pressure swing adsorption

1. 7th
International Chemical Engineering Congress & Exhibition
Kish, Iran, 21-24 November, 2011
Numerical Simulation of a Pressure Swing Adsorption
for Air Separation
Masoud Mofarahi, Ehsan Javadi Shokroo
Corresponding Authors Address:
Chemical Engineering Department, Faculty of Engineering, Persian Gulf University, Iran-Bushehr
Corresponding Author Email:
Mofarahi@pgu.ac.ir
Abstract
A two-bed four step pressure swing adsorption (PSA) using zeolite 5A adsorbent for oxygen
separation from air studied by dynamic mathematical simulation. The mathematical model contains
partial differential equations corresponding to the bulk gas phase mass, energy and momentum
balances. The effects of operational variables such as purge to feed ratio, high operating to low
operating pressure and feed flow rate on oxygen purity and recovery were investigated. The results
show that in a constant feed flow rate, increasing purge to feed ratio can lead to a reduction the oxygen
recovery, but instead will cause to increase the oxygen purity. In the same conditions, increase the feed
flow rate will result in a reduction the oxygen purity while the oxygen recovery increases. Results of
simulation indicated a very good agreement with some current literature experimental work.
Keywords: Pressure swing adsorption; Simulation; Oxygen production; Mathematical modeling;
zeolite 5A
Introduction
Air separation process can be done based on the cryogenic system and non-cryogenic. Recent
systems (non-cryogenic) based on cyclic batch adsorption processes, and membrane
technologies. Other systems in this field, such as separation systems based on chemical processes
are available but compared to these processes are not very important. More information is
available elsewhere [1]. Cyclic batch adsorption processes differ from each other, mainly in the
methods by which the adsorbent is regenerated during the desorption cycle. Adsorbent
regeneration can be done by increasing the temperature (in the thermal swing system), pressure
drop (in the pressure swing and vacuum swing system), purging with a non-adsorbing inert gas
(in the purge gas stripping system with constant T and P.) and or using a stream containing a
competitively adsorbed species. Choice of regeneration methods for each system depends on

2. Numerical Simulation of a Pressure Swing Adsorption … …
economic factors and also desired technical characteristics. The pressure swing system (PSA) is
well suited to rapid cycling, and this has the advantage of minimizing the absorbent inventory
and therefore, the capital costs of the system [2].
PSA process is a wide operating unit to separation and purification of gases, which is acts based
on the capability of solids adsorption and selective separation of gases. The most important
operational parameter in this system is pressure, and most industrial units operate ator vicinity of
surrounding temperature. In the recent years, the use of this method was followed by researchers
as a more important issue in the air separation, because in generally the PSA process is more
economical than the other separation processes. Sometimes, in order to justify economically, this
process can be replaced the other separation processes. The PSA process evolution around the
worldwide is still continuing and to achieve the best economic conditions each day newer acts are
done for this important process.
Use of this process to oxygen and nitrogen production from the air took for the first time in 1958
by skarstrom. He provided his recommended PSA cycles to enrich the oxygen and nitrogen in the
air under a subject of heatless drier [3]. The main reasons for the success of this technology are
many reforms that achieved in this field and that also is the new, designed and configured for
cycles and devices [4,5,6,7,8].
