Gas flow in ultra-tight shale strata
Gas flow in ultra-tight shale strata
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DOI：
10.1017/jfm.2012.424
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发表时间：
2012-11-10
影响因子：
3.7
通讯作者：
Sepehrnoori, K.
中科院分区：
文献类型：
--
作者：
Darabi, Hamed;Ettehad, A.;Sepehrnoori, K.
我们研究了超致密多孔介质中的气体流动过程，在这种介质中，基质孔隙网络由纳米到微米尺寸的孔隙组成。我们建立了一个与压力相关的渗透率函数，称为表观渗透率函数(APF)，假定Knudsen扩散和滑移流动(Klinkenberg效应)是多孔介质中整体流动的主要贡献者。APF预测，在纳米尺寸的孔隙中，气体渗透率值比连续介质流体动力学预测的结果大10倍，并且随着孔径的增加(即微米量级)，气体渗透率收敛到连续介质流体动力学值。此外，APF预测，孔表面分维的增加会导致克努森扩散的减少。使用均匀化方法，严格分析了APF在从局部尺度到大尺度的整个过程中是否保持不变。我们使用著名的脉冲衰减实验来估计APF的主要参数，即达西磁导率。在典型岩心-样品初始压力范围和压差范围内，我们的新推导的晚瞬变解析解和晚瞬变数值解一致地匹配了压力衰减数据，并得出了大致相同的达西渗透率估计值。APF的其他参数可以通过独立的实验室实验来确定；但是，如果执行多次测试和/或参数严格受上下限的限制，则可以使用脉冲衰减实验来估计APF的未知参数。
We study the gas flow processes in ultra-tight porous media in which the matrix pore network is composed of nanometre- to micrometre-size pores. We formulate a pressure-dependent permeability function, referred to as the apparent permeability function (APF), assuming that Knudsen diffusion and slip flow (the Klinkenberg effect) are the main contributors to the overall flow in porous media. The APF predicts that in nanometre-size pores, gas permeability values are as much as 10 times greater than results obtained by continuum hydrodynamics predictions, and with increasing pore size (i.e. of the order of the micrometre), gas permeability converges to continuum hydrodynamics values. In addition, the APF predicts that an increase in the fractal dimension of the pore surface leads to a decrease in Knudsen diffusion. Using the homogenization method, a rigorous analysis is performed to examine whether the APF is preserved throughout the process of upscaling from local scale to large scale. We use the well-known pulse-decay experiment to estimate the main parameter of the APF, which is Darcy permeability. Our newly derived late-transient analytical solution and the late-transient numerical solution consistently match the pressure decay data and yield approximately the same estimated value for Darcy permeability at the typical core-sample initial pressure range and pressure difference. Other parameters of the APF may be determined from independent laboratory experiments; however, a pulse-decay experiment can be used to estimate the unknown parameters of the APF if multiple tests are performed and/or the parameters are strictly constrained by upper and lower bounds.