Optimization of Water Flooding in Stratified Formations or Multiple Reservoirs

Water flooding of stratified reservoirs often resulted in non-uniform oil displacement and fast water breakthrough in high permeability layers. Increase in oil recovery may be achieved by improvement of oil displacement in different layers and getting simultaneous water breakthrough in production wells. A similar problem may arise when water flooding multiple reservoirs with constrains on total injection / production. Control of injection rate allocation may provide uniform oil displacement in a layered formation or multiple reservoirs. Constrains on local (per layer) and total (per formation) injection / production rates and on production period for each layer may be accounted for. In this study optimization algorithms have been developed to determine an optimal strategy enabling maximum possible oil production with minimum possible water cut from a group of non-communicating layers or reservoirs. A solution of the optimization problem was found using linear and discrete programming methods under an assumption of two-phase piston-like incompressible flow in the reservoir. An optimal strategy with maximum oil recovery is defined under constrains on local and total production rates, injection start-up time and duration of production period for each layer or reservoir. An analytical solution was also found for a partial statement of the problem, where injection rates remain constant over the whole production period, which in turn is the same for all layers. The general problem statement has flexible constrains available, while the analytical solution for the partial statement may be easily implemented and used without dimension (number of layers or reservoirs) limitations. Both solutions were coded and further tested at mechanistic reservoir models to confirm applicability and efficiency of the developed algorithms in the reservoir simulation practice. A two-dimensional cross-sectional model with non-communicating layers was set up to test efficiency of the optimization algorithms for a typical reservoir simulation problem where fluid / rock compressibility and relative permeability effects are accounted for. The reservoir simulation results have confirmed that the optimal solution remained in force and therefore the optimization algorithms may be successfully integrated in reservoir simulation workflow.