In overall, the PSA process performance strongly influenced by design parameters (such as: bed
size, adsorbent physical properties, configuration and number of beds) and operational variables
(such as: pressurization time, production time, purge time, feed flow rate, purge flow rate,
production flow rate, temperature and/or pressure variations). This could be an optimum amount
of process variables to achieve maximum possible performance. Therefore, it is important to
review the behavior of the PSA operating variables to knowing the optimum operating
conditions. Zeolite adsorbent used in this separation process is usually 5A or 13X. In this process
also argon with oxygen is removed as the product from the system due to having almost the same
adsorption behavior near the oxygen. During the progress made on the PSA process, zeolites
studies in order to improve their quality (capacity and selectivity) continually be looking away
from the years. Including improvements in this area has been set to reduce the inert inorganic
material named. More comprehensive information on zeolite developments can be found in other
sources [9,10]. The most important theoretical models to describe the PSA behavior based on
equilibrium between gas phase, and adsorbed phase can be founded are cited to Shendalman &
Mitchell (1972), Chan et al (1981), Kenney & Florez-Fernandez (1983) and Knaebel & Hill
(1985) [11]. In 1989, Farooq, Ruthven & Boniface, as the same models of inter-particle diffusion
which were provided to nitrogen separation from air previously, used a diffusion model for a
two-bed PSA system with zeolite 5A adsorbent to oxygen production from air [12]. The model
also in 2001 by Mendes et al [13] to separate oxygen from air was presented. They were studied a
system of two bed system with zeolite 5A, and they compared the results of the basic Skarstrom
cycle with cycle that includes the pressure equalization step. They used LDF-DG model to
describe the inter-particle mass transfer. The model gave very well results for steady state and
unsteady state. In the model presented by Jee et al. [14] also LDF model used to survey the
effects of co-pressure and pressure variable steps on the PSA performance. They also considered
temperature variation, and they were considered thermal equilibrium between the adsorbent and
fluid bulk flow. In this case, the system was used by those also that is a two-bed PSA system with
zeolite 5A.

3. 7th
International Chemical Engineering Congress & Exhibition
Kish, Iran, 21-24 November, 2011
In this work, we were studied the effect of operational variables on the Skarstrom PSA cycle to
survey the optimal conditions based on mathematical modeling and simulation under operational
conditions that use in this study.
Mathematical Modeling
To develop a mathematical model for a PSA system the main assumptions that have been applied
include:
1. Gas behaves an ideal gas.
2. The flow pattern is described by the axially dispersed plug-flow model.
3. Absorbing properties throughout the tower would remain constant and unchanged.
4. Radial gradient is to be negligible.
5. Equilibrium equations for the components of the air by two-component Langmuir
isotherm can be expressed.
6. Mass transfer rate by a linear driving force equation is expressed.
7. Thermal equilibrium between gas phase and solid is assumed.
8. Pressure drop along the bed is calculated by the Ergun’s equation.
And other common assumptions in the simulation of adsorption processes.
Overall and component mass balances for the bulk phase in the adsorption bed to form the
following equations are written
−𝐷𝑙
𝜕2
𝐶𝑖
𝜕𝑧2
+
𝜕(𝐶𝑖 𝑢)
𝜕𝑧
+
𝜕𝐶𝑖
𝜕𝑡
+ 𝜌 𝑝.
1 − 𝜀
𝜀
𝜕𝑞͞ 𝑖
𝜕𝑡
= 0 (1)
−𝐷𝑙
𝜕2
𝐶
𝜕𝑧2
+
𝜕(𝐶𝑢)
𝜕𝑧
+
𝜕𝐶
𝜕𝑡
+ 𝜌 𝑝.
1 − 𝜀
𝜀
𝜕𝑞͞ 𝑖
𝜕𝑡
𝑛
𝑖=1
= 0
(2)
When the ideal gas law ( 𝐶𝑖 = 𝑦𝑖 𝑃 𝑅𝑇and 𝐶 = 𝑃 𝑅𝑇) is applied to eqs 1 and 2, the component and
overall mass balances can be represented as follows:
−𝐷𝑙
𝜕2
𝑦𝑖
𝜕𝑧2
+ 𝑢
𝜕𝑦𝑖
𝜕𝑧
+ 𝑦𝑖
𝜕𝑢
𝜕𝑧
+
𝜕𝑦𝑖
𝜕𝑡
+
𝜌 𝑝 𝑅𝑇
𝑃
.
