Multiscale Modeling of Shale Apparent Permeability: An Integrated Study of Molecular Dynamics and Pore Network Model

Abstract

The physics of gas transport through shale systems is still ambiguous, even though several theoretical and experimental works have been reported. Most of the existing studies only concentrate on the permeability of shale kerogen. However, shales are composed of various amounts of organic matter and inorganic minerals (e.g., calcite, clay, and etc.). Inorganic pores could be larger than organic pores, hence, affect apparent permeability. To accurately predict shale apparent permeability, we couple molecular dynamics (MD) and a pore network model (PNM) to develop a multiscale framework for gas flow through shales. First, we use non-equilibrium MD to study the pressure-driven flow behavior of methane through organic, calcite, and clay (montmorillonite) nanopores under subsurface conditions, from which we build modified Hagen-Poiseuille equations to characterize the overall conductivity of each pore. Then we incorporate these formulations into a shale pore network model, in which the impact of shale composition and bimodal pore size distribution (PSD) are taken into account. Molecular dynamics simulations show that the streaming velocity of supercritical methane in an organic nanopore exceeds the prediction of Hagen-Poiseuille equation by orders of magnitude. However, methane exhibits a slightly enhanced flow in comparison to Hagen-Poiseuille equation in inorganic pores, which can even be ignored if the diameter of inorganic pore is larger than 10 nm. On the basis of these simulation results, we modify Hagen-Poiseuille equation to estimate hydraulic conductivity of methane through nanopores with different material types. We construct the multiscale pore network model conditioned to total organic carbon (TOC) and mineralogical composition. The pore/throat size ranging from nanometer to micrometer scales are assigned according to the pore size distributions in organic matter and inorganic matrix separated from nitrogen adsorption results. We validate our PNM model results with experimental data published in literature. We conclude that the pores located within inorganic matrix show a more pronounced effect on the shale apparent permeability than those associated with kerogen. We further examine the influence of TOC, pore network connectivity, mean pore size, and etc. Using molecular dynamics and pore network model, this work presents a multiscale framework that accounts for distinct pore size distributions and fluid transport properties in organic matter and inorganic matrix. In comparison with previous methods, our proposed model highlights the effect of inorganic matrix owing to their greater pore sizes. This work provides an efficient tool to better understand gas transport through shale systems at both molecular scale and pore scale.

Overview of the Adsorption and Transport Properties of Water, Ions, Carbon Dioxide, and Methane in Swelling Clays

“…77 The multiscale modeling of CO 2 and CH 4 transport in clay systems is an active research field. 81,91 The presence of CO 2 significantly affected the mobility of CH 4 , for example, in a hydration state with preadsorbed water. 72 However, the presence of CH 4 had less effect on the diffusion properties of CO 2 .…”

“…The molecular dynamics (MD) simulations allow one to assess the dynamic properties of the system. For the simulations of the clay systems, − the structure of the unit cell of the clay (Si 8 Al 4 O 20 (OH) 4 ) is obtained from, for example, Skipper et al The simulations mainly focus on the low-charge (Wyoming-type) montmorillonite M 0.75/ n (Si 8 )­(Al 3.25 Mg 0.75 )­O 20 (OH) 4 , where M represents a counterion (e.g., Li + , Na + , K + , Mg 2+ , Ca 2+ , or Sr 2+ ) and n is the charge on the ion. This clay contains coordinated tetrahedral silica sheet and octahedral alumina sheet forming 2:1 tetrahedral-octahedral-tetrahedral (TOT) layers.…”

“…Molecular simulations have provided important insights into the adsorption behavior of CO 2 and CH 4 in dry and wet clays. ,− It was shown that the uptake of CO 2 (Figure ) and CH 4 generally increases with increasing basal spacing. ,,,,, The total uptake is obtained in the simulations, whereas experiments usually provide the excess uptake. To convert the total uptake to the excess quantity, simulations should provide the estimates of the accessible pore volumes, for example, obtained from the GCMC simulation of adsorption of helium in clays. , However, due to the fluid–solid interactions, an enhanced adsorption of CO 2 and CH 4 is obtained at low pressures for relatively small basal d -spacings.…”

“…Molecular simulations have also provided important insights into the transport behavior of CO 2 and CH 4 in dry and wet clays. ,,,,,,− ,− ,,,,, The self-diffusion coefficients of CO 2 and CH 4 generally increased with increasing hydration/RH (Figure ) because of the associated swelling of the interlayer region. The mobility of CO 2 in the 1W state is about an order of magnitude lower than that of its bulk value, and a similar trend was observed for CH 4 .…”

“…The mobility of the interlayer water and ions generally increased with increasing RH. The adsorption and transport processes of CO 2 and CH 4 in swelling clays have also been extensively studied using molecular simulations. ,− These studies have shown that, for example, the presence of CO 2 and CH 4 hardly affects the distribution and mobility of the interlayer water and ions in these systems. The preferential adsorption of CO 2 over CH 4 plays important roles in diffusion processes.…”