Technical Notes - An Explanation of the Yuster Effect

Recent papers by S. T. Yuster have called attention to the largely ignored concept that there will be a transfer of viscous forces across fluid-fluid interfaces during the flow of immiscible fluid phases through porous media. This leads to the implication that the relative permeability us saturation function, as applied to each of the fluid phases of the system, will in some way be dependent on the viscosities of all the other fluid phases which are contiguous to the flowing fluid of interest. In fact, Yuster has selected and analyzed the properties of a capillary-tube model of the reservoir-prototype flow systems and concludes from his studies that relative permeability values will be very markedly influenced by the viscosity ratio in two-phase systems. On the other hand, relative permeability data have been reported in the literature for more than 20 years; and where these data are consistent at all, they consistently how no dependence on viscosity ratio (cf. chapter 7 of Muskat3 for a resume of past experiniental work). This paradoxical situation has prompted us to re-evaluate Yuster's work. The major flaw we find has to do with the properties of the model Yuster employed to give qualitative support to his predictions. This model is defective in that important surface area parameters characteristic of the prototype-reservoir flow system have not been propertly scaled. Fig. 1 shows how 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 two elements in series. The first part of length, L has the nonwetting phase flowing centrally out to a radius distance r, where an interfacial boundary exists with the wetting phase which flows in the concentric annular pace of the tube. The second part of length, L-L,. has the