Heuristic design of pressure swing adsorption: a preliminarystudy

S. Jain a, A.S. Moharir a, P. Li b,*, G. Wozny b

a Department of Chemical Engineering, Indian Institute of Technology, Bombay 400 076, Indiab Institut fur Prozess und Anlagentechnik, Technische Universitat Berlin, KWT9, 10623 Berlin, Germany

Abstract

Due to its complicated nature and multiple decision parameters including plant dimensionality and operation

condition, the design of pressure swing adsorption (PSA) processes is not a trivial task. Most previous studies on PSA

design have been made through rigorous modeling and experimental investigation for specific separation tasks. General

heuristics for a preliminary design of PSA processes are necessary but not well investigated so far. In this paper, we

attempt to develop easy-to-use rules for PSA process design, based on analysis of the inherent properties of adsorbate�/

adsorbent systems (i.e. equilibrium isotherm, adsorption kinetics, shape of breakthrough curves, etc.) and simulation

results. These rules include the selection of adsorbent, particle size, bed size, bed configuration, purge volume, pressure

equalization and vacuum swing adsorption. Results of two case studies are presented to verify the rules proposed in this

preliminary study.

Keywords: Pressure swing adsorption; Simulation; Design and operation; Heuristics

1. Introduction

Because pressure swing adsorption (PSA) has

the properties of high selectivity, high throughput

and high energy efficiency, more and more PSA

processes are designed and operated to carry out

gas bulk separation and purification tasks in the

chemical industry. In a PSA process, the adsorbent

adsorbs the preferential species of a gas mixture,

which is then desorbed by reduction in pressure.

Since the development of PSA, many improve-

ments in the process have been done to make it

more efficient. The most previous studies on PSA

design have been made through rigorous modeling

and experimental investigation for specific purifi-

cation tasks. Since a PSA process is quite compli-

cated and there are many parameters to be

decided, there have been no general easy-to-use

design rules so far. Because a pilot plant study of

PSA is costly compared with computational study,

simulation has become a viable alternative to pilot

plant experiments. Based on basic kinetics and

equilibrium data as well as operation parameters,

simulation provides a method of predicting outlet

Nomenclature

b Langmuir constant (atm�1)C concentration in gas phase (mole per m3 of fluid)D intracrystalline diffusivity (cm2 s�1)dp diameter of particle (cm)G purge/feed volume ratioK Henry’s Law constantk overall mass transfer coefficient (s�1)L total height of the column (m)N total number of componentsP pressure (atm)Q molar flow rateq adsorbed phase concentration (mole per m3 of solids)q* equilibrium concentration of adsorbed phase (mole per m3 of solids)qs Langmuir constant (mol cm�3)R universal gas constantT temperature (K)t time (s)v superficial velocity (m s�1)W power (kW)x adsorbed phase compositiony gas phase compositionz height of the bed (�/0 at feed end, �/L at product end) (m)Greek symbols

a separation factor (dimension less)o bed Porosityf factor defined in (Eq. (19))g ratio of specific heats in gas phaseh mechanical efficiencyr density (kg m�3)m gas viscosity (Cp)t residence time (s)Subscripts

0 initial1, 2 componentsact actualads adsorptionblow blowdown stepf feedg gas phaseH high pressure stepI componentL low pressure stepmin minimum valuepres pressurization stepprod productpurg purge steps solid phase

26

concentrations and the dynamic capacity of PSA,without recourse to experimentation. To this end,

a comprehensive model and a numerical solution

method are required [1,2].

Cen and Yang [3] showed that due to its

simplicity, the equilibrium model can be widely

used for PSA simulation. Alpay and Scott [4] used

the linear driving force (LDF) model to describe

the adsorption and desorption kinetics in sphericalparticles. Raghavan and Ruthven [5] presented

numerical simulation of PSA in the recovery of

trace adsorbable from an inert carrier using the

linear equilibrium and linear rate expressions.

