Implementation of Trust-region Algorithm for Well Placement Optimization in FieldOpt Framework

Abstract

Oil field development is a challenging engineering task that involves optimization problems such as the types, numbers, scheduling, location, and controls of wells. Optimization algorithm is the keyfactor for optimization model. Each algorithm has its own strengths and weaknesses, hence we need to apply efficent and effective methodologies to solve optimizatiom problems. This thesis concerns the implementation of local search trust-region derivative-free algorithm for well placement into the FieldOpt optimization framework developed at the Petroleum Cybernetics Group, NTNU. The C++-written FieldOpt software program serves as a framework and enabler for algorithm development aimed at petroleum problems that require the efficient computations of reservoir simulations for cost function evaluation. The reservoir simulation works as a Black Box , but the FieldOpt software allows for a straightforward one-to-one communication between the algorithm logic and the multiple driver files and settings needed by the simulator. We start with general introduction of well placement optimization and widely used algorithms for optimizaton problems. Gradients with respect to well place- ment variables are commonly not available and therefore derivative-free methods are often proposed for well placement optimization. The trust region method implemented in this work does not require cost function derivatives, but instead constructs surrogate models of the objective function obtained during the optimiza- tion process. Our approach is based on building a quadratic interpolation model, which reasonably reflects the local behavior of the original objective function in a subregion. After implementation of the algorithm in FieldOpt, we apply test functions to validate the performance of the algorithm. One of them is the plated-shaped Matyas function and the other one is the valley-shaped Rosen-brock function. We used Cauchy point calculation and Dogleg method to solve the optimization problem and analyzed their convergence properties. The results show that the convergence of the Cauchy point algorithm by taking the steepest descent direction is inefficient in some cases. A future improvement could be achieved by using the Dogleg method. We also notice that values of predetermined parameters can affect algorithm performance. Therefore, it is also important to choose a proper parameter value to improve the convergence of method. Then, we apply the model-based trust-region method to solve some well placement optimization cases, for exapmle single producer or five-spot model.