(359d) Approximate Dynamic Programming Based Control of Hydraulic Fracturing Process to Achieve Uniform Proppant Concentration Level

Harwinder Singh Sidhu^{[1, 2]},Prashanth Siddhamshetty ^{[1, 2]}, Abhinav Narasingam^{[1, 2]} ,

Joseph Sang-Il Kwon ^{[1, 2]}

[1] Artie McFerrin Department of Chemical Engineering, Texas A&M University, College Station, TX 77845 USA

[2] Texas A&M Energy Institute, Texas A&M University, College Station, TX 77845 USA

Petroleum and natural gas remain an important part of the global energy supply. In recent years, the extraction of underground resources such as shale gas and oil has been stimulated by hydraulic fracturing [1]. In hydraulic fracturing, achieving the desired fracture geometry, and uniform proppant concentration at the end of pumping are two primary objectives, because they are directly related to the overall efficiency of the process.

Over the last ten years, significant efforts have been made in the application of model predictive control (MPC) to the drilling processes to enhance pressure control flexibility, efficiency, and process safety [2, 3]. Recently, some work has been done in this direction with a focus on regulating the proppant concentration across the fracture [4, 5]. However, there are two remaining issues with MPC, which are both theoretical and practical in nature. First, the online computational burden can be significant to calculate the optimal control moves at each sampling time, when the underlying system is nonlinear and high-dimensional, which is usually the case in hydraulic fracturing. The second issue is its inability to consider the future interplay between uncertainty and estimation in the optimal control calculation. Alternatively, these issues can be addressed by the approximate dynamic programming (ADP) approach [6]. ADP is a model-based control technique, and can be employed to derive an improved control policy given some starting sub-optimal control policies (or alternatively, closed-loop identification data), while circumventing the ‘curse-of-dimensionality’ of the traditional dynamic programming (DP) approach.

Motivated by the recent success of ADP in several applications [7], we present an ADP based control framework for the closed-loop operation of a hydraulic fracturing process. First, we will derive a high-fidelity model for hydraulic fracturing process based on first-principles. Second, a numerical scheme will be described to handle the high computational requirement caused by coupling of PDEs defined over a time-varying spatial domain. Third, a reduced-order model (ROM) will be developed by using these simulation results. Fourth, a nonlinear MPC theory is employed to obtain the starting sub-optimal control policies in ADP. Lastly, ADP approach will be utilized for the design of the feedback control system that provides a foundation for the online control of proppant bank height to achieve uniformity at the end of the treatment, which is directly related to the overall efficiency of the hydraulic fracturing process.

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[2] Breyholtz, Ø., Nygaard, G. and Nikolaou, M., 2010, June. Automatic control of managed pressure drilling. In American Control Conference (ACC), 2010 (pp. 442-447). IEEE.

[3] Asgharzadeh Shishavan, R., Hubbell, C., Perez, H., Hedengren, J., Pixton, D.S. and Pink, A.P., 2014, October. Multivariate control for managed pressure drilling systems using high speed telemetry. In SPE Annual Technical Conference and Exhibition. Society of Petroleum Engineers.

[4] Gu, Q. and Hoo, K.A., 2015. Model-based closed-loop control of the hydraulic fracturing process. Industrial & Engineering Chemistry Research, 54(5), pp.1585-1594.

[5] Siddhamshetty, P., Yang, S. and Kwon, J.S.I., 2017. Modeling of hydraulic fracturing and designing of online pumping schedules to achieve uniform proppant concentration in conventional oil reservoirs. Computers & Chemical Engineering.

[6] Lee, J.H. and Lee, J.M., 2006. Approximate dynamic programming based approach to process control and scheduling. Computers & Chemical engineering, 30(10-12), pp.1603-1618.

[7] Tosukhowong, T. and Lee, J.H., 2009. Approximate dynamic programming based optimal control applied to an integrated plant with a reactor and a distillation column with recycle. AIChE journal, 55(4), pp.919-930.