Nonwetting phase

The determination of the capillary pressure of a diffusion layer is critical, not only to have a better understanding of the mass transport mechanisms inside DLs but also to improve their design. In addition, the accuracy of mafhemafical models can be increased with the use of experimental data obtained through reliable techniques. Both Gostick et al. [196] and Kumbur et al. [199] described and used the MSP method in detail to determine the capillary pressures of differenf carbon fiber paper and carbon cloth DLs as a function of the nonwetting phase saturation. Please refer to the previous subsection and these publications for more information regarding how the capillary pressures were determined. 

Swanson, B.F. (1979) Visualizing pores and nonwetting phase in porous rock. J. Petro. Tech. 31, 10-18... 

Ransohoff and Radke found that for C <10 lamella generation occurred only by the leave-behind mechanism. The lamellae moderately increased the resistance to flow, raising it by about a factor of five (40). (Here p is the viscosity of the nonwetting phase, U is the total superficial velocity, R is the bead radius, K is the absolute permeability, k is the relative permeability, L is length, and Y is the interSacial tension.) The use of this definition of the capillary number, instead of the usual C = jU/y, with J the viscosity of the wetting phase, was justified in the heoretical analysis ( ). 

For capillary numbers greater than the critical value, snap-off occurred even in homogenous bead packs (40). The resulting dispersions caused much greater resistance to flow than the resistance produced by leave-behind lamellae (which do not disperse the nonwetting phase). 

A lower limit on the capillary number required for snap-off arises from a static analysis of nonwetting flow into the constriction. Roof s analysis of snap-off in symmetric constrictions shows that there is a strictly geometrical requirement for the nonwetting phase to enter the constriction. Below this limit snap-off cannot occur. For example, in a circular constriction the relation... 

Capillary pressure effects appear to explain the very important 1964 discovery of Bernard and Holm that dispersions could make the mobility of the nonwetting phase essentially independent of the absolute permeability of the porous medium (52). (See above.) Indeed, the theoretical analysis of Khatib, et al., which was corroborated by experiments, gave dispersed-phase mobilities at the upper limiting capillary pressure (for coalescence) that were nearly constant for absolute permeabilities ranging from 7D to ca. 1,000D (41). 

As defined by Radke and Ransohoff (Equation 7), the "snap-off" capillary number, C, contains the effective grain radius, R the permeability, K anS the relative permeability of the nonwetting phase, k ( ). In field applications, the values of all of these parameters are set by the reservoir. Also contained in C are the total superficial velocity, U, and the distance between injection and production wells, L. Within narrow limits, L can be changed by... 

Since capillary snap-off disperses the nonwetting phase in the wetting fluid, wettability changes may drastically alter the effectiveness of the process. 

Once a discontinuous nonwetting phase is formed, the capillary forces opposing ganglia motion must be overcome, or the ganglia will be trapped. The maximum capillary pressure rise exhibited by ganglia of any length in a porous medium can be estimated in terms of throat radius r. and body radius... 

Relative permeability theory may not apply at high capillary number flow for the nonwetting phase since it becomes discontinuous and its flow rate may thus not be proportional to the macroscopic pressure gradient. 

Fig. 6 Schematic of nonwetting phase invasion into a pore (A) schematic representation of a pore formed by four grains (B) low capillary pressure (C) critical capillary pressure for invasion (D) phase distributions after Haines jump (E) high capillary pressure (F) disconnection of the nonwetting phase after snap-off.

Despite the suddenness of these pore-scale events, the displacement process appears smooth at the macroscopic scale As the capillary pressure is increased, the nonwetting phase flows into increasingly smaller pore spaces, and is thereby reduced. The macroscopic functionality (capillary pressure vs. saturation) is the capillary pressure curve mentioned previously. Fig. 7 is an example capillary pressure curve obtained by injecting mercury into a dry packing of glass... 

Fig. 7 Capillary pressure curve for mercury (nonwetting phase) intrusion into a packing of glass spheres. (From...

For nonwetting-phase fluids, a converse argument could be made that the relative permeability should... 

---