Comparative Analysis of Mathematical Models of Capillary Imbibition on Experimental Data

Abstract

In this paper, a comparative analysis of various approaches to modeling the process of capillary imbibition in oil-saturated rocks is carried out. Today, the permeability of developed oil fields is decreasing, due to which capillary processes begin to make a significant contribution to filtration. Therefore, the issue of reservoir-scale imbibition modeling is becoming increasingly relevant. Capillary imbibition is a process of spontaneous filtration of a liquid into a porous medium under the action of capillary forces. The aim of the study is to analyze approaches to the mathematical description of this process. To do this, one-dimensional models of single-phase imbibition by Handy, Lee and Horn, Benavente and Kai are considered, the Schmid one-dimensional two-phase imbibition equation is solved, and the ability of the filtration model in the tNavigator software package to predict imbibition is checked. For verification, real experiments on core are simulated. Based on the simulation results, conclusions are drawn that single-phase models have an increased error due to the interaction of water with the second phase and non-physical values of free parameters, which is why it is not recommended to scale them to large rock volumes. The two-phase model does not consider gravity, due to which the error increases at the last stages of vertical imbibition, so this approach must be modified to consider gravitational forces in the imbibition equation. A numerical one-dimensional experiment on a hydrodynamic simulator using the proposed core modeling technique showed the best convergence with experimental data with an error of 1 to 4%, which is why it is recommended for modeling capillary processes on the scale of a well.