A coupled dual continuum and discrete fracture model for subsurface heat recovery with thermoporoelastic effects

  • Ammosov Dmitry A., dmitryammosov@gmail.com Multiscale model reduction laboratory, North-Eastern Federal University, Yakutsk 677980, Russia
  • Vasilyeva Maria V., vasilyevadotmdotv@gmail.com Department of Computational Technologies, North-Eastern Federal University, Yakutsk 677980, Russia; Institute for Scientific Computation, Texas A&M University, College Station, TX 77843-3368
  • Babaei Masoud, masoud.babaei@manchester.ac.uk The University of Manchester, School of Chemical Engineering and Analytical Science, Manchester, M13 9PL, UK
  • Chung Eric T., tschung@math.cuhk.edu.hk Department of Mathematics, The Chinese University of Hong Kong (CUHK), Hong Kong SAR
Keywords: thermoporoelasticity, heat recovery, double porosity and double permeability, dual continuum, discrete fracture model, finite element method, mathematical modeling

Abstract

We consider heat recovery from geothermal fractured resources with thermo-poroelastic effects. To this end, a hierarchical fracture representation is considered, where small-scale highly connected fractures are represented by the classical dual porosity model whereas large scale dense fractures are represented by the discrete fracture model. The mathematical model is described by a system of equations for mass and heat transfer for coupled dual continuum model as well as discrete fractures. Geomechanical deformations are written in the general form. For numerical solution of the resultant coupled system of equations including multicontinuum temperatures, pressures and deformations, we use the finite-element method. Numerical results are presented for two- and three-dimensional examples, showing applicability of the proposed method.

References


[1]
Karvounis D. C., Simulations of Enhanced Geothermal Systems with an Adaptive Hierarchical Fracture Representation, Diss. Doct. Sci., ETH Zurich, Zurich (2013).

[2]
Sandve T. H., Berre I., Keilegavlen E., and Nordbotten J. M., “Multiscale simulation of flow and heat transport in fractured geothermal reservoirs: inexact solvers and improved transport upscaling,” in: 38th Workshop Geothermal Reservoir Engineering 2013, Stanford Geothermal Program, 1, 575–583 (2013).

[3]
Akkutlu I. Y., Efendiev Y., and Vasilyeva M., “Multiscale model reduction for shale gas transport in fractured media,” Comput. Geosci., 20, No. 5, 953–973 (2016).

[4]
Akkutlu I. Y., Efendiev Y., Vasilyeva M., and Wang Y., “Multiscale model reduction for shale gas transport in a coupled discrete fracture and dual-continuum porous media,” J. Nat. Gas Sci. Eng., 48, 65–76 (2017).

[5]
Praditia T., Helmig R., and Hajibeygi H., “Multiscale formulation for coupled flow-heat equations arising from single-phase flow in fractured geothermal reservoirs,” Comput. Geosci., 22, No. 5, 1305–1322 (2018).

[6]
Salimzadeh S., Nick H. M., and Zimmerman R. W., “Thermoporoelastic effects during heat extraction from low-permeability reservoirs,” Energy, 142, 546–558 (2018).

[7]
Wang X. and Ghassemi A., “A 3D thermal-poroelastic model for geothermal reservoir stimulation,” in: 37th Workshop Geothermal Reservoir Engineering 2012, Stanford Geothermal Program, 1, 936–946 (2012).

[8]
Karvounis D. C. and Jenny P., “Adaptive hierarchical fracture model for enhanced geothermal systems,” Multiscale Modeling & Simulation, 14, No. 1, 207–231 (2016).

[9]
Hao Y., Fu P., and Carrigan C. R., “Application of a dual-continuum model for simulation of fluid flow and heat transfer in fractured geothermal reservoirs,” in: 38th Workshop on Geothermal Reservoir Engineering 2013, Stanford Geothermal Program, 1, 462–469 (2013).

[10]
Nissen A., Keilegavlen E., Sandve T. H., Berre I., and Nordbotten J. M., “Heterogeneity preserving upscaling for heat transport in fractured geothermal reservoirs,” Comput. Geosci., 22, No. 2, 451–467 (2018).

[11]
Salimzadeh S., Paluszny A., Nick H. M., and Zimmerman R.W., “A three-dimensional coupled thermo-hydro-mechanical model for deformable fractured geothermal systems,” Geothermics, 71, 212–224 (2018).

[12]
Barenblatt G. I., Zheltov Iu. P., and Kochina I. N., “Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks [strata],” J. Appl. Math. Mech., 24, No. 5, 1286–1303 (1960).

