The effect of adsorption and Knudsen diffusion on the steady-state permeability of microporous rocks

Abstract

Microporous rocks are being increasingly researched as novel exploration and development technologies facilitate production of the reserves confined in the low-permeability reservoir. The ability to numerically estimate effective permeability is pivotal to characterizing the production capability of microporous reservoirs. In this study, a novel methodology is presented for estimating the steady-state effective permeability from FIB-SEM volumes. We quantify the effect of a static adsorbed monolayer and Knudsen diffusion on effective permeability as a function of pore pressure to better model production of microporous rock volumes. The adsorbed layer is incorporated by generating an effective pore geometry with a pore pressure-dependent layer of immobile voxels at the fluid-solid interface. Due to the steadystate nature of this study, surface diffusion within the adsorbed layer and topological variations of the layer within pores are neglected, potentially resulting in underestimation of effective permeability over extended production time periods. Knudsen diffusion and gas slippage is incorporated through computation of an apparent permeability that accounts for the rarefaction of the pore fluid. We determine that at syn-production pore pressures, permeability varies significantly as a function of the phase of the pore fluid. Simulation of methane transport in micropores indicates that, in the supercritical regime, the effect of Knudsen diffusion relative to adsorption is significantly reduced resulting in effective permeability values up to 10 nanodarcies (9.87 × 10 −21 m 2) less or 40% lower than the continuum prediction. Contrastingly, at subcritical pore pressures, the effective permeability is significantly greater than the continuum prediction due to rarefaction of the gas and the onset of Knudsen diffusion. For example, at 1 MPa, the effective permeability of the kerogen body is five times the continuum prediction. This study demonstrates the importance of, and provides a novel methodology for, incorporating noncontinuum effects in the estimation of the transport properties of microporous rocks.

Investigation of methane adsorption and its effect on gas transport in shale matrix through microscale and mesoscale simulations

“…Therefore, upscaling the MD results into a larger scale study is highly necessary. Recently, there have several studies using the LB method, which is considered as a mesoscopic numerical method beyond the microscopic MD, for shale gas flow in the nano/micro-size pores of shale matrix [16][17][18][19][20][21][22][23][24][25] regarding the effects of gas slippage [19-21, 23, 24] and adsorbed layer [18,22,25]. The MD simulation in the present study helps us to understand the adsorption of methane on the pore walls in shale matrix.…”

“…The effect of the adsorbed gas on the fluid flow can be neglected for conventional rocks with large pore size. However, it should be considered in shale matrix where nanosize pores are dominant [9,[15][16][17][18][19][20][21][22][23][24][25]. Adsorption will affect the fluid flow in a nanosize pore through two mechanisms [16].…”

Apparent permeability prediction of organic shale with generalized lattice Boltzmann model considering surface diffusion effect

“…In other words, if adsorbed gas is assumed to pre-exists in OM, the intrinsic permeability will increase with the decrease in pressure because the desorbed gas will release some pore space [4]. Nonetheless, no consensus on the volume occupied by adsorbed gas exists in these treatments [14,44,39], also the contribution of the surface diffusion is ignored. In this study, with the introduction of DGM-GMS model, the effect of surface diffusion on K app;om can be easily considered, and based on the assumption that the total flux N total is the sum of N DGM and N GMS , the ambiguity in the adsorption layer thickness can be avoided.…”

“…However the sensitivity of permeability to adsorption and surface diffusion are seldom mentioned. In others, the adsorbed gas is modeled by taking some pore space and therefore reducing the local pore size [27,44,7]. In other words, if adsorbed gas is assumed to pre-exists in OM, the intrinsic permeability will increase with the decrease in pressure because the desorbed gas will release some pore space [4].…”

The lattice Boltzmann method for isothermal micro-gaseous flow and its application in shale gas flow: A review

“…Later, it is confirmed that Klinkenberg's correlation is only first order accurate. Beskok and Karniadakis [18] proposed a second-order correlation by considering the different flow regimes from continuum flow to free molecular flow: [148] firstly used the combination of Beskok and Karniadakis -Florence's correlation along with a 3D incompressible LB model to estimate the for a shale image with a 167nm length in each dimension. In their study, the intrinsic permeability 0 was predicted by standard LBM.…”