Life-cycle production optimization of an oil field with an adjoint-based gradient approach

Life-cycle production optimization is performed on an oil reservoir to find the optimal well controls for a fifteen-year producing period. The objective is to find the set of well controls that yield a higher value of net-present-value (NPV) with respect to the one obtained based on the rate schedule currently proposed. This rate schedule is based on specifying the water injection rate schedule at three water injection wells and the oil rate schedule at each of thirteen producing wells subject to bottomhole pressure constraints, economic constraints, a total water injection rate constraint and a voidage replacement ratio constraint. The field operator specified rate schedule represents the base case. As the reference case is based on specifying rates, in the production optimization problem, the well control variables are specified as the oil rates at the producers at each control step and the water injection rates at the injectors at each control step. Thirty control steps with each control step equal to one-half year are selected. An original gradient-based augmented Lagrangian optimization code is used but the gradient of the NPV is computed from the adjoint code of a commercial simulator. For this reason, some difficulties arise because if a specific well is shut-in or changed from rate control to bottomhole pressure control in the middle of a specific control step due to the violation of a constraint, a zero value is given for the derivative of the cost function with respect to the rate control for that well at that time step and consequently, the optimization algorithm does not change that control variable. A procedure is adopted to reduce the effect of this problem. The optimization results provide new rate controls which improve the NPV by 8.9% compared to the reference case over the fifteen-year production period. Interestingly, for the optimized well controls, the voidage constraint on the field water injection rate is satisfied automatically for most of the reservoir production period without enforcing the constraint and the water cut constraint for all producers except one also is satisfied automatically. (C) 2013 Elsevier B.V. All rights reserved.