Mass and Heat Transfer of Pressure Swing Adsorption Oxygen Production Process with Small Adsorbent Particles
Abstract
:1. Introduction
2. Mathematical Models
2.1. Governing Equations
2.2. Model Parameters
2.3. Cycle Description
2.4. Initial and Boundary Conditions
2.5. Method of Solution
3. Experimental Section
4. Results and Discussions
4.1. Model Verification
4.2. Gas Concentration, Temperature Distributions at the End of Cycle Step
4.3. Effect of Mass Transfer Resistance
4.4. Effect of Particle Size
4.5. Effect of Bed Porosity
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Nomenclature
Latin letters | |||
b_{i} | Langmuir parameter (kPa^{−1}) | Q_{F} | feed flowrate (L·min^{−1}) |
b_{i}^{0} | Langmuir parameter (kPa^{−1}) | Q_{P} | product flowrate (L·min^{−1}) |
c | molar concentration (mol·m^{−3}) | R_{g} | gas constant (J·mol^{−1}·K^{−1}) |
c_{i} | component i molar concentration (mol·m^{−3}) | t | time (s) |
C_{f} | gas heat capacity (J·kg^{−1}·K^{−1}) | t_{AD} | duration of AD step (s) |
C_{s} | solid heat capacity (J·kg^{−1}·K^{−1}) | t_{BD} | duration of BD step (s) |
d_{p} | particle diameter (m) | t_{PED} | duration of PED step (s) |
d_{in} | bed diameter (m) | t_{PR} | duration of PR step (s) |
D_{L} | axial dispersion coefficient(m^{2}·s^{−1}) | t_{PEU} | duration of PEU step (s) |
L | N_{2} adsorbents loading height (m) | t_{PU} | duration of PU step (s) |
m | amount of adsorbents (kg) | T_{f} | gas temperature (K) |
Nu | Nusselt number | T_{F} | feed temperature (K) |
h_{f} | gas-solid heat transfer coefficient (W·m^{−2}·K^{−1}) | T_{PU} | purge gas temperature (K) |
h_{w} | internal gas-wall convective heat transfer coefficient (W·m^{−2}·K^{−1}) | T_{s} | solid temperature (K) |
k_{i} | mass transfer coefficient for adsorbate i (s^{−1}) | T_{w} | wall temperature (K) |
K_{f} | gas thermal dispersion coefficient (W·m^{−1}·K^{−1}) | u | interstitial gas velocity (m·s^{−1}) |
K_{s} | solid phase thermal conductivity (W·m^{−1}·K^{−1}) | u_{in} | feed velocity (m·s^{−1}) |
P | pressure (kPa) | y | oxygen purity of gas |
P_{i} | gas partial pressure (kPa) | y_{F} | oxygen purity of feed gas |
P_{H} | adsorption pressure (kPa) | y_{PU} | oxygen purity of purge gas |
P_{L} | desorption pressure (kPa) | z | axial position (m) |
P_{PED} | pressure at end of PED step (kPa) | Greek letters | |
P_{PEU} | pressure at end of PEU step (kPa) | μ | dynamic viscosity (Pa·s) |
P_{PR} | pressure at end of PR step (kPa) | ρ_{f} | gas density (kg·m^{−3}) |
Pr (=μC_{f}/K_{f}) | Prandtl number | ρ_{p} | apparent density (kg·m^{−3}) |
q_{i} | adsorbed concentration of the component i (mol·kg^{−1}) | ρ_{b} | bulk density (kg·m^{−3}) |
q_{i}* | equilibrium adsorption concentration of the component i, mol·kg^{−1} | ε_{b} | inter-particle porosity |
