Efficient pseudo-spectral solvers for the PKN model of hydrofracturing
Source abstract
Abstract
In the paper, a novel algorithm employing pseudo-spectral approach is developed for the PKN model of hydrofracturing. The respective solvers based on this approach compute both the solution and its temporal derivative. In comparison with conventional solvers, they demonstrate excellent cost effectiveness in terms of balance between the accuracy of computations and densities of the temporal and spatial meshes. Various leak-off regimes are considered.
Source: openaire · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Hydraulic Fracturing and Reservoir Analysis · Hydrocarbon exploration and reservoir analysis · Reservoir Engineering and Simulation Methods
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (33)
Show source-provided references
1. Adachi J, Detournay E (2002) Self-similar solution of a plane–strain fracture driven by a power-law fluid. Int J Numer Anal Methods Geomech 26:579–60410.1002/nag.213 ↗
2. Adachi J, Peirce A (2007) Asymptotic analysis of an elasticity equation for a finger-like hydraulic fracture. J Elast 90(1): 43–6910.1007/s10659-007-9122-4 ↗
3. Adachi J, Siebrits E, Peirce A, Desroches J (2007) Computer simulation of hydraulic fractures. Int J Rock Mech Min Sci 44:739–75710.1016/j.ijrmms.2006.11.006 ↗
4. Carter E (1957) Optimum fluid characteristics for fracture extension. In: Howard G, Fast C (eds) Drilling and production practices. American Petroleum Institute, pp 261–270
5. Crittendon BC (1959) The mechanics of design and interpertation of hydraulic fracture treatments. J Pet Tech 21:21–2910.2118/1106-G ↗
6. Detournay E (2004) Propagation regimes of fluid-driven fractures in impermeable rocks. Int J Geomech 4:1–1110.1061/(ASCE)1532-3641(2004)4:1(35) ↗
7. Dobroskok AA, Linkov AM (2011) Modeling of fluid flow, stress state and seismicity induced in rock by instant pressure drop in a hydrofracture. J Min Sci 47(1):10–1910.1134/S1062739147010023 ↗
8. Economides M, Nolte K (eds) (2000) Reservoir stimulation, 3rd edn. Wiley, Chichester
9. Garagash DI, Detournay E (2000) The tip region of a fluid-driven fracture in an elastic medium. J Appl Mech 67:183–19210.1115/1.321162 ↗
10. Geertsma J, de Klerk F (1969) A rapid method of predicting width and extent of hydraulically induced fractures. J Pet Tech 21:1571–1581 [SPE 2458]10.2118/2458-PA ↗
11. Hubbert MK, Willis DG (1957) Mechanics of hydraulic fracturing. J Pet Tech 9(6):153–168
12. Kemp LF (1989) Study of Nordgren’s equation of hydraulic fracturing. SPE Prod Eng 5:311–31410.2118/18959-PA ↗
13. Khristianovic SA, Zheltov YP (1955) Formation of vertical fractures by means of highly viscous liquid. In: Proceedings of the fourth world petroleum congress, Rome, pp 579–586
14. Kovalyshen Y, Detournay E (2009) A reexamination of the classical PKN model of hydraulic fracture. Transp Porous Media 81:317–33910.1007/s11242-009-9403-4 ↗
15. Kovalyshen Y (2010) Fluid-driven fracture in poroelastic medium. PhD thesis, The University of Minnesota
16. Kusmierczyk P, Mishuris G, Wrobel M (2012) Remarks on numerical simulation of the PKN model of hydrofracturing in proper variables. Various leak-off regimes. arXiv:1211.6474
17. Lecampion B, Detournay E (2007) An implicit algorithm for the propagation of a hydraulic fracture with a fluid lag. Comput Method Appl Mech 196(49–52):4863–488010.1016/j.cma.2007.06.011 ↗
18. Linkov AM (2011) Speed equation and its application for solving ill-posed problems of hydraulic fracturing. ISSM 1028-3358. Doklady Phys 56(8): 436–43810.1134/S1028335811080015 ↗
19. Linkov AM (2011) Use of a speed equation for numerical simulation of hydraulic fractures. arXiv:1108.6146
20. Linkov AM (2011) On efficient simulation of hydraulic fracturing in terms of particle velocity. Int J Eng Sci 52:77–8810.1016/j.ijengsci.2011.11.009 ↗
21. Mishuris G, Wrobel M, Linkov A (2012) On modeling hydraulic fracture in proper variables: stiffness, accuracy, sensitivity. Int J Eng Sci 61:10–2310.1016/j.ijengsci.2012.06.005 ↗
22. Mitchell SL, Kuske R, Peirce A (2007) An asymptotic framework for finite hydraulic fractures including leakoff. SIAM J Appl Math 67(2):364–38610.1137/04062059X ↗
23. Mitchell SL, Kuske R, Peirce AP (2007) An asymptotic framework for the analysis of hydraulic fractures: the impermeable case. ASME J Appl Mech 74(2):365–37210.1115/1.2200653 ↗
24. Moos D (2012) The importance of stress and fractures in hydrofracturing and stimulation performance: a geomechanics overview. Search and Discovery Article 80255
25. Nordgren RP (1972) Propagation of a vertical hydraulic fracture. J Pet Tech 253:306–314
26. Olson JE (2008) Multi-fracture propagation modeling: applications to hydraulic fracturing in shales and tight gas sands. In: The 42nd US rock mechanics symposium (USRMS), June 29–July 2, 2008, San Francisco, CA, USA
27. Peirce A, Detournay E (2008) An implicit level set method for modeling hydraulically driven fractures. Comput Methods Appl Mech Eng 197:2858–288510.1016/j.cma.2008.01.013 ↗
28. Peirce A, Detournay E (2009) An Eulerian moving front algorithm with weak-form tip asymptotics for modeling hydraulically driven fractures. Numer Methods Eng 25(2):185–20010.1002/cnm.1119 ↗
29. Perkins TK, Kern LR (1961) Widths of hydraulic fractures. J Pet Tech 13(9):37–49 [SPE 89]10.2118/89-PA ↗
30. Rubin AM (1995) Propagation of magma filled cracks. Annu Rev Earth Planet Sci 23:287–33610.1146/annurev.ea.23.050195.001443 ↗
31. Sneddon IN, Elliot HA (1946) The opening of a Griffith crack under internal pressure. Quart Appl Math 4:262–26710.1090/qam/17161 ↗
32. Tsai VC, Rice JR (2010) A model for turbulent hydraulic fracture and application to crack propagation at glacier beds. J Geophys Res 115:1–1810.1029/2009JF001474 ↗
33. Zhang X, Jeffrey R, Llanos EM (2004) A study of shear hydraulic fracture propagation. In: Gulf rocks, the 6th North America rock mechanics symposium (NARMS), June 5–9, 2004, Houston, TX, USA