Fully coupled XFEM formulation for hydraulic fracturing simulation based on a generalized fluid leak-off model. (English) Zbl 1506.74410
Summary: A novel fully coupled hydro-mechanical model is used to assess the effect of fluid loss on the efficiency of the fracturing treatment within saturated porous media. In the context of XFEM, the pore pressure is defined independently on either side of the hydro-fracture using the Heaviside enrichment function. Meanwhile, independent pressure degrees of freedom are employed to develop a generalized model for the hydro-fracture inflow. In this way, the pressure jump due to the formation of a bedding layer of settled proppants and/or additive chemicals in the vicinity of the hydro-fracture faces can be taken into account (technically referred to as the cake layer effect). On the other hand, the reduction in the hydraulic permeability of zones adjacent to those areas affected by the very high fracturing pressure, also known as filtrate effects, is taken into account through a series of experimental correlations. Finally, the ability of the developed framework to tackle the modelling of hydraulic fracturing, particularly in medium to low permeability formations, is illustrated by means of numerical simulations.
MSC:
| 74S05 | Finite element methods applied to problems in solid mechanics |
| 76S05 | Flows in porous media; filtration; seepage |
| 74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |
| 74R10 | Brittle fracture |
References:
| [1] | Bidarmaghz, A.; Narsilio, G., Shallow geothermal energy: emerging convective phenomena in permeable saturated soils, Geotech. Lett., 6, 2, 119-123 (2016) |
| [2] | Boone, T. J.; Ingraffea, A. R., A numerical procedure for simulation of hydraulically-driven fracture propagation in poroelastic media, Int. J. Numer. Anal. Methods Geomech., 14, 1, 27-47 (1990) |
| [3] | Detournay, E., Propagation regimes of fluid-driven fractures in impermeable rocks, Int. J. Geomech., 4, 1, 35-45 (2004) |
| [4] | Schrefler, B. A.; Secchi, S.; Simoni, L., On adaptive refinement techniques in multi-field problems including cohesive fracture, Comput. Methods Appl. Mech. Engrg., 195, 4-6, 444-461 (2006) · Zbl 1193.74158 |
| [5] | Hirmand, M. R.; Vahab, M.; Papoulia, K. D.; Khalili, N., Robust simulation of dynamic fluid-driven fracture in naturally fractured impermeable media, Comput. Methods Appl. Mech. Engrg., 357, Article 112574 pp. (2019) · Zbl 1442.74204 |
| [6] | Réthoré, J.; de Borst, R.; Abellan, M. A., A two-scale approach for fluid flow in fractured porous media, Internat. J. Numer. Methods Engrg., 71, 7, 780-800 (2007) · Zbl 1194.76139 |
| [7] | Réthoré, J.; de Borst, R.; Abellan, M. A., A two-scale model for fluid flow in an unsaturated porous medium with cohesive cracks, Comput. Mech., 42, 2, 227-238 (2008) · Zbl 1154.76053 |
| [8] | Dahi Taleghani, A.; Olson, J. E., How natural fractures could affect hydraulic-fracture geometry, SPE J., 19, 01, 161-171 (2013) |
| [9] | Khoei, A. R.; Vahab, M.; Haghighat, E.; Moallemi, S., A mesh-independent finite element formulation for modeling crack growth in saturated porous media based on an enriched-FEM technique, Int. J. Fract., 188, 1, 79-108 (2014) |
