Predicting gas–water relative permeability using Nuclear Magnetic Resonance and Mercury Injection Capillary Pressure measurements

Abstract

Relative permeability functions are useful in understanding gas–water two–phase flow in rocks and reservoirs. When direct laboratory data of relative permeability are not available for evaluating gas-water two-phase flow in rocks and reservoirs, indirect prediction models using gas-water relative permeability functions are widely used.In this research, four typical existing predicting models of relative permeability based on capillary pressure are investigated (the Purcell, Burdine, Brooks–Corey and Li models). These models notably simplify the gas–water spatial distribution in rocks: the Purcell, Burdine and Brooks–Corey models all assume that gas flows in large tubes, while water flows in small tubes, and irreducible water adsorbed on tube surfaces is not considered. Alternatively, the Li model considers irreducible water adsorbed on tube surface; however, the proportion of irreducible water, mobile water and gas are assumed to be constant in tubes with different radii, as this model was derived from a single tube flow structure.This research proposes a new relative permeability model in which the pore–size distribution, the tortuosity and the gas–water spatial distribution are all considered. A bundle of capillary tubes model and modified single-tube flow model are applied in the proposed model. Capillary tubes in the rock are divided into large tubes and small tubes. In large tubes, the water phase contacts the tube surface and is partially adsorbed onto the surface and partially mobile, while gas phase flows in the center of tubes and is surrounded by water. In small tubes, only irreducible water exists. Variables in the proposed model such as the thickness of irreducible water, mobile water and gas are usually unknown. Combined with a capillary pressure curve, the shift of the transversal time (T2) distribution of Nuclear Magnetic Resonance is used to determine these variables.The proposed model is validated by experimental data from six rock samples that have different lithology, diagenesis characteristics, pore structure characteristics, irreducible water saturation and different grades of T2 distribution shifts. The model results are compared with the calculated values from other four existing models and the experimental data. Our results show that the proposed model matches the experimental data better than other models, and diagenesis and pore structure characteristics are more sensitive to the proposed model than is lithology.