Several investigators including Muecke (1979), Sarkar (1988), and Sarkar and Sharma (1990) have determined that fine particles behave differently in a multi-phase fluid environment and formation damage follows a different course than the single-phase systems. However, the reported studies on the two-phase formation damage are very limited. Sutton and Roberts (1974) and Sarkar and Sharma (1990) have experimentally observed that formation damage in two-phase is less severe than in single-phase. Liu and Civan (1993, 1995, 1996) have shown that two-phase formation damage requires the consideration of other factors, such as the wettability affect and partitioning of particles between various phases.

Mutual interactions and affects between the two-phase flow systems, fine particles, and porous matrix are described mathematically to develop a predictive model for formation damage by fines migration in two-phase systems flowing through porous formations. The formulation is carried out by extending the Liu and Civan (1993, 1994, 1995, 1996) model for more realistic applications. The tests and case studies used by Liu and Civan (1995, 1996) are presented for demonstration and verification of the model. Although the model presented here involves some simplifications pertaining to the laboratory core damage experiments, it can be readily modified and generalized for the actual conditions encountered in petroleum reservoirs.


The equations describing the various aspects for formation damage by fines migration during two-phase fluid flow through porous formations are formulated here. However, the formulation can be extended readily to multi-phase fluid systems. It is safe to assume that the gas phase does not carry any solid particles (i.e., it is nonwetting for all particles). For convenience in modeling, the bulk porous media is considered in four phases as schematically depicted in this article:

(1) the solid matrix,

(2) the wetting fluid,

(3) the nonwetting fluid, and

(4) the interface region.

These phases are indicated by S, W, N, and /, respectively. The porous matrix is assumed nondeformable. Therefore, it is stationary and its volumetric flux is zero. The wetting and nonwetting phases flow at the volumetric fluxes denoted, respectively, by uw and UN. The interface region is located between the wetting and nonwetting phases and is assumed to move at a flux equal to the absolute value of the difference between the fluxes of the wetting and nonwetting phases.

The various particles involving the formation damage are classified as

(1) the foreign particles introduced externally at the wellbore,

(2) the indigeneous particles existing in the porous formation, and

(3) the particles generated inside the pore space by various processes, such as the wettability alteration considered in this chapter.

Another classification of particles is made with reference to the wettability as

(1) the wetting particles,

(2) the nonwetting particles, and

(3) the intermediately wetting particles.

These particles are identified, respectively, by wp, np, and ip. The latter classification is more significant from the modeling point of view. Because, as explained by Muecke (1979), the wettability affects the behavior of these particles in a multi-phase fluid system. By means of experimental

investigations, Muecke (1979) has observed that particles tend to remain in the phases that can wet them. Ku and Henry, Jr. (1987) have shown that intermediately wet particles accumulate at the interface of the wetting and nonwetting phases, because they are most stable there. Therefore, in the following formulation, an interface region containing the intermediately wet particles is perceived to exist in between the wetting and nonwetting phases as schematically indicated in this article.

Further, it is reasonable to consider that the wettability of some particles may be altered by various processes, such as asphaltene, paraffin, and inorganic precipitation or by other mechanisms such as the turbulence created by rapid flow in the near-wellbore region. Consequently, these altered particles should tend to migrate into the phases that wet them as inferred by the experimental studies of Ku and Henry, Jr. (1979). In addition to the particles, the various phases may contain a number of dissolved species. The salt content of the aqueous phase is particularly important, because it can lead to conditions for colloidally induced release of clay particles when its salt concentration is below a critical salt concentration (Khilar and Fogler, 1983).

For convenience in formulation, the locations for particles retention can be classified in three categories:

(1) the wetting pore surface,

(2) the nonwetting pore surface, and

(3) the pore space behind the plugging pore throats.

The areal fractions of the wetting and nonwetting sites can vary as a result of the various rock, fluid, and particle interactions during formation damage, such as by asphaltene, paraffin, and inorganic deposition. Therefore, a parameter fks indicating the fraction of the pore surface, that is wetting for species k, is introduced in the formulation. Because the applications to describe and interpret the laboratory core damage data, conducted at mild temperature and pressure conditions are intended, the formulation is carried out for one-dimensional flow in homogeneous core plugs, isothermal conditions, and incompressible particles and fluids. This allows the use of a simplified formulation based on volumetric balances and a fractional flow concept. However, the derivation can be readily extended for compressible systems encountered at the prevailing elevated pressure conditions of the reservoir formations.


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