Page 221 - gas transport in porous media

Chapter 12: Continuum Modeling of Gas Transport in Porous Media
M M M M 217
F F F F
Fractures
M M M M Matrix Blocks
F F F F
M M M M
F F F F
M M M M
F F F F
(a) (c)
Figure 12.1. Illustration of concepts used for modeling of multiphase flow in fractured rocks: (a) double-
porosity model (DPM; after Warren and Root, 1963); (b) dual permeability model (DKM), with global
flow in both fracture (F) and matrix continua (M); (c) MINC sub-gridding for resolution of gradients in
the matrix blocks (after Pruess and Narasimhan, 1985).

12.2.3 Fractured Media

In many cases of interest the media through which gas transport occurs are fractured.
Conceptually, the simplest approach for transport modeling involves an explicit rep-
resentation of fractures, which are described as more-or-less planar regions of large
permeability and porosity, with “small” spatial extent perpendicular to the fracture
plane. Such explicit representation of fractures is feasible only for flow systems with a
small number of fractures. For flow systems with ubiquitous interconnected fractures,
their explicit representation is neither practically possible nor desirable, and contin-
uum representations are used instead. Such representations always entail volume
averaging on some scale. For gas transport this has a firm basis in the fundamental
physical processes which tend to be diffusive in nature (described by parabolic or
nearly-parabolic PDEs). Commonly used modeling approaches for fractured media
include double-porosity (DPM), dual permability (DKM), and multiple interacting
continua (MINC); see Figure 12.1.
The DPM considers that global flow occurs only through the network of intercon-
nected fractures, while fractures and matrix rock of generally low permeability may
exchange fluid, solutes, and heat locally. The fracture system is characterized and
modeled with customary porous medium parameters. At each point (or grid node)
of the system, two sets of thermodynamic parameters are defined to characterize the
state of the flow system: one set involves an average over the fractures, the other an
average over the matrix rock. “Interporosity flow” between the fracture and matrix
continua is assumed to be proportional to the difference in the average values of the
intensive quantities driving flow and transport (such as pressures, mass fractions, or
temperatures).
For flow systems in which both the fracture and matrix continua contribute to global
flow, the DPM is generalized to allow global fracture-fracture as well as matrix-matrix
flow, in addition to fracture-matrix exchange (Figure 12.1b). This type of approach
is applicable for multiphase (or unsaturated) flow in fractured-porous media, where