Constrained Production Optimization with an Emphasis on Derivative-free Methods

Production optimization involves the determination of optimum well controls to maximize an objective function such as cumulative oil production or net present value. In practice, this problem additionally requires the satisfaction of physical and economic constraints. Thus the overall problem represents a challenging nonlinearly constrained optimization. This work entails a comparative study of several popular optimization methods applied to the solution of the fully constrained production optimization problem. The methods considered include gradient-based methods, a genetic algorithm, general pattern search and Hooke-Jeeves direct search. In the application of these methods to bound-constrained problems, it is shown that derivative-free methods tend to be about an order of magnitude slower than gradientbased methods that compute gradients using an adjoint procedure. The efficiency of the derivative-free methods is significantly improved through the use of surrogatebased optimization and distributed computing. A hybrid implementation combining the most desirable parts of some of the different methods is presented and shown to perform better than the individual methods. In order to address the solution of the fully constrained production optimization problem, different constraint handling techniques are investigated, including the sequential quadratic programming approach, penalty function approach, filter method, and a hybrid methodology. The results of the application of these methods indicate that the gradient-based sequential quadratic programming, general pattern search with filter and a hybrid method combining the genetic algorithm with a robust penalty function treatment and an efficient local search method are the most promising.