Effects of nano-pore wall confinements on rarefied gas dynamics in organic rich shale reservoirs

Abstract The advancements in horizontal well drilling and multistage hydraulic fracturing technology enabled us to unfold major sources of hydrocarbon trapped in ultra-tight formations such as organic rich shales. Tremendous gas production from these reservoirs has transformed today’s energy landscape [1]. Even though multi-stage hydraulic fracturing stimulation provides high permeability paths to transfer gas to the wellbore, however, most of the gas is stored in nano-organic pores of the ultra-low permeability shale matrix that needs to be transferred to the hydraulic fractures to be able to be produced. Studies using advanced imaging technologies such as FIB/SEM and low temperature adsorption measurements show that in the organic rich shale gas reservoirs, Kerogen, the finely dispersed organic nano-porous material with an average pore size of less than 10 nm holds bulk of the total gas in place (GIP). The molecular level interactions between fluid–fluid and fluid–solid organic pore walls govern the transport and storage in these organic nano-pores. To understand the high gas production rates from these ultra-tight formations, the objective of this study is to advance our understanding of non-ideal gas dynamics in multiscale pore structure of organic rich shale matrix (i.e., gas storage and transport influenced by adsorption and adsorbed gas transport) and develop a model to quantify these effects under wide range of reservoir conditions. Among different methods used to model gas dynamics in organic nano-pores such as the multi-continuum, molecular dynamics and Monte Carlo, the lattice Boltzmann method (LBM) is more effective method with much less computational cost relative to other techniques. In this study we focus on rarefied gas dynamics in Kerogen organic nano-tubes under wide range of reservoir pressure and temperature conditions using a two dimensional LBM model. In this model the Langmuir-slip boundary condition at capillary walls, convection or darcy flow and diffusive transport (slippage of free gas molecules and surface transport of adsorbed molecules combined) are considered to model gas transport. Different transport mechanisms and their contribution in gas transport is investigated in a large range of Knudsen numbers from continuum flow to transition flow regime under different reservoir conditions. The deviation from classical theory of fluid flow in micro channels such as Knudsen’s minimum in the mass flow rate is investigated and the effect of gas slippage and double slippage on Knudsen minimum is discussed in details. Finally the results are compared with analytical, and semi analytical solutions available in the literature. The LBM model results displays a clear indication that the gas transport in the capillary tube is highly depends on the pore width size, pressure and temperature. The relative impact of pore size, pressure and temperature on maximum gas velocity and gas wall velocity differs at different flow regime conditions. A critical Knudsen number exists at different reservoir conditions, where the anticipated parabolic fluid velocity profile in organic nano-pores alters and shows higher flow rate as capillary widths reduces due to the underlying effect of molecular phenomena of double slippage and the wall confinement. The comparison with traditional continuum Hagen-Poiseuille law, Klinkenberg slip theory, and recent modified versions of Klinkenberg slip flow equations show that the previous models are valid only in the continuum flow regime, however, they fail to capture high gas flow rates at high Knudsen number and transition flow regimes which is the case in most of the shale organic nano-pore conditions [2]. This work is not only important for the advancement of shale gas flow simulators, but also for organic rich shale characterization.