0 0 0 0 0 0 0 0 0 2. COMBINED FREQUENCY MATRIX FOR STATE ( i ) 2 COMBINED FREQUENCY MATRIX STATE ( j ) 1 2 3 4 5 A 4 5 3 1 0 CONTROL B 4 6 8 2 1 OPTIONS C 1 1 1 0 0 D 2 4 1 0 0 E 2 3 2 0 0 200 3. NORMALIZED FREQUENCIES AND PROBABILITIES BASED ON NUMBER OF COLUMNS CONTAINING DATA NORMALIZED FREQUENCY MATRIX STATE ( j ) 1 2 3 4 5 SUM A 1.23 1.54 0.92 0.31 0 4 CONTROL B 0.95 1.43 1.90 0.48 0.24 5 OPTIONS C 1.0 1.0 1.0 0 0 3 D 0.86 1.71 0.43 0 0 3 E 0.86 1.29 0.86 0 0 3 NORMALIZED PROBABILITIES STATE ( j ) 1 2 3 4 5 SUM A .31 .39 .22 .08 0 1 CONTROL B .19 .29 .38 .10 .04 1 OPTIONS C .33 .34 .33 0 0 1 D .29 .57 .14 0 0 1 E .29 .43 .28 0 0 1 ORIGINAL PROBABILITIES FROM HISTORICAL FREQUENCIES STATE ( j ) 1 2 3 4 5 SUM A .30 .40 .20 .10 0 1 CONTROL B .17 .28 .39 . 1 1 .06 1 OPTIONS C 0 0 0 0 0 0 D .25 .75 0 0 0 1 E .25 .50 .25 0 0 1 Note t h a t there i s l i t t l e d i f f e r e n c e between the p r o b a b i l i t y matrix generated with normalized h i s t o r i c a l and b a s e l i n e f r e q u e n c i e s , and the p r o b a b i l i t y matrix generated from non-normalized h i s t o r i c a l f r e q u e n c i e s . 201 In the above example, the a d j u s t e d h i s t o r i c a l frequency was normalized by the number of s t a t e s c o n t a i n i n g frequency data f o r each c o n t r o l . The value s e l e c t e d to normalize each c o n t r o l frequency d i s t r i b u t i o n i s dependent on the confidence the modeller has i n the h i s t o r i c data. As the n o r m a l i z i n g f a c t o r i n c r e a s e s , the i n e r t i a of the h i s t o r i c a l data i n c r e a s e s and i t w i l l take more t r i a l s to s h i f t an i n c o r r e c t p r o b a b i l i t y s t r u c t u r e . To allow f o r changing process c o n d i t i o n s , t h i s n o r m a l i z a t i o n procedure should be undertaken on a p e r i o d i c b a s i s . As the number of frequency elements i n c r e a s e , the i n e r t i a of the model i n c r e a s e s . Consequently, i t would be a d v i s a b l e to normalize the frequency matrix on a r e g u l a r b a s i s , such as a n n u a l l y , or whenever the process c o n d i t i o n s are b e l i e v e d to have changed. Such c o n d i t i o n s may i n c l u d e seasonal temperature regimes, or i n -creased sewage flows due to community development or an i n c r e a s e d sewerage a r e a . The a d d i t i o n of commercial or i n d u s t r i a l wastes may a l s o a f f e c t the p l a n t performance. Diminished P o l i c y -I t e r a t i o n performance s t r a t e g i e s may i n d i c a t e that the changing c o n d i t i o n s are too r a p i d f o r the model to adapt. Under such c o n d i t i o n s , i t i s a d v i s a b l e to normalize the frequency matrix and to examine a l t e r n a t i v e c o n t r o l o p t i o n s should the model f a i l to converge. 202 5.3 Comparison of Expected U t i l i t i e s With Operator Judgement In undertaking the s t a t i c d e c i s i o n theory approach, u t i l i t i e s were s o l i c i t e d from each of the three o p e r a t o r s at the French Creek WPCC f a c i l i t y , based on combinations of SVI and e f f l u e n t SS l e v e l s . These u t i l i t i e s , and a f o u r t h u t i l i t y c o n s t r u c t e d by the author, were a p p l i e d to a p r o b a b i l i t y d i s t r i b u t i o n s f o r s p e c i f i c DO and F/M c o n t r o l combinations as d e s c r i b e d i n S e c t i o n 4.1. Once the concept of r e l a t i v e u t i l i t y was e x p l a i n e d to the three o p e r a t o r s , they were l e f t t o c o n s t r u c t a matrix with u t i l i t y v a l u e s of 100, r e p r e s e n t i n g " i d e a l " or best " c o n d i t i o n s , and u t i l i t i e s of zero, r e p r e s e n t i n g i n t o l e r a b l e c o n d i t i o n s . Intermediate v a l u e s were then s c a l e d r e l a t i v e t o the extreme c o n d i t i o n s . Of the three s t a f f members A, B and C, operator C was the s e n i o r operator who i s s o l e l y r e s p o n s i b l e f o r the treatment f a c i l i t y . The operator ."D" u t i l i t y matrix was c o n s t r u c t e d based on a s i m i l a r r e l a t i v e u t i l i t y s c a l e , except t h a t an e f f o r t was made to maintain a uniform s c a l e d shape. As d e s c r i b e d i n S e c t i o n 3.3.6, the SVI u t i l i t y shape i s p a r a b o l i c with the h i g h e s t u t i l i t y o c c u r r i n g f o r a non b u l k i n g SVI of 100 to 200 mL/g. The u t i l i t y decreases with e i t h e r i n c r e a s e d or decreased SVI l e v e l s . As the " i d e a l " e f f l u e n t SS c o n c e n t r a t i o n would be the lowest value p o s s i b l e ( l e s s than 5 mg/L), the u t i l i t i e s f o r s p e c i f i c SVI l e v e l s d i m i n i s h f o r i n c r e a s e d e f f l u e n t SS c o n c e n t r a t i o n s t o a zero v a l u e ; t h i s occurs f o r combination of SVI > 500 mL/g and e f f l u e n t SS c o n c e n t r a t i o n g r e a t e r than 60 mg/L. 203 There are two c h a r a c t e r i s t i c d i f f e r e n c e s between the t h e o r e t i c a l ( h y p o t h e t i c a l ) u t i l i t y matrix and those of the p l a n t o p e r a t o r s . F i r s t , the t h e o r e t i c a l model has assumed that there i s only one treatment s t a t e which can have a maximum u t i l i t y of 100 and s i m i l a r l y only one may have a u t i l i t y of z e r o . A c c o r d i n g l y , a l l other u t i l i t i e s are s c a l e d between these extremes. The operator u t i l i t i e s do not f o l l o w t h i s assumption, as many combinations have been assig n e d equal u t i l i t y v a l u e s . The u t i l i t y d i s t r i b u t i o n of operator "A" i s most l i k e the t h e o r e t i c a l u t i l i t y d i s t r i b u t i o n (Operator "D"). C h a r a c t e r i s t i c of the three operator u t i l i t i e s , many combinations of SVI and e f f l u e n t SS have been a s s i g n e d the same u t i l i t i e s . The p l a n t can t o l e r a t e h i g h b u l k i n g c o n d i t i o n s , as i t i s p r e s e n t l y o p e r a t i n g at approximately h a l f of the design flows. Regardless of the b u l k i n g c o n d i t i o n , the p l a n t r a r e l y exceeds the permit r e q u i r e -ments of 60 mg/L e f f l u e n t SS. T h i s t o l e r a n c e of b u l k i n g i s r e f l e c t e d i n the r e l a t i v e l y h i g h u t i l i t i e s a ssigned to high SVI c o n d i t i o n s . On the other hand, t h i s operator c l e a r l y views the e f f l u e n t s o l i d s l e v e l as c r i t i c a l . A l l s o l i d s l e v e l s above the permit l e v e l of 60 mg/L SS have a zero u t i l i t y , while SS l e v e l s approaching the permit l e v e l of 40 to 60 mg/L have a u t i l i t y of 5 or lower. Operator "B's" u t i l i t y d i s t r i b u t i o n i s more "step" or " p l a t e a u -l i k e " than operator "A's" u t i l i t i e s . T h i s operator has l e s s u t i l i t y f o r low SVI c o n d i t i o n s than operator "A", and has a much 204 broader high u t i l i t y band. T h i s operator would appear to t o l e r -ate s o l i d s c o n c e n t r a t i o n s up to the permit l i m i t , with l i t t l e or no d i s c r i m i n a t i o n between SVI values from 100 to 200 ml/g and e f f l u e n t s o l i d s of l e s s than 20 mg/L. S i m i l a r to operator "A", the e f f l u e n t SS c o n c e n t r a t i o n s i n excess of the permit l e v e l s have no u t i l i t y and are unacceptable. Operator "C" has the most o p e r a t i o n s experience. T h i s operator has the h i g h e s t u t i l i t y v a l u e s f o r a l l combinations of SVI and e f f l u e n t SS. T h i s u t i l i t y d i s t r i b u t i o n r e f l e c t s a higher t o l e r -ances f o r extreme SVI c o n d i t i o n s . Greater d i f f e r e n t i a t i o n i s made between SVI v a l u e s than f o r v a r i a t i o n s i n e f f l u e n t s o l i d s q u a l i t y . T h i s i s p a r t i c u l a r l y evident i n the h i g h u t i l i t i e s a s s i g n e d to the near-permit e f f l u e n t q u a l i t y c h a r a c t e r i s t i c s and f o r the above zero v a l u e s a s s i g n e d to s e v e r a l of the s o l i d s l e v e l s i n excess of permit v a l u e s (but with SVI l e v e l s which i n d i c a t e a good s e t t l i n g s l u d g e ) . The u t i l i t y matrix f o r operator "C" has an i n t e r e s t i n g f e a t u r e i n the u t i l i t y s e l e c t i o n f o r high SVI l e v e l s and e f f l u e n t SS combinations. For a SVI v a l u e s of 20 and 1000 ml/g, operator " C has a higher u t i l i t y f o r 15 to 20 mg/L e f f l u e n t SS than f o r lower s o l i d s c o n c e n t r a t i o n s . Although the other two o p e r a t o r s i n d i c a t e d c o n s i s t e n t l y d e c r e a s i n g u t i l i t i e s f o r i n c r e a s e d e f f l u e n t SS c o n c e n t r a t i o n s , operator "C" i n d i c a t e d t h a t f o r the two extreme SVI v a l u e s , mid-range e f f l u e n t SS c o n c e n t r a t i o n s were p r e f e r a b l e . The o p e r a t o r ' s r a t i o n a l e f o r i n c r e a s e d u t i l i t y f o r mid range s o l i d s c o n c e n t r a t i o n s was that he had i n c r e a s e d c o n f i d e n c e that 205 the treatment process was behaving i n a manner c o n s i s t e n t with h i s p e r s o n a l experience. Low SVI c o n d i t i o n s were expected t o c o i n c i d e with higher e f f l u e n t s o l i d s c o n c e n t r a t i o n , due to the more p i n - p o i n t nature of the s o l i d s . S i m i l a r l y , extremely high SVI c o n d i t i o n s were a s s o c i a t e d with an extreme b u l k i n g c o n d i t i o n and g r e a t e r e f f l u e n t s o l i d s c o n c e n t r a t i o n s . By i n c r e a s i n g the u t i l i t y f o r higher s o l i d s c o n c e n t r a t i o n s , the operator was i n d i c a t i n g that the e f f l u e n t q u a l i t y was c o n s i s t e n t with the p l a n t c o n d i t i o n , as i n d i c a t e d by the SVI l e v e l . Combinations which were not c o n s i s t e n t caused t h i s operator t o be concerned, as he was unsure of what t o do. Regardless of the u t i l i t y d i s t r i b u t i o n d i f f e r e n c e s , the c o n t r o l combination with the highest expected u t i l i t y was f o r a d i s s o l v e d oxygen c o n c e n t r a t i o n of 1.5 t o 2.5 mg/L and an F/M o p e r a t i n g l e v e l of 0.18 to 0.25 kg BOD/kg MLVSS day. The s t r u c t u r e of the u t i l i t y d i s t r i b u t i o n and the r e s u l t a n t expected u t i l i t y r e f l e c t s the r i s k a v e r s i o n and o p e r a t i o n s p o l i c i e s of the o p e r a t o r s . The expected u t i l i t i e s d i s c u s s e d i n S e c t i o n 4.1 r e f l e c t e d a conserva-t i v e d e s i r e of operat o r s "A" and "B" to remain with an SVI range of 60 to 300 mL/g, with e f f l u e n t SS below 20 mg/L. Operator "C" i s l e s s c o n s e r v a t i v e , with an SVI range of approximately 40 t o 400 ml/g and an e f f l u e n t suspended s o l i d s c o n c e n t r a t i o n of up to the permit l e v e l . 