Numerical modeling of hyperbolic dominant transient fluid flow in saturated fractured rocks using Darcian approach

Abstract

A numerical model has been developed for simulating fluid flow in a coupled fracture-matrix system by considering a hyperbolic dominant fluid flow equation within the fracture as against the conventional parabolic dominant fluid flow equation. In addition, for the first time a transient fluid mass transfer function has been introduced in the governing equation of fluid flow within the rock-matrix in order to explicitly consider the fluid drainage from rock-matrix into the fracture. The effectiveness in modeling fluid flow using different governing equations developed by implementing the pseudo-steady state and transient models of transfer functions with parabolic and hyperbolic conditions within the fracture and rock-matrix has been discussed in detail. Numerical results suggest that the drainage of fluid from the rock-matrix to the fracture and thus the estimation of its fluid recovery from the reservoir are overestimated in a typical coupled fracture-matrix system using conventional parabolic dominant fluid flow equation. It has been further observed that among the hyperbolic and parabolic dominant mathematical models used to describe the fluid flow through fracture, the recent model proposed by the first author, which is associated with the rate limited fluid mass transfer term within the low permeable rock-matrix yields a significantly varying pressure distribution with reference to the rest of the cases. It is also observed that the resultant pressure distribution within a coupled fracture-matrix system is independent of the pseudo-steady state transfer or transient transfer function, which is used for modeling the fluid interaction at the fracture-matrix interface.