- Page 4 and 5: Library of Congress Cataloging-in-P
- Page 6 and 7: 4. FUNDAMENTALS OF ENVIRONMENTAL PR
- Page 8 and 9: PrefaceTHIS book is not a treatise
- Page 10 and 11: AcknowledgmentsIwould like to ackno
- Page 12 and 13: CHAPTER 1Introduction to ModelingCH
- Page 14 and 15: 1.1.2 EMPIRICAL MODELINGEmpirical m
- Page 16 and 17: can model the temperature profile i
- Page 18 and 19: esponses are additive in their effe
- Page 20 and 21: Table 1.1 Range of Mathematical Mod
- Page 22 and 23: organic contaminants. While A/S is
- Page 24 and 25: Chapter 7 contains a comparative pr
- Page 26 and 27: APPENDIX 1.2 SUGGESTED USES OF THE
- Page 28 and 29: CHAPTER 2Fundamentals of Mathematic
- Page 30 and 31: A system may have numerous attribut
- Page 32 and 33: 2.2.1 PROBLEM FORMULATIONAs in any
- Page 34 and 35: may have to be included. Examples o
- Page 36 and 37: y setting the reaction rate constan
- Page 38 and 39: 2.3 APPLICATION OF THE STEPS INMATH
- Page 40 and 41: VolatilizationHydrolysisPhotolysisB
- Page 42 and 43: standard mathematical manipulations
- Page 44 and 45: where g and j are, in turn, the pos
- Page 46 and 47: On substituting for g and j from th
- Page 48 and 49: CHAPTER 3Primer on MathematicsCHAPT
- Page 50 and 51: it can be simplified by dividing th
- Page 52 and 53:
Algebraic equationsLinear equations
- Page 54 and 55:
Figure 3.2 Gauss-Siedel algorithm i
- Page 56 and 57:
Figure 3.4 Using Mathematica ® for
- Page 58 and 59:
Figure 3.6 Implementation of binary
- Page 60 and 61:
Figure 3.7 Using Goal Seek function
- Page 62 and 63:
whereas all of them can be readily
- Page 64 and 65:
SolutionThe solution can be found b
- Page 66 and 67:
This procedure may be continued for
- Page 68 and 69:
Figure 3.11 Runge-Kutta method in E
- Page 70 and 71:
oundary conditions, or their combin
- Page 72 and 73:
thhti+hCi,n+1htiti-hCi-1,n+1Ci,nCi,
- Page 74 and 75:
deduce that the rate equation for B
- Page 76 and 77:
CHAPTER 4Fundamentals of Environmen
- Page 78 and 79:
Moles of material, iMolar concentra
- Page 80 and 81:
(2) In the water phase, the mass ra
- Page 82 and 83:
ChemicalinjectionAirMassinjectedm1A
- Page 84 and 85:
the phase contents is still equal t
- Page 86 and 87:
X A C A (4.15)Cwhere C A is the m
- Page 88 and 89:
The given value of K a-w indicates
- Page 90 and 91:
By introducing a proportionality co
- Page 92 and 93:
to the flow, the molar transport ra
- Page 94 and 95:
The mass transfer rate per unit vol
- Page 96 and 97:
where P w is the concentration of t
- Page 98 and 99:
The flux of solids to the sediment
- Page 100 and 101:
F= =BC Fg0.3 10 6 gL kg5000 k g
- Page 102 and 103:
where v i and v j are the stoichiom
- Page 104 and 105:
Table 4.3 Reactions of Order Zero,
- Page 106 and 107:
When the microbial population has a
- Page 108 and 109:
Rate of outflow of material out of
- Page 110 and 111:
One of the unknown concentrations,
- Page 112 and 113:
a. Develop MB equations for the liq
- Page 114 and 115:
CHAPTER 5Fundamentals of Engineered
- Page 116 and 117:
eactors. While most reactors are an
- Page 118 and 119:
5.3.1 COMPLETELY MIXED BATCH REACTO
- Page 120 and 121:
e characterized by their detention
- Page 122 and 123:
and replacing k in terms of the giv
- Page 124 and 125:
d[(A dd x)C]t= rAdx (Q RQ)C - (Q
- Page 126 and 127:
and therefore, the overall rate of
- Page 128 and 129:
eactant(s) flows through a tubular
- Page 130 and 131:
applications include stripping of v
- Page 132 and 133:
Substituting for Y in Equation (5.3
- Page 134 and 135:
the VOC inside the bubble (ML -3 );
- Page 136 and 137:
The above equation is implemented a
- Page 138 and 139:
CHAPTER 6Fundamentals of NaturalEnv
- Page 140 and 141:
6.2.1 FLOW OF WATER THROUGH THE SAT
- Page 142 and 143:
which has to be integrated with two
- Page 144 and 145:
6.2.2 GROUNDWATER FLOW NETSThe pote
- Page 146 and 147:
flow is along the x-direction, for
- Page 148 and 149:
SolutionThe potential function for
- Page 150 and 151:
Figure 6.6 Contours of potential an
- Page 152 and 153:
of mass M (M), applied at x = 0 and
- Page 154 and 155:
Figure 6.7 Mathcad ® model of benz
- Page 156 and 157:
d M →d[AL o ∏C] → AL o ∏ d
- Page 158 and 159:
where vp is the vapor pressure of c
- Page 160 and 161:
