Application of a quasi-implicit scheme to the simulation of non-Newtonian flows through porous media
R. de Loubens, L. Léon and L. Patacchini
Event name: ECMOR XVI - 16th European Conference on the Mathematics of Oil Recovery
Session: Physical Modelling III
Publication date: 03 September 2018
Info: Extended abstract, PDF ( 4.34Mb )
Price: € 20
When modeling non-Newtonian flows through porous media, numerical difficulties arise due to the velocity-dependence of phase mobilities. While a fully implicit treatment is unconditionally stable in the von Neumann sense, it leads to at least a 19-point stencil on 3D hexahedral grids; its implementation is therefore complex and its computational cost is high. Simpler semi-implicit schemes are often encountered, whereby the pressure gradient driving the flow is treated implicitly while the velocity-argument of mobilities is evaluated explicitly. These are however only conditionally stable, and in some practical situations of interest, clearly non-monotone. In this context, a quasi-implicit discretization has recently been proposed, where the velocity-argument of the mobilities is evaluated at cell edges with an implicit normal component, and an explicit transverse component. It has better stability and monotonicity properties than conventional semi-implicit schemes, while requiring only a 7-point stencil on 3D hexahedral grids. This quasi-implicit scheme was implemented in our parallel in-house research reservoir simulator to model non-Newtonian polymer flows. A detailed description of its implementation is provided, accommodating different rheological models. Extensive numerical tests in various geometries are then performed to validate the implementation and illustrate the advantages of the new scheme.