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Backflow from a model fracture network: an asymptotic investigation

  • Asaf Dana (a1), Gunnar G. Peng (a2), Howard A. Stone (a3), Herbert E. Huppert (a2) and Guy Z. Ramon (a1)...

Abstract

We develop a model for predicting the flow resulting from the relaxation of pre-strained, fluid-filled, elastic network structures. This model may be useful for understanding relaxation processes in various systems, e.g. deformable microfluidic systems or by-products from hydraulic fracturing operations. The analysis is aimed at elucidating features that may provide insight on the rate of fluid drainage from fracturing operations. The model structure is a bifurcating network made of fractures with uniform length and elastic modulus, which allows for general self-similar branching and variation in fracture length and rigidity between fractures along the flow path. A late-time $t^{-1/3}$ power law is attained and the physical behaviour can be classified into four distinct regimes that describe the late-time dynamics based on the location of the bulk of the fluid volume (which shifts away from the outlet as branching is increased) and pressure drop (which shifts away from the outlet as rigidity is increased upstream) along the network. We develop asymptotic solutions for each of the regimes, predicting the late-time flux and evolution of the pressure distribution. The effects of the various parameters on the outlet flux and the network’s drainage efficiency are investigated and show that added branching and a decrease in rigidity upstream tend to increase drainage time.

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Corresponding author

Email address for correspondence: ramong@technion.ac.il

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These two authors contributed equally.

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References

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Bonnet, E., Bour, O., Odling, N. E., Davy, P., Main, I., Cowie, P. & Berkowitz, B. 2001 Scaling of fracture systems in geological media. Rev. Geophys. 39 (3), 347383.10.1029/1999RG000074
Chau, V. T., Bažant, Z. P. & Su, Y. 2016 Growth model for large branched three-dimensional hydraulic crack system in gas or oil shale. Phil. Trans. R. Soc. Lond. A 374 (2078), 20150418.
Dana, A., Zheng, Z., Peng, G. G., Stone, H. A., Huppert, H. E. & Ramon, G. Z. 2018 Dynamics of viscous backflow from a model fracture network. J. Fluid Mech. 836, 828849.10.1017/jfm.2017.778
Holditch, S. A. 2007 Hydraulic fracturing: overview, trends, issues. Drilling Contractor 63, 116118.
Jinzhou, Z., Lan, R., Cheng, S. & Li, Y. 2018 Latest research progresses in network fracturing theories and technologies for shale gas reservoirs. Natural Gas Industry B 5 (5), 533546.
King, G. E. 2010 Thirty years of gas shale fracturing: what have we learned? In SPE Annual Technical Conference and Exhibition. Society of Petroleum Engineers.
Lai, C. Y., Zheng, Z., Dressaire, E., Ramon, G. Z., Huppert, H. E. & Stone, H. A. 2016 Elastic relaxation of fluid-driven cracks and the resulting backflow. Phys. Rev. Lett. 117 (26), 268001.10.1103/PhysRevLett.117.268001
Marck, J. & Detournay, E. 2013 Withdrawal of fluid from a poroelastic layer. In Poromechanics V: Proceedings of the Fifth Biot Conference on Poromechanics, pp. 12711278. ASCE.10.1061/9780784412992.152
Marck, J., Savitski, A. A. & Detournay, E. 2015 Line source in a poroelastic layer bounded by an elastic space. Intl J. Numer. Anal. Meth. Geomech. 39 (14), 14841505.10.1002/nag.2405
Matia, Y. & Gat, A. D. 2015 Dynamics of elastic beams with embedded fluid-filled parallel-channel networks. Soft Robotics 2 (1), 4247.10.1089/soro.2014.0020
Patzek, T. W., Male, F. & Marder, M. L. 2013 Gas production in the Barnett Shale obeys a simple scaling theory. Proc. Natl Acad. Sci. USA 110 (49), 1973119736.10.1073/pnas.1313380110
Santillán, D., Mosquera, J. C. & Cueto-Felgueroso, L. 2017 Fluid-driven fracture propagation in heterogeneous media: probability distributions of fracture trajectories. Phys. Rev. E 96 (5), 053002.
Weibel, D. B., Siegel, A. C., Lee, A., George, A. H. & Whitesides, G. M. 2007 Pumping fluids in microfluidic systems using the elastic deformation of poly(dimethylsiloxane). Lab on a Chip 7 (12), 18321836.10.1039/b714664g
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