Abstract
The objective of this study is to present a realistic application of our previously developed nonlinearly constrained stochastic gradient-based optimization framework that can efficiently solve nonlinearly constrained robust production optimization problems. We apply the optimization framework to a synthetic, yet realistic, field optimization problem using multiple history-matched realizations of the geologic model. For the synthetic realistic field example, the reservoir is assumed to undergo production for several years. Well controls (BHPs for producers and water injection rates for injectors) on a sequence of control steps (time intervals) are optimized during the forecast period by maximizing the expected value of the net present value (or ensemble average NPV) over multiple realizations of subsurface description for the subsequent 10 years of production under a waterflooding scenario subject to nonlinear constraints. The optimization framework is based on our in-house nonlinear optimizer employing sequential quadratic programming (SQP) coupled with stochastic simplex approximated gradients (StoSAG). It incorporates the line-search procedure within SQP and is referred to as line-search sequential quadratic programming (LS-SQP). We couple LS-SQP with two different constraint handling schemes; the expected value constraint scheme and minimum-maximum (min-max) constraint scheme, to avoid the explicit application of nonlinear constraints for each reservoir model. Both bound constraints on well controls and nonlinear constraints on field liquid production rate, field water injection rate, and/or individual producer water production rates are considered. We consider several different history-matched geological realizations of the realistic field example with several injectors and producers. A black-oil commercial reservoir simulator is utilized in the optimization workflow to assess the objective function with imposed constraints. Results show that the framework LS-SQP algorithm with StoSAG can effectively handle the nonlinear constraints in a robust life-cycle production optimization problem. Moreover, our results show that the LS-SQP framework with any of the two different constraint handling schemes considered effectively handles the nonlinear constraints in a life-cycle robust production optimization problem. However, the expected value constraint scheme results in higher optimal NPV than the min-max constraint scheme, but at the cost of possible constraint violation for some individual geological realizations. Application results demonstrate that our nonlinearly constrained stochastic gradient-based robust optimization framework has great potential to be a rapid approximate capability for performing life cycle production optimization under subsurface uncertainty with bound and nonlinear constraints.