1 − 𝜀
𝜀
𝜕𝑞͞ 𝑖
𝜕𝑡
= 0 (3)
−𝐷𝑙
𝜕2
𝑃
𝜕𝑧2
+
𝜕𝑃
𝜕𝑡
+ 𝑃
𝜕𝑢
𝜕𝑧
+ 𝑢
𝜕𝑃
𝜕𝑧
+ 𝑃𝑇 −𝐷𝑙
𝜕2
𝜕𝑧2
1
𝑇
+
𝜕
𝜕𝑡
1
𝑇
+ 𝑢
𝜕
𝜕𝑧
1
𝑇
− 2𝐷𝑙 𝑇
𝜕
𝜕𝑧
1
𝑇
𝜕𝑃
𝜕𝑧
+ 𝜌 𝑝 𝑅𝑇
1 − 𝜀
𝜀
𝜕𝑞͞ 𝑖
𝜕𝑡
𝑛
𝑖=1
= 0
(4)
Another characteristic of adsorption process is temperature variations caused by heat of
adsorption and desorption occur. In this system, energy balance for the gas phase and also heat
transfer to the bed wall is included.
−𝐾𝑙
𝜕2
𝑇
𝜕𝑧2
+ 𝜀𝜌 𝑔
𝐶 𝑃𝑔 𝑢
𝜕𝑇
𝜕𝑧
+ 𝑇
𝜕𝑢
𝜕𝑧
+ 𝜀𝑡 𝜌 𝑔
𝐶 𝑃𝑔 + 𝜌 𝐵
𝐶 𝑃𝑠
𝜕𝑇
𝜕𝑡
− 𝜌 𝐵
𝜕 𝑞͞ 𝑖
𝜕𝑡
− 𝛥𝐻͞ 𝑖
𝑛
𝑖=1
+
2𝑕𝑖
𝑅 𝐵𝑖
𝑇 − 𝑇 𝑤 = 0
(5)
To evaluate heat loss through the walls and the accumulation of energy, corresponding to an
energy balance has also been used.
𝜌 𝑤 𝐶 𝑃𝑤 𝐴 𝑤
𝜕𝑇𝑤
𝜕𝑡
= 2𝜋𝑅 𝐵𝑖 𝑕𝑖 𝑇 − 𝑇𝑤 − 2𝜋𝑅 𝐵𝑜 𝑕 𝑜 𝑇𝑤 − 𝑇𝑎𝑡𝑚 (6)

4. Numerical Simulation of a Pressure Swing Adsorption … …
Where
𝐴 𝑤 = 𝜋 𝑅 𝐵𝑜
2
− 𝑅 𝐵𝑖
2
(7)
The well-known Danckwerts boundary conditions are applied
Pressurization and production step
−𝐷𝑙
𝜕𝑦𝑖
𝜕𝑧
| 𝑧=0 = 𝑢 𝑦𝑖| 𝑧=0− − 𝑦𝑖| 𝑧=0+ ;
𝜕𝑦𝑖
𝜕𝑧
| 𝑧=𝐿 = 0 (8-1)
−𝐾𝑙
𝜕𝑇
𝜕𝑧
| 𝑧=0 = 𝜌 𝑔 𝐶 𝑃𝑔 𝑢 𝑇| 𝑧=0− − 𝑇| 𝑧=0+ ;
𝜕𝑇
𝜕𝑧
| 𝑧=𝐿 = 0 (8-2)
Where yi|z=0− means the feed composition for the component i.
Counter current purge step
−𝐷𝑙
𝜕𝑦𝑖
𝜕𝑧
| 𝑧=𝐿 = 𝑢 𝑦𝑖| 𝑧=𝐿+ − 𝑦𝑖| 𝑧=𝐿− ;
𝜕𝑦𝑖
𝜕𝑧
| 𝑧=0 = 0 (9-1)
−𝐾𝑙
𝜕𝑇
𝜕𝑧
| 𝑧=𝐿 = 𝜌 𝑔 𝐶 𝑃𝑔 𝑢 𝑇| 𝑧=𝐿+ − 𝑇| 𝑧=𝐿− ;
𝜕𝑇
𝜕𝑧
| 𝑧=0 = 0 (9-2)
Where 𝑦𝑖| 𝑧=𝐿+ means a volume-averaged composition of the effluent stream during the adsorption
step for the purge step.