[13]
Arbogast T., Douglas J., Jr., and Hornung U., “Derivation of the double porosity model of single phase flow via homogenization theory,” SIAM J. Math. Anal., 21, No. 4, 823–836 (1990).

[14]
Kazemi H., Merrill L. S., Jr., Porterfield K. L., and Zeman P. R., “Numerical simulation of water-oil flow in naturally fractured reservoirs,” Soc. Petrol. Eng. J., 16, No. 6, 317–326 (1976).

[15]
Warren J. E. and Root P. J., “The behavior of naturally fractured reservoirs,” Soc. Petrol. Eng. J., 3, No. 3, 245–255 (1963).

[16]
Vasilyeva M., Chung E. T., LeungW. T., and Alekseev V., “Nonlocal multicontinuum (NLMC) upscaling of mixed dimensional coupled flow problem for embedded and discrete fracture models,” 2018. arXiv preprint arXiv:1805.09407

[17]
Karimi-Fard M., Durlofsky L. J., and Aziz K., “An efficient discrete fracture model applicable for general purpose reservoir simulators,” SPE Reservoir Simulation Symp., Soc. Petrol. Eng., 2003.

[18]
Lee S. H., Jensen C. L., and Lough M. F., “Efficient finite-difference model for flow in a reservoir with multiple length-scale fractures,” Soc. Petrol. Eng. J., 5, No. 3, 268–275 (2000).

[19]
Vasilyeva M., Chung E. T., Cheung S. W., Wang Y., and Prokopiev G., “Nonlocal multicontinua upscaling for multicontinua flow problems in fractured porous media,” arXiv preprint arXiv:1807.05656 (2018).

[20]
Martin V., Jaffr´e J., and Roberts J. E., “Modeling fractures and barriers as interfaces for flow in porous media,” SIAM J. Sci. Comput., 26, No. 5, 1667–1691 (2005).

[21]
D’Angelo C. and Quarteroni A., “On the coupling of 1D and 3D diffusion-reaction equations: application to tissue perfusion problems,” Math. Models Meth. Appl. Sci., 18, No. 8, 1481–1504 (2008).

[22]
Formaggia L., Fumagalli A., Scotti A., and Ruffo P., “A reduced model for Darcy’s problem in networks of fractures,” ESAIM: Math. Model. Numer. Anal., 48, No. 4, 1089–1116 (2014).

[23]
D’Angelo C. and Scotti A., “A mixed finite element method for Darcy flow in fractured porous media with non-matching grids,” ESAIM: Math. Model. Numer. Anal., 46, No. 2, 465–489 (2012).

[24]
Gong B., Karimi-Fard M., and Durlofsky L. J., “Upscaling discrete fracture characterizations to dual-porosity, dual-permeability models for efficient simulation of flow with strong gravitational effects,” Soc. Petrol. Eng. J., 13, No. 1, 58–67 (2008).

[25]
Chung E. T., Efendiev Y., Leung T., and Vasilyeva M., “Coupling of multiscale and multi-continuum approaches,” GEM-Int. J. Geomath., 8, No. 1, 9–41 (2017).

[26]
Vasilyeva M., Babaei M., Chung E. T., and Spiridonov D., “Multiscale modelling of heat and mass transfer in fractured media for enhanced geothermal systems applications,” Appl. Math. Model., 67, 159–178 (2018).

[27]
Vasilyeva M. and Tyrylgin A., “Machine learning for accelerating effective property prediction for poroelasticity problem in stochastic media,” arXiv preprint arXiv:1810.01586 (2018).

[28]
Vasilyeva M., Chung E. T., Efendiev Y., and Kim J., “Constrained energy minimization based upscaling for coupled flow and mechanics,” arXiv preprint arXiv:1805.09382 (2018).

[29]
Akkutlu I. Y., Efendiev Y., Vasilyeva M., and Wang Y., “Multiscale model reduction for shale gas transport in poroelastic fractured media,” J. Comput. Phys., 353, 356–376 (2018).

[30]
Coussy O., Poromechanics, John Wiley & Sons, Chichester (2004).

[31]
Logg A., Mardal K.-A., and Wells G. (ed.), Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book, Springer Science & Business Media, New York (2012).
How to Cite
Ammosov, D., Vasilyeva, M., Babaei, M. and Chung, E. ( ) “A coupled dual continuum and discrete fracture model for subsurface heat recovery with thermoporoelastic effects”, Mathematical notes of NEFU, 26(1), pp. 93-105. doi: https://doi.org/10.25587/SVFU.2019.101.27250.
Section
Mathematical Modeling