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

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©2001 CRC Press LLC N = VdC W/dt = –k OWA(C W – C A/K AW) where C A and C W are concentrations in air and water and k OW the overall MTC. Assuming C A to be zero, integrating gives or C W = C WO exp(–k OWAt/V) = C WO exp (–k OWt/Y) f W = f WO exp(–D Vt/VZ W) Plotting C W on semilog paper vs. linear time gives a measurable slope of –k OW/Y, hence k OW can be estimated. A system of this type has been described by Mackay and Yuen (1983) and is illustrated in Figure 7.8. A very useful quantity is the evaporation half-life, which is 0.693Y/k OW and 0.693 VZ W/D V. Often, an order of magnitude estimate of this time is sufficient to show that volatilization is unimportant or that it dominates other processes, such as reaction. As noted earlier, measurement of the individual contributing air and water D values or MTCs is impossible, because the interfacial concentrations cannot be measured. If, however, the evaporation rates of a series of chemicals of different K AW are measured, it is possible to deduce k W and k A or D W and D A. The relationship 1/k OW = 1/k W + 1/k AK AW suggests plotting, as in Figure 7.8, 1/k OW versus 1/K AW for a series of chemicals. The intercept will be 1/k W and the slope 1/k A. A correction may be necessary for molecular diffusivity differences. k W or D W is measured by selecting chemicals of high K AW for which the term 1/k AK AW or 1/D A is negligible. Alkanes, oxygen, or inert gases are convenient. k A or D A is measured by choosing chemicals of low K AW such that 1/k AK AW or 1/D A is large compared to 1/k W or 1/D W. Alcohols are convenient for this purpose. Worked Example 7.4 A tank contains 2 m 3 of water at 25°C, 50 cm deep, with dissolved benzene (K AW = 0.22) and naphthalene (K AW = 0.017), each at a concentration of 0.1 mol/m 3 . After 2 hours, these concentrations have dropped to 47.1 and 63.9% of their initial value, respectively. What are the overall and individual MTCs and D values? In each case, C W = C WO exp(–k OWt/Y), Y being 0.5 m. Thus, k OW = –(Y/t) ln (C W/C WO). Substituting gives Benzene k OW = 0.188 m/h Naphthalene k OW = 0.112 m/h Assuming each k OW to be made up of identical k W and k A values, i.e., 1/k OW = 1/k W + 1/(K AWk A)
Figure 7.8 Movement of air phase (k A), water phase (k W), and overall (k OV) mass transfer coefficients by following the volatilization of substances with different air-water partition coefficients, K AW. This equation can be written twice, once for benzene and once for naphthalene, using the specific values of k OW and K AW. The two equations can be solved for k W and k A, giving ©2001 CRC Press LLC k W = 0.20 k A = 15 m/h In fugacity format, Z A is 4.04 ¥ 10 –4 for both substances, and Z W is 1.836 ¥ 10 –3 for benzene and 23.7 ¥ 10 –3 for naphthalene, thus the fugacities are initially 54 and 4.22 Pa, falling to 25 and 2.72 Pa. The D V values are obtained from
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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
Page 131 and 132: 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
Page 157 and 158: McKay, Donald. "Intermedia Transpor
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: ments of resuspension rates are par
Page 185 and 186: ates can thus be used to estimate m
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
Page 219 and 220: are similar to those described by M
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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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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