q_{i}^{s} | saturation adsorbed concentration of the component i, mol·kg^{−1} | ε_{p} | particle porosity |
q_{i}^{s} | saturation adsorbed concentration of the component i, mol·kg^{−1} | ε_{p} | particle porosity |
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Case | k_{i} [7,11,12,13,14,27] | Model of Dominant Resistance [7,11,12,13,14,27] |
---|---|---|
1 | ${k}_{i}={k}_{\mathrm{MD}}$ | $\frac{1}{{k}_{\mathrm{MD}}}=\frac{{r}_{\mathrm{p}}^{2}{K}_{i}}{15{\epsilon}_{\mathrm{p}}{D}_{\mathrm{p}}}$, ${D}_{\mathrm{p}}=\frac{{D}_{\mathrm{m}}{D}_{\mathrm{K}}}{\tau \left({D}_{\mathrm{m}}+{D}_{\mathrm{K}}\right)}$ ${D}_{\mathrm{m}}=0.0018583\frac{\sqrt{{T}_{\mathrm{f}}{}^{3}\left(\frac{1}{{M}_{1}}+\frac{1}{{M}_{2}}\right)}}{\mathrm{P}{\sigma}_{12}^{2}{\mathsf{\Omega}}_{12}}$, ${D}_{\mathrm{K}}=\frac{2{r}_{\mathrm{p}}}{3}\sqrt{\frac{8{R}_{\mathrm{g}}{T}_{\mathrm{f}}}{\pi M}}$ |
2 | $\frac{1}{{k}_{i}}=\frac{1}{{k}_{\mathrm{MD}}}+\frac{1}{{k}_{\mathrm{f}}}$ | $\frac{1}{{k}_{\mathrm{f}}}=\frac{{r}_{\mathrm{p}}{K}_{i}}{3{k}_{\mathrm{F}}}$, $\frac{{k}_{\mathrm{F}}2{r}_{\mathrm{p}}}{{D}_{\mathrm{m}}}=2.0+1.1S{c}^{1/3}{\mathrm{Re}}^{0.6}$ |
3 | $\frac{1}{{k}_{i}}=\frac{1}{{k}_{\mathrm{MD}}}+\frac{1}{{k}_{\mathrm{f}}}+\frac{1}{{k}_{\mathrm{L}}}$ | $\frac{1}{{k}_{\mathrm{L}}}=\frac{{D}_{\mathrm{L}}{K}_{i}\left(1-{\epsilon}_{\mathrm{b}}\right)}{{\epsilon}_{\mathrm{b}}{u}^{2}}$ ${D}_{\mathrm{L}}={\gamma}_{1}{D}_{\mathrm{m}}+\frac{2u{r}_{\mathrm{p}}}{Pe\left(1+{\gamma}_{1}{D}_{\mathrm{m}}/\left(2u{r}_{\mathrm{p}}\right)\right)}$ ${\gamma}_{1}=0.45+0.55{\epsilon}_{\mathrm{b}}$, $Pe=3.35{r}_{\mathrm{p}}$ |
Bed | Zeolite | Fluid | |||
---|---|---|---|---|---|
P_{H}/kPa | ~250 | C_{s}/J·kg^{−1}·K^{−1} | 1172 | Feed | 21% O_{2}, 79% N_{2} |
P_{L}/kPa | 101~103 | d_{p}/mm | 0.35~0.5 | M_{1}/kg·mol^{−1} | 0.032 |
y_{F} | 0.21 | ρ_{p}/kg·m^{−3} | 1035 | M_{2}/kg·mol^{−1} | 0.028 |
d_{in}/m | 0.026 | ρ_{b}/kg·m^{−3} | 625~630 | ρ_{f}/kg·m^{−3} | 1.743 |
L/m | 0.12 | ε_{b} | 0.31~0.43 | C_{f}/J·kg^{−1}·K^{−1} | 1005 |
T_{F}/K | 310.15 | ε_{p} | 0.33 | K_{f}/W·m^{−1}·K^{−1} | 0.2624 |
T_{PU}/K | 298.15 | K_{s}/W·m^{−1}·K^{−1} | 0.3 | ||
T_{W}/K | 298.15 |
Initial Conditions y(z) = 0.21; P(z) = 101.325 kPa; T_{f}(z) = T_{s}(z) = 298.15 K | ||
---|---|---|
Step | z = 0 (Feed End) | z = L (Product End) |
i | ${D}_{\mathrm{L}}\frac{\partial y}{\partial z}=-u\left({y}_{\mathrm{F}}-y\right)$ ${K}_{\mathrm{f}}\frac{\partial {T}_{\mathrm{f}}}{\partial z}=-u{\rho}_{\mathrm{f}}{C}_{\mathrm{f}}\left({T}_{\mathrm{F}}-{T}_{\mathrm{f}}\right)$ $P={P}_{\mathrm{PEU}}+({P}_{\mathrm{PR}}-{P}_{\mathrm{PEU}})\left(t/{t}_{\mathrm{PR}}\right)$ | $u=0$, $\frac{\partial y}{\partial z}=0$, $\frac{\partial {T}_{\mathrm{f}}}{\partial z}=0$ |
