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

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2.3.3 Summary In summary, our simplest view of the environment is that of a small number of phases, each of which is homogeneous or well mixed and unchanging with time. When this is inadequate, the number of phases may be increased; heterogeneity may be permitted in one, two, or three dimensions; and variation with time may be included. The modeler’s philosophy should be to concede each increase in complexity reluctantly, and only when necessary. Each concession results in more mathematical complexity and the need for more data in the form of kinetic or equilibrium parameters. The model becomes more difficult to understand and thus less likely to be used, especially by others. This is not a new idea. William of Occam expressed the same sentiment about 650 years ago, when he formulated his principle of parsimony or “Occam’s Razor,” stating ©2001 CRC Press LLC Essentia non sunt multiplicanda praeter necessitatem which can be translated as, “What can be done with fewer (assumptions) is done in vain with more,” or more colloquially, “Don’t make models more complicated than is necessary.” 2.4 MASS BALANCES When describing a volume of the environment, it is obviously essential to define its limits in space. This may simply be the boundaries of water in a pond or the air over a city to a height of 1000 m. The volume is presumably defined exactly, as are the areas in contact with adjoining phases. Having established this control “envelope” or “volume” or “parcel,” we can write equations describing the processes by which a mass of chemical enters and leaves this envelope. The fundamental and now axiomatic law of conservation of mass, which was first stated clearly by Antoine Lavoisier, provides the basis for all mass balance equations. Rarely do we encounter situations in which nuclear processes violate this law. Mass balance equations are so important as foundations of all environmental calculations that it is essential to define them unambiguously. Three types can be formulated and are illustrated below. We do not treat energy balances, but they are set up similarly. 2.4.1 Closed System, Steady-State Equations This is the simplest class of equation. It describes how a given mass of chemical will partition between various phases of fixed volume. The basic equation simply expresses the obvious statement that the total amount of chemical present equals the sum of the amounts in each phase, each of these amounts usually being a product of a concentration and a volume. The system is closed or “sealed” in that no entry or exit of chemical is permitted. In environmental calculations, the concentrations are usually so low that the presence of the chemical does not affect the phase volumes.
Worked Example 2.1 A three-phase system consists of air (100 m3), water (60 m3), and sediment (3 m3). To this is added 2 mol of a hydrocarbon such as benzene. The phase volumes are not affected by this addition, because the volume of hydrocarbon is small. Subscripting air, water, and sediment symbols with A, W, and S, respectively, and designating volume as V (m3) and concentration as C (mol/m3), we can write the mass balance equation. ©2001 CRC Press LLC total amount = sum of amounts in each phase mol 2 = VACA + VWCW + VSCS = 100 CA + 60 CW + 3 CS mol To proceed further, we must have information about the relationships between C A, C W, and C S. This could take the form of phase equilibrium equations such as C A/C W = 0.4 and C S/C W = 100 These ratios are usually referred to as partition coefficients or distribution coefficients and are designated K AW and K SW, respectively. We discuss them in more detail later. We can now eliminate C A and C S by substitution to give Thus, It follows that 2 = 100 (0.4 C W) + 60 C W + 3(100C W) = 400 C W mol C W = 2/400 = 0.005 mol/m 3 C A = 0.4 C W = 0.002 mol/m 3 C S = 100 C W = 0.5 mol/m 3 The amounts in each phase (m i) mol are the VC products as follows: mW = VWCW = 0.30 mol (15%) mA = VACA = 0.20 mol (10%) mS = VSCS = 1.50 mol (75%) Total 2.00 mol This simple algebraic procedure has established the concentrations and amounts in each phase using a closed system, steady-state, mass balance equation and equilibrium relationships. The essential concept is that the total amount of chemical present
Page 1 and 2: McKay, Donald. "Front matter" Multi
Page 3 and 4: Multimedia Environmental Models The
Page 5 and 6: hensive, and reliable, and they hav
Page 7 and 8: Chapter 1 Introduction Chapter 2 So
Page 9 and 10: McKay, Donald. "Introduction" Multi
Page 11 and 12: It is now evident that our task is
Page 13 and 14: McKay, Donald. "Some Basic Concepts
Page 15 and 16: give the derived units directly wit
Page 17 and 18: Energy (joule, J) The joule, which
Page 19: particles (aerosols), or biota in w
Page 23 and 24: (i) What is the concentration (C) i
Page 25 and 26: Answer ©2001 CRC Press LLC 5.1 kg,
Page 27 and 28: or or When t is zero, C is zero, th
Page 29 and 30: What is the absolute minimum piscic
Page 31 and 32: ©2001 CRC Press LLC C 1 = C O/(1 +
Page 33 and 34: containing nonequilibrium quantitie
Page 35 and 36: 1. Fallout of chemical from air to
Page 37 and 38: validated using real environments.
Page 39 and 40: ©2001 CRC Press LLC CHAPTER 3 Envi
Page 41 and 42: of other, somewhat similar or homol
Page 43 and 44: Table 3.2 List of Chemicals Commonl
Page 45 and 46: elatively high concentrations. This
Page 47 and 48: exists between toxicologists and ch
Page 49 and 50: determine priority. This is a subje
Page 51 and 52: Another important classification of
Page 53 and 54: Figure 3.1 (continued) ©2001 CRC P
Page 55 and 56: Table 3.5 (continued) dichlorometha
Page 57 and 58: Table 3.5 (continued) total PCB 326
Page 59 and 60: Figure 3.2 Plot of log K AW vs. log
Page 61 and 62: chlorofluoro compounds are very sta
Page 63 and 64: 3.3.2.7 Arsenic Compounds Arsenic,
Page 65 and 66: McKay, Donald. "The Nature of Envir
Page 67 and 68: Figure 4.1 Evaluative environments.
Page 69 and 70: 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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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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