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Dimensionality reduction for production optimization using polynomial approximations

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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.

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Authors and Affiliations

  1. Harold Vance Department of Petroleum Engineering, Texas A&M University, College Station, TX, 77843-3116, USA

    Nadav Sorek & Eduardo Gildin

  2. Artie McFerrin Department of Chemical Engineering, Texas A&M University, College Station, TX, 77843, USA

    Burcu Beykal & Christodoulos A. Floudas

  3. School of Chemical & Biomolecular Engineering, Georgia Institute of Technology, Atlanta, GA, 30332-0100, USA

    Fani Boukouvala

  4. Texas A&M Energy Institute, Texas A&M University, 302D Williams Administration Bldg, College Station, TX, 77843-3372, USA

    Burcu Beykal & Christodoulos A. Floudas

Authors
  1. Nadav Sorek
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  2. Eduardo Gildin
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  3. Fani Boukouvala
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  4. Burcu Beykal
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  5. Christodoulos A. Floudas
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Correspondence to Eduardo Gildin.

Additional information

C. A. Floudas, deceased on August 14, 2016.

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Sorek, N., Gildin, E., Boukouvala, F. et al. Dimensionality reduction for production optimization using polynomial approximations. Comput Geosci 21, 247–266 (2017). https://doi.org/10.1007/s10596-016-9610-3

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