Skip to main content

Advertisement

SpringerLink
Log in

Study of the relationship between surface subsidence and internal pressure in salt caverns

  • Thematic Issue
  • Published:
Environmental Earth Sciences Aims and scope Submit manuscript

Abstract

Because of the ultra-low permeability and favorable rheological properties of rock salt, salt caverns are globally considered to be an ideal medium for energy storage. The prediction and control of surface subsidence above storage caverns are the key problems that require steady attention to ensure their long-term safety and stable operation. For salt caverns already in existence factors such as depth, shape and geological conditions cannot be changed. Therefore, the operating condition (i.e., internal pressure) becomes a key factor in influencing surface subsidence. However, cyclic pressure change during the operation phase has not been seriously considered by analytical investigation yet. In this paper, theoretical models for the volume convergence rates in spherical and cylindrical caverns have been derived, thereby developing a new concept “equivalent internal pressure” that of rock salt is considered

also takes cyclic internal pressure into consideration. The analytic solution for surface subsidence was then derived from a combination of transfer and distribution functions. Analytical and numerical solutions for different conditions were compared and verified, while the FDM code, FLAC3D, was used for numerical simulations. This comparison reveals that the use of “equivalent internal pressure” is suitable for predicting surface subsidence in the long-term cyclic operation conditions.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16

Similar content being viewed by others

Abbreviations

\(\sigma_{r} ,\; \sigma_{\theta } ,\; \sigma_{\varphi }\) :

Normal stresses in spherical or cylindrical coordinates (MPa)

\(\tau_{\theta r} ,\; \tau_{\varphi r} ,\; \tau_{r\theta }\) :

Shear stresses in spherical or cylindrical coordinates (MPa)

\(F_{\text{br}}\) :

Body strength in radial direction (MPa)

\(\varepsilon_{r} ,\; \varepsilon_{\theta }\) :

Normal strains in spherical or cylindrical coordinates (–)

\(u_{\text{r}}\) :

Radial displacement (m)

\(\sigma_{t} ,\; \varepsilon_{t}\) :

Normal stress (MPa) and strain (–) in hoop direction in spherical coordinates

\(a\) :

Radius of cavern (m)

\(p_{0}\) :

Initial stress of rock (MPa)

\(p_{\text{t}} ,\; p_{\text{e}}\) :

Internal pressure and equivalent internal pressure of cavern (MPa)

\(q\) :

Mises stress, \(q = \sqrt {3J_{2} }\) (MPa)

\(J_{2}\) :

Second invariant of stress deviator, \(J_{2} = \frac{1}{2}S_{ij} S_{ij}\)

\(A_{1} ,\;n\) :

Parameters of the constitutive model BGRa (1/d) and (–)

\(\sigma^{*}\) :

=1 MPa

\(Q\) :

Activation energy value (KJ/mol)

\(R\) :

Universal gas constant (J/mol/K)

\(\dot{\varepsilon }_{ij} ,\;\dot{\varepsilon }_{\text{cr}}\) :

Strain rate tensor and creep strain rate (1/d)

\(\dot{\varepsilon }_{r} ,\;\dot{\varepsilon }_{t}\) :

Strain rate in radial and hoop direction (1/d)

\(\nu ,\;\nu_{0}\) :

Deformation rate and the rate at the inner wall (m/d)

\(V,\;\dot{V}\) :

Cavern volume (m3) and time derivative of the cavern volume (m3/d)

\(K,\; K_{\text{e}}\) :

Volume convergence rate and volume convergence rate under “equivalent internal pressure” (1/d)

\(\sigma^{e} ,\;\varepsilon^{e}\) :

Generalized stress (MPa) and strain (–)

\(V_{0}\) :

Initial volume of cavern (m3)

\(V_{\text{c}} \left( t \right),\;V_{\text{s}} \left( t \right)\) :

Volume convergence and subsidence volume at time \(t\) (m3)

\(\eta\) :

Transfer delay parameter (1/d)

\(\psi\) :

Distribution function

\(T\) :

Temperature (K)

