The Effect of Temperature on the Permeability Ratio of Different Fluid Pairs in Two-Phase Systems
Authors: Davidson L.B. 
Published: December 2007

Results of experiments involving the isothermal displacement of a refined oil by water, nitrogen, and steam indicate that gas-oil and water-oil permeability ratios may be functions of temperature.

Introduction
The petroleum literature contains many reports on the relative permeability properties of porous media. However, only recently have studies of relative permeability at elevated temperatures been made. permeability at elevated temperatures been made. Each of these studies presents relative permeability data on water-oil systems in linear sandpacks or sandstone cores under isothermal conditions. The results of these investigation are dissimilar. Edmondson found that in Berea sandstone a temperature-dependent effect was present, while Shilobod, using the same material, found no temperature dependence after normalizing for initial water saturation. Workers at Texas A and M U. found that the ratio kw/ko was temperature dependent in an unconsolidated system. The differences in results of these studies are probably a consequence of differences in the material employed, in the experimental procedures followed, and in the properties of the porous systems used. properties of the porous systems used. This paper describes an experimental investigation of permeability ratio temperature dependence, conducted to clarify some of the results obtained by previous workers. Each experiment described in this paper involved the isothermal displacement of Chevron No. 15 white oil by either nitrogen, steam, or distilled water and displacement of water by nitrogen. All permeability ratios were calculated using the Welge permeability ratios were calculated using the Welge procedure. procedure. Values of the water-oil permeability ratio were obtained over the temperature range 75 degrees F to 540 degrees F. Results indicate the ratio is temperature dependent at low water saturations, probably due to interfacial effects. However, as the saturation is increased, temperature dependence decreases until, above some minimum saturation, the ratio becomes insensitive to temperature. Previously published work indicates that the dependence reappears at very high water saturations, a region of the ratio curve not completely examined in the present study.
It appears that water-oil permeability ratios are temperature dependent at the extremes of the ratio curve where changes in interfacial tension with temperature induce variations in residual saturations. Between the extremes, there is a region in which the permeability ratio is insensitive to temperature. The permeability ratio is insensitive to temperature. The size and location of this region is probably a function of the characteristics of the porous system.
Gas-oil permeability ratios calculated from nitrogen-white oil displacement experiments indicate a definite temperature dependence over the range 75 degrees F to 500 degrees F and over the entire gas saturation range studied. Evidence discussed in this report indicates that this dependence is a consequence of molecular slippage in the gas phase. This is an extension of the Klinkenberg effects to two-phase systems at high temperatures (the existence of slippage in two-phase systems at room temperature has been demonstrated).
JPT
P. 1037