Reliable capillary pressure data are required for reservoir simulation and fluid flow characterization in porous media. The capillary pressure is commonly measured in the laboratory, which is costly, challenging, and accompanied by measurement uncertainties, especially for low-permeability core samples. Besides laboratory measurements, two-dimensional (2D) rock images reveal another prospect to obtain capillary pressure curves. This paper presents a new integrated approach combining image processing and fractal theory to infer the capillary pressure curve from 2D rock images in low-permeability sandstone. Our approach’s unique feature is its new representation of the pore structure based on information extracted from 2D cross-sections using image processing techniques (i.e. image segmentation and watershed partitioning). Furthermore, we derived an innovative analytical fractal model to calculate the capillary pressure from the newly proposed pore system representation. A new tortuous length equation is introduced to eliminate the developed fractal models’ dependency on the straight capillary length. The pore fractal dimension is computed using the box-counting method from the processed 2D image. The tortuosity fractal dimension is obtained from solving the developed fractal equations of porosity and permeability with the corresponding laboratory measurements. Additionally, a procedure for inferring capillary pressure from multiple cross-sections is proposed. The good accuracy in predicting capillary pressure for five low-permeability sandstone core samples demonstrates the developed approach’s robustness.

中文翻译：

---

基于分形理论的低渗透率砂岩二维岩石图像推断毛细压力曲线：一种新的综合方法

储层模拟和多孔介质中的流体流动表征需要可靠的毛细管压力数据。毛细管压力通常在实验室进行测量，成本高、具有挑战性，并且伴随着测量不确定性，尤其是对于低渗透率岩心样品。除了实验室测量之外，二维 (2D) 岩石图像还揭示了获得毛细管压力曲线的另一种前景。本文提出了一种结合图像处理和分形理论的新方法，从低渗透砂岩的二维岩石图像中推断毛管压力曲线。我们的方法的独特之处在于它基于使用图像处理技术（即图像分割和分水岭划分）从二维横截面提取的信息对孔隙结构进行了新的表示。此外，我们从新提出的孔隙系统表示中推导出了一个创新的分析分形模型来计算毛细管压力。引入了一个新的曲折长度方程，以消除所开发的分形模型对直毛细管长度的依赖性。孔隙分形维数是使用盒子计数方法从处理后的 2D 图像中计算出来的。曲折分形维数是通过求解已开发的孔隙度和渗透率分形方程与相应的实验室测量值获得的。此外，还提出了一种从多个横截面推断毛细压力的程序。预测五个低渗透砂岩岩心样品的毛细管压力的良好准确性证明了所开发方法的稳健性。