Dimensional and Scaling Analysis of Binary Gas in Shale Reservoirs

Abstract

Summary Understanding multicomponent gas transport in organic-rich ultratight reservoirs is essential for improving gas production and subsurface gas storage. This study develops a dimensionless framework for steady-state binary gas transport in nanoporous media using a species-based Maxwell-Stefan model that treats the free and sorbed phases separately. The extended Langmuir isotherm describes competitive adsorption; molecular diffusion and advection are represented in the free phase, and surface diffusion is represented in the sorbed phase. Dimensional analysis yields the Sherwood number (Shi), Péclet number (Pe), dimensionless molecular diffusion flux (ψi), adsorption-advection number (φi), and adsorption-diffusion number (χi). Three limiting cases are examined. In Case 1, Shi approaches ψi when molecular diffusion dominates and approaches Pe when advection dominates. Co-diffusion causes the contributions to add, whereas counter-diffusion produces flux cancellation and reversal when Pe becomes comparable to ψi. In Case 2, the relation Shi/Pe = 1 + φi identifies the transition from free-phase advection to sorbed-phase surface diffusion. In Case 3, Shi/ψi= 1 + χi identifies the transition from free-phase molecular diffusion to sorbed-phase surface diffusion. The proposed framework provides a systematic basis for comparing competing mechanisms, mapping transport regimes, and interpreting binary gas transport in organic-rich nanoporous media. Dimensional and Scaling Analysis of Binary Gas in Shale Reservoirs