5 Contaminant Transport Modeling A useful approximation of realty or an intellectual toy? 5.1 INTRODUCTION A contaminant transport model is a work-in-progress hypothesis. Contaminant trans- port models are useful because they simplify reality for the purpose of predicting outcomes. In environmental litigation, contaminant transport models are used to confirm or challenge the allegation that a contaminant release occurred at a discrete point in time based on the observed presence of a contaminant some distance from the source. This opinion is usually based on knowledge of the location of the release, chemical test results, and a contaminant transport model. When evaluating contaminant transport models, examine the modeling results by dividing the subsurface into the following discrete zones: (1) the surface (paved and unpaved), (2) the soil and capillary fringe, and (3) the groundwater. This division is necessary because each zone requires different governing assumptions and math- ematics that cumulatively determine the time required for a contaminant to travel from the ground surface to groundwater. The ability to reliably model contaminant transport is directly proportional to the representativeness of the input parameters. Given uncertainties associated with these input parameters, a range of values should be used that produces a range of contami- nant transport probabilities. Practical inversion tools now allow for rigorous determi- nation of optimal parameter values and what the data do and do not support. A key theme of this chapter is that a unique solution for contaminant transport models does not exist (see Figure 5.1). 5.2 LIQUID TRANSPORT THROUGH PAVEMENT A frequent inquiry is the determination of whether a solvent migrated through a paved surface such as asphalt, concrete, crushed rock, or compacted soil and, if so, ©2000 CRC Press LLC the time required. Ideally, direct measurements are performed to answer this question by collecting a representative pavement core sample, ponding the liquid of interest, and recording the time required for the liquid to drip from the bottom of the sample. Absent direct measurement, contaminant transport equations are used. In order to select the correct equation(s), identification of the most likely transport mechanism — such as liquid advection (Darcy flux; see Equation 2.8 in Chapter 2), gas diffusion, liquid diffusion and evaporation — is required. The transport of dense non-aqueous phase liquids (DNAPLs) via liquid advec- tion through pavement is commonly believed to be a rapid process. This assumption is true if the pavement is cracked, allowing unrestricted flow, or if the spill occurs over an expansion/control or isolation joint filled with permeable wood, oakum, or tar. Expansion joints are placed at the junction of the floor with walls, foundation columns, and footings. Given the sorptivity of the material used to fill expansion joints, sampling and testing of these materials are often useful to establish whether a contaminant was transported into the underlying soil via an expansion joint. Isolation joints are used to separate a concrete slab from other parts of a structure to permit horizontal and vertical movement of the concrete slab. Isolation joints extend the full depth of the slab and include pre-molded joint fillers (Kosmatak et al., 1988). In the absence of direct measurements or the presence of cracks or expansion joints or direct measurements with a pavement core, quantifiable transport variables can be identified that determine if and when a liquid permeated a paved surface. Variables used in calculating the time required for a liquid to infiltrate through a paved surface include: FIGURE 5.1 Concept of a unique solution vs. a range of probable solutions. ©2000 CRC Press LLC • The temporal nature of the release (steady state or transient) • The saturated and unsaturated hydraulic conductivity of the pavement • Physical properties of the contaminant (density, viscosity, vapor pressure) • Chemical properties of the liquid (pure phase, mixed solvents, or dissolved in water) which affect the evaporation rate • Liquid thickness and the length of time that the liquid was present on the paved surface • Volume of the release • Evaporative flux • Pavement thickness, porosity, composition and slope The circumstances of a contaminant release and