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Mathematical and numerical filtration–advection–dispersion model of miscible grout propagation in saturated porous media
Author(s) -
Bouchelaghem F.,
Vulliet L.
Publication year - 2001
Publication title -
international journal for numerical and analytical methods in geomechanics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.419
H-Index - 91
eISSN - 1096-9853
pISSN - 0363-9061
DOI - 10.1002/nag.173
Subject(s) - mechanics , discretization , porous medium , filtration (mathematics) , advection , galerkin method , mathematics , geotechnical engineering , finite element method , thermodynamics , porosity , physics , geology , mathematical analysis , statistics
The development of a predictive model of behaviour of porous media during injection of miscible grout, taking into account convection, dilution and filtration of grout solution with interstitial water, as well as consolidation aspects, is presented. Model assumptions are reviewed and discussed first. During the establishment of the model, we insist on surface terms and their physical relevance in expressing adsorption effects. Constitutive laws such as Fick's law for diffusive mass transport, hydrodynamic dispersion tensor dealing with miscibility, are modified by taking into account filtration effects. A new surface term appears in mass balance equations as a consequence of filtration. According to the filtration laws used, an initial filtration rate is estimated on the basis of a one‐dimensional experimental campaign. The field equations are discretized by using Galerkin finite element and θ ‐scheme standard method. For transport equation, Streamline Upwind Petrov Galerkin method is employed to prevent numerical oscillations. Lastly, confrontation of numerical results with laboratory experiments constitutes a first step to validate the model on a realistic basis. Copyright © 2001 John Wiley & Sons, Ltd.