McKay, Donald. "Front matter" Multimedia Environmental Models ...

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©2001 CRC Press LLC f W = f WO exp(–D Vt/VZ W) D V for benzene = 1.38 ¥ 10 –3 (note that this is k OWAZ W) D V for naphthalene = 10.6 ¥ 10 –3 Now, 1/D V equals (1/D A + 1/D W), the D A value being common to both chemicals. D W contains the variable Z W; therefore, D W for naphthalene is D W for benzene times 23.7 ¥ 10 –3 /1.836 ¥ 10 –3 or 12.9. Benzene D A = 0.0242 D W = 0.00146 Naphthalene D A = 0.0242 D W = 0.0189 In practice, it is unwise to rely on only two chemicals, it being better to use at least five, covering a wide range of K AW values. The air phase resistance, when viewed as 1/D A, is 41.3 units in both cases, but the water phase resistance for benzene is 685, while for naphthalene it is 52.9. Benzene experiences 5.7% of the transfer resistance in the air, while naphthalene experiences 44% resistance in the air, because it has a much lower K AW. Example 7.5 Ten kilograms each of benzene, 1,4 dichlorobenzene, and p cresol are spilled into a pond 5 m deep with an area of 1 km 2 . If k W is 0.1 m/h, and k A is 10 m/h, what will be the times necessary for half of each chemical to be evaporated? Use the property data from Chapter 3, and ignore other loss processes. Answer Benzene, 36 h, dichlorobenzene 38 h, p cresol 12400 h. Some of the earliest environmental modeling was of oxygen transfer to oxygendepleted rivers in which a “reaeration constant,” k 2, was introduced (with units of reciprocal time) using the equation dC W/dt = k 2(C E – C W) mol/m 3 h where C E is the equilibrium solubility of oxygen in water. Another term is usually included for oxygen consumption, but we ignore it here. Now, if the volume in question is 1 m 2 in horizontal area and Y m deep, it will have a volume of Y m 3 , and the flux N will be YdC w/dt mol/h. But N = k M(C E – C W) = YdC W/dt = Yk 2(C E – C W) k M is thus equivalent to Yk 2. A typical k 2 of 1 day –1 in a river of depth 2.4 m corresponds to a mass transfer coefficient of 2.4 m/day or 0.1 m/h. Oxygen reaeration
ates can thus be used to estimate mass transfer coefficients for other solutes having similar (large) H such as alkanes. Indeed, an ingenious experimental approach for determining k 2 for oxygen is to use a volatile hydrocarbon, such as propane, as a tracer, thus avoiding the complications of biotic oxygen consumption or generation, which confound environmental measurements of oxygen concentration change. It is erroneous to use k 2 to estimate the rate of volatilization of a chemical with low H, since k 2 contains negligible air phase resistance information. A correction should also be applied for the effect of molecular diffusivity, preferably using the dimensionless form of diffusivity, the Schmidt number raised to a power such as –0.5 or –0.67. This technique of probing interfacial MTCs by measuring N for various chemicals can be applied in other areas. When chemical is taken up by fish, it appears that it passes through one or more water layers and one or more organic membranes in series. By analogy with air-water transfer, we can write an organic membranewater transfer equation simply by replacing subscript A by subscript M, giving where ©2001 CRC Press LLC N = k OWA(C W – C M/K OW) 1/k OW = 1/k W + 1/k MK MW or more conveniently changing to an overall organic phase MTC, k OM, where N = k OMA(C WK MW – C M) 1/k OM = 1/k M + K MW/k W A plot of 1/k OM versus K MW, the organic-water or octanol-water partition coefficient, gives 1/k M as intercept and 1/k W as slope. This is essentially the fish bioconcentration equation (discussed in more detail in Chapter 8) in disguise, which is conventionally written dC F/dt = k 1C W – k 2C F where V F is fish volume and C O is C F/L, where L is the volume fraction lipid (equivalent to octanol) in the fish. It follows that dC F/dt = (k OMA/V F)(C WK MW – C F/L) k 1 is obviously K OWk OMA/V F, and k 2 is [k OMA/(V FL)]. k 1/k 2 is then LK OW, the bioconcentration factor. The area of the respiring gill surface is uncertain as is k OM, so it is convenient to lump these uncertainties in one unknown k 2. This suggests plotting
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McKay, Donald. "Front matter" Multi
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Multimedia Environmental Models The
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hensive, and reliable, and they hav
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Chapter 1 Introduction Chapter 2 So
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McKay, Donald. "Introduction" Multi
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It is now evident that our task is
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McKay, Donald. "Some Basic Concepts
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give the derived units directly wit
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Energy (joule, J) The joule, which
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particles (aerosols), or biota in w
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Worked Example 2.1 A three-phase sy
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(i) What is the concentration (C) i
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Answer ©2001 CRC Press LLC 5.1 kg,
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or or When t is zero, C is zero, th
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What is the absolute minimum piscic
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©2001 CRC Press LLC C 1 = C O/(1 +
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containing nonequilibrium quantitie
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1. Fallout of chemical from air to
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validated using real environments.
