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

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Conversely, if the contact time is short, we can expect to use 4B/pt . If we measure the transfer rates at several temperatures, and thus different diffusivities, or measure the transfer rate of different chemicals of different B, then plot kM versus B on loglog paper, the slope of the line will be 1.0 if steady-state applies, and 0.5 if unsteadystate applies. In practice, an intermediate power of about 2/3 often applies, suggesting that we have mostly penetration diffusion followed by a period of near-steady-state diffusion. ©2001 CRC Press LLC 7.6 DIFFUSION IN POROUS MEDIA When a solute is diffusing in air or water, its movement is restricted only by collisions with other molecules. If solid particles or phases are also present, the solid surfaces will also block diffusion and slow the net velocity. <strong>Environmental</strong>ly, this is important in sediments in which a solute may have been deposited at some time in the past, and from which it is now diffusing back to the overlying water. It is also important in soils from which pesticides may be volatilizing. It is therefore essential to address the question, “By how much does the presence of the solid phase retard diffusion?” We assume that the solid particles are in contact, but there remains a tortuous path for diffusion (otherwise, there is no access route, and the diffusivity would be zero). The process of diffusion is shown schematically in Figure 7.5, in which it is apparent that the solute experiences two difficulties. First, it must take a more tortuous path, which can be defined by a tortuosity factor, F Y, the ratio of tortuous distance to direct distance. Second, it does not have available the full area for diffusion, i.e., it is forced to move through a smaller area, which can be defined using an area factor, F A. This area factor F A, is equal to the void fraction, i.e., the Figure 7.5 Diffusion in a porous medium in which only part of the area is accessible, and the diffusing molecule must take a longer, tortuous path.
fraction of the total volume that is fluid, and thus is accessible to diffusion. It can be argued that the tortuousity factor, F Y, is related to void fraction, v, raised possibly to the power –0.5; therefore, in total, we can postulate that the effective diffusivity in the porous medium, B E, is related to the molecular diffusivity, B, by ©2001 CRC Press LLC B E = BF A/F Y = Bv 1.5 Such a relationship is found for packings of various types of solids, as discussed by Satterfield (1970). This equation may be seriously in error since (1) the effective diffusivity is sensitive to the shape and size distribution of the particles, (2) there may also be “surface diffusion” along the solid surfaces, and (3) the solute may become trapped in “cul de sacs” or become sorbed on active sites. At least the equation has the correct property that it reduces to intuitively correct limits that B E equals B when v is unity, and B E is zero when v is zero. There is no substitute for actual experimental measurements using the soil or sediment and solute in question. For soils, it is usual to employ the Millington–Quirk (MQ) expression for diffusivity as a function of air and water contents. An example is in the soil diffusion model of Jury et al. (1983). The MQ expression uses air and water volume fractions v A and v W and calculates effective air and water diffusivities as follows: B AE= B Av A 10/3 /(vA + v W) 2 B WE= B Wv W 10/3 /(vA + v W) 2 where B A and B W are the molecular diffusivities, and B AE and B WE are the effective diffusivities. Inspection of these equations shows that they reduce to a similar form to that presented earlier. If v W is zero, B AE is proportional to v A to the power 1.33 instead of 1.5. Occasionally, there is confusion when selecting the concentration driving force that is to be multiplied by B E. This should be the concentration in the diffusing medium, not the total concentration including sorbed form. In sediments, the pore water concentration may be 0.01 mol/m 3 , but the total sorbed plus pure water, i.e., bulk concentration, is 10 mol/m 3 . B E should then be multiplied by 0.01 not 10. In some situations (regrettably), the total concentration (10) is used, in which case B E must be redefined to be a much smaller “effective diffusivity,” i.e., by a factor of 1000. The problem is that diffusivity is then apparently controlled by the extent of sorption. In sediments, it is suspected that much of the chemical present in the pore or interstitial water, and therefore available for diffusion, is associated with colloidal organic material. These colloids can also diffuse; consequently, the diffusing chemical has the option of diffusing in solution or piggy backing on the colloid. From the Stokes–Einstein equation, the diffusivity B is approximately inversely proportional to the molecular radius. A typical chemical may have a molecular mass of 200 and a colloid an equivalent molar mass of 6000 g/mol, i.e., it is a factor of 30
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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
Page 121 and 122: ©2001 CRC Press LLC air Z = P S /R
Page 123 and 124: Table 5.1 Table 5.1 Summary of Defi
Page 125 and 126: Figure 5.7 Fugacity form 1 for dedu
Page 127 and 128: Calculate the following physical-ch
Page 129 and 130: ©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: where ©2001 CRC Press LLC X = y/ U
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 and 184: Figure 7.8 Movement of air phase (k
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
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Page 221 and 222: C F ª Z Ff W ª 1.608 mol/m 3 ª 4
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y Mackay et al. (1983), and an appl
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accordingly, but the final solution
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Figure 8.10 Fish bioaccumulation pr
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The nature of the processes control
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iomagnification is more significant
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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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