Immobile Pore-Water Storage Enhancement and Retardation of Gas Transport in Fractured Rock

The effect of immobile pore-water on gas transport in fractured rock has implications for numerical modeling of soil vapor extraction, methane leakage, gaseous $$\hbox {CO}_2$$ leakage from sequestration operations, radionuclide transport from underground nuclear explosions, and nuclear waste disposal. While the ability for immobile pore-water storage to effect gas transport has been recognized in the past, the details and specific scenarios leading to enhanced, retarded, or unaffected gas transport have not been explored. We performed numerical investigations into the enhancement and retardation of gas transport due to immobile pore-water storage in order to identify implications for gas transport applications. To do this, we developed a numerical approach to model gas transport with a single-phase flow solution coupled to the advection–dispersion equation modified to account for immobile pore-water storage. Other than the immobility of pore water, the formulation contains all other physics included in two-phase formulations (advective and diffusive gas transport in fractures and rock matrix and dissolution in immobile pore water). The assumption of immobile pore water is valid here since for many applications involving transport of soluble gases in fractured rock, the rate of aqueous transport is insignificant compared to gas transport. We verify our modeling approach with analytical solutions of: (1) 1D gas diffusion, (2) 1D gas advection, (3) barometric pumping of a fracture, and (4) gas transport with uniform fracture flow and diffusion into the matrix. We account for pore-water storage in our model by implementing a kinetic formulation of gas dissolution wherein the dissolved (aqueous) phase is considered an immobile constituent. Using this formulation, we model the effect of dissolution rate and saturation on the retardation of gas transport during pure diffusion and pure advection. We also demonstrate that although it is commonly believed that pore-water storage will always enhance gas transport in fractures during oscillatory flow (e.g., during reversing pressure gradients such as barometric pumping cycles), our simulations indicate that this may not always be the case. Our numerical investigations indicate that scenarios with lower effective diffusion coefficients ( $$\lessapprox \,10^{-5}\,\hbox { m}^2/\hbox {s}$$ ) and lower dissolution coefficients (i.e., the dissolution diffusion coefficient) ( $$\lessapprox \,10^{-11}\,\hbox { m}^2/\hbox {s}$$ ) will result in enhanced gas transport. Other combinations of gaseous diffusion and dissolution coefficients result in delayed gas transport or insignificant effect on gas transport. Based on these results, and given the fact that the free-air diffusion coefficients for many gases are slightly above $$10^{-5}\,\hbox { m}^2/\hbox {s}$$ (near the boundary of enhanced/non-enhanced gas transport), tortuosity would have to be significant for gas transport enhancement to occur. Similarly, if we consider the free-water diffusion coefficient of gases (around $$10^{-9}\,\hbox { m}^2/\hbox {s}$$ for many gases of interest) to be a maximum bound for the effective dissolution coefficients (i.e., the rate of diffusion into the water away from the air/water interface will limit the dissolution rate), the effective dissolution coefficient would have to be at least 2 orders of magnitude less for enhanced gas transport to occur. Otherwise, pore-water storage will delay or have negligible effect on the gas transport. The results also indicate that the assumption of instantaneous equilibrium, often invoked in numerical codes for dissolution processes (i.e., dissolution coefficient is effectively infinite), will fail to accurately capture important details of soluble gas transport. The implication of our results is that gas breakthrough times in fractured rock during oscillatory flow may be highly dependent on the effective gaseous diffusion and dissolution coefficients.