Incorporating the Effect of Gravity Into Image‐Based Drainage Simulations on Volumetric Images of Porous Media

Simulating drainage in volumetric images of porous materials is a key technique for studying multiphase flow and transport. Image‐based techniques based on sphere insertion are popular due to their computational efficiency and reasonable predictions, though they lack physical rigor. Since most tomograms are small, the impact of gravity on the fluid distributions has not been previously considered. With the advent of stochastically generated images of arbitrary size, and ever larger field‐of‐view images, the validity of neglecting gravity is becoming questionable. In this work, an image‐based technique that includes the effect of gravity during gravity stabilized displacements was developed and validated. Results compared favorably with analytical solutions of capillary rise in tubes, and to micromodel experiments in terms of the pseudo‐capillary pressure curves. The compactness of the invasion front was also shown to vary linearly with the inverse Bond number. Finally, a contour map of expected error as a function of image size and Bond number was generated to help identify when gravitational effects cannot be ignored. The presented algorithm utilizes only basic image processing tools and offers the same computational advantage as other image‐based sphere insertion methods. Key Points The effect of gravity was incorporated in an image‐based drainage algorithm Comparison to micromodel experiments from literature showed excellent agreement in pseudo‐capillary pressure curves, quantitatively predicting the slope while qualitatively matching the residual saturation Expected error for neglecting gravity was compiled into a contour plot to estimate which images and fluid pairs should consider gravity, with errors as high as 50% in some cases