Knudsen diffusion in pore-scale water-bearing shales: modelling and case study

Abstract

Gas diffusivity in shales is significantly affected by water. However studies on the model of diffusion coefficient for water-bearing shales are very limited. In this work, we proposed a model to calculate the Knudsen gas diffusion coefficient at the presence of water in shale nanopores. This model was used to study the gas diffusivity in a real shale pore structure composed of both organic pores and inorganic pores at different water saturations. The model was also utilized to analyze the sensitivity of the Knudsen diffusion coefficient on a variety of factors. Results indicate that the existence of water drastically reduces the Knudsen diffusion in shales. When water saturation increases from 10% to 50%, gas concentration in inorganic pores rises by 53.7%. This effect can happen both in organic pores and inorganic pores due to pore connectivity. Water in inorganic pores can transport into organic pores and hinders gas diffusion in organic pores. The sensitivity study demonstrates that the increase of temperature, pore radius and porosity can lead to the rise of Knudsen diffusion coefficient. Inversely, the increase of tortuosity induces the decrease of the Knudsen diffusion coefficient. The pore wall roughness also affects the Knudsen diffusion coefficient. The rough wall surface contributes to a lower Knudsen diffusion coefficient compared with the smooth wall surface.