206 5.4 S e n s i t i v i t y C o n s i d e r a t i o n s The Markov P o l i c y - I t e r a t i o n d e c i s i o n a n a l y s i s technique i s based on estimated p r o b a b i l i t y and u t i l i t y s t r u c t u r e s . There i s an i m p l i c i t assumption that a continuous p r o c e s s - c o n t r o l range can be d e s c r i b e d as a set of d i s c o n t i n u o u s ranges and t h a t the s t a t e d e s c r i p t i o n s are complete. While the s e l e c t i o n of s t a t e r e p r e s e n t a t i o n (as being a set of d i s c r e t e ranges) i s not l i k e l y to s e r i o u s l y a f f e c t the model, the assumption of a c c u r a t e s t a t e r e p r e s e n t a t i o n i s important. C o l l i n s (1975) i n d i c a t e s that the s i z e of the s t a t e may e f f e c t the t r a n s i t i o n p r o b a b i l i t i e s . G e n e r a l l y , l a r g e . s t a t e s i z e s , or fewer s t a t e s , are more l i k e l y to have a pronounced main di a g o n a l i n the STATE/STATE p r o b a b i l i t y d i s t r i b u t i o n . Smaller s t a t e s have a g r e a t e r tendency f o r " n o i s e " elements i n the o f f - d i a g o n a l p r o b a b i l i t i e s , or a g r e a t e r tendency to change by more than one s t a t e i n a given i t e r a t i o n p e r i o d . I f the s t a t e s are not a c c u r a t e l y d e s c r i b e d and are m i s s i n g a c r i t i c a l d e s c r i p t i v e element such as temperature, the " n o i s e " elements w i l l be more pronounced. Both the s i z e of the s t a t e s and the c l a s s i f i c a t i o n method can determine the u n d e r l y i n g Markov p r o p e r t y . T h i s i n f l u e n c e c o u l d be examined through a s e n s i t i v i t y a n a l y s i s , by which the s t a t e c l a s s i f i c a t i o n s and s i z e s are v a r i e d to determine i f they have an e f f e c t on the r e s u l t i n g i t e r a t i o n p o l i c y . T h i s concept of s e n s i t i v i t y a n a l y s i s can a l s o be a p p l i e d t o the u t i l i t y d i s t r i b u t i o n s t r u c t u r e s . As p r e v i o u s l y d e s c r i b e d , the s e l e c t i o n of r e l a t i v e u t i l i t i e s i s h i g h l y s u b j e c t i v e . Although 207 the s u b j e c t i v i t y may r e f l e c t the t r u e v a l u e system of a g i v e n i n d i v i d u a l , the p o l i c i e s s u i t e d to t h a t i n d i v i d u a l may not c o i n c i d e w i t h the p o l i c i e s of another o p e r a t o r or manager. For example, the u t i l i t y v a l u e s of a r e s e a r c h e r who i s i n t e r e s t e d i n i d e n t i f y i n g c o n d i t i o n s under which a p r o c e s s might f a i l , would be expec ted to have o v e r a l l h i g h e r u t i l i t y v a l u e s than a p l a n t o p e r a t o r who i d e n t i f i e s w i t h the performance l e v e l of the t reatment p r o c e s s . S i m i l a r l y , the r e l u c t a n c e of a d m i n i s t r a t i o n to a l l o w i n c r e a s e d o p e r a t i n g c o s t s , by i n c r e a s i n g the DO l e v e l , would r e s u l t i n a d i f f e r e n t u t i l i t y c u r v e . I t was demonstrated i n S e c t i o n 4.3 that the i n c r e a s e d s l o p e between low and h i g h energy o p e r a t i n g l e v e l s c r e a t e d a slow convergence c o n d i t i o n f o r low DO b u l k i n g c o n d i t i o n s . C o n s e q u e n t l y , a p p l i c a t i o n s of the P o l i c y - I t e r a t i o n t e c h n i q u e s h o u l d c o n s i d e r e v a l u a t i n g the i n f l u e n c e of v a r i e d u t i l i t y s t r u c t u r e s w i t h i n a reasonab le range . 5.5 F/M C o n t r o l The BOD l o a d to a p l a n t i s c o n t i n u a l l y changing on a d i u r n a l , as w e l l as d a i l y and s e a s o n a l b a s i s . Long term v a r i a t i o n can be r e l a t i v e l y e a s i l y accommodated i n a c o n v e n t i o n a l a c t i v a t e d s ludge p l a n t , i n terms of an F / M c o n t r o l s t r a t e g y , as biomass c o n c e n t r a -t i o n s can be g r a d u a l l y i n c r e a s e d or decreased w i t h i n the sys tem. With p l a n t a u t o m a t i o n , f a s t response F / M c o n t r o l becomes a p o s s i -b i l i t y , but r e q u i r e s some form of s o l i d s s t o r a g e so that changes 208 i n i n f l u e n t BOD l o a d i n g can be matched wi th a p r o p o r t i o n a l m i c r o -b i a l mass. C o n t r o l l i n g the F / M r a t i o r e q u i r e s both l a b o r a t o r y a n a l y s i s of i n f l u e n t o r g a n i c s t r e n g t h , i n a d d i t i o n to f r e q u e n t MLVSS d e t e r -m i n a t i o n s . The F / M r a t i o i s u s u a l l y h e l d c o n s t a n t by i n c r e a s i n g or d e c r e a s i n g s ludge w a s t i n g , or to c o n t r o l the MLVSS c o n c e n t r a t i o n p r o p o r t i o n a l to changes i n o r g a n i c l o a d i n g . A l t h o u g h c o n s i d e r e d t h e o r e t i c a l l y sound, i n p r a c t i c e t h i s type of c o n t r o l can be d i f f i c u l t . The v a l u e of F / M c o n t r o l i n a c t i v a t e d s ludge systems has been the s u b j e c t of debate f o r many y e a r s . A l i m i t e d s tudy of i n s t a n t a n e o u s F / M c o n t r o l by the US EPA and Clemson U n i v e r s i t y ( K e i n a t h and C a s h i o n , 1980) , u s i n g a mathemat ica l model which s i m u l a t e d d i u r n a l v a r i a t i o n s i n l o a d , found t h a t the c l a r i f i e r c o u l d not s t o r e enough s o l i d s to m a i n t a i n c o n t r o l , whi le a c h i e v i n g good l i q u i d - s o l i d s s e p a r a t i o n . F u r t h e r , they r e p o r t e d tha t i n c r e a s e d r e c y c l e to improve the mass of r e t u r n s ludge r e s u l t e d i n a more d i l u t e s ludge c o n c e n t r a t i o n i n the c l a r i f i e r and r e c y c l e f l o w s , such t h a t the mass s ludge r a t e r e c y c l e d d i d not change . The proposed s o l u t i o n was to i n t r o d u c e a s o l i d s s t o r a g e chamber i n t o the p r o c e s s s t r e a m . P l a n t s t u d i e s a t t e m p t i n g F / M c o n t r o l s t r a t e g i e s , r e p o r t e d by R o e s l e r (1982) , i n d i c a t e t h a t F / M c o n t r o l s t r a t e g i e s do h o l d promise but r e q u i r e more r e s e a r c h . However, the work to date 209 indicates that the secondary c l a r i f i e r should not be used in the dynamic control of the activated sludge plant and that some form of alternate s o l i d s storage should be provided. Current theories suggest that filaments are better scavengers than the floc-forming bacteria and consequently maintain higher growth rates under conditions of low organic concentrations (Palm et a l . 1980). Therefore to control low F/M bulking in a plant with a completely mixed activated sludge, some researchers have proposed the u t i l i z a t i o n of a selector, or reactor preceding the aeration reactor, in which the return activated sludge i s combined with the substrate. Under such conditions, the return sludge i s exposed to a higher organic substrate concentration than i f i t had been added to a single large completely-mixed tank. With higher substrate conditions, the floc-formers w i l l predominate as the i r growth rates are greater than the filamentous bacteria under conditions of high substrate concentrations (Palm et a l . , 1980, Daigger et a l . , 1985). The p r e f e r e n t i a l selection of floc-forming over filamentous microorganisms can also be achieved by periodic feeding, such as achieved by intermittent-feed or plug-flow configurations (Van den Eynde et a l . , 1983), or by varying the number of completely-mixed aeration basins to simulate plug flow (Stark, 1983). Recently, research indicates that the u t i l i z a t i o n of an anoxic zone, preceding the aeration zone, w i l l s e l e c t i v e l y i n h i b i t filamentous growth. S i l v e r s t e i n and Schroeder (1983) noted that the most stable s e t t l i n g c h a r a c t e r i s t i c s (low SVI) 210 were ob t a i n e d f o r a batch r e a c t o r when 90 minutes of anoxic c o n d i t i o n s occurred d u r i n g f i l l i n g . Although the adjustment of MLVSS c o n c e n t r a t i o n s , to maintain a constant F/M r a t i o , may not be p r a c t i c a l at most c o n v e n t i o n a l a c t i v a t e d sludge f a c i l i t i e s , the concept of process m o d i f i c a t i o n to c r e a t e a s e l e c t i v e environment appears to h o l d some promise. The use of e q u a l i z a t i o n b a s i n s to even out both the h y d r a u l i c and s u b s t r a t e l o a d i n g r a t e s would a s s i s t i n m a i n t a i n i n g a more u n i -form F/M r a t i o . 2 1 1 6.0 SUMMARY AND CONCLUSIONS Wastewater treatment p l a n t monitoring data i s d i f f i c u l t to analyze s t a t i s t i c a l l y . Many of the data c h a r a c t e r i s t i c s , such as s e r i a l c o r r e l a t i o n , non-normal d i s t r i b u t i o n s , m i s s i n g data and la c k of experimental d e s i g n , i n v a l i d a t e key assumptions of pa r a m e t r i c , non-parametric and time s e r i e s s t a t i s t i c a l a n a l y s i s t e c h n i q u e s . Poor sampling design, l a c k of q u a l i t y c o n t r o l , l a r g e a n a l y t i c a l e r r o r s , and u n t r a i n e d l a b o r a t o r y personnel r e s u l t i n data of q u e s t i o n a b l e q u a l i t y . Consequently, most of the data i s recorded on forms and s t o r e d away. Seldom i s the data p l o t t e d or analyzed i n any way. D e s p i t e these problems, c e r t a i n s t a t i s t i c a l techniques can be a p p l i e d to the data, p r o v i d i n g that the c o n c l u s i o n s made recognize the l i m i t a t i o n s of the data. A c o n s i d e r a b l e amount of e f f o r t has been expended by r e s e a r c h e r s to develop * k i n e t i c models f o r the p r e d i c t i o n of p l a n t performance. Most of these models are based on s t e a d y - s t a t e assumptions or a r b i t r a r y c o e f f i c i e n t v a l u e s , and are u s u a l l y not adaptable to d i f f e r e n t p l a n t c o n f i g u r a t i o n s or the f l u c t u a t i n g wastewater c h a r a c t e r i s t i c s encountered i n p r a c t i c e . S t o c h a s t i c models have found some success where they have been developed f o r a s p e c i f i c treatment p l a n t . These models are u s u a l l y s i t e s p e c i f i c , and because they are g e n e r a l l y based on l a r g e data bases they are not u s u a l l y adaptable t o changing p l a n t c o n d i t i o n s . 