A novel analytical solution to estimate residual saturation of the displaced fluid in a capillary tube by matching time-dependent injection pressure curves

Characterizing two-phase flow in a capillary tube is of great importance in many branches of engineering such as petroleum, civil, medicine, CO2 capture and sequestration, and polymer processing. Accurate estimation of the residual saturation in a multi-phase flow will aid engineers to optimize the investigated two-phase flow by altering the flow parameters. The main goal of this study is to develop a new analytical model to estimate the amount of the residual saturation solely by matching the injection pressure versus time data for the times before breakthrough. The proposed model is based on decomposing the total pressure drop into Poiseuille and Young-Laplace terms and assuming a linear decrease in the radius of the front with the traveled distance from the inlet. An optimization technique is required to find the slope of the linear function through matching the inlet pressure data. The saturation-time data can be reconstructed after obtaining a fair match over the pressure-time data. Results of the proposed model were compared with the outcomes of a numerical finite volume simulator, for wide ranges of Ca (Capillary) numbers and two different wetting systems. Observations showed a maximum relative error of around 11% over the predicted residual saturation for both oilwetting and water-wetting mediums. Based on the phase-diagram, the developed model is applicable for both capillary and viscous fingering flow regimes. Moreover, the introduced model accurately predicts the changes in the front velocity with time, for all investigated Ca numbers, which demonstrates that outcomes of the proposed technique are physically reliable. Published by AIP Publishing.