Shale gas transport in rock matrix: Diffusion in the presence of surface adsorption and capillary condensation

One characteristic of unconventional shale rock is the abundance of nanoscale pores and pore throats. For many shale reservoirs, these are the dominant factors controlling the total reserve, production rate, and overall production. Accordingly, many new phenomenon related to nanopore physics need to be considered for shale reservoir. A key mechanism controlling hydrocarbon gas transport from pores to fractures in shale reservoirs is molecular diffusion. As a result, the diffusion coefficient of light hydrocarbon becomes an important parameter in reservoir simulation to estimate production rate, especially for the long-term or late time production. The diffusion coefficient is also a key parameter in nuclear magnetic resonance (NMR) logging for fluid typing in determining hydrocarbon-in-place. Diffusion in nanopore systems is complicated by two important factors. First, the gas molecules collide more with pore surfaces than with each other; therefore, simple diffusion theory based on gas molecule collision is not applicable. Second, the occurrence of capillary condensation in small pores or pore throats and the adsorption to the pore surface makes the hydrocarbon transport a mixed process of liquid diffusion and gas diffusion in the reservoir. We derived a theoretical model for mixed phase diffusion under fast exchange for shale gas reservoirs. We obtained that the effective diffusion coefficient of mixed fluid is a fractional average of the liquid and gas diffusivity. We verified this model using NMR to measure n-hexane diffusion in a well-characterized hierarchical carbon with both nanometer pores and micrometer pores so that both gas and liquid can be prepared to exist in the sample simultaneously. We found that the diffusion coefficient of hexane in these hydrophobic nanopores is approximately one magnitude of order larger than the bulk liquid value. The effective diffusion coefficient in this study can be used in reservoir simulation and interpretation of NMR logs for shale gas reservoirs.