Poroelastic and Poroplastic Modeling of Hydraulic Fracturing in Brittle and Ductile Formations
- HanYi Wang (University of Houston) | Matteo Marongiu-Porcu (Economides Consultants, Inc.) | Michael J. Economides (University of Houston)
- Document ID
- Society of Petroleum Engineers
- SPE Production & Operations
- Publication Date
- February 2016
- Document Type
- Journal Paper
- 47 - 59
- 2016.Society of Petroleum Engineers
- cohesive zone method, brittle and ductile, poroplastic, poroelastic, hydraulic fracturing
- 6 in the last 30 days
- 893 since 2007
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The prevailing approach for hydraulic-fracture modeling relies on linear-elastic fracture mechanics (LEFM). Generally, LEFM that uses stress-intensity factor at the fracture tip gives reasonable predictions for hard-rock hydraulic-fracturing processes, but often fails to give accurate predictions of fracture geometry and propagation pressure in formations that can undergo plastic failures, such as poorly consolidated/unconsolidated sands and ductile shales. This is because the fracture-process zone ahead of the crack tip, elasto-plastic material behavior, and strong coupling between flow and stress cannot be neglected in these formations. Recent laboratory testing has revealed that in many cases, fracture-propagation conditions cannot be described by traditional LEFM models. Rather, fractures develop in cohesive zones. In this study, we developed a fully coupled poro-elasto-plastic hydraulic-fracturing model by combining the cohesive-zone method with the Mohr-Coulomb theory of plasticity, which not only can model fracture initiation and growth while considering process-zone effects, but also can capture the effects of plastic deformation in the bulk formation. The impact of the formation plastic properties on the fracture process is investigated, and the results are compared with existing models. In addition, the effects of different parameters on fracture propagation in ductile formations are also investigated through parametric study. The results indicate that plastic and highly deforming formations exhibit greater breakdown and propagation pressure. The more plastic the formation (lower cohesion strength), the higher the net pressure required to propagate the fracture. Also, lower cohesion strength leads to shorter and wider fracture geometry. The effect of formation plasticity on a hydraulic fracture is mostly controlled by initial stress contrast, cohesion strength of formation rock, and pore pressure. We also found that altering the effective fracture toughness can only partially mimic the consequences of increased toughness ahead of the fracture tip in ductile formations, but it fails to capture the effect of shear failure within the entire affected area, which can lead to underestimating the fracture width and overestimating the fracture length. For a more-accurate modeling of fracturing in ductile formations, the entire plastic-deformation region induced by the propagating fracture should be considered, especially when shear-failure areas are large.
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Adachi, J. I. and Detournay, E. 2008. Plain strain propagation of a hydraulic fracture in permeable rock. Engineering Fracture Mechanics 75 (16): 4666–4694. http://dx.doi.org/10.1016/j.engfracmech.2008.04.006.
Afrouz, A. 1992. Practical Handbook of Rock Mass Classification Systems and Modes of Ground Failure, first edition. Boca Raton, Florida: CRC Press.
Barenblatt, G. I. 1959. The Formation of Equilibrium Cracks During Brittle Fracture: General Ideas and Hypothesis, Axially Symmetric Cracks. Journal of Applied Mathematics and Mechanics 23 (3): 622–636. http://dx.doi.org/10.1016/0021-8928(59)90157-1.
Barenblatt, G.I. 1962. The Mathematical Theory of Equilibrium Cracks in Brittle Fracture. In Advances in Applied Mechanics, Vol. 7, 55–129. New York: Academic Press. http://dx.doi.org/10.1016/S0065-2156(08)70121-2.
Benzeggagh, M. L., and Kenane, M. 1996. Measurement of mixed-mode delamination fracture toughness of unidirectional glass/epoxy composites with mixed-mode bending apparatus. Composites Science and Technology 56 (4): 439–449. http://dx.doi.org/10.1016/0266-3538(96)00005-X.
Biot, M. A. 1941. General Theory of Three Dimensional Consolidation. Journal of Applied Physics 12 (2): 155–164. http://dx.doi.org/10.1063/1.1712886.
Boone, T. J. and Ingraffea, A. R. 1990. A numerical procedure for simulation of hydraulically-driven fracture propagation in poroelastic media. International Journal for Numerical and Analytical Methods in Geomechanics 14 (1): 27–47. http://dx.doi.org/10.1002/nag.1610140103.
