(247m) Modeling and Control of Proppant Bank Height to Achieve Uniformity of a Hydraulic Fracturing System

Typically, the term shale gas refers to natural gas trapped in rock of low porosity (2% or less) and ultra-low permeability (0.01 to 0.0001 md or even less) [1]. Therefore, if a well were drilled into such a rock, it would take extremely long time to reach economic amount of production. What has made the recovery of shale gas economically attractive is the extensive use of two crucial technologies: directional drilling and hydraulic fracturing. From a control engineering viewpoint, hydraulic fracturing has been traditionally viewed as an open-loop problem. Well logs and mini-frac test results are interpreted prior to operation in order to obtain petrolphysical and rock-mechanical properties of the formation. The operation is designed based on the properties and then is conducted accordingly. However, the open-loop operation may lead to poor performance, which has motivated this work that considers the closed-loop operation of hydraulic fracturing.

With respect to applying automatic control strategies to oil and gas production, it is important to point out that the literature over the last ten years has been focused on applying MPC to the drilling process, which is known as managed pressure drilling (MPD) that enhances pressure control flexibility, efficiency, and safety of the process [2, 3]. However, applying MPC to improve the uniformity of the proppant bank height while optimizing the fracture geometry, both of which significantly affect the productivity of the treated well, has not been considered because of the following reasons: (1) limited access to real-time measurements, (2) presence of uncertainties in the measurement data, (3) time-dependent spatial domain, and (4) large computational burden when solving high-fidelity models of hydraulic fracturing systems. While some attempts to employ model-based control schemes have been made [4, 5], there are a number of unresolved fundamental as well as practical implementation issues to make MPC a truly real-time control technique.

Motivated by these considerations, we will first address the development of a first-principles model for the hydraulic fracturing process. Second, a novel numerical scheme will be developed to deal with the high computational requirement caused by coupling of multiple partial differential equations (PDEs) defined over a time-dependent (evolving) spatial domain. Third, a reduced-order model will be constructed by using these simulation results. Lastly, nonlinear MPC theory will be utilized for the design of the feedback control system that provides a foundation for the online control of proppant bank height in order to achieve uniformity at the end of the treatment, which is directly related to the overall efficiency of the operation.

References:

[1] M. Nikolaou. Computer-aided process engineering in oil and gas production. Computers & Chemical Engineering, 51:96â??101, 2013.

[2] O. Breyholtz, G. Nygaard, and M. Nikolaou. Automatic control of managed pressure drilling. Proceedings of American Control Conference, Baltimore, MD, 442 â?? 447, 2010.

[3] R. A. Shishavan, C. Hubbell, H. D. Perez, J. D. Hedengren, D. S. Pixton, and A. P. Pink. Multivariate control for managed-pressure-drilling systems by use of high-speed telemetry. SPE Annual Technical Conference and Exhibition (SPE 170962), Amsterdam, Netherlands, 2014.

[4] Q. Gu and K. A. Hoo. Evaluating the performance of a fracturing treatment design. Ind. & Eng. Chem. Res., 53:10491â??10503, 2014.

[5] Q. Gu and K. A. Hoo. Model-based closed-loop control of the hydraulic fracturing process. Ind. & Eng. Chem. Res., 54:1585â??1594, 2015.