Effect of surface roughness and lithology on the water-gas and water-oil relative permeability ratios of oil-wet single fractures

This paper discusses the effect of surface roughness on the water-gas and water-oil relative permeabilities of single fractures. After manufacturing 20. ×. 20. cm transparent replicas of fractures developed under tensional load, constant injection rate displacement experiments were performed. Saturation distribution against time was visually monitored and the residual phases were determined for seven fracture samples of different rock types. These values were then correlated to the fractal and statistical properties of the fracture surfaces. Fractures developed from less porous and larger grain size rock samples (marbles) showed "larger scale" heterogeneity, which caused residual phase saturation in the form of large pockets. Porous rocks with small grain sizes (limestones) showed "small scale" heterogeneity yielding residual saturations in small pockets. The fractal dimension obtained by the triangular prism method has more control on the residual saturation distribution than the other fractal and statistical parameters.Subsequently, the relative permeability ratios were determined using the simplified Corey equation for fracture systems and the conditions causing deviations from the "cubic ratio" behavior were clarified qualitatively and quantitatively for four different displacement cases (water-gas, gas-water, oil-water, and water-oil).In the liquid-liquid cases, the deviations were due to a combined effect of wettability and roughness. Highly granular (and porous) limestone samples, with the smallest grain size out of the seven samples, presented the biggest deviation from the "cubic ratio" in the water displacing oil and gas cases.The semi-quantitative analysis presented in this paper is expected to give new insights into residual phase saturation development and the deviations of relative permeabilities from the traditionally accepted "cubic ratio" behavior.