Carrier, B. and Granet, S. 2013. Finite Element Modeling of Fluid-Driven Fracture in Permeable Medium. Poromechanics V, 462–470. http://dx.doi.org/10.1061/9780784412992.055.
Chen, Z., Bunger, A. P., Zhang, X. et al. 2009. Cohesive zone finite element-based modeling of hydraulic fractures. Acta Mechanica Solida Sinica 22 (5): 443–452. http://dx.doi.org/10.1016/S0894-9166(09)60295-0.
Dean, R. H. and Schmidt, J. H. 2009. Hydraulic-Fracture Predictions With a Fully Coupled Geomechanical Reservoir Simulator. SPE J. 14 (4): 707–714. SPE-116470-PA. http://dx.doi.org/10.2118/116470-PA.
Detournay, E. and Garagash, D. I. 2003. The near-tip region of a fluid-driven fracture propagating in a permeable elastic solid. J. Fluid Mech. 494: 1–32. http://dx.doi.org/10.1017/S0022112003005275.
Dugdale, D. S. 1960. Yielding of steel sheets containing slits. Journal of the Mechanics and Physics of Solids 8 (2): 100–104. http://dx.doi.org/10.1016/0022-5096(60)90013-2.
Economides, M. J. and Nolte, K. G. 2000. Reservoir Stimulation, 3rd edition. Chichester, UK: John Wiley & Sons.
Geertsma, J. and de Klerk, F. 1969. A Rapid Method of Predicting Width and Extent of Hydraulic Induced Fractures. J Pet Technol 21 (12): 1571–1581. SPE-2458-PA. http://dx.doi.org/10.2118/2458-PA.
Germanovich, L. N., Astakhov, D. K., Shlyapobersky, J. et al. 1998. Modeling multisegmented hydraulic fracture in two extreme cases: No leakoff and dominating leakoff. International Journal of Rock Mechanics and Mining Sciences 35 (4–5): 551–554. http://dx.doi.org/10.1016/S0148-9062(98)00119-3.
Griffith, A. A. 1921. The Phenomena of Rupture and Flow in Solids. Philosophical Transactions of the Royal Society of London, Series A 221 (582–593): 163–198. http://dx.doi.org/10.1098/rsta.1921.0006.
Howard, G. C. and Fast, C. R. 1970. Hydraulic Fracturing. SPE Monograph Series, Vol. 2. Richardson, Texas: SPE.
Irwin, G. R. 1957. Analysis of stresses and strain near the end of crack traversing a plate. J. Appl. Mech. 24: 361–364.
Kanninen, M. F. and Popelar, C. H. 1985. Advanced Fracture Mechanics, first edition. New York: Oxford University Press.
Khristianovich, S. A. and Zheltov, Y. P. 1955. Formation of Vertical Fractures by Means of Highly Viscous Fuids. Presented at the 4th World Petroleum Congress, Rome, 6–15 June. WPC-6132.
Marongiu-Porcu, M., Retnanto, A., Economides, M. J. et al. 2014. Comprehensive Fracture Calibration Test Design. Presented at the SPE Hydraulic Fracturing Technology Conference, The Woodlands, Texas, USA, 4–6 February. SPE-168634-MS. http://dx.doi.org/10.2118/168634-MS.
Mokryakov, V. 2011. Analytical solution for propagation of hydraulic fracture with Barenblatt’s cohesive tip zone. International Journal of Fracture 169 (2): 159–168. http://dx.doi.org/10.1007/s10704-011-9591-0.
Nassir, M. 2013. Geomechanical Coupled Modeling of Shear Fracturing in Non-Conventional Reservoirs. PhD dissertation, University of Calgary, Alberta, Canada (January 2013).
Nolte, K. G. 1986. A General Analysis of Fracturing Pressure Decline With Application to Three Models. SPE Form Eval 1 (6): 571–583. SPE-12941-PA. http://dx.doi.org/10.2118/12941-PA.
Nordgren, R. P. 1972. Propagation of a Vertical Hydraulic Fracture. J Pet Technol 12 (4): 306–314. SPE-3009-PA. http://dx.doi.org/10.2118/3009-PA.
Orowan, E. 1955. Energy Criteria of Fracture. Weld. Res. Supp. 34: 157–160.
Papanastasiou, P. 1997. The influence of plasticity in hydraulic fracturing. International Journal of Fracture 84 (1): 61–79. http://dx.doi.org/10.1023/A:1007336003057.
