Experimental study of gas-liquid diffusion in porous rocks and bulk fluids to investigate the effect of rock matrix hindrance

The design of oil recovery processes by gas injection or vapor solvent relies on knowledge of diffusion coefficients to enable meaningful production predictions. However, lab measurements of diffusion coefficients are often performed on bulk fluids, without accountability for the hindrance caused by the pore network structure and tortuosity of porous media. As such, our ability to predict effective diffusion coefficients in porous rocks is inadequate and, additional laboratory work is needed to investigate the impact of the medium itself on transport by diffusion. In addition, experimental data on multi-phase diffusion coefficients are particularly scarce for tight rocks. This study therefore proposes an experimental methodology, based on a pressure-decay technique, to measure diffusion of injected gas in oil saturated porous rocks. A diffusion experiment of gas into bulk oil (without porous medium) provides an upper limit estimation of this gas-liquid diffusion coefficient. Diffusion experiments using limestone and Bakken shale provide insight into different degrees of restriction in high permeability versus low permeability media. Two analytical models and one numerical model were implemented and compared to determine the diffusion coefficients from the time-dependent experimental pressure-decay data. These diffusion coefficients were found in agreement with literature on corresponding data, demonstrating the validity of the modeling approaches used. Results indicate considerable hindrance to diffusion in porous media relative to bulk oil and relates to the tortuosity and constrictivity of the rock matrix. The diffusion coefficient of methane in bulk oil is 3.8 × 10^-9 m²/s. In our limestone sample, this diffusion coefficient drops by one order of magnitude, ranging between 1.5 to 6.5 × 10^-10 m²/s and, it drops by another order of magnitude in the Bakken shale sample to 2.0 × 10^-11 m²/s.