Local Capillary Pressure Estimation Based on Curvature of the Fluid Interface – Validation with Two-Phase Direct Numerical Simulations

Abstract

With the advancement of high-resolution three-dimensional X-ray imaging, it is now possible to directly calculate the curvature of the interface of two phases extracted from segmented CT images during two-phase flow experiments to derive capillary pressure. However, there is an inherent difficulty of this image-based curvature measurement: the use of voxelized image data for the calculation of curvature can cause significant errors. To address this, we first perform two-phase direct numerical simulations to obtain the oil and water phase distribution, the exact location of the interface, and local fluid pressure. We then investigate a method to compute curvature on the oil/water interface. The interface is defined in two ways. In one case the simulated interface which has a sub-resolution smoothness is used, while the other is a smoothed interface which is extracted from synthetic segmented data based on the simulated phase distribution. Computed mean curvature on these surfaces are compared with that obtained from the fluid pressure computed directly in the simulation. We discuss the accuracy of image-based curvature measurements for the calculation of capillary pressure and propose the best way to extract an accurate curvature measurement, quantifying the likely uncertainties.

Quantification of Uncertainty and Best Practice in Computing Interfacial Curvature from Complex Pore Space Images

“…However, this was not appropriate for our cases—computed curvatures away from the solid wall do not necessarily give an accurate estimation as shown in Figure 9. This was also concluded from our other test cases reported in Akai et al [32].…”

“…We also tested constrained Gaussian smoothing for these cases; however, it was found that constrained Gaussian smoothing was inadequate resulting in larger errors when the curvature was small (contact angles close to 90∘). We refer to Akai et al [32] for a further detailed comparison of smoothing methods. Furthermore, Li et al [11] used an average weighted by the distance from the solid to obtain a representative curvature value for a patch of the interface.…”

“…Since this surface had a staircase shape, it had to be smoothed before computing curvature. In this study, we used Laplacian smoothing [31] since our previous study [32] showed that Laplacian smoothing gave the most accurate curvature estimation among the three smoothing methods tested: constrained Gaussian smoothing, Laplacian smoothing and boundary preserving Gaussian smoothing [33].…”