Skip to main content
SpringerLink
Log in

A numerical study of non-Darcy flow in EGS heat reservoirs during heat extraction

  • Research Article
  • Published:
Frontiers in Energy Aims and scope Submit manuscript

Abstract

Underground non-Darcy fluid flow has been observed and investigated for decades in the petroleum industry. It is deduced by analogy that the fluid flow in enhanced geothermal system (EGS) heat reservoirs may also be in the non-Darcy regime under some conditions. In this paper, a transient 3D model was presented, taking into consideration the non-Darcy fluid flow in EGS heat reservoirs, to simulate the EGS long-term heat extraction process. Then, the non-Darcy flow behavior in water- and supercritical CO2 (SCCO2)-based EGSs was simulated and discussed. It is found that non-Darcy effects decrease the mass flow rate of the fluid injected and reduce the heat extraction rate of EGS as a flow resistance in addition to the Darcy resistance which is imposed to the seepage flow in EGS heat reservoirs. Compared with the water-EGS, the SCCO2-EGS are more prone to experiencing much stronger non-Darcy flow due to the much larger mobility of the SCCO2. The non-Darcy flow in SCCO2- EGSs may thus greatly reduce their heat extraction performance. Further, a criterion was analyzed and proposed to judge the onset of the non-Darcy flow in EGS heat reservoirs. The fluid flow rate and the initial thermal state of the reservoir were taken and the characteristic Forchheimer number of an EGS was calculated. If the calculated Forchheimer number is larger than 0.2, the fluid flow in EGS heat reservoirs experiences non-negligible non-Darcy flow characteristic.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

A :

Area/m2

c p :

Specific heat capacity/(J·kg−1·K−1)

Fo :

Forchheimer number

Fo ch :

Characteristic Forchheimer number

g :

Acceleration of gravity/(m·s−2)

ha :

Volumetric heat exchange coefficient/(W·m−3·K−1)

k :

Thermal conductivity/(W·m−1·K−1)

K :

Permeability/m2

p :

Pressure/Pa

Q :

Mass flow rate/(kg·s−1)

Re :

Reynolds number

t :

Time/s

S ND :

Non-Darcy term

T :

Temperature/K

T g :

Ground temperature/K

u :

Velocity vector/(m·s−1)

x, y, z :

Cartesian coordinates

ρ :

Density/(kg·m−3)

ε :

Porosity

μ :

Dynamic viscosity/(Pa·s)

β :

Non-Darcy coefficient

γ :

Relative velocity reduction

ch:

Characteristic

eff:

Effective

f:

Fluid

H2O:

Water

inj:

Injection

ini:

Initial

out:

Production, outlet

ref:

Reference

s:

Solid or rock

SCCO2 :

Supercritical carbon dioxide

References

  1. Tester J W, Anderson B J, Batchelor A S, Blackwell D D, Di Pippo R, Drake E M, Garnish J, Livesay B, Moore MC, Nichols K, Petty S, Toksoz M N, Veatch R W. The Future of Geothermal Energy: Impact of Enhanced Geothermal Systems (EGS) on the United States in the 21st Century. DOE Contract DE-AC07-05ID14517 Final Report, Massachusetts Institute of Technology, 2006

    Google Scholar 

  2. Yang Y, Yeh H. Modeling heat extraction from hot dry rock in a multi-well system. Applied Thermal Engineering, 2009, 29(8–9): 1676–1681

    Article  Google Scholar 

  3. Olasolo P, Juárez M C, Morales M P, D´Amico S, Liarte I A. Enhanced geothermal systems (EGS): a review. Renewable & Sustainable Energy Reviews, 2016, 56: 133–144

    Article  Google Scholar 

  4. Forchheimer P. Water moving through soil. Zeitschrift des Vereines Deutscher Ingenieuer, 1901, 45: 1782–1788

    Google Scholar 

  5. Gelet R, Loret B, Khalili N. A thermo-hydro-mechanical coupled model in local thermal non-equilibrium for fractured HDR reservoir with double porosity. Journal of Geophysical Research, 2012, 117: B07205

    Article  Google Scholar 

  6. Held S, Genter A, Kohl T, Kölbel T, Sausse J, Schoenball M. Economic evaluation of geothermal reservoir performance through modeling the complexity of the operating EGS in Soultz-sous- Forêts. Geothermics, 2014, 51: 270–280

    Article  Google Scholar 

  7. Brown D W. A hot dry rock geothermal energy concept utilizing supercritical CO2 instead of water. In: The 25th Workshop on Geothermal Reservoir Engineering, Stanford University, Stanford, CA, USA, 2000

    Google Scholar 

  8. Pruess K. On production behavior of enhanced geothermal systems with CO2 as working fluid. Applied Thermal Engineering, 2008, 49: 1446–1454

    Google Scholar 

  9. Jiang F M, Luo L, Chen J L. A novel three-dimensional transient model for subsurface heat exchange in enhanced geothermal systems. International Communications in Heat and Mass Transfer, 2013, 41: 57–62

    Article  Google Scholar 

  10. Kohl T, Evans K F, Hopkirk R J, Jung R, Rybach L. Observation and simulation of non-Darcian flow transients in fractured rock. Water Resources Research, 1997, 33(3): 407–418

