An Explanation of the Yuster Effect

Recent papers by S. T. Yuster have called attention to the largely ignoredconcept that there will be a transfer of viscous forces across fluid-fluidinterfaces during the flow of immiscible fluid phases through porous media.This leads to the implication that the relative permeability vs saturationfunction, as applied to each of the fluid phases of the system, will in someway be dependent on the viscosities of all the other fluid phases which arecontiguous to the flowing fluid of interest. In fact, Yuster has selected andanalyzed the properties of a capillary-tube model of the reservoir-prototypeflow systems and concludes from his studies that relative permeability valueswill be very markedly influenced by the viscosity ratio in two-phase systems.On the other hand, relative permeability data have been reported in theliterature for more than 20 years; and where these data are consistent at all, they consistently show no dependence on viscosity ratio (cf. chapter 7 ofMuskat for a resume of past experimental work). This paradoxical situation hasprompted us to re-evaluate Yuster's work. The major flaw we find has to do with the properties of the model Yusteremployed to give qualitative support to his predictions. This model isdefective in that important surface area parameters characteristic of theprototype-reservoir flow system have not been pro pertly scaled. Fig. 1 showshow we believe Yuster's model should be modified to circumvent this difficulty.It depicts the capillary tube of radius R and length L, comprised of twoelements in series. The first part of length, Li has the nonwetting phaseflowing centrally out to a radius distance r, where an interfacial boundaryexists with the wetting phase which flows in the concentric annular space ofthe tube. T.N. 192