Abstract
One way of obtaining water-oil relative permeability curves is from co-injection (of water and oil) experiments at steady-state (SS) condition. The two-phase Darcy 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 describes an improved method for correcting for this effect by modifying the "intercept method" initially proposed by Gupta and Maloney (2014).
Similar to their work, we again envisage carrying out a steady-state co-injection experiment. For each ratio of water to oil flowrate (), we require experiments at several different total flowrates to be carried out. From each run, we obtain pressure drop across the core and average water saturation inside the core.
We demonstrate mathematically that 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. A plot of average water saturation vs. reciprocal of oil flowrate gives a straight line whose intercept is the water saturation associated with the oil/water relative permeability values just obtained. It is necessary to perform the same experiment for at least two values of water and oil flowrates while the ratio is constant since we require at least two points to construct a straight line. The same procedure is used for other values of F to obtain more data points to construct the relative permeability curves. We have also mathematically corrected Gupta and Maloney’s work and other works after them and arrived at a simpler and more rigorous method. The details of how our method builds upon and improves their work will be published in due course (Goodarzian and Sorbie, 2020).