\(S\left( {x,y,t} \right)\) :

Subsidence at point \((x,y)\) at time \(t\) (m)

\(Z\) :

Depth of cavern (m)

\(\beta\) :

Influence angle (°)

\(d,\;D\) :

Parameters in the analytical equation of surface subsidence (m) and (m)

References

  • Bauer S, Beyer C, Dethlefsen F, Dietrich P et al (2013) Impacts of the use of the geological subsurface for energy storage: an investigation concept. Environ Earth Sci 70:3935–3943

    Article  Google Scholar 

  • Bérest P, Brouard B (2003) Safety of salt caverns used for underground storage. Oil Gas Sci Technol 58(3):361–384

    Article  Google Scholar 

  • Bérest P, Bergues J, Brouard B, Durup JG, Guerber B (2001) A salt cavern abandonment test. Int J Rock Mech Min Sci 38(5):357–368

    Article  Google Scholar 

  • Brouard B, Bérest P (1998) A tentative classification of salts according to their creep properties. In: Proceedings of SMRI Spring Meeting, New Orleans, pp 18–38

  • Chan KS, Bodner SR, Fossum AF et al (1997) A damage mechanics treatment of creep failure in rock salt. Int J Damage Mech 6(2):121–152

    Article  Google Scholar 

  • Chen Y, Li X, Hou Z, He JM, Ma CF (2012) New prediction method for maximum surface deformation in salt rock storage field considering different cavity geometries. Chin J Geot Eng 34(5):826–833

    Google Scholar 

  • Cosenza PH, Ghoreychi M, Bazargan-Sabet B, de Marsily G (1999) In situ rock salt permeability measurement for long term safety assessment of storage. Int J Rock Mech Min Sci 36(4):509–526

    Article  Google Scholar 

  • Düsterloh U, Lux KH (2003) Rock mechanical investigation into bore core material from the Jintan location. Professorship for Waste Disposal Technologies and Geomechanics, Clausthal University of Technology, Germany

  • Evans DJ (2008) An appraisal of underground gas storage technologies and incidents, for the development of risk assessment methodology. British Geological Survey, Nottingham, British

    Google Scholar 

  • Hou Z (1997) Untersuchungen zum nachweis der standsicherheit für untertagedeponien im salzgebirge. Dissertation, Technical University of Clausthal, Germany

  • Hou Z (2003) Mechanical and hydraulic behavior of rock salt in the excavation disturbed zone around underground facilities. Int J Rock Mech Min Sci 40:725–738

    Article  Google Scholar 

  • Hou Z, Lux KH (2003) Vergleichende betrachtung der markscheiderischen methode und der finiten elementen methode bei der ermittlung der zeitabhängigen absenkung an der tagesoberfläche über salzbergwerk. Das Markscheidewesen 110(1):10–20 (in German)

    Google Scholar 

  • Hou Z, Lux KH (2004) A new coupling concept for hydromechanical interaction of clay stone and rock salt in underground waste repositories. Int J Rock Mech Min Sci 41(7):1–6

    Google Scholar 

  • Hou Z, Wu W (2003) Improvement of design of storage cavity in rock salt by using the Hou/Lux constitutive model with consideration of creep rupture criterion and damage. Chin J Geot Eng 25(1):105–108

    Google Scholar 

  • Hou Z, Chen Y, Li X (2010a) New developments of the pre-calculation method for the determination of time-dependent surface subsidence above salt mines and cavities. In: Hou Z et al (eds) Underground storage of CO2 and energy. CRC Press/Balkema, Beijing, China, pp 205–210

  • Hou Z, Gou Y, Xie LZ, Zhang R (2010b) Natural gas storage cavern design under special consideration of the thin bedded salt layer in Jintan and the intermediate layers of mudstone. In: Hou Z et al (eds) Underground storage of CO2 and energy. CRC Press/Balkema, Beijing, China, pp 211–216

  • Hou Z, Wundram L, Meyer R, Schmidt M, Schmitz S, Were P (2012) Development of a long-term wellbore sealing concept based on numerical simulations and in situ-testing in the Altmark natural gas field. Environ Earth Sci 67(2):395–409

