Probe permeameter has been widely used to obtain measurements and spatial distributions of permeability in both the laboratory and field outcrop applications. It provides cheap, fast, intensive, and nondestructive permeability measurements. In the literature, the difference between steady-state and unsteady-state measurements and the effects of heterogeneity and anisotropy on probe permeameter measurements have been investigated both numerically and experimentally. However, the available work provides a method for the determination of the permeability in two principal directions only. This study fills such a gap by providing a novel solution for the steady-state single-phase flow problem for the determination of permeability anisotropy in the three principal directions using probe permeameter measurements. The solution was obtained by solving the diffusivity equation describing the steady-state flow of a single-phase fluid in a three-dimensional (3D) rectangular system. Different permeability anisotropy ratios were tested for different anisotropy cases starting from a fully isotropic sample to a fully anisotropic sample. The obtained results are presented graphically in a dimensionless space. The dimensionless parameters include the dimensionless pressure and anisotropy ratios in different flow directions. A practical procedure based on the solution is then described to evaluate the permeability in a 3D rectangular rock sample. This method requires a few measurements of steady-state flow rate and pressure drop conducted using the probe permeameter at different directions on a rectangular rock sample. The applicability of the proposed solution and developed technique is demonstrated by conducting probe permeameter measurements on three different directions of one cubical cement sample and two outcrop carbonate samples. The results obtained from the proposed method show good match (an average root-mean-square error of 0.653 mD) when compared to the reference permeability values measured on directional plugs by conventional nitrogen permeameter. The procedure described in this work can be used to have a quick and robust evaluation of permeability anisotropy from rock samples in either outcrop or laboratory studies.

探针渗透仪已被广泛用于在实验室和野外露头应用中获得渗透率的测量值和空间分布。它提供便宜，快速，密集和无损的渗透率测量。在文献中，已通过数值和实验研究了稳态和非稳态测量之间的差异以及异质性和各向异性对探针渗透仪测量的影响。但是，现有工作仅提供了一种确定两个主要方向渗透率的方法。这项研究通过为稳态单相流动问题提供了一种新颖的解决方案，填补了这一空白，该问题用于使用探针渗透仪测量来确定三个主要方向的渗透率各向异性。通过求解扩散方程来获得解，该扩散方程描述了三维（3D）矩形系统中单相流体的稳态流。从完全各向同性的样品到完全各向异性的样品，针对不同的各向异性情况测试了不同的渗透率各向异性比率。获得的结果以图形方式显示在无量纲空间中。无量纲参数包括不同流向的无量纲压力和各向异性比。然后描述了基于该解决方案的实用程序，以评估3D矩形岩石样品中的渗透率。此方法需要使用矩形探头在不同方向上对矩形岩石样品进行稳态流量和压降的一些测量。通过对一个立方水泥样品和两个露头碳酸盐样品的三个不同方向进行探针渗透仪测量，证明了所提出的解决方案和开发的技术的适用性。与传统的氮气渗透仪在定向塞上测得的参考渗透率值相比，从该方法获得的结果显示出良好的匹配性（平均均方根误差为0.653 mD）。在露头或实验室研究中，可以使用这项工作中描述的程序对岩石样品的渗透率各向异性进行快速而可靠的评估。与通过常规氮气渗透仪在定向塞上测得的参考渗透率值相比，从该方法获得的结果显示出良好的匹配性（平均均方根误差为0.653 mD）。在露头或实验室研究中，可以使用这项工作中描述的程序对岩石样品的渗透率各向异性进行快速而可靠的评估。与传统的氮气渗透仪在定向塞上测得的参考渗透率值相比，从该方法获得的结果显示出良好的匹配性（平均均方根误差为0.653 mD）。在露头或实验室研究中，可以使用这项工作中描述的程序对岩石样品的渗透率各向异性进行快速而可靠的评估。