Mathematical and numerical filtration-advection-dispersion model of miscible grout propagation in saturated porous media. (Q2770904)

The authors present a model of behaviour of porous media during the injection of miscible grout, taking into account convection, dilution and filtration of grout solution with interstitial water, as well as consolidation aspects. Constitutive laws such as Fick's law for diffusion 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. The equations are discretized by Galerkin finite element and \(\theta\)-scheme standard method. For transport equation, streamline upwind Petrov-Galerkin's method is employed to prevent numerical oscillations.