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Discrete fracture model for coupled flow and geomechanics

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Abstract

We present a fully implicit formulation of coupled flow and geomechanics for fractured three-dimensional subsurface formations. The Reservoir Characterization Model (RCM) consists of a computational grid, in which the fractures are represented explicitly. The Discrete Fracture Model (DFM) has been widely used to model the flow and transport in natural geological porous formations. Here, we extend the DFM approach to model deformation. The flow equations are discretized using a finite-volume method, and the poroelasticity equations are discretized using a Galerkin finite-element approximation. The two discretizations—flow and mechanics—share the same three-dimensional unstructured grid. The mechanical behavior of the fractures is modeled as a contact problem between two computational planes. The set of fully coupled nonlinear equations is solved implicitly. The implementation is validated for two problems with analytical solutions. The methodology is then applied to a shale-gas production scenario where a synthetic reservoir with 100 natural fractures is produced using a hydraulically fractured horizontal well.

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References

  1. Annavarapu, C., Hautefeuille, M., Dolbow J: A robust nitsche’s formulation for interface problems. Comput. Methods Appl. Mech. Eng. 225–228, 44–54 (2012)

    Article  Google Scholar 

  2. Bagheri, M., Settari, A.: Modeling of geomechanics in naturally fractured reservoirs. SPE Reserv. Eval. Eng. 11(1), 108–118 (2008)

    Article  Google Scholar 

  3. Bandis, S., Lumsden, A., Barton, N.: Fundamentals of rock joint deformation. Int. J. Rock Mech. Min. Sci. 20(6), 249–268 (1983)

    Article  Google Scholar 

  4. Barsoum, R. S.: On the use of isoparametric finite elements in linear fracture mechanics. Int. J. Numer. Methods Eng. 10(1), 25–37 (1976)

    Article  Google Scholar 

  5. Barton, N., Bandis, S., Bakhtar, K.: Strength deformation and conductivity coupling of rock joints. Int. J. Rock Mech. Min. Sci. 22(3), 121–140 (1985)

    Article  Google Scholar 

  6. Biot, M.: General theory of three-dimensional consolidation. J. Appl. Phys. 12(2), 155–164 (1941)

    Article  Google Scholar 

  7. Borja, I.: Plasticity: modeling and computation. Springer (2013)

  8. Budhu, M.: Earth fissure formation from the mechanics of groundwater pum**. Int. J. Geomech. 11(1), 1–11 (2010)

    Article  Google Scholar 

  9. Chen, H., Teufel, L.: Coupling fluid-flow and geomechanics in dual-porosity modeling of naturally fractured reservoirs - model description and comparison. In: Proceedings of the SPE International Petroleum Conference and Exhibition of Mexico, pp. 483–492 (2000)

  10. Chen, Z., Narayan, S., Yang, Z., Rahman, S.: An experimental investigation of hydraulic behaviour of fractures and joints in granitic rock. Int. J. Rock Mech. Min. Sci. 37(7), 1061–1071 (2000)

    Article  Google Scholar 

  11. Coussy, O.: Poromechanics. Wiley (2004)

  12. Crouch, S., Staryeld, A.: Boundary element methods in solid mechanics. Unwin Hyman, London (1990)

  13. David, C., Wong, T.-F., Zhu, W., Zhang, J.: Laboratory measurement of compaction-induced permeability change in porous rocks: implications for the generation and maintenance of pore pressure excess in the crust. Pure Appl. Geophys. 143(1–3), 425–456 (1994)

    Article  Google Scholar 

  14. Dolbow, J., Moes, N., Belytschko, T.: An extended finite element method for modeling crack growth with frictional contact. Comput. Methods Appl. Mech. Eng. 190(51–52), 6825–6846 (2001)

    Article  Google Scholar 

  15. Dusseault, M.: Geomechanical challenges in petroleum reservoir exploitation. KSCE J. Civ. Eng. 15(4), 669–678 (2011)

    Article  Google Scholar 

  16. Eikemo, B., Lie, K.-A., Eigestad, G., Dahle, H.: Discontinuous galerkin methods for advective transport in single-continuum models of fractured media. Adv. Water Resour. 32(4), 493–506 (2009)

    Article  Google Scholar 

  17. Ferronato, M., Castelletto, N., Gambolati, G.: A fully coupled 3-d mixed finite element model of biot consolidation. J. Comput. Phys. 229(12), 4813–4830 (2010)

    Article  Google Scholar 

  18. Fredrich, J., Arguello, J., Deitrick, G., De Rouffignac, E.: Geomechanical modeling of reservoir compaction, surface subsidence, and casing damage at the belridge diatomite field. SPE Reserv. Eval. Eng. 3(4), 348–359 (2000)

    Article  Google Scholar 

  19. Garipov, T., Levonyan, K., Karimi-Fard, M., Tchelepi, H.: Coupled geomechanics and flow in fractured porous media. In: ECMOR 2012 - 13th European Conference on theMathematics of Oil Recovery (2012)

