Uncertainty Quantification of Allen-Cahn Phase Field Parameters in Multiphysics Simulation of Oil Shale Radio Frequency Heating

Abstract Radio frequency (RF) heating represents a dielectric heating technique for converting kerogen-rich oil shale into liquid oil through in-situ pyrolysis. This process can be modeled using a multiphysics finite element based coupled thermal, phase field, mechanical and electromagnetic (TPME) numerical framework. This work focuses on the combination of a two-dimensional (2D) TPME multiphysics simulation with uncertainty quantification (UQ) that incorporates the Allen-Cahn phase field parameters, specifically those which describe the associated reaction-diffusion process as electromagnetic energy being converted to thermal energy in the RF heating process. The breadth of UQ performed in this study includes not only the Allen-Cahn parameters but also selected thermal, statistical rock-type distribution in the geological model, as well as electromagnetic parameters of the applied quasi-static Maxwell equation. A Non-Intrusive Polynomial Chaos (NIPC) is used for: considering the affect of Allen-Cahn phase field parameters on the evaluation of plausible conversion timelines of TPME simulation and the evaluation of summary statistics to predict the order of Polynomial Chaos Expansion (PCE) that is representative of full kerogen-rich zonal conversion response in a geologically descriptive finite element model. A sparse representation of polynomial chaos coefficients is highlighted in the process of computing summary statistics for the complex stochastically-driven TPME simulation results. Additionally, Monte Carlo (MC) simulations were performed in order to validate the results of the sparse NIPC representation. This is done considering MC is a widely recognized stochastic simulation process. Additionally, NIPC was used to illustrate the potential performance improvement that are possible, with a sparse polynomial chaos expansion enhanced by the incorporation of Least Angle Regression (LAR), as compared to MC simulation. Although the parametic uncertainty of the reaction-diffusion parameters of the Allen-Cahn was comprehensive, they did not accelerate the conversion timelines associated with the full zonal conversion of the kerogen-rich rock type in the statistical simulation results. By executing the stochastic simulations for a greater length of time the extent of full zonal conversion is examined in the RF modeling.