Abstract
Dissolution of multi-species from a solid matrix is widely extended in different processes such as leaching of minerals; however, its modeling is often focused on a single species. A model for the simultaneous dissolution of soluble species was developed, which considers different solubilities and dissolution rates and considers that particle collapses when the rapidly soluble species is depleted. The collapsed matter is formed by inert material and a fraction of the soluble species with lower dissolution rate that has not dissolved yet. The model is applied to the leaching of a water-soluble mineral (caliche) with two soluble species dissolving simultaneously with different rates. Measured outlet concentrations of nitrate and magnesium were used to validate the model. Results showed that the model reproduced adequately the leaching of species with rapid and intermediate dissolution rate. Effect of the operating and kinetic parameters on the leaching process is also shown using the actual conditions of heap leaching for caliche mineral.
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Abbreviations
- A :
-
Cross-sectional area of reactor (m2)
- \( C_{Sx} \) :
-
Solubility concentration of x-species (kg/m3)
- \( C_{x} \) :
-
Concentration of x-species in reactor \( i \) (kg/m3)
- \( C_{{x\left( {i - 1} \right)}} \) :
-
Concentration of x-species in previous reactor (kg/m3)
- \( D \) :
-
Particle diameter (m)
- \( {\mathfrak{D}} \) :
-
Diffusivity (m2/h)
- \( H \) :
-
Initial reactor height (m)
- \( H_{heap} \) :
-
Initial heap height (m)
- \( h_{i} \) :
-
Height of reactor \( i \) (m)
- \( k_{x} \) :
-
Mass transfer rate coefficient of x-species (m/h)
- \( k_{B}^{*} \) :
-
Dissolution rate of collapsed material (1/h)
- \( m_{B} \) :
-
Mass of B in the collapsed material per unit area (kg/m2)
- \( N_{p} \) :
-
Number of particles
- \( q \) :
-
Irrigation rate (m3/m2/h)
- \( R \) :
-
Initial particle radius (m)
- \( Re \) :
-
Dimensionless number Reynolds
- \( r_{i} \) :
-
Particle radius in reactor \( i \) (m)
- \( Sc \) :
-
Dimensionless number Schmidt
- \( Sh \) :
-
Dimensionless number Sherwood
- \( t \) :
-
Time (h)
- \( V \) :
-
Volume of reactor (m3)
- \( \alpha_{x} \) :
-
Mass fraction of x-species in caliche, kg of x/kg mineral
- \( \varepsilon \) :
-
Mineral porosity
- \( \varepsilon_{w} \) :
-
Water fraction
- \( \rho \) :
-
Mineral density (kg/m3)
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Acknowledgments
The authors thank CONICYT and the Regional Government of Antofagasta for their funding through the PAI program, Project Anillo ACT 1201.
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Manuscript submitted June 4, 2016.
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Moreno, L., Ordóñez, J.I. & Cisternas, L.A. Dissolution Model of Multiple Species: Leaching of Highly Soluble Minerals. Metall Mater Trans B 48, 1817–1826 (2017). https://doi.org/10.1007/s11663-017-0936-6
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DOI: https://doi.org/10.1007/s11663-017-0936-6