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Numerical simulation on the effect of particle shape on mechanical response of proppants in horizontal fractures

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Abstract

Particle geometry significantly influences the mechanical characteristics of sand. Hence, understanding the mechanical response of different shaped granular particle pack under compressive stress is important for estimating their influence on fracture conductivity as reported by Mollanouri Shamsi et al. (in: SPE paper SPE-190024-MS presented at the SPE Western Regional Meeting held in Garden Grove, California, 2018). Consequently, when modeling the behavior of granular assemblies, it is crucial that they are appropriately simulated as accurate as possible. In this study, a clumped particle logic which combines two or more spherical particles and allows for overlap is adopted to model proppant particle shapes. Three groups of particles: Particle A, Particle B and Particle C with different sphericity and aspect ratio are generated randomly and assembled between two rough parallel fracture plates. The rough surfaces which adhere to normal distribution were generated using Gaussian distribution model. A discrete element method approach using linear contact model is then implemented to replicate the real particle shapes and their assembly. Then, the fracture closure condition on each proppant pack is simulated by uniaxial compression. Results show that particle shape influences mechanical response (unconfined pack bed height, packing porosity, constrained modulus and coordination number) of proppant pack in fractures. The proposed work provides an effective insight for understanding mechanics of proppant of different shape and how it later influences fracture. It also avails an avenue for optimizing proppant shape based on expected combinations of field operations.

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Abbreviations

A :

Contact area

AR:

Aspect ratio

E * :

Effective modulus

F c :

Contact force

\(F^{n}\) :

Normal force

F t :

Tangential force

F l :

Linear force

F d :

Damping force

d p :

Diameter of particle

C n :

Normal damping coefficient

C t :

Shear damping coefficient

\(S_{s}\) :

Sphere surface area

\(S_{p}\) :

Particle surface area

\(U_{n}\) :

Normal displacement

\(U_{{\rm si}}\) :

Shear displacement

\(V_{p}\) :

Particle volume

\(\varphi _{s}\) :

Sphericity

δn :

Overlap in normal direction

\(\Psi _{{\max }} ,\Psi _{{\min }}\) :

Maximum and minimum ferret diameter

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Acknowledgements

This work was supported by scientific research fund of China University of Petroleum (Beijing) -2462016YJRC004/2462017YJRC022/ RCYJ2017B-01-003 (At Karamay, and major projects in karamay-2018ZD001B).

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  1. Research Institute of Enhanced Oil Recovery, China University of Petroleum, Beijing, 102249, People’s Republic of China

    Nicholas Izuchukwu Osuji, Jingchen Zhang & Michelle Djuidje Tagne

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Osuji, N.I., Zhang, J. & Tagne, M.D. Numerical simulation on the effect of particle shape on mechanical response of proppants in horizontal fractures. Comp. Part. Mech. 9, 513–523 (2022). https://doi.org/10.1007/s40571-021-00425-x

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