Compositional Flow in Fractured Porous Media: Mathematical Background and Basic Physics - Selected Topics of Computational and Experimental Fluid Mechanics - page 3

1 Introduction
Multiphase and multicomponent fluid flow in fractured rocks occurs in a variety of
subsurface flows and transport processes, including contaminant subsurface migra-
tion, saltwater intrusion in coastal aquifers, geothermal hydrotransport, subsurface
sequestration of CO 2 , and oil production and recovery from underground reservoirs,
just to mention but a few. In particular, the transport of compositionally complex
fluids in fractured porous media has been the subject of extensive research over the
past three decades because of its practical interest in petroleum reservoir engineer-
ing. Whereas the occurrence of naturally fractured reservoirs over the world is well
acknowledged, more than 20% of the world's oil reserves are estimated to reside in
naturally fractured formations (Firoozabadi 2000 ).
In contrast to crystalline rocks in which any void space is due to fractures, void
space in fractured porous media is predominantly formed by pores, which manifest
themselves as microscopic perforations of the fracture matrix interface that alter in-
plane flow when fracture aperture is less than or equal to the grain size (Mätthai and
Belayneh 2004 ). Although above a certain aperture and length, fractures may become
preferential flow pathways that dominate fluid transport throughout the reservoir
(Phillips 1991 ), their actual impact on the transport is in general difficult to predict
because multiple fractures may exhibit self-similar and fractal properties in a wide
range of scales, with different orientations and intersecting each other. The problem
of compositional (i.e., multiphase and multicomponent) flow in fractured porous
rocks becomes even more complex owing to the strong nonlinear couplings among
viscous, gravitational, and capillary forces in the reservoir whichmanifest themselves
differently in the fracture and rock matrix domains.
The physics of multiphase flows in porous media seems to be reasonably well
established and it has been mostly developed in the framework of continuum mix-
ture theory (Allen 1985 ; Bear 1988 ; Adler and Brenner 1988 ; Miller et al. 1998 ; Chen
et al. 2006 ), where a multiphase mixture is treated as a set of overlapping continua
called constituents. In porous media a multiphase fluid mixture consists of several
phases if on the scale of typical pore apertures they are separated by sharp inter-
faces. If, on the other hand, the fluid mixture consists of several chemical species,
or components, in which their spatial segregation is only observable at intermolec-
ular length scales, we call it a multicomponent mixture. In underground petroleum
reservoirs, we deal in general with multiphase flows in which each phase comprises
several chemical species and so we refer to them as multiphase and multicompo-
nent flows, or simply, as compositional flows. In recent years, research efforts have
gone mostly into modelling compositional flow in fractured porous media in order
to optimize the recovery of hydrocarbons. The partial differential equations govern-
ing this type of flows were presented already in 1960 by Barenblatt et al. ( 1960 ),
and since then they have undergone little modifications. However, their solution still
remains a challenge owing to the nonlinear couplings among the variables, the scale-
varying heterogeneity of the fractured porous medium, and the large variations in
key material properties. At present, there is no a general satisfactory methodology
for quantitatively describing flow and reactive transport in multiscale media.