pavement composition are key variables. Variables regarding the circumstances of the release include whether the liquid was in contact with the pavement for a sufficient time to allow transport through the pavement to occur. If the model does not account for evaporation and/ or assumes that the liquid thickness on the pavement is constant, the model will overestimate the rate of transport. If clean-up activities were performed coincident with the release (e.g., sawdust, green sand, absorbent socks, crushed clay, etc.) or if the spill occurred in a building with forced air, these activities and evaporative loss will compete for the solvent available for transport through the pavement. Noting the physical condition of the paved surface is needed for its incorporation into the model. Such observations would include: • Is the surface treated with an epoxy coating to prevent corrosion from acid releases (common in plating shops)? • Was the concrete mixed with an additive to reduce its permeability to chemicals (e.g., addition of Dow Latex No. 560 to the concrete)? • What was the nature of the surface prior to the release (e.g., impregnated with oils and dirt, smooth or pitted, sloped toward a drain, etc.)? Once this specific information is collected, a conceptual model can be constructed. The saturated hydraulic conductivity or permeability value of the paved surface is a key variable. The terms hydraulic conductivity (K) and permeability (k) are associated with the ability of a porous media to transmit a fluid. While permeability and hydraulic conductivity are often used interchangeably, they are not synonymous. Permeability refers to properties associated with the media through which the con- taminant is migrating, such as the distribution of the grain sizes, the sphericity and roundness of the grains, and the nature of their packing (Freeze and Cherry, 1979). Fluid properties such as density and viscosity are not included. The saturated hydrau- lic conductivity of a material is a measurement of the ability of a fluid to move through the material (Lohman et al., 1972). Hydraulic conductivity accounts for fluid density and viscosity. The release of a DNAPL compound such as tetrachloroethylene (PCE) (1.63 g/ cm 3 at 20∞C) requires that the water-saturated hydraulic conductivity be adjusted to account for the differences in density and viscosity of PCE relative to water (Pankow and Cherry, 1996). As an example, the saturated hydraulic conductivity of water ©2000 CRC Press LLC through a mature, good-quality concrete is about 10 –10 cm/sec. (Norton et al., 1931; Whiting et al., 1988). This value is corrected using the following definition of hydraulic conductivity: K = kr w g/m w (Eq. 5.1) where K=intrinsic permeability. r w = fluid density. g=gravitational constant (980.7 cm/sec 2 ). m w = fluid viscosity. and k = K (m w /r w g) (Eq. 5.2) Table 5.1 lists conversions for non-water liquids assuming a saturated hydraulic conductivity of concrete to water of 10 –10 cm/sec. The liquid thickness on the pavement and the duration of time that the liquid is in contact with the pavement are additional model variables. If a trichloroethylene release occurs on a warm sunny day or in a building with forced air, evaporation is rapid. As a consequence, little liquid is available to initiate movement into the pavement. If trichloroethylene accumulates in a blind concrete sump/neutralization pit or clarifier, the trichloroethylene (TCE) may reside for a sufficient period of time with a significant DNAPL hydraulic head to allow penetration into concrete. Numerous models are available to calculate the rate of transport of a liquid through pavement. For saturated flow, a one-dimensional expression for the vertical TABLE 5.1 Saturated Hydraulic Conductivity of Concrete for Non-Water Liquids Compound Saturated Hydraulic Conductivity (K) for Concrete (cm/sec) Water 1 ¥ 10 –10 Trichloroethane (TCA) 6 ¥ 10 –9 Trichloroethylene (TCE) 4 ¥ 10 –9 Tetrachloroethylene (PCE) 6 ¥ 10 –9 Freon-111 3 ¥ 10 –9 Freon-113 (1,1,2-trichlorotrifluoroethane) 4 ¥ 10 –9 Methylene chloride 3 ¥ 10 –9 Methylethyl ketone (MEK) 5 ¥ 10 –9 Xylene 9 ¥ 10 –9 Toluene 7 ¥ 10 –9 Phenol 1.15 ¥ 10 –7 ©2000 CRC Press LLC transport of the liquid using Darcy’s Law is available. This expression defines the downward velocity (v) of the liquid as being equal to the downward