An analytical theory is presented that permits the formulation of a mathematical model to describe the variation of relative permeability with temperature in a water/oil system. The theory develops analytical equations for temperature-dependent relative permeability in terms of water saturation, irreducible water saturation, and differential change in irreducible water saturation with temperature. These equations predict and agree reasonably well with experimental results reported by other researchers. The implications of temperature-dependent relative-permeability data on reservoir performance of a thermal process are also presented. These data together with the application of the Buckley-Leverett frontal-advance theory and the fractional-flow equation are used to predict oil recovery. predict oil recovery.
Thermal oil-recovery processes have become well accepted in the oil industry during the last 2 decades. While much has been written on heat transfer and fluid-flow mechanisms as well as case histories and numerical simulations associated with the processes, there is only limited information on the effect of elevated temperature on the basic petrophysical properties of reservoir rocks. Relative permeability is one of those properties that are important and necessary in describing properties that are important and necessary in describing the mechanisms of fluid flow in porous media. Relative permeability is usually measured at room-temperature conditions. In many cases, relative-permeability curves obtained at room temperature are used to predict performance at reservoir temperature. Many reservoir simulators of thermal processes express relative permeability as a function of fluid saturation only. These practices can lead to inaccurate or, perhaps, erroneous forecasts of oil recovery. In their study of steamflooding, Coats et al. developed a numerical simulation model and then compared simulation results with several sets of experimental data. They observed a calculated oil-recovery curve lying below the experimental curve. After performing many simulation runs with altered data in an attempt to match the calculated oil recovery with the observed oil recovery, they concluded that the temperature dependence of relative permeability must be incorporated into the model to reproduce the experimental results properly. Edmondson found that a temperature-dependent effect existed in Berea sandstone. In an experiment that involved waterflooding at elevated temperatures ranging from 75 to 500F [24 to 260C], he showed a change in relative-permeability ratio accompanied by a decrease in the residual oil saturation with temperature increase. Edmondson showed no data for the water saturations below 40%, and his relative-permeability-ratio curves show a considerable amount of scatter in the middle-saturation range. He concluded his study with a remark that prediction of field hot-water floods required displacement prediction of field hot-water floods required displacement data at an actual flood temperature. Davidson investigated the temperature dependence of permeability ratio by conducting isothermal displacement permeability ratio by conducting isothermal displacement of No. 15 white oil from an unconsolidated sandpack by either nitrogen, steam, or distilled water; and displacement of water by nitrogen. Values of the water/oil permeability ratio were obtained over the temperature range of 75 to 540F [24 to 282C]. At low water saturation, the ratio appeared to be temperature-dependent. On the other hand, gas/oil permeability ratio calculated from nitrogen/ white-oil displacement indicated a definite dependence on temperature over the range 75 to 500F [24 to 260C] and over the entire gas-saturation range. Davidson also found a decrease in residual oil saturation with temperature increase. Poston et al. presented waterflood data for unconsolidated sandpacks containing oil with viscosities of 80, 99, and 600 cp [0.08, 0.1, and 0.6 Pas] at temperatures from 70 to 300F [24 to 149C], and observed an increase in the individual relative permeability as temperature was increased. Although water/oil permeability ratio appeared temperature-sensitive, no definite trend was found for the change of relative-permeability ratio with temperature. Poston et al. also found an increase in irreducible water saturation and a decrease in residual oil saturation as temperature increased. In addition, a decrease in contact angle for the water/oil/gas system and a decrease in oil/water interfacial tension (IFT) with increasing temperature were observed. They also pointed out that unconsolidated sands became more water-wet with an increase in temperature.