61st Annual Report on Research 2016

During the course of this project a simulator prototype was developed and implemented. The simulator was used to address the main hypotheses that had been proposed with regard to the nonlinear coupling between the multiphase flow and transport equations: a) the pressure variables can be separated and updated independently from the saturation variables, and b) the system of hyperbolic conservation equations can be entirely decoupled to solve. To verify the hypotheses, we proposed a new nonlinear solution strategy that is applicable to the conventional Fully Implicit discretization of the governing equations of the multiphase flow and transport in porous media. The developed simulator concurrently addresses the problems of convergence and computational cost per each nonlinear iteration. To solve the nonlinear system of equations, we decouple the pressure and saturation updates via a two-step scheme comprised of the linear pressure update in a reduced system, followed by the saturation update step. Moreover, the challenge with regard to the flow reversal phenomenon during Newton iterations was overcome by treating counter-current and co-current flow regions differently. The outcomes of the study show that the proposed algorithm allows for larger timestep sizes during the simulation timeframe. Moreover, as compared to the standard Newton solver, the computational cost associated with each nonlinear iteration is reduced significantly as a result of smaller linear systems of equations that need to be solved. Our results also indicate that the choice of linear solver is critical for efficient implementation of the simulator prototype based on the proposed nonlinear solver. Ultimately our algorithmic analysis and timing results show that the optimized version of the proposed solver is not able to outperform Newton-Raphson method when timestep sizes are small; however, for more practical simulation cases when larger timesteps are selected, the algorithm can outperform the state-of-the-art solvers.

The impact of the research on the PI’s career and the participating student:

This project had a great impact on the PI’s career trajectory. As part of this project, major collaboration with other faculty members involved in reservoir simulation research took place. In particular, the PI collaborated with a new research consortium at the department and ultimately secured his position as a Co-Principal Investigator. Moreover, the PI had several constructive discussions with industry experts, thereby drawing a great deal of attention to his research endeavors. One Master’s student was assigned to this project. The student had to acquire some technical background both in terms of fundamentals and implementation skills. As a result of working on this project, the student has gained a wide range of skills which he can utilize in future projects or industry positions. Moreover, the student was able to present an article based on the outcome of the study in the European Conference on Mathematics of Oil Recovery (ECMOR) which was held in Sicily, Italy. The student had great discussions with experts of the field during the course of the conference and consequently he acquired intriguing ideas as to how he can further expand his research endeavors on this very exciting topic.