10. CONCLUSIONS AND FUTURE RESEARCH
10.1 Future Research
everal potential research areas in process modeling and design were investigated during the development and utilization the optimization model. However, there are other areas that deserve future investigation. Two main directions can be identi fied.
The first is related to model development and the second is about utilizing the model for various purposes.
Concerning the first direction, several areas need further investigations. These include:
1 - Perfo rmance models of various unit operations still need more refinements.
Models that describe c larification/thickening behavior of settling tanks are very important while more investigations still required. Development of models that account for more design conditions and realistically describe such performance is a crucial requirement. The best option ·would be to develop speci fic purpose models when a certain problem is being addressed.
2- Cost funct ions are great sources of uncertainty in such type of problems.
Development of cost functions for UAE would reduce such uncertainty significantly.
3- The developed model can be extended to include other types of reactors, flow regim es, and activated sludge process variations. Reactors with mechanical aeration and plug flow pattern can be imbedded in the model with minimum modifications.
1 60
4- i mpiementing denitrificat ion, which is mitted in this study, is also a possible extension. In this regard, anoxic conditions should be assumed in the aeration tank. Phosphoru removal also can be added. A M2 model incorporates denitrificat i n and phosphorus r mo al and can be used for such a purpose.
Concerning the second direct ion, several studies and research can be conducted utilizing the developed model. These include:
1 - L ensit i ity analysis where information on the effect of a particular parameter in the model on the overall system design is useful for system design and an.alysis. Example o f such studies are given in thjs work that can be extended to cover all parameters in the model. Potential research areas can be identified where the system is very sensitive to a particular parameter.
2- Rel iability and uncertainty analysis using the system developed can be evaluated. Valuable information can be obtained when uncertainty of parameters is imp lemented. This information helps to establish guidelines for practical system design. A simple example o f implementing parameters uncertainty is given in this study. Such can be extended to couple a more comprehensive uncertainty analysis tool like Monte Carlo simulation to the developed model. Results of such coupling should produce a design that is more reliable.
The developed model can be appl ied on realistic situations. These include newly designed and operated wastewater treatment systems. A possible option is to apply the model on o ne o f the treatment plants operating in the UAE. I n such a case, performance models should be verified and design parameters should be determined through experimental procedures and field measurements. Such a study could reach a valuable design and operation recommendations.
1 . kya, L., C. Kina i, and M. Karpuzcu ( 1 993), " A Model for Optimum Design of Act ivated ludge Plants , Water Re . , 27, 9, pp. 1 461- 1 468.
2 . mano, K., K. Kageyama, S . Watanabe, T. Takemoto (2002), "Calibration of Model Constants in a B io logical Reaction Model for Sewage Treatment Plants", Wcuer Res. , 3 6, pp. 1 025- 1 033.
3. Argaman, Y. ( 1 995) "A Steady-State Model for the Single S ludge Activated ludge System-I . Model Description . Water Res. , 29, 1 , pp. 1 3 7- 1 45.
4. Argaman, Y., and G. Papkov ( 1 995), "A Steady-State Model for the S ingle Sludge Activated S ludge System- I I . Model Application". Water Res. , 29, 1 , pp. 1 47- 1 53 5 . Asfari. A. ( 2000), Fundamentals o
/
Sewage Facilities Design, 1 sl ed., ArabicScientific Organization, Tunis (In Arabic).
6. Ayesa, E., B . Goya, A. Larrea, L. Larrea, and A. Rivas ( 1 998), "Selection of Operational Strategies in Activated Sludge Processes Based on Optimization A lgorithms", Water Sci. Techno!. , 3 7, 1 2, pp.327-334.
7. Barker, P.S. and P.L. Dold ( 1 997a), "General Model for Biological Nutrient Removal Activated-Sludge Systems: Model Presentation", Water Environment Research, 69, 5, pp. 969-984.
8. Barker, P.S. and P.L. Dold ( 1 997b), "General Model for B iological Nutrient Removal Activated-S ludge Systems: Model Application", Water Environment Research, 69, 5, pp. 985-99 1 .
9. Benefield, L. D. and C. W. Randall ( 1 980), Biological Process Design/or Wastewater Treatment, Prentice-Hall I nc., Englewood Cliffs, NJ.
1 0. Bischof, F., M. Hoiken, and F. Durst ( 1 996), "Design and Construction of Aeration Systems for Optimum Operation of Large Wastewater Treatment P lants", Water Sci. Technol., 33, 1 2, pp. 1 89.
1 1 . B rooke, A., D. Kendrick, A. Meeraus, and R. Raman ( 1 998), GAMS A User 's Guide, GAMS Development Corporation, Washington.
1 2. Carlsson, B. ( 1 998), An Introduction to Sedimentation Theory in Wastewater Treatment, Report, Systems and Control Group, Uppsala University.
1 6 1
1 62
1 3 . 'ha huat, B . . Roche, and M. . Lat ifi (200 1 ), "Dynamic Opti.rpjzati n of mall lZe a tewater Treatment Plants I ncluding itrification and Denitrification Proces ,. Computers and ChemicaL Engineering, 25, pp. 5 85-593 .
1 4. Chapman, D. T. ( 1 983), "The Influence of Proces Variables on Secondary larificat ion," 1. Water Pollution Control Federation, 55, 1 2, pp. 1 425- 1 434.
1 5 . hatell ier, P., and 1. M . Audic (2000), "A New Model for Wastewater Treatment Plant Clarifier Simulat ion" , Water Res. , 34, 2, pp. 690-693.
1 6. Cho ., F. Colin, M. ardin, and C. Prost ( 1 993), "Settling Velocity Model of cti ated ludge' , Water Re . , 27, 7, pp. 1 23 7- 1 242.
1 7. Cho, ., H. Chang, and C. Prost ( 1 996), .. teady tate Analysis of the Coupling Aerator and Secondary Settling Tank in Activated Sludge Process", Water Res. , 30, ] 1 , pp. 260 1 -2608.
