Air separation by pressure swing adsorption

Air separation adsorption* D.M. Ruthven

by pressure

swing

and S. Farooq

Department of Chemical Brunswick, Canada Received 20 November

Engineering,

University

of New Brunswick,

Fredericton,

New

1989; revised 30 April 1990

The original pressure swing air separation process, developed almost simultaneously by Exxon and Air Liquide, uses a nitrogen selective zeolite adsorbent to produce a high purity oxygen product. The same basic process is still widely used in small scale units although, for larger scale units, many modifications to the cycle have been introduced in order to reduce power consumption. Although nitrogen can in principle be recovered from the blowdown stream of such systems, if high purity nitrogen is the required product, it is more economic to use an oxygen selective adsorbent. Most adsorbents show either no selectivity or preferential adsorption of nitrogen. However, in small pore carbon molecular sieves or 4A zeolite there is a substantial difference in diffusion rates so that an efficient kinetic separation is possible. Somewhat different cycles are generally used in such processes. Progress in modelling the dynamic behaviour of both types of PSA system is reviewed and comparisons between experimental performance and the model predictions are shown. A simple linear driving force model provides a good overall prediction of the effects of process variables but the computationally more cumbersome diffusion model gives better quantitative agreement with experiment. Comparisons are drawn between the performance achieved (in nitrogen production) with two different kinetically selective adsorbents; K-10 (a modified 4A zeolite) and Bergbau Forschung carbon molecular sieve. Keywords: PSA; models; air separation

Nomenclature Langmuir constant for component A Concentration of component A in cAl~ cA2 gas phase in bed 1 or 2 Concentration of component B in cBI~ cB2 gas phase in bed 1 or 2 C,, CL, C,, CZ Total gas phase concentration at high pressure, at purge pressure, during blowdown, during pressurization Effective diffusivity D, Axial dispersion coefficient Effective mass transfer coefficient for Z(k,,, kA2) component A (in bed 1 or 2) Effective mass transfer coefficient for kdkBI> kh2) component B (in bed 1 or 2) Adsorption equilibrium constant for KA, KB oxygen at T,, for nitrogen at To Bed length Column pressure (for high pressure Lpcp,, PL) step, for low pressure step) Concentration of component A in qAl, qA2 solid phase in bed 1 or 2 Concentration of component B in qBl3 qB2 solid phase in bed 1 or 2 Saturation constant (for component dqASt 4BS) A, for component B)

b/x,b,

(0950-42 14/90/03014) -09 Q 1990 Butterworth-Heinemann Ltd

4:,.41;2 4BI, q& R % S t(t,) TO “23 “I

“0 “OH

VOL

;I,@-)

Value of qA, in equilibrium with cA,, or qAz in equilibrium with cAz Value of qsl in equilibrium with ca,, or qsz in equilibrium with caZ Fractional recovery of N, product Particle radius Kinetic selectivity (Doz/DNz) Time (cycle time) Ambient temperature Interstitial velocity in bed 2 or 1 Interstitial inlet velocity during pressurization Interstitial inlet velocity during high pressure flow Interstitial inlet velocity during purge flow Axial distance from column inlet Position just inside (just outside) column

Greek letters & R

Bed voidage Constant in LDF rate expression (k = S1D,lRp2)

