Adaptive Hierarchical Fracture Model for Enhanced Geothermal Systems
Abstract
In enhanced geothermal systems, cold working fluid (usually water) is injected into a fractured reservoir to enhance the efficiency of the power plant by increasing the conductivity of existing fractures and by creating new ones. For the modeling of single phase flow and transport in such dynamically changing fractured reservoirs, a new approach is presented. It is based on a hierarchical fracture representation that results in a network of multiple dominant fractures through which most of the mass flow occurs. These large fractures have a discrete representation, i.e., each fracture is represented by a lower dimensional continuum. A single continuum representation is also employed for the damaged matrix, which consists of many small and medium sized fractures accounted for by appropriate effective properties. The main advantage of the new approach is that no expensive remeshing of the domain is required whenever new fractures are added. Here, discretization and coupling between the different continua (damaged matrix with discrete dominant fractures) are explained. In order to remove singularities, kernel functions have been introduced in the governing equations to capture discontinuities like fractures and intersections thereof. This way transfer coefficients are well defined. Numerical verification studies involving flow and heat transport are presented and discussed. It has to be emphasized that geomechanics, rock chemistry, and upscaling are not topics of this paper.
Keywords
MSC codes
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
L. André, V. Rabemanana, and F.-D. Vuataz, Influence of water--rock interactions on fracture permeability of the deep reservoir at Soultz-sous-Forêts, France, Geothermics, 35 (2006), pp. 507--531.
2.
R. G. Baca, R. C. Arnett, and D. W. Langford, Modelling fluid flow in fractured-porous rock masses by finite-element techniques, Internat. J. Numer. Methods Fluids, 4 (1984), pp. 337--348.
3.
D. Bächler and T. Kohl, Coupled thermal--hydraulic--chemical modelling of enhanced geothermal systems, Geophys. J. Internat., 161 (2004), pp. 533--548.
4.
G. I. Barenblatt, Iu. P. Zheltov, and I. N. Kochina, Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks [strata], J. Appl. Math. Mech., 24 (1960), pp. 1286--1303.
5.
R. Bertani, Geothermal power generation in the world 2005--2010 update report, Geothermics, 41 (2012), pp. 1--29.
6.
O. Bour, A statistical scaling model for fracture network geometry, with validation on a multiscale mapping of a joint network, J. Geophys. Res., 107 (2002), 2113.
7.
K. M. Bower and G. Zyvoloski, A numerical model for thermo-hydro-mechanical coupling in fractured rock, Int. J. Rock Mech. Mining Sci., 34 (1997), pp. 1201--1211.
8.
D. Bruel, Using the migration of the induced seismicity as a constraint for fractured Hot Dry Rock reservoir modelling, Int. J. Rock Mech. Mining Sci., 44 (2007), pp. 1106--1117.
9.
T. Clemo and L. Smith, A hierarchical model for solute transport in fractured media, Water Resources Res., 33 (1997), pp. 1763--1783.
10.
D. Coumou, S. Matthäi, S. Geiger, and T. Driesner, A parallel FE--FV scheme to solve fluid flow in complex geologic media, Comput. Geosci., 34 (2008), pp. 1697--1707.
11.
D. Bruel and W. C. Jeong, Numerical modeling of the coupling between mechanical and hydraulic properties in a granite rock mass subjecto high-pressure injection experiments, in Proceedings of the 38th U.S. Symposium on Rock Mechanics, Washington, DC, 2001.
12.
W. S. Dershowitz and C. Fidelibus, Derivation of equivalent pipe network analogues for three-dimensional discrete fracture networks by the boundary element method, Water Resources Res., 35 (1999), pp. 2685--2691.
13.
K. Evans, Permeability creation and damage due to massive fluid injections into granite at $3.5$ km at Soultz: 2. Critical stress and fracture strength, J. Geophys. Res., 110 (2005).
14.
K. F. Evans, Permeability creation and damage due to massive fluid injections into granite at $3.5$ km at Soultz: 1. Borehole observations, J. Geophys. Res., 110 (2005), B04203.
15.