1 8. C hristoulas, D.G., P . H . Yannakopoulos, and AD. Andreadakis ( 1 998), "An Empirical Model for Primary Sedimentation of Sewage", Environment International, 24, 8, pp. 925-934.
1 9. Columbo J., and 1. Nelson ( 1 994), "Processing Biosolids for Market Value", Environ. Prot., 5, 9, pp. 24.
20. de Melo, 1.1., and AS. Camara ( 1 994), "Models for the Optimization of Regional Wastewater Treatment System" Euro. 1. Oper. Research, 73, 1 .
2 1 . DeGarmo, E., W. Sullivan, 1. Bontadelli, and E. Wicks ( 1 997), Engineering Economy, 1 0th ed., Prentice-Hall I nternational, New Jersy.
22. D iehl S., and U. Jeppsson ( 1 998), "A Model of the Settler Coupled to the B io logical Reactor", Water Res. , 32, 2, pp. 33 1 -342.
23. Doby, T.A, D.H . Loughlin, J.J. Ducoste, and F.L. de Los Reyes I I I (2002),
"Optimization of Activated S ludge Designs Using Genetic Algorithms", Water Sci. Technol, 45 6 pp. 1 87- 1 98
24. Droste, R. L. ( 1 997), Theory and Practice o/ Water and Wastewater Treatment, John Wiley & Sons, New York.
2 5 . Dun.n, 1 . 1., E. Heinzle, J. I ngham, and 1. Prenosil ( 1 992), Biological Reaction Engineering, VCH, Weinheim.
26. Dupont, R. and C. Dahl ( 1 995), "A One-Dimensional Model for a Secondary Settling Tank I nc luding Density Current and Short Circuiting", Water Sci.
Technol, 3 1 , 2, pp. 2 1 5-224.
27. Dup nt, R. and M . Henze ( 1 992), "Modelling of the econdary Clarifier
ornbined with the Act ivated ludge Model o. l ' , Water Sci. Technol, 25. 6, pp.
285-300.
28. Eche erria, R., A. Seco, and 1. Ferrer ( 1 993), "Control of Activated ludge ettleabi lity Using Preaeration and Preprecipitat ion", Water Res. , 27, 2, pp. 293- 296.
29. Eckenfelder, W. W. (2000) Industrial Water Pollution Control, 3rd ed., McGraw
H il l I nc., Boston.
30. En ironrnental Protection Agency ( 1 980), Construction Costs for Municipal Wa tewater Treatment Plants: J 973- J 978, l:<,PA report 430/9-80-003, Washington.
D.C.
3 1 . Fels, M .. 1. Pinter, and D. Lycon ( 1 997), "Optimized Design of Wastewater Treatment Systems: Application to the Mechanical Pulp and Paper Industry: I . Design and Cost Relationships", The Canadian Journal of Chemical Engineering, 75, pp. 437-45 I .
3 2 . Fuj iwara, O. ( 1 990), "Preliminary Optimal Design Model for Wastewater Treatment Plant", Journal of Environmental Engineering, 1 1 6, 1 , pp. 206-2 1 0.
3 3 . Gemaey, K., P.A. Vamolleghem, and P. Lessard (200 1 ), "Modeling o f a Reactive Primary Clarifier", Water Sci. Technol, 43, 7, pp. 73-8 1 .
34. Giokas, D., Y . Kim, P. Paraskevas, E. Paleologos, and T. Lekkas (2002 ) "A S imple E mpirical Model for Activated Sludge Thickening in Secondary C larifiers " Wafer Res. , 36 1 3, pp. 3245-3252.
3 5 . Gomez-Quintero, G., I. Queinnec, and 1.P. Babary ( 1 999), A Reduced Nonlinear Model of A n Activated Sludge Process, LAAS-CN RS, France.
36. Grady, c.P.L., G. Daigger, and H. Lim ( 1 999), Biological Wastewater Treatment, 2nd ed., Marcel Dekker Inc., New York.
37. Grijspeerdt, K., P. Vanrolleghem, W. Verstraete ( 1 995), "Selection of One
Dimensional Sedimentation: Models for On-Line Use" , Water Science and Technology, 3 1 , 2, pp. 1 93-204.
3 8 . Gujer, W., M . Henze, T. M ino, and M. van Loosdrecht ( 1 999), "Activated Sludge Model No. 3", Water Sci. Technol, 39, 1 , pp. 1 83- 1 93 .
3 9 . H enze, M., C . P. Leslie Grady Jr. W . Gujer, G . Marais, and T . Matsuo ( 1 987), "A General Model for S ingle-Sludge Wastewater Treatment Systems", Water Res. , 2 1 , 5, pp. 505-5 1 5.
1 64
40. Henze, M., P. I Iarr rno s, J. Jan en, and E rvin (2002), Wastewater Treatment:
Biological and Chemical Processes, 3rd ed., pringer. Berlin.
4 l . Henze, M., W. Gujer, T. Mino, and M. an Loo drecht (2000), Activated Sludge Model A 'Ml, Al.. 'M2, A 'M2d, and ASM3. ( T WA Scientific and Technical Report No. 3 . ) London: I WA.
42. Henze M., W. Gujer, T. Mino, T. Matsuo, M. . Wentzel, and G. Marais ( 1 995), Activated Sludge Model No. 2. (I WA Scientific and Technical Report No. 3 . ) London: I W A.
43. Hennanowicz, S. W. ( 1 998), ,. econdary Clarification of Activated Sludge:
De elopment of Operating Diagrams", Water Environ. Research, 70, 1 0.
44. I nfanger G. ( 1 997), DECIS User 's Guide, Dr. Gred I n fanger, 1 590 Escondido Way, Belmont, CA 94002.
45. Jannssen, M . , L.N. Hopkins, B . Petersen, and P.A. Vanrol leghem ( 2000),
" Reduction of an Activated Sludge Process Model to Facilitate Controller Tuning", in: R. Van Langeghem (Ed.) Proceddings of the 1 4th European Simulation Multi-coriference, Society for Computer Simulation I nternational ( SCS) pp. 697-70 1 .
