NAPL-aqueous phase mass transfer in heterogeneous porous media

Groundwater Quality: Remediation and Protection (Proceedings of [he GQ'98 Conference held at Tubingen, Germany', September 1998). IAHS Publ. no. 250, f998.

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NAPL-aqueous phase mass transfer in heterogeneous porous media CASS T. MILLER, CLINTON S. WILLSON*, SIMON N. GLEYZER, MATTHEW W. FARTHING, JOHN F. McBRIDE Center for Multiphase Research, Department of Environmental Sciences and Engineering, University of North Carolina, Chapel Hill, North Carolina 27599-7400, USA

PAUL T. IMHOFF Department of Civil and Environmental Engineering, University of Delaware, Newark, Delaware 19716-3122, USA

Abstract Despite recent advances in the understanding of non-aqueous phase liquid (NAPL)-aqueous mass transfer, there is still a relatively poor understanding of the process at the laboratory scale and especially at the field-scale. In this work, we briefly summarize some of these limitations while focusing on heterogeneous, field-scale problems. We conclude that media heterogeneity plays a significant role in determining the morphology of the NAPL residual distribution, and this in turn plays a significant role in determining mass transfer from the NAPL residual. We review the factors affecting the NAPL residual morphology and use a high-resolution compositional modelling approach to simulate the dissolution process. Flowfield complexities affecting NAPL-aqueous phase mass transfer are demonstrated based upon simulations performed using this model.

INTRODUCTION NAPL-aqueous phase mass transfer is an important process for multiphase environmental systems because groundwater concentrations are often the basis of health concerns and regulated cleanup levels. This mass transfer phenomenon has received considerable attention in the literature (e.g. Miller et al, 1990; Geller & Hunt, 1993; Imhoff et al, 1994; Powers et al, 1994), but many issues remain unresolved (Miller et al., 1998a). While dimensional analysis has shown the mass transfer rate to be a function of at least ten non-dimensional variable groups (Miller et al, 1990), laboratory experimental work performed to date has examined only a few of these variables. These laboratory-scale systems have typically been comprised of homogeneous porous media with experimental length scales of the order of a centimetre and have modelled mass transfer using a first-order rate model. Results from these studies support the establishment of near equilibrium conditions over relatively short space and time scales (e.g. Miller et al., 1990; Powers et al., 1994). Field-scale observations do not, however, usually show groundwater systems to be near equilibrium conditions (Mackay et al, 1985; Mercer & Cohen, 1990).

* Now at: 3507 CEBA, Department of Civil and Environmental Engineering, Louisiana State University, Baton Rouge, Louisiana 70803, USA.

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Natural subsurface systems are heterogeneous in nature (Christakos, 1992; Gelhar, 1993), often over multiple scales (Cushman, 1990). Recent work has shown that the heterogeneous nature of field-scale systems probably causes the nonequilibrium conditions typically encountered in the field (Mayer & Miller, 1996). However, the most appropriate approach for modelling field-scale systems remains an open issue, including the adequacy of the first-order model. The overall goal of this work is to gain an improved understanding of NAPLaqueous phase mass transfer in heterogeneous porous media systems. The specific objectives of this work are: (a) to investigate factors that affect the nature of NAPL residual morphology for heterogeneous systems; (b) to visualize the dynamics of NAPL-aqueous phase dissolution in heterogeneous porous media systems; and (c) to consider approaches for modelling NAPL-aqueous phase mass transfer in heterogeneous systems. MODELLING APPROACH Generation of heterogeneous porous media field We assumed a scale-heterogeneous porous medium (Russo, 1991), using Millersimilar scaling to obtain porous media properties. The heterogeneity was expressed by generating correlated random fields of a scaling variable using a lognormal distribution and an anisotropic Gaussian covariance model. Spatially correlated random fields were generated from this scaling variable for permeability, NAPLentry pressure, and the mass transfer rate coefficient. Additional details can be found in Mayer & Miller (1996). Establishment of residual NAPL saturations We developed a fluid equilibrium model to establish the NAPL distribution used in the dissolution simulations, following a percolation-like approach. This approach accounted for density differences and allowed for spreading in all directions. The NAPL was introduced into the uniformly discretized, heterogeneous domain by assigning a constant capillary pressure to the NAPL phase in a source cell at the top of the domain. The NAPL invaded neighbouring cells if the balance of forces on the NAPL phase (i.e. buoyancy and capillary forces) was greater than the entry pressure of the neighbouring cell. The NAPL saturation in each cell was determined using the Brooks & Corey (1966) capillary pressure-saturation relationship for wetting phase drainage, which led to a well-defined NAPL-entry pressure for each cell. A breadthfirst search scheme (Cormen et al., 1990) was used to simulate the percolation process to establish a NAPL residual distribution. Compositional model We used a high-resolution finite-volume (FV) model to simulate water flow and NAPL dissolution and transport. Miller et al. (1998b) presents a detailed discussion of the formulation, discretization approach, and solution algorithm for this

