Physics-Based Data-Driven Interwell Simulator for Waterflooding Optimization Considering Nonlinear Constraints

Abstract

When nonlinear constraints such as field liquid and water production rate are imposed onto the problem and need to be honored, optimizing well controls such as producing bottom-hole pressures (BHPs) and injection rates becomes more challenging. Hence, the main objective of this paper is to present an efficient production optimization tool to handle nonlinear state constraints for well-control waterflooding optimization problems. The proposed efficient optimization tool uses our newly improved physics-based data-driven interwell waterflooding simulator (referred to as INSIM-BHP) that handles both rate and pressure controls. Our previous waterflooding optimization applications used an old version of INSIM which only considered the linear constraints and did not incorporate the correct well indices for computing BHPs in the case of well BHP control optimization. In this study, we use our newly developed interwell waterflooding simulator that removes the mentioned restrictions in well-control optimization to maximize the net-present-value (NPV) with nonlinear state constraints. We use a recently developed line-search sequential quadratic programming (LS-SQP) algorithm coupled with stochastic simplex approximate gradients (StoSAG). We tested our proposed methodology on a three-dimensional (3D) channelized reservoir with multi-segmented wells and compared it with a commercial simulator. Results show that our methodology provides optimal well controls that satisfy the specified nonlinear state constraints successfully. In addition, the optimal well controls and NPV obtained from our INSIM-based optimization method compare well with the corresponding results from a high-fidelity commercial reservoir simulator but in a far less computational time. The novelty of our work is its presentation of an improved physics-reduced data-driven proxy simulator (INSIM-BHP) to replace the high-fidelity simulators to simulate the oil saturation and pressures to perform computationally efficient well-control waterflooding optimization under nonlinear constraints.