Multiple-Porosity Contaminant Transport by Finite-Element Method
Publication: International Journal of Geomechanics
Volume 5, Issue 1
Abstract
An exponential finite-element model for multiple-porosity contaminant transport in soils is proposed. The model combines three compartments for dissolved contaminants: a primary compartment of diffusion–advection transport with nonequilibrium sorption, a secondary compartment with diffusion in rectangular or spherical soil blocks, and a tertiary compartment for immobile solutions within the primary compartment. Hence the finite-element model can be used to solve four types of mass-transfer problems which include: (1) intact soils, (2) intact soils with multiple sources of nonequilibrium partitioning, (3) soils with a network of regularly spaced fissures, and (4) structured soils. Hitherto, mobile/immobile compartments, fissured soils, and nonequilibrium sorption have been treated separately or in pairs. A Laplace transform is applied to the governing equations to remove the time derivative. A Galerkin residual statement is written and a finite-element method is developed. Both polynomial and exponential finite elements are implemented. The solution is inverted to the time domain numerically. The method is validated by comparison to analytical and boundary element predictions. Exponential elements perform particularly well, speeding up convergence significantly. The scope of the method is illustrated by analyzing contamination from a set of four waste repositories buried in fissured clay.
Get full access to this article
View all available purchase options and get full access to this article.
References
Agarwal, A. N., and Pinsky, P. M. (1996). “Stabilized element residual method (SERM): A posteriori error estimation for the advection-diffusion equation.” J. Comput. Appl. Math., 74, 3–17.
Bibby, R. (1981). “Mass transport of solutes in dual-porosity media.” Water Resour. Res., 17(4), 1075–1081.
Brooks, A. N., and Hughes, T. J. R. (1982). “Streamline upwind/Petrov–Galerkin formulations for convective dominated flows with particular emphasis on the incompressible Navier-Stokes equations.” Comput. Methods Appl. Mech. Eng., 32, 199–259.
Brusseau, M. L. (1991). “Application of a multi-process nonequilibrium sorption model to solute transport in a stratified porous medium.” Water Resour. Res., 27(4), 589–595.
Brusseau, M. L., Jessup, R. E., and Rao, P. S. C. (1989). “Modeling the transport of solutes influenced by multiprocess non-equilibrium.” Water Resour. Res., 25, 1971–1988.
Coats, K. H., and Smith, B. D. (1964). “Dead-end pore volume and dispersion in porous media.” Soc. Pet. Eng. J., 4, 73–84.
Crump, K. S. (1976). “Numerical inversion of Laplace transforms using a Fourier series approximation.” J. Assoc. Comput. Math., 23(1), 89–96.
Daus, A. D., Frind, E. O., and Sudicky, E. A. (1985). “Comparative error analysis in finite element formulations of the advection-dispersion equation.” Adv. Water Resour., 8, 86–95.
Elzein, A. H., and Booker, J. R. (1999a). “Groundwater pollution by organic compounds: A two-dimensional solution of contaminant transport equations in stratified porous media with multiple non-equilibrium partitioning.” Int. J. Numer. Analyt. Meth. Geomech., 23, 1717–1732.
Elzein, A. H., and Booker, J. R. (1999b). “Groundwater pollution by organic compounds: A three-dimensional solution of contaminant transport equations in stratified porous media with multiple non-equilibrium partitioning.” Int. J. Numer. Analyt. Meth. Geomech., 23, 1733–1762.
Elzein, A. H. (2003a). “Contaminant transport in fissured soils by three-dimensional boundary elements.” Int. J. Geomech., 3(1/2), 75–83.
Elzein, A. H. (2003b). “Exponential finite elements for diffusion-advection problems.” Int. J. Numer. Methods Eng., in press.
Elzein, A. H. (2003c). “Multiple-porosity model for the transport of reactive contaminants in fractured soils with nonequilibrium partitioning.” Int. J. Geomech., 3(3/4), 182–190.
