313 8 Modeling the Transport and Fate of Hydrophobic Chemicals Hydrophobic organic chemicals, such as PCBs and PAHs, often have large par- tition coefcients, on the order of 10 3 to 10 6 L/kg or even higher. In this case, much of the chemical is sorbed to particulate matter and is transported with it. This particulate matter, along with the sorbed HOC, usually settles onto the bottom of an aquatic system and forms deposits of contaminated sediments there that can be many meters thick. At most sites with contaminated sedi- ments, approximate calculations of the amounts of contaminants in these bot- tom sediments and also in the overlying water lead to the conclusion that there are orders of magnitude more contaminant in the bottom sediments than in the overlying water. As a result, even after the cleanup of point sources of contami- nation, these bottom sediments can serve as a major and long-lasting source of contaminants to the overlying water. To predict sediment and water quality over long periods of time, the ux of these contaminants between the bottom sediments and the overlying water needs to be quantitatively understood and modeled. The sediment-water ux of contaminants is primarily due to sediment ero- sion/deposition, molecular diffusion, bioturbation, and groundwater ow. Each of these processes acts in a different way, and hence each must be described and modeled in a different way. In general, they occur more or less simultaneously and there are interactions among them. All these processes are continuously and often signicantly modied by the nite rates of adsorption and desorption of the HOC between the solid sedimentary particles and the surrounding waters. These rates of sorption and the resulting partitioning depend on the hydrophobicity of the chemical, that is, on K p . Because of this, the transport of an HOC also strongly depends on K p . This is especially true for HOCs with large partition coefcients and is a major emphasis in this chapter. As bottom sediments erode, the contaminants associated with these sedi- ments are transported into the water column, where they may adsorb or desorb, depending on conditions in the overlying water relative to conditions in the bottom sediments. Because erosion rates are highly variable in space and time, contami- nant uxes due to erosion/deposition are also highly variable in space and time. During calm periods and average winds, these uxes are relatively small and are © 2009 by Taylor & Francis Group, LLC 314 Sediment and Contaminant Transport in Surface Waters probably comparable with the uxes due to molecular diffusion, bioturbation, and groundwater ow. However, major storms and oods can cause movement and mixing of bottom sediments by erosion/deposition more rapidly and to depths in the sediments much greater than that possible by these other processes. The contaminant ux due to the erosion of particles with their sorbed contaminants and the subsequent desorption of these contaminants into the surrounding water would also then be much greater than the contaminant uxes due to these other processes. The effects of bioturbation on sediment properties and the sediment-water ux are due to feeding and burrowing activities of benthic organisms, are quite diverse, and depend on the amounts and types of organisms. In fresh waters, benthic organisms disturb and/or mix the sediments down to depths of 2 to 10 cm. This does not occur instantaneously but over a period of time that depends on the number densities of the organisms and their activities; this can be months to years. For sea water, the depths of the disturbances due to benthic organisms are much greater, on the order of 10 cm to as much as 1 m. The ux of contaminants from the bottom sediments due to molecular dif- fusion has often been considered negligible by comparison with other processes. However, rapid erosion and deposition (as caused by oods and storms) as well as chemical spills can cause sharp gradients in contaminant concentrations and hence large contaminant uxes at the sediment-water interface. As will be seen below, nite sorption rates for HOCs with large partition coefcients will exac- erbate this effect. In addition, molecular diffusion is ubiquitous and inherently modies and is modied by all the other ux processes. As a result, the effects of molecular diffusion on uxes can be quite large and must be considered in calcu- lating and predicting sediment-water uxes of HOCs. In eld studies, groundwater ow has