S. Finsterle, Using the continuum approach to model unsaturated flow in fractured rock, Water Resources Res., 36 (2000), pp. 2055--2066.
16.
P. Fu, Y. Hao, and C. R. Carrigan, A Geomechanical Mechanism that Counteracts Flow Channeling Induced by Reservoir Thermal Drawdown, Stanford University, Stanford, CA, 2013.
17.
P. Fu, S. M. Johnson, and C. R. Carrigan, An explicitly coupled hydro-geomechanical model for simulating hydraulic fracturing in arbitrary discrete fracture networks, 37 (2013), pp. 2278--2300.
18.
S. Geiger, T. Driesner, C. A. Heinrich, and S. K. Matthäi, Multiphase thermohaline convection in the Earth's crust: II. Benchmarking and application of a finite element -- finite volume solution technique with a NaCl--H2O equation of state, Transp. Porous Media, 63 (2006), pp. 435--461.
19.
S. Geiger and S. Emmanuel, Non-Fourier thermal transport in fractured geological media, Water Resources Res., 46 (2010).
20.
D. Giardini, Geothermal quake risks must be faced, Nature, 462 (2009), pp. 848--849.
21.
H. Hajibeygi, D. Karvounis, and P. Jenny, A hierarchical fracture model for the iterative multiscale finite volume method, J. Comput. Phys., 230 (2011), pp. 8729--8743.
22.
M.-H. Hui, B. Mallison, and K.-T. Lim, An innovative workflow to model fractures in a giant carbonate reservoir, in Proceedings of the International Petroleum Technology Conference, Society of Petroleum Engineers, 2008.
23.
Z. Jing, J. Willis-Richards, K. Watanabe, and T. Hashida, A three-dimensional stochastic rock mechanics model of engineered geothermal systems in fractured crystalline rock, J. Geophys. Res., 105 (2000), 23663.
24.
R. Juanes, J. Samper, and J. Molinero, A general and efficient formulation of fractures and boundary conditions in the finite element method, Internat. J. Numer. Methods Engrg., 54 (2002), pp. 1751--1774.
25.
E. A. Kalinina, K. A. Klise, S. A. Mckenna, T. Hadgu, and T. S. Lowry, Applications of fractured continuum model to enhanced geothermal system heat extraction problems, SpringerPlus, 3 (2014), pp. 1--13.
26.
M. Karimi-Fard, L. J. Durlofsky, and K. Aziz, An efficient discrete-fracture model applicable for general-purpose reservoir simulators, SPE Journal, 9 (2004), pp. 227--236.
27.
M. Karimi-Fard and A. Firoozabadi, Numerical simulation of water injection in $2$D fractured media using discrete-fracture model, in Proceedings of the SPE Annual Technical Conference and Exhibition, Society of Petroleum Engineers, 2001.
28.
D. Karvounis and P. Jenny, Modeling of flow and transport in enhanced geothermal systems, in the Thirty-Sixth Workshop on Geothermal Reservoir Engineering, Stanford University, Stanford, CA, 2011.
29.
D. Karvounis and P. Jenny, Modeling of flow and transport for EGS cost optimization problems, in the Thirty-Seventh Workshop on Geothermal Reservoir Engineering, Stanford University, Stanford, CA, 2012.
30.
H. Kazemi, L. S. Merrill, K. L. Porterfield, and P. R. Zeman, Numerical simulation of water-oil flow in naturally fractured reservoirs, SPE Journal, 16 (1976), pp. 317--336.
31.
J. Ketilsson, R. Podgorney, T. Driesner, and K. Regenauer-Lieb, International partnership for geothermal technology geothermal reservoir modeling recommendations for research and development, 2012.
32.
T. Kohl, K. F. Evansi, R. J. Hopkirk, and L. Rybach, Coupled hydraulic, thermal and mechanical considerations for the simulation of hot dry rock reservoirs, Geothermics, 24 (1995), pp. 345--359.
33.
T. Kohl and R. J. Hopkirk, “FRACTure''---A simulation code for forced fluid flow and transport in fractured, porous rock, Geothermics, 24 (1995), pp. 333--343.
34.
