462509 Global Optimization of Constrained Grey-Box Models for Well Injection and Production
The first step of this workflow is based on parameterization of the well-control variable domain through a set of functional relationships, which is denoted as Functional Well-Control Method (FCM). The functional forms can range from Polynomial to Exponential or Hybrid Control Methods (PCM, ECM, HCM). Through this approach, we transform the optimization search space from the traditional pressure-based or rate-based control to a reduced space formed by the coefficients of the selected functional method. These new formulations are then optimized by the ARGONAUT algorithm [4-5], which has been developed for constrained derivative-free optimization problems. This optimizer is comprised of several mixed-integer and/or nonlinear optimization sub-problems for (a) sampling selection, (b) surrogate model identification and parameter estimation and, (c) global optimization of the formulated constrained surrogate formulations. The resulted non-linear constrained optimization problems are solved to global optimality using deterministic global optimization solver ANTIGONE [6-9], which is a state-of-the-art global solver for mixed-integer nonlinear optimization, used in a wide range of applications.
We test the efficiency of the entire framework, with and without constraints, on a realistic three-dimensional model (the UNSIM-I-D benchmark) . Our results demonstrate significant computational savings due to the coupling of ARGONAUT [4-5] and the FCM formulation. The FCM leads to a substantial reduction in the number of control parameters as we seek the optimal function coefficients to describe the control trajectories as opposed to directly searching for the optimal control values at each time interval. In addition, we compare our results with other gradient-free and gradient-based algorithms which have been traditionally used in the literature (such as NOMAD [11-12] and EGO [13-14]) and we demonstrate that our framework leads to improved solutions with higher consistency and with reduced sample-calls to the reservoir simulation.
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See more of this Group/Topical: Topical Conference: Advances in Fossil Energy R&D