Surrogate based optimal waterflooding management

Abstract

In this work we solve the optimal waterflooding management problem using as design variables the rates allocated to each injector and producer well under different operational conditions. The duration of each control cycle may also be optimally controlled. The objective function is the net present value. As the cost of numerical simulation can be very high it is generally not feasible to couple the simulator directly to the optimizer. Therefore a cheap surrogate model is used to capture the main trends of the objective and constraint functions. In this work we adopt Kriging data fitting approximation to build surrogate models to be used in the context of local optimization. The Sequential Approximate Optimization (SAO) strategy is used to solve the problem as a sequence of local problems. A trust region based framework is employed to adaptively update the design variable space for each local optimization. Sequential Quadratic Programming (SQP) is the algorithm of choice for the local problems. For illustrative purposes two reservoir problems are presented. The first is a small problem, with three wells, used to tune algorithmic parameters. The second is a medium sized reservoir, with 12 wells, used to demonstrate the potentials of the proposed method. The technique proved to be accurate and its performance confirms the efficient regularization of simulator numerical noise. It was successful in identifying wells that should be late started or shut-in before the end of the concession period and in handling different kinds of production strategies. Increase in operation flexibility resulted in NPV improvement. Cycle duration variables proved to be useful in decreasing the number of design variables while maintaining recovery efficiency.