Relative Permeabilities From Centrifuge Data

Abstract

Abstract The drainage of a wetting phase (say oil) by a non-wetting phase (say gas) may be simulated in the centrifuge by two liquids. Such experiments were conducted on a number of cores and they are discussed in a paper by Firoozabadi, et al.(1). In this paper we consider two of the cores with available capillary pressure data. Two forms of the relative permeability models are selected and the parameters of these models are obtained by history matching with a numerical simulator developed for this study that properly accounts for the capillary pressure and the boundary conditions in centrifuge experiments. It is shown that:recoveries can be matched with two — and maybe even more — very different sets of relative permeability curves;recoveries are sensitive to the parameters of each relative permeability model; andlate time predictions can be improved by using a linear relationship for the wetting phase relative permeability below some arbitrary value of the wetting phase saturation. It is concluded that both wetting and non-welling phase permeabilities can be estimated from a least-squares history match of the recovery data. However, for the oil-water system examined in this paper, the history match technique leads to a non-unique set of relative permeabilities. Introduction Relative permeability curves for a given rock sample may be measured from the steady-state or unsteady-state core displacement experiments. The steady-state(2) method requires simple calculations to derive relative permeabilities from experimental data. Either explicit or implicit approaches can be used to calculate relative permeabilities from the unsteady-state core flooding experiments. The Johnson, Bossler and Naumann(3) (JBN) or its modification(4) are explicit techniques. In the implicit method, relative permeability curves are adjusted so that the response simulated by a numerical model of the displacement process matches the measured quantities(5,6). The explicit JBN approach relates phase permeabilities and saturations at the effluent-end or some other point in the core. Relative permeabilities derived from the JBN method normally cover only a part of the saturation range over which both phases are mobile. The application of this method may yield anomalous relative permeability curve shapes for typical heterogeneous carbonate core samples and for strongly water-wet homogeneous cores(5,6). The JBN technique, however, seems to be valid for the conditions assumed in its development. A basic assumption of this method is that the capillary pressure and hence the capillary pressure end effects can be ignored. This is realized in practice by conducting experiments at sufficiently high flow rates. However, for many field scale calculations the flow rates are such that the inclusion of the capillary pressure is necessary. Also in heterogeneous cores, effective average relative permeabilities may be rate sensitive(7) and therefore the standard JBN method cannot be used. Archer and Wong(5) suggested that the use of a reservoir simulator to model laboratory tests can smooth the anomalous relative permeability curves obtained from the JBN method. They agreed that the smoothed curves reflect properties that are more consistent with the bulk behavior of the core sample than the results obtained from the standard JBN method.