Robust Constrained Optimization of Short- and Long-Term Net Present Value for Closed-Loop Reservoir Management

Abstract

Summary In this paper, we develop an efficient algorithm for production optimization under linear and nonlinear constraints and an uncertain reservoir description. The linear and nonlinear constraints are incorporated into the objective function using the augmented Lagrangian method, and the bound constraints are enforced using a gradient-projection trust-region method. Robust long-term optimization maximizes the expected life-cycle net present value (NPV) over a set of geological models, which represent the uncertainty in reservoir description. Because the life-cycle optimal controls may be in conflict with the operator's objective of maximizing short-time production, the method is adapted to maximize the expectation of short-term NPV over the next 1 or 2 years subject to the constraint that the life-cycle NPV will not be substantially decreased. The technique is applied to synthetic reservoir problems to demonstrate its efficiency and robustness. Experiments show that the field cannot always achieve the optimal NPV using the optimal well controls obtained on the basis of a single but uncertain reservoir model, whereas the application of robust optimization reduces this risk significantly. Experimental results also show that robust sequential optimization on each short-term period is not able to achieve an expected life-cycle NPV as high as that obtained with robust long-term optimization.