Global Sensitivity Analysis of Relative Permeability and Capillary Pressure in Unsteady-State Core-Flooding Experiment

Resumo

Numerical simulation stands as a pivotal method within the petroleum industry, enabling the prediction of fluid flow in porous media. Its primary goal lies in analyzing behavior and forecasting oil production through fluid injection. However, the necessity for numerous simulations, each encompassing diverse multidimensional and compositional characteristics, presents a challenge. This leads to a significant accumulation of physical information, exacerbating the computational demands on the numerical model, particularly in terms of computational cost. To address this challenge, one potential solution is to determine the essential input parameters required for accurate oil production prediction. Global sensitivity analysis emerges as a powerful tool for this purpose, aiming to identify which input parameters exert the most significant influence on the numerical model's response, thus optimizing computation time. Unlike traditional approaches that focus on sensitivity around a single operating point, this study adopts a holistic perspective, assessing sensitivity across the entire sample space of the inputs. Specifically, this research investigates the impact of changes in parameters related to relative permeability and capillary pressure curves within a plug during unsteady-state core-flooding experiments. The key metrics under scrutiny include water saturation profiles, pressure differentials, and cumulative oil production. Sobol indices, a method for quantifying global sensitivity, are employed to assess the contribution of each input parameter's variance to the outputs' variance. The mathematical framework employed here is based on the multiphase (water/oil) Darcy equation, incorporating capillarity effects in one-dimensional longitudinal flow, incompressible flow assumptions, and constant injection flow, commonly known as the Black Oil model. The model is solved utilizing an implicit finite difference methodology with time step control, with relative permeability and capillary pressure parameterized by the LET model. The outcomes of this analysis provide valuable insights, notably in reducing the number of estimable parameters in inverse problems on a global scale. This reduction significantly diminishes computing costs, offering greater flexibility in constructing surrogate models for future simulations.