Correct relative permeability data from steady-state experiments for capillary end effects

Abstract

Water-oil relative permeability curves can be obtained from co-injection experiments at steady-state (SS) conditions. The two-phase Darcy's law can be used to calculate the relative permeability directly only when water saturation is constant along the core. However, the capillary end effect (CEE) causes water accumulation or depletion at the end of the core depending upon the wettability. This work modifies the Intercept Method initially proposed by Gupta and Maloney. Similar to their work, we again envisage carrying out a steady-state (SS) co-injection experiment. For each ratio of water to oil flowrate (F=qwqo), we require experiments at different total flowrates. From each run, we obtain pressure drop across the core and average water saturation inside the core.We demonstrate mathematically that a plot of average water saturation vs. reciprocal of oil flowrate gives a straight line whose intercept is the water saturation in the unaffected region. A plot of pressure difference vs. oil flowrate yields a straight line whose slope gives the oil relative permeability which can be used to calculate water relative permeability. It is necessary to perform the SS experiment at least three times for the same F=qwqo (at different oil/water rates). The same procedure is used for other values of F to obtain more data points to construct the relative permeability curves. An experimental step-by-step procedure for experimental engineers to follow is given in appendix C.