Accurate estimation of macroscopic flow properties in porous media : from REV to upscaling

Abstract

Representative Elementary Volume (REV) is the smallest volume of a porous media above which further size increases do not yield any changes in the measurements of a specific property. It is well established that the REV can vary across geological scales for different static (e.g., porosity) and flow-based properties (e.g., permeability). Most REV studies available in the literature are focused on static properties at the pore scale. However, in this study, we have focused on determining REV for single-phase flow parameters at the core scale to investigate whether SCAL experiments are performed on a representative volume. Also, the feasibility of using tracer tests for determining core scale REV was investigated since the shape of the effluent tracer tests can be a good qualitative indication of the heterogeneity, and the Peclet number can be a quantitative measure. For this purpose, several heterogeneous reservoir sections were generated, and tracer flood simulations were conducted on sub-samples of various sizes. It was demonstrated that, in general, permeability-based REV based on the common approach in the literature closely match the corresponding REV figures showing the accuracy of the novel tracer-based technique. As part of this study, the numerical dispersion associated with various techniques available for the simulation of tracer flow were also investigated and quantified. After identifying REV and performing SCAL experiments on a representative volume, an upscaling method is needed to use the results in reservoir-scale simulations. In this study, a complete set of two-phase numerical coreflood tests, along with a Gaussian Process Regression algorithm (GPR), was used to obtain a data-driven model. This model relates the measured oil production and pressure drop to the basic fluid and rock properties through dimensionless groups. Using dimensionless groups eliminate the impact of sample size on the results. Therefore, a new oil production and pressure drop curve can be calculated using the data-driven model for any larger or smaller sample. The obtained curves can be history matched to find the relative permeability at a larger scale. Next, the proposed upscaling method is extended to three-phase flow by introducing relevant dimensionless groups. The three-phase upscaling methodology is validated against large-scale numerical tests representing different reservoir heterogeneity patterns and fluid properties. The proposed approach demonstrates excellent performance in predicting oil recovery, water production, and pressure drop in three-phase flow systems and also upscaling three-phase relative permeability functions in heterogeneous porous media. In summary, this study contributes to the advancement of REV characterisation and relative permeability upscaling techniques for multi-phase flow in porous media. The developed tracer technique and dimensional analysis approach, coupled with the GPR algorithm, provide an accurate and reliable framework for capturing reservoir heterogeneity and predicting flow behaviour at larger scales. Also, the proposed approach demonstrates superior performance compared to the existing methods. The findings of this study have implications for optimising sampling strategies and enhancing the predictive capabilities of reservoir upscaling models.