Psa oxygen

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: [email protected]

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

mailto:[email protected]

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 at\or 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.

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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𝜕2𝐶𝑖𝜕𝑧2

+𝜕(𝐶𝑖𝑢)

𝜕𝑧+𝜕𝐶𝑖𝜕𝑡

+ 𝜌𝑝 . 1 − 𝜀

𝜀 𝜕�͞�

𝑖

𝜕𝑡= 0

(1)

−𝐷𝑙𝜕2𝐶

𝜕𝑧2+𝜕(𝐶𝑢)

𝜕𝑧+𝜕𝐶

𝜕𝑡+ 𝜌𝑝 .

1 − 𝜀

𝜀

𝜕�͞�𝑖

𝜕𝑡

𝑛

𝑖=1

= 0 (2)

When the ideal gas law (𝐶𝑖 = 𝑦𝑖 𝑃 𝑅𝑇 and𝐶 = 𝑃 𝑅𝑇 ) is applied to eqs 1 and 2, the component and

overall mass balances can be represented as follows:

−𝐷𝑙𝜕2𝑦𝑖𝜕𝑧2

+ 𝑢𝜕𝑦𝑖𝜕𝑧

+ 𝑦𝑖𝜕𝑢

𝜕𝑧+𝜕𝑦𝑖𝜕𝑡

+𝜌𝑝𝑅𝑇

𝑃.

1 − 𝜀

𝜀 𝜕�͞�

𝑖

𝜕𝑡= 0

(3)

−𝐷𝑙𝜕2𝑃

𝜕𝑧2+𝜕𝑃

𝜕𝑡+ 𝑃

𝜕𝑢

𝜕𝑧+ 𝑢

𝜕𝑃

𝜕𝑧+ 𝑃𝑇 −𝐷𝑙

𝜕2

𝜕𝑧2

1

𝑇 +

𝜕

𝜕𝑡

1

𝑇 + 𝑢

𝜕

𝜕𝑧

1

𝑇

− 2𝐷𝑙𝑇𝜕

𝜕𝑧

1

𝑇 𝜕𝑃

𝜕𝑧+ 𝜌𝑝𝑅𝑇

1 − 𝜀

𝜀

𝜕�͞�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𝜕2𝑇

𝜕𝑧2+ 𝜀𝜌

𝑔𝐶𝑃𝑔 𝑢

𝜕𝑇

𝜕𝑧+ 𝑇

𝜕𝑢

𝜕𝑧 + 𝜀𝑡𝜌𝑔𝐶𝑃𝑔 + 𝜌

𝐵𝐶𝑃𝑠

𝜕𝑇

𝜕𝑡− 𝜌

𝐵

𝜕�͞�𝑖

𝜕𝑡 −𝛥�͞�𝑖

𝑛

𝑖=1

+2𝑕𝑖

𝑅𝐵𝑖 𝑇 − 𝑇𝑤 = 0

(5)

To evaluate heat loss through the walls and the accumulation of energy, corresponding to an

energy balance has also been used.

𝜌𝑤𝐶𝑃𝑤𝐴𝑤𝜕𝑇𝑤𝜕𝑡

= 2𝜋𝑅𝐵𝑖𝑕𝑖 𝑇 − 𝑇𝑤 − 2𝜋𝑅𝐵𝑜𝑕𝑜 𝑇𝑤 − 𝑇𝑎𝑡𝑚

(6)


Where

𝐴𝑤 = 𝜋 𝑅𝐵𝑜2 − 𝑅𝐵𝑖

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 = 𝜌𝑔𝐶𝑃𝑔𝑢 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 = 𝜌𝑔𝐶𝑃𝑔𝑢 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

𝑢𝑧=𝐿 = 0 (11-1)

Pressurization and production step

𝑢𝑧=0 = 𝑢𝑓𝑒𝑒𝑑 (11-2)

Counter current purge step

𝑢𝑧=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

4𝑅𝑝2

(1 − 𝜀)2

𝜀2, 𝑏 = 1.75

(1 − 𝜀)

2𝑅𝑝𝜀 (15-2)

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Where u is the interstitial velocity.

The multi-component adsorption equilibrium was predicted by the following LDF model.

𝑞𝑖 =𝑞𝑚𝑖𝐵𝑖𝑃𝑖

1 + 𝐵𝑗𝑃𝑗𝑛𝑗=1

(16)

Where,

𝑞𝑚𝑖 = 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]. 𝜕�͞�

𝑖

𝜕𝑡= 𝜔𝑖 𝑞𝑖

∗ − �͞�𝑖 , 𝜔𝑖 =

15𝐷𝑒𝑖𝑟𝑐2

(18)

Where [18], 15𝐷𝑒𝑖𝑟𝑐2

= 𝐶𝑃𝑟0.5(1 + 𝐵𝑖𝑃𝑖)

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 Equilibrium\Rate parameters and heat of adsorption of N2 and O2 on

zeolite 5A [14]

N2 O2

𝐤𝟏 × 𝟏𝟎𝟑(𝐦𝐨𝐥 𝐠 ) 6.210 7.252

𝐤𝟐 × 𝟏𝟎𝟓(𝐦𝐨𝐥 𝐠 .𝐤) -1.270 -1.820

𝐤𝟑 × 𝟏𝟎𝟒(𝟏 𝐚𝐭𝐦 ) 1.986 54.19

𝐤𝟒(𝐤) 1970 662.6

Heat of adsorption, -ΔH͞i (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.


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].

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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


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 𝑷𝑯 𝑷𝑳 ratios. As indicated, at all the 𝑷𝑯 𝑷𝑳 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 𝑷𝑯 𝑷𝑳 = 𝟐 𝟏 and 𝑷𝑯 𝑷𝑳 = 𝟓 𝟏 , than the other operating pressures ratios, the

highest purity achieved for oxygen in the product. In order to better compare the 𝑷𝑯 𝑷𝑳 = 𝟐 𝟏 and

𝑷𝑯 𝑷𝑳 = 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 𝑷𝑯 𝑷𝑳 = 𝟓 𝟏 . Fig. 7 shows oxygen recovery

profile, for the same ratios of 𝑷𝑯 𝑷𝑳 as previous, in terms of 𝑷 𝑭 ratio. Clearly, in any ratio of

𝑷𝑯 𝑷𝑳 , 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 𝑷𝑯 𝑷𝑳 =

𝟓 𝟎.𝟓 , despite being the least amount of oxygen purity, the oxygen recovery has the highest

quantity instead than the other 𝑷𝑯 𝑷𝑳 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 𝑷𝑯 𝑷𝑳 ratios. As indicated, for all 𝑷𝑯 𝑷𝑳

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, (𝑷𝑯 𝑷𝑳 = 𝟐.𝟓 𝟏 ; 𝑷 𝑭 = 𝟎.𝟑; feed flow rate=5lit(STP)/min)

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Figure 5: Steady state temperature profile at the top of the column, (𝑷𝑯 𝑷𝑳 = 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)


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, 𝑷𝑯 𝑷𝑳 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 𝑷𝑯 𝑷𝑳 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 𝑷𝑯 𝑷𝑳 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 𝑷𝑯 𝑷𝑳 equal to 𝟓 𝟏 was seen.

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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


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Psa oxygen

Design

Transcript of Psa oxygen