Gas Separation & Purification 1990

Vol 4 September

141

Air separation by PSA: D.M. Ruthven and S. Farooq

Figures la and 6. These cycles are commonly

Introduction Pressure swing adsorption technology has its origins in the early laboratory studies of Skarstrom (1960)’ and Montgareuil and Domine (1964)2. The transition from a laboratory scale curiosity to a widely used industrial process has been slow, however, with most of the development occurring during the last decade. Prior to 1975 less than ten US patents had been issued for pressure swing processes but by 1988 there were well over 100 such patents+. Most of these patents propose modifications to the basic process cycle aimed at improving the recovery of product and thus decreasing the power requirement, which is the major operating cost for a PSA system. These improvements in efficiency are generally achieved by using multiple adsorbent beds with a sequence of pressure equalization steps incorporated into the cycle. This allows recovery of some of the partially purified high pressure gas, which is present in the adsorbent bed at the end of the cycle, thereby conserving both energy and separative work at the cost of a somewhat more complex process scheme. In some large scale hydrogen purification PSA systems up to 12 adsorbent beds are used. In application to air separation PSA systems have been most successful at small and intermediate scales (< 10 ton per day). At this scale the increased capital cost associated with the multiple bed units is generally not justified and most of the smaller PSA air separation systems utilize a simple two bed system operated on a cycle which is quite similar to the original Skarstrom process. The first generation of PSA air separation processes were all designed to recover oxygen as the pure high pressure product using a zeolite adsorbent to selectively adsorb the nitrogen. Such systems are still widely used for small scale oxygen production but in recent years there has been increasing emphasis on processes for production of nitrogen for applications as diverse as the preservation of fruit and produce during trucking, the blanketing of fuel tanks of fighter aircraft and the inerting of reactors in a number of pharmaceutical processes. A pressure swing system lends itself naturally to recovery of the less strongly adsorbed component (the raffinate product) at high purity and high pressure. Although cycles have been devised to recover the more strongly adsorbed species, such cycles are generally less effective. PSA nitrogen processes, therefore. generally use an oxygen selective adsorbent; carbon molecular sieve or a modified 4A zeolite. In contrast to the 5A zeolite which has a higher equilibrium affinity for nitrogen, 4A zeolite and carbon sieve are kinetically selective for oxygen. Somewhat different process cycles are. therefore, required for these two classes of process. The interaction between the process variables in a PSA system is complex and difficult to visualize intuitively so, although final optimization of process operating conditions is generally achieved empirically, a reliable simulation is needed as a design guide. The aim of the present paper is to review briefly PSA technology, as applied to air separation, and the progress which has been achieved in the modelling and numerical simulation of such systems.

PSA cycles The Skarstrom cycle and the modified Skarstrom cycle incorporating a pressure equalization step are shown in +The author is grateful to S. Sircar of Air Products for these patent statistics

142

Gas Separation

8 Purification

1990

used with 5A or 13X zeolite adsorbent in small scale oxygen units. Desorption of the preferentially adsorbed nitrogen is achieved by pressure reduction followed by purging with a fraction of the oxygen product to remove the nitrogen from the interstices of the bed. Many modifications to this basic cycle have been introduced to improve the performance of the system. A useful review has been given by Yang’. The same basic cycle can be used, with the kinetically selective 4A zeolite or carbon molecular sieve adsorbent, in a nitrogen production process. However, in such a system purging with nitrogen to remove the faster diffusing oxygen from the bed is undesirable since, as well as wasting product, a certain fraction of the slowly diffusing nitrogen will be adsorbed, thus reducing the capacity for oxygen during the next adsorption step. The earlier kinetic nitrogen processes avoided this difficulty by using a vacuum to clean the bed, rather than a purge, as illustrated in Figure Ic. However. a better option is available. At the end of the blowdown step the adsorbent contains both oxygen (fast diffusing) and nitrogen (slowdiffusing). Thus if the bed is simply closed at one end and left for a period of time the oxygen will diffuse out first followed by the nitrogen so the system is, in effect. self purging. Most of the more modern nitrogen production units therefore operate on the cycle shown in Figure Idwhich incorporates both a (selfpurging) desorption step and a pressure equalization step.

