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James, A. (1993) An Introduction to Water Quality Modeling, John Wiley & Sons,New York.Johnson, P. C., Stanley, C. C., Kemblowski, M. W., Byers, D. L., and Colthart, J. D.,A practical approach to the design, operation, and monitoring of in situ soil-ventingsystems, Ground Water Monitoring Rev., 10, 159–178, 1990.Jorgensen, S. E. (1994) Fundamentals of Ecological Modeling, Elsevier, Amsterdam.Kharab, A. Spreadsheets solve boundary-value problems, Chem. Eng., 7, 145–148,1988.Laughlin, D. K., Edwards, F. G., Egemen, E., and Nirmalakhandan, N. Sequencingbatch reactor treatment of high COD effluent from a bottling plant, ASCE J. Env.Eng., 125, 285–289, 1999.Law, V. J., Johnson, N. L., Oyefodun, A., and Bhattachaya, S. K. Modeling methaneemissions from rice soils, Environmental Software, 8, 197–207, 1993.Levenspiel, O. (1972) Chemical Reaction Engineering, 2nd ed., John Wiley & Sons,New York.Lincoff A. H. and Gossett, J. M. (1984) The determination of Henry’s Constants forvolatile organics by equilibrium partitioning in closed systems. In: Gas Transferat Water Surfaces, Eds., Brutsaert, W. and Jirka, G. H. D. Reidel Publishing,Boston, pp. 17–25.Logan, B. E. (1999) Environmental Transport Processes, John Wiley & Sons, NewYork.Lyman, W. J., Reehl, W. F., and Rosenblatt, D. H. (1982) Handbook of ChemicalProperty Estimation Methods, McGraw-Hill, New York.Mackay, D. (1991) Multimedia Environmental Models, Lewis Publishers, Michigan.Mackay, D. and Paterson, S. Calculating fugacity, Environ. Sci. & Technol., 15,1006–1014, 1981.Mackay, D. and Paterson, S. Fugacity revisited, Environ. Sci. & Technol., 16,654a–660a, 1982.Mackay, D. and Paterson, S. Evaluating the multimedia fate of organic chemicals: ALevel III fugacity model, Environ. Sci. & Technol., 25, 427–436, 1991.Mackay, D., Paterson, S., and Schroeder, W. H. Model describing the rates of transferprocesses of organic chemicals between atmosphere and water, Environ. Sci. &Technol., 20, 810–816, 1981.Marchand, P. (1999), Graphics and GUIs with Matlab, CRC Press, Boca Raton,Florida.Murthy, D. N. P., Page, N. W., and Rodin, E. Y. (1990) Mathematical Modeling,Pergamon Press, Exeter, U.K.Nemerow, N. L. (1991) Stream, Lake, Estuary, and Ocean Pollution, van NostrandReinhold, New York.Nirmalakhandan, N., Lee, Y. H., and Speece R. E. Optimizing oxygen absorption andnitrogen desorption in packed towers, Aquacultural Eng., 7, 221–234, 1988.Nirmalakhandan, N., Jang, W., and Speece, R. E. Counter-current cascade air-strippingfor removal of low volatile organic contaminants, Water Res., 24, 615, 1990.Nirmalakhandan, N., Speece, R. E., and Peace G. L. Cascade air-stripping—A newtechnology to meet new regulations, Chem. Eng. Comm., 102, 47, 1991a.Nirmalakhandan, N., Jang, W., and Speece, R. E. Cascade air-stripping—Pilot andprototype scale experience, J. Env. Eng., ASCE, 117, 788, 1991b.© 2002 by CRC Press LLC
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© 2002 by CRC Press LLCModeling To
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ContentsPrefaceAcknowledgmentsFUNDA
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APPLICATIONS8. MODELING OF ENGINEER
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The contents of this book are organ
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PART IFundamentals© 2002 by CRC Pr
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The models resulting from the model
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within the grasp of only a few with
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1.2.3 STATIC VS. DYNAMICWhen a syst
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Real SystemsMathematical ModelsDete
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through several pathways. Consequen
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ange of complex environmental appli
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APPENDIX 1.1 TYPICAL USES OF MATHEM
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APPENDIX 1.2 (continued)Target Audi
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characteristics. The system is isol
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formation, inferencing, testing, va
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system-surroundings interactions ca
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2.2.4 INTERPRETATION AND EVALUATION
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to fill in where scientific theorie
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Figure 2.3 Schematic of real system
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Table 2.1 Variables, Symbols, Dimen
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∴Net diffusive inflow = -EA ∂
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in terms of the model parameters al
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Figure 2.8 Model predictions vs. me
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variables. Deterministic systems ca
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e possible, and a computational met
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or, in matrix forma 11 a 12 a 13a 2
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(a)(b)Figure 3.3 (a) Setting up Sol
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Figure 3.5 Using MATLAB ® for solv
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Another method, known as the Newton
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and so on up tof n (x 1 , x 2 , . .
