Production Optimization under Constraints Using Adjoint Gradients

The introduction of controllable downhole devices has greatly improved the ability of the reservoir engineer to implement complex well control strategies to optimize hydrocarbon recovery. The determination of these optimal control strategies, subject to limitations imposed by production and injection constraints, is an area of much active research and generally involves coupling some form of control logic to a reservoir simulator. Some of these strategies are reactive: interventions are made when conditions are met at particular wells or valves, with no account taken for the effect on the future lifetime of the reservoir. Moreover, it may be too late to prevent unwanted breakthrough when the intervention is applied. Alternative proactive strategies may be applied to the lifetime of the field and fluid flow controlled early enough to delay breakthrough. This paper presents a proactive, gradient-based method to optimize production throughout the field life. This method requires the formulation of a constrained optimization problem, where bottomhole pressure or target flow rates of wells, or flow rates of groups, represent the controllable parameters. To control a large number of wells or groups at a reasonably high frequency, efficient calculation of accurate well sensitivities (gradients) is required. Hence, the adjoint method has been implemented in a commercial reservoir simulator to compute these gradients. Once these have been calculated, the simulator can be run in optimization mode to find a locally optimal objective function (e.g., cumulative production). This optimization procedure usually involves progressively activating constraints, with each new constraint representing a significant improvement in the objective. Proper management of degrees of freedom of the parameters is essential when calculating the constrained optimization search direction. Adjoint methods have already been used for production optimization within reservoir simulation; however, an accurate analysis of optimal management of active and inactive constraints for different type of recovery processes in field-like cases has not been discussed to our knowledge.