Inferring capillary pressure curve from 2d rock images based on fractal theory in low-permeability sandstone: A new integrated approach

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.