They also assumed that during pressure changes

(blowdown and pressurization) there was no mass

transfer between the fluid and adsorbent. Ragha-

van and Ruthven [6] discussed numerical simula-tion for a simple two bed PSA process in which

effects of kinetics and changes in flow rate due to

adsorption are significant. They showed that when

the above effects are significant, adsorption equili-

brium and constant velocity assumptions are no

longer valid.

Chahbani and Tondeur [7] discussed the mass

transfer kinetics in PSA. They showed that thechoice of the pore diffusion model plays a key role

for obtaining reliable simulations. They compared

their results with other models like LDF and

equilibrium model. Kvamsdal and Hertzberg [8]

showed the effect of mass transfer during the

blowdown step. According to their results, the

frozen solid assumption is valid only in certain

cases, and taking into account the mass transferduring the blowdown step gives a better overall

model performance in the studied cases. A series

modeling and simulation studies have been done

aiming at finding proper PSA design and opera-

tion such as the particle size and pressure ratio [9�/

12].

These previous works mainly focused on mod-

eling and simulation of PSA. From these studies, itis found that for design and operation of PSA, one

has to go for a rigorous simulation. Modeling PSA

leads to a nonlinear dynamic partial differential

equation system, which is difficult to solve. The

parameters in PSA models affecting the behavior

of the process are highly coupled to each other.

Studies on the sensitivities of these parameters

through rigorous modeling and simulation arequite expensive. Therefore, it is necessary to

develop heuristic rules with which design and

operation of PSA processes can be made without

doing more rigorous simulation.

Heuristic rules (or rules of thumb) simplify the

design and/or operating options and shortlist a few

options which could be probed further. They thus

reduce the dimensionality of an otherwise combi-natorial design problem. Heuristics has found wide

applications in process design (usually a prelimin-

ary design). Potential designs from heuristic rules

can then be fine tuned using rigorous simulation, if

necessary.

The number of decision parameters, including

plant dimensionality and operation condition, is

quite large in the design of PSA. More and moreadsorbents are being developed, but adsorbent�/

adsorbate system characteristics themselves are

not fully understood. The accumulated experiences

with adsorptive separations are also insignificant

compared with those in the cases of thermal

distillation and chemical reaction.

This work attempts to develop a set of heuristic

rules for the design of PSA systems. A model ofadsorptive separation is used to generate case

studies. Based on the properties of adsorbate�/

adsorbent systems (i.e. equilibrium isotherm, ad-

sorption kinetics, shape of break through curves

etc.), systematic knowledge of the input/output

relations thus gained is extracted out to evolve

some simple rules for design. Product purity and

recovery are the performance factors studied toderive the rules for various decision steps in design

of PSA. They include decisions on size of particles,

pressure levels, configuration of PSA cycle, resi-

dence time in PSA bed, design of PSA bed, choice

for pressure equalization step and choice for VSA

process.

2. Modeling PSA processes

Fig. 1 shows a typical PSA process. The process

consists of two fixed-bed adsorbers undergoing a

cyclic operation of four steps: (1) adsorption, (2)

blowdown, (3) purge, and (4) pressurization. By

employing a sufficiently large number of beds and

27

using more complicated procedures in changing

bed pressure, PSA may be carried out as a

continuous process. Additional steps such as co-

current depressurization and pressure equalization

have been added to improve the purity and

recovery of products as well as to make the process

more energy-efficient. A common feature of all

PSA processes is that they are dynamic, i.e. they

have no steady state. After a sufficiently large

number of cycles, each bed in the process reaches a

cyclic steady state (CSS), in which the conditions

in the bed at the end of a cycle are approximately

the same as those at the beginning of the next

cycle.