Elzein, A. H., and Carter, J. P. (2003). “A multiple-porosity finite element model for reactive contaminants in soils.” Proc., 2nd MIT Conf. on Computational Fluid and Solid Mechanics, Cambridge, U.K.
Franca, L. P., and do Carmo, E. G. D. (1989). “The Galerkin gradient least-squares method.” Comput. Methods Appl. Mech. Eng., 74, 41–54.
Franca, L. P., Frey, S. L., and Hughes, T. J. R. (1992). “Stabilized finite element methods: I. Application to the advective-diffusive model.” Comput. Methods Appl. Mech. Eng., 95, 253–276.
Goltz, M. N., and Roberts, P. V. (1986). “Three-dimensional solutions for solute transport in infinite medium with mobile and immobile zones.” Water Resour. Res., 22, 113–1148.
Hatfield, K., Ziegler, J., and Burris, D. R. (1993). “Transport in porous media containing residual hydrocarbon. II: Experiments.” J. Environ. Eng., 119(3), 559–575.
Huyakorn, P. S., Lester, B. H., and Mercer, J. W. (1983). “An efficient finite element technique for modelling transport in fractured porous media, 1. Single species transport.” Water Resour. Res., 19(3), 841–854.
Leo, C. J., and Booker, J. R. (1993). “Boundary element analysis of contaminant transport in fractured porous media.” Int. J. Numer. Analyt. Meth. Geomech., 17, 471–492.
Leo, C. J., and Booker, J. R. (1996). “A time-stepping finite element method for analysis of contaminant transport in fractured porous media.” Int. J. Numer. Analyt. Meth. Geomech., 20, 847–864.
Lupini, R., and Tirabassi, T. (1983). “Solution of the advection-diffusion equation by the moments method.” Atmos. Environ., 17(5), 965–971.
Rowe, R. K., and Booker, J. R. (1990). “Contaminant migration in a regular two- or three-dimensional fractured network: reactive contaminants.” Int. J. Numer. Analyt. Meth. Geomech., 14, 401–425.
Strouboulis, T., and Oden, J. T. (1990). “A posteriori error estimation of finite element approximations in fluid mechanics.” Comput. Methods Appl. Mech. Eng., 78, 201–242.
Sudicky, E. A. (1989). “The Laplace transform Galerkin technique: A time-continuous finite element theory and application to mass transport in groundwater.” Water Resour. Res., 25, 1833–1846.
Sudicky, E. A., and McLaren, R. G. (1992). “The Laplace transform Galerkin technique for large-scale simulation of mass transport in discreetly fractured porous formations.” Water Resour. Res., 28(2), 499–514.
Therrien, R., and Sudicky, E. A. (1996). “Three-dimensional analysis of variably-saturated flow and solute transport in discreetly-fractured porous media.” J. Contam. Hydrol., 23, 1–44.
van Genuchten, M. Th. (1985). “A general approach for modeling solute transport in structured soils.” Proc., Hydrog. Locks Low Hydr. Conduct., Memoirs Int. Assoc. Hydrog., 17(1), 513–526.
Wang, J. C., and Booker, J. R. (1997). “A Laplace transform finite element method (LTFEM) for the analysis of contaminant transport in porous media.” Research Rep. No. R756, Civil Engineering Dept., Univ. of Sydney, Sydney, Australia.
Zienkiewicz, O. C., and Taylor, R. L. (1989). The finite element method, 4th Ed., Vol. 1, McGraw-Hill, London, 116.
Zienkiewicz, O. C., and Taylor, R. L. (1991). The finite element method, 4th Ed., Vol. 2, McGraw-Hill, London, 461–484.
Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 5 • Issue 1 • March 2005
Pages: 24 - 34
Copyright
© 2005 ASCE.
History
Received: Mar 24, 2003
Accepted: Jan 7, 2004
Published online: Mar 1, 2005
Published in print: Mar 2005
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.