Equilibrium

theory

The simplest approach to the modellingofan equilibrium controlled PSA separation process involves the use of equilibrium theory’-h. The advantage of this approach is that it allows analytic solution of the governing material balance equations by the method of characteristics. The approach is. however, limited to the idealized case where there are no dispersive effects such as axial mixing or finite resistance to mass transfer. (Under these conditions a perfectly pure raftinate product is obtained.) Equilibrium theory does not allow easy extension to the real situation where dispersive effects are significant and product purity is limited. Furthermore, in real PSA systems there are two problems with this approach. In bulk separations where the velocity varies through the bed the characteristic lines are curved and, although an analytic solution for the concentration front may still be obtained. except in the case of a linear isotherm, the solution will be in the form of a cumbersome integral which requires numerical evaluationh. A more serious difficulty arises in tracking the concentration waves for adsorption and desorption in partially loaded beds since. depending on the initial profile and the form of the equilibrium relationship, one may observe the formation of combined wave fronts (for example, partial shock plus simple wave). Under these conditions the simple model breaks down and it is necessary to track both waves and the transition point simultaneously7. Although equilibrium theory provides useful guidance concerning the effects of process variables (in an equilibrium controlled system) it is obviously inappropriate for a kinetic system and cannot be easily extended to account for the effects of axial mixing and mass transfer resistance which are present in all real systems, even when equilibrium controlled. We therefore elected to follow the alternative route and develop a dynamic simulation

Vol 4 September

Air separation by ?SA

Re prerion

co,. ,yctcc

+Product

Feed

Blowdown

Pu&e

pproduct

Id)

lb)

Blowdown

Pro

Vacuum

Repressurization

ul

uct rt

3 Pressure Equ.lizotion

Blf

Fb

LProduct

i

Feed Adsorption

and S. Faroog

Repressurization Feed

Prtssur/zation

D.M. Rut&en

,CIS”,.

UU

e

*

Blowdown

Dcsorptinn

Equoliration

Figure 1 PSA cycles: (a) Skarstrom cycle; (b) modified Skarstrom cycle with pressure equalization; (c) vacuum swing cycle (Air Liquide, 1964); (d) nitrogen production cycle for carbon sieve (self-purging system with pressure equalization)

model which is sufficiently general to be applied to both classes of process. The advantage of this approach is that it allows the effects of mass transfer resistance to be studied easily; the disadvantage is that the computations are bulky with no realistic possibility of analytic solutions even for the simplest cases.

Theoretical Simplifying

model assumptions

We consider a two bed process operated according to either a Skarstrom cycle (Figure la) or according to the modified self-purging cycle shown in Figure Id. We have not considered the vacuum desorption cycle (Figure lc). In order to develop a tractable model a number of simplifying assumptions are introduced as follows: The system is considered to be isothermal. This is a good approximation for the nitrogen production system since only the oxygen (21% of the feed air) is adsorbed. It is not such a good approximation for the oxygen production system in which the major component (nitrogen) is adsorbed. Nevertheless, in small scale units the heat capacity and thermal conductivity of the column greatly reduce the temperature variation. Frictional pressure drop through the bed is neglected. Total pressure in the bed is assumed constant during adsorption and purge steps (cycle a steps 2 and 4). During pressurization and blowdown the total pressure in the bed varies linearly with time (cycle a). The variation in fluid velocity through the bed, as determined by the mass balance, is accounted for. The flow pattern is represented by the axial dispersed plug flow model. (This aids the computation even when the Peclet number is high by slightly smoothing the profiles.)

The equilibrium relationship for both components is represented by either a linear isotherm or a binary Langmuir isotherm. The presence of argon is ignored. It is assumed that argon goes with oxygen in the oxygen production cycle and with the nitrogen in the nitrogen production cycle. In the oxygen system the controlling mass transfer resistance is assumed to be macropore diffusion - as verified experimentally in independent studies. The mass transfer rate is represented by a linearized driving force expression using the Glueckauf approximation* (k = 15 DJR’). The pressure dependence of this coefficient is allowed for as outlined by Hassan et ~1.~. In the kinetic nitrogen systems the mass transfer rate is controlled by micropore diffusion. The same form of linear driving force rate equation is used. The micropore diffusivities for oxygen and nitrogen in RS-10 were taken as pressure independent For CMS the pressure dependent micropore diffusivity values used were somewhat higher than those estimated from the analysis of Garg and Ruthven”. Pressurization and blowdown

