An adjoint inexact trust region method for nonlinear constraint production optimization

Production optimization is the method for seeking the best possible well control and schedule plans in order to enhance reservoir performance under a given state and economic constraints. Determining the optimal injection and production control strategies through adjoint gradient-based optimization is a well-known practice in today’s modern reservoir management. However, apt handling of nonlinear control inputs, state and output constraints can be quite tedious with effects on the computational efficiency of the optimization algorithms used in practical production optimal control problems. In this paper, we develop an adjoint based interior-point inexact trust filter sequential quadratic programming (IITRF-SQP) method for solving constrained production optimization problems. Inexact trust-region is an extension of a filter trust region approach, which is used when the control input constraints Jacobians are of high dimension and are expensive to compute. The output constraints are handled using an interior-point method called-modified barrier-augmented Lagrangian, in which inequality constraints are treated by a modified barrier term and equality constraints with augmented Lagrangian terms. The algorithm we present uses the approximate information of Jacobians achieved through composite-step computation, which eliminates the cost of direct calculation of Jacobians and Hessians (gradients). The gradient information that provides criticality measure of the objective function is calculated using the adjoint method. Two numerical experiments on optimal water-flooding are presented. Performance comparisons of the proposed IITRF-SQP method with Lagrangian barrier method and sequential linear quadratic programming (SLQP) for solving production optimization problem are carried out. Results indicate that the gradient-based adjoint coupled with IITRF-SQP was able to improve net present value (NPV) through optimal production profiles with better computational efficacy via reduced convergence time and number of gradient and objective function evaluations.