Numerical simulations for the evaluation of the free surface history in porous media. Comparison between two different approaches

Abstract This paper shown an empirical comparison of two different models for the theoretical analysis of the zero pressure surface position during the imbition of a partially saturated porous medium: the model based on the unsaturated-saturated approach, and the model which describes the zero pressure surface as a free external boundary for the fully saturated zone. A domain FD technique is applied for solving the governing equations of the first model, whereas a BEM formulation has been chosen for the equations of the second one. The comparison is based on numerical experiments which deal with the imbition of an academic system. The results obtained highlight the tendency of the fully saturated approximation to provide solutions where the rise of the free surface is much more localized near the injection zone than in the case of the unsaturated-saturated approach. In addition, owing to the capability of describing the capillary fringe, these latter solutions affect thicker layers of porous matrix. So, the users have to consider the system of interest with the greatest care before they choose the mathematical model which is the most suitable for the aims of the planned simulation.

[1]  Colin W. Cryer,et al.  On the Approximate Solution of Free Boundary Problems Using Finite Differences , 1970, JACM.

[2]  S. P. Neuman,et al.  Finite Element Method of Analyzing Steady Seepage with a Free Surface , 1970 .

[3]  Carlos Alberto Brebbia,et al.  Boundary Elements: An Introductory Course , 1989 .

[4]  J. Liggett,et al.  An integral formulation applied to the diffusion and Boussinesq equations , 1986 .

[5]  J. Liggett,et al.  Unsteady interzonal free surface flow in porous media , 1979 .

[6]  James A. Liggett,et al.  Boundary integral solutions to three‐dimensional unconfined Darcy's Flow , 1980 .

[7]  James A. Liggett.  Location of Free Surface in Porous Media , 1977 .

[8]  J. Liggett,et al.  Boundary integral equation solution to axisymmetric potential flows: 2. Recharge and well problems in porous media , 1979 .

[9]  J. Bear.  Hydraulics of Groundwater , 1979 .

[10]  P. Witherspoon,et al.  Application of the Finite Element Method to Transient Flow in Porous Media , 1968 .

[11]  P. K. Banerjee,et al.  Boundary element methods in engineering science , 1981 .

[12]  G. Bodvarsson,et al.  An approximate solution for one‐dimensional absorption in unsaturated porous media , 1989 .

[13]  G. Chavent.  Mathematical models and finite elements for reservoir simulation , 1986 .

[14]  Milton Edward Harr,et al.  Groundwater and Seepage , 1962 .

[15]  P. Huyakorn,et al.  Techniques for Making Finite Elements Competitve in Modeling Flow in Variably Saturated Porous Media , 1984 .

[16]  Colin B. Brown,et al.  Darcy Flow Solutions with a Free Surface , 1967 .

[17]  J. Liggett,et al.  The Boundary Integral Equation Method for Porous Media Flow , 1982 .

[18]  G. Pinder,et al.  A boundary integral technique for multiple‐front simulation of incompressible, immiscible flow in porous media , 1992 .

[19]  R. Allan Freeze,et al.  Three-Dimensional, Transient, Saturated-Unsaturated Flow in a Groundwater Basin , 1971 .

[20]  J. Philip.  Linearized unsteady multidimensional infiltration , 1986 .

[21]  J. Pickens,et al.  Finite element analysis of solute transport under hysteretic unsaturated flow conditions , 1980 .

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

[23]  Van Genuchten,et al.  A closed-form equation for predicting the hydraulic conductivity of unsaturated soils , 1980 .

[24]  R. J. Hanks,et al.  Numerical Solution of the Moisture Flow Equation for Infiltration into Layered Soils 1 , 1962 .

[25]  R. G. Hills,et al.  Modeling one‐dimensional infiltration into very dry soils: 1. Model development and evaluation , 1989 .

[26]  G. S. Taylor,et al.  Computer Methods for Transient Analysis of Water‐Table Aquifers , 1969 .

[27]  Tammo S. Steenhuis,et al.  Fingered flow in two dimensions: 2. Predicting finger moisture profile , 1992 .

[28]  S. Mukherjee,et al.  Boundary element techniques: Theory and applications in engineering , 1984 .

[29]  James A. Liggett,et al.  Boundary integral equation solution to axisymmetric potential flows: 1. Basic formulation , 1979 .