Hybrid PSO - adjoint-gradient Procedure for Well Control Optimization

Compositional simulation is commonly applied to evaluate enhanced oil recovery and carbon storage processes. Compositional simulation is expensive because the models may include multiple components along with complex phase behavior. Thus, when compositional systems are optimized, the optimization algorithms must be robust and efficient. In this work, we assess different procedures for well control optimization in oil-gas compositional systems. The optimization algorithms considered include a standalone adjoint-gradient-based method, a standalone particle swarm optimization (PSO) procedure, and several hybridizations of these two approaches. We introduce and evaluate two criteria for switching from PSO to adjoint-gradient-based optimization in the hybrid procedures. These approaches are referred to as deterministic switching, where we switch after a specified number of PSO iterations, and adaptive switching, where the algorithmic switch is based on PSO performance. All methods are implemented and run within Stanford’s Unified Optimization Framework (UOF).
The performance of the standalone and hybrid procedures is assessed for two example cases involving well control optimization in Gaussian and channelized geological models. The time-varying bottom-hole well pressures are treated as the optimization variables, and net present value (NPV) is optimized. Each method under consideration is run at least nine times to account for the stochastic nature of PSO and the sensitivity to the initial guess in the adjoint-gradient method. This allows us to draw meaningful conclusions on the relative performance of the various procedures. The two example cases presented in this study demonstrate that the hybrid PSO-adjoint-gradient procedure utilizing adaptive switching outperforms the standalone algorithms in terms of average optimal NPV. By plotting the average optimal NPV versus computational effort for the different methods, we can construct a Pareto front. For both cases, the Pareto-optimal procedures include standalone PSO (which provides lower average NPV but requires less computation) and the hybrid PSO-adjoint-gradient method using adaptive switching. The latter gives higher average NPV but at the cost of increased computational effort.