Mathematical modeling of suspension flow in a system of intersecting fractures
Sibirskij žurnal industrialʹnoj matematiki, Tome 26 (2023) no. 1, pp. 201-211.

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In this paper, mathematical modeling of the suspension flow in a complex system of fractures is carried out, when the main fracture is crossed by secondary fracture. The mathematical model of the process is built in the one-fluid approximation and includes the continuity equation for the suspension, the system of equations of suspension motion, the mass conservation equation in the form of a convective-diffusion transfer equation for the volume concentration of particles. The solution of the problem in a 3D formulation is implemented in the OpenFOAM software package. The dynamics of the distribution of solid spherical particles in a network of fractures was studied depending on the ratio of the characteristic Reynolds numbers for the flow and particles, as well as on the ratio of the length of the main and secondary fractures.
Keywords: suspension flow, intersecting fractures, mathematical modeling, one-fluid model, solid spherical particles. .
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R. R. Iulmukhametova; A. A. Musin; V. I. Valiullina; L. A. Kovaleva. Mathematical modeling of suspension flow in a system of intersecting fractures. Sibirskij žurnal industrialʹnoj matematiki, Tome 26 (2023) no. 1, pp. 201-211. http://geodesic.mathdoc.fr/item/SJIM_2023_26_1_a17/

[1] B. Kh. Khuzhaerov, Zh. M. Makhmudov, Sh. Kh. Zikiryaev, “Perenos zagryaznyayuschikh veschestv v vodonosnykh plastakh s uchetom dvukhmestnoi adsorbtsii”, Sib. zhurn. industr. matematiki, 14:1 (2011), 127–139 | MR | Zbl

[2] A. A. Osiptsov, “Fluid mechanics of hydraulic fracturing: A review”, J. Petrol. Sci. Engrg., 156 (2017), 513–535 | DOI

[3] R. Sahai, R. G. Moghanloo, “Proppant transport in complex fracture networks: A review”, J. Petroleum Sci. Engrg., 2019 | DOI

[4] Q. Wen, S. Wang, X. Duan, F. Wang, X. Jin, “Experimental investigation of proppant settling in complex hydraulic-natural fracture system in shale reservoirs”, J. Natural Gas Sci. Engrg., 33 (2016), 70–80 | DOI

[5] S. V. Golovin, M. Yu. Kazakova, “Odnomernaya model vytesneniya dvukhfaznoi zhidkosti v scheli s pronitsaemymi stenkami”, Prikl. mekhanika i tekhn. fizika, 58:1 (2017), 22–36 | Zbl

[6] R. I. Nigmatulin, Dinamika mnogofaznykh sred, v. 1, 2, Nauka, M., 1987

[7] S. A. Boronin, A. A. Osiptsov, “Dvukhkontinualnaya model techeniya suspenzii v treschine gidrorazryva”, Dokl. AN, 431:6 (2010), 758–761

[8] A. A. Gavrilov, A. V. Shebelev, “Odnozhidkostnaya model smesi dlya laminarnykh techenii vysokokontsentrirovannykh suspenzii”, Izv. RAN. MZhG, 2018, no. 2, 84–98 | DOI | Zbl

[9] Y. A. Pityuk, O. A. Abramova, N. B. Fatkullina, A. Z. Bulatova, “BEM based numerical approach for the study of the dispersed systems rheological properties”, Studies in Systems, Decision and Control, 199 (2019), 338–352 | DOI

[10] R. R. Iulmukhametova, A. A. Musin, L. A. Kovaleva, “Mathematical modelling of a laminar suspension flow in the flat inclined channel”, J. Physics. Conf. Ser., 2021, 012044 | DOI

[11] X. Kong, J. McAndrew, “A computational fluid dynamics study of proppant placement in hydraulic fracture networks”, SPE Unconventional Resources Conf. 2017 (Calgary, Alberta, Canada, 15-16 February 2017), SPE-185083-MS | DOI

[12] H. Wang, M. Wang, B. Yang, Q. Lu, Y. Zheng, H. Zhao, “Numerical study of supercritical CO$_2$ and proppant transport in different geometrical fractures”, Greenhouse Gases. Sci. Technol., 8 (2018) | DOI

[13] Y. Zhang, X. Lu, X. Zhang, P. Li, “Proppant transportation in cross fractures: some findings and suggestions for field engineering”, Energies, 13 (2020), 4912 | DOI

[14] I. M. Krieger, “Rheology of monodisperse lattice”, Adv. Colloid Interface Sci., 3 (1972), 111–136 | DOI

[15] J. F. Morris, F. Boulay, “Curvilinear flows of non-colloidal suspensions: the role of normal stresses”, J. Rheol., 43 (1999), 1213–1237 | DOI

[16] N. Tetlow, A. L. Graham, M. S. Ingber, S. R. Subia, L. A. Mondy, S. A. Altobelli, “Particle migration in a Couette apparatus: experiment and modeling”, J. Rheol., 42 (1998), 307–327 | DOI

[17] M. S. Ingber, A. L. Graham, L. A. Mondy, Z. Fang, “An improved constitutive model for concentrated suspensions accounting for shear-induced particle migration rate dependence on particle radius”, Internat. J. Multiphase Flow, 35 (2009), 270–276 | DOI

[18] R. R. Yulmukhametova, A. A. Musin, L. A. Kovaleva, “Chislennoe modelirovanie laminarnogo techeniya suspenzii v ploskom kanale”, Vestn. Bashkir. un-ta, 26:2 (2021), 281–286 | DOI

[19] R. R. Iulmukhametova, A. A. Musin, L. A. Kovaleva, “Mathematical modeling of the flow of viscous incompressible fluid with suspended particles in flat inclined channel”, Adv. Probl. Mech. II (2020), Lecture Notes Mech. Engrg., 2022 | DOI | MR