A tight sandstone multi-physical hydraulic fractures simulator study and its field application

Abstract

During the past years, the recovery of unconventional gas formation has attracted lots of attention and achieved huge success. To produce gas from the low-permeability unconventional formations, hydraulic fracturing technology is essential and critical. In this paper, we present the development of a three-dimensional thermal-hydraulic-mechanical numerical simulator for the simulation of hydraulic fracturing operations in tight sandstone reservoirs. Our simulator is based on integrated finite difference (IFD) method. In this method, the simulation domain is subdivided into sub domains and the governing equations are integrated over a sub domain with flux terms expressed as an integral over the sub domain boundary using the divergence theorem. Our simulator conducts coupled thermal-hydraulic-mechanical simulation of the initiation and extension of hydraulic fractures. It also calculates the mass/heat transport of injected hydraulic fluids as well as proppants. Our simulator is able to handle anisotropic formations with multiple layers. Our simulator has been validated by comparing with an analytical solution as well as Ribeiro and Sharma model. Our model can simulate fracture spacing effect on fracture profile when combining IFD with Discontinuous Displacement Method(DDM).

Keywords

Tight sandstone / Hydraulic fracture simulator / Integrated finite difference discretization / Stress contrast

References

[1] T.K. Perkins, L.R. Kern, Widths of hydraulic fractures, J. Pet. Technol. 13 (1961) 937-949 https://doi.org/10.2118/89-PA.

[2] I.N. Sneddon,The distribution of stress in the neighbourhood of a crack in an elastic solid, Proc. R. Soc. A Math. Phys. Eng. Sci. 187 (1946) 229-260.

[3] R.P. Nordgren, Propagation of a vertical hydraulic fracture, Soc. Petrol. Eng. J. 12 (1972) 306-314 https://doi.org/10.2118/3009-PA.

[4] J. Geertsma, F. De Klerk, A rapid method of predicting width and extent of hydraulically induced fractures, J. Pet. Technol. 21 (1969) 1571-1581 https://doi.org/10.2118/2458-PA.

[5] S.H. Advani, T.S. Lee, J.K. Lee, Three-dimensional modeling of hydraulic fractures in layered media: Part I—finite element formulations, J. Energy Resour. Technol. 112 (1990) 1 https://doi.org/10.1115/1.2905706.

[6] R.G. Baca, R.C. Arnett, D.W. Langford, Modelling fluid flow in fractured-porous rock masses by finite-element techniques, Int. J. Numer. Methods Fluids 4 (1984) 337-348 https://doi.org/10.1002/fld.1650040404.

[7] Z. Chen, Finite element modelling of viscosity-dominated hydraulic fractures, J. Pet. Sci. Eng. 88-89 (2012) 136-144 https://doi.org/10.1016/J.PETROL.2011.12.021.

[8] N. Moes, T. Belytschko, Extended finite element method for cohesive crack growth, Eng. Fract. Mech. 69 (2002) 813-833 https://doi.org/10.1016/S0013-7944(01)00128-X.

[9] N. Moes, J. Dolbow, T. Belytschko, A finite element method for crack growth without remeshing, Int. J. Numer. Methods Eng. 46 (1999) 131-150 https://doi. org/10.1002/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.0.CO;2-J.

[10] N. Sukumar, N. Moes, B. Moran, T. Belytschko, Extended finite element method for three-dimensional crack modelling, Int. J. Numer. Methods Eng. 48 (2000) 1549-1570 https://doi.org/10.1002/1097-0207(20000820)48:11<1549::AIDNME955>3.0.CO;2-A.

[11] B. Lecampion, An extended finite element method for hydraulic fracture problems, Commun. Numer. Methods Eng. 25 (2009) 121-133 https://doi.org/10.1002/cnm.1111.

[12] T. Mohammadnejad, A.R. Khoei, An extended finite element method for hydraulic fracture propagation in deformable porous media with the cohesive crack model, Finite Elem. Anal. Des. 73 (2013) 77-95 https://doi.org/10.1016/J.FINEL.2013.05.005.

[13] S. Salimzadeh, N. Khalili, A three-phase XFEM model for hydraulic fracturing with cohesive crack propagation, Comput. Geotech. 69 (2015) 82-92 https://doi.org/10.1016/J.COMPGEO.2015.05.001.

