Life-Cycle Reservoir Production Optimization Using Heuristic Schemes Implemented in Numerical Simulators for Handling Nonlinear State Constraints
Authors: Toktas Omer Lutfu , Nguyen Quang Minh , Onur Mustafa 
Published: September 2024

Abstract
This study focuses on the investigation of deterministic life-cycle reservoir production optimization by maximizing a net present value (NPV) subject to well controls with nonlinear state constraints [such as field liquid production rate (FLPR), and field water production rate (FWPR)] by enforcing these constraints to be satisfied using the heuristic schemes applied internally in a high-fidelity simulator. Our objective is to develop a methodology based on a heuristic production optimization method that provides an optimal solution of well controls that satisfy the given nonlinear state constraints over each of the control steps chosen for a life cycle production process. Our proposed heuristic nonlinearly constrained optimization methodology is based on performing optimization where we only consider linear bounds on well controls within a line-search, merit function-based sequential quadratic programming (SQP) framework coupled with stochastic simplex approximate gradient (StoSAG). The nonlinear state constraints are imposed over each control step by the simulator through its internal heuristic schemes during iterations. We refer to this heuristic method as the "hybrid SQP-heuristic constraint-handling method." An example is presented using the well-known Brugge model, where the NPV is maximized subject to nonlinear state constraints such as FLPR and FWPR. Two built-in heuristic schemes are investigated, namely rate balance action and prioritized balance action. We also compare our proposed method with two different optimization approaches: the "SQP-based constraint-handling method" utilizing a line-search strategy with StoSAG gradients for all constraints imposed, and the "existing heuristic-based constraint-handling method" considering optimization subject to only linear bounds on the well controls within the SQP framework, with the nonlinear state constraints are heuristically enforced directly on the optimal solution using a forward simulation run. Results show that the SQP-based constraint-handling method yields about 6.0% and 0.2% higher NPV values than the existing heuristic and hybrid SQP-heuristic constraint-handling methods, respectively. However, our proposed method is almost twice as computationally efficient in terms of the total number of simulations. Moreover, it provides no violations of any nonlinear state constraints, while the SQP-based constraint-handling method could violate the nonlinear state constraints over some control steps, which is not desirable. Although the existing heuristic-based constraint-handling method yields no violation of the nonlinear state constraints, the NPV maximized is suboptimal. The numerical examples illustrate that the novel hybrid constraint-handling method not only accelerates the optimizer convergence far beyond the other two methods but also achieves zero violations of nonlinear constraints and nearly matches the highest NPV obtained from the SQP-based constraint-handling method. Here, we present a novel hybrid heuristic approach for handling nonlinear constraints to solve the deterministic life-cycle production optimization problem. It is shown that, among the three methods compared, our hybrid heuristic nonlinear constraint handling approach proves useful for closed-loop reservoir management.