Heat and mass transfer during the sump development in a potash solution mine

Olivia Ellard


The following report addresses the problem of heating input water during the process of solution mining for potash. With an ever-increasing pressure to reduce reliance on fossil fuels, being able to warm inlet water with underground heat would be an advantage for any solution mining company. The report examines the problem in general to discover whether a temperature of 328K can be reached at the bottom of the mine. A finite difference method was used to simulate the heat transfer within a Microsoft Excel spreadsheet, with validation provided by SolidWorks Flow Simulation Software. Varying atmospheric temperature, flow rate and type of blanket fluid were all simulated, however at optimum design the simulation resulted in a temperature of 305.95 K. Although the results suggest that the underground heat source will not be sufficient, the lack of modelling of the heat transfer in the sump of the mine and the lack of data available for the properties of brine means that the results are just the first stage in the analysis of the problem. Further recommendations of how to approach the problem next have been made.

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Al-Arabi, M., 1982. Turbulent Heat Transfer in the Entrance Region of a Tube. Heat Transfer Engineering 3 (3-4), pp 76-83.

Almada, S., Haugen, H., Hernandez, H., Luli, D., Sasi, S., Zhange, L., 2010. Modelling of a Novel Solution Potash Mining Process [pdf]. Institute for Mathematics and its Applications. Available at

[Accessed 14th November 2013]

Bartlett, R. W., 1998. Solution Mining: Leaching and Fluid Recovery of Materials 2nd Ed. Gordon and Breach Science Publishers: Amsterdam. p 375

Beckmann, W., 2013. Crystallisation: Basic Concepts and Industrial Applications. John Wiley & Sons: Weinheim, Germany. P 55

Bell, F. G., Donnelly, L. J., 2006. Mining and its Impact on the Environment. Taylor & Francis: Oxon. p 229.

Bellarby, J., 2009. Well Completion Design. Elsevier: Amsterdam, The

Netherlands. p 606

Boyd, J. P., 2013. Chebyshev and Fourier Spectral Methods 2nd Ed. Courier Dover Publications: New York. Section 14.3.

Brenni, R., Eugster, W., Kohl, T., 2002. System Performance of a Deep Borehole Heat Exchanger. Geothermics 31. p.687-708.

Caenn, R., Darley, HCH., Gray, G. R., 2011. Composition and Properties of Drilling and Completion Fluids. Gulf Professional Publishing: Waltham, United States of America. p 507

Chari, M. V. K., Salon, S. J., 2000. Numerical Methods in Electromagnetism. Academic Press: San Diego.

Deissler, R. G., 1953. Analysis of Turbulent Heat Transfer and Flow in the

Entrance Regions of Smooth Passages [pdf] National Advisory Committee for Aeronautics. Available at [Accessed 19th November 2013].

Einsele, G., 2000. Sedimentary Basins: Evolution, Facies and Sediment. 2nd Ed. Springer: Berlin, Germany. p 276.

Environmental Resources Management, 2012. Dallol Potash Project - Final Scoping Report [pdf] Available at: p.2-20

Esch, D. C., 2004. Thermal Analysis, Construction and Monitoring Methods of Frozen Ground. ASCE Publications: Reston. p.172

Fridleifsson, I. B., Bertani, R., Huenges, E., Lund, J. W., Ragnarsson, A., Rybac, 2008. The Possible Role and Contribution of Geothermal Energy to the Mitigation of Climate Change. In: Intergovernmental Panel on Climate Change, IPCC Scoping Meeting on Renewable Energy Sources.

Lübeck, Germany, 20-25 January 2008. [pdf] Available at [Accessed 21st November 2013].

Geo Drilling Fluids, 2010. Brine Fluids [pdf] Available at

[Accessed 17th November 2013].

Gornitz, V., 2009. Encyclopaedia of Paleoclimatology and Ancient Environments. Springer: Dordrecht, The Netherlands. p 104.

Government of Canada, 2013. Daily Data Report 2013 [Spreadsheet] Available at:

&Year=2013&Month=1&Day=1> [Accessed 4th April 2014]

Gupta, C. K., Mukherjee, T. K., 1990. Hydrometallurgy in Extraction Processes, Volume 1. CRC Press: Florida. p 42.

Hamm, B. M., Peterson, K. R., 2012. Corrugated Wall Effects in Vertical Concentric Ground-Source Heat Pumps. Worcester Polytechnic Institute. Available at:

/unrestricted/CorrugatedGSHP.pdf> [Accessed 17th November 2013]

Hartman, H. L., 1992. SME Mining Engineering Handbook, Volume 1. SME: Colorado. p 1499

Hartman, H. L., Mutmansky, J. M., 2002. Introductory Mining Engineering 2nd Ed. John Wiley & Sons: New Jersey. p 255

Haywood, R. W., 1990. Thermodynamic Tables in SI Units. Cambridge University Press: Cambridge. p. 32

Hocking, M. B. B., 2006. Handbook of Chemical Technology and Pollution Control. 3rd Ed. Academic Press: San Diego, United States of America. p 191

Holman, J. S., Stone, P., 2001. Chemistry. Nelson Thornes: Cheltenham, United Kingdom. pp 44-45

Husband, W. H. W., Ozsahin, S., 1967. Rates of Dissolution of Potash Ore. The Canadian Journal of Chemical Engineering 45 (4), pp 234.