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c. Second-order equation with equid
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Figure 3.9 Solution of ODE by Mathe
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over the entire step, which may be
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Hence, the original problem is now
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2∂ f f i1,j1 - f i-1,j1 - f i1,j-
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modeling, in diagnosis and troubles
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For the reach x ≥ a: C S D K
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contaminants that do not undergo an
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known as an intensive property. Oth
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Dissolved mass in sample = dissolve
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Figure 4.2 Illustration of steady s
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4.3.2.2 Dalton’s LawDalton’s La
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Table 4.2 Different Forms of Quanti
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M olesoxygenHence, K a-w = = 8 - 3
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SolutionThe flux, N, which is the d
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Figure 4.3 Illustration of the Two-
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where C s is the concentration of t
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Fraction in dissolved form = f d =
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in the air (M/L -3 ), C a is the co
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ackward reactions can expressed in
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4.7.2 ELEMENTARY REACTIONSThe rate
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excess energy. The direct photolysi
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4.8 MATERIAL BALANCEAs indicated in
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SolutionLet M be the mass of chemic
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CpHence, the final result isEXERCIS
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APPENDIX 4.1 COMMON PARTITION COEFF
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analyzing and modeling them. The ex
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\5.2.2 HETEROGENEOUS REACTORSHetero
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CC = in -(t t 0 )k C t in0 k- C
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Worked Example 5.1A wastewater trea
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or,C L = C 0 e -(k /u)L = C 0 e -k
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HRT = 1 k (1 - )The overall HRT
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The MB equation for the above syste
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the particle surface (ML -2 T -1 ),
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0 = QX - Q(X - dX) - K L (aAdz)(X -
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chemical engineering applications.
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This expression does not provide an
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If the WWTP used air instead of pur
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and degradation of the natural envi
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The solution to the above PDE gives
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• river 2: x = 15000.5 dmay ∴u
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These functions are valuable tools
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this problem. Once the basic “syn
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giving the condition Q > 4πRu for
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directions, and the last term repre
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SolutionTo be conservative, it may
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zone, because the hydraulic conduct
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6.2.5 FLOW OF AIR AND CONTAMINANTS
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time-dependent volumetric flow rate
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Solution(1) The steady state concen
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As a first step in modeling a river
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where a 1,4 is the conversion facto
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© 2002 by CRC Press LLCFigure 6.8
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Figure 6.106.5 Consider the stream
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Case 4: Pulse Source in Two Dimensi
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End users often adapted these model
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to further enhance the capabilities
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are always expressed in the standar
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know the program’s environment. M
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typing in the equations in algebrai
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accessed in Simulink ® models. The
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By combining the above simple funct
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Concentration [mg/L]Figure 7.3 Lake
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saving considerable model building
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dependent variable, the dependent v
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command is used to keep the plot fr
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Figure 7.10 Lake problem solved wit
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simulation. This enables, for examp
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Figure 7.13 Lake problem modeled in
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It is hoped that the above overview
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APPENDIX 7.2 EXAMPLES OF TYPES OF E
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CHAPTER 8Modeling of EngineeredEnvi
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MB on dissolved oxygen: dC od xyt=
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Table 8.2 SBR Model Equations Gener
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Figure 8.4 Predicted vs. measured C
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mathematical model. First, a proces
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Figure 8.9 Pretreatment system—ef
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Figure 8.11 CMFRs in series: optimi
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Other improvements can include alte
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Figure 8.15 Model of wastewater tre
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8.5 MODELING EXAMPLE: CHEMICAL OXID
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When Mathematica ® cannot find ana
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Figure 8.20 Chemical oxidation proc
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fairly large and may not be suitabl
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where q is the mass of color adsorb
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Figure 8.29 Results of activated ca
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and d X = (µ - b)Xdtwhere b is the
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Figure 8.32 Results of bioregenerat
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under a set of known data, the stat
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MB across element on oxygen in gas
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Figure 8.38 Typical results of oxyg
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Figure 8.39 Mathematica ® script f
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entered as a function of x and y, u
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To generalize the approach, the gov
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Figure 8.44 Concentration in pore g
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Page 263 and 264: Figure 9.2 Lakes in series modeled
Page 265 and 266: Figure 9.4 Two lakes in series mode
Page 267 and 268: In this example, a two-compartment
Page 269 and 270: in the sediments, v b is the burial
Page 271 and 272: Figure 9.9 Algal growth modeled in
Page 273 and 274: Figure 9.11 Algal growth modeled in
Page 275 and 276: Once the basic model is constructed
Page 277 and 278: Figure 9.15 Graphical user interfac
Page 279 and 280: Figure 9.17 Contaminant transport v
Page 281 and 282: Figure 9.19 Contaminant transport v
Page 283 and 284: © 2002 by CRC Press LLCFigure 9.20
Page 285 and 286: Figure 9.21 Chemical equilibrium mo
Page 287 and 288: MB on liver:MB on bones: d P2 = k 2
Page 289 and 290: Table 9.3 Model Equations in ithink
Page 291 and 292: Figure 9.25 Problem definition for
Page 293 and 294: Figure 9.28 Groundwater flow visual
Page 295 and 296: W and the second to V, in line 6. T
Page 297 and 298: Figure 9.30 Three-dimensional conto
Page 299 and 300: VerticalDispersion CoefficientsHori
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Page 303 and 304: 342Chemical Mass Distribution [%]11
Page 305 and 306: water quality standard of 500 mg/L
Page 307 and 308: Hence, Q π tan-1 - 1 - UL - 1Q/
Page 309 and 310: Figure 9.38d Stream lines and veloc
Page 311: BibliographyBedient P. B., Rifai, H
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