steps

Since, in the nitrogen production systems, diffusion is relatively slow, we may use the ‘frozen bed’ approximation to avoid detailed calculations for the pressurization, pressure equalization and blowdown steps. The gas phase mole fractions at the end of the blowdown step remain the same at each and every position in the bed as at the end of the preceding high pressure adsorption step but the total pressure is reduced instantaneously from P, to P, with the solid phase remaining frozen. During pressurization with feed air the fluid phase oxygen and nitrogen remaining in the bed from the preceding low pressure purge flow step are assumed to be

Gas Separation & Purification 1990

Vol 4 September

143

Air separation by PSA: D.M. Ruthven and S. Farooq

pushed, in plug flow, towards the end of the bed through a distance given by 1 - P,IP, from the feed end; the remainder of the bed being filled by the pressurizing feed air. Again the adsorbed phase concentrations of oxygen and nitrogen are assumed to remain unchanged at the values prevailing at the end of the preceding low pressure purge step. Such approximations are clearly inappropriate for the oxygen production process in which mass transfer resistance is much smaller. For that system full calculations of the pressurization and blowdown steps were therefore included assuming a linearvariation oftotal pressure with time.

ization column

the inlet pressure.

Material

balance

Step l.Pressurization balance

describing

of bed 2 and blowdown

for bed 2 (component

a2cAz ac, +V>~+C&$+++~~= az2

av2

-D, ~

Continuity

&

Continuity cAl

+

CB,

material

av2 ac,

ac,,

aqA, __

1 - dq,

o

(1)

(2)

qAS

material

=

Es=

(3)

Boundary

D$&i’

qA,)

47,, at = kB,(qB*,- qB,)

Adsorption

equilibrium:

sA, -=

b,c,, 1 +

b,cA,

+

(10)

bBcB,

qBS

bBcB, 1 +

bAcA,

(11) +

bBCB,

conditions:

(12)

(4)

equilibrium:

bAClu

Equation (6) which defines the standard (Danckwerts) inlet and exit boundary conditions for a dispersed plug flow system reduces to Equation (12) when the inlet velocity is set to zero. Step 2.High pressure adsorption in bed 2 and purge in bed 1. For bed 2 other than the following changes all other equations for step 1 remain unchanged in step 2.

+ bBcB2

b,C,

(5)

+ bBcB2

= -v,(cAzl;=o-

condition:

cAZ + cBZ = C, (constant) Overall

conditions:

material

(13)

balance:

(14)

- cmll=,,) Boundary

~I;=,=0

condition

at the inlet:

(6)

Note that in a commercial operation the feed stream would be supplied by a compressor. Hence a constant flow situation is probably more appropriate rather than a constant pressure feed stream. Therefore, during pressur-

144

-

qA2)

-

b,c,z

1+

balance:

~

Continuity 482

(8)

rates:

kA,(qi,

4B, -_=

bAcM 1 +

f(z) = f(r)

z

balance:

k*?(q& - qsz)

4Z2 -_=

(7)

rates:

= k,(KL

Adsorption

c,

=

Boundary

+2 =

o

condition:

Mass transfer

of bed 1.

at

IgE($r+f$+o

c2dz+ar+

at

at

(9)

qAS

dq, ~

l -eaqAl

the

condition:

Mass transfer

aCAl

changing

A):

dz+dt+--=

LT+vI%+cA,

A):

CM + c*z = cz # f(z) = f(t) Overall

avl

with

formulation

Subject to these assumptions, the equations cyclic operation are as follows.

Material

v,, changes

for bed 1 (component

a2CAl

_D

Overall Mathematical

velocity,

Gas Separation

8 Purification

1990

acA2 D,---Iz=o az

= -VOH(CAZI~=~,-- cA?i.-=O)

Similarly for bed 1, except for the following other equations in step 1 remain unchanged

Vol 4 September

(15) changes all in step 2:

sir separation by PSA: D.M. Ruthven

Continuity CA1

+

condition:

CBI = C, (constant)

Overall

material

(16)

balance:

(17) Boundary

condition

at the inlet:

(18)

cA,lz=o-=

(1

PL CAzlr=L

p

(19)

H

The equations describing the operations in the two beds in steps 1 and 2 are interchanged in steps 3 and 4, but with the change in the direction of flow taken into account. The appropriate initial conditions for the startup ofthe cycle operation from a clean bed are as follows: CM (2, 0) = 0

;

CBl (z, 0) = 0;

q,Q (z. 0) = 0

;

qa2 (z. 0) = 0;

CA1(z. 0) = 0

;

CBj

qAl

;

461 (z, 0) = 0:

cz? O)

=

o

(z,

0)

=

0;

(20)

Equations (l)-(20) were rearranged and written in dimensionless form. The dimensionless equations were then solved by the method of orthogonal collocation to give gas and solid phase concentrations of oxygen and nitrogen as a function of dimensionless bed length (z/L) for various values of time. Five internal collocation points were used. On an IBM 3090 (Model 180) the CPU time required to compute one complete cycle was 2-5 s for a dual bed system and 0.25-0.5 s for a single bed system. Computations were continued until cyclic steady state was achieved. Depending on parameter values 15-25 cycles were required to achieve cyclic steady state. The mathematical model used by Shin and Knaebel”.” is basically similar except that diffusion equations were used to represent the mass transfer rate making the calculations more cumbersome. We therefore modelled the same system (N, production on RS-10 (4A zeolite)) using the LDF model in order to provide a comparison between the two approaches.

Parameter

and S. Farooq

The macropore diffusivity for the 5A sieve was estimated in the usual way assuming a tortuosity factor of 3 and a porosity 0.33. The pressure dependence was allowed for in the manner recommended by Hassan et a1.9. The saturation capacity for oxygen is taken from the equilibrium data of Miller et al.15 and since 0, and N, molecules are about the same size, the same value is assumed for both species. The Henry constants for 02 and N, were measured chromatographically by Boniface16. The kinetic and equilibrium parameters for the RS-10 sieve are taken from the data of Shin and Knaebel12. The diffusivity values for oxygen and nitrogen used in their study were obtained by matching the pore model simulation to the experimental results for a large number of runs. The diffusivity ratio thus obtained is comparable with extrapolated 4A data from the earlier measurements of Ruthven and Derrah” but the absolute values of the diffusional time constants are about 50 times higher. This difference could result from a difference in the crystal size which for RS-10 is not specified.

Experimental The experimental studies were carried out in a small laboratory scale two-bed PSA unit containing either Bergbau-Forschung carbon molecular sieve or 5A zeolite pellets. Brief details of the adsorbents, the bed dimensions and the operating conditions are given in Table I. The oxygen concentration in the product stream was monitored continuously with a Servomex paramagnetic oxygen analyzer and the sequence of valve switching was controlled by a Xanadu universal programmable timer. The flowrates of feed, purge and product were controlled by Matheson flow controllers. In some of the experimental run the effluent from the blowdown and desorption steps was collected over water to complete the mass balance. Prior to the experiments the zeolite adsorbent was dehydrated by purging at 400°C in a stream of dry helium for 12 h. In the case of the carbon sieve a less severe pretreatment (purging overnight at SO’C) was used. The system was operated under a range ofconditions including different pressures, different feed and product rates and different cycle times. In some of the measurements with the carbon adsorbent the transient behaviour was followed but in the present discussion we are concerned only with the final cyclic steady state which is approached after about 30 cycles of operation. The experimental system used by Shin and Knaebel (1988) (Nz production on RS-10) was similar in concept but differed in that it used only a single column with stored product gas used for purging.

estimation

It was shown by Raghavan et al. I3that in a cyclic process such as PSA the parameter, Sz. in the Glueckauf approximation k = ClD,/R,’ is in fact dependent on cycle time and the diffusional time constant. However. under all conditions of the present study the cycle times are relatively long so the limiting value Sz = 15 was used throughout for O2 with a somewhat larger value (n = 20) for N2. This value was chosen on the basis of the goodness of fit of the simulation results to the experimental data. The correlation of Raghavan et al. suggests a somewhat larger value (- 30). Kinetic and equilibrium data for the carbon sieve were taken from our own laboratory measurements (Ruthven et al.“).

