Summary
Model-based dynamic optimization of oil production has a significant potential to improve economic life-cycle performance, as has been shown in various studies. However, within these studies, short-term operational objectives are generally neglected. As a result, the optimized injection and production rates often result in a considerable decrease in short-term production performance. In reality, however, it is often these short-term objectives that dictate the course of the operational strategy. Incorporating short-term goals into the life-cycle optimization problem, therefore, is an essential step in model-based life-cycle optimization. We propose a hierarchical optimization structure with multiple objectives. Within this framework, the life-cycle performance in terms of net present value (NPV) serves as the primary objective and shortterm operational performance is the secondary objective, such that optimality of the primary objective constrains the secondary optimization problem. This requires that optimality of the primary objective does not fix all degrees of freedom (DOF) of the decision variable space. Fortunately, the life-cycle optimization problem is generally ill-posed and contains many more decision variables than necessary. We present a method that identifies the redundant DOF in the life-cycle optimization problem, which can subsequently be used in the secondary optimization problem. In our study, we used a 3D reservoir in a fluvial depositional environment with a production life of 7 years. The primary objective is undiscounted NPV, while the secondary objective is aimed at maximizing shortterm production. The optimal life-cycle waterflooding strategy that includes short-term performance is compared to the optimal strategy that disregards short-term performance. The experiment shows a very large increase in short-term production, boosting first-year production by a factor of 2, without significantly compromising optimality of the primary objective, showing a slight drop in NPV of only -0.3%. Our method to determine the redundant DOF in the primary objective function relies on the computation of the Hessian matrix of the objective function with respect to the control variables. Although theoretically rigorous, this method is computationally infeasible for realistically sized problems. Therefore, we also developed a second, more pragmatic, method relying on an alternating sequence of optimizing the primary-and secondary-objective functions. Subsequently, we demonstrated that both methods lead to nearly identical results, which offers scope for application of hierarchical long-term and short-term production optimization to realistically sized flooding-optimization problems.
A modification of steepest descent method for solving large-scaled unconstrained optimization problems
