Transport modeling in heterogeneous aquifers: 2. Three‐dimensional transport model and stochastic numerical tracer experiments

Statistical information on the coherent sedimentary structures of highly heterogeneous gravel deposits (Jussel et al., this issue) is used to investigate numerically the transport of conservative tracers. The data are the basis for a numerical generation of synthetic aquifer models, whose statistical distributions of the sedimentary structures and their hydraulic conductivity and porosity correspond to the findings in the investigated deposits. A three-dimensional finite element flow model and a corresponding random-walk transport model were developed for this purpose. Because of the large number of finite elements needed, the solution algorithm is optimized for applications on vector-type computers. In order to minimize the discretization errors a special interpolation technique is applied to the determination of the local velocity vector. Ten stochastic, numerical transport experiments over a transport distance of 100 m were carried out with synthetic gravel aquifer models. They allow the mean tracer velocity, the effective hydraulic conductivity, and the dispersion parameters to be estimated. These estimates are compared with estimates of these parameters from current theories for the flow and the tracer transport in random, correlated, anisotropic hydraulic conductivity fields.

[1]  G. J. M. Uffink,et al.  A random walk method for the simulation of macrodispersion in a stratified aquifer , 1985 .

[2]  R. Ababou,et al.  Implementation of the three‐dimensional turning bands random field generator , 1989 .

[3]  R. Ababou,et al.  Numerical simulation of three-dimensional saturated flow in randomly heterogeneous porous media , 1989 .

[4]  T. A. Prickett,et al.  A "random-walk" solute transport model for selected groundwater quality evaluations , 1981 .

[5]  A. Desbarats,et al.  Macrodispersion in sand‐shale sequences , 1990 .

[6]  Dietrich Braess,et al.  Comparison of Fast Equation Solvers for Groundwater Flow Problems , 1988 .

[7]  C. Axness,et al.  Three‐dimensional stochastic analysis of macrodispersion in aquifers , 1983 .

[8]  G. Matheron The intrinsic random functions and their applications , 1973, Advances in Applied Probability.

[9]  P. Jussel,et al.  Transport modeling in heterogeneous aquifers: 1. Statistical description and numerical generation of gravel deposits , 1994 .

[10]  M. V. Genuchten,et al.  Flux-Averaged and Volume-Averaged Concentrations in Continuum Approaches to Solute Transport , 1984 .

[11]  Adrian E. Scheidegger,et al.  Statistical Hydrodynamics in Porous Media , 1954 .

[12]  Logan K. Kuiper,et al.  A comparison of the incomplete cholesky-conjugate gradient method with the strongly implicit method as applied to the solution of two-dimensional groundwater flow equations , 1981 .

[13]  G. Dagan Flow and transport in porous formations , 1989 .

[14]  O. Zienkiewicz,et al.  The finite element method in structural and continuum mechanics, numerical solution of problems in structural and continuum mechanics , 1967 .

[15]  Peter Jussel Modellierung des Transports gelöster Stoffe in inhomogenen Grundwasserleitern , 1992 .

[16]  J. Bear Dynamics of Fluids in Porous Media , 1975 .

[17]  Andrew F. B. Tompson,et al.  Numerical simulation of solute transport in three-dimensional, randomly heterogeneous porous media , 1990 .

[18]  Thomas J. R. Hughes,et al.  LARGE-SCALE VECTORIZED IMPLICIT CALCULATIONS IN SOLID MECHANICS ON A CRAY X-MP/48 UTILIZING EBE PRECONDITIONED CONJUGATE GRADIENTS. , 1986 .

[19]  Emmanuel Ledoux,et al.  Evaluation of hydrogeologic al parameters in heterogeneous porous media , 1989 .

[20]  J. C. Jaeger,et al.  Conduction of Heat in Solids , 1952 .

[21]  L. Lake,et al.  SECOND INTERNATIONAL RESERVOIR CHARACTERIZATION CONFERENCE , 1991 .

[22]  R. Ababou,et al.  Three-dimensional flow in random porous media , 1988 .

[23]  Emil O. Frind,et al.  Comparative error analysis in finite element formulations of the advection-dispersion equation , 1985 .

[24]  S. P. Neuman,et al.  Stochastic theory of field‐scale fickian dispersion in anisotropic porous media , 1987 .

[25]  Perry Bartelt Finite element procedures on vector/tightly coupled parallel computers , 1989 .