Results

and discussion

The effects of pressure ratio and cycle time on the performance of a PSA oxygen unit. operated according to the Skarstrom cycle under the conditions given in Table I, are shown in Fi’re2. The oxygen purities quoted are averages over the cycle. It is clear that the precise assumptions concerning the blowdown step have only a minor effect and the simplified model provides a reasonably close prediction of the experimentally observed performance. Under properly selected operating conditions an oxygen product purity in excess of 95% was achieved, the balance being almost entirely argon.

Gas Separation 8 Purification 1990

Vol 4 September

145

Air separation by PSA: D.M. Ruthven and S. Farooq Table 1

Summary of operating conditions and parameters

os(m mol cme3) PU (atm) P,(atmj Feed (cm3 s-l)

Linde 5A 0.07 cm diameter 35 3.5 0.4 25 4.7 14.8 62 20 5.3 1.48-4.35 1 .o 25-67

:: 0.4 25 9.25 8.9 5.6 x lo-’ 2.34 X 1O-3 2.64 2.0-6.7 1 .o 1 l-36

4A (RS-10)8 0.16 cm diameter 102 2.08 0.6 27 3.82 8.2 7.0 0.14 (linear isotherm) 3.5 1.15 4.0-7.2

(STP) Product (cm3 s-l)

1.13-4.0

2.1-17

0.7-6.2

(STP) Cycle time (s) Feed Blowdown Purge Pressurization Total

0.2 0.3 0.2 0.3 100-2

60 2 60 2 128’

25-70 2-6 3 15 45-90

Adsorbent Particle Size Bed length (cm) Bed diameter (cm) Voidage Temperature (“C) K,(h)

h_#Jz) kA(02) k&‘Jz)

(s-‘I* @-‘I*

CMS l/8 in. pellet

t, t,

t, t, 50

aData of Shin and Knaebel (1988) Walue at 1 atm CPressure equalization step: 2 s X 2

0 50

.

i 0 ?. I.25

Experimental Theo.linear change during Theo.instant change during ’ . ’ 100 150 Cycle time

pressure blordarn ~r~sswe blowdorn ’ ’ 200 250 kec)

I 0 v

Theo.-

instant

pressure blowdoxn

prossure

during bloxdown ’ . ’ ’ ’ 250 150 200 100 Cycla time (sac) change

300

Experimental Theoretical 1. 1.75 2.25 1. Adsorption

Experimental Theo.linear change during

o50

x

0

2.75 1. 3.25 1. 3. 175 prossuro (otm)

p.25 L.I.1.

’

4 300

Expwimantal Theoretical 1.75 2.25 Adsorption

2.75 t, 3.25 1.1 3.7: p!-PSSWP (atm)

Performance of small scale PSA oxygen process using 5A zeolite adsorbent: comparison of theory and experiment. (a), (b) Effect of Figure 2 cycle time on purity and recovery of oxygen product. (c), (d) Effect of pressure on purity and recovery of oxygen product. (Experimental conditions and parameter values are summarized in Table 1)

146

Gas

Separation

8

Purification

1990

Vol

4 September

Air separation by PSA: D.M. Ruthven and S. Farooq

expression. Although a pore diffusion model provides a more realistic representation of the adsorption kinetics. the LDF model can correctly predict the trends of the experimentally observed behaviour. Moreover the pore diffusion model will have no real advantage when the model parameters are calibrated against experimental performance. The advantages gained by adopting LDF approximation are the simplicity and the computational speed (at least 10 times fasterthan the pore model solution on the same machine).