flux (q) divided by the porosity of the pavement. The downward flux is the saturated hydraulic conductivity multiplied by the vertical gradient. Porosity values for paved materials are measured directly or obtained from the literature. This calculation results in a value in units of length over time that is divided into the pavement thickness to estimate the transport time. This approach does not consider the transient nature of the spill in which liquid thickness is changed due to evaporative loss. Pavement transport models that use Darcy’s Law assume that the pavement is saturated with liquid prior to the release. If the pavement is unsaturated, liquid transport is dominated by unsaturated flow resulting in contaminant velocities sev- eral times slower than for saturated flow. The importance of moisture content on unsaturated hydraulic conductivity relative to saturated flow conditions (100% satu- rated) is shown in Figure 5.2. For unsaturated flow, an equation analogous to Darcy’s equation called the Richard’s equation is used (Richards, 1931). A one-dimensional expression of this equation is C(∂y/∂t) = ∂/∂z(K∂y/∂z) + ∂K/∂z (Eq. 5.3) where C = the specific water capacity or change in water content in a unit volume of soil per unit change in the moisture content. y = suction head (i.e., matric potential). K = unsaturated hydraulic conductivity. FIGURE 5.2 Difference between saturated and unsaturated hydraulic conductivity values. ©2000 CRC Press LLC If the pavement is partially or fully water saturated and a hydrophobic fluid such as trichloroethylene is released, the pore water in the pavement will repel the trichloro- ethylene. While the extent of repulsion is difficult to quantify, the net result is some degree of trichloroethylene retardation. 5.3 VAPOR TRANSPORT THROUGH PAVEMENT Gaseous diffusion through pavement can be more rapid than liquid transport, assuming that no cracks or preferential pathways are present. The development of a model to estimate vapor velocity through pavement requires the following infor- mation: • Vapor density and pressure of the contaminant • Whether the vapor source is constant or transient above the pavement • Henry’s Law constant of the contaminant • Pavement thickness, porosity, and moisture content • Concentration of the vapor above the pavement • Concentration of the vapor within and below the pavement prior to the spill The vapor density of the compound diffusing through the pavement is a key variable. The vapor density is approximately equal to the molecular weight (MW) of the compound divided by the molecular weight of air (29). The molecular weight of PCE is about 166 g/mol, so the vapor density is 166/29 = 5.7. Table 5.2 lists vapor densities of common compounds relative to air (Montgomery 1991; Pankow and Cherry, 1996). The value in knowing the vapor density of a volatile compound is that it provides a qualitative basis to determine if a sufficient period of time has occurred to allow the vapor to permeate through a paved surface; therefore, the topography of the paved TABLE 5.2 Vapor Density of Selected Compounds Compound Vapor Density Relative to Air Gasoline 4.0 Benzene 3.0 Xylene 4.0 1,1,1-Trichloroethane (TCA) 4.5 Trichloroethylene (TCE) 4.5 Tetrachloroethylene (PCE) 5.7 Vinyl chloride (VC) 3.0 Methyl-tertiary-butyl-ether (MTBE) 3.0 ©2000 CRC Press LLC surface is required to determine if features exist to allow accumulation of the vapor. Vapor degreasers, for example, are often set in a concrete catch basin to capture any liquid spills. While cement catch basins are effective at mitigating liquid spills, they exacerbate the potential for vapor transport through the concrete because they act as an accumulator for the solvent vapor. The catch basin also minimizes the dilution of the vapor with the atmosphere. Soil samples collected under degreaser catch basins are often non-detect for chlorinated solvents while soil vapor concentrations are high. An explanation for this observation is the presence of a vapor cloud in the soil (Hartman 1999). The significance of vapor clouds is that they migrate through the subsurface and can potentially contribute to groundwater contamination. Using the effective diffusion coefficient for the compound approximates the transport rate of a vapor cloud through soil. For many vapors, this value is about 0.1 cm 2 /sec. A