46. Jeppsson, U. ( 1 996), Modeling Aspects of Wastewater Treatment Processes, PhD Thesis, Lund I nstitute of Techno logy, Lund, Sweden.
47. Kabouris, J.C. ( 1 996), "Modeling, I nstrumentation, Automation, and Optimization of Wastewater Treatment Facilities", Water Environment Research, 68, 4, pp. 520.
48. Kabouris, J.C. ( 1 997), "Modeling I nstrumentation, Automation, and Optimization of Wastewater Treatment Facilities", Water Environment Research, 69, 4, pp. 562.
49. Kabouris, J.C. ( 1 998), "Modeling, Instrumentation, Automation, and Optimization of Wastewater Treatment Facilit ies", Water Environment Research, 70, 4, pp. 590.
50. Kabouris J.e. ( 1 999), "Modeling, I nstrumentation, Automation, and Optimization of Wastewater Treatment Facilities " Water Environment Research 7 1 , 5, pp. 729.
5 1 . Koch, G . , M . Ktihni, and H . Siegrist ( 200 1 ), "Calibration and Validation of an ASM3-Based Steady-State Model for Activated Sludge Systems-Part I : Prediction of N itrogen Removal and Sludge Production" Water Res. , 35, 9, pp. 223 5-2245.
52. Krebs, P., D. V ischer, and W. Gujer ( 1 995), ''Inlet-Structure Design for Final Clarifiers", J Environ. Eng. , 1 2 1 , 8, pp. 558-564.
5 3 . Kurata, G., K. Tsumura, S. Nakamura, M. Kuwahara, A. Sato, and T. Kanaya ( 1 996), "Retrofit of Biological Nutrient Removal Process Assisted by Numerical
imulation with Acti ated ludge lode] o. 2", Wafer Sci. Technol., 34, 1 -2, pp.
22 l .
54. Lee, TT., F. Y. Wang, and R.B. ewell (2002) "Robust Model-Order Reduction of omplex B io logical Proce se ", Journal of Process Control, 1 2, 7, pp. 807- 82 1 .
5 5 . Lessard, P. and B. Beck ( 1 988), "Dynamic Modeling of Primary Sedimentation", .! Env. Eng. , 1 1 4, 4, pp. 753-769.
56. Matko, T, N. Fawcett, A Sharp and T. Stephenson ( 1 996b), "Recent Progress in the Numerical Modeling of Wastewater Sedimentation Tanks," Trans JchemE, 74, pp. 245-258.
5 7. Mays, L., and Y. Tung ( 1 992), Hydrosystems Engineering and Management, 1 st ed., McGraw-Hill, New York.
5 8 . Metcalf and Eddy ( 1 99 1 ), Wastewater Engineering: Treatment, Disposal, and Reu e, 3 rd ed., G. Tchobanoglous and F. L. Burton, eds., Tata McGraw-Hill, New Delhi, I ndia.
59. M i l ler, 1 . , and M. M iller ( 1 999), John E. Freund 's Mathematical Statistics, 6th ed., Prentice Hall I nternational, New Jersy.
60. Novak, 1.T ( 1 997), "The E ffect of Nitrification on Activated Sludge Settling Properties" Proc. Water Environ. Fed. 70th Annu. Con! Exposition, Chicago, I I I .
1 pp. 3 77.
6 l . Padukone, N., and G. Andrews ( 1 989), "A S imple, Conceptual Mathematical Model for t he Activated Sludge Process and its Variants ', Water Res. , 23, 1 2, pp.
1 53 5- 1 545.
62. Petrides, D., R. Cruz, and 1. Calandranis ( 1 998), "Optimization of Wastewater Treatment Fac i l it ies Using Process S imulation", Computers chem. Engng, 22, Suppl.. S339.
63 . P incince, AB., B .G. Braley, K. H . Sangrey, and R . D. Reardom ( 1 997),
"Minimizing Cost of Activated S ludge Systems", Water Environ. Research, 69, 3, pp. 3 26-3 30.
64. P incince, A B . et al. ( 1 995) "Minimizing Costs of Activated S ludge Systems:
Apl ication to Deer I sland Treatment Plant", Proc. 68th A nnu Con! Water Environ. Fed. , M iami Beach, FL, 1 , 693 .
1 66
65. Pipes, W., and Y . Kim ( 1 996), " Discus ion f: � implc Empirical Model for H indered ettling in ct i ated ludge Clarifier, . Roche, 1. Vaxelaire, C. Prost.
67, 5, pp. 775 ( 1 995 )", Water Environment Re 'earch, 68, 1 , pp. 1 23 .
66. Potter, T.G. , c . c . T eng, and B. Koopman ( 1 998), ''Nitrogen Removal in a Partial itrificat ion/CompJete Denitrificat ion Process" Water Environ. Research, 70 pp.
334.
67. Queinnec, I ., and D. Dochain (200 1 ), " Modell ing and Simulation of the teady�
tate of econdar ett lers in Wastewater Treatment Plants' , Water Science and Technology, 43, 7, pp. 39-46.
68. Rensink, J.H., and W. H. Rulkens ( 1 997), "Using Metazoa to Reduce Sludge Production", Water Sci. Technol., 36, 1 1 , pp. 1 7 1 .
69. Reyno lds, T. D. and P.A. Richards ( 1 996), Unit Operations and Processes in Environmental Engineering, PWS Publishing, Boston.
70. R ivas, A, E. Ayesa, A. Galarza, and A Salterain (200 1 ), "Application of Mathematical Tools to I mprove the Design and Operation of Activated Sludge P lants. Case Study: The New WWTP of Galindo-Bilbao Part I : Optimum Design", Water Sci. Techno!. 43, 7, pp. 1 57.
