Poroelasticity and gas slippage on the walls of nanopores are two major mechanisms that regulate shale permeability concurrent with hydrocarbons depletion. Nonlinear Klinkenberg plots reported in experiments indicate that gas slippage has a complex relationship with the variation of effective stress; however, a theoretical framework that explains the underlying physics is still missing. In the present contribution, a series of experiments were designed and conducted on intact Utica shale samples to study the simultaneous effects of gas slippage and poroelasticity under constant confining and constant effective stress conditions. In addition, an apparent permeability model was developed considering the effects of rock poroelasticity and a non-constant velocity gradient for gas flow at the pore wall. The model was calibrated and tested against the presented experimental results for Utica shale as well as previously published data. Results show that the concavity in Klinkenberg plots is caused by two separate parameters, each dominant within different ranges of pore pressures: second-order gas slippage and effective stress coefficient. The model demonstrates that gas slippage is inherently coupled with effective stress at low pore pressures. However, the evolution of apparent permeability with gas pressure deviates from the classical Klinkenberg theory only when the pore diameter is sufficiently small. When the effective stress coefficient is smaller than unity, the permeability evolution deviates from the linear Klinkenberg trend only at high pore pressures. In addition to the pore size, gas slippage is found to be closely correlated with the variation of gas viscosity with pressure and temperature.

纳米孔壁上的孔隙弹性和气体滑脱是调节页岩渗透率和碳氢化合物耗竭的两个主要机制。实验报道的非线性Klinkenberg图表明，气体滑脱与有效应力的变化具有复杂的关系；但是，仍然缺少解释基础物理学的理论框架。在目前的贡献中，设计并在完整的 Utica 页岩样品上进行了一系列实验，以研究在恒定约束和恒定有效应力条件下气体滑脱和孔隙弹性的同时影响。此外，还建立了考虑岩石孔隙弹性和非常数影响的表观渗透率模型。孔隙壁处气体流动的速度梯度。该模型已针对 Utica 页岩的现有实验结果以及先前公布的数据进行了校准和测试。结果表明， Klinkenberg 曲线中的凹度是由两个独立的参数引起的，每个参数在不同的孔隙压力范围内占主导地位：二阶气体滑脱和有效应力系数。该模型表明，气体滑脱本质上与低孔隙压力下的有效应力有关。然而，表观渗透率随气体压力的演变仅在孔径为足够小。当有效应力系数小于 1 时，渗透率演化仅在高孔隙压力下才偏离线性 Klinkenberg 趋势。除孔径外，还发现气体滑脱与气体粘度随压力和温度的变化密切相关。