In the present work, the following assumptions

are made to model a PSA process: (1) the system is

isothermal with negligible pressure drop through

the adsorbent beds; (2) the pressure change in the

steps of pressurization and blowdown is so rapid

that no significant exchange between adsorbed

phase and gas phase occurs. This is also called the

frozen solid assumption; (3) Langmuir isotherm is

valid for the system; (4) the mass transfer rate is

represented by a linear driving force expression;

(5) the ideal gas law is applicable and (6) plug flow

is assumed, i.e. there is no axial or radial disper-

sion. The component balance for species i in the

bed is [1,2]:

@Ci

@t�

@vCi

@z�

(1 � o)

o

@qi

@t�0; i�1 and 2 (1)

The last term in Eq. (1) is the mass transfer term

between solid and gas, where qi is the concentra-

tion of component i in the solid. For pressure

changing steps (pressurization and depressuriza-

tion) this term is zero due to assumption (2).Summation of Eq. (1) for all the components leads

to the total mass balance equation. For constant

pressure steps (adsorption and purge) the total

concentration of the fluid remains constant in the

bed, thus the total mass balance will be

C@v

@z�

(1 � o)

o

XN

i�1

@qi

@t�0 (2)

while for pressure changing steps the total mass

balance is

@v

@z�

1

P

@P

@t�0 (3)

where it is assumed that the pressure drop in the

bed is negligible. Eqs. (1)�/(3) are applied for the

flow from z�/ 0 to L . If the flow is reverse, the

term @/@z will be negative. The mass transfer

kinetics is modeled using the LDF approximation,

based on the simplification of Fick’s second law of

diffusion

@qi

@t�ki(qi��qi) (4)

where qi� denotes the equilibrium concentration of

component i. It is calculated using either extended

Langmuir isotherm,

qi�

qSi

�bipi

1 �Xj�n

j�1

bjpj

(5a)

or using Henry’s law,

qi��KiCi (5b)

The following boundary conditions are consid-

ered for Eqs. (1)�/(3). For the adsorption and

pressurization steps, the concentration of fluid at

the inlet is assumed to be equal to the feed

condition, since axial and radial dispersion is

Fig. 1. Basic two-bed PSA process.

28

neglected, namely

Cijz�0�Cfi (6)

for the purge step it is

Ci½z�L�PL

PH

(Ci½z�L)ads (7)

and for the depressurization step

@Ci

@zjz�0�0 (8)

The velocity boundary condition for the pres-

surization and adsorption step is

v½z�0�vf (9)

where vf is the superficial velocity of feed at z�/0.

(Velocity need not be constant with time duringpressurization step unless specifically controlled.

Normally, controllers are not used in PSA. Above

could be seen as a simplifying assumption.) For

the purge step the velocity boundary condition is

v½z�L�Gvf (10)

where G is the purge-to-feed velocity ratio. For the

blowdown step the velocity boundary condition is

v½z�L�0 (11)

In the cyclic operation, the initial condition in

the bed is the condition at the end of the previous

step. For startup, either a clean bed or a saturated

bed can be used. For a clean bed the initial

conditions are

Ci(z; 0)�0; qi(z; 0)�0 (12)

and for a saturated bed they are

Ci(z; 0)�C0; qi(z; 0)�qi� (13)

The above set of equations is discretized by

using finite difference and then solved by the

Newton�/Raphson algorithm.

The performance of a PSA process is measured

on the basis of product purity and productrecovery. Product purity of the desired component

2 is defined as its average composition in the

adsorption step

y2;prod�gtads

0

y2;prod(t)dt

tads

(14)

while product recovery is defined as

Eq. (15) is valid only for a PSA process havingre-pressurization step with feed.

3. Heuristics for PSA process

When an adsorption for separating a gas

mixture is determined, a logical sequence of

decision steps in design of a PSA process is as

follows:

1) Selection of a proper adsorbent based on its

equilibrium and kinetic characteristics.2) Selection of particle size distribution and

particle shape.

3) Selection of operating pressure levels for a

PSA system.

4) PSA cycle configuration and duration of each

individual steps.

Reco�

amount of component 2 obtained during adsorption step

�amount of component 2 used in purge step

� �amount of component 2 used during adsorption step in feed

�amount of component 2 fed during pressurization step

� �

�y2;prod(PHvf tads � PLGvf tpurg)

y2;f (PHvf tads � (PH � PL=2)vf tpres)(15)

29

5) PSA bed dimensions.6) Inclusion/exclusion of pressure equalization

step.

7) Vacuum swing adsorption (VSA) as an alter-

native.