  20. Garipov T. T., Voskov, D., Tchelepi, H. A.: Rigorous coupling of geomechanics and thermal-compositional flow for sagd and es-sagd operations. In: SPE Canada Heavy Oil Technical Conference (2015)

  21. Geiger, S., Matthai, S., Niessner, J., Helmig, R.: Black-oil simulations for three-component, three-phase flow in fractured porous media. SPE J. 14(2), 338–354 (2009)

    Article  Google Scholar 

  22. Goodman, R.E.: Methods of geological engineering in discontinuous rocks. West Group (1975)

  23. Granet, S., Fabrie, P., Lemonnier, P., Quintard, M.: A two-phase flow simulation of a fractured reservoir using a new fissure element method. J. Pet. Sci. Eng. 32(1), 35–52 (2001)

    Article  Google Scholar 

  24. Hansbo, A., Hansbo, P.: An unfitted finite element method, based on nitsche’s method, for elliptic interface problems. Comput. Methods Appl. Mech. Eng. 191(47–48), 5537–5552 (2002)

    Article  Google Scholar 

  25. Henshell, R., Shaw, K.: Crack tip finite elements are unnecessary. Int. J. Numer. Methods Eng. 9(3), 495–507 (1975)

    Article  Google Scholar 

  26. Hoteit, H., Firoozabadi, A.: Multicomponent fluid flow by discontinuous galerkin and mixed methods in unfractured and fractured media. Water Resour. Res. 41(11), 1–15 (2005)

    Google Scholar 

  27. Hoteit, H., Firoozabadi, A.: An efficient numerical model for incompressible two-phase flow in fractured media. Adv. Water Resour. 31(6), 891–905 (2008)

    Article  Google Scholar 

  28. Huang, T., Chang, C., Chao, C.: Experimental and mathematical modeling for fracture of rock joint with regular asperities. Eng. Fract. Mech. 69(17), 1977–1996 (2002)

    Article  Google Scholar 

  29. Hughes, T.: The finite element method: linear static and dynamic finite element analysis. Courier Dover Publications (2012)

  30. Jha, B., Juanes, R.: 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 (2014)

    Article  Google Scholar 

  31. **g, L., Stephansson, O.: Fundamentals of discrete element methods for rock engineering theory and applications, vol. 85. Elsevier (2007)

  32. Juanes, R., Samper, J., Molinero, J.: A general and efficient formulation of fractures and boundary conditions in the finite element method. Int. J. Numer. Methods Eng. 54(12), 1751–1774 (2002)

    Article  Google Scholar 

  33. Karimi-Fard, M., Firoozabadi, A.: Numerical simulation of water injection in fractured media using the discrete-fracture model and the galerkin method. SPE Reserv. Eval. Eng. 6(2), 117–126 (2003)

    Article  Google Scholar 

  34. Karimi-Fard, M., Durlofsky, L., Aziz, K.: An efficient discrete-fracture model applicable for general-purpose reservoir simulators. SPE J. 9(2), 227–236 (2004)

    Article  Google Scholar 

  35. Kikuchi, N., Oden, J.: Contact problems in elasticity. SIAM (1988)

  36. Kim, J., Tchelepi, H., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Eng. 200(13–16), 1591–1606 (2011)

    Article  Google Scholar 

  37. Kim, J.-G., Deo, M.: Finite element, discrete-fracture model for multiphase flow in porous media. AIChE J. 46(6), 1120–1130 (2000)

    Article  Google Scholar 

  38. Lamb, H.: Hydrodynamics. Cambridge University Press (1932)

  39. Liu, F., Borja, R.: Stabilized low-order finite elements for frictional contact with the extended finite element method. Comput. Methods Appl. Mech. Eng. 199(37–40), 2456–2471 (2010)

    Article  Google Scholar 

  40. Mandel, J.: Consolidation des sols. Geotechnique, 30 (1953)

  41. Martin, V., Jaffre, J., Roberts, J.: Modeling fractures and barriers as interfaces for flow in porous media. SIAM J. Sci. Comput. 26(5), 1667–1691 (2005)

    Article  Google Scholar 

  42. Matthai, S., Mezentsev, A., Belayneh, M.: Finite element-node-centered finite-volume two-phase-flow experiments with fractured rock represented by unstructured hybrid-element meshes. SPE Reserv. Eval. Eng. 10(6), 740–756 (2007)

    Article  Google Scholar 

  43. Maxwell, S., Urbancic, T., Steinsberger, N., Zinno, R.: Microseismic imaging of hydraulic fracture complexity, in the barnett shale. In: Proceedings - SPE Annual Technical Conference and Exhibition, p.p 965–973 (2002)

  44. Mikelic, A., Wheeler, M.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013)

    Article  Google Scholar 

  45. Moes, N., Dolbow, J., Belytschko, T.: A finite element method for crack growth without remeshing. Int. J. Numer. Methods Eng. 46(1), 131–150 (1999)

