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

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and that sorbed is ©2001 CRC Press LLC j A = C A /C T = 1/(1 + K BAv B) j B = (1–C A/C T) = K BAv B/(1 + K BAv B) The key quantity is thus K BAv B or the product of the dimensionless partition coefficient and the volume fraction of the dispersed sorbing phase. When this product is 1.0, half the solute is in each state. When it is smaller than 1.0, most is dissolved, and when it exceeds 1.0, more is sorbed. When the phase B is solid, it is usual to express the concentration C B in units of moles or grams per unit mass of B in which case K BA has units of volume/mass or reciprocal density. For example, it is common to use mg/L for C A, mg/kg for C B, and L/kg for K P; then, with M in mg and V A in L, then it can be shown that M = C A(V A + m BK P) = C TV A where m B is the mass of sorbing phase (kg) from which C A = C T/(1 + K Pm B/V A) = C T/(1 + K PX B) where X B is the concentration of sorbent in kg/L. The units of the partition coefficient K BA or K P and concentration of sorbent v B or X B do not matter as long as their product is dimensionless and consistent, i.e., the amounts of sorbing phase, continuous phase, and chemical are the same in the definition of both the partition coefficient and the sorbent concentration. Care must be taken when interpreting sorbed concentrations to ascertain if they represent the amount of chemical per unit volume or mass of sorbent, or the per unit volume of the environmental phase such as water. The analogous fugacity equations are simply j A = V AZ A/(V AZ A + V BZ B) j B = V BZ B/(V AZ A + V BZ B) In some cases, it is preferable to calculate a Z value for a bulk phase consisting of other phases in equilibrium. Examples are air plus aerosols; water plus suspended solids; and soils consisting of solids, air, and water. If the total volume is V T, the effective bulk Z value is Z T, and equilibrium applies, then the total amount of chemical must be Thus, V TZ Tf = Sv iZ if
©2001 CRC Press LLC Z T = S(V i/V T)Z i =Sv iZ i where v i is the volume fraction of each phase. The key point is that the component Z values add in proportion to their volume fractions. The use of bulk Z values helps to simplify calculations by reducing the number of compartments, but it does assume that equilibrium exists within the bulk compartment. Worked Example 5.9 An aquarium contains 10 m 3 of water and 200 fish, each of volume 1 cm 3 . How will 0.01 g (i.e., 10 mg) of benzene and the same mass of DDT partition between water and fish, given that the fish are 5% lipids, and log K OW is 2.13 for benzene and 6.19 for DDT? K FW will be 0.05 K OW or 6.7 for benzene and 77440 for DDT. C T is 0.001 g/m 3 or 1 mg/m 3 in both cases. The fraction dissolved j 2 is 1/(1 + K FWv F), where v F is the volume fraction of fish, i.e., 200 ¥ 10 –6 /10 = 2 ¥ 10 –5 . For benzene, K FWv F is 0.00013. For DDT, K FWv F is 1.55. The fractions dissolved are 0.99987, essentially 1.0, for benzene and 0.39 for DDT. The dissolved concentrations are thus 0.00099987 g/m 3 or 0.99987 mg/m 3 (benzene) and 0.00039 g/m 3 or 0.39 mg/m 3 (DDT), and the sorbed concentrations (per m 3 of water) are 0.00013 mg/m 3 and 0.61 mg/m 3 , respectively. The sorbed concentrations per m 3 of fish are 0.0067 g/m 3 and 30 g/m 3 , respectively. Example 5.10 A lake of volume 10 6 m 3 contains 15 mg/L of sorbing material. The total concentration of a chemical of K P equal to 10 5 L/kg is 1 mg/L. What are the dissolved and sorbed concentrations? Answer 0.4 mg/L dissolved and 0.6 mg/L sorbed. 5.6.5 Maximum Fugacity When fugacities are calculated, it is advisable to check that the value deduced is lower than the fugacity of the pure phase, i.e., the solid or liquid fugacity or, in the case of gases, of atmospheric pressure. If these fugacities are exceeded, supersaturation has occurred, a “maximum permissible fugacity” has been exceeded, and the system will automatically “precipitate” a pure solute phase until the fugacity drops to the saturation value. It is possible to calculate inadvertently and use (i.e.,
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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
Page 67 and 68: Figure 4.1 Evaluative environments.
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Page 73 and 74: carbon figure for deeper sediments
Page 75 and 76: flows. The quality of this groundwa
Page 77 and 78: Table 4.2 Evaluative Environments A
Page 79 and 80: McKay, Donald. "Phase Equilibrium"
Page 81 and 82: Figure 5.1 Some principles and conc
Page 83 and 84: likely using an equilibrium criteri
Page 85 and 86: Another useful quantity is the rati
Page 87 and 88: experimentally, but not directly, u
Page 89 and 90: ©2001 CRC Press LLC 5.3 PROPERTIES
Page 91 and 92: 1.0. This, then, is the fugacity or
Page 93 and 94: where ©2001 CRC Press LLC pH is -l
Page 95 and 96: In terms of solubilities, S iA and
Page 97 and 98: The temperature coefficient is the
Page 99 and 100: (1982), Baum (1997) and Leo (2000).
Page 101 and 102: Although it may appear environmenta
Page 103 and 104: Figure 5.4 Illustration of quantita
Page 105 and 106: 5.5 ENVIRONMENTAL PARTITION COEFFIC
Page 107 and 108: C S = K PC W benzene = 1.1 ¥ 0.001
Page 109 and 110: Mackay (1986), in an attempt to sim
Page 111 and 112: Compartment Definition of Fugacity
Page 113 and 114: high concentration in the fish, but
Page 115 and 116: heat capacity of 0.38 J/g°C requir
Page 117: Therefore, ©2001 CRC Press LLC f =
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
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Page 165 and 166: ©2001 CRC Press LLC N = ABDC/ Dy m
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diffusivity, and some unknown layer
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where ©2001 CRC Press LLC X = y/ U
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fraction of the total volume that i
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Figure 7.6 Mass transfer at the int
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partition coefficient. The signific
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and the series retains a similar ra
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ments of resuspension rates are par
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Figure 7.8 Movement of air phase (k
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ates can thus be used to estimate m
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Figure 7.9 Combination of D values
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Figure 7.10 Four-compartment Level
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Table 7.2 Order of Magnitude Values
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Unlike the Level II calculation, it
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Figure 7.12 Sample Level III output
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McKay, Donald. "Applications of Fug
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applications. Citations are given t
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Another approach is to employ Monte
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LEVEL1B A six-compartment Level I p
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Figure 8.1 Air-water exchange proce
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The total rates of transfer are thu
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Figure 8.2 Chemical transport and t
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mean. For chemical between depths o
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8.5.2 Process Description The water
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learn the benefits of using fugacit
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where Figure 8.5 QWASI model: stead
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are similar to those described by M
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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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