Fluid Distributions Characterizing Gas-Liquid Flow

Abstract

It is the purpose of this note to call attention to the circumstancecomplicating the attainment of uniform gas-liquid distributions in multi-phaseflow systems, and especially in those of the so-called Hassler type. Althoughthe complication arises directly as a consequence of gas compressibility andthe dependence of fluid distributions on interfacial curvature phenomena, little reference to the problem has yet appeared in the literature. In fact, itis only the paper of Geffen et al. which gives any experimental evidence that aproblem exists. On the other hand, previous authors have made the tacit, albeitfallaceous assumption that uniform gas-liquid distributions automatically areestablished in linear flow systems by the expedient of maintaining the pressuregradients equal in the flowing gas and liquid phases. Such a device, it can beshown, will succeed only if the immiscible fluids are both equally compressibleor both essentially non-compressible. Another necessary condition requiredbefore uniform fluid-fluid distributions can be achieved is that the porousmatrix is isotropic. Uniform fluid saturation distribution conditions obtain in isotropic mediaonly when the curvature of each interface of contact between wetting andnon-wetting fluids is everywhere the same throughout the interspaces. This is anecessary condition which follows from the consideration that variation ininterfacial curvature gives rise to finite capillary pressure gradients andtherefore to variation in the saturation distribution. That this is not asufficient condition follows from the consideration that hysteric possibilitiesallow for different saturations even though the capillary pressure gradient iszero. In any event, it will be recalled that it is the intent in the Hasslerscheme of relative permeability determination to obtain initially (by thecapillary pressure drainage or imbibition process) uniform conditions of fluiddistribution in the core sample, and then to maintain this uniformity duringmixture flow so that the resultant fluid mobilities which are calculated willrefer to steady-state transfer under fixed conditions of uniformsaturation. T.N. 66