Counter current blowdown step
𝜕𝑦𝑖
𝜕𝑧
| 𝑧=0 =
𝜕𝑦𝑖
𝜕𝑧
| 𝑧=𝐿 = 0 (10-1)
𝜕𝑇
𝜕𝑧
| 𝑧=0 =
𝜕𝑇
𝜕𝑧
| 𝑧=𝐿 = 0 (10-2)
Boundary conditions for the interstitial velocity
Pressurization and counter current blodown step
𝑢 𝑧=𝐿 = 0 (11-1)
Pressurization and production step
𝑢 𝑧=0 = 𝑢 𝑓𝑒𝑒𝑑 (11-2)
Counter current purge step
𝑢 𝑧=𝐿 = 𝐺. 𝑢𝑓𝑒𝑒𝑑 (11-3)
The initial conditions for feed flow
𝑦𝑖 𝑧, 0 = 0; 𝑧, 0 = 0; 𝑢(𝑧, 0) = 0 (12)
𝑇 𝑧, 0 = 𝑇𝑎𝑡𝑚; 𝑇𝑤 (0) = 𝑇𝑎𝑡𝑚 (13)
In this study, the pressure time function is assumed as an exponential function which is adapted
to the literature [21].
𝑃 𝑡 = 𝑎. 1 − 𝑓 𝑡 . 𝑒−𝑓(𝑡)
+ 𝑏. 𝑓 𝑡 (14)
In the above equation a, b and f(t) parameteres defined regared to duration and initial and final
pressures of each step.
To consider the pressure drop effect across the bed, Ergun’s equation was introduced as a
momentum balance [15].
−
𝑑𝑃
𝑑𝑧
= 𝑎𝜇𝑢 + 𝑏𝜌𝑢 𝑢 (15-1)
𝑎 =
150
4𝑅 𝑝
2
(1 − 𝜀)2
𝜀2
, 𝑏 = 1.75
(1 − 𝜀)
2𝑅 𝑝 𝜀
(15-2)

5. 7th
International Chemical Engineering Congress & Exhibition
Kish, Iran, 21-24 November, 2011
Where u is the interstitial velocity.
The multi-component adsorption equilibrium was predicted by the following LDF model.
𝑞𝑖 =
𝑞 𝑚𝑖 𝐵𝑖 𝑃𝑖
1 + 𝐵𝑗 𝑃𝑗
𝑛
𝑗=1
(16)
Where,
𝑞 𝑚𝑖 = 𝑘1 + 𝑘2 𝑇, 𝐵𝑖 = 𝑘3 exp
𝑘4
𝑇 (17)
The sorption rate into an adsorbent pellet is described by the LDF model with a single lumped
mass-transfer parameter[17].
𝜕𝑞͞ 𝑖
𝜕𝑡
= 𝜔𝑖 𝑞𝑖
∗
− 𝑞͞ 𝑖
, 𝜔𝑖 =
15𝐷𝑒𝑖
𝑟𝑐
2
(18)
Where [18],
15𝐷𝑒𝑖
𝑟𝑐
2
= 𝐶𝑃𝑟
0.5
(1 + 𝐵𝑖 𝑃𝑖)2 (19)
The adsorption isotherm parameters and diffusion rate constant of N2 and O2 over zeolite 5A are
also shown in Table 1. Table 2 and Table 3 shows the adsorbent and bed characteristics,
respectively [14].
Table 1 EquilibriumRate parameters and heat of adsorption of N2 and O2 on
zeolite 5A [14]
N2 O2
𝐤 𝟏 × 𝟏𝟎 𝟑
(𝐦𝐨𝐥 𝐠) 6.210 7.252
𝐤 𝟐 × 𝟏𝟎 𝟓
(𝐦𝐨𝐥 𝐠 . 𝐤) -1.270 -1.820
𝐤 𝟑 × 𝟏𝟎 𝟒
(𝟏 𝐚𝐭𝐦) 1.986 54.19
𝐤 𝟒(𝐤) 1970 662.6
Heat of adsorption, -Δ͞Hi (cal/mol) 5470 3160
Diffusion rate constant(s-1
) [22] 0.0066 0.0267
Results and Discussion
The implicit finite difference scheme was used to solve a mathematical model that considered of
coupled partial differential equations. The central first order difference is used to discretize the
first order space derivatives and the second order derivatives discretized by using a second order
central difference. The forward finite difference is used to time spacial. Solving of algebraic
equations were done by MATLAB software.
