Gas Slippage in Two-Phase Flow and the Effect of Temperature

Gas slippage in single-phase gas flow (Klinkenberg Effect) has been investigated extensively. Few papers, however, have been published on the gas slippage in gas-liquid two-phase flow. The gas relative permeabilities at water saturations close to the residual value have been found to be significantly greater than one in both nitrogen-water and steam-water flow through rocks. These values became less than one after the calculation was calibrated by taking the two-phase gas slip effect into consideration. The gas relative permeabilities have been measured at different mean pore pressures and the values of two-phase gas slip factor have been computed at different water saturations. The effects of temperature on both nitrogen and steam slip factors have also been studied and compared. These data have then been used to conduct a calibration in order to obtain intrinsic gas relative permeabilities that do not vary with the test pressures. It has been found from the present work that neglecting the two-phase gas slip effect may overestimate gas relative permeabilities. It is the intrinsic gas relative permeabilities instead of those measured at low test pressure that should be utilized in numerical simulation or other reservoir engineering calculation. Introduction Gas-liquid relative permeabilities are fundamental properties in reservoir engineering and numerical simulation. There may be significant effect of gas slippage in gas-liquid two-phase flow. However, few experimental data regarding the gas slip effect in two-phase flow have been published. If the slip effect is not considered correctly, the gas relative permeabilities will vary with test pressures and may be greater than one at some water saturations. On the other hand, little attention has been paid to the measurements of steam slip factor even in singlephase flow. Reliable data for steam flow is essential to the study of steam injection in heavy oil reservoirs or water injection in geothermal reservoirs where steam is produced. Rose conducted experimental measurements of gas relative permeabilities in both synthetic cores (Alundum filters) and natural sandstone cores. Rose reported that the gas slip factor of the sandstone cores decreased with the increase of the liquid (water) saturation. Fulton performed experiments on Pyrex cylindrical filters and also found that the gas slip factor decreased with the increase of the liquid (water) saturation in a range from 0 to about 30%. These experiments were not conducted at liquid saturations above 30%. Therefore, Estes and Fulton extended their experiments to liquid saturations over 30%, ranging from 0 to about 88% using Soltrol oil as the liquid phase; they found a similar phenomenon to that described by Rose and Fulton. Although many researchers, including Sampath and Keighin, demonstrated the decrease of gas slip factor with the increase of liquid saturation, the reason for which is not readily apparent. Actually, the experimental data presented by these authors are contradictory to the Klinkenberg equation, which is expressed as follows: ) 4 1 ( r c k k g g f (1) where kg is the gas permeability at a mean pressure, pm, and kgf the intrinsic permeability of gas at an infinite pressure; c is a proportionality factor with an apparent value of slightly less than 1; is the mean free path of the gas and r the average radius of the capillaries. As the mean free path of the gas is inversely proportional to the mean pressure, pm, Klinkenberg 5 reduced Eq. 1 as follows: