A numerical dual‐porosity model with semianalytical treatment of fracture/matrix flow

TLDR

Flow is assumed to occur through the fracture network and between fractures and matrix blocks. The study develops a new dual‑porosity model for single‑phase fluid flow in fractured/porous media. Matrix blocks are lumped with a single average pressure, and a nonlinear fracture/matrix flux equation—validated against analytical solutions for spherical blocks—is used as a source/sink term in the TOUGH simulator, replacing the linear Warren‑Root assumption. The modified code yields more accurate simulations than the conventional Warren‑Root method while reducing computational time by about 90% relative to explicit matrix discretization.

Abstract

A new dual‐porosity model is developed for single‐phase fluid flow in fractured/porous media. Flow is assumed to take place through the fracture network and between the fractures and matrix blocks. The matrix blocks are treated in a lumped parameter manner, with a single average pressure used for each matrix block. Rather than assuming that fracture/matrix flux is proportional to the difference between the fracture pressure and matrix pressure at each point, as is done in the Warren‐Root model, we use a nonlinear equation which more accurately models the flux over all time regimes, including both early and late times. This flux equation is compared with analytical solutions for spherical blocks with prescribed pressure variations on their boundaries. The nonlinear flux equation is also used as a source/sink term in the numerical simulator TOUGH. The modified code allows more accurate simulations than the conventional Warren‐Root method, with a large savings (about 90%) in computational time compared to methods which explicitly discretize the matrix blocks.