Abstract Current computing capabilities, in combination with available theoretical frameworks, allow for the petrophysical evaluation of porous rocks from simple images. This procedure represents a less expensive alternative and it complements, generally expensive, laboratory measurements. A porosity, permeability and Forchheimer tensors estimation is reported here through a numerical solution of associated closure problems within digital images of porous rock thin sections. The solution of these steady-state boundary-value problems allows direct computation of all permeability elements and Forchheimer tensors. The digital images were obtained from a computer procedure that identifies the network of pores in thin sections. The results of the numerical estimation of permeability and porosity and its scopes were compared with those obtained via experimental measurements in four samples representing three distinct lithologies (travertine, sandstone and limestone), and were found to be in acceptable agreement. Once the permeability was computed, the Forchheimer tensor was calculated as function of the pore-scale Reynolds number. The Forchheimer coefficient varied with fluid velocity at an exponent close to 2 (range from 1.7 up to 4.2) depending on the lithology and local microstructure. The critical Reynolds number at which the Forchheimer coefficient became relevant was approximately 0.25. We found that the Forchheimer tensor exhibited anisotropy not only according to the local microstructure but also according to the flow path.

中文翻译：

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通过闭合问题和数字图像计算多孔岩石的渗透率和 Forchheimer 张量

摘要 当前的计算能力，结合可用的理论框架，允许从简单的图像对多孔岩石进行岩石物理评估。该程序代表了一种较便宜的替代方法，它补充了通常昂贵的实验室测量。本文通过多孔岩石薄片数字图像中相关闭合问题的数值解来报告孔隙度、渗透率和 Forchheimer 张量估计。这些稳态边界值问题的解决方案允许直接计算所有渗透率元素和 Forchheimer 张量。数字图像是从计算机程序中获得的，该程序可识别薄片中的孔隙网络。将渗透率和孔隙度及其范围的数值估计结果与通过代表三种不同岩性（石灰华、砂岩和石灰岩）的四个样品的实验测量获得的结果进行比较，发现一致。一旦计算出渗透率，Forchheimer 张量就被计算为孔隙尺度雷诺数的函数。Forchheimer 系数随流体速度变化，指数接近 2（范围从 1.7 到 4.2），具体取决于岩性和局部微观结构。Forchheimer 系数变得相关的临界雷诺数约为 0.25。我们发现 Forchheimer 张量不仅根据局部微观结构而且根据流动路径表现出各向异性。