Quantificação de incertezas do campo de permeabilidade através da expansão de Karhunen-Loève na recuperação avançada de petróleo utilizando injeção de espuma

Abstract

A method for enhanced oil recovery (EOR) that has been extensively studied is the injection of foam into the porous medium, as it allows for a more uniform sweep of the reservoir. In this context, mathematical models have been widely used to make predictions and studies on how to optimize production. Therefore, it is important to study and clearly understand the influence of each parameter of the mathematical model on the flow. Many characteristics of fluids must be taken into consideration, but in addition, the influence of heterogeneity and uncertainties in the absolute permeability field play an important role in flow and foam performance. The objective of the work is to carry out Uncertainty Quantification (UQ) and Sensitivity Analysis (SA) of Quantities of Interest (QoIs) relevant to the understanding and study of EOR in cases of foam flow and considering uncertainties in the permeability field, in order to understand how these can be mitigated by the presence of foam. To achieve this, the Karhunen-Loève expansion was used to introduce uncertainties in the permeability field and the Polynomial Chaos expansion (PCE) technique was used to create emulators of two-phase water-gas flow models with the presence of foam to conduct the studies efficiently, due to the high computational cost of the mathematical models involved. mathematicians involved. Within this context, SA through the calculation of Sobol indices can be carried out appropriately through emulators. The uncertainty quantification results corroborate the foam’s ability to mitigate the effects of the heterogeneity of the porous medium, reduce variations and increase process efficiency. It was observed that the stronger foam explored contributed to a delay in breakthrough and to reduce the uncertainties of the results. Emulators based on PCE have proven to be effective in predicting results, with satisfactory metrics.