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Figure 8.2 SBR model in ithink ® .8.2.2 MODEL CALIBRATIONOne set of experimental data was used to establish a value for K o . Startingfrom literature values, a trial-and-error approach was used to find the optimalvalue of K o = 90 mg/L. The criterion was to achieve a correlation of r 2 > 0.8between calculated and measured COD and biomass values at the end of thereact phase. Some of the biokinetic parameters were also adjusted to bewithin ±10% of the measured values to improve the degree of fit between calculatedand measured COD and MLSS results.© 2002 by CRC Press LLC
Table 8.2 SBR Model Equations Generated by ithink ®STOCK EQUATIONS:Biomass(t) = Biomass(t – dt) + (Input2 – Death) * dtINIT Biomass = 5000INFLOWS: Input2 = if(TIME < FillTime) then (-(FlowIn/Vol@t)*Biomass)else (Monod*OxyControl*Biomass)OUTFLOWS: Death = Biomass*kdOxygen(t) = Oxygen(t – dt) + (Aeration – Endo – Dilution) * dtINIT Oxygen = .1INFLOWS: Aeration = if (TIME < FillTime) then 0 else(Kla*(Csat–Oxygen)–OxyUptake)OUTFLOWS: Endo = Biomass*bDilution = if (TIME < FillTime) then (-FlowIn*Oxygen/Vol@t)else 0Substrate(t) = Substrate(t – dt) + (lput1 – Biouptake) • dtINIT Substrate = 100INFLOWS: Iput1 = if(TIME < FillTime) then (FlowIn*SubstrateIn/Vol@t)–(FlowIn*Substrate/Vol@t) else 0OUTFLOWS: Biouptake = if (TIME < FillTime) then 0 else(Monod*Biomass/Yield)*OxyControlCONSTANTS: b = 0.0075Yield = 0.53Csat = 7.7QDesign = 3.2SubstrateIn = 338FillTime = 1InitVol = 1.8kd = 0.01/24KLa = 12Ko = 9Ks = 800MuMax = 5/24Monod = if (TIME < FillTime) then 0 elseMuMax*Substrate/(Ks+Substrate)OxyControl = Oxygen/(Oxygen+Ko)OxyUptake = –a*DERIVN(Substrate,1)FlowIn = IF(TIME < FillTime) then QDesign else 0Vol@t = InitVol+ (if(TIME < FillTime) then TIME*QDesign elseFillTime*Qdesign)a = if (TIME < FillTime) then 0 else 0.28.2.2.1 Model ValidationThe model is validated using the following measures:(1) Predicted vs. measured concentrations of substrate (COD) and biomass(MLSS) at the end of the react phase(2) Predicted vs. measured temporal concentration profiles of substrate(COD) and biomass (MLSS) during the fill and react phases© 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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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
Page 175 and 176: to further enhance the capabilities
Page 177 and 178: are always expressed in the standar
Page 179 and 180: know the program’s environment. M
Page 181 and 182: typing in the equations in algebrai
Page 183 and 184: accessed in Simulink ® models. The
Page 185 and 186: By combining the above simple funct
Page 187 and 188: Concentration [mg/L]Figure 7.3 Lake
Page 189 and 190: saving considerable model building
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
Page 197 and 198: simulation. This enables, for examp
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: © 2002 by CRC Press LLCFigure 8.1
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
Page 227 and 228: When Mathematica ® cannot find ana
Page 229 and 230: Figure 8.20 Chemical oxidation proc
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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 249 and 250: MB across element on oxygen in gas
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
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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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