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©2001 CRC Press LLC CHAPTER 3 Envi
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of other, somewhat similar or homol
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Table 3.2 List of Chemicals Commonl
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elatively high concentrations. This
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exists between toxicologists and ch
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determine priority. This is a subje
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Another important classification of
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Figure 3.1 (continued) ©2001 CRC P
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Table 3.5 (continued) dichlorometha
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Table 3.5 (continued) total PCB 326
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Figure 3.2 Plot of log K AW vs. log
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chlorofluoro compounds are very sta
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3.3.2.7 Arsenic Compounds Arsenic,
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McKay, Donald. "The Nature of Envir
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Figure 4.1 Evaluative environments.
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are subject to two important deposi
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metals and organic chemicals from w
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carbon figure for deeper sediments
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flows. The quality of this groundwa
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Table 4.2 Evaluative Environments A
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McKay, Donald. "Phase Equilibrium"
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Figure 5.1 Some principles and conc
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likely using an equilibrium criteri
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Another useful quantity is the rati
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experimentally, but not directly, u
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©2001 CRC Press LLC 5.3 PROPERTIES
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1.0. This, then, is the fugacity or
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where ©2001 CRC Press LLC pH is -l
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In terms of solubilities, S iA and
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The temperature coefficient is the
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(1982), Baum (1997) and Leo (2000).
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Although it may appear environmenta
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Figure 5.4 Illustration of quantita
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5.5 ENVIRONMENTAL PARTITION COEFFIC
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C S = K PC W benzene = 1.1 ¥ 0.001
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Mackay (1986), in an attempt to sim
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Compartment Definition of Fugacity
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high concentration in the fish, but
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heat capacity of 0.38 J/g°C requir
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Therefore, ©2001 CRC Press LLC f =
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©2001 CRC Press LLC Z T = S(V i/V
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©2001 CRC Press LLC air Z = P S /R
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Table 5.1 Table 5.1 Summary of Defi
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Figure 5.7 Fugacity form 1 for dedu
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Calculate the following physical-ch
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©2001 CRC Press LLC CHAPTER 6 Adve
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that all water will spend 100 days
Page 133 and 134: This enables us to conceive of, and
Page 135 and 136: ©2001 CRC Press LLC f = 15/0.5 = 3
Page 137 and 138: D AS dominates. A residence time of
Page 139 and 140: and Therefore, ©2001 CRC Press LLC
Page 141 and 142: eaction situation in which there is
Page 143 and 144: The rate constants in each case are
Page 145 and 146: ©2001 CRC Press LLC 1/t O = SD Ai/
Page 147 and 148: e achieved in 10 days. Detractors o
Page 149 and 150: sulfate to sulfide or by dechlorina
Page 151 and 152: to Zepp and Cline (1977) for the or
Page 153 and 154: ©2001 CRC Press LLC 6.7 LEVEL II C
Page 155 and 156: Figure 6.3 Fugacity Level II calcul
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Page 159 and 160: Figure 7.1 Illustration of nonequil
Page 161 and 162: 5. Diffusion within soils, and from
Page 163 and 164: sionally, the term flux rate is use
Page 165 and 166: ©2001 CRC Press LLC N = ABDC/ Dy m
Page 167 and 168: no currents or eddies. In practice,
Page 169 and 170: diffusivity, and some unknown layer
Page 171 and 172: where ©2001 CRC Press LLC X = y/ U
Page 173 and 174: fraction of the total volume that i
Page 175 and 176: Figure 7.6 Mass transfer at the int
Page 177 and 178: partition coefficient. The signific
Page 179 and 180: and the series retains a similar ra
Page 181 and 182: ments of resuspension rates are par
Page 183: Figure 7.8 Movement of air phase (k
Page 187 and 188: Figure 7.9 Combination of D values
Page 189 and 190: Figure 7.10 Four-compartment Level
Page 191 and 192: Table 7.2 Order of Magnitude Values
Page 193 and 194: Unlike the Level II calculation, it
Page 195 and 196: Figure 7.12 Sample Level III output
Page 197 and 198: McKay, Donald. "Applications of Fug
Page 199 and 200: applications. Citations are given t
Page 201 and 202: Another approach is to employ Monte
Page 203 and 204: LEVEL1B A six-compartment Level I p
Page 205 and 206: Figure 8.1 Air-water exchange proce
Page 207 and 208: The total rates of transfer are thu
Page 209 and 210: Figure 8.2 Chemical transport and t
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Page 213 and 214: 8.5.2 Process Description The water
Page 215 and 216: learn the benefits of using fugacit
Page 217 and 218: where Figure 8.5 QWASI model: stead
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Page 221 and 222: C F ª Z Ff W ª 1.608 mol/m 3 ª 4
Page 223 and 224: y Mackay et al. (1983), and an appl
Page 225 and 226: accordingly, but the final solution
Page 227 and 228: Figure 8.10 Fish bioaccumulation pr
Page 229 and 230: The nature of the processes control
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Page 233 and 234: An alternative and more elegant met
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8.11.2 Model of a Chemical Evaporat
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Paterson et al. (1991), and Hung an
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8.14.1 Introduction ©2001 CRC Pres
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mated again in mg/day. Food, the ot
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models. Most interest is in LRT in
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available from the University of To
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McKay, Donald. "Appendix" Multimedi
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©2001 CRC Press LLC
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