Three-Phase Relative Permeability of Berea Sandstone
Authors: Oak M.J. , Baker L.E. , Thomas D.C. 
Published: December 2007

Summary
Reservoir engineering calculations frequently require consideration ofcoexisting oil, water, and gas phases. Such three-phase flow occurs when oil isdisplaced by simultaneous gas/water flow as in CO2, water-alternating-gasflooding, steamflooding, or other enhanced recovery processes. For this reason, reservoir simulators generally include three-phase relative permeabilityprediction methods. Two- and three-phase relative permeabilities were measuredon a water-wet fired Berea sandstone core with a fully automated steady-statemethod to investigate prediction methods experimentally.

Introduction
Reservoir studies often require use of three-phase relative permeabilitiesbecause of the presence of both water and gas in oil reservoirs, but laboratorymeasurement is almost prohibitively difficult. To resolve this problem, Stonesuggested two prediction methods that approximate three-phase relativepermeabilities from the more readily available two-phase data. His methods havebeen used widely, but with some skepticism, to estimate three-phase relativepermeabilities. Controversy exists about which method to use becausepredictions with the two methods differ significantly. When Stone introducedhis second method (Method 2), he reported that it gave better agreement withthen-available experimental data than his earlier method (Method 1) did. Later, Saraf et al. measured three-phase relative permeabilities for fired Bereasandstone and compared the data with predictions from Stone's methods. Theyreported that Method 1 was better than Method 2 in low oil-saturation ranges.while Method 2 was better in high oil-saturation ranges. Neither method, however, predicts oil relative permeabilities that are reasonably close totheir experimentally determined values. Van Spronsen reported that oil isoperms(saturation contours of equal relative permeability) predicted by Stone'sMethod 2 are convex, whereas their experimental isoperms (measured by acentrifuge method) are concave when viewed from the oil apex of the saturationternary diagram. Using a computer plotting program to improve the data fit. Fayers and Matthews tested the two methods against selected publishedexperimental data. They concluded that Method 1 was superior to Method 2. Bakerextensively re-evaluated the relationships between two- and three-phaserelative permeabilities of published data and concluded that a simple linearinterpolation of two-phase data works as well as, or better than any othercurrently available method. Current methods of estimating three-phase relativepermeabilities are uncertain and require further experimental verification. Such verification needs accurate experimental data for both two- andthree-phase relative permeabilities. Special consideration should be given tothe effects of saturation history in three-phase flow. Investigators have madeexperimental measurements of three-phase relative permeabilities since Leverettand Lewis reported their three-phase-study results. Compared with the enormousnumber of two-phase-flow studies, the relatively small number of three-phasestudies highlights the difficulties in experimental determination ofthree-phase relative permeabilities. Table 1 summarizes the experimentalstudies, listing reported core materials, saturation histories, experimentalmethods, and types of isoperm curves. Refs. 3, 16, and 17 provide detailedreviews with discussions on factors affecting experimental measurements (suchas capillary end effects). Previous experimental studies reported mostlyincomplete two-phase relative permeability data. Saraf et al. reportedextensive two-phase data, but the two-phase relative permeabilities are notconsistent with the isoperms reported in their three-phase ternary diagrams. Stone, Fayers and Matthews, and Baker supplemented the missing two-phase databy estimation and with some necessary assumptions from other reported two-phasedata or from isoperms in the ternary diagrams. Relative permeability depends onfluid saturation and on the saturation history. Most previous experimentalstudies either have ignored or incompletely reported saturation-historyeffects. From the experimental procedures reported, previous studies can begrouped into three saturation-history cases: primary DDI, secondary DDI, andIDI (see Table 1). Here, Saraf et al. nomenclature (i.e., D=decreasing andI=increasing) is adopted to name the saturation histories. For instance, DDIindicates the case of water saturation decreasing, oil saturation decreasing, and gas saturation increasing. IDI indicates the case of water saturationincreasing, oil saturation decreasing, and gas saturation increasing.

JPT
P. 1054⁁