general approximation is that the soil porosity reduces the gaseous diffusivity by a factor of 10. For many organic vapors, the gaseous diffusion coefficient is approxi- mated as 0.01 cm 2 /sec. A rule-of-thumb calculation for the distance a vapor cloud moves through soil for many volatile compounds is estimated by Equation 5.4 (Hartman, 1997): Distance = (2)(0.01 cm 2 /sec ¥ 31,536,000) 1/2 = 800 cm = 25 ft (Eq. 5.4) A more rigorous approach to this problem is via a differential equation for the unsteady, diffusive radial flow of vapor from a source (Cohen et al., 1993): ∂ 2 C a /∂r 2 + [1/r(∂C a /∂r)] = (R a D * )(∂C a /∂t) (Eq. 5.5) where the air-filled porosity (n a ) is assumed to be constant (see Equation 5.7), R a is the soil vapor retardation coefficient, C a is the computed concentration of the vapor in air, and r is the source radius. The effective diffusion coefficient, D * (for TCE, 3.2 ¥ 10 –6 m 2 /sec; for PCE, 0.072 cm 2 /sec) (Lyman et al., 1982) is equal to: D * = Dt a (Eq. 5.6) where t a = n a 2.333 /n 2 t , n 2 t is the total soil porosity which is the sum of the air-filled porosity and the volumetric water content (Millington, 1959), and the soil vapor retardation factor (R a ) is determined by: R a = 1 + n w /(n a K H ) + r b K d /(n a K H ) (Eq. 5.7) where n w is the bulk water content, n a is the air-filled soil porosity, r b is the soil bulk density, K d is the distribution coefficient, and K H is the dimensionless Henry’s Law constant. Numerous vapor transport equations are available to estimate the travel time of vapor through pavement (Crank, 1985; McCoy and Roltson, 1992). These equations describe specific conditions that best represent the events associated with the vapor release. Appendix A provides a sample calculation for the vapor transport of PCE through a concrete pavement. ©2000 CRC Press LLC 5.4 CONTAMINANT TRANSPORT IN SOIL If a liquid has penetrated the pavement, estimated transport times for the contaminant can be calculated for the second zone (soil). Variables used to perform this calcula- tion include: • Saturated hydraulic conductivity and porosity of the soil • Variability of vertical vs. lateral hydraulic conductivity • Presence of lower permeability horizons such as clay • Fluid properties (density, viscosity, etc.) • Depth to groundwater As with contaminant transport through asphalt or concrete, the hydraulic conductiv- ity of a contaminant (if in pure form) is adjusted using the relationship for intrinsic permeability. For diesel, the conversion is described as: (K diesel – K water )([m water /m diesel ][r diesel /r water ]) (Eq. 5.8) Assuming that diesel viscosity is 0.042 cP (water = 0.1 cP) and diesel density is 0.84 g/cm 3 (water = 1.0 g/cm 3 ), then Equation 5.8 yields an expression that describes the saturated hydraulic conductivity of diesel through a soil as equal to about 0.20 the velocity of water; therefore, diesel travels slower than water through this soil. If differences in the viscosity and density of diesel are not considered, the calculated transport time using the hydraulic conductivity for water overestimates the rate of diesel transport. Numerous equations exist to describe contaminant transport through soil (Ghadiri et al., 1992; Selim et al., 1998). A common equation for the one-dimensional transport of a single component via advection and diffusion in the unsaturated zone is described by Equation 5.9 (Jury and Roth, 1990; Jury and Sposito, 1985; Jury et al., 1986). R l ∂C l /∂t = D u ∂ 2 C l /∂z 2 – V∂C l /∂z – lmR l C l (Eq. 5.9) where R l = liquid retardation coefficient. C l = pore water concentration in the vadose zone. D u = effective diffusion coefficient. lm = decay constant. V=infiltration rate. The retardation coefficient (R l ) is estimated by: R l = r bu K du + qm + (fm + qm) K H (Eq. 5.10) where r bu = soil bulk density. K du = distribution coefficient for the contaminant of interest. ©2000 CRC Press LLC qm = soil moisture content. fm = soil porosity. K H = Henry’s Law constant for the contaminant of interest. The distribution coefficient (K du ) of the contaminant of interest can be estimated via: K du = 0.6 f oc,u K ow (Eq. 5.11) where f oc,u = fraction of organic carbon in the soil. K ow = octanol-partition coefficient of the contaminant of interest. The degradation rate constant can be estimated by Equation 5.12: lm = ln(2)/T 1/2 m (Eq. 5.12) where T 1/2 m is the degradation half-life of the contaminant of interest. The effective diffusion coefficient is D u = t L D LM + K H t G D GM (Eq. 5.13) where t L = soil tortuosity to water diffusion. D LM = molecular diffusion coefficient in water. t G = soil tortuosity to air diffusion. D GM = molecular diffusion coefficient in air. The tortuosity associated with the diffusion of a compound in water and air is described by Equation 5.14 (Millington and Quirk, 1959): t L = qm 10/3 /fm 2 and t G = (fm – qm) 10/3 /fm 2 (Eq. 5.14) For a non-aqueous phase liquid (NAPL), the NAPL velocity (n u ) for the vertical migration via a constant rate release is approximated by Equation 5.15 (Parker, 1989): n u = (r ro k ro Kn)/(h ro fa S) (Eq. 5.15) where r ro = specific gravity of the NAPL. k ro = relative permeability of the NAPL. Kn = vertical saturated hydraulic conductivity to water. h ro = the light non-aqueous phase liquid (LNAPL)-water viscosity ratio. fa = the initial air-filled porosity of the soil. S=the effective NAPL saturation behind the infiltration front. ©2000 CRC Press LLC The travel time for the LNAPL to move through the unsaturated zone is therefore equal to the distance from the source to the water table divided by the NAPL velocity (n u ). A question that arises in environmental litigation is when did the contamination enter the groundwater? This question is answered by using Darcy’s Law. An example is the release of diesel from an underground storage tank. If the diesel flows through more than one soil type, a transport rate through each soil horizon is required. Input variables include the saturated hydraulic conductivity of the soil, soil porosity, and the hydraulic gradient for each horizon. Assuming a knowledge of the underlying soils (pea gravel and mixed sands) and the saturated hydraulic conductivity of these soils between the tank bottom and the groundwater table (ª24.5 ft) and that Darcy’s Law is valid, Table 5.3 is an example of the tabulated results. The total travel time for the release of diesel into the soil is about 225 days. An issue regarding the results in Table 5.3 is that it offers a unique solution. A more defensible approach is the use of a range of input parameter values (primarily the saturated hydraulic conductivity value) (Morrison, 1998). A novel approach for identifying when a DNAPL has been released into a low- permeability layer of base of an aquifer has been reported (Parker and Cherry, 1995). Soil cores collected at discrete distances from the DNAPL provide the basis for identifying the concentration of the dissolved contaminant. Diffusion calculations are then employed to estimate the length of time that diffusion has occurred and therefore the time since the DNAPL was immobilized. Assumptions include the premise that low-permeability layers of silt and clay underlying the perched DNAPLs have sufficient porosity to allow, without advection, migration of the dissolved constitu- ents into the soils via molecular diffusion and that the location of the DNAPL is precisely known. 5.4.1 CHALLENGES TO CONTAMINANT TRANSPORT MODELS FOR SOIL Transport mechanisms and pathways exist that are rarely included in contaminant transport models. Artificial examples include dry wells, foundation borings, utility trenches, sewer or stormwater backfill, cisterns, and septic lines. Natural preferential pathways include high-permeability soils, mechanical disturbance, and cosolvent transport. Table 5.4 lists some of these pathways and common computer model variables along with their impact on contaminant transport. 5.4.2 COLLOIDAL TRANSPORT Colloidal transport is a mechanism by which a hydrophobic compound preferentially sorbs to a colloid particle in water and is transported to depth. Colloids are generally regarded as materials up to 10 mm (10 –6 m) in size. Colloids exist as suspended organic and inorganic matter in soil or aquifers. In sandy aquifers, the predominant ©2000 CRC Press LLC [...]...TABLE 5. 3 Summary of Transport Calculations for Individual Soil Layers Layer Pea gravel Sand Sand Sand Total Kwater (cm/sec) Thickness (ft) Kdiesela (cm/sec) Vb (cm/sec) Travel Time 0.1 1.1 ¥ 10–4 6.6 ¥ 10 5 2.7 ¥ 10 5 1.0 7. 75 10. 75 5.0 0.02 2.2 ¥ 10 5 1.3 ¥ 10 5 5.4 ¥ 10–6 20 7.3 ¥ 10 5 4.3 ¥ 10 5 1.8 ¥ 10 5 1 .5 sec 900 hr 2100 hr 2400 hr 2 25 days Kdiesel – Kwater (mwater/mdiesel)(rdiesel/rwater),... (Bisdom et al., 1993; Glass and Nicholl, 1996), funnel flow (Diment and Watson, 19 85; Hill and Parlange, 1972; Kung, 1990a,b; Philip, 19 75) , and macropore flow (Bouma, 1981; Morrison and Lowry, 1990; White, 19 85) Finger flow (also dissolution fingering) is initiated by small- and large-scale heterogeneities in soil such as a textural interface between a coarse-textured sand that underlies a silt (Fishman,... M., and D LeBlanc, 1988 Long-term fate of organic micropollutants in sewage contaminated groundwater, Environmental Science and Technology, 22:2 05 211 Bear, J., 1979 Hydraulics of Groundwater, McGraw-Hill, New York, p 210 Bear, J., Beljin, M., and R Ross, 1992 Fundamentals of Ground-Water Modeling: EPA Ground Water Issue, EPA /54 0/S-92/0 05, Office of Research and Development, Office of Solid Waste and. .. Response, U.S Environmental Protection Agency, Washington, D.C., p 11 Bisdom, E., Dekker, L., and J Schoute, 1993 Water repellency of sieve fractions from sandy soils and relationships with organic materials and soil structure, Geoderma, 56 :1 05 118 Bois, T and B Luther, 1996 Groundwater and Soil Contamination: Technical Preparation and Litigation Management, John Wiley & Sons, Somerset, NJ, pp 1 35 144 Bouma,... morphology and preferential flow along macropores, Agricultural Water Management, 3:2 35 250 Carrier Corp v Detrex Corp., 1996 Superior Court of the State of California, County of Los Angeles, No C7036 25 Cleary, R., 19 95 Introduction to applied mathematical modeling in groundwater pollution and hydrology with IBM-PC applications, in Proc of the NGWA IBM-PC Applications in Groundwater Pollution and Hydrology... pollution, in Selim, H and L Ma (Eds.), Physical Nonequilibrium in Soils: Modeling and Application, Ann Arbor Press, Chelsea, MI, p 492 Kung, J., 1990a Preferential flow in a sandy vadose zone 1 Field observation, Geoderma, 45: 51 58 Kung, J., 1990b Preferential flow in a sandy vadose zone 2 Mechanism and implications, Geoderma, 46 :59 –71 Jury, W and K Roth, 1990 Transfer Functions and Solute Movement through... Morrison, R and R Erickson, 19 95 Groundwater investigations, in Morrison, R and R Erickson (Eds.), Environmental Reports and Remediation Plans: Forensic and Legal Review, John Wiley & Sons, Somerset, NJ, p 155 Morrison, R and B Lowry, 1990 Sampling radius of a porous cup sampler: experimental results, Ground Water, 28(2):262–267 Morrison, R and E Newell, 1999 The cosolvation transport of DDT and xylene... hydrocarbons in two creosote-contaminated aquifers in Denmark, Environmental Science and Technology, 33 (5) :691–699 Wei, C and P Ortoleva, 1990 Reaction front fingering in carbonate-cemented sandstones, Earth Sciences Review, 29:183–198 White, R., 19 85 The influence of macropores on the transport of dissolved and suspended matter through soil, Advances in Soil Science, 3: 95 113 Whiting, D and A Walitt, 1988... (Plate 5. 1*), soil fractures, swelling and shrinking clays, insect burrows, dry wells (Plate 5. 2*), open cisterns, septic lines, macropores, and highly permeable soil layers The significance of preferential flow is that the actual travel time of a compound to the water table is * Plates 5. 1 and 5. 2 appear at the end of the chapter ©2000 CRC Press LLC TABLE 5. 4 Variables of Contaminant Transport in Soil and. .. 19 85 Water Quality Assessment: A Screening Procedure for Toxic and Conventional Pollutants in Surface and Ground Water, Parts I and II, rev ed., EPA/600/ 6-8 50 02a (Part I, 609 pp.), EPA/600/ 6-8 5/ 002b (Part II, 444 pp.), U.S Environmental Protection Agency, Environmental Research Laboratory, Athens, GA Van der Heijde, P., 1984 Availability and applicability of numerical models for ground water resources . sec Sand 1.1 ¥ 10 –4 7. 75 2.2 ¥ 10 5 7.3 ¥ 10 5 900 hr Sand 6.6 ¥ 10 5 10. 75 1.3 ¥ 10 5 4.3 ¥ 10 5 2100 hr Sand 2.7 ¥ 10 5 5.0 5. 4 ¥ 10 –6 1.8 ¥ 10 5 2400 hr Total 2 25 days a K diesel –. 0.01 cP and r water = 1.0 g/cm 3 and m diesel and r diesel = 0.042 cP and 0.84 g/cm 3 , respectively. b Porosity = 0.30 and dH/dL = 1.0. * Plates 5. 1 and 5. 2 appear at the end of the chapter. ©2000. diffusion of a compound in water and air is described by Equation 5. 14 (Millington and Quirk, 1 959 ): t L = qm 10/3 /fm 2 and t G = (fm – qm) 10/3 /fm 2 (Eq. 5. 14) For a non-aqueous phase liquid (NAPL),