Prediction of Relative Permeability Characteristics Of Intergranular Reservoir Rocks from Electrical Resistivity Measurements
Authors: Pirson S.J. , Boatman E.M. 
Published: December 2007

Abstract
More than a decade ago some theoretically derived relationships were proposed that permitted the prediction of the relative ability of reservoir fluids (oil, gas, water) to flow simultaneously within the porous structure of rocks. While many successful predictions of fluid-flow ratios from wells have been made from electric logs, the theoretical deductions have not been subjected to laboratory verifications. For the relative permeability to liquid and gas, simultaneous flow of water and air was used, employing the familiar external-gas-drive technique. While in the process of water desaturation, the resistivities of the test cores (Woodbine sand) were measured. Their permeabilities varied from 10 to 280 md. The laboratory results indicated the need for changing the values of exponents in the theoretically derived formulas, whereas the form of the functions of resistivities and saturations remained as derived by theory. For the relative permeability to oil and water, the three-core dynamic technique was used on six cores. In this case it was found that the formulas were valid with but slight modification as derived by theory, to a sufficient degree of accuracy for engineering use and for well productivity prediction from electric logs.
Introduction
Conventional quantitative well log interpretation generally stops after reasonable values for formation porosities and water saturations have been established. Yet such information is insufficient to predict either the outcome or the desirability of well tests and completion, let alone the economic aspect of producing oil- and gas-bearing sections which might have been established by conventional log analysis. To give an engineering answer to such questions, it is necessary to predict the expected fluid flow ratios, the productivity index and the ultimate recovery from potentially productive wells. This problem requires in part for its solution a determination of the relative permeability characteristics of the potentially producing formations, both to oil (or water) and gas, and to oil and water.
GAS LIQUID RELATIVE PERMEABILITIES
Few methods for determining or calculating relative permeability values, other than from flow tests on reservoir cores, have been proposed. Corey proposed a method of calculation derived from capillary pressure concepts, using the observation that for certain cases, 1/pc is approximately a linear function of the effective saturation. The Corey equations are
........................(1)
..........(2)
These equations check out very well in the laboratory and are accurate for somewhat more than the limited range of conditions they were derived for. This is due to the smoothing effect of the derivation method. Corey measured the gas permeability and calculated from this the value of So* and the oil phase permeability. Corey's formulas, however, were derived for the drainage process only. Torcaso and Wyllie modified Corey's equations and used them to define a kg/ko ratio:
(3)
For low values of irreducible water saturation (i.e., for relatively permeable and porous rocks), the curve agrees closely with field correlation. From petrophysical considerations, Pirson derived equations for the wetting and non-wetting phase relative permeabilities for both imbibition and drainage processes. These equations are:
(4)
(5)
(6)
JPT
P. 564ˆ