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

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.Comment: 16 pages, 8 figure

The impact of wettability and fluid saturations on multiphase representative elementary volume estimations of micro-porous media

The occurrence of multi-phase flows in porous media is a complex phenomenon that involves multiple scales, ranging from individual pores to larger continuum scales. Upscaling frameworks have emerged as a response to the need for addressing the disparity between micro-scale processes and macroscopic modelling. Determination of the representative elementary volume is important for understanding fluid dynamics in micro-porous materials. The size of the representative elementary volume for multiphase flow in porous media is significantly affected by wettability and fluid saturations. Previous studies have overlooked this aspect by conducting simulations under conditions of constant medium wettability and fluid saturations. This study uses finite volume simulations with a volume of fluid approach for two distinct asymptotic homogenization methods, namely hydrodynamic bounds of relative permeability and thermodynamic bounds of entropy production. Strong wetting conditions with high wetting phase saturation were found to require a smaller sample size to establish representative elementary volume, while mixed-wettability scenarios necessitate the largest sample sizes. These findings improve our understanding of multiphase fluid flow behaviour in micro-porous materials and aid in enhancing techniques for scaling up observations and predictive modelling in engineering and environmental fields.Document Type: Short communicationCited as: Hussain, S. T., Regenauer-Lieb, K., Zhuravljov, A., Hussain, F., Rahman, S. S. The impact of wettability and fluid saturations on multiphase representative elementary volume estimations of micro-porous media. Capillarity, 2023, 9(1): 1-8. https://doi.org/10.46690/capi.2023.10.0

Asymptotic hydrodynamic homogenization and thermodynamic bounds for upscaling multiphase flow in porous media

This paper presents a novel technique for upscaling multiphase fluid flow in complex porous materials that combines asymptotic homogenization approach with hydrodynamicand thermodynamic bounds. Computational asymptotic homogenization has been widely utilised in solid mechanics as a method for analysing multiscale expansion and convergence coefficients in heterogeneous systems. Computations are performed over several volumes by increasing the size until convergence of the material parameters under different load scenarios is achieved. It works by simplifying the problem with a homogenization method and is ideally suited for estimating the representative elementary volume of microporous material by expanding algorithms. The validity of the method to include complex multiphase hydrodynamic processes and their interaction with the matrix structure of porous media lacks a sound theoretical foundation. To overcome this problem, a variational thermodynamic approach is used. Upper and lower bounds of entropy production are proposed to provide effective material properties with uncertainties. This allows multiple possibilities to address dynamics via thermodynamically linked processes. This work utilizes volume of fluid approach to model multiphase porous media flow in models based on micro-computerized tomography x-ray data of Bentheimer sandstone and Savonnieres carbonate. It is found that the representative elementary volume sizes obtained by the conventional asymptotic homogenization methods do not satisfy thermodynamic bounds which consistently require larger representative elementary volume sizes. For the Savonnieres carbonate the entropic bounds have not converged fully questioning the reliability of the effective properties obtained from the classical method.Document Type: Original articleCited as: Hussain, S. T., Regenauer-Lieb, K., Zhuravljov, A., Hussain, F., Rahman, S. S. Asymptotic hydrodynamic homogenization and thermodynamic bounds for upscaling multiphase flow in porous media. Advances in Geo-Energy Research, 2023, 9(1): 38-53. https://doi.org/10.46690/ager.2023.07.0