Abstract: A model for flows in low permeability porous media with nano scale pores has been derived with assumptions including homogeneity, the Darcy's law, ideal gas model and the Klinkenberg effect. Numerical simulations are carried out for pressure pulse decay experiment with spherical crushed samples using the finite difference method with suitable boundary conditions. Non-dimensional parameters Z,Z^* and b_K are introduced when the governing equations are non-dimensionalized. Various pressure decay curves are investigated numerically when various parameters Z,Z^* and b_K are applied. A data processing method for the present pressure pulse decay experiment is proposed. Porosity, permeability and the Klinkenberg coefficient can be determined by combining both the measured pressure decay curves at the sample boundaries and the numerical solutions of the governing equations. The permeability and the Klinkenberg coefficient of a porous medium sample cannot be determined using only one pressure decay curve.

Key words: permeability, porous medium, Klinkenberg slip, numerical simulation, pressure pulse decay

摘要： 基于均匀各向同性多孔介质、达西渗流和理想气体假设，考虑Klinkenberg效应建立了针对具有纳米尺度孔径的低渗透率多孔介质中的渗流模型。针对致密球形破碎样品的压力脉冲实验，建立了相应的边界条件，同时利用有限差分方法获得其实验腔的压力变化曲线的数值解。通过对渗流方程进行量纲1化，引入了与孔隙率、渗透率和滑移参数有关的量纲1参数Z、Z^*和b_K。通过改变参数Z、Z^*和b_K研究了样品边界处压力的变化规律，给出了一种数据处理方法，对于致密球形破碎多孔介质的压力脉冲实验，通过对实验测量的样品边界处压力曲线的分析，结合偏微分方程正问题的数值解，可以确定样品的孔隙率、渗透率和滑移参数，从而更为简便地分析压力脉冲衰减曲线实验数据，得到致密多孔介质样品渗透率。

关键词: 渗透率, 多孔介质, Klinkenberg滑移, 数值模拟, 压力脉冲