T. Kohl and T. Mégel, Predictive modeling of reservoir response to hydraulic stimulations at the European EGS site Soultz-sous-Forêts, Int. J. Rock Mech. Mining Sci., 44 (2007), pp. 1118--1131.
35.
T. Kraft, P. M. Mai, S. Wiemer, N. Deichmann, J. Ripperger, P. Kästli, C. Bachmann, D. Fäh, J. Wössner, and D. Giardini, Enhanced geothermal systems: Mitigating risk in urban areas, Eos Transactions American Geophysical Union, 90 (2009), p. 273.
36.
S. H. Lee, M. F. Lough, and C. L. Jensen, Hierarchical modeling of flow in naturally fractured formations with multiple length scales, Water Resources Res., 37 (2001), pp. 443--455.
37.
L. Li and S. Lee, Efficient field-scale simulation of black oil in a naturally fractured reservoir through discrete fracture networks and homogenized media, SPE Reservoir Eval. Eng., 11 (2008), pp. 750--758.
38.
K.-T. Lim, M.-H. Hui, and B. Mallison, A next-generation reservoir simulator as an enabling technology for a complex discrete fracture modeling workflow, in Proceedings of the SPE Annual Technical Conference and Exhibition, Society of Petroleum Engineers, 2009.
39.
M. F. Lough, S. H. Lee, and J. Kamath, An efficient boundary integral formulation for flow through fractured porous media, J. Comput. Phys., 143 (1998), pp. 462--483.
40.
J. W. Lund, D. H. Freeston, and T. L. Boyd, Direct utilization of geothermal energy 2010 worldwide review, Geothermics, 40 (2011), pp. 159--180.
41.
S. K. Matthäi, A. Mezentsev, and M. Belayneh, Control-volume finite-element two-phase flow experiments with fractured rock represented by unstructured 3D hybrid meshes, in Proceedings of the SPE Reservoir Simulation Symposium, Society of Petroleum Engineers, 2005.
42.
S. Matthai, A. Mezentsev, and M. Belayneh, Finite element--node-centered finite-volume two-phase-flow experiments with fractured rock represented by unstructured hybrid-element meshes, SPE Reservoir Eval. Eng., 10 (2007), pp. 740--756.
43.
S. K. Matthai, S. Geiger, S. G. Roberts, A. Paluszny, M. Belayneh, A. Burri, A. Mezentsev, H. Lu, D. Coumou, T. Driesner, and C. A. Heinrich, Numerical simulation of multi-phase fluid flow in structurally complex reservoirs, Geological Society of London, 292 (2007), pp. 405--429.
44.
M. W. McClure and R. N. Horne, Investigation of injection-induced seismicity using a coupled fluid flow and rate/state friction model, Geophysics, 76 (2011), pp. WC181--WC198.
45.
C. I. McDermott, A. R. L. Randriamanjatosoa, H. Tenzer, and O. Kolditz, Simulation of heat extraction from crystalline rocks: The influence of coupled processes on differential reservoir cooling, Geothermics, 35 (2006), pp. 321--344.
46.
A. Moinfar, A. Varavei, K. Sepehrnoori, and R. Johns, Development of a novel and computationally-efficient discrete-fracture model to study IOR processes in naturally fractured reservoirs, in Proceedings of the SPE Improved Oil Recovery Symposium, Society of Petroleum Engineers, 2012.
47.
J. E. P. Monteagudo and A. Firoozabadi, Control-volume method for numerical simulation of two-phase immiscible flow in two- and three-dimensional discrete-fractured media, Water Resources Res., 40 (2004).
48.
H. Murphy, D. Brown, R. Jung, I. Matsunaga, and R. Parker, Hydraulics and well testing of engineered geothermal reservoirs, Geothermics, 28 (1999), pp. 491--506.
49.
J. R. Natvig and K. A. Lie, On efficient implicit upwind schemes, in the 11th European Conference on the Mathematics of Oil Recovery, 2008.
50.
J. Noorishad and M. Mehran, An upstream finite element method for solution of transient transport equation in fractured porous media, Water Resources Res., 18 (1982), pp. 588--596.
51.
