Modeling of Solid Diverter Particles to Improve the Cluster Efficiency in Hydraulic Fracturing




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Multi-stage fracturing in horizontal wells is a crucial technique for boosting production in unconventional reservoirs. Solid diverter particles are often used to enhance cluster stimulation efficiency by promoting uniform fracture propagation. However, the physical processes involved in rock deformation, fluid flow, and particle transport during this technology remain unclear. This dissertation aims to develop an efficient fracturing model with dynamic particle transport to better understand the effectiveness of diversion technology. The developed model utilizes the 3D displacement discontinuity method (DDM), global tip asymptotic solution, and implicit level set algorithm to create a computationally efficient fracturing simulator. The particle transport model uses the ‘wind’ scheme to track nonlinear particle waves in multiple fractures and the Kozeny-Carman model to evaluate the permeability of diverter pack. By treating the dispersed phase as continua, the coupled fracturing model and particle transport model enable the field-scale modeling of the effectiveness of diversion technology in multiple non-parallel fractures. The accuracy of the proposed model is validated through comparisons with analytical and numerical solutions of single fracture, multiple parallel/non-parallel fractures, and 2D particle transport. The evaluated examples demonstrate the feasibility of fracture entrance diversion in a KGD-type fracture model with strong stress interaction at S⁄H= 0.125. However, the PKN-type fracture model with low stiffness and less stress interference (S⁄H= 0.1875) fails to create a stable low permeability diverter pack near the fracture entrance in overgrown fractures. The implementation of a particle swelling and dissolving model promotes successful fluid diversion in the low stiffness (S⁄H= 0.1875) and high stiffness (S⁄H= 0.5) PKN-type fracture models. Besides creating equal unpropped fracture length using the developed model, this study is able to deliver equal propped fracture length by using the proposed slurry pumping schedule. Overall, this dissertation provides a better understanding of the effectiveness of diversion technology in PKN-type fractures. The proposed model can be applied to cases with different fracture stiffness and slurry pumping schedules, providing insights into the optimal use of swelling particles for enhancing cluster stimulation efficiency in unconventional reservoirs. The developed model and insights presented in this dissertation could contribute to more efficient and effective fracture designs in the field.



Diverter agent, Particle transport, Fluid partition, Cluster eff


Portions of this document appear in: Luo, Bo, George K. Wong, Jianchun Guo, Wei Fu, Guanyi Lu, and Andrew P. Bunger. "Modeling of solids particle diversion to promote uniform growth of multiple hydraulic fractures." Journal of Petroleum Science and Engineering 220 (2023): 111159; and in: Luo, Bo, George K. Wong, and Yanhui Han. "Modeling of dynamic bridging of solid particles in multiple propagating fractures." International Journal of Solids and Structures 262 (2023): 112078.