been shown to be a major inuence on the sediment-water ux of HOCs in certain areas. However, these uxes are dif- cult to measure and, in addition, models of this ux as modied by nite sorp- tion rates have not been extensively applied or veried. As a result, the effects of groundwater ow on the sediment-water ux of HOCs have not been well quanti- ed. Nevertheless, the ux of HOCs due to groundwater ow can be signicant and is a process that deserves careful consideration. In water quality models, a common approach to modeling the contaminant ux between the bottom sediments and the overlying water is to use the equation q D h CC HC C wwo wwo   () () (8.1) where q is the ux; D is a diffusion coefcient; C w and C wo are representative contaminant concentrations in the pore waters of the sediment and in the overly- ing water, respectively; h is the thickness of an assumed “well-mixed” or “active” sediment layer; and H = D/h and is a mass transfer coefcient with units of © 2009 by Taylor & Francis Group, LLC Modeling the Transport and Fate of Hydrophobic Chemicals 315 centimeters per second (cm/s). If local chemical equilibrium in the sediments is assumed, the above equation can be written as q D h C K C s p wo  ¤ ¦ ¥ ³ µ ´ (8.2) where C s is a representative contaminant concentration of the solids in the sedi- ment. The parameters D, h, and H (only two of the three are independent) are generally determined by parameterization, that is, by comparison of results cal- culated from the water quality model with eld measurements and then modify- ing these parameters until the model and eld results agree (e.g., see the texts by Thomann and Mueller, 1987; Chapra, 1997). As a rst approximation, typical recommended values for h are 10 to 15 cm, whereas a suggested value for D is the molecular diffusion coefcient for the HOC being considered. The effects of nite sorption rates on these uxes are generally not explicitly considered. The difculty with Equations 8.1 and 8.2 is that they do not describe (espe- cially in functional form) the time-dependent uxes due to sediment erosion/ deposition, molecular diffusion, bioturbation, or groundwater ow. Because these equations do not correspond to any real process, the parameters D, h, and H are purely empirical functions chosen to t existing data; they generally are not valid for conditions for which they have not been calibrated, and the solutions to these equations do not have the proper functional dependence on time. Because of this, these equations have very little predictive capability. Equations 8.1 and 8.2 are often called diffusion equations, but they are not; a better term would be a mass transfer approximation. The major processes that affect HOC transport and sediment-water ux as well as the modeling of these processes are described in this chapter. Erosion/deposi- tion and the subsequent transport of HOCs in the overlying water are discussed in the following section. Section 8.2 describes the conventional one-dimensional, time-dependent diffusion (Fickian) approximation that is often used for the sedi- ment-water ux of nonsorbing chemicals or for sorbing chemicals when chemical sorption equilibrium is a good approximation, that is, when sorption rates are relatively high. The mass transfer approximation as described by Equation 8.1 or 8.2 is also discussed and compared with the diffusion approximation. For the diffusion of sorbing chemicals with nite sorption rates, the Fickian approximation is not valid. In this case, the basic conservation equations for the HOC must be supplemented by a rate equation for the transfer of the HOC between the solids and the pore water. This is done for the molecular diffusion of HOCs in Section 8.3, where experimental and theoretical results for HOCs with a wide range of partition coefcients are discussed; nite sorption rates are inherent in the results and analyses. The effects of bioturbation (including nite sorption rates) on the sediment-water ux are discussed in Section 8.4. Comparisons of the magnitudes and time dependencies of the different sediment-water uxes, as well as a discus- sion of the approximation of a “well-mixed” layer, are given in Section 8.5. © 2009 by Taylor & Francis Group, LLC 316 Sediment and Contaminant Transport in Surface Waters A simple and idealized problem of contaminant release and transport during environmental dredging is discussed in Section 8.6; the purpose is to charac- terize and estimate the magnitudes of various processes that affect this release without the use of a complex model. Previously, in Section 1.2, an introduction to the problem of water quality modeling, parameterization, and the resulting non-unique solutions was given. In Section 8.7, this discussion is continued in the context of a more general model of PCB transport and water quality. 