Abstract
A hydromechanical model with explicit fracture flow is presented for the fully coupled analysis of flow and deformation in fractured porous media. Extended finite-element method (XFEM) was utilized to model the fracture discontinuity in the two-dimensional plane-strain mechanical model. Two flow models, a one-dimensional laminar flow within the fracture and a two-dimensional Darcy flow through porous media, were considered. The flow domains were coupled through a mass exchange term (leak-off) accounting for discontinuous Darcy flow velocity across the fracture. Particular attention was given to the coupling of the flow domains with the mechanical model. Spatial and temporal discretization was achieved using the standard Galerkin method and the finite-difference technique, respectively. Unlike the successive coupled models in which the results of the mechanical model are used to update the fracture flow model and vice versa, the fully coupled hydromechanical formulation is solved simultaneously. The model was verified against several closed-form solutions from the literature. The impact of coupled fracture flow and formation flow on the fracture response to external mechanical loading as well as internal hydraulic loading from fluid injection was investigated, and the results are discussed.
Get full access to this article
View all available purchase options and get full access to this article.
References
Adachi, J., Siebrits, E., Peirce, A., and Desroches, J. (2007). “Computer simulation of hydraulic fractures.” Int. J. Rock Mech. Min. Sci., 44(5), 739–757.
Aliabadi, M. H., and Brebbia, C. A. (1993). Advanced formulations in boundary element methods, Elsevier Applied Science, London.
Anderson, E. (2014). “Exact and approximate solutions for seepage through semipermeable cutoff walls.” Int. J. Geomech., 04014087.
Areias, P. M., Song, J., and Belytschko, T. (2006). “Analysis of fracture in thin shells by overlapping paired elements.” Comput. Methods Appl. Mech. Eng., 195(41–43), 5343–5360.
Asferg, J. L., Poulsen, P. N., and Nielsen, L. O. (2007). “A consistent partly cracked XFEM element for cohesive crack growth.” Int. J. Numer. Methods Eng., 72(4), 464–485.
Batchelor, G. K. (1967). An introduction to fluid dynamics, Cambridge University Press, Cambridge, U.K.
Belytschko, T., and Black, T. (1999). “Elastic crack growth in finite elements with minimal remeshing.” Int. J. Numer. Methods Eng., 45(5), 601–620.
Berumen, S., Tiab, D., and Rodriguez, F. (2000). “Constant rate solutions for a fractured well with an asymmetric fracture.” J. Pet. Sci. Eng., 25(1–2), 49–58.
Bittencourt, T. N., Ingraffea, A. R., and Llorca, J. (1992). “Simulation of arbitrary, cohesive crack propagation.” Fracture mechanics of concrete structures, Z. P., Bazant, ed.,Elsevier, London, 339–350.
Board, M., Rorke, T., Williams, G., and Gay, N. (1992). “Fluid injection for rock burst control in deep mining.” Proc., 33rd U.S. Symp. on Rock Mechanics, J. R. Tillerson and W. R. Wawersik, ed., Balkema, Rotterdam, 111–20.
Budyn, E., Zi, G., Moës, N., and Belytschko, T. (2004). “A method for multiple crack growth in brittle materials without remeshing.” Int. J. Numer. Methods Eng., 61(10), 1741–1770.
Carrier, B., and Granet, S. (2012). “Numerical modeling of hydraulic fracture problem in permeable medium using cohesive zone model.” Eng. Fract. Mech.79, 312–328.
Carter, B. J., Wawrzynek, P. A., and Ingraffea, A. R. (2000). “Automated 3-d crack growth simulation.” Int. J. Numer. Methods Eng., 47(1–3), 229–253.
Curtin, W. A., and Scher, H. (1990). “Mechanics modeling using a spring network.” J. Mater. Res., 5(3), 554–562.
Dahi-Taleghani, A. (2009). “Analysis of hydraulic fracture propagation in fractured reservoirs: An improved model for the interaction between induced and natural fractures.” Ph.D. dissertation, Univ. of Texas, Austin, TX.
Daneshy, A. A. (1973). “On the design of vertical hydraulic fractures.” J. Pet. Technol., 25(1), 83–97.
de Borst, R., Rethore, J., and Abellan, M. (2006). “A numerical approach for arbitrary cracks in a fluid-saturated medium.” Arch. Appl. Mech., 75(10), 595–606.
Detournay, E. (2004). “Propagation regimes of fluid-driven fractures in impermeable rocks.” Int. J. Geomech., 35–45.
Duflot, M., (2008). “The extended finite element method in thermoelastic fracture mechanics.” Int. J. Numer. Methods Eng., 74(5), 827–847.
Economides, M. J., Nolte, K. G., and Ahmed, U. (1989). Reservoir stimulation, Prentice Hall, Englewood Cliffs, NJ.
Fu, P., Johnson, S. M., and Carrigan, C. R. (2013). “An explicitly coupled hydro-geomechanical model for simulating hydraulic fracturing in arbitrary discrete fracture networks.” Int. J. Numer. Anal. Methods Geomech., 37(14), 2278–2300.
Geertsma, J., and de Klerk, F. (1969). “A rapid method of predicting width and extent of hydraulically induced fractures.” J. Pet. Technol., 21(12), 1571–1581.
Hainey, B. W., Keck, R. G., Smith, M. B., Lynch, K. W., and Barth, J. W. (1999). “On-site fracturing disposal of oilfield-waste solids in Wilmington field, California.” SPE Prod. Facil., 14(2), 88–93.
Hughes, T. J. R. (1987). “The finite element method.” Linear static and dynamic finite element analysis, Prentice-Hall, Englewood Cliffs, NJ.
Indraratna, B., Kumara, C., Zhu, S., and Sloan, S. (2014). “Mathematical modeling and experimental verification of fluid flow through deformable rough rock joints.” Int. J. Geomech., 04014065.