References 1

0

2

3

L

‘1. 02

6

5

Skarstrom, C.W. US Patent 2 944 627 to Esso Research and

7

in Product

Figure 5 Recovery-purity plot for nitrogen production on RS-10 and CMS adsorbents. The effect of changing the kinetic selectivity (for CMS) is indicated for one point on curve 2. The four points (A) show the effect of increasing (and decreasing) the selectivity by a factor of 1.5 by changing the O2 and N2 mass transfer coefficients. (The arrows indicate the direction in which the point is shifted corresponding to increases in ON and DO ). The comparison between cycle (a) and the self purg?ng cycle fd) is also shown

5

6 70

”

I

60-’

7

I 8 9

IO

11

0

1

2

3 4 ‘1. 02 in

5 N,

6 7 Product

8

9

10

I2

Figure 6 Comparison between performance of CMS and RS-10 adsorbents for nitrogen production showing process power requirement as function of product purity

13

14

Conclusions

15

The dynamic PSA simulation model developed has been successfully applied for predicting the performance of both equilibrium and kinetically controlled PSA air separation processes. The present model approximates the mass transfer rate by linear driving force rate

148

Gas Separation

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1990

I6 I7

Vol 4 September

Engineering (1960) de Montgareuil, P. Guerin and Domine, D. US Patent 3 155 468 to Air Liquide (1964) Yang, R.T. Gas Separation bv Ad.qorptiott Prortwc~.~ Ch 7. Buttetworths. Stoneham. MA. USA (1960) Knaebel, K.S. and Hill, F.B. Pressure sting adsorption: development of equilibrium theory for gas separations Chin Eng Sci (1985) 40 2351-2360 Kayser, J.C. and Knaebel, K.S. Pressure swing adsorption: experimental study of an equilibrium theory Chum Eng S(,i (1986) 41 2931-2938 Kayser, J.C. and Knaebel, KS. Pressure swing adsorption: development of an equilibrium theory for binary gas mixture5 with non-linear isotherms Chem Eng Sri (1988) 44 I-X Flores-Femandez, G. and Kenney, C.N. Modelling of the pressure swing air separation process Chem Eng Sri (19X3) 38 827-834 Glueckauf, E. Theory of chromatography. Part 10 Ircrm Furada.v Sot (1955) 51 1540-1551 N.S., Ruthven, D.M. and Hassan, M.M., Ragbavan, Boniface, H.A. Pressure swingadsorption. IIAIChE.I( 1985) 31 2008-2016 Garg, D.R. and Ruthven, D.M. Effect of concentration dependence of diffusivity on zeolitic sorption curves C/IWI E/IX Sci (1972) 23 417-423 Shin, H-S. and Knaebel, K.S. Pressure swing adsorption: theoretical study of diffusion induced separations AIChE .I (1987) 33 654-662 Shin, H-S. and Knaebel, K.S. Pressure swing adsorption: experimental study of diffusion induced separations AIChE .I (1988) 34 1409-1416 Raghavan, N.S., Hassan, M.M. and Ruthven, D.M. Numerical simulation of a PSA system using a pore diffusion model c‘l~m Eng Sci (1986) 41 2787-2793 Ruthven, D.M., Raghavan, N.S. and Hassan, M.M. Adsorption and diffusion of Nz and 0, in carbon molecular sieve Chem &IX Sci (1986) 41 1325-1332 Miller,G.W., Knaebel, K.S. and Ikds, K.G. Equilibria ofN,. Oz.Arand airon molecularsieveSAAIChEJ( 1987)33 194-201 Boniface, H. Separation of Ar from air using zeolites PhD Thesis University of New Brunswick. Federation. Canada (19x3) Ruthven, D.M and Derrah, R.I. Diffusion monatomic and diatomic gases in 4A and 5A zeolitesJ Chrm Sot fivudcly Trant I (1975) 71 2031-2044