1887

Abstract

Summary

A novel cell-centred control-volume distributed multi-point flux approximation (CVD-MPFA) finite-volume formulation is presented for discrete fracture-matrix simulations. The fractures are modelled as lower-dimensional interfaces between matrix cells. The nD pressure equation is solved in the matrix, coupled with an (n−1)D pressure equation solved in the fractures. Matrix-fracture fluxes are expressed in terms of matrix and fracture pressures and must be added to the lower-dimensional flow equation (called the transfer function). An additional transmission condition is used between matrix cells adjacent to low permeable fractures to link the velocity and pressure jump across the fractures. Convergence and accuracy of the lower-dimensional fracture model for highly anisotropic fields is assessed. A transport equation for tracer flow is coupled via the Darcy flux. The lower-dimensional approach for intersecting fractures avoids the more restrictive CFL condition corresponding to the equi-dimensional approximation with explicit time discretisation. Fractures and barriers are efficiently modelled by lower-dimensional interfaces which yield comparable results to those of the hybrid-grid and equi-dimensional models. In addition, the lower-dimensional fracture model yields improved results when compared to those of the hybrid-grid model for fractures with low-permeability in the normal direction.

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2014-09-08
2020-04-01
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