Approximate Dynamic Programming Based Control of Proppant Concentration in Hydraulic Fracturing

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. Rec...

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Bibliographic Details
Published in:Mathematics (Basel) Vol. 6; no. 8; p. 132
Main Authors: Singh Sidhu, Harwinder, Siddhamshetty, Prashanth, Kwon, Joseph S.
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.08.2018
Subjects:
approximate dynamic programming (ADP)
Batch processes
Computer simulation
Dynamic programming
Fairs & exhibitions
Geometry
Hydraulic fracturing
Kalman filter
Mathematics
Measurement techniques
Mechanical properties
model predictive control (MPC)
model reduction
Modulus of elasticity
Natural gas
Partial differential equations
Predictive control
Pumping
Quality control
Uncertainty
United States > US
Texas
ISSN:2227-7390, 2227-7390
Online Access:Get full text
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Summary: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.
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ISSN:2227-7390
2227-7390
DOI:10.3390/math6080132