212 In t h i s t h e s i s , i t i s proposed t h a t d e c i s i o n a n a l y s i s techniques can be used to improve process performance through the develop-ment of process c o n t r o l s t r a t e g i e s . To apply d e c i s i o n a n a l y s i s techniques t o process c o n t r o l , the problem i s reduced to a manageable number of d i s c r e t e s t a t e s . Bayesian d e c i s i o n a n a l y s i s techniques o f f e r a method of combining o b j e c t i v e h i s t o r i c a l m o n i t o r i n g data with s u b j e c t i v e i n f o r m a t i o n such as operator judgement and ex p e r i e n c e . Markov P o l i c y - I t e r a t i o n techniques can be used to s e l e c t c o n t r o l p o l i c i e s which maximize the average long-term expected u t i l i t y . These r e q u i r e that estimates be made of the p r o b a b i l i t y of successs f o r each c o n t r o l a l t e r n a t i v e c o n s i d e r e d . A " u t i l i t y " i n monetary or other form of value i s a s s i g n e d to each p o s s i b l e outcome or s t a t e c o n d i t i o n . As p l a n t performance i s d i f f i c u l t to assess i n terms of a t a n g i b l e v a l u e , a system of u t i l i t y assignments must be used. A c t i v a t e d sludge b u l k i n g i s a process c o n t r o l problem which i s w e l l - s u i t e d t o d e c i s i o n a n a l y s i s . Sludge b u l k i n g i s most commonly a s s o c i a t e d with e x c e s s i v e f i l a m e n t o u s microorganism growth, and i s c h a r a c t e r i z e d by poor mixed l i q u o r s e t t l i n g p r o p e r t i e s and a sludge volume index (SVI) i n excess of 150 mL/g. With over 30 d i f f e r e n t types of fil a m e n t o u s microorganisms having been i d e n t i f i e d i n a c t i v a t e d sludge, each with i t s own " i d e a l " growth c o n d i t i o n s , and c o n s i d e r i n g the v a r y i n g o p e r a t i n g c o n d i t i o n s t y p i c a l of most p l a n t s , i t i s not s u p r i s i n g t h a t there are a v a r i e t y of a s s o c i a t e d causes. The most common cause appears to be r e l a t e d t o e i t h e r a e r a t i o n b a s i n d i s s o l v e d oxygen (DO) concentra-213 t i o n s or s u b s t r a t e l o a d i n g , represented by the food-to-microorganism (F/M) r a t i o . For Case "A", s i x SVI and e f f l u e n t suspended s o l i d s (SS) concen-t r a t i o n ranges were s e l e c t e d , to form 36 s t a t e s f o r use i n a Bayesian d e c i s i o n a n a l y s i s format. F i v e DO and F/M ranges were a l s o s e l e c t e d , forming 25 process c o n t r o l a l t e r n a t i v e s . P r o b a b i l i t y estimates were based on s i x years of monitoring data obtained from a c o n v e n t i o n a l a c t i v a t e d sludge f a c i l i t y with c h r o n i c b u l k i n g problems. The data was d i v i d e d i n t o groups re p r e -s e n t i n g the 25 c o n t r o l o p t i o n s . Each group was then subdivided i n t o the s i x SVI and e f f l u e n t SS ranges from which f r e q u e n c i e s and c o r r e s p o n d i n g p r o b a b i l i t i e s were c a l c u l a t e d based on a one week l a g p e r i o d . These p r o b a b i l i t i e s were then used i n c o n j u n c t i o n with four operator u t i l i t y m a t r i c e s to determine the c o n t r o l a l t e r n a t i v e with the maximum expected u t i l i t y . The f o l l o w i n g c o n c l u s i o n s were drawn from the Case "A" analyses based on the French Creek WPCC data base: 1. The u t i l i t y s t r u c t u r e has l i t t l e e f f e c t on the maximum expected u t i l i t y p o l i c y . 2. The c a l c u l a t e d expected u t i l i t y m a t r i c e s appeared to be banded with r e s p e c t to F/M c o n t r o l , with higher expected u t i l i t i e s c a l c u l a t e d f o r extreme (high/low) F/M c o n t r o l s e t t i n g s and l i t t l e v a r i a t i o n a c r o s s DO s e t t i n g s . 3. The maximum expected u t i l i t y was g e n e r a l l y observed f o r low DO and high F/M c o n t r o l s e t t i n g s , which i s not c o n s i s t e n t with low DO b u l k i n g theory. 214 4. Expected u t i l i t i e s f o r high DO and low F/M c o n t r o l s e t t i n g s , which i s c o n s i s t e n t with low DO b u l k i n g theory, were u s u a l l y second i n rank and approximately equal to the maximum expected u t i l i t y v a l u e . 5. I t i s b e l i e v e d that the p o l i c y of c h l o r i n a t i n g under hi g h b u l k i n g c o n d i t i o n s may have bi a s e d the data base, and r e s u l t e d i n i n a c c u r a t e p r o b a b i l i t y e s t i m a t e s . I f the a c t i v a t e d sludge i s c h l o r i n a t e d under o p e r a t i n g c o n d i t i o n s which promote b u l k i n g , those o p e r a t i n g c o n d i t i o n s may be i n c o r r e c t l y a s s o c i a t e d with improved sludge b u l k i n g . 6. The Bayesian d e c i s i o n theory approach, of n e c e s s i t y , r e s u l t e d i n a s i n g l e c o n t r o l p o l i c y r e g a r d l e s s of s t a t e . T h i s i s u n r e a l i s t i c f o r dynamic c o n t r o l of wastewater treatment f a c i l i t i e s . The l a c k of d i f f e r e n t i a t i o n between c a l c u l a t e d expected u t i l i t i e s over a broad range of c o n t r o l c o n d i t i o n s i n d i c a t e s that the technique i s not w e l l s u i t e d to process c o n t r o l . The Markov P o l i c y - I t e r a t i o n technique takes i n t o account the u t i l i t y of f u t u r e s t a t e s . In t h i s case i t a l s o determines optimal c o n t r o l s t r a t e g i e s i n terms of s t a t e c o n d i t i o n s . By s e p a r a t i n g the data i n t o s t a t e c o n d i t i o n s the problem of masking the " t r u e " c o n t r o l e f f e c t by c h l o r i n e treatment can be i s o l a t e d t o the h igher b u l k i n g s t a t e s . S i m i l a r to the p r e v i o u s technique, p r o b a b i l i t i e s are estimated f o r DO and F/M c o n t r o l a l t e r n a t i v e s , and u t i l i t i e s are a s s i g n e d to the p o s s i b l e outcomes or s t a t e s . For Case "B", three DO and F/M (low, medium, and high) c o n t r o l s e t t i n g s were s e l e c t e d to form 9 p o s s i b l e c o n t r o l s e t t i n g s f o r use i n a Markov P o l i c y - I t e r a t i o n format. The e f f l u e n t SS s t a t e c o n d i t i o n s were removed and the SVI s t a t e c o n d i t i o n s reduced to 5 d i s c r e t e ranges. Seven u t i l i t y m a t r i c e s were then c o n s t r u c t e d , r e l a t i n g the 5 SVI b u l k i n g c o n d i t i o n s with the 9 a l t e r n a t i v e c o n t r o l s t r a t e g i e s . D i f f e r e n c e s i n the u t i l i t y s t r u c t u r e s p r i m a r i l y r e f l e c t e d energy p o l i c i e s , with lower u t i l i t i e s f o r 215 i n c r e a s e d DO and F/M l e v e l s . The concept of u s i n g a b a s e l i n e frequency matrix to c a l c u l a t e the i n i t i a l s t a r t i n g s t a t e / p o l i c y v e c t o r was developed, and the e f f e c t s of the u t i l i t y s t r u c t u r e on the i n i t i a l s t a t e / p o l i c y v e c t o r were e x p l o r e d . The b a s e l i n e frequency matrix i s proposed as a r e l a t i v e l y unbiased f i r s t guess p r o b a b i l i t y estimate f o r use when no h i s t o r i c a l data i s a v a i l a b l e . The b a s e l i n e f r e q u e n c i e s were then added to h i s t o r i c a l data f r e q u e n c i e s t o generate a p r o b a b i l i t y or t r a n s i t i o n matrix. The data base was then f u r t h e r s u b d i v i d e d i n t o t h r e e temperature groups t o ex p l o r e the i n f l u e n c e of temperature on the optimal p o l i c y v e c t o r . F i n a l l y , Markov P o l i c y - I t e r a t i o n c a l c u l a t i o n s were undertaken f o r a simulated low DO b u l k i n g p r o c e s s , using a l l seven u t i l i t y s t r u c t u r e s . C o n c l u s i o n s drawn from the Case "B" analyses were as f o l l o w s : 1. F i n a l i t e r a t i o n p o l i c y v e c t o r s and average expected u t i l i t i e s were independent of the u t i l i t y matrix s t r u c t u r e s examined. 2. P o l i c y v e c t o r s f o r a l l seven u t i l i t y s t r u c t u r e s , based on h i s t o r i c a l data from the French Creek WPCC, are c o n s i s t e n t with low DO sludge b u l k i n g c o n d i t i o n s . G e n e r a l l y , low F/M c o n t r o l s e t t i n g s are recommended f o r a l l s t a t e s , with i n c r e a s i n g DO c o n c e n t r a t i o n s as the b u l k i n g s t a t e worsens. Where there i s no u t i l i t y d i f f e r e n t i a t i o n between F/M c o n t r o l s ( u t i l i t y m a t r i c e s #4-#7) higher F/M s e t t i n g s are recommended f o r s t a t e s 1 and 2, than with a u t i l i t y d i f f e r e n c e . 3. The p r a c t i c e of c h l o r i n e treatment under c o n d i t i o n s of b u l k i n g are r e f l e c t e d i n the low DO c o n t r o l p o l i c y recommended f o r s t a t e 5 c o n d i t i o n s . I f i t can be assumed t h a t p o l i c i e s which have r e s u l t e d i n a s t a t e 5 c o n d i t i o n are maintained i n s t a t e 5 u n t i l c h l o r i n e i s a p p l i e d , these p o l i c i e s w i l l be a s s o c i a t e d with improved b u l k i n g i n s t a t e 5, while i n lower s t a t e s they w i l l be a s s o c i a t e d with i n c r e a s e d b u l k i n g . T h i s demonstrates the value of c o n s i d e r i n g s t a t e c o n d i t i o n s i n s e l e c t i n g c o n t r o l p o l i c i e s . 216 4. The f i n a l i t e r a t i o n p o l i c y v e c t o r s f o r the high and low temperature extremes were e s s e n t i a l l y the same, i n d i c a t i n g t h a t the b u l k i n g c o n t r o l p o l i c y v e c t o r i s independent of temperature. 5. The f i n a l i t e r a t i o n p o l i c y v e c t o r f o r the simulated low DO b u l k i n g process was independent of the u t i l i t y s t r u c t u r e , r e s u l t i n g i n a c o n s i s t e n t low F/M p o l i c y f o r a l l s t a t e s and i n c r e a s e d DO c o n c e n t r a t i o n s as b u l k i n g c o n d i t i o n s worsened. 6. The number of i t e r a t i o n s r e q u i r e d to obtain a f i n a l i t e r a t i o n p o l i c y v e c t o r i n c r e a s e s as the slope of the u t i l i t y s u r f a c e i n c r e a s e s . Case " C e x p l o r e d the a d a p t a t i o n of the Markov P o l i c y - I t e r a t i o n technique to a simulated treatment p l a n t process o p t i m i z a t i o n problem. The i n f l u e n c e of the u t i l i t i t y matrix s t r u c t u r e , on the r a t e of convergence towards the known optimal s o l u t i o n , was examined, based on a b a s e l i n e frequency s t a r t i n g p o i n t . To improve the r a t e of convergence, an i n t e r v e n t i o n p o l i c y was proposed to overcome i n s t a b i l i t i e s i n the d e c i s i o n model. In e f f e c t , t h i s i n v o l v e d d e l i b e r a t e experimentation with c o n t r o l o p t i o n s not i n the optimal p o l i c y v e c t o r i n order to improve the i n f o r m a t i o n base. The French Creek WPCC monitoring data base was used to examine a frequency n o r m a l i z a t i o n methodology f o r i n c o r p o r a t i n g h i s t o r i c a l data i n t o the d e c i s i o n model p r o c e s s . The f o l l o w i n g c o n c l u s i o n s were drawn as a r e s u l t of the Case "C" Markov P o l i c y - I t e r a t i o n approach: 1. The r a t e of convergence and the s t a b i l i t y of the f i n a l i t e r a t i o n p o l i c y v e c t o r i s i n f l u e n c e d by the s t r u c t u r e of the u t i l i t y m a t r i x . T h i s c o n d i t i o n w i l l occur when the c o r r e c t p o l i c y i s i n c o n f l i c t with the u t i l i t y s t r u c t u r e ; f o r example, where hig h DO l e v e l s are r e q u i r e d to reduce sludge b u l k i n g , but low u t i l i t i e s have been assigned to the h i g h DO c o n t r o l a l t e r n a t i v e s . 217 2. The r a t e of convergence towards the f i n a l i t e r a t i o n p o l i c y v e c t o r for a s i m u l a t e d low DO b u l k i n g f a c i l i t y , i s independent of the F / M u t i l i t y s t r u c t u r e . 