8.1 EFFECTS OF EROSION/DEPOSITION AND TRANSPORT Two HOC transport problems are discussed in this section: (1) the transport of PCBs in the Saginaw River, including the assumption of equilibrium partitioning; and (2) the transport of PCBs in Green Bay as affected by nite sorption rates. 8.1.1 THE SAGINAW RIVER The transport of sediments in the Saginaw River has been modeled, and results of these numerical calculations were presented in Section 6.4. Based on these sediment transport calculations, the transport of PCBs in the river has also been modeled (Cardenas et al., 1995); the specic problem was to investigate and make preliminary estimates of the erosion, deposition, transport, and fate of PCBs from a contaminated area in the river (Figure 6.22). Some interesting results of this investigation are presented here. In the calculations, it was assumed that there was equilibrium sorption of the PCBs to the sediments with a K p of 2×10 4 L/kg; the nonerosional/nondepositional sediment-water ux of PCBs was not included in order to isolate the ux due to sediment erosion/deposition. The rst calculations were to investigate the effects of the magnitude of ow events on the erosion and deposition of sediments and the subsequent transport of PCBs; calculations were therefore made for ow events of 500, 1000, 1500, and 1900 m 3 /s. For reference, from 1940 to 1990, the median ow rate was 57 m 3 /s and the maximum was 1930 m 3 /s. In these rst calculations, the following was assumed: 1. Surcial sediments initially in the intensive study area were contami- nated with PCBs at a level of 4 µg/g of sediment. This is a reasonable rst approximation to the average of the PCB concentrations actually measured at this site. 2. The thickness of this surcial layer was 10 g/cm 2 (on the order of 10 cm), but only where the water depth was less than 3 m (Figure 6.22). This excluded the river channel, where contaminants were generally not found. For the contaminated area, the total amount of PCBs initially in the sediment bed per unit of surface area was then 40 µg/cm 2 , whereas the total amount of PCBs initially in the sediment bed was 90 kg. 3. There were sediments coming in from upstream, but they contained no PCBs. © 2009 by Taylor & Francis Group, LLC Modeling the Transport and Fate of Hydrophobic Chemicals 317 During a ow event, sediments and sorbed PCBs are eroded from the sediment bed. Some of the eroded PCBs are transported and deposited further downstream in the river, and some are transported to Saginaw Bay. From the calculations, it was shown that erosion of PCBs originally in the bed occurs (1) in the shallow nearshore area to a sediment depth generally less than 1 g/cm 2 and (2) at the edge of the channel to sediment depths as great as 30 g/cm 2 . The amount of PCBs eroded (in µg/cm 2 ) for a 1500-m 3 /s event is shown in Figure 8.1. The large erosion of PCBs at the edge of the channel is clearly evident. During this event, a total of 28 kg PCBs were eroded and transported downstream; almost all of the eroded PCBs were transported to the bay. A small amount (0.02 kg) was deposited in the wide shallow part of the river, primarily near shore, with the amount of PCBs per unit area increasing toward shore. A comparison of the amounts of PCBs transported by the different ow events is given in Table 8.1. The amounts transported to the bay increase nonlin- early with the ow rate, from a small amount (0.28 kg) for the 500-m 3 /s event to 36.5 kg for the 1900-m 3 /s event. However, even for the largest ow event, only about a third of the total PCBs in the bed are eroded. The reason for this is as follows. Because of the currents, the highest shear stresses occur in the deepest water, the channel, whereas the lowest shear stresses occur in the shallow, near- shore areas. Although the shear stresses and erosion rates are high in the channel, no PCBs are present there and therefore no erosion and transport of PCBs occur there. Conversely, in the nearshore region, the shear stresses are low, only small erosion occurs, and little transport of PCBs occurs. The region where the highest erosion and transport of PCBs occurs is on