Papanastasiou, P. 1999. The effective fracture toughness in hydraulic fracturing. International Journal of Fracture 96 (2): 127–147. http://dx.doi.org/10.1023/A:1018676212444.
Parker, M., Petre, E., Dreher, D. et al. 2009. Haynesville Shale: Hydraulic Fracture Stimulation Approach. Presented at the International Coalbed & Shale Gas Symposium Tuscaloosa, Alabama, USA, 18–22 May. Paper 0913.
Perkins, T. K. and Kern, L. R. 1961. Widths of Hydraulic Fractures. J Pet Technol 13 (9): 937–949. SPE-89-PA. http://dx.doi.org/10.2118/89-PA.
Sarris, E., and Papanastasiou, P. 2012. Modeling of Hydraulic Fracturing in a Poroelastic Cohesive Formation. Int. J. Geomech. 12 (2): 160–167. http://dx.doi.org/10.1061/(ASCE)GM.1943-5622.0000121.
Sone, H. and Zoback, M. D. 2011. Visco-plastic Properties of Shale Gas Reservoir Rocks. Presented at the 45th U.S. Rock Mechanics/Geomechanics Symposium, San Francisco, California, USA, 26–29 June. ARMA-11-417.
Stegent, N. A., Wagner, A. L., Mullen, J. et al. 2010. Engineering a Successful Fracture-Stimulation Treatment in the Eagle Ford Shale. Presented at the SPE Tight Gas Completions Conference, San Antonio, Texas, USA, 2–3 November. SPE-136183-MS. http://dx.doi.org/10.2118/136183-MS.
Tomar, V., Zhai, J., and Zhou, M. 2004. Bounds for element size in a variable stiffness cohesive finite element model. International Journal for Numerical Methods in Engineering 61 (11): 1894–1920. http://dx.doi.org/10.1002/nme.1138.
Turon, A., Camanho, P. P., Costa, J. et al. 2006. A damage model for the simulation of delamination in advanced composites under variable-model loading. Mechanics of Materials 38 (11): 1072–1089. http://dx.doi.org/10.1016/j.mechmat.2005.10.003.
Valkó, P. P. and Economides, M. J. 1999. Fluid-Leakoff Delineation in High-Permeability Fracturing. SPE Prod & Fac 14 (2): 110–116. SPE-56135-PA. http://dx.doi.org/10.2118/56135-PA.
van Dam, D. B., Papanastasiou, P., and de Pater, C. J. 2002. Impact of Rock Plasticity on Hydraulic Fracture Propagation and Closure. SPE Prod & Fac 17 (3): 149–159. SPE-78812-PA. http://dx.doi.org/10.2118/78812-PA.
Vermeer, P. A. and de Borst, R. 1984. Non-Associated Plasticity for Soils, Concrete and Rock. HERON 29 (3): 3–64.
Wang, H. 2015a. Numerical Modeling of Non-Planar Hydraulic Fracture Propagation in Brittle and Ductile Rocks using XFEM with Cohesive Zone Method. Journal of Petroleum Science and Engineering (in press). http://dx.doi.org/10.1016/j.petrol.2015.08.010.
Wang, H. 2015b. Poro-Elasto-Plastic Modeling of Complex Hydraulic Fracture Propagation: Simultaneous Multi-Fracturing and Producing Well Interference. Acta Mechanica (in press). http://dx.doi.org/10.1007/s00707-015-1455-7.
Weng, X. 2015. Modeling of Complex Hydraulic Fractures in Naturally Fractured Formation. Journal of Unconventional Oil and Gas Resources 9: 114–135. http://dx.doi.org/10.1016/j.juogr.2014.07.001.
Yao, Y. 2012. Linear Elastic and Cohesive Fracture Analysis to Model Hydraulic Fracture in Brittle and Ductile Rocks. Rock Mechanics and Rock Engineering 45 (3): 375–387. http://dx.doi.org/10.1007/s00603-011-0211-0.
Yuan, R., Jin, L., Zhu, C. et al. 2013. High Pressure Stimulation – Impact of Hydraulic Fracture Geometry to Unconventional Gas Appraisal and Development in Compressional Settings. Presented at the SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana, USA, 30 September–2 October. SPE-166348-MS. http://dx.doi.org/10.2118/166348-MS.