y a continuous, constant input load
- Page 162 and 163:
orC e - t W oV1 - µ e(-µ)t
- Page 164 and 165:
The above equations can be applied
- Page 166 and 167:
6.3.3 ESTUARY SYSTEMSThe model for
- Page 168 and 169:
EXERCISE PROBLEMS6.1 Consider the W
- Page 170 and 171:
The above equations are simulated u
- Page 172 and 173:
CHAPTER 7Software for DevelopingMat
- Page 174 and 175:
Currently available software packag
- Page 176 and 177:
the top of a worksheet followed by
- Page 178 and 179:
7.3.3 MATLAB ®MATLAB ® is yet ano
- Page 180 and 181:
would solve the problem with just m
- Page 182 and 183:
The flow diagram in Simulink ® is
- Page 184 and 185:
where K is the sum of the first-ord
- Page 186 and 187:
contain references to other cells,
- Page 188 and 189:
Figure 7.4 Lake problem modeled in
- Page 190 and 191:
Figure 7.5 Analytical solution for
- Page 192 and 193:
Figure 7.8 Lake example modeled in
- Page 194 and 195:
Figure 7.9 Steady state lake proble
- Page 196 and 197:
Figure 7.11 Lake problem modeled in
- Page 198 and 199:
Figure 7.12 Lake problem modeled in
- Page 200 and 201:
to use. If repeated solutions are r
- Page 202 and 203:
APPENDIX 7.1 SELECTED EXAMPLES OF S
- Page 204 and 205:
PART IIApplications© 2002 by CRC P
- Page 206 and 207:
high variation in waste flow rate a
- Page 208 and 209:
Because the ODEs are coupled, a num
- Page 210 and 211:
Figure 8.2 SBR model in ithink ® .
- Page 212 and 213:
Figure 8.3 Graphical user interface
- Page 214 and 215:
Figure 8.6 Predicted vs. measured d
- Page 216 and 217:
Graph of Toxicant and bODFigure 8.8
- Page 218 and 219:
Now, the equations are coupled ODEs
- Page 220 and 221:
Figure 8.13 Graphical user interfac
- Page 222 and 223:
where V (t) is the volume remaining
- Page 224 and 225:
allow users to study overall impact
- Page 226 and 227:
Figure 8.17 Chemical oxidation proc
- Page 228 and 229:
Figure 8.19 Chemical oxidation proc
- Page 230 and 231:
Figure 8.21 Chemical oxidation proc
- Page 232 and 233:
Figure 8.23 Chemical oxidation proc
- Page 234 and 235:
Figure 8.25 Chemical oxidation proc
- Page 236 and 237:
in the Input column. In this exampl
- Page 238 and 239:
diffusion would be controlling the
- Page 240 and 241:
Figure 8.28 Activated carbon proces
- Page 242 and 243:
In this example, a mathematical mod
- Page 244 and 245:
Table 8.4 Bioregeneration Model Equ
- Page 246 and 247:
equations are set up in a certain o
- Page 248 and 249:
Figure 8.35 Results of pipe flow an
- Page 250 and 251:
Figure 8.36 Oxygen/nitrogen transfe
- Page 252 and 253:
functions, introduced in Section 6.
- Page 254 and 255:
Figure 8.40 Groundwater flow modele
- Page 256 and 257:
4C = C o (C a - C o ) π ∞ (-1
- Page 258 and 259:
© 2002 by CRC Press LLCFigure 8.43
- Page 260 and 261:
CHAPTER 9Modeling of NaturalEnviron
- Page 262 and 263:
Figure 9.1 Two lakes in series mode
- Page 264 and 265:
© 2002 by CRC Press LLCFigure 9.3
- Page 266 and 267:
Figure 9.5 Multiple lakes modeled i
- Page 268 and 269:
where C 1 and C 2 are the concentra
- Page 270 and 271:
suitable. The use of the ithink ®
- Page 272 and 273:
Figure 9.10 Results from the ithink
- Page 274 and 275:
These two equations can be easily i
- Page 276 and 277:
order process with respect to algae
- Page 278 and 279:
in visualizing the temporal and spa
- Page 280 and 281:
Figure 9.18 Script for generating a
- Page 282 and 283:
d X kSX = -Ydt K + S - bX d M kSX1
- Page 284 and 285:
The governing equations are develop
- Page 286 and 287:
9.8 MODELING EXAMPLE: TOXICOLOGICAL
- Page 288 and 289:
Figure 9.23 Toxicant in blood, live
- Page 290 and 291:
Figure 9.24 Graphical user interfac
- Page 292 and 293:
Figure 9.26 Groundwater flow visual
- Page 294 and 295:
Even though the final result is an
- Page 296 and 297:
In the example shown, a three-dimen
- Page 298 and 299:
Important assumptions behind these
- Page 300 and 301:
Figure 9.32 Graphical user interfac
- Page 302 and 303:
Figure 9.33 Level II fugacity model
- Page 304 and 305:
Figure 9.35 Results of Level II fug
- Page 306 and 307:
ytwo roots, at L = t ± - 1 if >
- Page 308 and 309:
Figure 9.38b Stream lines generated
- Page 310 and 311:
Figure 9.39b Velocity potential lin
- Page 312 and 313:
James, A. (1993) An Introduction to