3 . D e s p i t e the l a r g e number of p o s s i b l e s t a t e / a l t e r n a t i v e c o m b i n a t i o n s , the model r a p i d l y converges on the c r i t i c a l a l t e r n a t i v e s , a v o i d i n g the n o n - c r i t i c a l o p t i o n s . Where an a l t e r n a t i v e r e s u l t s i n worsening b u l k i n g c o n d i t i o n s at a p a r t i c u l a r s t a t e , the next time that the s t a t e occurs an a l t e r n a t i v e p o l i c y ( lower u t i l i t y ) w i l l be s e l e c t e d . S i m i l a r l y , r epeated b u l k i n g improvements f o r a g iven p o l i c y r e i n f o r c e s tha t p o l i c y , such t h a t the o c c a s i o n a l i n c r e a s e d b u l k i n g o c c u r r e n c e w i l l not r e s u l t i n the a l t e r n a t i v e b e i n g abandoned by the model . 4. The two l e v e l c o n t r o l s t r u c t u r e cannot be opera ted as a s i n g l e c o n t r o l s t r u c t u r e ( i . e . DO c o n t r o l o n l y , and i g n o r i n g F / M s e t t i n g s ) wi thout the use of some form of i n t e r v e n t i o n . The i n t e r v e n t i o n p r o c e d u r e a l l o w s the o p e r a t o r to i n t e r v e n e to o b t a i n i n f o r m a t i o n f o r input to the p o l i c y d e c i s i o n p r o c e s s . 5. H i s t o r i c a l data bases can be used to i n i t i a l i z e the p o l i c y -i t e r a t i o n p r o c e s s and improve the convergence r a t e . However, the f requency m a t r i x s h o u l d be n o r m a l i z e d to an i n t e g e r v a l u e to ensure tha t the c o n t r o l l e d e x p e r i m e n t a l d a t a generated i s not o v e r l y i n f l u e n c e d by p r e v i o u s d a t a . A dynamic Markov P o l i c y - I t e r a t i o n t e c h n i q u e has been deve loped f o r use i n a c t i v a t e d s ludge p r o c e s s c o n t r o l . The procedure r e q u i r e s t h a t a range of p o s s i b l e s t a t e s and r e l e v a n t c o n t r o l a l t e r n a t i v e s be d e f i n e d and tha t a v a l u e or u t i l i t y be a s s i g n e d to each of the s t a t e s . The p r i n c i p a l advantage of the procedure i s i n i t s c a p a b i l i t y f o r u t i l i z i n g both a v a i l a b l e m o n i t o r i n g da ta and o p e r a t o r i n p u t , i n d e t e r m i n i n g an o p t i m a l s o l u t i o n . By u s i n g a u t i l i t y v a l u e s t r u c t u r e , both system performance and energy e x p e n d i t u r e v a l u e s can be c o n s i d e r e d i n the o p t i m a l p o l i c y c a l c u l a t i o n s . D e s p i t e the models r e l i a n c e on p r o b a b i l i t y e s t i m a t e s , the i t e r a t i v e procedure r a p i d l y converges on the o p t i m a l p o l i c y s o l u t i o n and the r e s u l t i n g i n f o r m a t i o n r e f i n e s the 218 c r i t i c a l p r o b a b i l i t i e s . Where c o n d i t i o n s of non-convergence or p o l i c y i n s t a b i l i t y i s encountered, a i n t e r v e n t i o n procedure has been proposed to speed the r a t e of convergence. As a f i r s t step a p p l i c a t i o n , the Markov P o l i c y - I t e r a t i o n technique shows promise f o r use i n process c o n t r o l at c o n v e n t i o n a l a c t i v a t e d sludge f a c i l i t i e s . The technique has been demonstrated f o r the problem of sludge b u l k i n g c o n t r o l based on DO and F/M c o n t r o l o p t i o n s . By c o n t i n u a l l y updating the p r o b a b i l i t y matrix, and re - r u n n i n g the P o l i c y - I t e r a t i o n c a l c u l a t i o n s , the technique can adapt to changing p l a n t c o n d i t i o n s . Because the i n i t i a l p o l i c y c a l c u l a t i o n s are o f t e n based on p r o b a b i l i t y e s t i m a t e s , c o n s t r u c t e d from h i s t o r i c a l data of q u e s t i o n a b l e q u a l i t y or from "best guess" approximations, i n f o r m a t i o n o b t a i n e d through c o n t r o l l e d experimentation should be added t o update the p r o b a b i l i t y estimates i n the l i g h t of new i n f o r m a t i o n . 219 7.0 FUTURE RESEARCH DIRECTIONS T h i s r e s e a r c h forms a f i r s t attempt at a p p l y i n g d e c i s i o n a n a l y s i s techniques to a c t i v a t e d sludge process c o n t r o l . While Howard's (1960) Markov P o l i c y - I t e r a t i o n technique i s promising, there are other d e c i s i o n a n a l y s i s techniques which may a l s o h o l d promise. P o s s i b l e m o d i f i c a t i o n s i n c l u d e adaptation of Bayes' Theorem for p r o b a b i l i t y e s t i m a t i n g and updating, development of a two-stage Markov c h a i n to account f o r the a u t o c o r r e l a t e d data c h a r a c t e r i s t i c s , a p p l i c a t i o n of p r o b a b i l i t y updating to the Bayesian d e c i s i o n a n a l y s i s , and use of f i l t e r i n g t e chniques, such as the Kalman F i l t e r , f o r p r o b a b i l i t y e s t i m a t i n g . Where s i g n i f i c a n t f a c t o r s are beyond the c o n t r o l of the o perator, such as the i n f l u e n c e of extreme l i q u i d temperature f l u c t u a t i o n s , a m u l t i p l e c o n t r o l s t r a t e g y model c o u l d be developed. The key to t h i s concept would be the a b i l i t y to recognize when the p r e d i c t e d s t a t e outcomes were s i g n i f i c a n t l y and c o n s i s t e n t l y d i f f e r e n t from the observed outcomes. T h i s may be achieved through the weight-ing of h i s t o r i c a l p r o b a b i l i t i e s , such that they do not overwhelm i n f o r m a t i o n t h a t i n d i c a t e s the system i s changing. To f a c i l i t a t e the a p p l i c a t i o n of d e c i s i o n theory to process o p t i m i z a t i o n , a computer program needs to be developed. The program would i n c o r p o r a t e g r a p h i c a l p r e s e n t a t i o n techniques i n a d d i t i o n to non-parametric s t a t i s t i c a l r o u t i n e s . As d e c i s i o n a n a l y s i s r e q u i r e s an e x t e n s i v e amount of l i n e a r a l g e b r a , a computer language which i s s u i t a b l e to matrix m a n i p u l a t i o n i n an 220 i n t e r a c t i v e mode would be d e s i r a b l e . The APL language, which was used i n t h i s r e s e a r c h , i s very w e l l s u i t e d to t h i s type of programming, and i s a v a i l a b l e f o r use on IBM PC compatible computers. Although f i e l d s t u d i e s were not undertaken i n the course of t h i s work, the developed techniques h o l d promise f o r the c o n t r o l of DO or F/M r e l a t e d sludge b u l k i n g problems. Key to t h i s undertaking i s the r e a l - t i m e c o n t r o l of DO and/or F/M. Although the o b j e c t i v e parameter SVI was used i n t h i s work, other b u l k i n g measurements, such as the s t i r r e d sludge volume index (SSVI) or filamentous enumeration and l e n g t h measurements, co u l d a l s o be a p p l i e d . Although Tomlinson (1982) has noted that the i d e n t i f i -c a t i o n of the dominant f i l a m e n t present does not n e c e s s a r i l y i n d i c a t e the cause of the b u l k i n g , the i n f o r m a t i o n c o u l d be i n c o r p o r a t e d i n t o the d e c i s i o n model. F u r t h e r , the techniques can be r e a d i l y adapted to other process c o n t r o l and o p t i m i z a t i o n r e s e a r c h . 221 REFERENCES Abraham B., " I n t e r v e n t i o n A n a l y s i s and M u l t i p l e Time S e r i e s . " B i o m e t r i k a , 67, 73, (1980). Adams, C. E. J r . and W. W. E c k e n f e l d e r J r , "Response of A c t i v a t e d Sludge to Organic T r a n s i e n t Loadings." J . S a n i t . Eng. Div.,  Proc. Am. Soc. C i v . Eng., 96, 333 (1910T. A l d e n h o f f , G. A. and L. A. E r n e s t , "A Q u a l i t y Assurance Program at a M u n i c i p a l Wastewater Treatment P l a n t L a b o r a t o r y . " J .  Water P o l l u t . C o n t r o l Fed., 55, 1132 (1983). Alexander, W. V., G. A. Ekama, and G. v. R. Marais, "The A c t i v a t e d Sludge Process Part 2. A p p l i c a t i o n of the General K i n e t i c Model to the Contact S t a b i l i z a t i o n P rocess." Water  Res., 1 4 , 1737, (1980). Ames, A. E. and G. S z o n y i , "How To Avoid L y i n g With S t a t i s t i c s . " Chemometrics: Theory and A p p l i c a t i o n , John Wiley & Sons, Inc., New York, NY. (1982). Anderson, J . M., " E f f e c t of N i t r a t e C o n c e n t r a t i o n i n Lake Water on Phosphate Release From the Sediment." Water Res. (G.B.) 16, 1 1 1 9 , (1982). Andrews, J . F., " S p e c i f i c Oxygen U t i l i z a t i o n Rate f o r C o n t r o l of the A c t i v a t e d Sludge Process." Prog. Water Technol., 8, 451, (1977). Anon. "Wastewater L a b o r a t o r i e s - F u l l P a r t n e r s i n Environmental P r o t e c t i o n . " J . Water P o l l u t . C o n t r o l Fed., 57, 266, (1985). A r t h u r , R. M., "Measurement and V a l i d i t y of Oxygen Uptake as an A c t i v a t e d Sludge Process C o n t r o l Parameter." J . Water  P o l l u t . C o n t r o l Fed., 52, 1546, (1980). A r t h u r , R.M., A p p l i c a t i o n of O n - l i n e A n a l y t i c a l Instrumentation  to Process C o n t r o l , Ann Arbour Science P u b l i s h e r s , Michigan, (1982a). A r t h u r , R.M., New Concepts and P r a c t i c e s In A c t i v a t e d Sludge  Process C o n t r o l , Ann Arbour Science P u b l i s h e r s , Michigan, (1982b). Awong, J . , G. B i t t o n and B. Koopman, "ATP, Oxygen Uptake Rate and INT-Dehydrogenase A c t i v i t y of Actinomycete Foams." Water  Res., 1 9 , 917, (1985). Barahona, L. and W. W. E c k e n f e l d e r J r . , " R e l a t i o n s h i p s Between Or g a n i c s Loading and Zone S e t t l i n g V e l o c i t y i n the A c t i v a t e d Sludge Process." Water Res., 1 8 , 9 1 , (1984). 222 Barnard, J . L., "Cut N and P Without Chemicals." Water and  Wastes Eng., 11, 33, (1974). Barnard, J . L., "Nu t r i e n t Removal i n B i o l o g i c a l Systems." Wat. P o l l u t . C o n t r o l . 74, 143, (1975). Barnard, J . L., "A Review of B i o l o g i c a l Phosphorus Removal in the A c t i v a t e d Sludge Process." Water S.A. 2, 136, (1976). Bates, M. H. and N. J . E. Neafous, "Phosphorus Release From Sediments From Lake C a r l B l a c k w e l l , Oklahoma." Water Res., 14, 1477, (1980). B e n e f i e l d . L. D., R a n d a l l , C.W. and King, "Process C o n t r o l by Oxygen Uptake and S o l i d s A n a l y s i s . " J . Water P o l l u t . C o n t r o l  Fed., 47, 2498, (1975). B e n e f i e l d , L. D. and F. Molz, "A K i n e t i c Model f o r A c t i v a t e d Sludge Process Which Considers D i f f u s i o n and Reaction i n the M i c r o b i a l F l o e . " B i o t e c h n o l Bioenq., 25, 2591, (1983). Berthouex, P. M. , Hunter W. G., P a l l e s e n L and Shih C. Y., "Use of Time S e r i e s Models to I n t e r p r e t H i s t o r i c a l Sewage T r e a t -ment Pl a n t Records." Water Research, 10, 689, (1976). Berthouex, P. M., W.G. Hunter, L. P a l l e s e n , "The Use of S t o c h a s t i c Models i n the I n t e r p r e t a t i o n of H i s t o r i c a l Data From Sewage Treatment P l a n t s . " Water Res., 10, 689, (1976). Berthouex, P. M., W. G. Hunter, L. P a l l e s e n and C. Y. Shih, "Dynamic Behavior of an A c t i v a t e d Sludge P l a n t . " Water Res. (G.B.), 12, 957, (1978). Berthouex, P. M., W. G. Hunter and L. P a l l e s e n , " A n a l y s i s of Dynamic Behavior of the A c t i v a t e d Sludge P l a n t - Comparison of R e s u l t s with Hourly and B i - h o u r l y Data." Water Res. (G.B)., 13, 1281, (1979). Berthouex, P. M., W. G. Hunter and L. P a l l e s e n , "Wastewater Treatment: A Review of S t a t i s t i c a l A p p l i c a t i o n s . " From E n v i r o n m e t r i c s 81: S e l e c t e d Papers, USEPA-SIAM-SIMS Conference. A l e x a n d r i a , V i r g i n i a , (1981). B i e s i n g e r , M. G., S t e n s e l H.D. and D. J e n k i n s , "Brewery Wastewater Treatment Without A c t i v a t e d Sludge Problems." Proceedings of the 35th I n d u s t r i a l Waste Conference, Purdue U n i v e r s i t y , 569, (1980). B l a c k w e l l , L. G., A T h e o r e t i c a l and Experimental E v a l u a t i o n of  the T r a n s i e n t Response of the A c t i v a t e d Sludge Process., Ph.D. D i s s e r t a t i o n , Clemson U n i v e r s i t y , Clemson, S.C, (1971). Blok, J . , "Respirometric Measurement on A c t i v a t e d Sludge." Water  Res., 8, 112, (1974). 