    Article  Google Scholar 

  46. Moinfar, A., Sepehrnoori, K., Johns, R., Varavei, A.: Coupled geomechanics and flow simulation for an embedded discrete fracture model. In: Society of Petroleum Engineers - SPE Reservoir Simulation Symposium 2013, vol. 2, pp. 1238–1250 (2013)

  47. Monteagudo, J., Firoozabadi, A.: Control-volume method for numerical simulation of two-phase immiscible flow in two- and three-dimensional discrete-fractured media. Water Resour. Res. 40(7), W074,051–W0740,520 (2004)

    Google Scholar 

  48. Monteagudo, J., Rodriguez, A., Florez, H.: Simulation of flow in discrete deformable fractured porous media. In: Society of Petroleum Engineers - SPE Reservoir Simulation Symposium 2011, vol. 1, pp. 276–291 (2011)

  49. Nocedal, J., Wright, S.: Numerical Optimization. Springer (2002)

  50. Nordbotten, J.: Finite volume hydromechanical simulation in porous media. Water Resour. Res. 50(5), 4379–4394 (2014)

    Article  Google Scholar 

  51. Oden, J., Martins, J.: Models and computational methods for dynamic friction phenomena. Comput. Methods Appl. Mech. Eng. 52(1–3) (1985)

  52. Palmer, I., Moschovidis, Z., Cameron, J.: Modeling shear failure and stimulation of the barnett shale after hydraulic fracturing. In: SPE - Hydraulic Fracturing Technology Conference 2007, vol. 2007, pp. 279–287 (2007)

  53. Phan, A.-V., Napier, J., Gray, L., Kaplan, T.: Symmetric-galerkin bem simulation of fracture with frictional contact. Int. J. Numer. Methods Eng. 57(6), 835–851 (2003)

    Article  Google Scholar 

  54. Puso, M., Laursen, T.: A mortar segment-to-segment frictional contact method for large deformations. Comput. Methods Appl. Mech. Eng. 193(45–47), 4891–4913 (2004)

    Article  Google Scholar 

  55. Rutqvist, J., Stephansson, O.: The role of hydromechanical coupling in fractured rock engineering. Hydrogeol. J. 11(1), 7–40 (2003)

    Article  Google Scholar 

  56. Rutqvist, J., Tsang, C.-F.: A study of caprock hydromechanical changes associated with co2-injection into a brine formation. Environ. Geol. 42(2–3), 296–305 (2002)

    Article  Google Scholar 

  57. Simo, J., Laursen, T.: An augmented lagrangian treatment of contact problems involving friction. Comput. Struct. 42(1), 97–116 (1992)

    Article  Google Scholar 

  58. Simo, J., Wriggers, P., Taylor, R.: A perturbed lagrangian formulation for the finite element solution of contact problems. Comput. Methods Appl. Mech. Eng. 50(2), 163–180 (1985)

    Article  Google Scholar 

  59. Sneddon, I. N., Berry, D. S.: The classical theory of elasticity. encyclopedia of physics (1958)

  60. Voskov, D., Tchelepi, H.: Comparison of nonlinear formulations for two-phase multi-component eos based simulation. J. Pet. Sci. Eng. 82–83, 101–111 (2012)

    Article  Google Scholar 

  61. Wriggers, P.: Computational contact mechanics. Wiley (2002)

  62. Younis, R.: Modern advances in software and solution algorithms for reservoir simulation. PhD thesis, Stanford University (2011)

  63. Zaydullin, R., Voskov, D., Tchelepi, H.: Nonlinear formulation based on eos-free method for compositional flow simulation. In: Proceedings - SPE Annual Technical Conference and Exhibition, vol. 4, pp. 3210–3223 (2011)

  64. Zhang, J., Kamenov, A., Zhu, D., Hill, A.: Laboratory measurement of hydraulic-fracture conductivities in the barnett shale. SPE Prod. Oper. 29(3), 216–227 (2014)

    Article  Google Scholar 

  65. Zhou, Y., Tchelepi, H., Mallison, B.: Automatic differentiation framework for compositional simulation on unstructured grids with multi-point discretization schemes. In: Society of Petroleum Engineers - SPE Reservoir Simulation Symposium 2011, vol. 1, pp. 607–624 (2011)

  66. Zienkiewicz, O., Taylor, R.: The finite element method for solid and structural mechanics. Elsevier (2005)

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  1. Energy Resources Engineering, Stanford University, Stanford, CA, 94305, USA

    T. T. Garipov, M. Karimi-Fard & H. A. Tchelepi

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  1. T. T. Garipov
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  2. M. Karimi-Fard
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Garipov, T.T., Karimi-Fard, M. & Tchelepi, H.A. Discrete fracture model for coupled flow and geomechanics. Comput Geosci 20, 149–160 (2016). https://doi.org/10.1007/s10596-015-9554-z

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