7 1 . Roche, N . , 1. Vaxelaire, and C. Prost ( 1 995), "A Simple Empirical Model for hindered Settling in Activated Sludge C larifier", Water Environment Research, 67, 5, pp. 775�780.
72. Rousseau, D., F. Verdonck O. Moerman, R. Carrette, C. Thoeye 1. Meirlaen, and P.A. VamolJeghem (200 1 ), "Development of a R isk Assessment Based Technique for Design/Retrofitting of WWTPs". Water Science and Technology, 43, 7, pp.
287�294.
73 . Samuelsson, P., M. Ekman, and B. Carlsson (200 1 ) "A J ava Based S imulator of Act ivated S ludge Processes ', Mathematics and Computer in Simulation, 56 pp.
3 3 3�346.
74. Scuras, S.E., A Jobbagy, and c.P. Leslie Grady (200 1 ), "Optimization of
Activated S ludge Reactor Configurat ion: Kinetic Considerations" Water Res. , 35, 1 8, pp. 4277-4284.
75. Steffens, M. A, P. A Lant, and R. B. Newell ( 1 997) "A systematic approach for reducing complex bio logical wastewater treatment models" Water Res. 3 1 , 3, pp.
590-606.
76. uidan LT. F. aunders, C. G dfrey, and H . tewart ( 1 983), "Wastewater Treatment : ensit ivity nalysis", Journal of Environmental Engineering, 1 09, 1 , pp. 1 20- 1 3 8.
77. Takacs, 1 . , G. Patry, and D. olasco ( 1 99 1 ), 'A Dynamic Model of the lari ficat ion-Thickening Process", Water Res. 25, 1 0, pp. 1 263- 1 27 1 . 78. Tang, c., E. D. Brill Jr .. and 1. Pfeffer ( 1 984) Mathematical Models and
Optimization Techniques for Use in A nalysis and Design of Wastewater Treatment System , Re earch Report No. 1 94, Water Resources Center, University of I llinois.
79. Tang c., E. D. Brill Jr., and 1. Pfeffer ( 1 987a). "Comprehensive Model of Acti ated S ludge Wastewater Treatment System", Journal of Environmental Engineering, 1 1 3, 5, pp. 952-969.
80. Tang, ., E. D. Brill Jr. , and 1. Pfeffer ( 1 987b), "Optimizat ion Techniques for econdary Wastewater Treatment System", Journal of Environmental
Engineering, 1 1 3 , 5, pp. 935-95 l .
8 l . Tench, H . B. ( 1 994), "A Theory of the Operation of Full Scale Activated S ludge P lants", Water Res. , 28, pp. 1 0 1 9.
82. Truax, D . D . ( 1 994), "Wastewater Treatment Plant Optimization and Automation' , Water Environment Research, 66, 4, pp. 3 8 3 .
8 3 . Truax, D.D. ( 1 995), "Optim ization, Modeling, and Automation of Wastewater Treatment Fac i l it ies", Water Environment Research, 67, 4, pp. 499.
84. Tyteca, D. ( 1 985), Mathematical Modelsfor Cost-Effective Biological Wastewater Treatment, in Mathematical Models in Biological Waste water Treatment, S . E . Jorgensen and M . 1 . Grorniec, eds., E lsevier Science Publishers, Amsterdam.
85 . U . S . Department of the Army Corps of Engineers ( 1 987), Evaluation Criteria Guide for Water Pollution Prevention, Control, and A batement Programs, Technical Manual TM 5-8 1 4-8, Washington, D.C.
86. Ueberl, 1 . , and W.H. Hager (1 997), "I mproved Design of Final Settling Tanks" J Environ. Eng. 1 23, pp. 259.
87. Vanderhasselt, A., and P. Vanrolleghem ( 1 999), "Estimation of S ludge
Sedimentation Parameters from S ingle Batch Settling Curves", Water Res., 34, 2, pp. 395-406.
88. Vanro lleghem, P. A., U. Jeppsson, 1. Carstensen, B. Caslsson, and G. Olsson ( 1 996), "Integration of Wastewater Treatment Plant Design and Operation - A
, y tcmatic pproach mg 0 t Functions", Waf. Sci. Tech. , 34, 3-4, pp. 1 59- 1 7 1 .
89. Voutchko . ( 1 992), "Relat ion hip for Clarification Efficiency of Circular econdary Clarifiers" , Waf. Sci. Tech. , 26, 9, pp. 2539-2542.
90. Voutchkov ., and P.F. Boulos ( 1 993), " Heuristic Screening Methodology for Regional Waste\! ater-treatment Planning", J. Environ. Eng. , 1 1 9, pp. 603 . 9 1 . Water En ironment Federation and ASCE ( 1 992), Design oj Municipal
Waste-water Treatment Plant , vo l. 1 and 2, WEF, Alexandria, VA.
92. Watts, R. W., S. A. Svoronos, and B. Koopman ( 1 996), "One-Dimensional Modeling of econdary C lari fiers Using a Concentration and Feed Velocity
Dependent Dispersion Coefficient", Water Res., 30, 9, pp. 2 1 1 2-2 1 24.
1 68
93 . Wentzel. M.e., and G.A. Ekama ( 1 997), "Principles in t he Design of Single
ludge Activated-Sludge Sy terns for B io logecal Removal of Carbon, Nitrogen, and Phosphorus", Wafer Environment Research, 69, 7, pp. 1 222- 1 23 1 .
94. Wett, B. (2002), "A Straight I nterpretation of the Solids Flux Theory for a Three
La er edimentation Model", Water Res. , 36, pp. 2949-2958.
95. Wright, D. G., and D . R. Woods ( 1 993), "Evaluation of Capital Cost Data. Part 7 : Liquid Waste Disposal with Emphasis on Physical Treatment", The Canadian Journal o.fChemical Engineering, 7 1 pp. 575-590.