the edge of the channel where PCBs are present and where moderately high shear stresses occur. Here, the depth of 5 35 FIGURE 8.1 Amount of PCBs eroded (µg/cm 2 ) in the Saginaw River for a 1500-m 3 /s ow event. (Source: From Cardenas and Lick, 1996. With permission.) © 2009 by Taylor & Francis Group, LLC 318 Sediment and Contaminant Transport in Surface Waters erosion and the amount of PCBs eroded and transported depend on the shear stress and hence on the ow rate, at least until the layer of contaminated sediment is eroded. Thereafter, additional PCB erosion and transport is caused only by ero- sion of surcial layers near shore. Contaminants initially at the surface of the sediment bed will be buried by sediments depositing during low ows. This process will reduce the subsequent erosion and transport of the contaminated sediments by later and larger ows. To make a preliminary investigation of this process, several calculations were made. In these calculations, it was assumed that (1) as in the rst example, a layer of contaminated sediments 10 g/cm 2 thick was initially present at the surface and had a PCB concentration of 4 µg/g of sediment in the intensive study area; (2) layers of clean sediments were deposited on top of these contaminated sediments for different periods of time at approximately 2 g/cm 2 per year; and (3) after this deposition, a 1500-m 3 /s ow event occurred. The erosion and deposition of sediment for the 1500-m 3 /s event were the same as in the above example. As far as PCB transport and fate are concerned, the dif- ferences in the results described here are that clean overlying sediments must be eroded rst before the contaminated sediments can be eroded and transported. Of course, the more clean sediments that are deposited over the contaminated sediments, the less the amount of contaminated sediments that are eroded and transported downstream to the bay. Calculations were made for no deposition and for deposition time periods of 1, 5, and 20 years. For these scenarios, the masses of PCBs transported to the bay were 28.1, 26.1, 23.1, and 15.2 kg, respectively. There is little difference in PCB transport to the bay without and with 1 year of deposition. Although the newly deposited sediments cover almost all the shallow, nearshore area with a layer of sediment sufcient to eliminate the erosion of contaminated sediments from this area, little erosion occurs there, even without any deposited sediment. Almost all the erosion of contaminated sediments occurs in a narrow region at the edge of the channel, between the deep channel and the shallow, nearshore area. In this region, the currents during a big event are sufcient to erode the newly deposited sediments as well as the older contaminated sediments. Only after 5 years of TABLE 8.1 PCB Transport in the Saginaw River for Different Flow Events Flow Event (m 3 /s) Transported to Bay (kg) Deposited Downstream (kg) Remaining in Bed (kg) 500 0.28 0.02 89.8 1000 11.6 0.06 78.5 1500 28.1 0.09 62.0 1900 36.5 0.11 53.6 © 2009 by Taylor & Francis Group, LLC Modeling the Transport and Fate of Hydrophobic Chemicals 319 deposition (approximately 10 g/cm 2 ) is there a signicant decrease in the amount of PCBs resuspended and transported to the bay. As shown in these calculations, most of the erosion of contaminants occurs at the edge of the channel; that is, the amounts of erosion/deposition vary greatly across a river. This is signicant in that, when considering the transport and fate of contaminated sediments and potential remedial actions, it is essential to deter- mine the contaminant concentrations and sediment erosion/deposition rates as a function of distance across the river and, most importantly, at the edge of a chan- nel where the depth and ow velocities may be changing rapidly. In this investigation, effects of variable sediment properties were not consid- ered. However, sediment properties and hence erosion rates should vary signi- cantly across the channel (because of the changing bathymetry, ow velocities, and deposition of different size particles) as well as with depth (because of ood events). Because of this, variable sediment properties should be considered in a more realistic calculation. 