Dynamic Optimization for Petrophysical Property Estimation in Unsteady-State Coreflooding Using Pyomo

This paper deals with a mathematical modeling and optimization-based approach for estimating relative permeability and capillary pressure from average water saturation data collected during unsteady-state waterflooding experiments. Assuming the Lomeland-Ebeltoft-Thomas (LET) model for the variation of the relative permeability with saturation, the appropriate governing equations, boundary, and initial conditions were solved within the Pyomo framework. Using interior point optimization (IPOPT) with a least-squares objective function, the six parameters of the LET model that ensure the history matching between the measured and calculated average saturation are determined. Additionally, we inferred the capillary pressure function and performed a Sobol sensitivity analysis on the LET model parameters. The results showcase the reliability and robustness of our proposed approach, as it estimates the crucial parameters driving the variation of oil-water flow relative permeability across several cases and effectively predicts the capillary pressure trend. The proposed approach can be seen as an alternative to experimental and numerical simulation-based techniques for predicting relative permeability and capillary pressure curves.