Finite element techniques for modeling groundwater flow in fractured aquifers

A mathematical description of groundwater flow in fractured aquifers is presented. Four alternative conceptual models are considered. The first three are based on the dual-porosity approach with different representations of fluid interactions between the fractures and porous matrix blocks, and the fourth is based on the discrete fracture approach. Two numerical solution techniques are presented for solving the governing equations associated with the dual-porosity flow models. In the first technique the Galerkin finite element method is used to approximate the equation of flow in the fracture domain and a convolution integral is used to describe the leakage flux between the fractures and porous matrix blocks. In the second the Galerkin finite element approximation is used in conjunction with a one-dimensional finite difference approximation to handle flow in the fractures and matrix blocks, respectively. Both numerical techniques are shown to be readily amendable to the governing equations of the discrete fracture flow model. To verify the proposed numerical techniques and compare various conceptual models, four simulations of a problem involving flow to a well fully penetrating a fractured confined aquifer were performed. Each simulation corresponded to one of the four conceptual models. For the three simulated cases, where analytical solutions are available, the numerical and the analytical solutions were compared. It was found that both solution techniques yielded good results with relative coarse spatial and temporal discretizations. Greater accuracy was achieved by the combined finite element-convolution integral technique for early time values at which steep hydraulic gradients occurring near the fracture-matrix interface could not be accommodated by the linear finite difference approximation. Finally, the results obtained from the four simulations are compared and a discussion is presented on practical implications of these results and the utility of various flow models.

[1]  W. G. Gray,et al.  Finite Element Simulation in Surface and Subsurface Hydrology , 1977 .

[2]  Robert Bibby,et al.  Mass transport of solutes in dual‐porosity media , 1981 .

[3]  H. J. Ramey,et al.  Unsteady-State Pressure Distributions Created by a Well With a Single Infinite-Conductivity Vertical Fracture , 1974 .

[4]  T. D. Streltsova-Adams.  Well Hydraulics in Heterogeneous Aquifer Formations , 1978 .

[5]  A. S. Odeh,et al.  Unsteady-State Behavior of Naturally Fractured Reservoirs , 1965 .

[6]  T. N. Narasimhan,et al.  Multidimensional numerical simulation of fluid flow in fractured porous media , 1982 .

[7]  A. Gureghian.  A Study by the Finite-Element Method of the Influence of Fractures in Confined Aquifers , 1975 .

[8]  Hossein Kazemi,et al.  Pressure transient analysis of naturally fractured reservoirs with uniform fracture distribution , 1969 .

[9]  L. HeberCinco,et al.  Transient Pressure Behavior for a Well With a Finite-Conductivity Vertical Fracture , 1978 .

[10]  R. H. Rossen.  Simulation of Naturally Fractured Reservoirs With Semi-Implicit Source Terms , 1977 .

[11]  P. J. Clossman.  An Aquifer Model for Fissured Reservoirs , 1975 .

[12]  N S Boulton,et al.  ANALYSIS OF DATA FROM NON-EQUILIBRIUM PUMPING TESTS ALLOWING FOR DELAYED YIELD FROM STORAGE. , 1963 .

[13]  M. S. Hantush.  Hydraulics of Wells , 1964 .

[14]  G. I. Barenblatt,et al.  Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks [strata] , 1960 .

[15]  James O. Duguid,et al.  Flow in fractured porous media , 1977 .

[16]  Anders Rasmuson,et al.  Exact solution of a model for diffusion in particles and longitudinal dispersion in packed beds , 1980 .

[17]  H. Kazemi,et al.  NUMERICAL SIMULATION OF WATER-OIL FLOW IN NATURALLY FRACTURED RESERVOIRS , 1976 .

[18]  Anders Rasmuson,et al.  Migration of radionuclides in fissured rock: The influence of micropore diffusion and longitudinal dispersion , 1981 .

[19]  H. J. Ramey,et al.  Applied Pressure Analysis for Fractured Wells , 1975 .

[20]  G. Pinder,et al.  Numerical solution of partial differential equations in science and engineering , 1982 .

[21]  J. Bear,et al.  On the Flow of Two Immscible Fluids in Fractured Porous Media , 1972 .

[22]  J. E. Warren,et al.  The Behavior of Naturally Fractured Reservoirs , 1963 .

[23]  B. Finlayson.  The method of weighted residuals and variational principles : with application in fluid mechanics, heat and mass transfer , 1972 .