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compositional model. We provide below a brief summary of the formulation, discretization, and solution algorithm for this model. We assumed that the solid phase was rigid, incompressible, and essentially inert and that all sources were accommodated through the specification of boundary conditions. Additionally, we used a multiphase extension of Darcy's law and assumed that the fluid phase densities were constant, yielding:

if=v 'lir^ Pa+PagS/z >) +Iap

for a = a n

'

(1)

where 9 a is the volumetric fraction (i.e., 9 a = Sa§, where Sa is the fluid saturation and the media porosity), k the intrinsic permeability, km the relative permeability, jj.a the fluid dynamic viscosity, pa the pressure, z is the unit vector in the upward direction, Iap = IJpa, Ia is the interphase exchange term, p a is the density, a is a phase qualifier, and a and n represent the aqueous and NAPL phases, respectively. Because the NAPL phase was considered immobile, the divergence term in equation (1) vanishes for the NAPL flow equation. For species transport, we assumed that the NAPL was a single species, sparingly soluble, and did not sorb to the solid phase, yielding: f ( e „ C „ ) = V-(D.VC„-q a C a )

+ /;K,

(2)

in which Ca is the concentration of the dissolved species in the aqueous phase, qa is the aqueous phase Darcy velocity vector, D is the dispersion tensor, and Im represents interphase mass transfer from the NAPL to the aqueous phase. Several constitutive relations are required for the closure of equations (1) and (2), including capillary pressure-saturation-permeability relations and interphase exchange terms. However, since the NAPL phase was assumed to be immobile, the capillary pressure effects were not important and only the aqueous phase relative permeability was calculated, which was accomplished following Corey (1994): r

i-s„-sk 1-5,.

(3)

where Sla is the irreducible aqueous phase saturation, and y is an experimental parameter that depends upon the pore-size distribution. The interphase mass transfer is accounted for using a first-order rate model with the mass transfer coefficient given from the model of Powers et al. (1994). The pressure equation was solved implicitly by a modified line successive overrelaxation method. A high-resolution, explicit, Godunov-type finite-volume method was used to solve the species conservation equation (Miller et al., 1998b). To discretize the problem, we consider a rectangular domain covered by a uniform orthogonal grid. The numerical model described in the previous section is solved via the following algorithm: (a) a discrete form of equation (1) was solved for pa using current values of Sa(x,t) and kra[Sa(x,t)]; (b) Darcy's law was used to compute qa(x,t); (c) qjx,t) and S„(x,f) were used to compute the mass transfer coefficient km(x,f)

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using the model of Powers et al. (1994); and (d) the NAPL balance equation and equation (2) were solved simultaneously to determine S„(x,t + At) and Ca(x,t + At) using the available solution for qa. This approach is reasonable for the simulations in this research, since Sa, and hence qa, vary slowly with time. RESULTS We simulated the release of trichloroethylene (TCE) into an otherwise water saturated porous media using the percolation model previously described. The density, interfacial tension, and aqueous phase solubility of TCE was taken as 1.45 g cm3, 35 dyne cm"1, and 1270 mg l"1, respectively (Mercer & Cohen, 1990). The domain was a two-dimensional, vertical section, 200 cm long by 100 cm high, discretized into 20 000 regularly spaced nodes with 200 nodes in the x-direction and 100 nodes in the z-direction. The statistics for the heterogeneous random field were var(lnk) = 2.32, x-direction correlation length = 15 cm and z-direction correlation length = 1 . 5 cm. The mean permeability for the media was 1 x 10 s cm2, the mean Brook-Corey pore size distribution index X was 1.0, and the mean air-entry pressure was 45 cm H 2 0. Figure 1 shows the NAPL distribution before any NAPL dissolution has occurred. Note the degree of lateral spreading and occurrence of pockets of high NAPL saturation (i.e. >0.50). These pockets of high NAPL saturation have low aqueous phase relative permeabilities, which significantly impacted the aqueous phase flow

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field. Because the percolation model does not account for flow dynamics, the resulting NAPL distribution showed significant lateral spreading, which resembled the expected conditions for a slow, steady release of a NAPL (Kueper & Gerhard, 1995). Figure 2 shows the NAPL distribution after 173 pore volumes have been flushed. Of particular interest are the aqueous phase preferential flow paths that form due to the removal of NAPL from several regions. Also note how the NAPL distribution is shifting to the right as dissolution occurs. Figures 3 and 4 show the TCE aqueous phase concentrations after 1 and 173 pore volumes respectively. Figure 4 shows the impact of preferential flow on the concentration field. As NAPL is removed, the aqueous phase begins to flow through channels and the mass transfer rate, and hence the concentrations begin to decrease in certain locations. DISCUSSION The percolation model developed was an efficient tool to investigate residual distributions in heterogeneous porous media. A series of simulations performed with this code showed that the residual distribution was markedly affected by the variance and correlation lengths of the scaling parameter. Fluid densities and interfacial tensions were also important, while the neglect of fluid motion led to no dependence upon fluid viscosity. For instantaneous releases of a fixed volume of NAPL, dynamic effects would be important and the percolation model used here would not be an adequate tool to describe residual distributions in such systems.

