Modeling Tools for Environmental Engineers and Scientists

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Table 1.1 Range of Mathematical ModelsModels Systems Calculi ApplicationsWhite-boxElectrical}Ordinary Highly Designdifferentialdeductive andMechanical}equations deterministicControlChemical}PartialdifferentialBiologicalEnvironmental}equationsOrdinaryAnalysisEcologicaldifferentialequationsEconomic}PredictionDifferenceSocialequationsHighlyAlgebraicinductive andSpeculationPsychologicalequationsprobabilisticBlack-box© 2002 by CRC Press LLC
through several pathways. Consequently, modeling of large-scale environmentalsystems is often a complex and challenging task. The impetus fordeveloping environmental models can be one or more of the following:(1) To gain a better understanding of and glean insight into environmentalprocesses and their influence on the fate and transport of pollutants in theenvironment(2) To determine short- and long-term chemical concentrations in the variouscompartments of the ecosphere for use in regulatory enforcement andin the assessment of exposures, impacts, and risks of existing as well asproposed chemicals(3) To predict future environmental concentrations of pollutants under variouswaste loadings and/or management alternatives(4) To satisfy regulatory and statutory requirements relating to environmentalemissions, discharges, transfers, and releases of controlled pollutants(5) To use in hypothesis testing relating to processes, pollution control alternatives,etc.(6) To implement in the design, operation, and optimization of reactors,processes, pollution control alternatives, etc.(7) To simulate complex systems at real, compressed, or expanded time horizonsthat may be too dangerous, too expensive, or too elaborate to studyunder real conditions(8) To generate data for post-processing, such as statistical analysis, visualization,and animation, for better understanding, communication, and disseminationof scientific information(9) To use in environmental impact assessment of proposed new activitiesthat are currently nonexistentAbove all, the formal exercise of designing and building a model may bemore valuable than the actual model itself or its use in that the knowledgeabout the problem is organized and crystallized to extract the maximum benefitfrom the effort and the current knowledge about the subject. Typicalissues and concerns in various environmental systems and the use of mathematicalmodels in addressing them are listed in Appendix 1.1, showing thewide scope of environmental modeling.The use of and need for mathematical models, their scope and utility value,and the computer-based approaches used in developing them can best beillustrated by a case history (Nirmalakhandan et al., 1990, 1991a, 1991b,1992a, 1992b, 1993).Case History: Improvement of the Air-Stripping ProcessThe air-stripping (A/S) process has been used in the chemical engineeringfield for over 50 years. During the early 1980s, this process was adapted byenvironmental engineers for remediating groundwaters contaminated with© 2002 by CRC Press LLC
Page 2: © 2002 by CRC Press LLCModeling To
Page 5 and 6: ContentsPrefaceAcknowledgmentsFUNDA
Page 7 and 8: APPLICATIONS8. MODELING OF ENGINEER
Page 9 and 10: The contents of this book are organ
Page 11 and 12: PART IFundamentals© 2002 by CRC Pr
Page 13 and 14: The models resulting from the model
Page 15 and 16: within the grasp of only a few with
Page 17 and 18: 1.2.3 STATIC VS. DYNAMICWhen a syst
Page 19: Real SystemsMathematical ModelsDete
Page 23 and 24: ange of complex environmental appli
Page 25 and 26: APPENDIX 1.1 TYPICAL USES OF MATHEM
Page 27 and 28: APPENDIX 1.2 (continued)Target Audi
Page 29 and 30: characteristics. The system is isol
Page 31 and 32: formation, inferencing, testing, va
Page 33 and 34: system-surroundings interactions ca
Page 35 and 36: 2.2.4 INTERPRETATION AND EVALUATION
Page 37 and 38: to fill in where scientific theorie
Page 39 and 40: Figure 2.3 Schematic of real system
Page 41 and 42: Table 2.1 Variables, Symbols, Dimen
Page 43 and 44: ∴Net diffusive inflow = -EA ∂
Page 45 and 46: in terms of the model parameters al
Page 47 and 48: Figure 2.8 Model predictions vs. me
Page 49 and 50: variables. Deterministic systems ca
Page 51 and 52: e possible, and a computational met
Page 53 and 54: or, in matrix forma 11 a 12 a 13a 2
Page 55 and 56: (a)(b)Figure 3.3 (a) Setting up Sol
Page 57 and 58: Figure 3.5 Using MATLAB ® for solv
Page 59 and 60: Another method, known as the Newton
Page 61 and 62: and so on up tof n (x 1 , x 2 , . .
Page 63 and 64: c. Second-order equation with equid
Page 65 and 66: Figure 3.9 Solution of ODE by Mathe
Page 67 and 68: over the entire step, which may be
Page 69 and 70: 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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modeling of a sample problem from T
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Figure 9.2 Lakes in series modeled
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Figure 9.4 Two lakes in series mode
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In this example, a two-compartment
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in the sediments, v b is the burial
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Figure 9.9 Algal growth modeled in
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Figure 9.11 Algal growth modeled in
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Once the basic model is constructed
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Figure 9.15 Graphical user interfac
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Figure 9.17 Contaminant transport v
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Figure 9.19 Contaminant transport v
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Figure 9.21 Chemical equilibrium mo
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MB on liver:MB on bones: d P2 = k 2
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Table 9.3 Model Equations in ithink
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Figure 9.25 Problem definition for
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Figure 9.28 Groundwater flow visual
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W and the second to V, in line 6. T
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Figure 9.30 Three-dimensional conto
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VerticalDispersion CoefficientsHori
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configuration of the unit world pro
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342Chemical Mass Distribution [%]11
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water quality standard of 500 mg/L
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Hence, Q π tan-1 - 1 - UL - 1Q/
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Figure 9.38d Stream lines and veloc
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BibliographyBedient P. B., Rifai, H
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Nirmalakhandan, N., Jang, W., and S
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