    Article  Google Scholar 

  • Huang YX (2012) Study on theoretical model and numerical simulation of surface subsidence caused by gas storage of rock salt. Master thesis in Chongqing University, China (in Chinese)

  • Hunsche U, Hampel A (1999) Rock salt—the mechanical properties of the host rock material for a radioactive waste repository. Eng Geol 52:271–291

    Article  Google Scholar 

  • Jing WJ, Yang CH, Chen F (2011) Risk assessment of salt cavern oil/gas storage based on accident statistical analysis. Rock Soil Mech 32(6):1787–1793 (in Chinese)

    Google Scholar 

  • Jing WJ, Cheng L, Yang CH, Xu YL, Zhang YJ, Shi XL (2012) Volume shrinkage risk analysis of salt rock cavern gas storage based on reliability method. Chin J Rock Mech Eng 31(2):3673–3680 (in Chinese)

    Google Scholar 

  • Li YP, Kong JF, Xu YL, Ji WD, Jing WJ, Yang CH (2012) Prediction of surface subsidence above salt rock gas storage using Mogi model. Chin J Rock Mech Eng 31(9):1737–1745 (in Chinese)

    Google Scholar 

  • Liu JF, Pei JL, Ma K, Zhou H, Hou Z (2010) Damage evolution and fractal property of salt rock in tensile failure. In: Hou Z et al (eds) Underground storage of CO2 and energy. CRC Press/Balkema, Beijing, China, pp 105–112

  • Liu JF, Xie HP, Hou Z, Yang CH, Chen L (2014) Fatigue damage evolution of rock salt under cyclic loading. Acta Geotech 9(1):153–160

    Article  Google Scholar 

  • Lux KH (2013) Recent developments in geotechnical design of natural gas storage cavities regarding physical modelling as well as numerical simulation. In: Hou Z et al (eds) Clean energy systems in the subsurface: production, storage and conversion. Springer, Berlin, pp 451–485

  • Lux KH, Düsterloh U, Hou Z (2002a) Erhöhung der Wirtschaftlichkeit von Speicherkavernen durch Anwendung eines neuen Entwurfs- und Nachweiskonzeptes (Teil 1). Erdöl Erdgas Kohle 118(6):294–300

    Google Scholar 

  • Lux KH, Düsterloh U, Hou Z (2002b) Erhöhung der Wirtschaftlichkeit von Speicherkavernen durch Anwendung eines neuen Entwurfs- und Nachweiskonzeptes (Teil 2). Erdöl Erdgas Kohle 118(7/8):354–360

    Google Scholar 

  • Ma JL, Liu XY, Ma SN, Wang D (2009) Numerical analysis of in situ ground stress in deep rock salt stratum containing mud stone inter-layers. PLA Univ of Sci Tech 10(6):604–609 (in Chinese)

    Google Scholar 

  • Ma HL, Yang CH, Li YP, Shi XL, Liu JF, Wang TT (2015) Stability evaluation of the underground gas storage in rock salts based on new partitions of the surrounding rock. Environ Earth Sci. doi:10.1007/s12665-015-4019-1

    Google Scholar 

  • Maas K (2003) GIS-trends in research and development related to cavern industries. Technical Class Paper presented at Spring 2003 Meeting of the Solution Mining Research Institute (SMRI). Published under http://www.solutionmining.org, Houston, Texas USA, 27–30 April, 2003

  • Maas K (2006) Volume calculation of caverns. Paper presented at Spring 2006 Meeting of the Solution Mining Research Institute (SMRI). Published under http://www.solutionmining.org, Brussels, April 30–May 3, 2006

  • Reitenbach V, Ganzer L, Albrecht D, Hagemann B (2015) Influence of added hydrogen on underground gas storage: a review of key issues. Environ Earth Sci. doi:10.1007/s12665-015-4176-2