In order to validate the simulation results, first the results of this work were compared with the
other experimental data in the literature. In an experimental study, Ade´lio M. M. Mendes et al
[19] were simulated a PSA commercial unit performance to evaluate the effects of some
operational variables. They concluded that to affect of pressure rising in the adsorption step, in a
constant feed flow rate, increased pressure is leading to decrease both purity and recovery of
oxygen. The experimental results by these authors together with the simulation in this work has
come in Fig. 1. As obvious in this figure, the simulation and presented the model in this work
make predict the results of the other experimentally work with relatively high accuracy.

6. Numerical Simulation of a Pressure Swing Adsorption … …
Table 2 Characteristics of adsorbent [14]
Adsorbent Zeolite 5A
Type Sphere
Average pellet size, RP (cm) 0.157
Pellet density, ρP (g/cm3
) 1.16
Heat capacity, Cps (cal/g.k) 0.32
Particle porosity, α 0.65
Bed density, ρB (g/cm3
) 0.795
Table 3 characteristics of adsorption bed
Length, L (cm) [in this work] 76
Inside radius, RBi (cm) [in this work] 2.138
Outside radius, RBo (cm) [in this work] 2.415
Heat capacity of the column, Cpw (cal/g.K) [14] 0.12
Density of column, ρw (g/cm3
) [14] 7.83
Internal heat-transfer coefficient, hi (cal/cm2
.K.s) [14] 𝟗. 𝟐 × 𝟏𝟎−𝟒
External heat-transfer coefficient, ho (cal/ cm2
.K.s) [14] 𝟑. 𝟒 × 𝟏𝟎−𝟒
Axial thermal conductivity, KL (cal/cm.s.K) [14] 𝟔. 𝟐 × 𝟏𝟎−𝟓
Axial dispersion coefficient, DL (cm2
/s) [14] 𝟏 × 𝟏𝟎−𝟓
Another work which was done by Ade´lio M. M. Mendes et al [13] the effects of some other
operational variables on the PSA unit performance were studied by experiments and simulations.
They concluded that to affect of the purge flow rate on oxygen purity and recovery, increasing
the purge flow rate led to decreased recovery but instead the oxygen purity will increase. The
experimental results of these authors together with presented results of modeling in this work are
shown in Fig. 2. In this consideration also can be seen that the results of simulation indicate a
very good agreement with same current literature experimental work.
Figure 1: O2 purity a recovery as a function of production pressure, compare the model prediction in this work and
experimental data by Mendes et al [19].

7. 7th
International Chemical Engineering Congress & Exhibition
Kish, Iran, 21-24 November, 2011
Figure 2: O2 purity and recovery as a function of purge flow rate, compare the model prediction in this work and
experimental data by Mendes et al [13].
In a PSA process, the duration of the adsorption step is determined by studying the breakthrough
curve. The term breakthrough curve refers to the response of the initially clean bed to an influent
with a constant composition. It can be seen by monitoring the concentration of the effluent.