| [10] | Salimzadeh, S.; Khalili, N., Fully coupled XFEM model for flow and deformation in fractured porous media with explicit fracture flow, Int. J. Geomech., 16, 4, Article 04015091 pp. (2016) |
| [11] | Gordeliy, E.; Abbas, S.; Peirce, A., Modeling nonplanar hydraulic fracture propagation using the XFEM: An implicit level-set algorithm and fracture tip asymptotics, Int. J. Solids Struct., 159, 135-155 (2019) |
| [12] | Sobhaniaragh, B.; Mansur, W.; Peters, F., The role of stress interference in hydraulic fracturing of horizontal wells, I Int. J. Rock Mech. Min., 106, 153-164 (2018) |
| [13] | Sobhaniaragh, B.; Haddad, M.; Mansur, W.; Peters, F., Computational modelling of multi-stage hydraulic fractures under stress shadowing and intersecting with pre-existing natural fractures, Acta Mech., 230, 3, 1037-1059 (2019) |
| [14] | Escobar, R. G.; Sanchez, E. C.M.; Roehl, D.; Romanel, C., Xfem modeling of stress shadowing in multiple hydraulic fractures in multi-layered formations, J. Nat. Gas Sci. Eng., 70, Article 102950 pp. (2019) |
| [15] | Jin, W.; Arson, C., Fluid-driven transition from damage to fracture in anisotropic porous media: a multi-scale XFEM approach, Acta Geotech., 15, 1, 113-144 (2020) |
| [16] | Karimi, M.; Bayesteh, H.; Mohammadi, S., An adapting cohesive approach for crack-healing analysis in SMA fiber-reinforced composites, Comput. Methods Appl. Mech. Engrg., 349, 550-575 (2019) · Zbl 1441.74251 |
| [17] | Parchei Esfahani, M.; Gracie, R., On the undrained and drained hydraulic fracture splits, Internat. J. Numer. Methods Engrg., 118, 12, 741-763 (2019) · Zbl 07865195 |
| [18] | Samimi, S.; Pak, A., A fully coupled element-free Galerkin model for hydro-mechanical analysis of advancement of fluid-driven fractures in porous media, Int. J. Numer. Anal. Methods Geomech., 40, 16, 2178-2206 (2016) |
| [19] | Ghaffaripour, O.; Esgandani, G. A.; Khoshghalb, A.; Shahbodaghkhan, B., Fully coupled elastoplastic hydro-mechanical analysis of unsaturated porous media using a meshfree method, Int. J. Numer. Anal. Methods Geomech., 43, 11, 1919-1955 (2019) |
| [20] | Wheeler, M. F.; Wick, T.; Wollner, W., An augmented-Lagrangian method for the phase-field approach for pressurized fractures, Comput. Methods Appl. Mech. Engrg., 271, 69-85 (2014) · Zbl 1296.65170 |
| [21] | Mikelic, A.; Wheeler, M. F.; Wick, T., A phase-field method for propagating fluid-filled fractures coupled to a surrounding porous medium, Multiscale Model. Simul., 13, 1, 367-398 (2015) · Zbl 1317.74028 |
| [22] | Miehe, C.; Mauthe, S., Phase field modeling of fracture in multi-physics problems. Part III. Crack driving forces in hydro-poro-elasticity and hydraulic fracturing of fluid-saturated porous media, Comput. Methods Appl. Mech. Engrg., 304, 619-655 (2016) · Zbl 1425.74423 |
| [23] | Lee, S.; Mikelic, A.; Wheeler, M. F.; Wick, T., Phase-field modeling of two phase fluid filled fractures in a poroelastic medium, Multiscale Model. Simul., 16, 4, 1542-1580 (2018) · Zbl 1401.74084 |
| [24] | Economides, M. J.; Nolte, K. G., Reservoir Stimulation, Vol. 2 (1989), Prentice Hall: Prentice Hall Englewood Cliffs, NJ |
| [25] | Howard, G. C.; Fast, C., Optimum fluid characteristics for fracture extension, (Drilling and Production Practice (1957), American Petroleum Institute) |
| [26] | Detournay, E., Mechanics of hydraulic fractures, Annu. Rev. Fluid Mech., 48, 311-339 (2016) · Zbl 1356.74181 |