223 Blok, J . , "Measurements of the V i a b l e Biomass Co n c e n t r a t i o n i n A c t i v a t e d Sludge by Respirometric Techniques." Water Res., 10, 919, (1976). Box, G. E. P. and T i a o , G. C , "A Change i n L e v e l of a Non-S t a t i o n a r y Time S e r i e s . " B i o m e t r i c a , 52, 181, (1965) Box, G. E. P. and G. M. J e n k i n s , Time S e r i e s F o r e c a s t i n g and  C o n t r o l . , Holden-day, San F r a n c i s c o , C.A., ( 1 970). Box, G. E. P. and T i a o , G. C , " I n t e r v e n t i o n A n a l y s i s With A p p l i c a t i o n s to Economic and Environmental Problems." J . of  the Am. S t a t . Assoc., 70, 70, (1975). Busby, J . B. and J . F. Andrews, "Dynamic Modeling and C o n t r o l S t r a t e g i e s f o r the A c t i v a t e d Sludge Process." J . Water  P o l l u t . C o n t r o l Fed., 47, 1055, (1975). Busch, A. E., "Aerobic B i o l o g i c a l Treatment", J . Water P o l l u t .  C o n t r o l Fed., 56,215, (1984). Cashion, B. S. and T. M. Keinath, " I n f l u e n c e of Three F a c t o r s on C l a r i f i c a t i o n i n the A c t i v a t e d Sludge Pro c e s s . " J . Water  P o l l u t . C o n t r o l Fed., 55, 1337 (1983). Chaing, C. H., "Process S t a b i l i t y of A c t i v a t e d Sludge Process." Proc. Am. Soc. C i v . Eng., J . E n v i r o . Eng. Div. 103, 259, (1977). Chambers, B., " E f f e c t of L o n g i t u d i n a l Mixing and Anoxic Zones on S e t t l e a b i l i t y of A c t i v a t e d Sludge." In: B u l k i n g of A c t i v a t e d  Sludge: Prevention and Remedial Methods" (B. Chambers, and E. J . Tomlinson, E d s . ) , E l l i s Horwood L t d . , (1982). Chambers, B. and E . J . Tomlinson (Eds), BULKING OF ACTIVATED  SLUDGE: P r e v e n t a t i v e and Remedial Methods. E l l i s Horwood L t d . , (1982). Chapman, D. T., " F i n a l S e t t l e r Performance During T r a n s i e n t Loading." J . Water P o l l u t . C o n t r o l Fed., 57, 227, (1985). Charley R. C , D. G. Hopper, and A. G. McLee, " N i t r i f i c a t i o n K i n e t i c s i n A c t i v a t e d Sludge at V a r i o u s Temperatures and D i s s o l v e d Oxygen C o n c e n t r a t i o n s . " Water Res., 14, 1387, (1980). Chen, C. Y., Roth, I. A., and W. W. E c k e n f e l d e r , "Response of D i s s o l v e d Oxygen to Changes i n I n f l u e n t Organic Loading to A c t i v a t e d Sludge Systems." Water Res., 14, 1449, (1980). Chen, Y. R. and A. G. Hashimoto, "Substrate U t i l i z a t i o n K i n e t i c Model f o r B i o l o g i c a l Treatment Processes." B i o t e c h , and Bio  Eng., 22, 2081, (1980). 224 C h i e s a , S. C , and R. L. I r v i n e , "Growth and C o n t r o l of Filamen-tous Microbes i n A c t i v a t e d Sludge: An I n t e g r a t e d Hypothesis." Water Res., 1 9 , 471, (1985). Chudoba. J . , Ottova V. and V. Madera, " C o n t r o l of A c t i v a t e d Sludge Filamentous B u l k i n g - I. E f f e c t of the H y d r a u l i c Regime or Degree of Mixing i n an A e r a t i o n Tank." Water Res., 7 , 1163, (1973a). Chudoba, J . , Grau, P. and V. Madera, " C o n t r o l of A c t i v a t e d Sludge Filamentous B u l k i n g - II S e l e c t i o n of Microorganisms by Means of a S e l e c t o r . " Water Res., 7 , 1389, (1974a). Chudoba, J . , Blaha J . and V. Madera, " C o n t r o l of A c t i v a t e d Sludge Filamentous B u l k i n g - I I I E f f e c t of Sludge Loading." Water Res., 8, 231, (1974). Chudoba, J . , Dohanyos, M. and P. Grav, " C o n t r o l of A c t i v a t e d Sludge Filamentous B u l k i n g - IV E f f e c t of Sludge Regeneration." Wat. S c i . Techn., 1 4 , 73, (1982). Chudoba, J . , " C o n t r o l of A c t i v a t e d Sludge Filamentous B u l k i n g -VI. Formation of Basic P r i n c i p l e s . " Water Res., 1 9 , 1017, (1985). C l i f t , R. C. and J . F. Andrews, " P r e d i c t i n g the Dynamics of the Oxygen U t i l i z a t i o n i n the A c t i v a t e d Sludge Process." Water  P o l l u t . C o n t r o l Fed., 5 3 , 1219, (1981). Cole, C. A., Stamberg, J . B., and D. F. Bishop, "Hydrogen Peroxide Cures Filamentous Growth i n A c t i v a t e d Sludge." J .  Water P o l l u t . C o n t r o l Fed., 4 5 , 829, (1973). C o l l i n s , L. , An I n t r o d u c t i o n to Markov Chain A n a l y s i s , Study Group i n Q u a l i t a t i v e Methods of the I n s t i t u t e of B r i t i s h Geographers, (1975). Committee on Water P o l l u t i o n Management of the Environmental E n g i n e e r i n g D i v i s i o n . " E n g i n e e r i n g Design V a r i a b l e s f o r the A c t i v a t e d Sludge Process." J . E n v i r o n . Eng. Div., Amer Soc.  C i v i l Eng. 1 0 6 , 473, (1980). Conover, W. J . , P r a c t i c a l Nonparametric S t a t i s t i c s , J . Wiley & Sons, L t d . , New York, (1971). Daigger, G. T. Robbins, M. H. J r , and M a r s h a l l , B. R., "The Design of a S e l e c t o r t o C o n t r o l low-F/M Filamentous B u l k i n g " . J . Water P o l l u t . C o n t r o l Fed., 5 7 , 220, (1985). Debelak, K. A. and C. A. Sims, " S t o i c h a s t i c Modeling of an I n d u s t r i a l A c t i v a t e d Sludge Process." Water Res. (G.B), 1 5 , 1173, (1981). .225 Diamadopoulos, E., and A. Benedek, "The P r e c i p i t a t i o n of Phosphorus From Wastewater Through pH V a r i a t i o n i n the Presence and Absence of Coagulants." Water Res., 18, 1175, (1984). Dick R. I. and P. A. V e s i l i n d , "The Sludge Volume Index - What i s i t ? " J . Water P o l l u t . C o n t r o l Fed., 41, 1285, (1969). Dold, P. L., G. A. Ekama, and G. v. R. M a r a r i s , "A General Model fo r the A c t i v a t e d Sludge Process." Prog. Wat. Tech., 12, 47, (1980). Draper, N. R. and H. Smith, A p p l i e d Regression A n a l y s i s , John Wiley & Sons, Inc., New York, NY., (1966). Droste, R. C. and W. A. Sancher, " M i c r o b i a l A c t i v i t y i n Aerobic Sludge D i g e s t i o n . " Water Res., 17, 975, (1983). Duggan, J . B. and J . L. Cleasby, " E f f e c t of V a r i a b l e Loading on Oxygen Uptake." J . Water P o l l u t . C o n t r o l Fed., 48, 540, (1976). Edwards, G. L., G. L. Sh e r r a r d , "Measurement and V a l i d i t y of Oxygen Uptake as an A c t i v a t e d Sludge Process C o n t r o l Parameter." J . Water P o l l u t . C o n t r o l Fed., 54, 1546, (1982). Eikelboom, D. H., "Filamentous Organisms i n A c t i v a t e d Sludge." Water Research., 9 , 365, (1975). Eikelboom, D. H., " I d e n t i f i c a t i o n of Filamentous Organisms i n B u l k i n g A c t i v a t e d Sludge." Progress i n Water Technology, 8, 153, (1977). Eikelboom, D. H., "M i c r o s c o p i c Sludge I n v e s t i g a t i o n i n R e l a t i o n to Treatment P l a n t O p e r a t i o n . " In: B u l k i n g of A c t i v a t e d  Sludge: P r e v e n t i o n and Remedial Methods, (B. Chambers, and E. J . Tomlinson, E d s . ) , E l l i s Horwood L t d . , (1982). Eisenhauser, D. L., S e i g e r , R. B., and D. F. Parker, "Design of an I n t e g r a t e d Approach to N u t r i e n t Removal", Proc. Am.  S o c . C i v i l Eng., Jour. Env. Eng. Div. No. E E l , 37^ (1976). Ekama, G. A. and G. v. R. Marais, "Dynamic Behavior of the A c t i v a t e d Sludge Process." J . Water P o l l u t . C o n t r o l Fed., 51, 534, (1979). Ekama, G. A. and G. v. R. Marais, The Dynamic Behavior of the A c t i v a t e d Sludge Process, Res. Report No. W27. Dept. of C i v i l Eng. U n i v e r s i t y of Cape Town, (1980). Ekama, G. A., I. P. S i e b r i t z , and G. v. R. Marais, "Considera-t i o n s i n the Process Design of N u t r i e n t Removal A c t i v a t e d Sludge Process." S e l e c t e d Papers on A c t i v a t e d Sludge  Process Research at the U n i v e r s i t y of Cape Town, Dept. of C i v i l Eng., U n i v e r s i t y of Cape town (1982). 226 Environmental P r o t e c t i o n Agency, Process Design Manual f o r  Nitrogen C o n t r o l . O f f i c e of Technology T r a n s f e r , C i n c i n n a t i , Ohio, T T 9 7 5 ) . Feyen, H. A. and G. Krenzer, " O p t i m i z a t i o n f o r P u r i f i c a t i o n E f f i c i e n c y and Process S t a b i l i t y by Using Process Computer -Conducted Measurement and C o n t r o l Technology i n K r e f e l d and Wuerselen-Euchen Wastewater Treatment P l a n t s . " Gewaesser- shutz, Wasser. Abwasser (Ger.), 50, 579, ( 1 982V. Chem.  Ab s t r . 96, 204819, (1983). Ford, D. C. and W. W. E c k e n f e l d e r J r . , " E f f e c t of Process V a r i a b l e s on Sludge Flow Formation and S e t t l i n g C h a r a c t e r -i s t i c s . " J . Water P o l l u t . C o n t r o l Fed., 39, 1850, (1967). Forde, L., S. Niku and E. D. Schroeder, " D i s c u s s i o n : Process S t a b i l i t y of A c t i v a t e d Sludge Processes." Proc. Am. Soc.  C i v i l Eng., J . Env. Eng. Div., 104, 178, (1978). F o r e s t e r , C. F., " F a c t o r s Involved i n the Settlement of A c t i v a t e d Sludge - I, N u t r i e n t s and Surface Polymers." Water Res., 19, 1259, (1985). Fuh, G. W. and Min Chen, " M i c r o b i a l B a s i s of Phosphorus Removal in the A c t i v a t e d Sludge Process f o r the Treatment of Waste-water." M i c r o b i a l Ecology, 2, 119, (1975). G a n c z a r c z i j k , J . , " V a r i a t i o n i n the A c t i v a t e d Sludge Volume Index." Water Res., 4, 69, (1970). G a r r e t , M. T. J r . , J . Ma, W. Yang, G. Hyare, T. Norman and Z. Ahmad, "Improving the Performance of Houston's Southwest Wastewater Treatment P l a n t , USA." Wat. S c i . Tech., 16, 317, (1984). Gaudy, A. F. J r . and E. T. Gaudy, M i c r o b i o l o g y f o r Environmental  S c i e n t i s t s and Engineers. McGraw-Hill Book Co., (1980). Gaudy, A. F. J r . and T. R. Blachy, "A Study of the Biodegra-d a b i l i t y of R e s i d u a l COD." J . Water P o l l u t . C o n t r o l Fed., 57, 332, (1985). Giona, A. R. and M. C. A n n e s i n i , "Oxygen Uptake i n the A c t i v a t e d Sludge Process." J . Water P o l l u t . C o n t r o l Fed., 51, 1009, (1979). Grady, C. P. L., J r . and D. R. W i l l i a m s , " E f f e c t s of I n f l u e n t Substrate C o n c e n t r a t i o n on the K i n e t i c s of N a t u r a l M i c r o b i a l P o p u l a t i o n i n Continuous C u l t u r e . " Water Res., 9, 171, (1975). Gray, A. C , P a u l , P. E., and H. D. Roberts, " O p e r a t i o n a l F a c t o r s A f f e c t i n g B i o l o g i c a l Treatment P l a n t Performance." Water  P o l l u t . C o n t r o l Fed., 52, 1880, (1980). 