A Petrophysical Model to Estimate Relative and Effective Permeabilities in Hydrocarbon Systems and to Predict Ratios of Water to Hydrocarbon Productivity

Abstract

Abstract Permeability estimates from petrophysical interpretations rely mostly on relations between porosity and irreducible water saturation, for example using the approach developed by Timur (1968). If core data are available for calibration, it is common that the transform used can be quite reliable. However, relative permeability estimates require quantification of water saturation greater than irreducible saturation. In a previous publication by the authors (Holmes, et al, 2009), methodology was presented to distinguish rocks at irreducible saturation from those that contain mobile water. The technique involves a modified interpretation of porosity/saturation cross plots to identify levels at irreducible water saturation using a Buckles (1965) relationship. Once this data trend has been identified, water saturation at any given data point can be compared with theoretical irreducible saturation. Values of water saturation above irreducible water saturation indicate the presence of mobile water. Using a representative relative permeability curve, or a reservoir-specific relative permeability curve, relations can be established between water saturations above irreducible and the accompanying relative permeability, both to hydrocarbons and water. Once this is available, effective permeabilities to each phase can be calculated level-by-level. The procedure involves comparing differences between water saturation and irreducible water saturation with measured relative permeabilities to both wetting and non-wetting phases, expressed as exponential equations. Effective permeabilities are then available as the product of relative permeability and log-estimated permeability. By factoring in mobility ratios of hydrocarbons and water, it is then possible to estimate profiles of water cuts in oil/water systems, or barrels of water per million cubic feet of gas (Bbl/MMCFG) in gas/water systems. Examples are presented for both oil/water and gas/water systems, showing good correlation with fluid production from well tests.