| [27] | Bunger, A. P.; Detournay, E.; Garagash, D. I., Toughness-dominated hydraulic fracture with leak-off, Int. J. Fract., 134, 2, 175-190 (2005) · Zbl 1148.74336 |
| [28] | Mohammadnejad, T.; Khoei, A., An extended finite element method for hydraulic fracture propagation in deformable porous media with the cohesive crack model, Finite Elem. Anal. Des., 73, 77-95 (2013) · Zbl 1302.74167 |
| [29] | Khoei, A. R.; Vahab, M.; Hirmand, M. R., An enriched-FEM technique for numerical simulation of interacting discontinuities in naturally fractured porous media, Comput. Methods Appl. Mech. Engrg., 331, 197-231 (2018) · Zbl 1439.74432 |
| [30] | Remij, E. W.; Remmers, J. J.C.; Huyghe, J. M.; Smeulders, D. M.J., The enhanced local pressure model for the accurate analysis of fluid pressure driven fracture in porous materials, Comput. Methods Appl. Mech. Engrg., 286, 293-312 (2015) · Zbl 1423.74844 |
| [31] | Nguyen, V. P.; Lian, H.; Rabczuk, T.; Bordas, S., Modelling hydraulic fractures in porous media using flow cohesive interface elements, Eng. Geol., 225, 68-82 (2017) |
| [32] | de Borst, R., Fluid flow in fractured and fracturing porous media: A unified view, Mech. Res. Commun., 80, 47-57 (2017) |
| [33] | Pervaiz Fathima, K. M.; de Borst, R., Implications of single or multiple pressure degrees of freedom at fractures in fluid-saturated porous media, Eng. Fract. Mech., 213, 1-20 (2019) |
| [34] | Cook, J.; Guo, Q.; Way, P.; Bailey, L.; Friedheim, J., The role of filtercake in wellbore strengthening, (IADC/SPE Drilling Conference and Exhibition (2016), SPE) |
| [35] | Settari, A., A new general model of fluid loss in hydraulic fracturing, SPE J., 25, 04, 491-501 (1985) |
| [36] | Biot, M. A., General solutions of the equations of elasticity and consolidation for a porous material, J. Appl. Mech., 23, 1, 91-96 (1956) · Zbl 0074.19101 |
| [37] | Camacho, G. T.; Ortiz, M., Computational modelling of impact damage in brittle materials, Int. J. Solids Struct., 33, 20-22, 2899-2938 (1996) · Zbl 0929.74101 |
| [38] | Ortiz, M.; Pandolfi, A., Finite-deformation irreversible cohesive elements for three-dimensional crack-propagation analysis, Internat. J. Numer. Methods Engrg., 44, 9, 1267-1282 (1999) · Zbl 0932.74067 |
| [39] | Mohammadi, S., Extended Finite Element Method: For Fracture Analysis of Structures (2008), John Wiley & Sons · Zbl 1132.74001 |
| [40] | Li, S.; Ghosh, S., Extended Voronoi cell finite element model for multiple cohesive crack propagation in brittle materials, Internat. J. Numer. Methods Engrg., 65, 7, 1028-1067 (2006) · Zbl 1179.74152 |
| [41] | Zienkiewicz, O. C.; Chan, A. H.C.; Pastor, M.; Schrefler, B. A.; Shiomi, T., Computational Geomechanics, Vol. 613 (1999), Wiley: Wiley Chichester · Zbl 0932.74003 |
| [42] | Witherspoon, P. A.; Wang, J. S.Y.; Iwai, K.; Gale, J. E., Validity of cubic law for fluid flow in a deformable rock fracture, Water Resour. Res., 16, 6, 1016-1024 (1980) |
| [43] | Williams, B., Fluid loss from hydraulically induced fractures, J. Pet. Technol., 22, 07, 882-888 (1970) |
| [44] | Penny, G. S.; Conway, M. W.; Lee, W., Control and modeling of fluid leakoff during hydraulic fracturing, J. Pet. Technol., 37, 06, 1-071 (1985) |