227 Grau, P., Chudoba, J . and M. Dohanyos, "Theory and P r a c t i c e of Accumulation-Regeneration Approach t o the C o n t r o l of A c t i v a t e d Sludge Filamentous B u l k i n g . " In: B u l k i n g of  A c t i v a t e d Sludge: P r e v e n t i o n and Remedial Methods, (B. Chambers, and E. J~. Tomlinson, Eds.), E l l i s Horwood L t d . , (1982). Green, M. and G. S h e l e f , "Sludge V i a b i l i t y i n a B i o l o g i c a l Reactor." Water Res., 1 5 , 953, (1981). Grimestad, D. E. and R. L. Wetegrove, B i o l o g i c a l Process  T r o u b l e s h o o t i n g - A Guide to Improved Waste Pl a n t O p e r a t i o n .  P o l l u t i o n E n g i n e e r i n g . 25, (1982). G r i n k e r , J . R. and R. F. Meagher, "Computer C o n t r o l l e d Operation of an A c t i v a t e d Sludge P l a n t . " J . Water P o l l . C o n t r o l Fed., 5 6 , 823, (1984). Guo, P. H. M., D. Thirumurthi and B.E. Jank, " E v a l u a t i o n of Extended A e r a t i o n A c t i v a t e d Sludge P l a n t s . " Water P o l l u t .  C o n t r o l Fed. 5 3 , (1981). Gupta, A.K., W. K. Oldham and P. Coleman, "The E f f e c t s of Temperature, pH and R e t e n t i o n Time on V o l a t i l e F a t t y A c i d P r o d u c t i o n From Primary Sludge." I n t ' l Conf. New D i r e c t i o n s  and Research i n Waste Treatment and R e s i d u a l s Management, U n i v e r s i t y of B r i t i s h Columbia. 1 , 376, (1985). Hahn, G. J . , "Random Samplings: P u t t i n g Bounds on a P r e d i c t i o n " , Chemtech. US, 381, (1974). Hansen, J . L., A. E. F i o k and J . C. Hovious, "Dynamic Modeling of I n d u s t r i a l Wastewater Treatment Plant Data." J . Water  P o l l u t . C o n t r o l Fed., 5 2 , 1966, (1979). Hass, C. N., "Oxygen Uptake Rate as an A c t i v a t e d Sludge C o n t r o l Parameter." J . Water P o l l u t . C o n t r o l Fed., 5 1 , 938, (1979). Hao, O. J . , Ri c h a r d , M. G., J e n k i n s , D., and H. W. Blanch, "The H a l f - S a t u r a t i o n C o e f f i c i e n t f o r D i s s o l v e d Oxygen: A Dynamic Model f o r I t s Determination and I t s E f f e c t on Dual Species Competition." B i o t e c h n o l . Bioeng., 2 5 , 403, (1983). Haung, J . Y. C. and M. D. Cheng, "Measurement and New A p p l i -c a t i o n s of Oxygen Uptake Rates i n A c t i v a t e d Sludge P r o c e s s e s . " J . Water P o l l u t . C o n t r o l Fed., 5 6 , 259, (1984). Hovey, W. H., and E. D. Schroeder, " A c t i v a t e d Sludge E f f l u e n t Q u a l i t y . " Jour. E n v i r . Eng. Div., Proc. Amer. Soc. C i v i l  Eng., 1 0 5 , 819, (1979). Howard, R. A., Dynamic Programming and Markov Processes, The M.I.T. Press, Massachusetts I n s t i t u t e of Technology, Cambridge, Massachusetts, (1960). 228 Howell, J . A., L. J . Yust and P. R e i l l y , "On-line Measurement of R e s p i r a t i o n and Mass T r a n s f e r Rates i n an A c t i v a t e d Sludge A e r a t i o n Tank." J . Water P o l l u t . C o n t r o l Fed., 56, 319, (1984). Hsieh, H. N., Economical S o l u t i o n f o r B u l k i n g Sludge A s s o c i a t e d  With A c t i v a t e d Sludge, D o c t o r a l T h e s i s . U n i v e r s i t y of P i t t s b u r g h , (1983). Huang, J . Y. C , Cheng, M. D., and J . T. Mueller, "Oxygen Uptake Rates For Determining M i c r o b i a l A c t i v i t y and A p p l i c a t i o n . " Water. Res. (G.B), 1 9 , 373, (1985). James, A., "Some P e r p e c t i v e s i n the Modeling of B i o l o g i c a l T r e a t -ment of Wastewaters." Water S c i . Technology (G.B), 1 4 , 227, (1982). Jones, P. H., "The E f f e c t of N i t r o g e n and Phosphorus Compounds on One of the Microorganisms Responsible f o r Sludge B u l k i n g . " Proc. 20th Purdue Ind. Waste Conf., 297, (1965). Jones, P. H. and D. Prasad, "The Use of T e t r a z o l i u m S a l t s as a Measure of Sludge A c t i v i t y . " J . Water P o l l u t . C o n t r o l Fed., 4 1 , 449, (1969). Jorgensen, K. P., "Determination of the Enzyme A c t i v i t y of A c t i -vated Sludge by Methylene Blue Reduction." J . Water P o l l u t .  C o n t r o l Fed., 56, 89, (1984). Joyce, R. J . , C. Ortman and C. Z i c k e f o o s e , "How to Optimize an A c t i v a t e d Sludge P l a n t . " Water & Sewage Works, 96, (1974). Keinath, T.M. and B.S. Cashion, C o n t r o l S t r a t e g i e s f o r the  A c t i v a t e d Sludge Process, Report-600/2-80-131, (1980). K e l l e y , D. L., R. C. A l l i s o n , " F a u l t Tree A n a l y s i s and Treatment Pl a n t Instrumentation." J . Water P o l l u t . C o n t r o l Fed., 53, 43, (1981). Kiesow, L. A., "On the A s s i m i l a t i o n of Energy from Inorganic Sources i n A u t o t r o p h i c Forms of L i f e . " Proc. Nat. Acad.  S c i . , U.S.A., 52, 980, (1974). Klapwijk, A. K., Drent, J . and J . H.' Stenvoo, "A M o d i f i e d Procedure f o r the TTC - Dehydrogenase Test i n A c t i v a t e d Sludge." Water Res., 8, 121, (1974). Kucnerowicz, F. and W. V e r s t r a e t e , " D i r e c t Measurement of M i c r o b i a l ATP i n A c t i v a t e d Sludge Samples." J o u r n a l Chemical  Technology and Biotechnology, 2 9 , 707, (197971 Kucnerowicz F. and W. V e r s t r a e t e , " E v o l u t i o n of M i c r o b i a l Communities i n the A c t i v a t e d Sludge Process." Water Res. 1 7 , 1275, (1983). 229 Lau, J . C , L. B e n e f i e l d and C. W. R e n d a l l , "Phosphorus Removal in the A c t i v a t e d Sludge Process." Water Res., 17, 1193, (1983). Lau, A. 0., P. F. Strom, and D. Jenkins, "Growth K i n e t i c s of S p h a e r o t i l u s natans and a Floe Former in Pure and Dual Continuous C u l t u r e . " J . Water P o l l u t . C o n t r o l Fed., 56, 41, (1984a). ~ Lau, A. O., P. F. Strom and D. Jenkins, "The Competitive Growth of Floc-Forming and Filamentous B a c t e r i a : A Model For A c t i v a t e d Sludge B u l k i n g . " J . Water P o l l u t . C o n t r o l Fed., 56, 52, (1984b). Lawrence, A. W. and P. L. McCarty, " U n i f i e d B a s i s f o r B i o l o g i c a l Treatment Design and Operation." J . Sanit Eng. D i v i s i o n , Am.  Soc. C i v i l Eng., 96, 757, (1980). Lawler, D. F. and P. C. Singer, "Return Flows From Sludge T r e a t -ment." J . Water P o l l u t . C o n t r o l Fed., 56, 110, (1984). Lee, S. E. E f f e c t of A e r a t i o n Basin C o n f i g u r a t i o n on A c t i v a t e d  Sludge B u l k i n g at Low Organic Loading, D o c t o r a l T h e s i s . U n i v e r s i t y of C a l i f o r n i a , Berkley, (1983). Lee, G. F. and R. A. Jones, " A c t i v e Versus Passive Water Q u a l i t y M o n i t o r i n g Programs For Wastewater Discharges." J . Water  P o l l u t . C o n t r o l Fed., 55, 405, (1983). Lee, T. C , G. G. Judge, and A. Z e l l n e r , C o n t r i b u t i o n s to  Economic A n a l y s i s , E s t i m a t i n g the Parameters of the Markov  P r o b a b i l i t y Model From Aggregate Time S e r i e s Data, North-H o l l a n d P u b l i s h i n g Co., New York, (1977). Less, S., " E v a l u a t i o n of A l t e r n a t i v e Sludge S e t t l e a b i l i t y I n d i c e s " . Water Res. 17, 1421 (1983). L e s t e r , J . N., Perry, R., and A. H. Dudd, " C u l t i v a t i o n of a Mixed B a c t e r i a l P o p u l a t i o n of Sewage O r i g i n i n the Chemostat." Water Res. (G.B.), 13, 545, (1979). Lettenmaier, D. P., "Design C o n s i d e r a t i o n s For Ambient Stream Q u a l i t y M o n i t o r i n g . " Water Resources B u l l e t i n , 14, 884, (1978). L i a n g , D. H., Yong, P. Y., and T. L i a n g , " B i - p o p u l a t i o n Approach to CMAS S i m u l a t i o n . " J o u r . E n v i r o n . Eng. D i v . , Proc. Amer.  Soc. C i v i l Eng., 105, 905, (1979). L o f t i s , J . C , P. C. Ward and G. M. S m i l l i e , " S t a t i s t i c a l Models f o r Water Q u a l i t y R e g u l a t i o n . " J . Water P o l l u t . C o n t r o l  Fed., 55, 1098, (1983). 230 Logun, R. P. and W. E. Budd, " E f f e c t of BOD Loading on A c t i v a t e d Sludge P l a n t O p e r a t i o n . " In B i o l o g i c a l Treatment of Sewage  and I n d u s t r i a l Wastes, V o l . I; Aerobic O x i d a t i o n . J . McCabe and W.W. E c k e n f e l d e r J r . [ E d s . ] , Reinhold P u b l i s h i n g Corp., New York. (pp271-276), (1956) Manickam, T. S. and A. F. Gaudy J r . , "Comparison of A c t i v a t e d Sludge Response to Q u a n t i t a t i v e , H y d r a u l i c and Combined Shock f o r the Same Increases i n Mass Loading." J . Water  P o l l u t . C o n t r o l Fed., 57, 241, 1985). Marais, G. v. R., and G. A. Ekama, "The A c t i v a t e d Sludge Process Part I - Steady State Behaviour." Water S.A., 2, (1976). Matsumae, K., "Automatic COD Meter." Kankyo G i j u t s u (Jap) 9, 324, (1980); Chem Abs. 93, 209617, (1980). M e t c a l f & Eddy Inc., (ed Sawyer C. N., H. D. W i l d , J r . , and T. C. McMahon). N i t r i f i c a t i o n and D e n i t r i f i c a t i o n F a c i l i t i e s :  Waste Water Treatment, Technol. T r a n s f e r Seminar Publ. USEPA, Washington, D.C, ( 1973). Mona, R., Dunn, L., and J . R. Bourna, " A c t i v a t e d Sludge Process -Dynamics with Continuous T o t a l Organic Carbon and Oxygen Uptake Measurements." B i o t e c h n o l and Bioeng, 21, 1561, (1979) . Monod, J . , Recherces sur l a C r o i s s a n c e des C u l t u r e s B a c t e r i e n n e s , P a r i s , Hermann & C i e , (1942). Nelson, J . K., and B. B. Mishra, " D i g i t a l O n l i n e C l o s e d - l o o p C o n t r o l f o r Wastewater Treatment O p e r a t i o n . " J . Water  P o l l u t . C o n t r o l Fed., 52, 406, (1980). Nelson, P. O. and A. W. Lawrence, " M i c r o b i a l V i a b i l i t y Measure-ments and A c t i v a t e d Sludge K i n e t i c s . " Water Res., 14, 217, (1980) . N e s b i t t , J . B., "Phosphorus Removal - The S t a t e of the A r t . " , J .  Water P o l l u t . C o n t r o l . Fed., 43, 1617, (1969). Neufeld, R. D., "Heavy Metals Induced D e f l o c c u l a t i o n of A c t i v a t e d Sludge." J . Water. P o l l u t . C o n t r o l Fed., 48, (1966). N i c h o l l s , H. A., " F u l l S c a l e Experimentation on the New Johannes-burg Extended A e r a t i o n P l a n t . " Water S.A., 1, 121, (1975). N i c h o l l s , H. A., " A p p l i c a t i o n of the Marais-Ekama A c t i v a t e d Sludge Model to Large P l a n t s . " Wat. S c i . Tech., 14, 581, (1982). Niku, S. and E. D. Schroeder, " F a c t o r s A f f e c t i n g E f f l u e n t V a r i a -b i l i t y From A c t i v a t e d Sludge Processes." Water P o l l u t .  C o n t r o l Fed., 53, 540, (1981). 231 Novak, J . T., R. 0. Mines and J . H. S h e r r a r d , " A c t i v a t e d Sludge Process and E f f l u e n t Standards." Water P o l l u t . C o n t r o l Fed., 54, 1043, (1981). Olsson, G. and J . F. Andrew, "The D i s s o l v e d Oxygen P r o f i l e - A V a l u a b l e Tool f o r C o n t r o l of the A c t i v a t e d Sludge Process." Water Res. 12, 985, (1979). Ortman, C , T. L a i b , and C. S. Z i c k e l f o o s e , TOC, ATP & Res- p i r a t i o n Rate as C o n t r o l Parameters f o r the A c t i v a t e d Sludge  Process., NTIS PB-272-615. EPA 600/2/78-036. (1978). Ouano, E. A., " D i s c u s s i o n of Process S t a b i l i t y of A c t i v a t e d Sludge Process." Proc. Am. Soc. C i v i l Eng., J . Env. Eng.  D i v . , 104, 177, (1978). Ouano, E. A. R., P r i n c i p l e s of Wastewater Treatment, V o l . 