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.

This paper presents a novel technique for upscaling multiphase fluid flow in complex porous materials that combines asymptotic homogenization approach with hydrodynamic- and 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 multi-phase 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.

Acid enhanced oil recovery has been a focus of interest in the oil industry due to its significant results on improved recovery, especially in carbonate reservoirs. However, in carbonate reservoirs, highly conductive pathways called "wormholes" are created when acidic fluids are injected into carbonate rocks. Wormholes could jeopardize the enhanced oil recovery outcome and sweep efficiency leaving a substantial volume of oil in the reservoir unswept. This phenomenon has not been investigated yet. The main objective of this study is to identify the impact of these wormholes on the overall oil recovery during enhanced oil recovery practices. This was achieved by injecting acidic fluid into Indiana limestone at various injection rates to control the creation of wormholes. The injection rates were selected based on a proposed dimensionless phase space that predicts the wormholes development and dissolution phase. Our results show that wormholes have a significant impact on the enhanced oil recovery performance resulting in a decrease in the overall oil recovery by 9.6% for portions of the reservoir that experience wormholing. In real field applications, it is recommended to avoid creating wormholes over large portions of the reservoir affected by acid injection as it may jeopardize the field development outcome leaving an unspecified amount of oil in virgin regions in the reservoir which results in additional operational complications. Wormholes are only beneficial near the wellbore for wellbore cleanup and matrix treatment purposes thus providing easier access to the reservoir. However, care needs to be taken to constrain wormhole formation to skin factor reduction and avoid far-reaching wormholes in the reservoir.