Abstract
In this paper we describe self-consistent mathematical model for large scale hydraulic fracture development in poroelastic medium is proposed together with appropriate simulation techniques. The model includes Biot poroelasticity equations, fracture fluid flow model based in Reynolds lubrication equation, criteria for fracture development based on vector valued form of Rice-Cherepanov J-integral and bulk/fracture coupling conditions defined at fracture mid-surface. The proposed numerical algorithms is a new variant of the widely used eXtended Finite element (X-FEM) method which utilize closest-point projection technique for both fracture geometrical representation and fracture flow solver. A robust and efficient algorithm is proposed based on direct evolution of closest point projector. Numerical results which illustrate the developed numerical techniques are presented.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Coussy, O.: Poromechanics. Wiley, Chichester (2004)
Belytschko, T., Black, T.: Elastic crack growth in finite elements with minimal remeshing. Internat. J. Numer. Methods Engrg. 45, 601–620 (1999)
Moës, N., Dolbow, J., Belytschko, T.: A finite element method for crack growth without remeshing. Internat. J. Numer. Methods Engrg. 46, 131–150 (1999)
Ivanov, A.V., Savenkov, E.B.: Simulation and visualization of the dynamics of a surface with a movable boundary on a stationary unstructured mesh. Sci. Vis. 9(2), 64–81 (2017)
Linkov, A.M.: The particle velocity, speed equation and universal asymptotics for the efficient modelling of hydraulic fractures. J. Appl. Math. and Mech. 79(1), 54–63 (2015)
Stolarska, M., Chopp, D., Moës, N., Belytschko, T.: Modelling crack growth by level sets in the extended finite element method. Int. J. Numer. Meth. Engng. 51, 943–960 (2001)
Moës, N., Gravouil, A., Belytschko, T.: Non-planar 3D crack growth by the extended finite element and level sets – Part I: mechanical model. Int. J. Numer. Meth. Engng. 53, 2549–2568 (2002)
Gravouil, A., Moës, N., Belytschko, T.: Non-planar 3D crack growth by the extended finite element and level sets–Part II: level set update. Int. J. Numer. Meth. Engng. 53, 2569–2586 (2002)
Macdonald, C.B., Ruuth, S.J.: The implicit closest point method for the numerical solution of partial differential equations on surfaces. SIAM J. Sci. Comput. 31, 4330–4350 (2009)
Savenkov, E.B., Borisov, V.E., Kritsky, B.V.: Utilization of closest point projection surface representation in extended finite element method. Math. Models and Computer Simulations (in press, 2019)
Acknowledgments
This research was supported by Russian Science Foundation, project No. 15-11-00021.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Borisov, V., Ivanov, A., Ramazanov, M., Savenkov, E.B. (2019). Poroelastic Hydraulic Fracture Simulation Using X-FEM/CPP Approach. In: Karev, V., Klimov, D., Pokazeev, K. (eds) Physical and Mathematical Modeling of Earth and Environment Processes (2018). Springer Proceedings in Earth and Environmental Sciences. Springer, Cham. https://doi.org/10.1007/978-3-030-11533-3_32
Download citation
DOI: https://doi.org/10.1007/978-3-030-11533-3_32
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-11532-6
Online ISBN: 978-3-030-11533-3
eBook Packages: Earth and Environmental ScienceEarth and Environmental Science (R0)