(734e) Model Predictive Control Designs to Achieve Uniform Growth of Simultaneously Propagating Multiple Fractures in Hydraulic Fracturing

Natural gas and oil resources are found in shale rock formations with ultra-low permeability. In ultra-low permeability formations, horizontal wells are typically drilled and each horizontal well is stimulated with massive fractures for enhanced recovery of oil and gas [1]. In multi-stage hydraulic fracturing treatments, simultaneously propagating multiple fractures with close spacing often induce non-uniform fracture development, resulting in one or two dominant fractures due to the uneven distribution of fracturing fluids [2]. One of the important contributing factors for the uneven distribution is the well-known phenomenon called ``stress shadow effects'' [3]. In general, fracturing fluids are distributed to multiple fractures inversely proportional to their flow resistances, which is a function of perforation friction, wellbore friction and fracture propagation. The problem with the stress shadow effects is that it exerts extra compressional stresses on the interior fractures and increases the flow resistance within interior fractures, resulting in fluid diverting into the exterior fractures. Therefore, to achieve uniform growth of simultaneously propagating multiple fractures and facilitate more fracturing fluids entering into the interior fractures, the stress shadow effects should be balanced or mitigated.

In this regard, several hydraulic fracture simulators have been developed to describe the stress shadow effects in simultaneously propagating multiple fractures [4]. Typically, these high-fidelity hydraulic fracture simulators require several days, and sometimes over one week, to compute the growth of simultaneously propagating multiple fractures at real reservoir length and time scales. Hence, optimization of hydraulic fracturing to find the operating condition for uniform growth of hydraulic fractures, which may often require hundreds or thousands of simulation runs, were not practically viable; in these directions, very limited efforts have been made by selecting a few important parameters via sensitivity analysis [4, 5].

Motivated by our previous efforts on single fracture propagation [6, 7, 8], in this work, we focus on the development of a new model order-reduction technique for simultaneously propagating multiple fractures by integrating the analytical models to calculate the pressure drop due to perforation friction and wellbore friction and a data-based ROM to describe the pressure drop along the fractures due to stress shadow effects and fracture interaction. Then, we propose a model-based pumping schedule design technique by utilizing the ROM and the uniform limited entry design technique to compute the flow rate of fracturing fluids which will promote equal distribution of fracturing fluids to achieve uniform growth of multiple fractures while mitigating the undesired stress shadow effects. Simulation results are presented to compare the proposed technique with state-of-the-art techniques in the field.

References:

[1] Lecampion, B., & Desroches, J. (2015). Simultaneous initiation and growth of multiple radial hydraulic fractures from a horizontal wellbore. Journal of the Mechanics and Physics of Solids, 82, 235-258.

[2] Wu, K., & Olson, J. E. (2016). Mechanisms of simultaneous hydraulic-fracture propagation from multiple perforation clusters in horizontal wells. SPE Journal, 21(03), 1000-1008.

[3] Germanovich, L. N., Astakhov, D. K., Mayerhofer, M. J., Shlyapobersky, J., & Ring, L. M. (1997). Hydraulic fracture with multiple segments I. Observations and model formulation. International Journal of Rock Mechanics and Mining Sciences, 34(3-4), 97.e1-97.e19.

[4] Kan, W., Anusarn, S., & Jizhou, T. (2016). Numerical study of flow rate distribution for simultaneous multiple fracture propagation in horizontal wells. In 50th US Rock Mechanics/Geomechanics Symposium. American Rock Mechanics Association (ARMA-2016-038), Houston TX.

[5] Cheng, C., Bunger, A.P., Peirce, A.P., 2016. Optimal perforation location and limited entry design for promoting simultaneous growth of multiple hydraulic fractures. In SPE Hydraulic Fracturing Technology Conference. Society of Petroleum Engineers (SPE 179158), The Woodlands TX.

[6] Siddhamshetty, P., Yang, S., & 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. URL: https://doi.org/10.1016/j.compchemeng.2017.10.032.

[7] Siddhamshetty, P., Kwon, J. S. I., Liu, S., & Valkó, P. P. (2017). Feedback control of proppant bank heights during hydraulic fracturing for enhanced productivity in shale formations. AIChE Journal, 64(05), 1638-1650.

[8] Narasingam, A., & Kwon, J. S. I. (2017). Development of local dynamic mode decomposition with control: Application to model predictive control of hydraulic fracturing. Computers & Chemical Engineering, 106, 501-511.