Assisted Upscaling of Miscible CO₂-Enhanced Oil Recovery Floods Using an Artificial Neural Network-Based Optimisation Algorithm

Due to the high computing cost of the fine-scale compositional simulations needed to effectively model miscible CO₂ flooding, upscaling techniques are needed to approximate the behaviour of these fine-scale grids on more realistic coarse-scale models. The use of transport coefficients to better represent small-scale interactions, such as the time-dependent flux of the components within the hydrocarbon phases (molecular diffusion), and the pseudoisation of relative permeabilities to ensure the matching of large-scale effects, such as the volumetric fluxes of the phases, are two of these procedures. Most times, a mismatch between the phase fluxes of the integrated fine-scale and that of the coarse-scale is observed. By adjusting or calibrating some of the generated coarse-scale pseudo functions, such as the transport coefficients, absolute permeability, or relative permeability endpoints, the accuracy of the upscaling results can be improved. This procedure can be treated a reservoir history matching problem which is typically computationally expensive. In this study, we provide a framework for representing the dynamics of small-scale molecular diffusion and macro-scale heterogeneity-induced channelling related to miscible CO₂ displacements on upscaled coarser grid reservoir models. The method used was based on the pseudoisation of relative permeability and transport coefficients and was applied to two benchmark reservoir models from the Society of Petroleum Engineers (SPE). Our results demonstrated that using effectively calibrated transport coefficients improved the upscaling results, so that the  calculated pseudo-relative permeability functions can be ignored. We proposed a unique approach to upscaling miscible floods that utilised a genetic algorithm and a neural-network-based proxy model to minimise the associated computing cost. The data-driven approximation model considerably decreased the computing cost associated with the assisted tuning technique, and the optimisation algorithm was used to reduce the error between the predictions of the upscaled models. In conclusion, the methodology described in this study effectively captured the small- and large-scale behaviour related to the miscible displacements on upscaled coarse-scale reservoir models while reduced associated computational costs.