Breakthrough occurs when the effluent concentration reaches a specific value. The adsorbate
concentration in the flow at any given point in a bed is a function of time, resulting from the
movement of concentration front in the bed. The breakthrough curve for a gas containing a single
adsorbate can be obtained by the solution of the mass balance equations for both the bed and
adsorbent particles, along with the equilibrium isotherm. The duration of the adsorption step is
the time period needed for breakthrough to occur. After this time, the product purity will decline,
and before this time the full bed capacity will not be employed. Thus the adsorption time should
Figure 3: O2 effluent mole fraction at the end of the bed during AD step
be near the breakthrough time. This time depends upon isotherm, diffusivity and residence time
of the feed in the bed [20]. In this work, we have considered AD time based on start time the
release of absorbed nitrogen (t=35 seconds). Fig. 3 shows oxygen concentration versus time at
the top of the bed during AD step. The temperature profile during the AD step at the cyclic steady
state illustrated in Fig. 4. It can be seen that the changes in temperature are too small. In Fig. 5 it
also shows the changes in temperature in the cyclic steady state for successive cycles at the top

8. Numerical Simulation of a Pressure Swing Adsorption … …
the bed. As it implies, the temperature variation is very low for the conditions studied in this
figure. Fig. 6.a represents the effect of 𝑷 𝑭 ratio on the oxygen purity in the AD step effluent for
different 𝑷 𝑯 𝑷 𝑳 ratios. As indicated, at all the 𝑷 𝑯 𝑷 𝑳 ratios, increase the 𝑷 𝑭 will lead to
increasing oxygen purity. Reason of this is due to the increased purge flow rate that ultimately
led to a better desorption bed in the low pressure step. Therefore, at higher 𝑷 𝑭 ratio with a
cleaner bed it can be achieved the higher levels of oxygen purity. In this figure also it can be seen
that for ratios of 𝑷 𝑯 𝑷 𝑳 = 𝟐 𝟏 and 𝑷 𝑯 𝑷 𝑳 = 𝟓 𝟏 , than the other operating pressures ratios, the
highest purity achieved for oxygen in the product. In order to better compare the 𝑷 𝑯 𝑷 𝑳 = 𝟐 𝟏 and
𝑷 𝑯 𝑷 𝑳 = 𝟓 𝟏, in Fig. 6.b changes in oxygen purity are given for these two cases separately.
Obviously, the system gives the best pure oxygen in 𝑷 𝑯 𝑷 𝑳 = 𝟓 𝟏. Fig. 7 shows oxygen recovery
profile, for the same ratios of 𝑷 𝑯 𝑷 𝑳 as previous, in terms of 𝑷 𝑭 ratio. Clearly, in any ratio of
𝑷 𝑯 𝑷 𝑳, unlike the behavior of purity, increased 𝑷 𝑭 ratio lead to decrease the levels of oxygen
recovery. It is evident the reduction of product flow rate causes by increased purge flow rate will
be led to reduce the amount of oxygen recovery. In addition, this figure shows for 𝑷 𝑯 𝑷 𝑳 =
𝟓 𝟎. 𝟓, despite being the least amount of oxygen purity, the oxygen recovery has the highest
quantity instead than the other 𝑷 𝑯 𝑷 𝑳 values. The reversal behavior of the purity and recovery is
an evident effect and is also seen in the other sources. Fig. 8 indices the variation of oxygen
purity versus to the feed flow rate for different values of 𝑷 𝑯 𝑷 𝑳 ratios. As indicated, for all 𝑷 𝑯 𝑷 𝑳
ratios, increased feed flow rate will be led to decrease the oxygen purity. Increasing the feed flow
rate led to rises the AD step pressure that eventually causes the co-absorption of nitrogen with the
oxygen and finally decreases oxygen purity in the product output. In Fig.9 it is clear that
increasing feed flow rate will increase the oxygen recovery in the system. This effect is an
evident treat for the system, because in the same conditions increased feed flow causes the
enhanced product flow and ultimately goes up the amount of oxygen to be recovered.