[14] K. Wu, J.E. Olson, Simultaneous multifracture treatments: fully coupled fluid flow and fracture mechanics for horizontal wells, SPE J. 20 (2015) 337-346 https://doi.org/10.2118/167626-PA.

[15] K. Wu, J.E. Olson, Mechanics analysis of interaction between hydraulic and natural fractures in shale reservoirs, Unconventional Resources Technology Conference (URTEC). Denver, CO, 2014 https://doi.org/10.15530/URTEC-2014-1922946.

[16] K. Wu, J.E. Olson, Investigation of the impact of fracture spacing and fluid properties for interfering simultaneously or sequentially generated hydraulic fractures, SPE Prod. Oper. 28 (2013) 427-436 https://doi.org/10.2118/163821-PA.

[17] S.L. Crouch,Solution of plane elasticity problems by the displacement discontinuity method. I. Infinite body solution, Int. J. Numer. Methods Eng. 10 (1976) 301-343.

[18] S. Li, X. Li, D. Zhang, A fully coupled thermo-hydro-mechanical, three-dimensional model for hydraulic stimulation treatments, J. Nat. Gas Sci. Eng. 34 (2016) 64-84 https://doi.org/10.1016/J.JNGSE.2016.06.046.

[19] K. Wu, J.E. Olson, M.T. Balhoff, W. Yu, Numerical analysis of promoting moreuniform development of simultaneous multiple fracture propagation in horizontal wells, SPE Prod. Oper. 32 (01) (2017).

[20] H. Tang, P.H. Winterfeld, Y.-S. Wu, Z. Huang, Y. Di, Z. Pan, J. Zhang, Integrated simulation of multi-stage hydraulic fracturing in unconventional reservoirs, J. Nat. Gas Sci. Eng. 36 (2016) 875-892 https://doi.org/10.1016/j.jngse.2016.11.018.

[21] S. Prashanth, K. Wu, K. Joseph, Optimizaiton of simultaneously propagating multiple fractures in hydraulic fracturing to achieve uniform growth using data-based model reduction, Chem. Eng. Res. Des. 136 (2018) 675-686.

[22] X. Guo, K. Wu, C. An, J. Tang, J. Killough,Numerical investigation of effects of subsequent parent well injection on Interwell fracturing interference using reservoir-geomechanics-fracturing modeling, SPE J. (2018) accepted https://doi.org/10.2118/195580-PA.

[23] W. Yu, Y. Xu, R. Weijermars, K. Wu, K. Sepehrnoori, A numerical model for simulating pressure response of well interference and well performance in tight oil reservoirs with complex-fracture geometries using the fast embedded-discretefracture-model method, SPE Reservoir Eval. Eng. 21 (02) (2018) 489-502 https://doi.org/10.2118/184825-PA.

[24] W. Yu, Y. Xu, M. Liu, K. Wu, K. Sepehrnoori, Simulation of shale gas transport and production with complex fractures using embedded discrete fracture model, AIChE J. 64 (06) (2018) 2251-2264.

[25] C.H. Yew, X. Weng, Mechanics of Hydraulic Fracturing, second ed., Gulf Professional Publishing, Waltham, MA, 2015.

[26] E.N. Mastrojannis, L.M. Keer, T. Mura, Growth of planar cracks induced by hydraulic fracturing, Int. J. Numer. Methods Eng. 15 (1980) 41-54 https://doi.org/10.1002/nme.1620150105.

[27] A.E.H. Love, E.H. Augustus, A Treatise on the Mathematical Theory of Elasticity, Cambridge University Press, 2013.

[28] K.E. Friehauf, Simulation and Design of Energized Hydraulic Fractures, The University of Texas at Austin, 2009.

[29] T.N. Narasimhan, P.A. Witherspoon, An integrated finite difference method for analyzing fluid flow in porous media, Water Resour. Res. 12 (1976) 57-64 https://doi.org/10.1029/WR012i001p00057.

[30] K. Pruess, A practical method for modeling fluid and heat flow in fractured porous media, Soc. Petrol. Eng. J. 25 (1985) 14-26 https://doi.org/10.2118/10509-PA.

[31] L. Ribeiro, M.M. Sharma, A new three-dimensional, compositional, model for hydraulic fracturing with energized fluids, SPE Annual Technical Conference and Exhibition. Soc. Petrol. Eng, 2012. Y. Wang, et al. Petroleum 6 (2020) 198-205 205