Optimization Algorithm for Surfactant Flooding: Comparative Study of Brent's Hybrid and Adapted Newton-Rapson Method

An optimization algorithm was deployed to solve the single-objective function for uncertainty modeling of surfactant flooding. The cost function had an appearance of discontinuity, which may result in convergence problems. Brent's hybrid root finding method can be applied to the nonlinear equations of the fractional-flow curves to find the oil bank water saturation. Due to a complicated set of rules that prevent modification of Brent's hybrid method to easily select which root-finding method is used, the Newton-Rapson was adapted and considered as an alternative. The adapted Newton-Rapson method was compared with Brent's hybrid method for the overall performance of the optimization algorithm. Various optimization search intervals were used, and each was constrained to 3600 test evaluations. The Newton-Rapson method converges faster with a lower value of the cost function and an average execution time of 8.79 seconds for the case studies. On the other hand, Brent's method converges at an average execution time of 41.04 seconds with more intervals on the cost function with no convergence. We concluded that Newton's method was a better solution capable of minimizing a noisy cost function with fewer iteration and faster execution times. Therefore, it should be considered the most effective optimization algorithm.