In this paper, we introduce an estimation of the random Klinkenberg slip coefficient in the apparent permeability model using a chaos decomposition technique. The apparent permeability expression (Klinkenberg model) is used to describe natural gas transport in low-permeability media. In this process, the Klinkenberg factor is considered as a random parameter that depends on two random variables. The mean and variance (or standard deviation) of the two random variables can be estimated from the empirical data available in the literature. Therefore, the variation in the pressure is related directly to the random variation in the Klinkenberg factor. The polynomial chaos expansion is used to decompose the governing equation into a set of coupled deterministic equations that are solved and then used to compute the mean and variance of the solution. The algorithm of how to solve the deterministic coupled system is also presented. For verification, the model and its solution have been compared with the analytical solution of the basic steady-state version of the model. The comparison shows a very good agreement. The effects of a number of important parameters have been presented in graphs and discussed. It was found that the stochastic model works very well with small values of the liquid equivalent permeability, which meets the characteristics of low-permeability reservoirs. Also, the stochastic model works very well with small values of gas viscosity. On the other hand, the porosity seems to be not engaged well with the low-permeability model. The sensitivity of selection of random parameters is also investigated as well as the transient effect.

在本文中，我们介绍了使用混沌分解技术对视在渗透率模型中的随机Klinkenberg滑移系数的估计。表观渗透率表达式（Klinkenberg模型）用于描述低渗透率介质中的天然气传输。在此过程中，克林肯贝格因数被视为取决于两个随机变量的随机参数。两个随机变量的均值和方差（或标准差）可以根据文献中的经验数据进行估算。因此，压力的变化与克林根贝格因子的随机变化直接相关。多项式混沌展开用于将控制方程式分解为一组耦合的确定性方程式，这些方程式得以求解，然后用于计算解的均值和方差。提出了求解确定性耦合系统的算法。为了进行验证，将模型及其解决方案与模型的基本稳态版本的解析解决方案进行了比较。比较显示出很好的一致性。许多重要参数的影响已在图表中显示并进行了讨论。发现该随机模型在液体当量渗透率较小的情况下效果很好，符合低渗透油藏的特征。同样，随机模型在气体粘度较小的情况下也能很好地工作。另一方面，孔隙率似乎与低渗透率模型没有很好地结合。还研究了随机参数选择的敏感性以及瞬态效应。