Analytical solution of a mathematical model for rock salt dissolution in still water
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ORIGINAL PAPER
Analytical solution of a mathematical model for rock salt dissolution in still water Xin Yang 1,2,3 & Xinrong Liu 2,4 & Junbao Wang 5 & Zhenwei Zhao 1,3 & Hujun Lei 1 Received: 22 February 2018 / Accepted: 23 November 2018 # Saudi Society for Geosciences 2018
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. Keywords Rock salt . Dissolution model . Different influencing factors . Dissolution mechanism in still water
Introduction Solution mining technology is a special mining method that takes advantage of the solubility of saline minerals in water. Water is injected into a mineral deposit as a solvent and undergoes physical and chemical reactions in the interior of the deposit to locally dissolve the saline minerals in the deposit
* Xinrong Liu [email protected] 1
School of Civil Engineering, Fujian University of Technology, Fuzhou 350118, China
2
School of Civil Engineering, Chongqing University, Chongqing 400045, China
3
Key Laboratory of Underground Engineering, Fujian Province University, Fuzhou 350118, China
4
Key Laboratory of New Technology for Construction of Cities in Mountain Area (Chongqing University), Ministry of Education, Chongqing 400030, China
5
School of Civil Engineering, Xi’an University of Architecture and Technology, Xi’an 710055, China
and transform the solid salt minerals into a flowing salt solution (the bittern) (Zechner et al. 2011). This method differs greatly from underground mining and open pit mining technologically; in that, it integrates mining, processing, and metallurgy and directly extracts liquid useful com
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