Computational Aspects of Dual-Porosity Models

Abstract

Macroscopic microstructure models of the dual-porosity type were introduced in several places earlier, such as Chapter 1, section 1.5, Chapter 3, section 3.4, and Chapter 9, section 9.3. Among other things, they model, the flow of fluids in highly fractured porous media; that is, media comprised of porous matrix rock divided into relatively small blocks by thin fractures [BZK60], [WR63], [Arb89a], [ADH90], [DA90], [ADH91], and [Arb93a]. Mathematically, dual-porosity models are a relatively complex system of partial differential equations in seven variables, (t, x, y). At first glance, it may not be apparent that there is any advantage to the macroscopic description versus the mesoscopic (i.e., the Darcy-scale description that explicitly models flow within the fractures and matrix). However, the dual-porosity model explicitly captures the length scales of the physical problem and is, thus, much easier to approximate computationally.