N. E. Odling, Scaling and connectivity of joint systems in sandstones from western Norway, J. Struct. Geology, 19 (1997), pp. 1257--1271.
52.
M. J. O'Sullivan, K. Pruess, and M. J. Lippmann, State of the art of geothermal reservoir simulation, Geothermics, 30 (2001), pp. 395--429.
53.
A. Paluszny and S. K. Matthäi, Numerical modeling of discrete multi-crack growth applied to pattern formation in geological brittle media, Int. J. Solids Struct., 46 (2009), pp. 3383--3397.
54.
D. W. Peaceman, Interpretation of Well-Block Pressures in Numerical Reservoir Simulation, SPE Journal, 18 (1978), pp. 183--194.
55.
R. Podgorney, H. Huang, and D. Gaston, Massively Parallel Fully Coupled Implicit Modeling of Coupled Thermal-Hydrological-Mechanical Processes for Enhanced Geothermal System Reservoirs, Vol. 2, Stanford University, Stanford, CA, 2010.
56.
S. K. Sanyal, S. J. Butler, D. Swenson, and B. Hardeman, Review of the state-of-the-art of numerical simulation of Enhanced Geothermal Systems, in Proceedings of the World Geothermal Congress 2000, Kyushu-Tohoku, Japan, 2000.
57.
S. Sarda, L. Jeannin, and B. Bourbiaux, Hydraulic characterization of fractured reservoirs: Simulation on discrete fracture models, in Proceedings of the SPE Reservoir Simulation Symposium, Society of Petroleum Engineers, 2001, pp. 154--162.
58.
Y. Seol, T. J. Kneafsey, and K. Ito, An evaluation of the active fracture concept in modeling unsaturated flow and transport in a fractured meter-sized block of rock, Vadose Zone J., 5 (2006), p. 1.
59.
J. Taron and D. Elsworth, Thermal--hydrologic--mechanical--chemical processes in the evolution of engineered geothermal reservoirs, Int. J. Rock Mech. Mining Sci., 46 (2009), pp. 855--864.
60.
J. Taron, D. Elsworth, and K.-B. Min, Numerical simulation of thermal-hydrologic-mechanical-chemical processes in deformable, fractured porous media, Int. J. Rock Mech. Mining Sci., 46 (2009), pp. 842--854.
61.
S. Vitel and L. Souche, Unstructured upgridding and transmissibility upscaling for preferential flow paths in $3$D fractured reservoirs, in Proceedings of the SPE Reservoir Simulation Symposium, Society of Petroleum Engineers, 2007, pp. 1--11.
62.
J. E. Warren and P. J. Root, The behavior of naturally fractured reservoirs, SPE Journal, 3 (1963), pp. 245--255.
63.
J. Willis-Richards and T. Wallroth, Approaches to the modelling of hdr reservoirs: A review, Geothermics, 24 (1995), pp. 307--332.
64.
J. Willis-Richards, K. Watanabe, and H. Takahashi, Progress toward a stochastic rock mechanics model of engineered geothermal systems, J. Geophys. Res., 101 (1996), 17481.
65.
P. A. Witherspoon, J. S. Y. Wang, K. Iwai, and J. E. Gale, Validity of Cubic Law for fluid flow in a deformable rock fracture, Water Resources Res., 16 (1980), pp. 1016--1024.
66.
T. Yamamoto, Y. Fujimitsu, and H. Ohnishi, Hot dry rock reservoir 3D simulation of the Ogachi site, in Proceedings of the Annual Meeting of the Geothermal Resources Council, Reno, NV, Vol. 19, 1995.
Information & Authors
Information
Published In
Copyright
© 2016, Society for Industrial and Applied Mathematics.
History
Submitted: 27 August 2014
Accepted: 3 December 2015
Published online: 18 February 2016
Keywords
MSC codes
Authors
Metrics & Citations
Metrics
Citations
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.
