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Mathematics 2018, 6(8), 132; https://doi.org/10.3390/math6080132

Approximate Dynamic Programming Based Control of Proppant Concentration in Hydraulic Fracturing

1
Artie McFerrin Department of Chemical Engineering, Texas A&M University, College Station, TX 77843, USA
2
Texas A&M Energy Institute, Texas A&M University, College Station, TX 77843, USA
*
Author to whom correspondence should be addressed.
Received: 16 June 2018 / Revised: 26 July 2018 / Accepted: 27 July 2018 / Published: 1 August 2018
(This article belongs to the Special Issue New Directions on Model Predictive Control)
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Abstract

Hydraulic fracturing has played a crucial role in enhancing the extraction of oil and gas from deep underground sources. The two main objectives of hydraulic fracturing are to produce fractures with a desired fracture geometry and to achieve the target proppant concentration inside the fracture. Recently, some efforts have been made to accomplish these objectives by the model predictive control (MPC) theory based on the assumption that the rock mechanical properties such as the Young’s modulus are known and spatially homogenous. However, this approach may not be optimal if there is an uncertainty in the rock mechanical properties. Furthermore, the computational requirements associated with the MPC approach to calculate the control moves at each sampling time can be significantly high when the underlying process dynamics is described by a nonlinear large-scale system. To address these issues, the current work proposes an approximate dynamic programming (ADP) based approach for the closed-loop control of hydraulic fracturing to achieve the target proppant concentration at the end of pumping. ADP is a model-based control technique which combines a high-fidelity simulation and function approximator to alleviate the “curse-of-dimensionality” associated with the traditional dynamic programming (DP) approach. A series of simulations results is provided to demonstrate the performance of the ADP-based controller in achieving the target proppant concentration at the end of pumping at a fraction of the computational cost required by MPC while handling the uncertainty in the Young’s modulus of the rock formation. View Full-Text
Keywords: approximate dynamic programming (ADP); model predictive control (MPC); hydraulic fracturing; model reduction; Kalman filter approximate dynamic programming (ADP); model predictive control (MPC); hydraulic fracturing; model reduction; Kalman filter
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Singh Sidhu, H.; Siddhamshetty, P.; Kwon, J.S. Approximate Dynamic Programming Based Control of Proppant Concentration in Hydraulic Fracturing. Mathematics 2018, 6, 132.

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