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

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8.1.2 Model-Building Strategies The general model-building strategy is first to evaluate the system being simulated, then to decide how many compartments and thus mass balances are required. There is a compelling incentive to start with a simple model then build up complexity only when justified. The volumes and bulk Z values are deduced for each compartment. All inputs and outputs are identified, preferably as arrows on a mass balance diagram. Equations are written for each flux, either as an emission or a Df product. For a steady-state model, the inputs are equated to outputs for each of the n compartments, leading to n equations with n unknown fugacities. These equations are solved, either algebraically or using a matrix method. For a dynamic system, the differential equations for each medium are written in the form ©2001 CRC Press LLC d(VZf)/dt = inputs – outputs mol/h These equations are then solved, either analytically or numerically, for a defined initial condition and defined inputs. The integration time step can be selected as 5% of the shortest half-time for transport or transformation and the stability of the result checked by decreasing the time step systematically. Integration is best done using a Runge–Kutta method, but the simple Euler’s method may be adequate. Results should be checked for a mass balance. For steady-state models, this is simply a comparison of inputs and outputs for each compartment. For dynamic models, the initial mass plus the cumulative inputs should equal the final mass and the cumulative outputs. To gain a pictorial appreciation of the results, a mass balance diagram should be drawn listing all inputs and outputs beside the appropriate arrows. The dominant processes then become apparent. It is often useful to play “sensitivity games” with the model to gain an appreciation of how variation in an input quantity such as an emission rate, Z value, or D value propagates through the calculation and affects the results. An input quantity can be increased by 1% and the effect on the desired output quantity determined. The best way to quantify this sensitivity S is to deduce S = (Doutput/output)/( Dinput/input) For example, if the input quantity of 100 is increased to 101 and the output quantity changes from 1000 to 1005, then S is (5/1000)/(1/100) or 0.5. This is actually an estimate of the partial derivative of log output with respect to log input, and it is dimensionless. For linear systems of the types treated here, all values of S should be less than 1.0. It may be useful to list the input parameters, deduce S for each, then rank them in order of decreasing S. The most sensitive parameters, for which the most accurate data are necessary, are then identified. Often, the sensitivity of a parameter is surprisingly small, and only a rough estimate is needed. It may be desirable to revisit and improve the accuracy of the estimates of most sensitive parameters.
Another approach is to employ Monte Carlo analysis and run the model repeatedly, allowing the input data to vary between prescribed limits and deducing the variation in the output quantities. This gives an impression of the likely variability in the output, but it does not necessarily reveal the individual quantitative sources of this variability. The model results can then be compared with measured values to achieve a measure of validation. Complete validation is impossible, because chemicals or conditions can always be found for which the model fails. For a philosophical discussion of the feasibility of validation, the reader is referred to a review by Oreskes et al. (1994). A model can be useful, even if not validated, because it can give reliable results for a restricted set of conditions. A final note on transparency. It is unethical for an environmental scientist to assert that a chemical experiences certain fate characteristics as a result of model calculations unless the full details of the calculations inherent in the model are made available. The scientific basis on which the conclusions are reached must be fully transparent. For various reasons, the modeler may elect to prevent the user from modifying the code, but the calculations themselves must be readable. For this reason, all model calculations described here are fully transparent. Table 8.1 Summary of Z Value Equations All partition coefficients are dimensionless unless otherwise noted. All densities are kg/m3. Air Z A To aid in formulating models, Table 8.1 summarizes the expressions for estimating Z values, and Table 8.2 summarizes equations for estimating D values. Bulk Z values are SviZi, where vi is the volume fraction of phase i, and Zi is its Z value. For example, for bulk air, ©2001 CRC Press LLC = 1/RT R is gas constant, 8.314 Pa m3/mol K T is temperature Water ZW = 1/H = ZA/KAW H is Henry’s Law Constant Pa m3/mol KAW is air-water partition coefficient Octanol ZO = ZWKOW KOW is octanol-water partition coefficient Lipid ZL = ZO Lipid is equivalent to octanol Aerosols ZQ = KQAZA KQA is aerosol-air partition coefficient Organic carbon ZOC = KOCZW ( rOC/1000) KOC is organic carbon partition coefficient (L/kg) rOC is density or organic carbon (~1000) Organic matter ZOM = KOMZW ( rOM/1000) KOM is organic matter partition coefficient (L/kg) rOM is density or organic matter (1000) Mineral matter ZMM = KMMZW ( rMM/1000) KMM is mineral-water partition coefficient (L/kg) rMM is density of mineral matter Biota ZB = LZL L is lipid volume fraction ZTA = vAZA + vQZQ For a solid phase (subscript s) containing organic carbon of mass fraction yOC, in which sorption to mineral matter is negligible and the partitioning coefficient with respect to water is KD L/kg,
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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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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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Page 171 and 172: where ©2001 CRC Press LLC X = y/ U
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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
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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
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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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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