Thermodynamic Modeling of the Drowning-Out Crystallization Process for LiOH and CHLiO2
Abstract
:1. Introduction
2. Thermodynamic Framework
2.1. Solubility Product
2.2. Modified Pitzer Model
3. Bibliographic Background
3.1. Lithium Hydroxide
3.2. Lithium Formate
3.3. Data Analysis
4. Results and Discussion
4.1. Lithium Hydroxide
4.1.1. Binary System LiOH + H2O
4.1.2. Ternary System LiOH + H2O + C2H6O
4.2. Lithium Formate
4.2.1. Binary System
Parameter Estimation
4.2.2. Ternary System CHLiO2 + H2O + C2H6O
4.3. Precipitate Calculation
4.3.1. Lithium Hydroxide
4.3.2. Lithium Formate
4.4. Drowning-Out Crystallization Process
4.4.1. Lithium Hydroxide
4.4.2. Lithium Formate
5. Conclusions
- A comprehensive compilation of bibliographic data for lithium hydroxide and lithium formate, including the activity, osmotic, and solubility coefficients, was undertaken from various authors. The analysis for lithium hydroxide involved assessing the activity coefficient data from different sources to identify the most suitable for modeling, with the conclusion highlighting the necessity for a more thorough examination of these experimental data. In contrast, for lithium formate, a similar analysis could not be conducted due to the limited and generally sparse information available in the literature.
- The application of the modified Pitzer model to model the thermodynamic properties was successful for both salts, involving parameterization for both binary and ternary systems, with an average standard deviation of less than 1%. However, limitations arose due to the limited data available in the literature. In particular, for lithium formate in the ternary system, determining the solubility product required the use of an alternative procedure.
- The examination of the temperature and antisolvent (ethanol) in the ternary system of lithium formate revealed that higher temperatures lead to an increased precipitate yield, aligning with expectations. The study also identified the optimal amount of antisolvent to achieve the highest process yield. In the design of the crystallization process using the drowning method, for both lithium hydroxide and lithium formate, three stages were considered: the crystallizer, filter, and dryer. This approach is advantageous, as it eliminates the need for mixing or recrystallization stages, resulting in significant energy savings.
Supplementary Materials
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Di | di (kg/m3) | Vi (m3/mol) | PM (g/mol) | ri | |||||
---|---|---|---|---|---|---|---|---|---|
H2O | Ethanol | H2O | Ethanol | H2O | Ethanol | H2O | Ethanol | H2O | Ethanol |
78.3040 | 24.2000 | 997.0449 | 785.1000 | 1.81 × 10−5 | 5.87 × 10−5 | 18.0200 | 46.0700 | 1 | 1 |
/kg∙mol−1 | /kg∙mol−1 | /kg∙mol−1 | /kg2∙mol−2 | α1 | α2 | AAD% a |
---|---|---|---|---|---|---|
0.1523 | 27.5274 | −27.0778 | −0.0216 | 2 | 1.9345 | 0.7625 |
kg∙mol−1 | kg∙mol−1 | kg∙mol−1 | C112 kg2∙mol−2 | C122 kg2∙mol−2 | AAD% a |
---|---|---|---|---|---|
−0.5449 | 8.5285 | −3.7190 | −0.0188 | 0.1325 | 0.5963 |
/kg∙mol−1 | /kg∙mol−1 | /kg2∙mol−2 | α1 | AAD% a |
---|---|---|---|---|
−0.4735 | 0.1272 | 0.5307 | 2 | 0.0805 |
