Wettability Transformation and Interface Transfer of Particles
The literature on studies of the mechanisms of wettability alteration and interface particle transfer is rather limited and insufficient to formulate these processes accurately and rigorously. Therefore, Liu and Civan (1996) have resorted to a simplified approach, which yielded reasonably good results. They have combined the rate processes of the wettability transformation and the phase to phase particle transfer into one step assuming that the particles would immediately migrate into the phases, which wet them once their wettabilities change from one type to another.
Based on the experimental observations and the studies of the mechanisms of interface particle transfer of Ku and Henry (1987), Liu and Civan (1996) assumed that the rate of the combined processes of wettability transformation and interface transfer of particles can be expressed as being proportional to the particle concentration according to:
Particle Retention in Porous Media
Although particle retentions may occur at various locations in porous media by various mechanisms, only the most likely mechanisms are considered here. The wetting and nonwetting particles preferentially deposit over the similar wettability type pore surfaces. They can also be captured at and detained behind the pore throats under favorable conditions. The intermediately wet particles most likely move directly towards the pore throats and are captured there under certain conditions, because they migrate along the interface.
The volumetric rate of deposition of the particle species j from phase J over a similar wetting pore surface can be expressed by (Civan, 1996):
Similar to Gruesbeck and Collins (1982), Liu and Civan (1996) assumed that the porosity variation by deposition of small amounts of particles is negligible (i.e., (|) is a constant). Liu and Civan (1996) considered a homogeneous wettability porous media, hence fjs = 1, and neglected the stationary deposition, therefore ocy =0.
Pore Throat Plugging
The volumetric rate of retention of particles in the pore space following the pore throat plugging can be expressed by (Gruesbeck and Collins, 1982, Civan, 1996):
Liu and Civan (1996) assumed the porosity change is negligible in Eq. 11-35 (i.e., (}) = constant). In Eq. 11-35, ktiJtS denotes the rate constant for deposition by pore throat plugging. Civan (1990, 1996) proposed a dimensionless correlation to determine the conditions favorable for pore throat plugging in single phase fluid media. This equation determines the critical ratio of the pore throat-to-particle diameters below which pore throat plugging by jamming of particles occurs. Thus,
where the pore throat-to-particle diameter ratio and the particle Reynolds numbers are given, respectively, by:
Liu and Civan (1993, 1995, 1996) have resorted to a simplified approach in an adhoc manner and demonstrated by comparison of the results with experimental data that it works. They assumed that the fraction of the plugged pore throats is proportional to the amount of particles detained behind the plugged pore throats. Therefore, their expression for the fraction of the nonplugged pore throats can be written as:
where ktjj are some empirical coefficients. They considered that there is a minimum characteristic value of (ƒt)min. for which the rpore throat blocking happens. Thus,
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