96. Wright, D. G., and D. R. Woods ( 1 994), "Evaluation of Capital Cost Data. Part 8:
Liquid Waste Disposal with Emphasis on B io logical Treatment", The Canadian Journal ojChemical Engineering, 72, pp. 342-35 l .
97. Yuan, Z. , H. Bogaert G. Vansteenkiste, and W. Verstraete, ( 1 998) "Sludge Storage for Countering N itrogen Shock Loads and Toxicity I nc idents" Water Sci.
Techno!., 3 7, 1 2, pp. 1 73.
98. Yuan, Z., P.A. VanroUeghem, and G.C. Vansteenkiste ( 1 997), "Modeling Error Ident ification of Activated Sludge Models", Water Science and Technology, 36, 5, pp. 8 1 -88.
99. Zhao, H., S.H. I saacs, H. Soeberg, and M. Kummel ( 1 994) "A Novel Control Strategy for I mproved N itrogen Removal in an Alternating Activated Sludge Process - Part I ", Water Res. , 28, 3, pp. 52 1 -534.
L ist of GAMS I n p u t F i le
$ T � le Opt �m� z a t i o n of Ac �vated S l udge Model ( AS M , SEQ= 6 B ) S O n t e x t
2 4 / 4 / 2 0 0 3
up 1: im i z i ng a s y :; tem � Il c l udes p r i rr,a r y c l a r i f i e r and act i va te d s l udge p roce s s . T h e a c t i v a t e d s l udge i s modeled ba sed o n the a mode l de r i ve d f rom t he recent ASM 3 model which was p roposed b y I WA � n 1 9 9 9
S O f f t e x t
$ O f f l i s b n g
* S o n s ym x r e f
* S o n s ym l i s t P a r ame t e r S c a l a r
U l , 0 2 , U 3 ;
* I n f l ue n t cha r a c t e r i s t i c s
F l o w r a t e ( m 3 pe r hou r ) / 1 5 0 0 /
I n e r t s o l u b l e o r g a n � c mat t e r ( mg p e r L a s COD ) / 3 2 /
R e a d i l y b i od e g r a d a b l e sub s t r a t e ( m g p e r L a s COD) / 1 6 1 / Ammo n i UIll p l u s Amm o n i a n i t rogen ( mg p e r L a s N ) / 2 5 /
N L t r a t e p l u s n i t r i t e n i t rogen ( mg p e r L a s N ) / 0 /
I ne r t pa r t i cu l a t e o r g a n i c m a t t e r ( mg pe r L a s COD) / 9 2 / S l o w l y b i odeg r a d a b l e s ub s t r a t e ( mg p e r L a s COD ) / 2 1 4 / H e t e r o t rophic o r g a n i sms ( mg p e r L a s COD ) / 0 / Ql
S l 1 S S I S N H I S N O I X I l X S I X H I XSTOl XAI X S S I
A c e l l i n t e r n a l s t o r a g e product o f hectographs ( mg p e r L as COD ) / 0 / N l t r � f y i ng o r g a n i sms ( mg p e r L a s COD) / 0 /
S u s pended s o l i ds ( mg p e r L a s S S ) / 2 3 0 /
• P a r amet e r s f o r s e d i me n t a t i o n mode l s
a b c
cons t a n t � n C h r l s t o u l a s Mode l / 1 . 1 1 / cons t a n t i n C h r i s t o u l a s Mode l ( mg p e r L ) con s t a n t i n C h r i s t ou l a s Model ( da y p e r m )
/ 2 6 1 /
/ 0 . 0 0 3 5 /
k s e t t l i ng co n s t a n t of p r ima r y s l udge (m p e r day ) / 4 0 0 / n s e t t l i ng co n s t a n t of p r i m a r y s l udge / 2 . 3 /
kw s e t t l lng c o n s t a n t o f f i n a l c l a r i f i e r ( m p e r da y ) / 3 8 5 / nw s e t t l i ng c o n s t a n t o f f i n a l c l a r i f i e r / l . B /
S V I S l udge vo l UIlle i n d e x (ml p e r g ) / 1 5 0 /
H S i d e w a t e r depth o f f i n a l s e t t l e r ( m ) / 3 . 7 / ;
* K i n e t i c p a r a me t e r s i n ASM 3
s c a l a r
kH H y d ro l y s i s r a t e con s t ant / 3 / Kx H yd r o l ys i s s a t u r a t ion co n s t a n t / 1 / k S TO S t o r a g e r a t e cons t a n t / 5 /
Ks S a t u r a t i on cons t a n t f o r s ub s t ra t e / 2 / k kSTO S a t u r a t i o n c o n s t a n t f o r X S TO / 1 /
mH H e t e rot roph i c max . g r o w t h r a t e o f X H / 2 / KNH S a t u r a t i o n cons t a n t f o r ammo n i UIll / 0 . 0 1 /
bH Ae r o b i c e n dogenous r e s p � r a t i o n r a t e o f X H / 0 . 2 / b S TO Ae r o b i c r e s p � r a t i o n r a t e f o r X S TO / 0 . 2 /
rnA Aut o t r op h i c max . g r o w t h r a t e o f XA / 1 / KA Ammon � um sub s t r a t e s a t u r a t i o n f o r X A / 1 /
1 69
1 70
Aerob � r endogenous respi r a t �on r a t e of XA / 0 . 1 5 / ;
S ca l a r