8.1.2 GREEN BAY,EFFECTS OF FINITE SORPTION RATES To investigate the effects of nite sorption rates on the transport and fate of HOCs in surface waters, calculations were made of the transport and fate of PCBs during storms of different magnitudes on Green Bay (Chroneer and Lick, 1997). Calcula- tions of the hydrodynamics and sediment transport were summarized in Section 6.5 (bathymetry is shown in Figure 6.30) and were the basis for the calculations of PCB transport presented here. For these calculations, it was assumed that the bottom sediments of the bay were uniformly contaminated with PCBs at a concentration of 1 µg/kg. The over- lying water was initially free of PCBs. A moderate wind of 10 m/s from right to left (as in Figure 6.30) for a period of 2 days then caused a resuspension of sedi- ments and contaminants; this was followed by a low wind of 2 m/s for 12 days, during which time the sediments deposited. As the sediments and associated con- taminants were resuspended, the contaminants desorbed from the sediments and dissolved in the water. This desorption was quantied by means of the model described in Section 7.2 with the mass transfer coefcient, k, given by Equation 7.34. An average partition coefcient of 10 4 L/kg was assumed. As in Section 7.2, the diffusion coefcient for the HOC within the particle, D, was taken to be 2×10 −14 cm 2 /s. Three sizes of particles were assumed, with diameters of 4, 14, and 29 µm and size fractions of 10, 60, and 30%, respectively. From this, the mass transfer coefcient for each size class was calculated. Calculations were done for nite rates of sorption and also for chemical equilibrium, the more usual assump- tion in contaminant transport and fate calculations. Results of these calculations are shown in Figures 8.2 and 8.3. Figure 8.2 shows the changes in C s and C w as a function of time at the location in the outer bay denoted by a * in Figure 6.29. Subscripts s and w denote suspended sedi- ment and water, respectively; e and ne denote equilibrium and nonequilibrium, respectively; f, m, and c denote ne, medium, and coarse sediments; and avg © 2009 by Taylor & Francis Group, LLC 320 Sediment and Contaminant Transport in Surface Waters 10 m/s (a) 40 40 20 20 2 10 1 1 1 N 5 0.5 0.2 2 5 80 0 10 20 km 10 10 m/s (b) 800 0 10 20 km 400 200 200 400 100 100 10 25 25 5 10 2 10 N 50 50 FIGURE 8.3 Concentrations of PCBs in Green Bay at the end of the 14-day event. Solid lines are for the equilibrium calculation, whereas the dashed lines are for the nonequilibrium calculation: (a) C w in ng/L, and (b) C s in µg/kg. (Source: From Chroneer and Lick, 1997.) 1000 3.0 2.5 2.0 1.5 1.0 C w (ng/L) C s (µg/kg) C sf C se C savg C wne C sm C we C sc 0.5 0.0 900 800 700 600 500 400 300 02468 Time (days) 10 12 14 200 100 0 FIGURE 8.2 Green Bay. Contaminant concentrations as a function of time at the point denoted by a * in Figure 6.29. Subscripts s and w denote suspended sediment and water, respectively; e and ne denote equilibrium and nonequilibrium; f, m, and c denote ne, medium, and coarse sediments; and avg denotes the average of all size classes. (Source: From Chroneer and Lick, 1997.) © 2009 by Taylor & Francis Group, LLC Modeling the Transport and Fate of Hydrophobic Chemicals 321 denotes the average of all size classes. For the equilibrium case, C se =K p C we and C we is therefore proportional to C se . As the sediments are resuspended and also transported to this location from sites in shallower waters near shore, C se and C we increase rapidly at rst (due primarily to resuspension) and then more slowly due to transport of sediments and contaminants from the nearshore. This transport of PCBs is greatly modied by nite sorption rates. In this case, C wne is initially much lower and C savg is much higher than their equilib- rium values due to the slow desorption of PCBs from the suspended sediments to the water. In more detail, the ne sediments (C sf ) desorb rapidly, whereas the medium (C sm ) and coarse (C sc ) sediments desorb much more slowly; the medium and coarse sediments lose only a small fraction of their sorbed PCBs during the 14-day event. Because the ne fraction tends to stay in suspension much longer than the medium and coarse fractions, C savg is dominated by the ne fraction and approaches C sf as time increases. For nite rates of sorption and for the rst few days, the sediments retain signicantly more of their PCBs as they are trans- ported than in the equilibrium case (i.e., C savg >> C se ); after deposition, the bottom sediments that are deposited during this time would also have a much higher concentration of PCBs. As time increases, C sf decreases below C se because of the desorption to a low C wne ; C savg decreases below C se for the same