International Plant Nutrition Institute, n.d. Nutrient Source Specifics: Potassium Chloride [pdf]. Available at

[Accessed 11th April 2014]

International Union of Pure and Applied Chemistry, 1991. Solubility Data Series 47.

Jeffrey, A., 2003. Applied Partial Differential Equations: An Introduction. Academic Press: San Diego. p. 2.

Jenkins, D. B., 2008. Chemical thermodynamics at a Glance. John Wiley & Sons: Oxford. p.31

Kjerfve, B., 1994. Coastal Lagoon Processes. Elsevier: Amsterdam. p.93

Kogel, J. E., 2006. Industrial Minerals & Rocks: Commodities, Markets and Uses. SME: Colorado, United States of America. pp 723-735

Kondepudi, D., 2008. Introduction to Modern Thermodynamics. John Wiley & Sons: Chichester, United Kingdom. p 55

Lee, K. S., 2012. Underground Thermal Energy Storage. Springer: London, United Kingdom. p 17

Lide, D. R., 2004. CRC Handbook of Chemistry and Physics 85th Ed. CRC Press: Boca Raton. p. 8-73

Mel, V. C., Fischer, S. K., 1983. Vertical Concentric-Tube Ground-Coupled Heat Exchangers. In: 1983 Semi-Annual ASHRAE Meeting, Atlantic City, New Jersey, June 1983. Oakridge National Laboratory.

Mittal, A., 2007. Chemistry. APH Publishing: New Delhi. p. 511.

Mozley, J. M., 1956. Predicting Dynamics of Concentric Pipe Heat Exchangers. Industrial and Engineering Chemistry, 48 (6), pp 1035–1041.

Oliver, J., Braud, H., 1981. Thermal Exchange to Earth with Concentric Pipes. Transactions of the ASAE 24(4), pp 906-910.

Pruppacher, H. R., Klett, J. D., 2010. Microphysics of Clouds and Precipitation 2nd Ed. Springer: London. p. 251.

Rathmore, M. M., Kapuno, R. R., 2011. Engineering Heat Transfer. Jones & Bartlett Learning: Sudbury. P.162.

Rees, S. J., Spitler, J. D., Deng, Z., Orio, C. D., Johnson, C. N., 2004. A Study of Geothermal Heat Pump and Standing Column Well Performance [pdf]. American Society of Heating, Refrigeration and Air Conditioning Engineers. Available at

[Accessed 14th November 2013].

Reger, D., Goode, S., Ball, D., 2009. Chemistry: Principles and Practice 3rd Ed. Cengage Learning: Belmont. p 482.

Remson, D. R., Dommers, O. B., Jesson, F. W., 1965. Techniques for Developing Predetermined Shaped Cavities in Solution Mining. Rau, J.L., Proceedings of the Second Symposium on Salt, Northern Ohio Geological Society, Cleveland. pp 297-310.

Sawhney, G. S., 2010. Heat and Mass Transfer 2nd Ed. I. K. International PVT Ltd: New Delhi. p.57.

Simpson, R., 2010. Engineering Aspects of Thermal Food Processing. CRC Press: Boca Raton. p 52

Taniguchi, M., 2011. Groundwater and Subsurface Environments: Human

Impacts in Asian Coastal Cities. Springer: London, United Kingdom. p 203

Thirumarimurugan, M., Kannadasan, T., Ramasamy, E., 2008. Performance Analysis of Shell and Tube

Heat Exchanger Using Miscible System. American Journal of Applied Sciences 5(5), pp 548-552.

Titkov, S., 2003. Flotation of water-soluble mineral resources. International Journals of Mineral Processing 74 (1-4), pp107-113

Wagner, C., 1949. The Dissolution Rate of Sodium Chloride with Diffusion and Natural Convection as Rate-Determining Factors. Journal of Physical Chemistry 53(7), pp 1030-1033.

Walsh, B. V., 2011. Analysis of a Coupled Heat Exchanger. M.Eng Dissertation, Rensselaer Polytechnic Institute. Available at

[Accessed 17th November 2013].

Wishart, D. J., 2004. Encyclopaedia of the Great Plains. U of Nebraska Press: Lincoln. p 433.

Worsoe-Schmidt, P. M., 1966. Heat Transfer in the Thermal Entrance Region of Circular Tubes and Annular Passages with Fully Developed Laminar Flow. International Journal of Heat and Mass Transfer 10 (4), pp 541.

Zen-Stoves, 1999. Gasoline [pdf]. Available at:

Zen-Stoves, 1999. Kerosene [pdf]. Available at:

Zen-Stoves, 1999. Oils Diesel [pdf]. Available at:

Zen-Stoves, 1999. Naphtha [pdf]. Available at:


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