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Computational Geosciences

, Volume 21, Issue 2, pp 247–266 | Cite as

Dimensionality reduction for production optimization using polynomial approximations

  • Nadav Sorek
  • Eduardo Gildin
  • Fani Boukouvala
  • Burcu Beykal
  • Christodoulos A. Floudas
Original Paper

Abstract

The objective of this paper is to introduce a novel paradigm to reduce the computational effort in waterflooding global optimization problems while realizing smooth well control trajectories amenable for practical deployments in the field. In order to overcome the problems of slow convergence and non-smooth impractical control strategies, often associated with gradient-free optimization (GFO) methods, we introduce a generalized approach which represent the controls by smooth polynomial approximations either by a polynomial function or by a piecewise polynomial interpolation, which we denote as function control method (FCM) and interpolation control method (ICM), respectively. Using these approaches, we aim to optimize the coefficients of the selected functions or the interpolation points in order to represent the well-control trajectories along a time horizon. Our results demonstrate significant computational savings, due to a substantial reduction in the number of control parameters, as we seek the optimal polynomial coefficients or the interpolation points to describe the control trajectories as opposed to directly searching for the optimal control values (bottom hole pressure) at each time interval. We demonstrate the efficiency of the method on two and three-dimensional models, where we found the optimal variables using a parallel dynamic-neighborhood particle swarm optimization (PSO). We compared our FCM-PSO and ICM-PSO to the traditional formulation solved by both gradient-free and gradient-based methods. In all comparisons, both FCM and ICM show very good to superior performances.

Keywords

Optimization dimensionality reduction Polynomial control method Control set cardinality reduction Parametrization Waterflooding optimization Production optimization Adjoint method Particle swarm optimization Smooth well-control 

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Copyright information

© Springer International Publishing Switzerland 2017

Authors and Affiliations

  1. 1.Harold Vance Department of Petroleum EngineeringTexas A&M UniversityCollege StationUSA
  2. 2.Artie McFerrin Department of Chemical EngineeringTexas A&M UniversityCollege StationUSA
  3. 3.School of Chemical & Biomolecular EngineeringGeorgia Institute of TechnologyAtlantaUSA
  4. 4.Texas A&M Energy InstituteTexas A&M UniversityCollege StationUSA

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