In this study, a mathematical model for fast determination of the permeabilities of tight rocks using measurements taken from the initial period of the One Chamber Pressure Pulse Decay (OC-PPD) test is presented. The model applies to measurements taken both before and after the pressure pulse front has reached the downstream end of the specimen. The analytical solutions for the pressure decay in the upstream chamber are derived based on a parabolic arc approximation of pore pressure distribution along the test specimen. This approximation allows converting the initial–boundary value problem of fluid diffusion in the specimen, governed by partial differential equations, to a system of ordinary differential equations that can be easily solved by explicit formulae. Thus, an explicit formula for the pressure decay rate is obtained, which enables inverse analysis of the initial experimental data to estimate the rock permeability. The proposed method expedites the pulse decay test as it does not require the system to reach equilibrium. The method is validated with three sets of experimental data of the OC-PPD test using helium as the diffusing fluid, for which the relative error of the permeability is found to be less than 6%. This method is particularly useful if the equilibrium time of the pulse decay test for rock specimens with permeabilities in the range of nano-Darcy takes hours or days.

中文翻译：

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仅使用单室压力脉冲衰减测试的初始数据快速测量致密储层岩心渗透率


在这项研究中，提出了一种利用单室压力脉冲衰减（OC-PPD）测试初始阶段的测量结果快速确定致密岩石渗透率的数学模型。该模型适用于压力脉冲前沿到达样本下游端之前和之后进行的测量。上游室中压力衰减的解析解是基于沿测试样本的孔隙压力分布的抛物线弧近似得出的。这种近似允许将由偏微分方程控制的样本中流体扩散的初始边界值问题转换为可以通过显式公式轻松求解的常微分方程组。因此，获得了压力衰减率的明确公式，这使得能够对初始实验数据进行反分析来估计岩石渗透率。所提出的方法加快了脉冲衰减测试，因为它不需要系统达到平衡。利用氦气作为扩散流体进行OC-PPD测试的三组实验数据对该方法进行了验证，发现渗透率相对误差小于6%。如果渗透率在纳达西范围内的岩石样本的脉冲衰减测试的平衡时间需要数小时或数天，则该方法特别有用。