Based on the model described in the last section,

simulation studies were carried out to analyze the

performances of PSA and to develop heuristics for

the decision steps indicated above. The systems

considered for the simulation, as given in Appen-

dix A, cover a wide range of adsorbate�/adsorbentalternatives. The resultant heuristic rules are pre-

sented in the following.

3.1. Selection of adsorbent

Adsorption is achieved due to the interaction

forces between the adsorbing molecules and the

adsorption surface. Different substances are ad-

sorbed with different affinities. It is this ‘selectiv-ity’ that provides the basis for adsorption

separation processes. The task of adsorbent is to

provide the surface area required for selective

adsorption of the preferentially adsorbed species.

A high selectivity is of user’s interest. The separa-

tion factor (a ) can be used as a measure of

selectivity. The separation factor of an absorbent

is defined as [1]:

a12�x1=x2

y1=y2

(16)

where x1 and y1 are, respectively, the mole fraction

of component 1 in adsorbed phase and fluid phase.

The separation factor depends on the adsorptionproperty, either adsorption kinetics or adsorption

equilibrium, or both. In an equilibrium controlled

adsorption process, it is simply the ratio of the

equilibrium constants. For an extended Langmuir

isotherm and a linear isotherm, this separation

factor is the ratio of Henry’s constants

a12�K1

K2

(17)

In a kinetically controlled adsorption, the selec-

tivity depends on the difference of kinetic para-

meters. The time-dependent concentration within

the adsorbent particle depends on the diffusivity ofadsorbing molecules. For short time intervals this

dependency can be approximated by [1]:

qt8ffiffiffiffiD

p(18)

Thus the separation factor for kinetically con-

trolled process is calculated by

a12�

ffiffiffiffiffiffiD1

D2

s(19)

It is always useful that the separation factor is

calculated by considering both equilibrium and

kinetic effect. Thus the separation factor can be

defined as

a12�K1

K2

ffiffiffiffiffiffiD1

D2

s(20)

In this study, Eq. (20) is used to calculate the

separation factor for all cases considered. Table 1

shows some simulation results. Adsorbents with

different selectivities are used to separate a two-

component fluid mixture (such as say air with 20%oxygen and 80% nitrogen) with a mole-fraction of

0.2 for the highly adsorbed species (species 1).

While doing simulation the other parameters are

kept constant. Fig. 2 shows a graphical represen-

tation of these results. From Table 1 and Fig. 2, it

can be seen that the product purity will be

increased, if a higher separation factor is selected.

Thus a high separation factor is a key for a quickscreening of various adsorbents.

Table 1

Comparison of adsorbents based upon separation factor

K1/K2 /

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiD1=D2

pa Product purity of component B

1 0.68 0.68 0.78

1 2.14 2.14 0.821

1 6.76 6.76 0.952

1 21.4 21.4 0.999

0.11 6.76 0.75 0.787

2.5 6.76 17.1 0.993

10 6.76 67.6 0.999

2.14 1 2.14 0.812

7 1 7 0.942

10 1 10 0.954

The conditions for the simulation are given in the caption of

Fig. 2.

30

3.2. Size distribution and shape of particles

In adsorption processes, the particle size dis-

tribution and particle shape decide the bed poros-

ity. Porosity affects bed performance in two ways.

If other parameters remain constant, a lower

porosity leads to a higher bed pressure drop. On

the other hand, a lower porosity means a higher

adsorbent content of the bed and hence a higher

adsorption capacity. Moreover, a lower porosity

means less loss of the adsorbable component

during the blowdown step and less requirement

of product gas for an effective extraction during

the purge step. Both of these properties increase

the product recovery.

Bed porosity can be varied using different

shapes and sizes of adsorbent particles and to

some extent packing techniques. Simulation stu-

dies are made using various values of bed porosity.