    Article  Google Scholar 

  11. Zhang J, Xing H L. Numerical modeling of non-Darcy flow in nearwell region of a geothermal reservoir. Geothermics, 2012, 42: 78–86

    Article  Google Scholar 

  12. Haghshenas Fard M, Hooman K, Chua H T. Numerical simulation of a supercritical CO2 geothermosiphon. International Communications in Heat and Mass Transfer, 2010, 37(10): 1447–1451

    Article  Google Scholar 

  13. Xu C S, Dowd P, Li Q. Carbon sequestration potential of the Habanero reservoir when carbon dioxide is used as the heat exchange fluid. Journal of Rock Mechanics and Geotechnical Engineering, 2016, 8: 50–59

    Article  Google Scholar 

  14. Borgia A B, Oldenburg C M, Zhang R, Pan L, Daley T M, Finsterle S, Ramakrishnan T S. Simulations of CO2 injection into fractures and faults for improving their geophysical characterization at EGS sites. Geothermics, 2017, 69: 189–201

    Article  Google Scholar 

  15. Wang C L, Cheng W L, Nian Y L, Yang L, Han B B, Liu M H. Simulation of heat extraction from CO2-based enhanced geothermal systems considering CO2 sequestration. Energy, 2018, 142: 157–167

    Article  Google Scholar 

  16. Cao W J, Huang W B, Jiang F M. Numerical study on variable thermophysical properties of heat transfer fluid affecting EGS heat extraction. International Journal of Heat and Mass Transfer, 2016, 92: 1205–1217

    Article  Google Scholar 

  17. Chen J L, Jiang F M. A numerical study of EGS heat extraction process based on a thermal non-equilibrium model for heat transfer in subsurface porous heat reservoir. Heat and Mass Transfer, 2016, 52(2): 255–267

    Article  Google Scholar 

  18. Chen J L, Jiang F M. Designing multi-well layout for enhanced geothermal system to better exploit hot dry rock geothermal energy. Renewable Energy, 2015, 74: 37–48

    Article  Google Scholar 

  19. Jiang F M, Chen J L, Huang W B, Luo L. A three-dimensional transient model for EGS subsurface thermo-hydraulic process. Energy, 2014, 72: 300–310

    Article  Google Scholar 

  20. Friedel T, Voigt H D. Investigation of non-Darcy flow in tight-gas reservoirs with fractured wells. Journal of Petroleum Science Engineering, 2006, 54(3–4): 112–128

    Article  Google Scholar 

  21. Janicek J D, Katz D L. Applications of unsteady state gas flow calculations. In: Research Conference on Flow of Natural Gas Reservoirs, University of Michigan, 1955

    Google Scholar 

  22. Pascal H, Quillian R G, Kingston J. Analysis of vertical fracture length and non-Darcy flow coefficient using variable rate tests. SPE 9348, 1980

    Book  Google Scholar 

  23. Koтяxoв Ф И. The Physical Foundation of Reservoir. Beijing: Petroleum Industry Press, 1958

    Google Scholar 

  24. Li C. The research of natural gas small leakage & dispersion rule. Dissertation for the Doctoral Degree. Beijing: China University of Petroleum, 2011

    Google Scholar 

  25. Saboorian-Jooybari H, Pourafshary P. Significance of non-Darcy flow effect in fractured tight reservoirs. Journal of Natural Gas Science and Engineering, 2015, 24: 132–143

    Article  Google Scholar 

  26. Wen Z, Huang G, Zhan H. An analytical solution for non-Darcian flow in a confined aquifer using the power law function. Advances in Water Resources, 2008, 31(1): 44–55

    Article  Google Scholar 

  27. Zhang Z Y, Nemcik J. Fluid flow regimes and nonlinear flow characteristics in deformable rock fractures. Journal of Hydrology (Amsterdam), 2013, 477: 139–151

    Article  Google Scholar 

  28. Brinkman H C. A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles. Applied Scientific Research, 1949, 1: 27–34

    MATH  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Key R&D Program of China (2018YFB1501804), the Strategic Priority Research Program of Chinese Academy of Sciences (XDA21060700), the National Natural Science Foundation of China (Grant No. 41702256), and the Natural Science Foundation of Guangdong Province (2017A030310328).

Author information

Authors and Affiliations

  1. Laboratory of Advanced Energy Systems, Guangdong Key Laboratory of New and Renewable Energy Research and Development, CAS Key Laboratory of Renewable Energy, Guangzhou Institute of Energy Conversion, Chinese Academy of Sciences, Guangzhou, 510640, China

    Wenjiong Cao, Wenbo Huang & Fangming Jiang

  2. Guangdong Hydrogeology Battalion, Guangzhou, 510510, China

    Guoling Wei & Yunlong Jin

Authors
  1. Wenjiong Cao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wenbo Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Guoling Wei
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yunlong Jin
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Fangming Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Fangming Jiang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Cao, W., Huang, W., Wei, G. et al. A numerical study of non-Darcy flow in EGS heat reservoirs during heat extraction. Front. Energy 13, 439–449 (2019). https://doi.org/10.1007/s11708-019-0612-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11708-019-0612-4

Keywords

Search

Navigation