Waterflooding Optimization Using Gradient Based Methods

Abstract Finding the best strategy for production optimization is currently an important research task for closed-loop reservoir management. The closed-loop reservoir management consists of two main tasks: history matching and production optimization. A comparative closed loop reservoir management exercise was performed in connection with the SPE Applied Technology Workshop "Closed-loop reservoir management" in Bruges June 2008. The model used in this exercise was a synthetic reservoir with typical geological features of Northern Sea fields and considerably larger than those used in most previous studies. In a previous work (Lorentzen et al., 2009), a set of history matched models were obtained using the ensemble Kalman filter. We will use these models to investigate the effect of formulation and initial guess on gradient based optimization methods. Within production optimization, most of the works are focused on optimizing the reservoir performance under waterflooding. We will review the waterflooding optimization studies so far. The mathematical theories of an optimization problem as well as the practical issues regarding reactive and proactive approaches are discussed. The formulation of a waterflooding optimization problem is investigated using three different optimization variables: bottomhole pressure, oil and liquid production rates. Results show that proper formulation improves the performance of gradient based methods considerably. Then it is verified that manual optimization of the initial guess based on reservoir concepts enhances both the result and efficiency of the gradient based optimization. The manual optimization saves the gradient based methods from a number of local optima and also decreases the simulation costs substantially. Two line search methods, steepest descent and conjugate gradient, are used and compared in the adjoint based optimization approach. The conjugate gradient acts slightly faster than the steepest descent method. However, the selection of a proper initial guess is far more important for the performance. Finally, the optimal solution is applied on ten more history matched realizations to check the robustness of the solution. It is shown that the well liquid rates are the best variables used for maximizing the net present value using gradient based optimization. In previous works, well bottomhole pressure has been suggested.