Modeling Tools for Environmental Engineers and Scientists

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would solve the problem with just m equations. When the equations are interrelated,building a general model to simulate the system by traditional methodsbecomes complex.7.4 DYNAMIC SIMULATION-BASED SOFTWARECommonly available dynamic simulation software are Extend 9 ,ithink ®10 , Simulink ®11 , etc. Dynamic simulation packages typically feature aflow diagram interface, enabling modelers to assemble a flow diagram of thesystem being modeled using graphical icons. The icons contain preprogrammed“subroutines” and can take one or more inputs, perform a calculation,and produce an output. The icons are assembled in an ordered fashionby the modeler to represent the mathematical model. The flow diagrams arenot only mere visual representations of the system being modeled, but arealso “active” in that they can simulate the system based on the underlyingmathematical model encoded.The icons that are used to build the flow diagram are comparable, in a way,to the cells in the spreadsheet programs. Whereas the links between the cellsare “abstract” and not normally visible in the spreadsheets, the links betweenthe icons in the dynamic packages are “physical” and visible. (It is possibleto show the links between cells in Excel ® , for example, by turning on theTrace Precedents and Trace Dependents feature through the Tools > Auditingmenu.) Spreadsheets, however, represent a snapshot of a system, whiledynamic simulation packages provide an equivalent of a moving picture. Thefollowing three dynamic simulation packages are illustrated in this book:Extend , ithink ® , and Simulink ® . Specific features of these three packagesare outlined next.7.4.1 Extend The capability of Extend to handle dynamic models enables problemsinvolving time-based variations of the inputs be modeled with ease. Extend can handle discrete or continuous variables and linear or nonlinear systems.It has a built-in library of programmed subroutines in the form of icons thatcan take one or more inputs, perform some calculation, and produce an output.The icons are provided with input and output connectors, and the model is constructedin the form of a block diagram, by interconnecting icons in an orderedfashion. The developer can also build custom icons with custom functions by9 Extend is trademarked by Imagine That, Inc. All rights reserved.10 ithink ® is a registerd trademark of High Performance Systems, Inc. All rights reserved.11 Simulink ® is a registered trademark of The MathWorks, Inc. All rights reserved.© 2002 by CRC Press LLC
typing in the equations in algebraic form and feeding in inputs from the inputconnectors to produce a desired output at the output terminal of the icon.Some of the built-in features of Extend that make it ideal for modelingand simulation are animation, plotting, customizable graphical interface, sensitivityanalysis, and optimization. Extend allows models to be developedin a modular and stepwise manner, whereby users can begin with simpleblocks and add features as they learn more about the problem. Differentgroups of users can develop separate blocks and assemble their blocks effortlesslyto complete the model. Automatic dimensional consistency is not maintainedby ithink ® .7.4.2 ithink ®While ithink ® also features a flow diagram interface, only four basicbuilding blocks are used: stocks, flows, converters, and connectors. Stockblocks, represented by rectangles in the flow diagram and functioning asreservoirs, are accumulators that keep track of the state values at any instantin time. Flow blocks, represented by a pipeline with a spigot, let material flowinto or out of the stocks at rates specified at the spigots. Converters, representedby circles, function as modifiers of flows or containers for modelparameters. In a way, stocks can be considered the nouns in the ithink ® modelinglanguage, flows are the verbs, and converters are the adverbs. The connectors,represented by arrows, link the other three blocks according to thesystem logic, serving to transmit information (not material) between them.The converters can receive one or more inputs and generate an output byperforming a calculation. The calculation is entered into the dialog box forthe converter in the form of an algebraic equation, just as is done in the cellin the spreadsheet-based programs. Once the blocks are connected accordingto the program logic, and the program is run, ithink ® performs a “materialbalance” across each stock at every time step to update all the state values.The ithink ® package also includes built-in animation, plotting, customizablegraphical interface, sensitivity analysis, and optimization features. Automaticdimensional consistency is not maintained by the program.7.4.3 Simulink ®Simulink ® is another flow diagram-based simulation package for modelingdynamic systems. Simulink ® is driven by the mathematical equationsolver-based package, MATLAB ® . It supports linear as well as nonlinear systemsmodeled in continuous time or discrete time or a hybrid of the two. Ithas a unique feature of multirating, i.e., different parts of a system are sampledor updated at different times, if necessary.© 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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Page 131 and 132: 0 = QX - Q(X - dX) - K L (aAdz)(X -
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Page 135 and 136: This expression does not provide an
Page 137 and 138: If the WWTP used air instead of pur
Page 139 and 140: and degradation of the natural envi
Page 141 and 142: The solution to the above PDE gives
Page 143 and 144: • river 2: x = 15000.5 dmay ∴u
Page 145 and 146: These functions are valuable tools
Page 147 and 148: this problem. Once the basic “syn
Page 149 and 150: giving the condition Q > 4πRu for
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Page 153 and 154: SolutionTo be conservative, it may
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Page 157 and 158: 6.2.5 FLOW OF AIR AND CONTAMINANTS
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Page 161 and 162: Solution(1) The steady state concen
Page 163 and 164: As a first step in modeling a river
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Page 167 and 168: © 2002 by CRC Press LLCFigure 6.8
Page 169 and 170: Figure 6.106.5 Consider the stream
Page 171 and 172: Case 4: Pulse Source in Two Dimensi
Page 173 and 174: End users often adapted these model
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Page 179: know the program’s environment. M
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Page 187 and 188: Concentration [mg/L]Figure 7.3 Lake
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Page 191 and 192: dependent variable, the dependent v
Page 193 and 194: command is used to keep the plot fr
Page 195 and 196: Figure 7.10 Lake problem solved wit
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Page 199 and 200: Figure 7.13 Lake problem modeled in
Page 201 and 202: It is hoped that the above overview
Page 203 and 204: APPENDIX 7.2 EXAMPLES OF TYPES OF E
Page 205 and 206: CHAPTER 8Modeling of EngineeredEnvi
Page 207 and 208: MB on dissolved oxygen: dC od xyt=
Page 209 and 210: © 2002 by CRC Press LLCFigure 8.1
Page 211 and 212: Table 8.2 SBR Model Equations Gener
Page 213 and 214: Figure 8.4 Predicted vs. measured C
Page 215 and 216: mathematical model. First, a proces
Page 217 and 218: Figure 8.9 Pretreatment system—ef
Page 219 and 220: Figure 8.11 CMFRs in series: optimi
Page 221 and 222: Other improvements can include alte
Page 223 and 224: Figure 8.15 Model of wastewater tre
Page 225 and 226: 8.5 MODELING EXAMPLE: CHEMICAL OXID
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Page 229 and 230: Figure 8.20 Chemical oxidation proc
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Figure 8.22 Chemical oxidation proc
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Figure 8.24 Chemical oxidation proc
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fairly large and may not be suitabl
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© 2002 by CRC Press LLCFigure 8.27
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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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© 2002 by CRC Press LLCFigure 9.20
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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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