A Revised Analytic Solution to the Linear Displacement Problem Including Capillary Pressure Effects

Fokas and Yortsos (SIAM J. Appl. Math. 42(2), 318-332, 1982) and Yortsos and Fokas (SPEJ 23(1), 115-124, 1983) presented the only published exact solution of the linear waterflood problem that includes capillary effects. Despite the importance of this breakthrough, their approach has largely been disregarded due to the perceived limitations that it presented in modeling real physical situations. In this article, we show that by appropriately normalizing relevant parameters of the governing equation involved, a substantial level of the limitations is taken care of. The resultant governing equation obtained is one in terms of a parameter N (M) related to the mobility ratio and another parameter N (V), representing a ratio of the viscous to capillary forces. The results of the explicit solutions obtained indicate that these two parameters are indeed the controlling parameters of the flow, and that the capillary effects are practically non-existent even when N (V) = 100. These analytical results serve a very useful utility in validating numerical simulators.