• S � I � h lome r I C p a r ame e r s
1 0 Fr a c t i on o f b i oma s s con t r i bu t i ng t o b i oma s s deb r i s (mg deb r i s COD per mg bi oma s s COD) / 0 . 2 /
Y H Ae rob l c y i e l d o f h e t e rot roph i c b i oma s s (mg C O D per m g COD ) / 0 . 6 3 / YA Y i e l d o f a u t o t roph i c b i om s s (mg COD p e r mg COD) / 0 . 2 4 /
, O t he r p a rame t e r s
ne A I RU A I R L
SCOD T S S S N H
C R F B C I C I
E f f i c iency depends o n d i f f u s e r a nd dep t h a t W h I C h a i r pumped / 1 0 / M I n imum a I r � nput r a t e m 3 p e r m i n t imes 1 0 0 0m 3 / 9 0 /
M I n i mum a � r i nput r a t e m 3 per m i n t imes 1 0 00m3 / 2 0 /
S o l u b l e deg r a da b l e COD r e s t r i c t i on i n t he e f f l ue n t ( g p e r m " 3 ) 1 2 1 To t a l s u spended s o l i d s re s t r i c t i o n i n t h e e f f l ue n t ( g pe r m " 3 ) / 1 0 1 Ammo n i a n i t rogen i n t h e e f f l ue n t ( g pe r m " 3 ) / 1.0 1
Ca p i t a l Recovery f a c t o r / 0 . 0 9 4 4 / B a s e ( 1 9 7 1 ) C o s t I ndex / 1 5 8 1 1 C o s t I ndex f o r 2 0 0 3 1 6 5 8 1 /
OMW Ope r a t i n g M a i n t ena nce wages ( $ p e r h r ) / 8 . 3 / E C E l ec t i r i cit y Cos t ( $ per kW h r ) / 0 . 0 5 / P H PumpIng Head ( me t e r s ) / 1 0 . 0 /
P E Pump i ng E f f i c iency / 0 . 6 / ;
U l C R F * C I / B C I ; U 2 C I / BC I ;
u 3 E C * 2 3 . 8 5 * PH / P E ; Free V a r I a b l e s
, S t a t e v a r i a b l e s
Q 2 m 3 p e r hou r Q 5 m 3 p e r hou r Q 8 m 3 p e r hour S S 3 9 p e r m 3 S N H 3 g p e r m 3 S N 0 3 g p e r m 3 X I 3 k g p e r m 3 X S 3 k g p e r m 3 X R 3 k g p e r m 3 XA3 kg p e r m 3 X S S 3 kg per m3 X S S 8 k g p e r m 3 X S T03 9 p e r m3 , Other v a r i a b l e s
q Ap X l
SRT HRT
V r w
o ve r f l ow r a t e o f p r ima r y s e t t l i ng t a n k (m per d a y ) s u r face a re a o f t he p r ima r y c l a r i f I e r ( 1 0 0m" 2 ) X S S 2 d i v i ded by X S S I
s l udge r e t e n t ion t i me ( da y s ) h y d ra u l i c r e t e n t i o n t ime ( da y s )
v o l ume o f t h e a e r a t i o n t a n k ( 1 0 0 0m " 3 )
s l udge r e c yc l e r a t i o w h i c h i s t h e r a t i o o f Q 6 t o Q2 1 0 0 * wa s t a g e r a t i o w h i ch i s the r a t i o of Q7 to Q2
A f s u r f a ce a r e a o f t he f i n a l c l a r i f i e r ( 1 0 0 m " 2 ) S R ove r f l ow r a t e o f f i n a l c l a r i f i e r ( m p e r da y )
ROH Oxygen Requ i r ement for remova l of o r g a n I C m a t t e r ( kg per d a y ) ROA Oxygen ReqU I reme n t a s s o c I a t e d w i t h n i t r i f l ca t i o n ( k g per da y ) AFR Air f low rate ( m * * 3 a i r p e r m i n )
x 2 1 0 0 * XS S 4 d i v i de d b y X S S 3 X 3 X S S S d i v i ded b y X S S 3
* C o s t f u n c t i o n v a r i a b l e s
C C P S T , COPST , CMPST, CSPST
CCPSP, COPS P , CM P S P , CSPSP, C P P S P CCAT , CCDAA , CODAA , CMDAA
C C F S T , COFST , CHFS T , C SFST
C CRS P , CORSP , CMRS P , CSRS P , C PRSP c o s co s t funct lon ( do l l a rs ) ;
Equ a t l o n s
C 1 , C2 , C 3 , C 4 , C 5 , C 6 , C 7 , ca, C9, C I O , C l l , C 1 2 , C 1 3 , C 1 4 , C 1 5 C 1 - , C 1 7 , C I S , C 1 9 , C 2 0 , C2 1 , C 2 2 , C2 J , C 2 4 , C 2 5 , C 2 6 , C 2 7 , C2 S , C29 C 3 0 , C 3 l , C 3 2 , C 3 3 , C 3 4 , C 3 5 , C 3 6 , C 3 7 , C 3 S , C 3 9 , C4 0 , C 4 1 , C 4 2 C 4 3 , C 4 4 , C 4 5 , C 4 6 , C 4 7 , C 4 S , C 4 9 , C 5 0 , C 5 1 , C 5 2
o b J fun o b j e c t i ve func t lon
• P r im a r y S e t t 1 1 ng Tank Design C 1 . .
X l =e= l - ( a *e xp ( - b / XSSl - c * q » ; C2 . .
q =e= 2 4 * Q Z / ( l e Z * Ap ) ; C l . .
Q l =e= QZ t QS ; C 4 . .
xssa = e= ( k* ( n- 1 » * * ( 1 / n ) * ( n / ( n- l » * « leZ * Ap ) / ( QS * 2 4 » * * ( l / n ) ; C 5 . .
l * X S S l =e= Q2 *XS S 1 * X 1 t Q S * l e 3 *XSS S ;
* Act l v a t e d S ludge Des i gn c 6 . .
HRT =e= ( l e 3 * v ) / ( 2 4 * QZ ) ; C7 . .