1  B i o l o g i c a l P r ocesses. N a t i o n a l Science Development Board. M a n i l l a , P h i l i p p i n e s , (1981). P a i n t e r , H. A., " M i c r o b i a l T ransformations of Inorganics N i t r o -gen." In Prog. Wat. Technol. (ed. Jenkins, S. H.) Pergamon Pr e s s , N.Y., N.Y., (1977). P a i n t e r , H. A.G ,and J . E. L o v e l e s s , " E f f e c t of Temperature and pH Value on the Growth Rate Constants of N i t r i f y i n g B a c t e r i a i n the A c t i v a t e d Sludge Process." Water Res., 17, 237, (1983). P a l l e s e n . L, Berthouex, P. M. and K. Booman, "Environmental I n t e r v e n t i o n A n a l y s i s , Wisconsin's Ban on Phosphate Detergents." Water Research, 19, 353, (1985). Palm, J . C , J e n k i n s , D. and D. S. Parker, " R e l a t i o n s h i p Between Organic Loading, D i s s o l v e d Oxygen Concentration and Sludge S e t t l e a b i l i t y i n the Completely Mixed A c t i v a t e d Sludge P r o c e s s . " J . Water P o l l u t . C o n t r o l Fed., 52, 2417, (1980). Parker, D. S., "Assessment of Secondary C l a r i f i c a t i o n Design Concepts." J . Water P o l l u t . C o n t r o l Fed., 55, 632, (1983). P a t t e r s o n , J . W. , "Sludge A c t i v i t y Parameters and T h e i r A p p l i c a t i o n to T o x i c i t y Measurements i n A c t i v a t e d Sludge." Proc. Purdue I n d u s t r i a l Waste Conf., 24, 127, (1969). Pearse, L., "Bulking of Sludge i n the A c t i v a t e d Sludge Process of Sewage Treatment." American P u b l i c H e a l t h A s s o c i a t i o n , Year  Book, 27, 164, (I937"n Petersack, J . R. and R. G. Smith, Advanced Automatic C o n t r o l  S t r a t e g i e s f o r the A c t i v a t e d Sludge Treatment Process, EPA S e r i e s EPA-670/2-75-039, (1975). P i p e s , W. O. " B u l k i n g , D e f l o c c u l a t i o n , and P i n p o i n t F l o e . " J .  Water P o l l u t . C o n t r o l Fed., 51, 52, (1979). 232 Pitman, A. R., " S e t t l i n g P r o p e r t i e s of Extended A e r a t i o n Sludge." J . Water P o l l u t . C o n t r o l Fed., 52, 524, (1980) Poduska, R. A. and J . K. Andrews, "Dynamics of N i t r i f i c a t i o n i n the A c t i v a t e d Sludge Process." J . Water P o l l u t . C o n t r o l  Fed., 47, 2599, (1975). Rabinowitz, B and G. v. R. Marais, Chemical and B i o l o g i c a l Phos- phorus Removal i n the A c t i v a t e d Sludge Process. Research Report No. W32. Department of C i v i l E n g i n e e r i n g , U n i v e r s i t y of Cape Town, (1980). Rabinowitz, B. and W. K. Oldham, "The Use of Primary Sludge Fermentation i n the Enhanced B i o l o g i c a l Phosphours Removal Process." Proc. I n t ' l Conf. New D i r e c t i o n s and Research i n  Waste Treatment and R e s i d u a l s Management, U n i v e r s i t y oT B r i t i s h Columbia, 1 , 347, (1985). Raina, S., Combined Treatment of L a n d f i l l Leachate and Domestic  Sewage, Master of A p p l i e d Science T h e s i s , Department of C i v i l E n g i n e e r i n g , U n i v e r s i t y of B r i t i s h Columbia (October, 1984) R a l s t o n , D and E. Caicedo, "How Can CE's Improve O & M?", Water  and Wastes Eng., 17, 30, (1980). R a n d a l l , C. W., L. D. B e n e f i e l d , and D. Buth, "The E f f e c t s of Temperature on the Biochemical Reaction Rates of the A c t i -v ated Sludge Process." Water S c i Tech., 14, 413, (1982). Rensink, J . H., "New Approach to Preventing B u l k i n g Sludge." J .  Water P o l l u t . C o n t r o l Fed., 46, 1888, (1974). R i c e , J . K., " A n a l y t i c a l Issues i n Compliance M o n i t o r i n g . " E n v i r o n . S c i . Technology, 14, 1455, (1980). R i c h a r d , M., Hao, 0. and D. J e n k i n s , "Growth K i n e t i c s of S p h a e r o t i l u s S pecies and T h e i r S i g n i f i c a n c e i n A c t i v a t e d Sludge." J . Water P o l l u t . C o n t r o l Fed., 57, 68, (1985). R i c h a r d , M. G., Shimizu, G. P. and D. J e n k i n s , "The Growth Phy-s i o l o g y of the Filamentous Organism Type 021N and i t s S i g n i -f i c a n c e to A c t i v a t e d Sludge B u l k i n g . " J . Water P o l l u t .  C o n t r o l Fed., 57, 1152, (1985). Rittmann, B. E. and W. E. Langeland, "Simultaneous D e n i t r i f i c a -t i o n With N i t r i f i c a t i o n i n Single-Channel O x i d a t i o n D i t c h e s . " Water P o l l u t . C o n t r o l Fed., 57, 300, (1985). Roe, P. C. J r . , and S. K. Bhagat, "Adenosine Triphosphate as a C o n t r o l Parameter f o r the A c t i v a t e d Sludge Process." Water  P o l l u t . C o n t r o l Fed., 54, 244, (1982). 233 R o e s l e r , J.F. (1982) Advances i n Instrumentation and Automation of Wastewater Treatment P l a n t s , In, New Concepts and  P r a c t i c e s In A c t i v a t e d Sludge Process C o n t r o l . Ann Arbour P u b l i s h e r s , Ann Arbour Michigan. Roy, D., A. LeDuy and P. H. Roy, "One-year Survey of ATP and Dynamic Behavior of an A c t i v a t e d Sludge Treatment P l a n t . " Water P o l l . C o n t r o l Fed., 55, 1352, (1982). Ryssov T. and H. N e i l s e n , "Measurement of the I n h i b i t i o n of R e s p i r a t i o n i n A c t i v a t e d Sludge by a M o d i f i e d Determination of the TTC - Dehydrogenese A c t i v i t y . " Water Res. 9, 1179, (1975). S c h a e f f e r , D. J . , K e r s t e r , H. W., Bauer, D. R., Rees, K., and S. McCormick, "Composite Samples Over-estimate Waste Loads." J .  Water P o l l u t . C o n t r o l Fed., 55, 1387, (1983). Schroeder, E. D. and R. C. I r v i n e , "Parameter Choice For Process C o n t r o l . " J . Environ Eng. D i v . , Proc. Am Soc. C i v . Eng., EE2. 217, (1979). Schwinn, D. E. and B. H. Dickson J r . , "Nitrogen and Phosphorus V a r i a t i o n s i n Domestic Wastewater." J . Wat. P o l l u t . C o n t r o l  Fed., 44, 2059, (1972). Sharma, B and R. C. A h l e r t , " N i t r i f i c a t i o n and Nitrogen Removal." Wat. Res., 1 1 , 879, (1977). Shereani, J . K. and P. H. Moreau, S t r a t e g i e s f o r Water Q u a l i t y  M o n i t o r i n g . , Rep. No. 107. Water Resour. Res. I n s t . North C a r o l i n a S t a t e Univ. R a l e i g h N.C., (1975). S h e r r a r d , J . H., "Oxygen Uptake Rate as an A c t i v a t e d Sludge C o n t r o l Parameter." J . Water P o l l u t . C o n t r o l Fed., 52, 2033, (1980). S i e b r i t z , I. P., G. A. Ekama, and G. v. R. Marais, "Excess B i o l o -g i c a l Phosphorus Removal i n the A c t i v a t e d Sludge Process at Warm Temperate Cl i m a t e s . " Proc. Waste Treatment and U t i l i z a - t i o n . (Eds. C. W. Robinson, et a l . ) Pergamon Press, Toronto. V o l . 2 pp 233-251, (1980). S i e b r i t z , I. P., G. A. Ekama, and G. v. R. Marais, "A Parametric Model f o r B i o l o g i c a l Excess Phosphorus Removal." S e l e c t e d  Papers on A c t i v a t e d Sludge Process Research at the U n i v e r - s i t y of Cape Town., (1982). Sezgin, M., J e n k i n s D. and D. S. Parker, "A U n i f i e d Theory of Filamentous A c t i v a t e d Sludge B u l k i n g " . J . Water P o l l u t .  C o n t r o l Fed., 50, 362, (1978). S i l v e r s t e i n , J . and E. D. Schroeder, " C o n t r o l of A c t i v a t e d Sludge S e t t l i n g i n an SBR." Proc. Am. Soc. C i v i l Eng. E n v i r o n . Eng.  Spec. Conf., 238, (1983). 234 Simkins, M. J . and R. A. McLaren, "Consistent B i o l o g i c a l Phos-phate and N i t r a t e Removal i n an A c t i v a t e d Sludge P l a n t . " Prog. Wat. Tech., 1 0 , 433, (1978). S t a l l , T. R. and J . H. Sherrard, " E f f e c t of Wastewater Composi-t i o n and C e l l Residence Time on Phosphorus Removal i n A c t i -vated Sludge." J . Water P o l l u t . C o n t r o l Fed., 4 8 , 307, (1976). Starkey, J . E. and P. R. Karr, " E f f e c t of Low D i s s o l v e d Oxygen Co n c e n t r a t i o n on E f f l u e n t T u r b i d i t y . " J . Water P o l l u t .  C o n t r o l Fed., 5 6 , 837, (1984). Staud, R., and I. J . Kugelman, " O p t i m i z a t i o n and C o n t r o l of the A c t i v a t e d Sludge Treatment Process by Quasi-Continuous O p e r a t i o n : Concept, S t r a t e g y and R e s u l t s . " Proc. of the 37th  Indust. Waste Conf. 1982, Purdue Univ, (Ann Arbor S c i Pub, Ann Arbor, Mich.) 639, (1983). S t e n s e l , H. D., Loehr, R. C , and A. W. Lawrence, " B i o l o g i c a l K i n e t i c s of Suspended Growth D e n i t r i f i c a t i o n . " J . Water  P o l l u t . C o n t r o l Fed., 4 5 , 249, (1973). Stenstrom, M. K. and J . F. Andrews, "Real Time C o n t r o l of the A c t i v a t e d Sludge Process." J . E n v i r o n . Eng. Div., Proc. Am.  Soc. C i v . Eng., 1 0 5 , 245, (1979). Stenstrom, M. K. and R. A. Poduska, "The E f f e c t of D i s s o l v e d Oxygen C o n c e n t r a t i o n on N i t r i f i c a t i o n . " Water Res. , 1 4 , 643, (1980). Stephanopoulos, G. and A. G. F r e d r i c k s o n , " E f f e c t of S p e c i a l In-homogenities on the Co-existance of Competing M i c r o b i a l P o p u l a t i o n s . " B i o t e c h n o l . Bioeng. 21, 1491, (1979). Stephensen, S c a l e I n v e s t i g a t i o n of Computerized C o n t r o l of the  A c t i v a t e d Sludge Process. Report Prepared f o r Canada Mortgage and Housing C o r p o r a t i o n . (Report SCAT-12). (1982). Strom, P. F. and D. J e n k i n s , " I d e n t i f i c a t i o n and S i g n i f i c a n c e of Filamentous Microorganisms i n A c t i v a t e d Sludge." Water  P o l l u t . C o n t r o l Fed., 5 6 , 449, (1984). Stukenburg, J . R., L. C. Rodman, and J . E. Touslee, " A c t i v a t e d Sludge C l a r i f i e r Design Improvements." J . Water P o l l .  C o n t r o l Fed., 5 5 , 803, (1983). Sykes, R. M., A. F. Rozich and T. A. T i e f o r t , " A l g a l and B a c t e r i a l Filamentous B u l k i n g of A c t i v a t e d Sludge." J . Water  P o l l u t . C o n t r o l Fed., 5 1 , 2829, (1979). Sykes, R. M., " L i m i t i n g N u t r i e n t Concept i n A c t i v a t e d Sludge Models." J . Water P o l l . C o n t r o l Fed., 5 3 , 1213, (1981). 235 Sykes, R. M., "Indeterminacy i n M e c h a n i s t i c B i o l o g i c a l Models. J .  Water P o l l u t . C o n t r o l Fed., 56, 209, (1984). Sykes, R. M., "Indeterminacy in M e c h a n i s t i c B i o l o g i c a l Models." J . Water P o l l u t . C o n t r o l Fed., 56, 209, (1984). Tanaka, H., N. Kurano, Se. Ueda, Sa. Ueda, M. Okazaki and Y. Miura, "Model System of B u l k i n g and F l o c u l a t i o n i n Mixed C u l t u r e s of S p h a e r o t i l u s sp. and Pseudomonas sp. f o r D i s s o l v e d Oxygen D e f i c i e n c y and High Loading." Water. Res. 1 9 , 563, (1985). Tomlinson, E. J . , "The Emergence of the B u l k i n g Problem and the Current S i t u a t i o n i n the UK." In: B u l k i n g of A c t i v a t e d  Sludge: P r e v e n t a t i v e and Remedial Methods. B. Chambers and E. J . Tomlinson ( E d s . ) , (1982). Tomlinson, E . J . and B. Chambers, " C o n t r o l S t r a t e g i e s f o r B u l k i n g Sludge." Wat. S c i . Tech. 1 6 , 15, (1984). T u n t o o l a v e s t , M. and C. P. Grady, " E f f e c t of A c t i v a t e d Sludge O p e r a t i o n a l C o n d i t i o n s on Sludge T h i c k e n i n g C h a r a c t e r -i s t i c s . " J . Water P o l l u t . C o n t r o l Fed., 54, 1112, (1982). T y t e c a , D., and E. Nyns, "Design and O p e r a t i o n a l Charts f o r Complete Mixing A c t i v a t e d Sludge Systems." Water Res., 1 3 , 929, (1979). T y t e c a , D. , "Nonlinear Programming Model of Wastewater Treatment P l a n t . " J . E n v i r o n . Eng. Div., Amer. Soc. C i v i l Eng. 1 0 7 , 747, ( 1 9 8 T T ; T y t e c a , D. and Y. Smeers," "Nonlinear Programming Design of Waste-water Treatment P l a n t . " J . E n v i r o n . Eng. D i v . Amer. Soc.  