Use of the explicit time integration scheme within the Planar3D approach for simulating hydraulic fracturing
https://doi.org/10.24887/2587-7399-2019-2-15-19
Abstract
This paper focuses on the Planar3D model for a hydraulic fracture in a layered medium. The specificity of the described approach is to use the explicit time integration scheme and reduce the system of partial differential equations to a dynamic system. The position of the crack front is determined using the universal asymptotics of the crack tip written for non-Newtonian fluids. The calculations are compared with the published results of the ILSA and EP3D models, and methods of acceleration and ways to account for additional effects are discussed.
About the Authors
E. B. Starobinskii
Peter the Great St.Petersburg Polytechnic University
Russian Federation
Russian Federation
A. D. Stepanov
AIRT LLC
Russian Federation
Russian Federation
Saint-Petersburg
References
1. Pitakbunkate T. et al., Hydraulic fracture optimization with a p-3D model, SPE 142303-MS, 2011.
2. Adachi J. et al., Computer simulation of hydraulic fractures, International Journal of Rock Mechanics and Mining Sciences, 2007, V. 44, no. 5, pp. 739-757.
3. Peirce A., Implicit level set algorithms for modelling hydraulic fracture propagation, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2016, V. 374, no. 2078, pp. 20150423.
4. Mack M.G., Warpinski N.R., Mechanics of hydraulic fracturing, Reservoir stimulation, 3rd ed., Chichester: Wiley, 2000, 856 r.
5. Linkov A. M. et al., Modified formulation, ε-regularization and the efficient solution of hydraulic fracture problems, Proceedings of ISRM International Conference for Effective and Sustainable Hydraulic Fracturing, 20-22 May 2013, Brisbane, Australia, Publ. of Society for Rock Mechanics and Rock Engineering, 2013.
6. Osiptsov A.A., Fluid mechanics of hydraulic fracturing: a review, Journal of Petroleum Science and Engineering, 2017, V. 156, pp. 513-535.
7. Khasanov M.M., Paderin G.V., Shel’ E.V. et al., Approaches to modeling hydraulic fracturing and their development (In Russ.), Neftyanoe khozyaystvo = Oil Industry, 2017, no. 12, pp. 37–41.
8. Peirce A., Modeling multi-scale processes in hydraulic fracture propagation using the implicit level set algorithm, Computer Methods in Applied Mechanics and Engineering, 2015, V. 283, pp. 881-908.
9. Dontsov E. V. et al., Implementing a universal tip asymptotic solution into an implicit level set algorithm (ILSA) for multiple parallel hydraulic fractures, Proceedings of 50th US Rock Mechanics/Geomechanics Symposium, 26-29 June 2016, Houston, Texas, Publ. of American Rock Mechanics Association, 2016, V. 1, pp. 722-729.
10. Stepanov A. D., Linkov A. M., On increasing efficiency of hydraulic fracture simulation by using dynamic approach of modified theory, Proceedings of Summer School-Conference “Advanced Problems in Mechanics 2016”, 2016, pp. 393-403.
11. Markov N.S., Linkov A.M., An effective method to find Green’s functions for layered media, Materials Physics and Mechanics, 2017, V. 32, no. 2, pp. 133-143.
12. Peirce A., Detournay E., An implicit level set method for modeling hydraulically driven fractures, Computer Methods in Applied Mechanics and Engineering, 2008, V. 197, no. 33-40, pp. 2858-2885.
13. Hills D. A. et al., Solution of crack problems: the distributed dislocation technique, Springer Science & Business Media, 2013.
14. Stepanov A.D., Statistical method for tracing hydraulic fracture front without evaluation of the normal, International Journal of Engineering&Technology, 2018, no. 7(4.26), pp. 274-278.
15. Garagash D.I., Detournay E., Adachi J.I., Multiscale tip asymptotics in hydraulic fracture with leak-off, Journal of Fluid Mechanics, 2011, V. 669, pp. 260-297.
16. Linkov A.M., Universal asymptotic umbrella for hydraulic fracture modeling, arXiv preprint arXiv:1404.4165, 2014, URL: https://arxiv.org/ftp/arxiv/papers/1404/1404.4165.pdf.
17. Linkov A. M., The particle velocity, speed equation and universal asymptotics for the efficient modelling of hydraulic fractures, Journal of Applied Mathematics and Mechanics, 2015, V. 79, no. 1, pp. 54-63.
18. Dontsov, E.V., Peirce, A.P., An enhanced pseudo-3D model for hydraulic fracturing accounting for viscous height growth, non-local elasticity, and lateral toughness, Engineering Fracture Mechanics, 2015, DOI: 10.1016/j.engfracmech.2015.05.043.
Review
For citations:
Starobinskii E.B., Stepanov A.D. Use of the explicit time integration scheme within the Planar3D approach for simulating hydraulic fracturing. PROneft. Professionally about Oil. 2019;(2):15-19. (In Russ.) https://doi.org/10.24887/2587-7399-2019-2-15-19
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