Figure 4: Temperature dependency in terms of time and length during AD step at cyclic
steady state, ( 𝑷 𝑯 𝑷 𝑳 = 𝟐. 𝟓 𝟏; 𝑷 𝑭 = 𝟎. 𝟑; feed flow rate=5lit(STP)/min)

9. 7th
International Chemical Engineering Congress & Exhibition
Kish, Iran, 21-24 November, 2011
Figure 5: Steady state temperature profile at the top of the column, ( 𝑷 𝑯 𝑷 𝑳 = 𝟓 𝟎. 𝟏;
𝑷 𝑭 = 𝟎. 𝟑; feed flow rate=11 lit(STP)/min; cycle time=110 s)
Figure 6: O2 purity as a function of P/F ratio for various ratios of PH/PL, (feed flow
rate=5 lit. (STP)/min; cycle time=110s)
Figure 7: O2 recovery as a function of P/F ratio, for various ratios of PH/PL, (feed flow
rate=5 lit. (STP)/min; cycle time=110s)

10. Numerical Simulation of a Pressure Swing Adsorption … …
Figure 8: O2 purity as a function of feed flow rate, for various ratios of PH/PL, (P/F=0.3;
cycle time=110)
Figure 9: O2 recovery as a function of feed flow rate, for various ratios of PH/PL,
(P/F=0.3; cycle time=110)
Conclusions
In this work, a two-bed four step PSA process under laboratory scale using zeolite 5A adsorbent
was studied by mathematical simulation. First, to determine the accuracy of predictions, the
results of this work have been compared with the other simulations and other experiments.
Simulation results indicated a satisfactory compliance with the current sources. The effect of
operational variables such as 𝑷 𝑭 ratio, 𝑷 𝑯 𝑷 𝑳 ratio and feed flow rate on product purity and
recovery in a oxygen production PSA unit was investigated.
In a constant feed flow rate, increase 𝑷 𝑭 ratio causes the reduction oxygen recovery, but instead
will cause to increase the oxygen purity. In the same conditions, increase the feed flow rate will
result in the reduction oxygen purity, but against the oxygen recovery rises. In this study, values
of 𝑷 𝑯 𝑷 𝑳 equal to 𝟐. 𝟓 𝟏, 𝟓 𝟏, 𝟑. 𝟓 𝟎. 𝟓, 𝟓 𝟎. 𝟓 and 𝟐 𝟏 side the effects of 𝑷 𝑭 ratio and feed flow
rate were studied. Based on the area that studied in this work, in terms of oxygen purity, the best
ratio of 𝑷 𝑯 𝑷 𝑳 equal to 𝟓 𝟏 was found. Furthermore, in terms of oxygen purity and recovery, in
lower amounts of feed flow rate, the best ratio of 𝑷 𝑯 𝑷 𝑳 equal to 𝟓 𝟏 was seen.

11. 7th
International Chemical Engineering Congress & Exhibition
Kish, Iran, 21-24 November, 2011
Nomenclature
Aw cross-sectional area of the wall (cm2
)
AD adsorption step
B equilibrium parameter for the Langmuir model (atm-1
)
BD blowdown step
Cpg, Cps, Cpw gas, pellet, and wall heat capacities, respectively (cal/g.K)
DL axial dispersion coefficient (cm2
/s)
hi internal heat-transfer coefficient (cal/cm2
.K.s)
ho external heat-transfer coefficient (cal/cm2
.K.s)
ΔH͞ average heat of adsorption (cal/mol)
k parameter for the LDF model
KL axial thermal conductivity (cal/cm.s.K)
L bed length (cm)
P total pressure (atm)
PG purge step
PR pressurization step
P/F ratio of purge flow rate to feed flow rate
PH/PL ratio of operating pressures
q, q*, q͞ amount adsorbed, equilibrium amount adsorbed, and average amount adsorbed,
respectively (mol/g)
qm equilibrium parameter for the Langmuir model (mol/g)
R gas constant (cal/mol.K)
Rp radius of the pellet (cm)
RBi, RBo inside and outside radii of the bed, respectively (cm)
T time (s)
Tatm temperature of the atmosphere (K)
T, Tw pellet or bed temperature and wall temperature, respectively (K)
u interstitial velocity (cm/s)
yi mole fraction of species i in the gas phase
z axial distance in the bed from the inlet (cm)
Greek Letters
α particle porosity
ε, εt voidage of the adsorbent bed and total void fraction, respectively
ρg, ρp, ρB, ρw gas density, pellet density, bulk density, and bed wall density, respectively (g/cm3
)
Subscripts
B bed
H higher operating pressure
i component i
L lower operating pressure
p pellet
g gas phase
s solid
w wall

12. Numerical Simulation of a Pressure Swing Adsorption … …
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