Modeling Tools for Environmental Engineers and Scientists

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Figure 9.23 Toxicant in blood, liver, and bone, modeled in ithink ® .The above equations now form the basis of the integrated model. They canbe implemented using the ithink ® software package with a user-friendly interfaceas shown in Figure 9.24. The necessary tools to construct such an interfacein ithink ® are built in. This enables users not familiar with the ithink ®environment to run the model under different scenarios.© 2002 by CRC Press LLC
Table 9.3 Model Equations in ithink ®Blood(t) = Blood(t – dt) + (In1 – Out1) * dtINIT Blood = 2INFLOWS: In1 = R + k12*Liver + Bone*k13OUTFLOWS: Out1 = k31*Blood + k21*Blood + kol*BloodBone(t) = Bone(t – dt) + (In3 – Out3) * dtINIT Bone = 0INFLOWS: In3 = Blood*k31OUTFLOWS: Out3 – Bone*k13Liver(t) = Liver(t – dt) + (In2 – Out2) * dtINIT Liver = 4INFLOWS: In2 = Blood•k21OUTFLOWS: Out2 = k12*Liver + Rate*Liver/(km + Liver)K12 = 0.5k13 = 0.8k21 = 0.8k31 = 0.1km = 5kol = 0.4R = 3Rate = 1.29.9 MODELING EXAMPLE: VISUALIZATIONOF GROUNDWATER FLOWThis example illustrates the use of equation solver-based packages in performingsymbolic series calculations involving abstract mathematics to generatevisual aids to interpret the results. A groundwater flow in small drainagebasins between a water divide and a valley bottom is modeled here as an illustration.The system can be simplified as shown in Figure 9.25.The governing equation for groundwater flow in this system, derived fromDarcy’s Law, assuming an isotropic, homogeneous aquifer, is the well-knownLaplace equation:or xx + zz = 0 ∂2 (x,z)2∂X + ∂2 (x,z)∂ = 02zIt is desired to develop the flow potential lines and the velocity vectors for theflow field for the system.© 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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© 2002 by CRC Press LLCFigure 8.1
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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
Page 237 and 238: © 2002 by CRC Press LLCFigure 8.27
Page 239 and 240: where q is the mass of color adsorb
Page 241 and 242: Figure 8.29 Results of activated ca
Page 243 and 244: and d X = (µ - b)Xdtwhere b is the
Page 245 and 246: Figure 8.32 Results of bioregenerat
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Page 251 and 252: Figure 8.38 Typical results of oxyg
Page 253 and 254: Figure 8.39 Mathematica ® script f
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Page 257 and 258: To generalize the approach, the gov
Page 259 and 260: Figure 8.44 Concentration in pore g
Page 261 and 262: modeling of a sample problem from T
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: MB on liver:MB on bones: d P2 = k 2
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 307 and 308: Hence, Q π tan-1 - 1 - UL - 1Q/
Page 309 and 310: Figure 9.38d Stream lines and veloc
Page 311 and 312: BibliographyBedient P. B., Rifai, H
Page 313: Nirmalakhandan, N., Jang, W., and S
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