Modeling of Limestone Dissolution for Flue Gas Desulfurization with Novel Implications
Abstract
:1. Introduction
2. Materials and Methods
2.1. Experimental Procedure
2.2. Mathematical Modeling
3. Results
3.1. Limestone Analysis
3.2. Reactivity Estimation of Limestone
Quantity | Symbol | Units | Min Value | Median Value | Max Value | Reference |
---|---|---|---|---|---|---|
Reynolds number (agitated tank) | Re | none | 42,000 | This Work | ||
Convective mass transfer coefficient | 10−3 dm/s | 0.01 | 2 | 12 | [2,43] | |
Limestone particle size | dp | 10−6 m | 150 | 320 | 500 | This Work |
Solid calcite concentration | g/L | 2 | 3 | 5 | This Work | |
Calcite absolute contact area | A | dm2 | 3 | 4 | 5 | This Work |
Conductivity (local) | σ | mS/cm2 | 0.4 | 100 | 105 | [46] |
Hydron concentration | mol/L | 10−6 | 6 × 10−6 | 2 × 10−3 | This Work | |
Hydron surface activity coefficient | none | 0 | 0.2 | 1 | [2,47,48] | |
Hydron ion diffusivity in water | 10−5 cm2 s−1 | 9.3 | [2,46] | |||
Hydroxide anion diffusivity in water | 10−5 cm2 s−1 | 5.273 | [46] | |||
Hydrogen Carbonate ion diffusivity in water | 10−5 cm2 s−1 | 1.185 | [46] | |||
Carbonate ion diffusivity in water | 10−5 cm2 s−1 | 0.923 | [46] | |||
Calcium ion diffusivity in water | 10−5 cm2 s−1 | 0.79 | 0.792 | 0.84 | [2,46] | |
Magnesium ion diffusivity in water | 10−5 cm2 s−1 | 0.706 | [46] | |||
Boundary layer thickness (mass transfer) | δ | 10−5 m | 1 | 2.4 | 5 | [5,43] |
Diffusive mass transfer coefficient | 10−3 dm/s | 0.14 | 2.8 | 9.3 | This Work [2] | |
Effective reactivity parameter | M−2 dm−2 s−1 | 105 | 106 | 107 | This work [2,41] | |
First Damköhler number | none | 104 | 106 | 109 | This work | |
Second Damköhler number | none | 30 | 300 | 3000 | This work |
4. Discussion
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Nomenclature
Latin Symbols | Significance | Units |
Polynomial multiplicative factor | dimensionless | |
A | Absolute contact area | dm2 |
Particles’ superficial area | dm2 | |
Polynomial multiplicative factor | dimensionless | |
Substitute variable | dimensionless | |
Polynomial multiplicative factor | dimensionless | |
Hydrogen ion concentration | M | |
Initial Hydrogen ion concentration | M | |
Undissolved limestone concentration | g/L (or M) | |
Shape factor | dimensionless | |
dp | Limestone particle size | µm |
D | Average ionic diffusivity | cm2 s−1 |
Hydrogen ion diffusivity in water | cm2 s−1 | |
Hydroxide anion diffusivity in water | cm2 s−1 | |
Hydrogen carbonate ion diffusivity in water | cm2 s−1 | |
Carbonate ion diffusivity in water | cm2 s−1 | |
Calcium ion diffusivity in water | cm2 s−1 | |
Magnesium ion diffusivity in water | cm2 s−1 | |
First Damköhler number | dimensionless | |
Second Damköhler number | dimensionless | |
Reaction rate constant | M−2 dm−2 s−1 | |
Model rate parameter | M−1 dm−2 s−1 | |
Interfacial mass transfer coefficient | dm/s | |
Convective mass transfer coefficient | dm/s | |
Diffusive mass transfer coefficient | dm/s | |
