Relevance of analytical Buckley-Leverett solution for immiscible oil displacement by various gases

TL;DR

This paper evaluates when the Buckley-Leverett analytical solution remains valid for gas injection in oil displacement, highlighting the importance of gas compressibility and pressure effects on model accuracy.

Contribution

It provides a comparative analysis of compressible versus incompressible gas models in oil displacement, identifying conditions where each model is appropriate.

Findings

Increased injection pressure amplifies model discrepancies.

Incompressible model fails for CO2 at low pressures.

2D simulations show larger model mismatches.

Abstract

In order to generate the valid numerical simulation model, the sufficient amount of gathered data from the oil field is required. However, it is not always possible to acquire such data at the initial stage of project development. Buckley and Leverett (1942) developed the analytical solution allowing to assess the oil displacement efficiency. One of the main assumptions of this model is incompressibility of oil and injected fluid. For slightly compressible water and oil such assumption is rational. However, that is not always the case when the gas is injected. This research aims to identify the conditions at which the usage of the incompressible gas model is appropriate. Likewise, the cases when the model of compressible gas is required are also evaluated. To accomplish the goals of this research, the comparative analysis between the injection of compressible and incompressible gases was undertaken using the numerical solution of the correspondent reservoir engineering problem. The validation of the numerical model was undertaken showing that it matches the analytical Buckley-Leverett solution. The findings of this research indicate that the relative and absolute density change with the pressure of the injected gas has the profound impact on the convergence between two models under consideration. With the increase in the injection pressure, the discrepancy between the models of compressible and incompressible gas raises for all the considered injection fluids (CO2, CH4 and N2). Due to a steep slope of 'density-pressure' curve for CO2 at low initial reservoir pressure, the incompressible model cannot accurately predict the oil displacement efficiency by this gas at any reasonable injection pressure. All 1D results are also representative for 2D simulation. However, the mismatch between two models increases considerably for 2D simulation scenarios.