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The percolation model produced significant spatial variability of the NAPL saturation at the discretized block scale. Included in this variability, especially for the more heterogeneous cases, were significant volumes of entrapped NAPL in blocks with NAPL saturations greater than 50% of the pore space, which corresponds to pooled conditions. NAPL pools are expected to persist for long periods of time. It should also be noted that existing mass transfer correlations were not developed for pooled conditions (Miller et al., 1998a). Since existing mass transfer correlations do not include a dependence on the random field characteristics of most natural systems, existing correlations should only be applied when discretization of a numerical model is performed at a level consistent with a scale at which the porous media may be considered homogeneous. Extensive numerical experiments and modified correlations parameterized in terms of the quantitative characteristics of the heterogeneous porous media will be required for discretization at a level in which each grid block consists of heterogeneous media. This difficulty is similar to the scaling problem facing constitutive relations in general for multiphase systems (Miller et al., 1998a), and this area is the focus of our ongoing work.

Acknowledgements This work supported in part by US Army Waterways Experiment Station Contract DACA39-95-K-0098, Army Research Office Grant DAAL03-92-G-0111, and National Institute of Environmental Health Sciences Grant 5 P42 ES05948. Computing activity was partially supported by allocations from the North Carolina Supercomputing Center. REFERENCES Brooks, R. H. & Corey, A. T. (1966) Properties of porous media affecting fluid flow. Irrig. Drain. Div., Proc. ASCE IR2, 61-88. Christakos, G. (1992) Random Field Models in Earth Sciences. Academic Press, San Diego, California, USA. Corey, A. T. (1994) Mechanics of Immiscible Fluids in Porous Media. Water Resources Publication, Highlands Ranch, Colorado, USA. Cormen, T. H., Leiserson, C. E. & Rivest, R. L. (1990) Introduction to Algorithms. MIT Press, Cambridge, Massachusetts, USA. Cushman, J. H. (1990) Dynamics of Fluids in Hierarchical Porous Media. Academic Press, New York, USA. Gelhar, L. W. (1993) Stochastic Subsurface Hydrology. Prentice Hall, Englewood Cliffs, New Jersey, USA. Geller, J. T. & Hunt, J. R. (1993) Mass transfer from nonaqueous phase organic liquids in water-saturated porous media. Wat. Resour. Res. 29, 833-845. Imhoff, P. T., Jaffe, P. R. & Pinder, G. F. (1994) An experimental study of complete dissolution of a nonaqueous phase liquid in saturated porous media. Wat. Resour. Res. 30, 307-320. Kueper, B. H. & Gerhard, J. I. (1995) Variability of point source infiltration rates for two-phase flow in heterogeneous porous media. Wat. Resour. Res. 31, 2971-2980. Mackay, D. M. , Roberts, P. V. & Cherry, J. A. (1985) Transport of organic contaminants in groundwater. Environ. Sci. & Technol. 19, 384-392. Mayer, A. S. & Miller, C. T. (1996) The influence of mass transfer characteristics and porous media heterogeneity on nonaqueous phase dissolution. Wat. Resour. Res. 32, 1551-1567. Mercer, J. W. & Cohen, R. M. (1990) A review of immiscible fluids in the subsurface: Properties, models, characterization and remediation. /. Contain. Hydrol. 6, 107-163. Miller, C. T., Christakos, G., Imhoff, P. T., McBride, J. F., Pedit, J. A. & Trangenstein, J. A. (1998a) Multiphase flow and transport modeling in heterogeneous porous media: challenges and approaches. Adv. Wat. Resour. 21, 77-120. Miller, C. T., Gleyzer, S. N. & Imhoff, P. T. (1998b) NAPL dissolution fingering in porous media. In: Physical Nonequilibrium in Soils: Modeling and Application (ed. by H. M. Selim & L. Ma). Ann Arbor Press, Ann Arbor, Michigan, USA.

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Miller, C. T., Poirier-McNeill, M. M. & Mayer, A. S. (1990) Dissolution of trapped nonaqueous phase liquids: mass transfer characteristics. Wat. Resour. Res. 26, 2783-2796. Powers, S. E., Abriola, L. M. & Weber, Jr, W. J. (1994) An experimental investigation of nonaqueous phase liquid dissolution in saturated subsurface systems: 2. Transient mass transfer rates. Wat. Resour. Res. 30, 321-332. Russo, D. (1991) Stochastic analysis of simulated vadose zone solute transport in a vertical cross section of heterogeneous soil during nonsteady water flow. Wat. Resour. Res. 27, 267-283.