Lumped rate parameter | M−1 dm−2 s−1 | |
Reactivity parameter | M−2 dm−2 s−1 | |
Effective reactivity parameter | M−2 dm−2 s−1 | |
Agitation rate | rpm | |
Substitute variable | dimensionless | |
Characteristic length of the particle | dm | |
Re | Reynolds number (agitated tank) | dimensionless |
Particle volume | dm3 | |
Substitute variable | dimensionless | |
Conversion | dimensionless | |
Substitute parameter | dimensionless | |
Greek symbols | Significance | Units |
Agitator impeller diameter | m | |
Substitute variable | dimensionless | |
δ | Mass transfer boundary layer thickness | m |
Hydrogen surface activity coefficient | dimensionless | |
Dynamic viscosity | Pa.s | |
Mass density | Kg/m3 | |
σ | Local conductivity | mS/cm2 |
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Rate Determining Steps | Reactions |
---|---|
Absorption of gaseous SO2 in liquid water | |
Oxidation of (liquid phase) | |
Solid limestone is dissolving in acidic environment (pH 5.5, industrial process) | |
Crystallization of gypsum |
Sample | ρ (kg/m3) | CaCO3 wt % | CaO wt % | Al2O3 wt % | SiO2 wt % | MgO wt % |
---|---|---|---|---|---|---|
Metamorphic Limestone | 2720 | 98.5 | 54.5 | 0.13 | 0.5 | 0.59 |
Sedimentary Limestone | 2703 | 99.1 | 55.2 | 0.01 | 0.05 | 0.32 |
Experiment | kr,eff A (107 M−2 s−1) | Goodness of Fit (r2) | Averaged Contact Area (dm2) | kr,eff (107 M−2 dm−2 s−1) | Goodness of Fit (r2) |
---|---|---|---|---|---|
Metamorphic_step1 | 0.159 ± 0.008 | 0.9329 | 3.76 ± 0.33 | 0.038 ± 0.001 | 0.9634 |
Metamorphic_step2 | 0.129 ± 0.009 | 0.8835 | 3.78 ± 0.31 | 0.031 ± 0.002 | 0.9216 |
Metamorphic_step3 | 0.112 ± 0.008 | 0.8683 | 3.72 ± 0.38 | 0.027 ± 0.002 | 0.9126 |
Metamorphic_step4 | 0.132 ± 0.010 | 0.8719 | 3.80 ± 0.28 | 0.032 ± 0.002 | 0.9085 |
Metamorphic_step5 | 0.109 ± 0.008 | 0.8512 | 3.74 ± 0.36 | 0.026 ± 0.002 | 0.8935 |
Sedimentary_step1 | 0.636 ± 0.034 | 0.9020 | 3.45 ± 0.70 | 0.137 ± 0.005 | 0.9589 |
Sedimentary_step2 | 1.018 ± 0.057 | 0.9124 | 3.74 ± 0.35 | 0.223 ± 0.008 | 0.9619 |
Sedimentary_step3 | 0.409 ± 0.032 | 0.8527 | 3.78 ± 0.30 | 0.097 ± 0.006 | 0.9109 |
Sedimentary_step4 | 0.327 ± 0.030 | 0.8035 | 3.75 ± 0.34 | 0.079 ± 0.006 | 0.8730 |
Sedimentary_step5 | 0.428 ± 0.035 | 0.8329 | 3.74 ± 0.36 | 0.101 ± 0.006 | 0.9062 |
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De Blasio, C.; Salierno, G.; Sinatra, D.; Cassanello, M. Modeling of Limestone Dissolution for Flue Gas Desulfurization with Novel Implications. Energies 2020, 13, 6164. https://doi.org/10.3390/en13236164
De Blasio C, Salierno G, Sinatra D, Cassanello M. Modeling of Limestone Dissolution for Flue Gas Desulfurization with Novel Implications. Energies. 2020; 13(23):6164. https://doi.org/10.3390/en13236164
Chicago/Turabian StyleDe Blasio, Cataldo, Gabriel Salierno, Donatella Sinatra, and Miryan Cassanello. 2020. "Modeling of Limestone Dissolution for Flue Gas Desulfurization with Novel Implications" Energies 13, no. 23: 6164. https://doi.org/10.3390/en13236164