# Orthogonal numerical simulation on multi-factor design for rapid pressure swing adsorption

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## Abstract

A two-dimensional model is established to simulate the rapid pressure swing adsorption (RPSA) process used for air separation with single bed. The model considers the transport phenomena occurring in both axial and radial direction. The decision variables include five factors (two heights of dead zone, durations of pressurization and adsorption steps, product extraction ratio), and the performance indexes consist of four variables (product purity, product recovery, bed size factor and average volume product yield). Based on an L_{16} (4^{5}) orthogonal design, 16 cases are arranged and the corresponding simulations are performed until the cycle steady states are reached from a given initial state. Range analysis is used to investigate the relative importance of the five factors on each performance index. Each factor’s optimal level and the corresponding combination is found out for each performance index successively.

## Keywords

Two-dimensional Rapid/pressure swing adsorption Orthogonal design Dynamic simulation Air separation Oxygen concentrator## List of symbols

*a*Thermal diffusion coefficient, m

^{2}s^{-1}*d*_{p}Diameter of adsorbent particle, m

*D*_{im}Mass dispersion rate, m

^{2}s^{-1}*e*_{f}Total fluid energy, kJ kg

^{-1}*e*_{p}Total solid medium energy, kJ kg

^{-1}**F**Momentum source term, kg m

^{-2}s^{-2}*H*_{in}Dead-zone height of feed-in, m

*H*_{out}Dead-zone height of product-end, m

- Δ
*H* Heat of adsorption, J mol

^{-1}*K*_{i}Langmuir parameter, mol kg

^{-1}kPa^{-1}*K*_{ij}Summation of experimental results of factor

*j*at level*i*- \(\bar{K}_{ij}\)
The average of

*K*_{ ij }*k*_{1}Langmuir temperature dependence constant, mol kg

^{-1}kPa^{-1}*k*_{2},*k*_{4}Langmuir temperature dependence constant, K

*k*_{3}Langmuir temperature dependence constant, kPa

^{-1}*k*Mass transfer rate coefficient, s

^{-1}*k*_{t}Turbulent kinetic energy, m

^{2}s^{-2}*k*_{eff}Effective bed thermal conductivity, W m

^{-2}K*k*_{p}Solid medium thermal conductivity, W m

^{-2}K*k*_{f}Fluid phase thermal conductivity, W m

^{-2}K- \(\dot{m}_{{\text {O}_{2} }}\)
O

_{2}-enriched product gas per cycle, lbs moles cycle^{-1}*M*_{i}Molar weight of component i, kg mol

^{-1}*M*_{w}Molar weight of fluid, kg mol

^{-1}*q*Solid-phase adsorbate concentration, mol kg

^{-1}- \(q_{feed}\)
Feeding flow rate, kg s

^{-1}*q*_{penetrate}Molar flow rate of gas penetrated, mol s

^{-1}- \(\bar{q}_{prod}\)
Average product flow rate, L min

^{-1}- \(\bar{q}_{purge}\)
Average purge mass flow rate, kg s

^{-1}*q*^{*}Adsorbate concentration in equilibrium with gas phase, mol kg

^{-1}*Q*_{penetrate}Total amount of gas penetrated from the adsorber top per cycle, mol

*Q*_{product}Total amount of production obtained per cycle, mol

*Q*_{purge}Total mount enriched gas used to purge the adsorber per cycle, mol

*r*Radial coordinate, m

*R*Gas constant, J mol

^{-1}K^{-1}/ radius of bed, m- Rec
Oxygen recovery

*S*_{i}Mass source term of the ith component, kg m

^{-3}s^{-1}*S*_{m}Total mass source term, kg m

^{-3}s^{-1}- t
_{c} Total cycle time of PSA process, s

*T*Temperature, K

*T*_{ad}Adsorption time, s

*T*_{dp}Desorption time,s

*T*_{pg}Purge time, s

*T*_{pr}Pressurization time, s

*u*_{i}Velocity in the

*i*direction, m s^{-1}- \({\mathbf{u}}\)
Velocity vector, m s

^{-1}*w*The total amount of zeolite adsorbent in the system, lbs

*y*Distance from the adsorber side wall, m

*y*_{i}Mass fraction of component i

*y*_{O2}Transient oxygen mole fraction

- \(y_{{{\text O}_{2} ,feed}}\)
Oxygen mass fraction in feed-in gas

- \(\bar{Y}_{{{\text O}_{2} }}\)
Average oxygen mole fraction of product gas

- \(\bar{Y}_{{{ \text O}_{2} ,n}}\)
Average oxygen mole fraction of product gas of the nth cycle

*z*Axial coordinate, m

## Greek symbols

*ε*Porosity of the fixed bed

*ε*_{t}Dissipation rate of turbulence kinetic energy, m

^{2}s^{-3}*ρ*_{p}Density of adsorbent particle, kg m

^{-3}*ρ*_{f}Fluid density, kg m

^{-3}*γ*Product extraction ratio

## Subscripts

*f*Fluid

*p*Particle

*r*Radial

*i*Species

- *
Equilibrium

## Notes

### Acknowledgements

The authors acknowledge the financial support provided by the National Key Technology R&D Program (No. 2015BAA01B02), Ministry of Science and Technology, People’s Republic of China. The authors also thank the anonymous reviewers and the editor for their valuable comments.

## Supplementary material

Supplementary material 1 Oxygen contour varying with time inside adsorber .mpeg: This animation shows the oxygen concentration varying with time during 14 cycles. (MOV 11884 KB)

Supplementary material 2 y_{o2}’s variation along axial line.mpeg: This animation shows the axial oxygen concentration’s variation during 14 cycles. (MOV 17918 KB)

Supplementary material 3 y_{o2}’s swing of point p_{vent}.mpeg: This animation shows the oxygen concentration’s swing of point p_{vent} during 14 cycles. (MOV 3036 KB)

Supplementary material 4 pressure’s swing of point pvent.mpeg: This animation shows the pressure’s swing of point p_{vent} during 14 cycles. (MOV 3260 KB)

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