    Google Scholar 

  • Schober F, Sroka A (1983) Die berechnung von bodenbewegungen ueber kavernen unter beruecksichtigung des zeitlichen konvergenz- und gebirgsverhaltens. Kali und Steinsalz 8 H. 10 S:352–358

  • Schober F, Sroka A, Hartmann A (1987) Ein konzept zur senkungsvoraussetzungsberechnung über kavernenfeldern. Kali und Steinsalz 9 H. 11 S:374–379

  • Schulze O, Popp T, Kern H (2001) Development of damage and permeability in deforming rock salt. Eng Geol 61(2–3):163–180

    Article  Google Scholar 

  • Shi XL, Li YP, Yang CH, Xu YL, Ma HL, Liu W, Ji GD (2015) Influences of filling abandoned salt caverns with alkali wastes on surface subsidence. Environ Earth Sci. doi:10.1007/s12665-015-4135-y

    Google Scholar 

  • Siedel H (2013) Magnesium sulphate salts on monuments in Saxony (Germany): regional geological and environmental causes. Environ Earth Sci 69(4):1249–1261

    Article  Google Scholar 

  • Van Sambeek LL (1993) Evaluating cavern tests and subsurface subsidence using simple numerical models. 7th symposium on salt, Elsevier, Amsterdam, pp 433–439

  • Wang TT, Yan XZ, Yang XJ, Yang HL (2010) Dynamic subsidence prediction of ground surface above salt cavern gas storage considering the creep of rock salt. Sci China Tech Sci 53:3197–3202

    Article  Google Scholar 

  • Wang G, Xing W, Liu JF, Hou Z (2015) Influences of water-insoluble content on the short-term strength of bedded rock salt in China. Environ Earth Sci (submitted to this TI)

  • Wu W, Yang CH, Hou Z (2005) Investigation studied situations associated with mechanical aspects and development for underground storage of petroleum and natural gas in rock salt. Chin J Rock Mech Eng 24(11):5561–5568 (in Chinese)

    Google Scholar 

  • Xing W, Zhao J, Hou Z, Were P (2015) Horizontal natural gas caverns in thin bedded rock salt formations. Environ Earth Sci (submitted to this TI)

  • Yang GT (2004) Introduction to elasticity and plasticity. Tsinghua University Press, Beijing, China (in Chinese)

  • Yang CH, Li YP, Chen F (2009) Mechanics theory and engineering of bedded salt rock. Science Press, Beijing, p 76 (in Chinese)

    Google Scholar 

  • Zhang GM, Li YP, Yang CH, Daemen JJK (2014) Stability and tightness evalution of bedded rock salt formations for underground gas/oil storage. Acta Geotech 9(1):161–180

    Article  Google Scholar 

  • Zhou HW, Wang CP, Han BB, Duan ZQ (2011) A creep constitutive model for salt rock based on fractional derivatives. Int J Rock Mech Min Sci 48(1):116–121

    Article  Google Scholar 

Download references

Acknowledgments

The work presented in this paper was funded by the National Natural Science Foundation of China (Grant No. 51120145001). The authors wish to offer their gratitude and regards to the colleagues who contributed to this work.

Author information

Authors and Affiliations

  1. Sino-German Energy Research Center, Sichuan University, Chengdu, 610065, China

    Mengyao Li, Haipeng Zhang, Wei Xing & Zhengmeng Hou

  2. Energy Research Center of Lower Saxony (EFZN), Clausthal University of Technology, 38640, Goslar, Germany

    Wei Xing, Zhengmeng Hou & Patrick Were

  3. Institute of Petroleum Engineering, Clausthal University of Technology, 38678, Clausthal-Zellerfeld, Germany

    Zhengmeng Hou

Authors
  1. Mengyao Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Haipeng Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Wei Xing
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Zhengmeng Hou
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Patrick Were
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wei Xing.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, M., Zhang, H., Xing, W. et al. Study of the relationship between surface subsidence and internal pressure in salt caverns. Environ Earth Sci 73, 6899–6910 (2015). https://doi.org/10.1007/s12665-015-4405-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12665-015-4405-8

Keywords

Search

Navigation