| [45] | Yarushina, V. M.; Bercovici, D.; Oristaglio, M. L., Rock deformation models and fluid leak-off in hydraulic fracturing, Geophys. J. Int., 194, 3, 1514-1526 (2013) |
| [46] | Yarushina, V. M.; Bercovici, D.; Oristaglio, M. L., Effect of rock rheology on fluid leak-off during hydraulic fracturing, (EGU General Assembly Conference Abstracts, Vol. 14 (2012)) |
| [47] | Dong, J. J.; Hsu, J.; Wu, W.; Shimamoto, T.; Hung, J.; Yeh, E.; Wu, Y.; Sone, H., Stress-dependence of the permeability and porosity of sandstone and shale from TCDP Hole-A, Int. J. Rock Mech. Min., 47, 7, 1141-1157 (2010) |
| [48] | M. Vahab, N. Khalili, An X-FEM formulation for the optimized graded proppant injection into hydro-fractures within saturated porous media, Transp. Porous Media 121 (2) 289-314. |
| [49] | Vahab, M.; Khoei, A. R.; Khalili, N., An X-FEM technique in modeling hydro-fracture interaction with naturally-cemented faults, Eng. Fract. Mech., 212, 269-290 (2019) |
| [50] | Geertsma, J.; De Klerk, F., A rapid method of predicting width and extent of hydraulically induced fractures, J. Pet. Technol., 21, 1571-1581 (1969) |
| [51] | Spence, D. A.; Sharp, P., Self-similar solutions for elastohydrodynamic cavity flow, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 400, 289-313 (1985) · Zbl 0581.76007 |
| [52] | Peruzzo, C.; Simoni, L.; Schrefler, B. A., On stepwise advancement of fractures and pressure oscillations in saturated porous media, Eng. Fract. Mech., 215, 246-250 (2019) |
| [53] | Lecampion, B.; Detournay, E., An implicit algorithm for the propagation of a hydraulic fracture with a fluid lag, Comput. Methods Appl. Mech. Engrg., 196, 49-52, 4863-4880 (2007) · Zbl 1173.74383 |
| [54] | Shen, Y., A variational inequality formulation to incorporate the fluid lag in fluid-driven fracture propagation, Comput. Methods Appl. Mech. Engrg., 272, 17-33 (2014) · Zbl 1296.74029 |
| [55] | Vahab, M.; Khalili, N., Computational algorithm for the anticipation of the fluid-lag zone in hydraulic fracturing treatments, Int. J. Geomech., 18, 10, Article 04018139 pp. (2018) |
| [56] | Adachi, J. I., Fluid-Driven Fracture in Permeable Rock (2002), University of Minnesota: University of Minnesota Minneapolis, (PhD. Thesis) |
| [57] | Adachi, J. I.; Detournay, E., Plane strain propagation of a hydraulic fracture in a permeable rock, Eng. Fract. Mech., 75, 16, 4666-4694 (2008) |
| [58] | Dontsov, E., An approximate solution for a plane strain hydraulic fracture that accounts for fracture toughness, fluid viscosity, and leak-off, Int. J. Fract., 205, 2, 221-237 (2017) |
| [59] | Garagash, D. I.; Detournay, E.; Adachi, J. I., Multiscale tip asymptotics in hydraulic fracture with leak-off, J. Fluid Mech., 669, 260-297 (2011) · Zbl 1225.76270 |
| [60] | Kanin, E. A.; Dontsov, E. V.; Garagash, D. I.; Osiptsov, A. A., A radial hydraulic fracture with pressure-dependent leak-off, J. Mech. Phys. Solids., 143, 104062 (2020) |
| [61] | McDaniel, R. R.; Deysarkar, A. K.; Callanan, M. J.; Kohlhaas, C. A., An improved method for measuring fluid loss at simulated fracture conditions, SPE J., 25, 04, 482-490 (1985) |
| [62] | Vahab, M.; Khalili, N., Empirical and conceptual challenges in Hydraulic Fracturing with Special reference to the Inflow, Int. J. Geomech., 20, 3, Article 04019182 pp. (2020) |
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