Constrained short-term and long-term multi-objective production optimization using general stochastic approximation algorithm

In the water flooding reservoir management, engineers aim to make an optimal production strategy to maximize both the net present value (NPV) in life-cycle and the short-term NPV. Previous researches of multi-objective optimization of long-term and short-term find that the short-term production optimization decreases the long-term NPV and the gradient calculation using adjoint gradient is hard to be applied. Therefore, we implement a multi-objective optimization method in which the long-term NPV is lumped into the short-term objective function as a constraint in order not to decrease the life-cycle NPV, linear and nonlinear constraints are lumped into the augmented Lagrangian objective function. Also, we propose a new gradient-free algorithm general stochastic approximation algorithm (GSA) to obtain the better approximate gradient. We proved that the research direction of GSA algorithm is always uphill, the simultaneous perturbation stochastic approximation algorithm (SPSA) and the ensemble-based optimization algorithm (EnOpt) are also two special forms of GSA algorithm. Toy problem results show that GSA has a more efficient approximation gradient than SPSA. Optimization results of a 2D reservoir show that the increase of the long-term NPV is about 86.5% and the increase of the short-term NPV is about 18.8%. The field case of Brugge field also shows that the long-term and short-term NPV increase by 64.7 and 48.9%.