Jha, B., and Juanes, R. (2014). “Coupled multiphase flow and poromechanics: A computational model of pore pressure effects on fault slip and earthquake triggering.” Water Resour. Res., 50(5), 3776–3808.
Jirasek, M. (2000). “Comparative study on finite elements with embedded discontinuities.” Comput. Methods Appl. Mech. Eng., 188(1–3), 307–330.
Khoei, A. R., Vahab, M., Haghighat, E., and Moallemi, S. (2014). “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.
Mack, M. G., and Warpinski, N. R. (2000). “Mechanics of hydraulic fracturing.” Chapter 6, Reservoir stimulation, 3rd Ed.,M. J. Economidesand K. G. Nolte, eds., Wiley, Chichester, U.K.
Merle, R., and Dolbow, J. (2002). “Solving thermal and phase change problems with the extended finite element method.” Comput. Mech., 28(5), 339–350.
Moës, N., Dolbow, J., and Belytschko, T. (1999). “A finite element method for crack growth without remeshing.” Int. J. Numer. Methods Eng., 46(1), 131–150.
Moës, N., Gravouil, A., and Belytschko, T. (2002). “Non-planar 3D crack growth by the extended finite element and level sets—Part I: Mechanical model.” Int. J. Numer. Methods Eng., 53(11), 2549–2568.
Mohammadnejad, T., and Khoei, A. R. (2013). “Hydro-mechanical modeling of cohesive crack propagation in multiphase porous media using the extended finite element method.” Int. J. Numer. Anal. Methods Geomech., 37(10), 1247–1279.
Murdoch, L. C., and Slack, W. W. (2002). “Forms of hydraulic fractures in shallow fine grained formations.” J. Geotech. Geoenviron. Eng., 479–487.
Raaen, A. M., Skomedal, E., Kjørholt, H., Markestad, P., and Økland, D. (2001). “Stress determination from hydraulic fracturing tests: The system stiffness approach.” Int. J. Rock Mech. Min. Sci., 38(4), 529–541.
Rethore, J., de Borst, R., and Abellan, M. A. (2007). “A two-scale approach for fluid flow in fractured porous media.” Int. J. Numer. Methods. Eng., 71(7), 780–800.
Rethore, J., de Borst, R., and Abellan, M. A. (2008). “A two-scale model for fluid flow in an unsaturated porous medium with cohesive cracks.” Comput. Mech., 42(2), 227–238.
Réthoré, J., Gravouil, A., and Combescure, A. (2005). “A combined space time extended finite element method.” Int. J. Numer. Methods Eng., 64(2), 260–284.
Salimzadeh, S., and Khalili, N. (2014). “Consolidation of unsaturated lumpy clays.” J. Geo-Eng. Sci., 2(1–2), 67–82.
Salimzadeh, S., and Khalili, N. (2015a). “Three-dimensional numerical model for double-porosity media with two miscible fluids including geomechanical response.” Int. J. Geomech., 04015065
Salimzadeh, S., and Khalili, N. (2015b). “A three-phase XFEM model for hydraulic fracturing with cohesive crack propagation.” Comput. Geotech., 69, 82–92.
Sasaki, S. (1998). “Characteristics of microseismic events induced during hydraulic fracturing experiments at the Hijiori hot dry rock geothermal energy site, Yamagata, Japan.” Tectonophysics, 289(1–3), 171–188.
Shao, Q., Bouhala, L., Younes, A., Núñez, P., Makradi, A., and Belouettar, S. (2014). “An XFEM model for cracked porous media: Effects of fluid flow and heat transfer.” Int. J. Fract., 185(1–2), 155–169.
Simone, A., Duarte, C. A., and Van der Giessen, E. (2006). “A generalized finite element method for polycrystals with discontinuous grain boundaries.” Int. J. Numer. Methods Eng., 67(8), 1122–1145.
Spence, D. A., and Sharp, P. (1985). “Self-similar solutions for elastohydrodynamic cavity flow.” Proc. R. Soc. London Ser. A, 400(1819), 289–313.
Song, J. H., Areias, P. M. A., and Belytschko, T. (2006). “A method for dynamic crack and shear band propagation with phantom nodes.” Int. J. Numer. Methods Eng., 67(6), 868–893.
Sukumar, N., Moës, N., Moran, B., and Belytschko, T. (2000). “Extended finite element method for three-dimensional crack modelling.” Int. J. Numer. Methods Eng., 48(11), 1549–1570.
Usmani, A., Kannan, G., Nanda, A., and Jain, S. (2015). “Seepage behavior and grouting effects for large rock caverns.” Int. J. Geomech., 06014023.
Ventura, G., Moran, B., and Belytschko, T. (2005). “Dislocations by partition of unity.” Int. J. Numer. Methods Eng., 62(11), 1463–1487.
Warpinski, N. R. (1990). Dual leak-off behavior in hydraulic fracturing of tight, lenticular gas sands, SPE Prod. Eng., 5(3), 18259.
Wells, G. N., and Sluys, L. J. (2001). “A new method for modelling cohesive cracks using finite elements.” Int. J. Numer. Methods Eng., 50(12), 2667–2682.
Witherspoon, P. A., Wang, J. S. Y., Iwai, K., and Gale, J. E. (1980). “Validity of cubic law for fluid flow in a deformable rock fracture.” Water Resour. Res., 16(6), 1016–1024.
Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 16 • Issue 4 • August 2016
Copyright
© 2015 American Society of Civil Engineers.
History
Received: Nov 10, 2014
Accepted: Oct 13, 2015
Published online: Dec 31, 2015
Discussion open until: May 31, 2016
Published in print: Aug 1, 2016
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.