Page 143 - gas transport in porous media

Sahimi et al.
136
where C s is the solvent concentration, and µ s and µ o are the viscosities of the solvent
and oil, respectively. Sometimes, instead of C s , the solvent volume fraction is used
in Eq. (8.1). If, in addition to the solvent, another fluid, such as water, is also injected
into the porous medium, as is often done in order to reduce the mobility of the solvent,
then defining an effective value of M can become problematic. The mobility ratio
when a solvent displaces oil at irreducible water saturation (the saturation at which
the water phase becomes disconnected), with negligible mixing of the solvent and
oil, is simply the ratio of oil and solvent viscosities, M = µ o /µ s (assuming that
the porous medium is homogeneous, though microscopically disordered, so that the
permeabilities K o and K s experienced by the two fluids are essentially equal), and is
always greater than unity. When M > 1, the mobility ratio is said to be unfavorable,
since it may lead to formation of fingers which reduce the efficiency of a miscible
displacement (see below). Defining an effective mobility ratio is more complicated
and uncertain when mobile water is present.
In many miscible displacement processes, one must deal with more than one dis-
placing front. For example, in tertiary oil recovery (which is carried out when, for
example, water flooding is no longer effective) there are usually more than one dis-
placing fronts. The problem of defining an effective M is even more complex in such
situations, and no completely satisfactory method has been developed yet to address
it. In such processes, motion of any particular front is affected not only by the mobility
ratio across that front (i.e., the mobility ratio of the two fluids on the two sides of the
front), but also by the mobilities of the other regions behind and ahead of the front
and by their relative sizes.

8.2.2 Diffusion and Dispersion
Under certain conditions, mixing of the displacing and displaced fluids by diffusion
can be important. For example, during both secondary and tertiary displacement of a
reservoir’s oil by CO 2 , the development of multiple-contact miscibility strongly con-
trols the ultimate recovery efficiency. At the microscopic scale, molecular diffusion
is the mechanism by which molecular mixing of CO 2 and oil occurs. It is at this scale
that the usual assumption of rapid local equilibrium is made, and is used for numeri-
cal simulation of CO 2 flooding. Similarly, during flooding of rich gases that contain
hydrocarbons of intermediate molecular weight, miscibility with the in-place oil is
developed by a multiple-contact condensing mechanism, during which diffusive mass
transfer plays an important role. Moreover, a significant oil saturation may exist in
the dead-end pores, or be traped by water films in a water-wet porous medium during
a miscible displacement. Such isolated oil remains largely unrecoverable unless the
gas injected into the porous medium can efficiently traverse the surrounding water
barriers to contact and swell the trapped oil. The injected gas also penetrates the oil by
molecular diffusion which in turn inhibits viscous fingering (since diffusion helps the
fingers join together), delays premature gas breakthrough and, therefore, increases
the oil production rate.