Relative-Permeability Measurements: An Overview

Fluid transport through reservoir recks is complex and cannot be described by theory alone. Darcy’s law, an empirical equaiion describing the Iami”ar flow of incompressible fluids, is largely used for calculation of fluid flow through porous media. It relates the macroscopic veloci~ (flux) of a fluid of known viscosity to the pressure gradient by a pmpotiionalky factor called absolute permeability, expressed in darcies. Permeability is a measure of the abtily of porous materials to conduct flow and is, dictated by the geometry of the pore network. Generally, the fluid flow in hydrocarbon reservoirs involves more than one fluid, in which case the ablity of each fluid to flow is reduced by the presence of other fluids. Darcy’s equation has been extended to such situations using the concept of effective permeabtky, which is the apparent permeability of a fluid at a given saturation. The sum of the effective permeabllities for all phases is less than the absolute permeability because of the interference between fluids tlat share the same channels. The effective permeability to a fluid becomes zero while its saturation is finite because the fluids bikome discontinuous at low satmaticms. Another meti. concept in describing the flow of nlultiphase systems is relative permeability, which is defined as the ratio of the effective permeability of a fluid to the absolute permeability of the rock. Relative permeability has a first-order dependency on saturation level. However, many interstitial fluid distributions are possible for each level of satwation, dependins on the direction of saturation changes, Thus, values of relative permeabili~ vs. saturation obtained for drainage (reduction of wetting-phase saturation) maybe different from those for imbibition (increase in wetting-phase saturation). This phenomenon is called hysteresis. Fig. 1 shows a typical plot of two-phase relative permeability vs. saturation. It is ASOhelpful to present such plots on a semilog scale to expand the relative-permeability characteristics nea the endpoint saturation. Relative-permeability data are essential for almost all calculations of fluid flow in hydrocarbon reservoirs. The data are used in making mgimming esdrnatm of pmdwdivity, i~ectivity, and ultimate recove~ from reservoirs for evaluation and planning of production operations and also can be used to diagnose formation damage expected under vxious operational conditions. These data are unquestionably one of the most important data sets required in reservoir simulation studies.