C i v i l Eng., 1 0 7 , 767, (1981). Van B e l l e , G., and J . P. Huges, "Monitoring f o r Water Q u a l i t y : F i x e d S t a t i o n Versus I n t e n s i v e Surveys." J . Water P o l l u t .  C o n t r o l Fed., 55, 400, (1983). Van den Eynde, Geerts, J . , Verachte, H., and B. Maes, "I n f l u e n c e of the Feeding P a t t e r n on the Glucose Metabolism of Anthro- bac t e r sp. and S p h a e r o t i l u s natans, Growing in Chemostat C u l t u r e , S i m u l a t i n g A c t i v a t e d Sludge B u l k i n g . " Europ. J .  A p p l . M i c r o b i o l . B i o t e c h n o l . 1 7 , 35, (1983). Van Haandel, A. C , G. A. Ekama, and G. v. R. Marais, "The A c t i -v ated Sludge Process - 3 S i n g l e Sludge D e n i t r i f i c a t i o n . " Water Res., 1 5 , 1135, (1981). Van Haandel, A.C., P. C. Dold and G v. R. M a r a r i s , "Optimization of N i t r o g e n Removal i n the S i n g l e Sludge A c t i v a t e d Sludge P r o c e s s " . S e l e c t e d Papers on A c t i v a t e d Sludge Process  Research at the U n i v e r s i t y of Cape Town, (1982). 236 V a s i c e k , P. R., "Use of a K i n e t i c Study to Optimize the A c t i v a t e d Sludge Process." J . Water P o l l u t . C o n t r o l Fed., 54, 1174, (1982) . Wagner, F., "Study of the Causes and Prevention of Sludge B u l k i n g in Germany." In: B u l k i n g of A c t i v a t e d Sludge: P r e v e n t a t i v e  and Remedial Methods. B. Chambers and E . J . Tomlinson (Eds), (1982) . Walker, I . and M. Davies, "The R e l a t i o n s h i p Between V i a b i l i t y and R e s p i r a t i o n Rate i n the A c t i v a t e d Sludge Processes." Water.  S c i . Technol., 13, 397, (1977) . Wang, L. K. Poon, C. P. C. and M. H. Wang, " C o n t r o l T e s t s and K i n e t i c s of A c t i v a t e d Sludge Processes." Water, A i r and  S o i l P o l l u t i o n , 8, 315, (1977) . Ward, R. W.., R e l a t i n g Stream Standards to Water Q u a l i t y  M o n i t o r i n g P r a c t i c e s , F i n a l Rep. f o r Nat. S c i . Foundation Grant Number PRA-7913073. Colorado State Univ. F o r t C o l l i n s . Colorado, (1981) . Weber, J . D., H i s t o r i c a l Aspects of the Bayesian Controversy, D i v i s i o n of Economic and Business Research C o l l e g e of Business and P u b l i c A d m i n i s t r a t i o n , U n i v e r s i t y of A r i z o n a , Tucson, (1973) . Weddle, C. L. and D. J e n k i n s , "The V i a b i l i t y and A c t i v i t y of A c t i v a t e d Sludge." Wat. Res., 5, 621, (1971) . W i l l i a m s o n , K. J . and P. 0 . Nelson, "Influence of D i s s o l v e d Oxygen on A c t i v a t e d Sludge V i a b i l i t y . " J . Water P o l l u t .  C o n t r o l Fed., 53, 1456, (1981) . Wilson, T. E. and J . S. Lee, "Comparison of F i n a l C l a r i f i e r Design Techniques." J . Water P o l l u t . C o n t r o l Fed., 54, 1376, (1982) . Wong, P.T. and D.S. Mavi n i c , "Treatment of a M u n i c i p a l Leachate Under M u l t i - V a r i a b l e C o n d i t i o n s " , Water P o l l . Res. Jour.  Canada, 17, 135, (1982) . Wu, Y. C , A r n o l d S. L. and 0 . C. Kun, " E c o l o g i c a l Study S e t t l i n g Property i n the Completely Mixed System." Water  Res., 18, 1535, (1984) . Yeung, S. Y. S., D. S i n c i c and J . E. B a i l e y , "Optimal P e r i o d i c C o n t r o l of A c t i v a t e d Sludge Process: I I . Comparison With Con v e n t i o n a l C o n t r o l For S t r u c t u r e d Sludge K i n e t i c s . " Water  Research, 14, 77, (1980) . Young, J . C , " S p e c i f i c Oxygen Demand as an Operating Parameter f o r A c t i v a t e d Sludge Processes." Water S c i . Technol., 13, 397, (1981) . 237 Z a p f - G i l j e , R. and D.S. Mavinic, "Temperature E f f e c t s on B i o s t a b i l i z a t i o n of Leachate", Proc. Am. Soc. C i v i l Eng., J .  Env. Eng. Div., 107, 653, (1981"T! 238 APPENDIX A DATA PLOTS 239 — L 0000001 S3iu-cj MOHJ i N s n u N i OOd ^ 3 3 d 3 H 3 N 3 d J to Q Q_ CD FRENCH CREEK PCC RETURN ACTIVATED SLUDGE FLON RATES 400000 -360000 -320000 -280000 240000 H ^ 200000 -j c n cn _^ 160000 H o EI? 120000 H 80000 4 40000 -0 -0 1 1 1 1 l r T 183 366 549 732 915 1098 1281 1464 1647 1830 2013 2196 DRYS (beglnnLng J a n u a r y 1, 1979) F R E N C H C R E E K P C C NRSTE A C T I V A T E D S L U D G E F L O N S 140000 - i IO Mi 366 549 732 915 1098 1281 1464 1647 1830 DRYS ( b e g i n n i n g J a n u a r y \, 1979) — I — . 2013 2196 243 FRENCH CREEK PCC INFLUENT - P H 8 . 5 - 1 FRENCH CREEK PCC INFLUENT - TOTAL SUSUPENDED SOLIDS l o o o - i n 8 0 0 -o H 1 1 1 1 1 1 1 1 1 1 1 " 0 1 8 3 3 6 6 5 4 9 7 3 2 9 1 5 1 0 9 8 1 2 8 1 1 4 6 4 1 6 4 7 1 8 3 0 2 0 1 3 2196 DRYS ( b e g i n n i n g J a n u a r y 1, 1979) 247 FRENCH CREEK PCC PRIMARY CLARIFIER BOD 300 250 H o H 1 1 1 1 1 1 i 1 i i 1 ' 0 183 366 549 732 915 1098 1281 1464 1647 1830 2013 2196 D A Y S ( b e g i n n i n g J a n u a r y 1 , 1 9 7 9 ) FRENCH CREEK PCC PRIMARY CLARIFIER - TOTAL SUSPENDED SOLID 400 -i FRENCH CREEK PCC PRIMARY CLARIFIER - VOLATILE SUSPENDED SOLIDS 300 T • • 1 DRYS ( b e g i n n i n g J a n u a r y 1, 1979) I S 3 £92 F/M RRTIO (KG BOD/KG MLVSS*DflY) o o o -4— CO -OJ OJ CO -CD a z o -< cn -b. -CO CD .—. c r \1 CD OJ -cn CSJ r • • CD D c • cn 3 CD , . o ( _ CD • CO D c •—» Q 00 1 1— CC ! , CO ~ CD CO \ ] CD \1 CO OJ o o OJ ro co CD 70 n I D T l CD T J •-3 m o T J \ m _Z 7\ o C J E-» C J CC Q_ cn \/ JZ LxJ \ L J L _ cn C J C M tt C J cn L J t-H QZ O L _ C E L J (AUQxSSAIW 9)1/009 9>l) OUUcJ W/J 254 FRENCH CREEK PCC REACTOR « 1 - LIQUID TEMPERATURE FRENCH CREEK PCC RERCTOR « 2 - LIQUID TEMPERATURE -1 1 1 1 1 1 1 1 1 1 1 f 183 366 549 732 915 1098 1281 1464 1647 1830 2013 2196 DAYS ( b e g i n n i n g J a n u a r y 1, 1979) CJ Q _ \/ LJ LJ cn Q_ CJ L J cn LL_ n c r o E—' C J cn [_J cn smy-A H d 257 FRENCH CREEK PCC REACTOR » 2 - P H 1 1 i 1 1 1—•• 1 1 1 1 1 f 183 366 549 732 915 1098 1281 1464 1647 1830 2013 2196 DRYS ( b e g i n n i n g J a n u a r y 1, 1979) FRENCH CREEK PCC RERCTOR «1 - SLUDGE VOLUME INDEX 1200 - 1 — 1000 -DAYS ( b e g i n n i n g J a n u a r y 1, 1979) FRENCH CREEK PCC REACTOR « 2 - SLUDGE VOLUME INDEX 1200 T ;  1000 H DRYS ( b e g i n n i n g J a n u a r y \, 1979) FRENCH CREEK PCC REACTOR « 1 - SUSPENDED SOLIDS 4000 -i — 3500 \ 3000 -E z 2500 -o t——4 - C O 2000 -o 4 — — i 1 1 1 1 1 1 1 1 1 1 1 0 183 366 549 732 915 1098 1281 1464 1647 1830 2013 2196 DAYS ( b e g i n n i n g J a n u a r y 1 , 1 9 7 9 ) FRENCH CREEK PCC REACTOR » 2 - SUSPENDED SOLIDS 4 0 0 0 - 1 — 3 5 0 0 -\ 3 0 0 0 •CD E ^ 2 5 0 0 -O i—i E— a z x 2 0 0 0 -^ I 1 I 1 1 1 1 I I I f 1 8 3 3 6 6 5 4 9 7 3 2 9 1 5 1 0 9 8 1 2 8 1 1 4 6 4 1 6 4 7 1 8 3 0 2 0 1 3 2196 DRYS ( b e g i n n i n g J a n u a r y 1, 1979) LD CO oo ro o CM o ro CD Ol [\ CD CD T 1 LD T 1 '—1 -— _ L CO ro 0 c CO o • CO ) o CD c in ._) — —« c CO c -_J oo CD - ro CD _Q CO CO - •*ri LO >-> CE o CD LO ro ro CO o ( H / 6 ^ ) N0UUyiN30N00 SSA 263 CO a _ j o CO a L J a C J L J CJ o_ CL_ CO ^ CO L J L J L J C J •z cn C J _ j z o L J > L L _ I C M « o C J cn L J or (1/6^) N0UUdlN30N00 SSA 264 Q CD C J Q Q C J Q _ I M E - H L J L J C J L _ J Z L _ C J L J L J c r c n L _ Z L _ ( 1 / 6 u j ) NOIlUcJINJGNOO Q09 265 992 FRENCH CREEK PCC FINAL EFFLUENT - pH 1 1 '—I 1 1 1 1 1 1 1 1 1 1 0 183 366 549 732 915 1098 1281 1464 1647 1830 2013 2196 DRYS ( b e g i n n i n g J a n u a r y l , 1 9 7 9 ) c o Q i—i o CO Q LxJ o C J C J L J c o L J C O L J c t : i C J oo x n C J ~ZL E — « L J Z Q L " L J L _ Z D L _ L _ L J a z L _ (1/ 6 u j) N0IlricJlN33N0G SS 269 APPENDIX B FREQUENCY CURVES 270 K i t F R E N C H C R E E K P C C X TOTAL BOD REMOVAL CUM. FREQUENCY 100 CUMULATIVE FREQUENCY (X) I a. i 100 90 -80 -70 60 SO 40 -30 F R E N C H C R E E K P C C X AERATION BOD REMOVAL CUM. FREQUENCY 100 CUMULATIVE FREQUENCY (X) 2 7 1 700 600 -300 -400 -300 -200 -100 -FRENCH CREEK PCC INFLUENT BOD CUMULATIVE FREQUENCY 100 ajuuLxnvE FREQUENCY (X) FRENCH CREEK PCC WFUJENT pK CUM. FREQUENCY X a 7.9 -7.B -7.7 -7.6 7 J -7.4 -7 J -7.2 -7.1 -7 -6.9 -SJB 6.7 -6.6 -6 J 6.4 BJ &2 8.1 H 6 i i 20 —r-40 -r-60 — I — 80 I I 100 CUMULATIVE FREQUENCY (*) 272 FRENCH CREEK PCC X TOTAL BOO REMOVAL CUM. FREQUENCY CUMULATIVE FREQUENCY (%) FRENCH CREEK PCC % AERATION BOO REMOVAL CUM. FREQUENCY I I I I I I I I 1 1 1 0 20 40 80 80 100 CUMULATiVE FREQUENCY (X) 273 FRENCH CREEK P C C INFLUENT TEMP CUMULATIVE FREQUENCY 20 i • f I I 1 I I I I I I 0 20 40 60 80 100 CUMULATIVE FREQUENCY (X) FRENCH CREEK P C C PRIMARY EFF. BOD CUMULATIVE FREQUENCY 280 -i 260 -20 H 1 1 -^1 1 1 I I 1 1 0 20 40 60 80 100 CUMULATIVE FREQUENCY (X) 2 7 4 FRENCH CREEK PCC PRIMARY CLARIFIER pH CUM. FREQUENCY X a. 100 400 CUMULATIVE FREQUENCY (X) FRENCH CREEK PCC PRIMARY CLARIFIER TSS CUM. FREQUENCY CUMULATIVE FREQUENCY (X) 275 FRENCH CREEK PCC PRIMARY CLARIFIER VSS CUM. FREQUENCY 1 0 0 CUMULATIVE FREQUENCY (X) FRENCH CREEK PCC AERATION #1 DO CUM. FREQUENCY 100 CUMULATIVE FREQUENCY (X) 276 FRENCH CREEK PCC AERATION #2 OO CUM. FREQUENCY 9 _ 8 -7 H o H 1 1 1 1 1 1 1 1 1 1 O 20 40 80 80 100 CUMULATIVE FREQUENCY (X) FRENCH CREEK PCC AERATION #1 F/M RATIO CUM. FREQUENCY  1 > 5 _ — 1.4 -1.3 -1.2 -20 40 SO 80 100 CUMULATIVE FREQUENCY (X) 277 w 2 o o o o - I E O • t • V 3 te o o « a 2 1.5 1.4 -I J -1.2 -1.1 -1 -0.9 -0.8 -0.7 -0.6 -0.5 -OA -03 -0.2 0.1 H 0 3JS FRENCH CREEK PCC AERATION #2 F/VI RATIO CUM. FREQUENCY —r— 20 — r — 40 T 60 T —T— 80 100 CUMULATIVE FREQUENCY CO FRENCH CREEK PCC AERATION #1 MLSS CUM. FREQUENCY 100 CUMULATIVE FREQUENCY (X) 278 FRENCH CREEK PCC AERATION #2 ULSS CUM. FREQUENCY 13 3 -E 0 I I I I 1 I 1 I I I f 0 20 40 60 80 100 CUMULATIVE FREQUENCY (X) FRENCH CREEK PCC AERATION #1 MLVSS CUM. FREQUENCY 3 . — — 2.8 -2.6 -2.4 -5 2.2 -1 2 -0 20 40 60 80 100 CUMULATIVE FREQUENCY (X) 279 FRENCH CREEK PCC AERATION #2 MLVSS CUM. FREQUENCY 100 CUMULATIVE FREQUENCY (X) FRENCH CREEK PCC AERATION #1 pH CUM. FREQUENCIES 100 CUMULATIVE FREQUENCY CX) 280 FRENCH CREEK PCC AERATION #2 pH CUM. FREQUENCIES 20 - r —r— 4 0 T— 8 0 6 0 1 0 0 CUMULATIVE FREQUENCY (3) FRENCH CREEK PCC AERATION #1 SVI CUM. FREQUENCY 1 0 0 CUMULATtyE FREQUENCY (X) 281 FRENCH CREEK PCC AERATION #2 SVI CUM. FREQUENCY u K I i 100 OJMULATTVE FREQUENCY (X) FRENCH CREEK PCC AERATION #1 TEMPERATURE CUM. FREQUENCY 100 CUMULATIVE FREQUENCY (X) 282 FRENCH CREEK PCC AERATION #2 TEMPERATURE CUM. FREQUENCY 9 t Id K g y. 100 CUMULATIVE FREQUENCY CO FRENCH CREEK P C C FINAL EFF. BOO CUMULATIVE FREQUENCY 100 CUMULATIVE FREQUENCY (X) 283 FRENCH CREEK P C C FINAL EFF. #1 SS CUM. FREQUENCY 110 -] 100 -90 -0 T 1 1 1 1 1 1 1 1 T 0 20 40 60 80 100 CUMULATIVE FREQUENCY (X) FRENCH CREEK P C C FINAL EFF. #2 SS CUM. FREQUENCY 110 -t 100 -90 -0 -+• 1 1 1 I 1 1 I I 1 0 20 40 60 80 100 CUMULATIVE FREQUENCY (X) 284 FRENCH CREEK P C C EFFLUENT TEMP CUMULATIVE FREQUENCY 0 2 0 4 0 6 0 8 0 1 0 0 CUMULATIVE FREQUENCY (X) FRENCH CREEK P C C INFLUENT FLOW CUMULATIVE FREQUENCY 9 0 0 -i 1 3 0 0 -2 0 0 -1 0 0 - J 1 1 r — i 1 1 1 1 1 1 0 2 0 4 0 6 0 8 0 1 0 0 CUMULATIVE FREQUENCY 285 FRENCH CREEK PCC RETURN FLOW CUMULATIVE FREQUENCY a o • on £3 1 0 0 CUMULATIVE FREQUENCY u £3 7 0 ao -5 0 -4 0 -3 0 2 0 -1 0 -FRENCH CREEK P C C WASTE FLOW CUMULATIVE FREQUENCY 1 0 0 CUMULATIVE FREQUENCY 286 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
https://iiif.library.ubc.ca/presentation/dsp.831.1-0062699/manifest

Comment

Related Items