Ksp | Q1 | Q2 | Q3 | ||
---|---|---|---|---|---|
A1 | −0.0002 | 0.0022 | 0.0019 | −0.5627 | |
A2 | −0.0058 | 7.46 × 10−5 | 6.47 × 10−5 | −0.0189 | |
A3 | −8.13 × 10−5 | 0.0095 | 0.0114 | 6.51 × 10−5 |
T/K | kg∙mol−1 | kg∙mol−1 | kg2∙mol−2 | kg2∙mol−2 | Ksp | AAD% a |
---|---|---|---|---|---|---|
283.15 | −0.3167 | 1.3382 | −0.0018 | 0.0461 | 0.0225 | 0.2821 |
293.15 | −0.2494 | −2.1863 | 0.0055 | 0.0332 | 0.0197 | 0.1620 |
298.15 | −0.2135 | 0.7527 | −0.0007 | 0.0297 | 0.0184 | 0.1584 |
303.15 | −0.2527 | 0.4829 | 0.0002 | 0.0295 | 0.0172 | 0.1653 |
313.15 | −0.1299 | −1.2661 | 0.0025 | 0.0168 | 0.0150 | 0.2113 |
Ksp | X0 | a | P (frac. Mol) | P (g/kg solv) | w/w % Ethanol | Y% |
---|---|---|---|---|---|---|
0.0037 | 0.0853 | 0.9322 | 0.0000 | 0.0000 | 0.00 | 0.00 |
0.8140 | 0.0158 | 37.2295 | 9.94 | 3.72 | ||
0.7685 | 0.0284 | 61.5564 | 19.97 | 6.16 | ||
0.7478 | 0.0339 | 68.4350 | 28.52 | 6.84 | ||
0.7296 | 0.0436 | 79.7250 | 40.07 | 7.97 | ||
0.7447 | 0.0482 | 82.3849 | 47.37 | 8.24 | ||
0.8273 | 0.0510 | 80.1891 | 56.50 | 8.02 | ||
0.8167 | 0.0600 | 93.8761 | 56.49 | 9.39 | ||
0.8875 | 0.0586 | 88.6288 | 60.05 | 8.86 |
Flows | w/w % | Total H | |||||
---|---|---|---|---|---|---|---|
Stream | T/K | kg/s | LiOH∙H2O | Ethanol | LiOH | Water | MJ/kg∙s |
1 | 298.15 | 100.0000 | 0.0000 | 0.0000 | 0.1278 | 0.8722 | −1655.12 |
2 | 298.15 | 93.0097 | 0.0000 | 1.0000 | 0.0000 | 0.0000 | −579.90 |
3 | 298.15 | 15.5717 | 14.8302 | 0.0000 | 0.5710 | 0.4290 | −288.83 |
4 | 298.15 | 177.4379 | 0.0000 | 0.5220 | 0.0242 | 0.4538 | −1954.32 |
5 | 298.15 | 15.1268 | 14.8302 | 0.5220 | 0.0242 | 0.4538 | −283.75 |
6 | 298.15 | 0.4449 | 0.0000 | 0.5220 | 0.0242 | 0.4538 | −4.88 |
7 | 373.15 | 14.8401 | 14.8401 | 0.0000 | 0.0000 | 0.0000 | −277.93 |
8 | 373.15 | 0.2867 | 0.0000 | 0.5220 | 0.0242 | 0.4538 | −2.76 |
Flows | w/w % | Total H | |||||
---|---|---|---|---|---|---|---|
Stream | T/K | kg/s | CHLiO2∙H2O | Ethanol | CHLiO2 | Water | MJ/kg∙s |
1 | 298.15 | 100.0000 | 0.0000 | 0.0000 | 0.2920 | 0.7080 | −1519.40 |
2 | 298.15 | 46.1320 | 0.0000 | 1.0000 | 0.0000 | 0.0000 | −287.63 |
3 | 298.15 | 27.6230 | 26.3080 | 0.0000 | 0.7430 | 0.2570 | −388.14 |
4 | 298.15 | 118.5090 | 0.0000 | 0.3850 | 0.0800 | 0.5350 | −1434.64 |
5 | 298.15 | 26.8340 | 26.3080 | 0.3850 | 0.0800 | 0.5350 | −378.69 |
6 | 298.15 | 0.2630 | 0.0000 | 0.3850 | 0.0800 | 0.5350 | −9.45 |
7 | 364.15 | 26.3650 | 26.3650 | 0.0000 | 0.0000 | 0.0000 | −371.32 |
8 | 364.15 | 0.4690 | 0.0000 | 0.3850 | 0.0800 | 0.5350 | −5.34 |
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González, R.; Barrueto, Y.; Jiménez, Y.P. Thermodynamic Modeling of the Drowning-Out Crystallization Process for LiOH and CHLiO2. Metals 2024, 14, 78. https://doi.org/10.3390/met14010078
González R, Barrueto Y, Jiménez YP. Thermodynamic Modeling of the Drowning-Out Crystallization Process for LiOH and CHLiO2. Metals. 2024; 14(1):78. https://doi.org/10.3390/met14010078
Chicago/Turabian StyleGonzález, Raquel, Yahaira Barrueto, and Yecid P. Jiménez. 2024. "Thermodynamic Modeling of the Drowning-Out Crystallization Process for LiOH and CHLiO2" Metals 14, no. 1: 78. https://doi.org/10.3390/met14010078