S R T =e= HRT / « 1 - ( l e - Z * w » * ( 1 e - 2 * X2 ) + ( l e - Z *w ) * X 3 ) ; C 8 . .
o = e = S S I - S S 3 + HRT * ( l e 3 * XH 3 ) * ( kH * ( X S J / XH J ) / ( KX + X S 3 / X H 3 ) - k STO* S S 3 / ( KS + S S 3 » ; C9 . .
o =e= S N H I - S N H 3 +
H RT * ( l e J * X H J * ( 0 . 0 1 * kH * ( X S 3 / X H J ) / ( KX + X S J / XH 3 ) t O . 0 3 * kSTO * S S J / ( KS + S S J )
- 0 . 0 7 *mH * S N H J / ( KN H + S N H 3 ) * ( X ST 0 3 / ( l e 3 * X H J » / ( k kSTO+XST0 3 / ( l e 3 * X H 3 » + 0 . 0 6 6 * b H ) - 4 . 2 4 * mA * S N H 3 / ( KA + S N H J ) * l e 3 * XA J + 0 . 0 6 6 * bA * 1 e J * X A J ) ;
C l O . .
o =e= S N O l - SNOJ + HRT * 4 . l 7 *mA * S N H J / ( KA + S NH 3 ) * l e 3 * XA 3 ; C l l . .
o = e = X l 1 * X l - l e J * X I J * ( HR T / S RT ) + HRT * ( 0 . 2 * bH * l e J * X H 3 + 0 . 2 * bA* l e J * XA J ) ; C 1 2 . .
o =e= X S 1 * X 1 - l e J * X S 3 * ( HRT / S RT ) + H RT * l e J * XH J * ( - kH * ( X S J / X H J ) / ( KX + XS J / X H J » ; C 1 3 . .
o =e= X H l * X l - l e J * X H J * ( HR T / S R T ) + HRT * l e J * X H J * ( m H * S N H 3 / ( KN H + S N H J )
* ( XSTO J / ( l e J * XH J » / ( k kSTO+XSTO J / ( l e J * XH 3 » - b H ) ; C 1 4 . .
o =e= X S TO l * X 1 - X S T O J * ( H RT / SRT ) + HRT * ( O . S 5 * kS TO * S S 3 / ( KS + S S J ) * l e J * X H J - 1 . 6 0 * mH * S N H J / ( KN H + S N H J ) * ( X STO J / ( l e 3 * X H ) ) / ( k kSTO+XSTO ) / ( l e 3 * X H 3 »
* l e 3 * XH J - b S TO * XS T0 3 ) ; C I S . .
o =e= X A l * X l - l e 3 * X A 3 * ( HR T / S R T ) + H R T * ( mA * S NH J / ( KA + S N H 3 ) * l e J * XA 3 - bA * l e 3 * X A J ) ; C 1 6 . .
X S S 3 =e= 0 . 7 5 * X I J + 0 . 7 5 * X S J + 0 . 9 * ( X H 3 + X A 3 ) + 0 . 6 * ( X STOJ / l O O O ) ; C 1 7 . .
l + r =e= ( 1 - ( l e - Z * w » ) * ( l e - Z * X 2 ) + « l e - Z * w ) + r ) * X J ; C 1 8 . .
ROH =e= ( Z 4 / l 0 0 0 ) * QZ * ( S S l + X S l * X 1 - S S 3 ) * ( 1 - « 1 + f D * b H * S RT ) * Y H ) / ( 1 + b H * S R T » ; C 1 9 . .
ROA =e= ( 2 4 / 1 0 0 0 ) * QZ * ( SNH 1 + S N01 - S N H 3 ) * ( 4 . 5 7 - « 1 + f D *bA * S RT ) * YA ) / ( l + bA * S RT » ; C Z O . .
A F R = e = 6 * « ROH + ROA ) / Z 4 ) / n e ; C 2 l . .
S R =e= Z 4 * « 1 - ( l e - 2 * w » * Q2 ) / ( 1 0 0 * A f ) ; C 2 Z . .
( l e - 2 * X 2 ) * l e 3 * XS S 3 =e= 6 . 2 1 * l o g ( XS S 3 * S V I ) / ( O . 6 7 * 1 og ( H ) - l og « S R / 2 4 » ) - 2 6 . 4 J ; C 2 3 . .
X 3 * X S S 3 =e= ( kw * ( nw - l » * * ( l / nw ) * ( nw / ( nw- 1 » * « l e 2 * A f ) / « r + 1 e - 2 * w ) * 2 4 * Q2 » * * ( 1 / nw ) ;
* E f f l ue n t W a t e r Qua l l t y S t andards C24 . .
SCOD =g= S S 3 ; C 2 5 . .
T S S =g= l e 3 * XS S 3 * ( 1 e - Z " X 2 ) ; C Z 6 . .
S N H =g= S N H J ;
• M l l n g and o x ygen t ra ns f e r Reoui remen s 1n Aera t I on Tank
C � I . . .
1 0 0 0'V =g= « ROH + ROA ) / 2 4 ) / 0 . 1 0 ; C 2 8 . .
l O O O'V cg= 1 0 0 0 ' A FR / A I R U ; C 2 9 . .
1 0 0 0*V 1 = 1 0 0 0 *AFR/AI R L ;
, Cos t Func t i o n s , P r im a r y c l a r i f i e r C 3 0 . .
C C PST =e- 8 2 4*( l e 2'Ap )" .7 7; C 3 1 . .
CO PST -e= 1 7 . l * ( l e2 * A p ) ' * . 6 ; C 3 2 . .
C M P S T =e - 9 . 2 3' ( 1 e 2 * Ap ) • • . 6 ; C 3 3 . .
C S PST =e= 8 . 62 * ( l e 2 * Ap ) * * . 7 6 ;
• P r I ma r y S l udge pump ing C 3 4 . .
C C P S P = e = 9 8 7 0 * Q 8 * * . 5 3 ; C 3 5 . .
COPS P =e= 2 5 7 * Q B * · . 4 1 ; C 3 6 . .
C M P S P =e = 1 1 2 * Q 8 * * . 4 3 ; C 3 7 . .
C S P S P = e = 2 1 4 * QB * * . 6 4 ; C 3 B . .
