Skip to main content
SpringerLink
Log in

Analytical solution of a mathematical model for rock salt dissolution in still water

  • Original Paper
  • Published:
Arabian Journal of Geosciences Aims and scope Submit manuscript

Abstract

In this study, an ordinary differential equation for dissolution of rock salt in still water is established, for the purpose of researching the dissolution mechanism of rock salt in still water, by calculating the concentration distribution of the boundary layer of the rock salt solution. On this basis, a dissolution model for rock salt in still water with different dissolution areas, solution concentrations, and solution temperatures is established. The corresponding analytical solutions are derived and solved, and parameter inversion is conducted with experimental data on rock salt dissolution, from which the dissolution parameter convective mass transfer coefficient k in still water is obtained. In addition, the results of previous dissolution tests are interpreted and discussed from a theoretical perspective using the derived dissolution model. It is found that the dissolution area has no obvious influence on the dissolution rate and the dissolution rate gradually decreases with increasing solution concentration when the solution volume is 5 L and the water is changed every 5 min. It is also proved that parameter a1 is relevant to the molar mass M and saturation concentration Cs, and parameter a2 is relevant to the convective mass transfer coefficient k. The model established in this paper may describe well the dissolution mechanism of rock salt in still water, and provides a basic theoretical foundation and analytical method for research on the dissolution characteristics of rock salt.

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

Similar content being viewed by others

References

  • Anderson NL, Hinds RC (1997) Glacial loading and unloading: a possible cause of rock salt dissolution in the western Canada basin. Carbonates Evaporites 12(1):43–52

    Article  Google Scholar 

  • Cosenza P, 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 

  • Cuevas CL (1997) Pore structures characterization in rock salt. Eng Geol 47:17–30

    Article  Google Scholar 

  • Durie RW, Jessen FW (1964) Mechanism of the dissolution of salt in the formation of underground salt cavities. Soc Petrol Eng J 4(2):183–190. https://doi.org/10.2118/678-PA

    Article  Google Scholar 

  • Fairchild IJ, Killawee JA, Hubbard B, Dreybrodt W (1999) Interactions of calcareous suspended sediment with glacial meltwater: a file test of dissolution behaviour. Chem Geol 155:243–263

    Article  Google Scholar 

  • Liang WG, Zhao YS, Xu SG, Dusseat MB (2008) Dissolution and seepage coupling effect on transport and mechanical properties of glauberite salt rock. Transport Porous Med 74(2):185–189

  • Liu CL (2000) Study on the physicochemical characteristics and cavity form of drilling water dissolving for thin-layer salt rock. Dissertation, Chongqing University. (in Chinese)

  • Liu CL, Xu LJ, Xian XF (2002) Fractal-like kinetic characteristics of rock salt dissolution in water. Colloid Surface A 201(1–3):231–235

    Article  Google Scholar 

  • Liu XR, Yang X, Zhong ZL, Liang NH, Wang JB, Huang M (2015) Research on dynamic dissolving model and experiment for rock salt under different flow conditions. Adv Mater Sci Eng 2015:1–10. https://doi.org/10.1155/2015/959726

    Article  Google Scholar 

  • Mokni N, Olivella S, Li XL, Smets S, Valcke E (2008) Deformation induced by dissolution of salts in porous media. Phys Chem Earth 33:436–443

    Article  Google Scholar 

  • Spangenberg E, Spangenberg U, Heindorf C (1998) An experimental study of transport properties of porous rock salt. Phys Chem Earth 23(3):367–371

    Article  Google Scholar 

  • Stormont JC (1997) In situ gas permeability measurements to delineate damage in rock salt. Int J Rock Mech Min Sci 34(7):1055–1064

    Article  Google Scholar 

  • Tsang CF, Bemier F, Davies C (2005) Geohydromechanical processes in the excavation damaged zone in crystalline rock, rock salt, and indurated and plastic clays-in the context of radioactive waste disposal. Int J Rock Mech Min Sci 42(1):109–125

    Article  Google Scholar 

  • Voznesenskii AS, Ertuganova EA, Vli’yamov SV, Tavostin MN (2006) Studying the mechanism of acoustic emission in failure of rock salt by dissolving. J Min Sci 42(1):35–42

    Article  Google Scholar 

  • Wang QM (2003) Solution mining of salt deposit. Chemical Industry Press, Beijing (in Chinese)

    Google Scholar 

  • Wang CR (2009) Experimental study of the influencing factors on dissolution rate of rock salt. Dissertation, Chongqing university. (in Chinese)

  • Xu SG, Liang WG, Zhao YS (2005) Experimental study on dissolution characteristics of glauberite of rock salt. J Taiyuan Univ Technol 36(6):243–244 (in Chinese)

    Google Scholar 

  • Yang CH, Jing WJ, Daemen JJK, Zhang GM, Du C (2013) Analysis of major risks associated with hydrocarbon storage caverns in bedded salt rock. Reliab Eng Syst Saf 113:94–111

    Article  Google Scholar 

  • Zechner E, Konz M, Younes A, Huggenberger P (2011) Effects of tectonic structures, salt solution mining, and density-driven groundwater hydraulics on evaporite dissolution (Switzerland). Hydrogeol J 19:1323–1344

    Article  Google Scholar 

  • Zhao ZC (2003) Theory of fluid transportation and configuration development in solution mining cavern for underground gas storage. Dissertation, Percolation mechanics research institute of Chinese academy of sciences. (in Chinese)

  • Zhao ZC, Zhu WY, Shan WW, Wan YJ (2000) Research on mechanism of solution mining for building underground gas storage in salt cavern. Pet Explor Dev 30(5):107–109 (in Chinese)

    Google Scholar 

  • Zidane A, Zechner E, Huggenberger P, Younes A (2014) Simulation of rock salt dissolution and its impact on land subsidence. Hydrol Earth Syst Sci 18:2177–2189

    Article  Google Scholar 

Download references

Funding

This study was supported by the Fujian Provincial Natural Science Foundation Projects (grant nos. 2017J05070, 2016J05108, 2018J01624), the Research and Development Fund of Fujian University of Technology (grant no. GY-Z17160), and the National Natural Science Foundation of China (grant no. 51608120).

Author information

Authors and Affiliations

  1. School of Civil Engineering, Fujian University of Technology, Fuzhou, 350118, China

    Xin Yang, Zhenwei Zhao & Hujun Lei

  2. School of Civil Engineering, Chongqing University, Chongqing, 400045, China

    Xin Yang & Xinrong Liu

  3. Key Laboratory of Underground Engineering, Fujian Province University, Fuzhou, 350118, China

    Xin Yang & Zhenwei Zhao

  4. Key Laboratory of New Technology for Construction of Cities in Mountain Area (Chongqing University), Ministry of Education, Chongqing, 400030, China

    Xinrong Liu

  5. School of Civil Engineering, Xi’an University of Architecture and Technology, Xi’an, 710055, China

    Junbao Wang

Authors
  1. Xin Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xinrong Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Junbao Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Zhenwei Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Hujun Lei
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xinrong Liu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yang, X., Liu, X., Wang, J. et al. Analytical solution of a mathematical model for rock salt dissolution in still water. Arab J Geosci 11, 732 (2018). https://doi.org/10.1007/s12517-018-4122-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s12517-018-4122-1

Keywords

Search

Navigation