Towards large-scale modelling of fluid flow in fractured porous media

Abstract

To date, the complexity of fractured porous media still precludes the direct incorporation of small-scale features into field-scale modelling. These features, however, can be instrumental in shaping and triggering coarsening instabilities and other forms of emergent behaviour which need to be considered on the field-scale. Here we develop numerical simulation methods for this purpose and demonstrate their improved performance in single-and two-phase flow simulations with models of fractured porous media. Material discontinuities in fractured porous media strongly influence single-and multi-phase fluid flow. When continuum methods are used to model transport across such interfaces, they smear out jump discontinuities of concentration or saturation. To overcome this drawback, we “explode” hybrid finite-element node-centred finite-volume models along these introducing complementary finite-volumes along the material interfaces. With this embedded discontinuity discretization we develop a transport scheme that realistically represents the dependent variable discontinuities arising at these interfaces. The main advantage of this new scheme is its ability to honour the flow effects that we know that these discontinuities have in physical experiments. We have also developed a new time-stepping control scheme for the transport equation. It allows the user to specify the volume fraction of the model in which he/she is prepared to relax the CFL condition. This scheme is applied in a study of the impact of fracture pattern development on solute transport. These two-dimensional simulations quantify the effect of the fractures on macro-scale dispersion in geomechanically generated fracture geometries, as opposed to stochastically generated ones. Among other insights, the results indicate that fracture density, fracture spacing, and the fracture-matrix flux ratio control anomalous mass transport in such media. We also find that it is crucial to embed discontinuities into large-scale models of heterogeneous porous media.