Well Control Optimization with Output Constraint Handling by Means of a Derivative-Free Trust Region Algorithm

Abstract

Abstract The Derivative-Free Trust-Region (DFTR) optimization is well-suited for reservoir engineering problems where gradient information is often unavailable, unreliable, or unacceptably costly to obtain by numerical means. As opposed to direct search methods, the DFTR method is known to exhibit early convergence due to its capability to capture function curvatures with approximation models, which is important for simulations with long run-time. In this paper, we propose a new DFTR optimization algorithm which is capable of handling output constraints in well control problems. The method relies on building polynomials using interpolation points generated from the simulation runs to model the objective function and constraints that are valid within the region around an incumbent solution. The models are subject to improvement when appropriate to ensure good geometry and accuracy of the approximation. The algorithm utilizes the models to find the next optimum iterate and introduces safeguards to ensure improvement in both the objective function and the constraints violation. The algorithm is open source and has a clear interface with capability for integration to different reservoir simulators. The method is tested on the SPE10 benchmark model for reservoir simulation with realistic output constraint scenarios. The result of this study shows that the DFTR algorithm can achieve optimal operating points that improve the objective function in well control optimization problems while still honoring the constraints within a reasonable number of iterations. A comparison study is also conducted with two other derivative-free methods: NOMAD and COBYLA, where it is shown in the case studies that the proposed DFTR algorithm performs better in terms of the objective function value, number of function evaluation, and the feasibility of the solutions. This paper addresses the handling of output-constraints by introducing an algorithm called Derivative-Free Trust-Region Filter Sequential Quadratic Programming (DFTR-FSQP) that can handle black-box type of simulators. This allows a non-intrusive optimization routine that can be naturally added into any reservoir modeling frameworks in order to handle practical operational limitations typical of field operations that can be expressed as constraints on acceptable solutions, such as water production and topside capacity. Further, using this method, one may express constraints independently from the simulators if the information is available. While reservoir simulators may be able to impose such restrictions internally, it introduces discontinuities in the cost function by control-variables switching and therefore could jeopardize the consistency of the dynamics and therefore the optimality of the solution.