reason. The distributions of C w and C s in the water of the bay at the end of the 14-day event are shown in Figures 8.3(a) and (b), respectively. Both C wne <C we and C savg <C se throughout the bay, by approximately a factor of two in the inner bay and by a factor of ve or more in the outer bay. At the end of the 14 days, the percentage of PCBs originally resuspended and still remaining in the water (dissolved in the water plus the small amount sorbed to the remaining suspended particles that have not yet deposited) is 27% for the equilibrium case and only 11% for the nonequilibrium case. This per- centage depends on the amount of sediment resuspension. At low wind speeds, sediment resuspension is low; a higher percentage of the PCBs desorbs from the resuspended sediments to the water and remains there as the particles settle. At high wind speeds, the resuspension is high; a lower percentage of the PCBs des- orbs, and most of the PCBs are therefore still sorbed to the particles and are trans- ported with the particles as they settle to the bottom. Results for winds of 5, 10, and 20 m/s from the northeast for 2 days are summarized in Table 8.2. Of course, although the percentage of resuspended PCBs that remains in the water decreases as the wind speed increases, the total amount of PCBs remaining in the water increases because of the very nonlinear increase of sediment and contaminant resuspension as the wind speed increases. In these calculations, K p was assumed to be 10 4 L/kg, a relatively low average value for PCBs. Because desorption rates are inversely proportional to K p , the transport of PCBs with higher values of K p , say 10 5 to 10 6 L/kg, would differ con- siderably from that shown here; because of the much lower desorption rates, there would be much lower values of C w in the overlying water and higher values of C s © 2009 by Taylor & Francis Group, LLC 322 Sediment and Contaminant Transport in Surface Waters in the overlying water and in the deposited sediments for sediments with high K p as compared with those with low K p or with equilibrium partitioning. PCBs are generally mixtures of PCB congeners, each with a different K p . These K p values can differ from one another by more than an order of magnitude, and hence congener desorption rates also can differ by more than an order of magnitude. This dependence on K p of the congener desorption rate and hence transport in the overlying water also pertains to the nonerosion/nondeposition sediment-water ux (Sections 8.3 and 8.4). Because of this as well as differing solubilities, volatilization rates, and dechlorination rates (all of which depend on K p ), the relative concentrations of PCB congeners will change during transport. This dependence on K p probably is a signicant contributor to the “weathering” of PCBs (e.g., as reported for PCBs in the Hudson River (National Research Council, 2001)). 8.2 THE DIFFUSION APPROXIMATION FOR THE SEDIMENT-WATER FLUX As a more accurate approximation than the mass transfer approximation of Equa- tion 8.1 or 8.2, the vertical transport of a chemical within the sediment to the overlying water has often been described as simple, or Fickian, diffusion. This approximation is usually only valid for molecular diffusion of an inert, nonreact- ing substance. Alternately, when chemical reactions are present and are fast (e.g., when adsorption and desorption times are small compared to diffusion transport times in the sediments), then a quasi-equilibrium diffusion approximation can be used. These two limiting approximations are described below and also are com- pared with results from the mass transfer approximation as described by Equation 8.1 or 8.2. 8.2.1 SIMPLE, OR FICKIAN,DIFFUSION The basic equations for the diffusion of an inert chemical are essentially the same as those for heat conduction (e.g., Carslaw and Jaeger, 1959) and can be derived in a similar manner. For the one-dimensional, time-dependent diffusive transport of an inert chemical with concentration C(x,t), the ux is given by TABLE 8.2 Percentage of Resuspended Contaminants in Green Bay That Are Still in the Water at End of Event Wind Speed(m/s) 51020 Equilibrium 76 27 13 Nonequilibrium 30 11 8 © 2009 by Taylor & Francis Group, LLC [...]... of contaminant between the sediments and the overlying water due to diffusion of the dissolved contaminant is given by q( t ) © 2009 by Taylor & Francis Group, LLC Dw Cw (0, t ) x (8. 