To the problem of forming the equation system for pressure swing adsorption mathematical model
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Oleg Golubyatnikov
,
Evgeny Akulinin
Abstract
The complexity of the pressure swing adsorption (PSA) mathematical model, the need for its multiple calculations to reach the cyclic steady state and a large number of functional dependencies lead to unstable numerical circuits, physically unrealistic oscillations in adsorption profiles, an increase in the calculation time, and the failure of the solver. The paper proposes an approach to optimizing the calculation process, which consists in finding a reasonable balance between the completeness of the PSA mathematical model and the accuracy of the results obtained. The effectiveness of the approach is demonstrated on the example of air oxygen enrichment and hydrogen recovery from synthesis gas. The gas separation processes were simulated for the two-adsorber PSA unit with a granulated 13X adsorbent. The effect of the changes in the model coefficients on its accuracy in the operating range of input variables is investigated. A distinctive feature of this study is the recommendations for choosing a set of the model equations to calculate the PSA processes which are particularly relevant when solving optimization problems with uncertainty. The productivity, cycle duration, the diameter of the adsorbent particles and the flow rate, at which it is advisable to use the isothermal and external diffusion reduced PSA model in the calculations, are established, which will save at least 24.3 and 47.1% of the CPU time with a small loss in accuracy. The proposed approach can be used to form a set of equations for the PSA, rPSA, ultra rPSA, VSA, VPSA models, separation of various gas mixtures on various adsorbents.
Award Identifier / Grant number: President Grant MK-1604.2020.8
Funding source: Ministry of Science and Higher Education of the Russian Federation
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Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
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Research funding: This research was supported by the Ministry of Science and Higher Education of the Russian Federation within the President Grant MK-1604.2020.8.
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Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
Values of adsorbent characteristics and gas mixture in the PSA model.
| Initial data | Air | Synthesis gas |
|---|---|---|
| Zeolite adsorbent | 13X | 13X |
| Density of the adsorbent, ρ a (kg/m3) | 2140 | 2140 |
| Porosity coefficient of the adsorbent, ε (m3/m3) | 0.39 | 0.39 |
| Thermal conductivity coefficient of the adsorbent, λ a (W/m K) | 0.139 | 0.139 |
| Sphericity coefficient of adsorbent particles, ψ | 1 | 1 |
| Specific heat of the adsorbent, C a (J/kg K) | 830 | 830 |
| Input temperature in the adsorbent, |
25 | 25 |
| Characteristic energy of adsorption, E (J/mol) | 12902 | 12902 |
| Average lifetime of an adsorbate molecule in the adsorbate state, τ0 (s) | 10–13 | 10–13 |
| Relative volume of adsorbent macropores, |
0.7 | 0.7 |
| Relative volume of adsorbent micropores, |
0.25 | 0.25 |
| Component concentration, c (vol %) | 22/78 (O2/N2) | 68/27/5 (H2/CO2/CO) |
| Temperature of gas mixture, |
25 | 25 |
| Latent heat of vaporization, |
6819.9/5577.3 (O2/N2) | 903.7/17154.4/6041.7 (H2/CO2/CO) |
| Diffusion volume, V | 16.6/17.9 (O2/N2) | 7.07/26.9/18.9 (H2/CO2/CO) |
Parameters of the Dubinin–Radushkevich isotherm.
| Initial data | Air | Synthesis gas |
|---|---|---|
| Limiting adsorption volume, W0 (cm3/g) | 0.262 | 0.262 |
| Parameter of the dominant micropore size, B (10−6 1/K2) | 2.2 | 2.2 |
| Affinity coefficient, |
0.65/1 (O2/N2) | 0.15/2.2/1.05 (H2/CO2/CO) |
| Critical molar volume, |
0.04/0.06 (O2/N2) | 0.007/0.04/0.05 (H2/CO2/CO) |
| Thermal coefficient of limiting adsorption, |
1.7861/2.1753 (O2/N2) | 5.1448/2.626/1.7372 (H2/CO2/CO) |
| Saturation pressure, P s (atm) | 498.08/525.99 (O2/N2) | 620.78/212.49/343.99 (H2/CO2/CO) |
Adsorber design and mode parameters of PSA processes.
| Initial data | Air | Synthesis gas |
|---|---|---|
| Inner diameter of the adsorber, D (m) | 0.04 | 0.1 |
| Adsorbent bed length, L (m) | 0.2 | 1.0 |
| Desorption input pressure, |
1 | 0.75 |
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Articles in the same Issue
- Frontmatter
- Research Articles
- CFD simulation of the ethylbenzene dehydrogenation reaction in the fixed bed reactor with a cylindrical catalyst of various sizes
- Energy and exergy optimization of oxidative steam reforming of acetone–butanol–ethanol–water mixture as a renewable source for H2 production via thermodynamic modeling
- A novel LSSVM-L Hammerstein model structure for system identification and nonlinear model predictive control of CSTR servo and regulatory control
- Environmental and thermodynamic performance assessment of biomass gasification process for hydrogen production in a downdraft gasifier
- Modeling of lime production process using artificial neural network
- Control of TITO processes using sliding mode controller tuned by ITAE minimizing criterion based Nelder-Mead algorithm
- To the problem of forming the equation system for pressure swing adsorption mathematical model
- Review
- A comparative study of various Smith predictor configurations for industrial delay processes
