Computational Fluid Dynamics to develop novel correlations for residual saturation of the displaced fluid in a capillary tube

Abstract

The main goal of this study is to numerically investigate the immiscible fluid-fluid displacement at the micro-level under low inertial and buoyancy forces. To this end, a micro capillary tube was constructed, and the fluid-fluid interface and fluid-fluid-wall triple line were tracked using VOF (Volume of Fluid)-CSF (Continuum Surface Force) strategy. Mesh-independency analysis was conducted by utilizing the Adaptive Mesh-Refinement (AMR) technique. Simulation results agreed well with the experimental data obtained from literature with the AARD (Average Absolute Relative Deviation) of around 10%. The validated model was then used to generate the CDC (Capillary Desaturation Curve) curves for different wall wettabilities, considering the dynamic contact angle in the simulations. The generated CDC curves at the breakthrough time showed that there are three different zones, namely low-Ca, transitional, and high-Ca region. The only difference between saturation profiles of different wettabilities was in the transition zone, based on the CDC analysis. The saturation and velocity profiles at the central plane of the tube were constructed and compared. Phase separation can happen depending on Ca number and the magnitude of the dynamic contact angle. Eventually, outcomes of the numerical simulator were used to develop new correlations for the residual saturation as functions of dynamic contact angle and Ca number. Nonlinear regression analysis with Levenberg-Marquart algorithm was used to find coefficients of the correlations. The developed correlations showed to be highly robust for the transition and high-Ca regions with the correlation coefficients (R2) up to 0.96 and the maximum AARD of 12%. Results of this study are applicable to both capillary-fingering and viscous-fingering flow-regimes based on the Lenormand's phase-diagrams.