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

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must equal the sum of the individual amounts in each compartment. We later refer to this as a Level I calculation. It is useful because it is not always obvious where concentrations are high, as distinct from amounts. Example 2.2 In this example, 0.04 mol of a pesticide of molar mass 200 g/mol is applied to a closed system consisting of 20 m 3 of water, 90 m 3 of air, 1 m 3 of sediment, and 2 L of biota (fish). If the concentration ratios are air/water 0.1, sediment/water 50, and biota/water 500, what are the concentrations and amounts in each phase in both gram and mole units? Answer The fish contains 0.1 g or 0.0005 mol at a concentration of 50 g/m 3 or 0.25 mol/m 3 . Example 2.3 A circular lake of diameter 2 km and depth 10 m contains suspended solids (SS) with a volume fraction of 10 –5 , i.e., 1 m 3 of SS per 10 5 m 3 water, and biota (such as fish) at a concentration of 1 mg/L. Assuming a density of biota of 1.0 g/cm 3 , a SS/water partition coefficient of 10 4 , and a biota/water partition coefficient of 10 5 . Calculate the disposition and concentrations of 1.5 kg of a PCB in this system. Answer In this case, 8.3% is present in each of SS and biota and 83% in water with a concentration in water of 39.8 µg/m 3 . 2.4.2 Open System, Steady-State Equations In this class of mass balance equation, we introduce the possibility of the chemical flowing into and out of the system and possibly reacting or being formed. The conditions within the system do not change with time, i.e., its condition looks the same now as in the past and in the future. The basic mass balance assertion is that the total rate of input equals the total rate of output, these rates being expressed in moles or grams per unit time. Whereas the basic unit in the closed system balance was mol or g, it is now mol/h or g/h. Worked Example 2.4 A 10 4 m 3 thoroughly mixed pond has a water inflow and outflow of 5 m 3 /h. The inflow water contains 0.01 mol/m 3 of chemical. Chemical is also discharged directly into the pond at a rate of 0.1 mol/h. There is no reaction, volatilization, or other losses of the chemical; it all leaves in the outflow water. ©2001 CRC Press LLC
(i) What is the concentration (C) in the outflow water? We designate this as an unknown C mol/m 3 . ©2001 CRC Press LLC total input rate = total output rate 5 m 3 /h ¥ 0.01 mol/m 3 + 0.1 mol/h = 0.15 mol/h = 5 m 3 /h ¥ C mol/m 3 = 5 C mol/h Thus, C = 0.03 mol/m 3 The total inflow and outflow rates of chemical are 0.15 mol/h. (ii) If the chemical also reacts in a first-order manner such that the rate is VCk mol/h where V is the water volume, C is the chemical concentration in the well mixed water of the pond, and k is a first-order rate constant of 10 –3 h –1 , what will be the new concentration? The output by reaction is VCk or 10 4 ¥ 10 –3 C or 10 C mol/h, thus we rewrite the equation as: Thus, 0.05 + 0.1 = 5 C + 10 C = 15 C mol/h C = 0.01 mol/m 3 The total input of 0.15 mol/h is thus equal to the total output of 0.15 mol/h, consisting of 0.05 mol/h outflow and 0.10 mol/h reaction. An inherent assumption is that the prevailing concentration in the pond is constant and equal to the outflow concentration. This is the “well mixed” or “continuously stirred tank” assumption. It may not always apply, but it greatly simplifies calculations when it does. The key step is to equate the sum of the input rates to the sum of the output rates, ensuring that the units are equivalent in all the terms. This often requires some unit-to-unit conversions. Worked Example 2.5 A lake of area (A) 10 6 m 2 and depth 10 m (volume V 10 7 m 3 ) receives an input of 400 mol/day of chemical in an effluent discharge. Chemical is also present in the inflow water of 10 4 m 3 /day at a concentration of 0.01 mol/m 3 . The chemical reacts with a first-order rate constant k of 10 –3 h –1 , and it volatilizes at a rate of (10 –5 C) mol/m 2 s, where C is the water concentration and m 2 refers to the air-water area. The outflow is 8000 m 3 /day, there being some loss of water by evaporation. Assuming that the lake water is well mixed, calculate the concentration and all the inputs and outputs in mol/day. Use a time unit of days in this case.
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 and 20: particles (aerosols), or biota in w
Page 21: Worked Example 2.1 A three-phase sy
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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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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