Cited By
- Numerical analysis of coupled thermal–hydraulic processes based on the embedded discrete fracture modeling methodApplied Thermal Engineering, Vol. 253 | 1 Sep 2024
- Rigorous derivation of discrete fracture models for Darcy flow in the limit of vanishing apertureNetworks and Heterogeneous Media, Vol. 19, No. 1 | 1 Jan 2024
- A discrete fracture hybrid model for forecasting diffusion-induced seismicity and power generation in enhanced geothermal systemsGeophysical Journal International, Vol. 230, No. 1 | 24 February 2022
- Comparison of cell- and vertex-centered finite-volume schemes for flow in fractured porous mediaJournal of Computational Physics, Vol. 448 | 1 Jan 2022
- Soft stimulation treatment of geothermal well RV-43 to meet the growing heat demand of ReykjavikGeothermics, Vol. 96 | 1 Nov 2021
- A (Dual) Network Model for Heat Transfer in Porous MediaTransport in Porous Media, Vol. 140, No. 1 | 4 May 2021
- Modeling study of the thermal-hydraulic-mechanical coupling process for EGS based on the framework of EDFM and XFEMGeothermics, Vol. 89 | 1 Jan 2021
- Sub-representative elementary volume homogenization of flow in porous media with isolated embedded fracturesJournal of Fluid Mechanics, Vol. 901 | 26 August 2020
- Fluid Flow Characterization Framework for Naturally Fractured Reservoirs Using Small-Scale Fully Explicit ModelsTransport in Porous Media, Vol. 134, No. 2 | 21 July 2020
- An embedded 3D fracture modeling approach for simulating fracture-dominated fluid flow and heat transfer in geothermal reservoirsGeothermics, Vol. 86 | 1 Jul 2020
- An extended finite volume method and fixed‐stress approach for modeling fluid injection–induced tensile opening in fractured reservoirsInternational Journal for Numerical and Analytical Methods in Geomechanics, Vol. 44, No. 8 | 15 February 2020
- Modeling tissue perfusion in terms of 1d-3d embedded mixed-dimension coupled problems with distributed sourcesJournal of Computational Physics, Vol. 410 | 1 Jun 2020
- Study on a POD reduced-order model for steady-state flows in fractured porous mediaInternational Communications in Heat and Mass Transfer, Vol. 112 | 1 Mar 2020
- WITHDRAWN: Modeling tissue perfusion in terms of 1d-3d embedded mixed-dimension coupled problems with distributed sourcesJournal of Computational Physics: X | 1 Feb 2020
- A comparative study on simulating flow-induced fracture deformation in subsurface media by means of extended FEM and FVMOil & Gas Science and Technology – Revue d’IFP Energies nouvelles, Vol. 75 | 18 June 2020
- Induced seismicity risk analysis of the hydraulic stimulation of a geothermal well on Geldinganes, IcelandNatural Hazards and Earth System Sciences, Vol. 20, No. 6 | 4 June 2020
- Upscaling of the single-phase flow and heat transport in fractured geothermal reservoirs using nonlocal multicontinuum methodComputational Geosciences, Vol. 23, No. 4 | 6 April 2019
- Multiscale modeling of heat and mass transfer in fractured media for enhanced geothermal systems applicationsApplied Mathematical Modelling, Vol. 67 | 1 Mar 2019
- Study on the Thermal-Hydraulic Coupling Model for the Enhanced Geothermal SystemsComputational Science – ICCS 2019 | 8 June 2019
- Multiscale formulation for coupled flow-heat equations arising from single-phase flow in fractured geothermal reservoirsComputational Geosciences, Vol. 22, No. 5 | 20 June 2018
- A global review of enhanced geothermal system (EGS)Renewable and Sustainable Energy Reviews, Vol. 81 | 1 Jan 2018
- Modeling of shear failure in fractured reservoirs with a porous matrixComputational Geosciences, Vol. 21, No. 5-6 | 19 July 2017
- Projection-based Embedded Discrete Fracture Model (pEDFM)Advances in Water Resources, Vol. 105 | 1 Jul 2017
- Algebraic multiscale method for flow in heterogeneous porous media with embedded discrete fractures (F-AMS)Journal of Computational Physics, Vol. 321 | 1 Sep 2016
View Options
- Access via your Institution
- Questions about how to access this content? Contact SIAM at [email protected].