16) 326 Sediment and Contaminant Transport in Surface Waters It is assumed that there is no flux of contaminant from the solid particles directly into the overlying water Equations 8. 14 and 8. 15 are coupled equations and. .. Taylor & Francis Group, LLC 96 64 64 32 96 285 202 1 78 1 28 78 1.12 1.36 1.44 1. 68 2.16 Modeling the Transport and Fate of Hydrophobic Chemicals 335 are shown in Figure 8. 8 for TPCB, Kp = 46,000 L/kg, Detroit River sediments (Figure 8. 8(a)); MCB, Kp = 1200 L/kg, Detroit River sediments (Figure 8. 8(b)); and naphthalene, Kp = 80 L/kg, Lake Michigan sediments (Figure 8. 8(c)) The results for these HOCs as well... Transport in Surface Waters The fluxes Sw and Ss appearing in Equations 8. 44 and 8. 45 also must be determined As in Equation 8. 48, it follows that these are given by Sw Ss A f (x)C w A(1 (8. 53) ) s f (x)Cs (8. 54) The depositional flux of fecal pellets at the sediment- water interface is the integral of the flux over depth due to feeding, that is, q s (0, t ) Ss dx 0 A(1 ) (8. 55) f (x)Cs (x, t)dx s 0 8. 4.2.3... one-dimensional, time-dependent transport by diffusion of a dissolved, inert chemical at constant concentration, Co, in the overlying water into clean sediment From continuity, the chemical concentration in the sediment at the surface is Co The governing equation, initial condition, and boundary conditions can then be written as C t 2 C x2 D (8. 6) C(x,0) = 0 (8. 7) C(0,t) = Co (8. 8) lim C(x, t) x 0 (8. 9)... thoroughly in Section 8. 5 8. 3 THE SEDIMENT- WATER FLUX DUE TO MOLECULAR DIFFUSION For HOCs, the sediment- water flux due to molecular diffusion is often significantly modified by finite-rate sorption, with the amount and rate of sorption © 2009 by Taylor & Francis Group, LLC 3 28 Sediment and Contaminant Transport in Surface Waters dependent on the partition coefficient This has been demonstrated and quantified... divided by the time interval © 2009 by Taylor & Francis Group, LLC 346 Sediment and Contaminant Transport in Surface Waters 8. 4.2.2 Theoretical Model In describing the sediment- water flux of an HOC due to the activity of Lumbriculus variegatus, the processes that are most significant and necessary are (1) sediment convection due to the organisms feeding at depth followed by the transport and deposition... FIGURE 8. 14 Observed 137Cs activity in sediment compared with predictions by the convection-diffusion theory (Source: From Fisher et al., 1 980 With permission.) in the sediments and the sediment- water flux of this HOC due to organisms, including the effects of finite-rate sorption dynamics (Luo et al., 2006) 8. 4.2.1 Experimental Procedures The experiments were one-dimensional and time dependent and were... ) (8. 35) The flux of contaminant between the sediment and the overlying water is again given by q Dw C w (0, t ) x (8. 36) The spatial variations in the diffusion coefficient and porosity are represented by Dw Dw 0 0 1x ) D w1 (1 e 1 (1 e 2x ) (8. 37) (8. 38) where Dw0, Dw1, 0, 1, 1, and 2 are constants and are to be determined from the experiments The variations of Dw and with depth for different sediments... (1 980 ) and is f (x) N a1 (1 a1 ) exp[ b(x x m )2 ] for x xm exp[ b(x x m )2 ] xm for x (8. 52) where a1 and b are constants, xm is the depth of maximum feeding, and N is a normalizing factor chosen to satisfy Equation 8. 43 The form of f(x) was estimated from observations of organism feeding and is similar to that shown in Figure 8. 13 © 2009 by Taylor & Francis Group, LLC 3 48 Sediment and Contaminant Transport. .. than 30% in 100 years 8. 3.4 RELATED PROBLEMS The above examples were all concerned with the flux from an HOC dissolved in the overlying water into clean sediments Related problems and analyses of (1) flux from contaminated bottom sediments to clean overlying water and (2) flux due to a contaminant spill are as follows 8. 3.4.1 Flux from Contaminated Bottom Sediments to Clean Overlying Water In contrast . Contaminant Transport in Surface Waters A simple and idealized problem of contaminant release and transport during environmental dredging is discussed in Section 8. 6; the purpose is to charac- terize and. of C w in the overlying water and higher values of C s © 2009 by Taylor & Francis Group, LLC 322 Sediment and Contaminant Transport in Surface Waters in the overlying water and in the deposited. and nonequilibrium, respectively; f, m, and c denote ne, medium, and coarse sediments; and avg © 2009 by Taylor & Francis Group, LLC 320 Sediment and Contaminant Transport in Surface Waters 10