Optimal switching time control of petroleum reservoirs

•A new approach to the optimization of oil production is presented.•The gradient can be computed by evaluating the limits of the Hamiltonian.•Examples of realistic reservoir settings are presented.

Production optimization involving injection has successfully improved oil production by increasing recovery. This technique is now combined with information obtained from gradient-based methods for calculating the optimal flow rate or bottom-hole pressure (BHP) during life cycle optimization. It has been shown that if the objective functional is linear in the control and the only constraints are the upper and lower bounds on the control, then the problem will sometimes have bang–bang (on–off) optimal solutions. This paper discusses an optimal control approach to the life cycle optimization of water-flooding problem by calculating the optimal switching times given the optimal wells settings to be bang–bang controls. The optimal switching times are obtained using the gradient obtained from the adjoint-based method combined with the line search algorithm. Two numerical examples that use realistic reservoir settings are included to illustrate the application of the proposed method.