C P P S P = e = Q8 ;
* A e r a t I o n t a n k C 3 9 . .
CCAT = e = 4 6 1 * ( l e 3 * V ) * * . 7 l ; C 4 0 . .
C C DAA =e= 8 5 3 3 * A F R * * . 6 6 ; C 4 l . .
CODAA =e= l 8 7 * AF R * * . 4 8 ; C 4 2 . .
CM DAA =e= 7 4 . 4 * AFR * ' . 5 5 ;
* F i n a l C l a r i f I e r C 4 3 . .
C C F S T =e= 8 2 4 * ( l e 2 * A f ) * * . 7 7 ; C 4 4 . .
COFST =e= 1 7 . l * ( l e 2 * A f ) * * . 6 ; C 4 5 . .
CMFST =e= 9 . 2 3 * ( l e 2 * A f ) * * . 6 ; C 4 6 . .
C S FS T = e = 8 . 6 2 * ( l e 2 * A f ) * * . 7 6 ;
* R e t u r n a n d w a s t e S l udge C 4 7 . .
5 =e= ( r + ( l e - 2 * w ) * Q2 ; C 4 8 . .
C C R S P =e= 9 8 7 0 * Q 5 * * . 5 3 ; C 4 9 . .
CORSP =e= 2 5 7 * Q 5 * * . 4 1 ; C 5 0 . .
C M R S P =e= 1 1 2 * Q5 * * . 4 3 ; C S 1 . .
C S R S P =e= 2 1 4 * Q 5 * * . 6 4 ; C 5 2 . .
C P R S P = e = Q 5 ;
o b j f un . .
c o s t =e= O l * ( C C P S T + C C P S P + C C AT + CCDAA + CCFST+CCRS P )
+ OMW * ( COPST+CMPST +COPS P + C M P S P+ CODAA+CM DAA+ COFST +CMFST+CORS P + CMRS P ) + 0 2 * ( C S PS T + C S P S P + C S FST+CSRS P )
+ 0 3 * ( C P P S P + C P R S P ) ; bounds
q . l o = 3 0 ; Ap . l o = 1 . 1 5 ; S RT . lo 1 ; HRT . l o = . 1 2 5 ;
q . up= 1 2 0 ; Ap . up= l e 6 ; S RT . up 2 0 ; HRT . up = . 6 2 5 ;
1 72
r . l o '" . 2 S ; X S S L l o 0 . ') ; S R . l o = 1 6 ;
J2 . 1 0 - 1 e � 6 ; 8 . 10 L l e � 6 ; X l . l o = l e � 6 ; S S 3 . 1 0 = l e � 6 ; S N H 3 . 1 0 = l e - 6 ; S N 0 3 . 1 0- l e - 6 ; X I 3 . 1 0 = l e � 6 ; X S 3 . 1 0 = l e - 6 ; X H 3 . 1 0 = l e - 6 ; XA3 . 1 0= l e - 6 ; X S S 8 . 1 0= l e - 6 ; X S T03 . 1 0 = l e - 6 ; V . l 0 = I e - 6 ; ROH . 1 0 l e - 6 ; ROA . l o - I e - 6 ; AFR . 1 0 = l e - 6 ; 0 5 . 1 0 = l e - 6 ; w . l o = l e - 6 ; A r . 1 0 l e - 6 ; X 2 . I o I e - 6 ; x 3 . 1 0 I e - 6 ;
.l n i t .l a 1 va l ue s q . l = 3 0 . 0 0 0 Ap . 1 = 1 1 . 9 9 5 X 1 . 1 = 0 . 67 9
2 . 1 = 1 4 9 9 . 3 9 2 0 8 . 1 = 0 . 6 0 8
r . u p - 1 . S ; X S S 3 . up= l e 6 ; S R . up = 3 2 ;
02 . up � l e 6 ; 0 8 . up= l e 6 ; X l . up= l e 6 ; S S 3 . up= l e 6 ; S N H 3 . up= I e 6 ; S N0 3 . up= I e 6 ; X I 3 . up= l e 6 ; XS 3 . u p= 1 e 6 ; X H 3 . up=l e 6 ; XA3 . up= 1 e 6 ; X S S 8 . up= l e 6 ; XST03 . lIp= 1 e 6 ; V . up = 1 e 6 ; ROH . Up l e 6 ; ROA . up = l e 6 ; AFR . up = l e 6 ; 0 5 . up= 1 e 6 ; w . up= l e 6 ; A f . up= l e 6 ; X 2 . up= 1 e 6 ; X 3 . up= l e 6 ;
X S S B . l = 1 8 2 . 4 9 3
S R T . 1 = 1 0 . 0 0 0 H RT . 1 = 0 . 2 0 0 V . l = 7 . 1 9 7 r . l = 0 . 4 0 0
w . 1 = 0 . 5 5 9 X 2 . 1 = 0 . 0 7 1 x 3 . 1 = 3 . 4 5 0 A f . 1 = 2 4 . 5 4 3
S S 3 . 1 = 0 . 2 8 8
S N H 3 . 1 = 0 . 3 3 3
SN03 . 1 = 3 1 . 1 5 3
X ! 3 . 1 = 4 . 1 2 6 X S 3 . 1 = 0 . 2 5 9 X H 3 . 1 = 2 . 3 9 6 X A 3 . 1 = 0 . 1 4 9 X S T 0 3 . 1 = 4 3 8 . 2 2 1 X S S 3 . 1 = 5 . 8 4 4
ROH . l = 7 7 9 8 . 4 5 3 ROA . l = 3 9 4 5 . 7 3 8 A FR . I = 2 9 3 . 6 0 5
Q 5 . 1 = 6 0 8 . 1 4 0 S R . l = 1 4 . 5 8 0
M o de l A S M 3 MODEL / a l l / ; Op t i on N L P-= CONOPT2
S o l ve ASM 3_MODEL us �ng nIp m i nimi z i ng cos t ;