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

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The total of all D values is 0.7587. Therefore, ©2001 CRC Press LLC E = 40 f = 40/SD = 52.7 The total amount is 1264 mols, giving a mean residence time of 31.6 hours. The most important loss process is advection in air, which accounts for 21.08 mol/h. Next is soil reaction at 7.31 mol/h, the water advection at 5.27 mol/h, etc. Each individual rate is D f mol/h. 6.4.1 Advection as a Pseudo Reaction Examination of these equations shows that the group G/V plays the same role as a rate constant having identical units of h –1 . It may, indeed, be convenient to regard advective loss as a pseudo reaction with this rate constant and applicable to the phase volume of V. Note that the group V/G is the residence time of the phase in the system. Frequently, this is the most accessible and readily remembered quantity. For example, it may be known that the retention time of water in a lake is 10 days, or 240 hours. The advective rate constant, k, is thus 1/240 h –1 , and the D value is V Z k, which is, of course, also G Z. It is noteworthy that this residence time is not equivalent to a reaction half-time, which is related to the rate constant through the constant 0.693 or ln 2. Residence time is equivalent to 1/k. 6.4.2 Residence Times and Persistence Confusion may arise when calculating the residence time or persistence of a chemical in a system in which advection and reaction occur simultaneously. The overall residence time in Example 6.4 is 31.6 hours and is a combination of the advective residence time and the reaction time. The presence of advection does not influence the rate constant of the reaction; therefore, it cannot affect the persistence of the chemical. But, by removing the chemical, it does affect the amount of chemical that is available for reaction, and thus it affects the rate of reaction. It would be useful if we could establish a method of breaking down the overall persistence or residence time into the time attributable to reaction and the time attributable to advection. This is best done by modifying the fugacity equations as shown below for total input I. I = SD Aif + SD Rif But I = M/t O, where M is the amount of chemical and t O is the overall residence time. Furthermore, M = SVZf or fSVZ. Thus, dividing both sides by M and cancelling f gives
©2001 CRC Press LLC 1/t O = SD Ai/SVZ + SD Ri/SVZ = 1/t A + 1/t R The key point is that the advective and reactive residence times t A and t R add as reciprocals to give the reciprocal overall time. These are the residence times that would apply to the chemical if only that process applied. Clearly, the shorter residence time dominates, corresponding, of course, to the faster rate constant. It can be shown that the ratio of the amounts removed by reaction and by advection are in the ratio of the overall rate constants or the reciprocal residence times. Example 6.5 Calculate the individual and overall residence times in Example 6.4. Each residence time is VZ/D and the rate constant is D/VZ. VZ SVZ/D (advection) VZ/D (reaction) Air 4 60 866 Water 10 240 260 Soil 10 • 173 Total 24 Adding the reciprocals, i.e., the rate constants, gives 1/60 + 1/240 + 1/866 + 1/260 + 1/• + 1/173 = 0.0167 + 0.0042 + 0.0012 + 0.0038 + 0 + 0.0058 = 0.0209 + 0.0108 = 0.0317 = 1/31.5 The advection residence time is 1/0.0209 or 47.8 h, and for reaction it is 1/0.0108 or 92.6 h. Each residence time (e.g., 60, 866, etc.) contributes to give the overall residence time of 31.5 hours, reciprocally. In mass balance models of this type, it is desirable to calculate the advection, reaction, and overall residence times. An important observation is that these residence times are independent of the quantity of chemical introduced; in other words, they are intensive properties of the system. Concentrations, amounts, and fluxes are dependent on emissions and are extensive properties. These concepts are useful, because they convey an impression of the relative importance of advective flow (which merely moves the problem from one region to another) versus reaction (which may help solve the problem). These are of particular interest to those who live downwind or downstream of a polluted area. 6.5 UNSTEADY-STATE CALCULATIONS A related calculation can be done in unsteady-state mode in which we introduce an amount of chemical, M, into the evaluative environment at zero time, then allow
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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
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 and 118: Therefore, ©2001 CRC Press LLC f =
Page 119 and 120: ©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
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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
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 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
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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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