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

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QWASI Multi-segment Equations I(i) is total input (mol/h) to each reach from emissions, the atmosphere, and any tributaries. It does not include advective inputs from other reaches. DT(i) is the sum of D values for losses by reaction, burial, and volatilization plus all advective losses from water, including net loss to sediment. The (i) refers to reach 1, 2, 3, or 4. D(i,j) is water and particle flow between reaches i and j. J(i) is a D value for the net output from each reach. J(1) = DT(1) J(2) = DT(2) – D(2,1) D(1,2)/J(1) J(3) = DT(3) – D(3,2) D(2,3)/J(2) J(4) = DT(4) – D(4,3) D(3,4)/J(3) X(i) is the ratio of D values and is the fraction of the chemical in water and particle flow that enters downstream reach (reach 1 is upstream of reaches 2, 3, and 4). X(1) = D(1,2)/J(1) X(2) = D(2,3)/J(2) X(3) = D(3,4)/J(3) Fraction of total input received by each reach, including upstream reaches. Q(1) = I(1) Q(2) = I(2) + I(1) X(1) = I(2) + Q(1) X(1) Q(3) = I(3) + I(2) X(2) + I(1) X(1) X(2) = I(3) + Q(2) X(2) Q(4) = I(4) + I(3) X(3) + I(2) X(2) X(3) + I(1) X(1) X(2) X(3) = I(4) + Q(3) X(3) The solution for water fugacities fW(i) for each reach is as follows: fW(4) = {Q(4) + [fW(5) D(5,4)]}/J(4) fW(3) = {Q(3) + [fW(4) D(4,3)]}/J(3) fW(2) = {Q(4) + [fW(3) D(3,2)]}/J(2) fW(1) = {Q(4) + [fW(2) D(2,1)]}/J(1) The sediment fugacities fS(i) can then be calculated from the steady-state equation in Fig. 8.5. fs(i) = fw(i)(DD(i) + DT(i))/(DB(i) + DS(i) + DR(i) + DT(i)) with D values specific to each segment. Figure 8.8 Steady-state mass balance equations for a series of four QWASI models with flows in both directions. X, is a ratio of D values, namely the ratio of the box-to-box advective transfer D value and the total loss D value from the source. The denominators, J, contain terms for losses from each box, again modified by fractions undergoing box-to-box transfer. Inspection of the equations reveals the significance of each term. When the connections are more complex with branching, the equations must be modified ©2001 CRC Press LLC
accordingly, but the final solution can still be inspected to reveal the significance of each term. If the number of boxes is very large (above about 8) and there is appreciable branching, it may be easier to set up the equations in differential form and solve them numerically in time, with constant inputs to reach a steady-state solution. Details of how this can be accomplished are given in Figure 8.9. The dynamic version allows the user to observe changes in concentrations with time. The steady-state version gives the concentrations when the system has reached a nonchanging condition with respect to time. If a long enough integration period is used for the dynamic version, the concentrations approach those in the steadystate version. It is best to use the steady-state version if the user is concerned only with the end result, and the dynamic version if it is desired to track changes in the system over time or how long it will take the system to approach a steady state. It is good practice to check the consistency between steady-state and dynamic solutions by comparing the steady-state output with the dynamic output obtained after integrating for a prolonged period at constant input rates, such that a steady state has been achieved. The following papers are examples of multi-QWASI model applications. Lun et al. (1998) describe the fate of PAHs in the Saguenay River in Quebec. Ling et al. (1993) treat the fate of chemicals in a harbor including vertical segmentation. Hickie Numerical Integration of QWASI Differential Equations Define time interval between sampling, e.g., 10 h. DTIM = 10 Note: It is recommended that DTIM be selected as about 5% of the smallest response time VZ/D. Define number of iterations, e.g., 5000. N = 1 to 5000 Note: This should cover a sufficiently long period that the system will reach steady state. Changes in fugacity in water (dfW) and sediment (dfS) as a function of time for each reach, as pseudocode. For I = 1 to 4 dfW(I) = DTIM ((I(I) + fA(I) (DM(I) + DQ(i) + DC(I) + DV(I)) + fS(I)(DT(I) + DR(I)) + fW(I + 1) D(I + 1, I) + fW(I – 1) D(I – 1, I)) – fW(I)(DW(I) + DV(I) + DD(I) + DT(I) + D(I, I – 1) + D(I, I + 1))}/(VW(I) ZWT(I)) dfS(I) = DTIM ((fW(I) (DD(I) + DT(I))) – fS(I) (DB(I) + DS(I) + DR(I) + DT(I)))/(VS(I) ZST(I)) Next I For I = 1 to 4 fW(I) = fW(I) + dfW(I) fS(I) = fS(I) + dfS(I) Next I Note: VW is volume of water, VS is volume of sediment, ZWT is Z for bulk water, and ZST is Z for bulk sediment. Figure 8.9 Dynamic mass balance equations for a four-reach multi-QWASI system. ©2001 CRC Press LLC
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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
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This enables us to conceive of, and
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©2001 CRC Press LLC f = 15/0.5 = 3
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D AS dominates. A residence time of
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and Therefore, ©2001 CRC Press LLC
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eaction situation in which there is
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The rate constants in each case are
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©2001 CRC Press LLC 1/t O = SD Ai/
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e achieved in 10 days. Detractors o
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sulfate to sulfide or by dechlorina
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to Zepp and Cline (1977) for the or
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©2001 CRC Press LLC 6.7 LEVEL II C
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Figure 6.3 Fugacity Level II calcul
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McKay, Donald. "Intermedia Transpor
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Figure 7.1 Illustration of nonequil
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5. Diffusion within soils, and from
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sionally, the term flux rate is use
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©2001 CRC Press LLC N = ABDC/ Dy m
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no currents or eddies. In practice,
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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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Page 183 and 184: Figure 7.8 Movement of air phase (k
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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
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Page 195 and 196: Figure 7.12 Sample Level III output
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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
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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
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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: y Mackay et al. (1983), and an appl
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
Page 235 and 236: 8.11.2 Model of a Chemical Evaporat
Page 237 and 238: Paterson et al. (1991), and Hung an
Page 239 and 240: 8.14.1 Introduction ©2001 CRC Pres
Page 241 and 242: mated again in mg/day. Food, the ot
Page 243 and 244: models. Most interest is in LRT in
Page 245 and 246: available from the University of To
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