ii | $u={u}_{\mathrm{in}}$, ${D}_{\mathrm{L}}\frac{\partial y}{\partial z}=-u\left({y}_{\mathrm{F}}-y\right)$ ${K}_{\mathrm{f}}\frac{\partial {T}_{\mathrm{f}}}{\partial z}=-u{\rho}_{\mathrm{f}}{C}_{\mathrm{f}}\left({T}_{\mathrm{F}}-{T}_{\mathrm{f}}\right)$ $P={P}_{\mathrm{PR}}+({P}_{\mathrm{H}}-{P}_{\mathrm{PR}})\left(t/{t}_{\mathrm{AD}}\right)$ | $\frac{\partial y}{\partial z}=0$, $\frac{\partial {T}_{\mathrm{f}}}{\partial z}=0$ |
iii | $\frac{\partial y}{\partial z}=0$, $\frac{\partial {T}_{\mathrm{f}}}{\partial z}=0$ $P={P}_{\mathrm{H}}+\left({P}_{\mathrm{PED}}-{P}_{\mathrm{H}}\right)\left(t/{t}_{\mathrm{PED}}\right)$ | $u=0$, $\frac{\partial y}{\partial z}=0$, $\frac{\partial {T}_{\mathrm{f}}}{\partial z}=0$ |
iv | $\frac{\partial y}{\partial z}=0$, $\frac{\partial {T}_{\mathrm{f}}}{\partial z}=0$ $P={P}_{L}+({P}_{\mathrm{PED}}-{P}_{\mathrm{L}}){\left(t/{t}_{\mathrm{BD}}-1\right)}^{2}$ | $u=0$, $\frac{\partial y}{\partial z}=0$, $\frac{\partial {T}_{\mathrm{f}}}{\partial z}=0$ |
v | $\frac{\partial y}{\partial z}=0$, $\frac{\partial {T}_{\mathrm{f}}}{\partial z}=0$, $P={P}_{\mathrm{L}}$ | $u={u}_{\mathrm{PU}}$, ${D}_{\mathrm{L}}\frac{\partial y}{\partial z}=-{u}_{\mathrm{PU}}({y}_{\mathrm{PU}}-y)$ ${k}_{\mathrm{f}}\frac{\partial {T}_{\mathrm{f}}}{\partial z}=-{u}_{\mathrm{PU}}{\rho}_{\mathrm{f}}{c}_{\mathrm{f}}({T}_{\mathrm{PU}}-{T}_{\mathrm{f}})$ |
vi | $\frac{\partial y}{\partial z}=0$, $\frac{\partial {T}_{\mathrm{f}}}{\partial z}=0$ $P={P}_{\mathrm{L}}+\left({P}_{\mathrm{PEU}}-{P}_{\mathrm{L}}\right)\left(t/{t}_{\mathrm{PEU}}\right)$ | $u=0$, $\frac{\partial y}{\partial z}=0$, $\frac{\partial {T}_{\mathrm{f}}}{\partial z}=0$ |
Adsorbate | q^{s} (mol·kg^{−1}) | b_{i}^{0} (kPa^{−1}) | $\mathbf{\Delta}{\mathit{H}}_{\mathit{i}}$ (J·mol^{−1}) |
---|---|---|---|
O_{2} | 2.29 | 2.8901 × 10^{−6} | 14,071.54 |
N_{2} | 2.29 | 6.6988 × 10^{−7} | 23,638.76 |
Case | 1 | 2 | 3 | Experimental Results |
---|---|---|---|---|
Purity (%) | 96.3 | 95.7 | 93.2 | 92.6 |
Recovery (%) | 34.7 | 34.6 | 32.4 | 31.4 |
Productivity (L·(h·kg)^{−1}) | 433.4 | 430.8 | 420.3 | 416.6 |
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Sun, Y.; Zhang, C.; Zhu, X.; Dong, L.; Sun, X. Mass and Heat Transfer of Pressure Swing Adsorption Oxygen Production Process with Small Adsorbent Particles. Processes 2023, 11, 2485. https://doi.org/10.3390/pr11082485
Sun Y, Zhang C, Zhu X, Dong L, Sun X. Mass and Heat Transfer of Pressure Swing Adsorption Oxygen Production Process with Small Adsorbent Particles. Processes. 2023; 11(8):2485. https://doi.org/10.3390/pr11082485
Chicago/Turabian StyleSun, Yuan, Chuanzhao Zhang, Xianqiang Zhu, Liang Dong, and Xianhang Sun. 2023. "Mass and Heat Transfer of Pressure Swing Adsorption Oxygen Production Process with Small Adsorbent Particles" Processes 11, no. 8: 2485. https://doi.org/10.3390/pr11082485