The results are shown in Fig. 3. The effect of bed

porosity on product purity is significant for both

bulk separation and purification processes. The

effect on product recovery is significant only in

bulk separation cases. Fig. 3a�/d show that as

porosity increases both the product purity and

recovery will decrease. From Fig. 3e, it can be seen

that as the porosity increases, product recovery

remains almost constant for purification processes

(where the highly adsorbing species is in very low

concentration, e.g. air containing moisture).On the other hand, the porosity of a bed also

affects the bed pressure drop. In a packed bed the

pressure drop can be calculated from Blake�/

Kozeny equation

�@P

@z�

180mv

d2p

(1 � o)2

o3; �z � [0; L] (21)

From Eq. (21), as the porosity increases the bed

pressure drop will decrease. Fig. 4 shows the

pressure drop versus the bed porosity. For a given

system, Eq. (21) can be rewritten as

�@P

@z�f

(1 � o)2

o3(22)

where f is given as

f�180mv

d2p

(23)

There are two opposite effects of porosity: high

product purity requires low porosity and a low

pressure drop is achieved with high porosity. From

Fig. 4, it can be seen that for bed porosity lower

than 0.3, the pressure drop increases rapidly. Thus

this should be the lower limit of porosity (which

can be achieved for most practical particle shapes

and sizes). For bed porosity higher than 0.5, thechange in pressure drop becomes moderate, thus

this can be considered as the upper limit. Similarly,

the effect of the porosity on the product purity, as

shown in Fig. 3a�/e, indicates that when bed

porosity is higher than 0.5, the purity will decrease

significantly, thus confirming the use of 0.5 as the

upper limit of the bed porosity.

3.3. Selection of adsorption pressure

Selection of the adsorption pressure is based onthe equilibrium relationship of the system. An

isotherm describes the equilibrium loading of a

species, which is dependent on the partial pressure

of the species in an adsorption process. As the

adsorption pressure increases, the amount of fluid

adsorbed on the adsorbent will increase. To

determine the pressure level for adsorption, one

should keep in mind that the larger the differencebetween the capacities of the competing adsor-

bates, the purer the raffinate will be. The selectiv-

ity of an extended Langmuir isotherm and a linear

isotherm is constant [1,2]. These isotherms are,

therefore, called ‘constant selectivity isotherm’.

For constant selectivity systems, if the pressure is

Fig. 2. Effect of separation factor on product purity (PH�/3

atm, PL�/1 atm, tads�/tpurg�/40 s, tpres�/tblow�/5 s, o�/0.4,

vf�/0.007 m s�1, purge/feed�/2, L�/0.65 m).

31

increased, which causes more adsorption of the

highly adsorbed species, the product purity will be

increased. The less favorable species is also ad-

sorbed more, but in comparison to the more

favorable species it is always less, as long as the

more adsorbing species is present in significant

quantities in the bulk phase. Therefore, for such

systems a higher pressure always leads to a purer

product.

Besides this advantage of high pressure for

constant selectivity systems, there is one disadvan-

tage too, that is energy loss. A higher pressure level

leads to higher compression costs and a higher loss

of energy in the blowdown step. If an adiabatic

compression is assumed, the power requirement

can be approximated as [1]:

Fig. 3. Effect of porosity on bed performance (a): Bed porosity vs. product purity. (b): Bed porosity vs. product recovery. (c): Product

recovery for system 3. (d): Product purity for systems 4 and 5 (purification process). (e): Product recovery for systems 4 and 5

(purification process).

Fig. 4. Effect of bed porosity on bed pressure drop.

32

W �g

g� 1

QRT

h

��PH

PL

�(g�1)=g

�1

�(24)

where PH and PL are high and low pressure levels,

respectively, Q is the volumetric flow rate, and T is

the operating temperature. Simulation results of

extended Langmuir and linear isotherms are given

in Fig. 5a�/c for various adsorption pressure levels.

It can be seen that as the pressure increases, the

product purity will be increased. At the same time

the power required for compression also rises. If a

high purity product is desired, the adsorption

pressure should be as high as possible. Fig. 6

shows that the power requirement increases with

the increase of the adsorption and the desorption

pressure ratio. Considering the trade-off between

product quality and power requirement, the ad-

sorption pressure should be taken as the value at

which the change of the adsorbed phase concen-

tration with pressure becomes moderate.

If the selectivity varies with the operating

pressure, the adsorption pressure should be that

at which the selectivity is maximum. To study the

effect of pressure for varying selectivity systems,

two hypothetical systems (with imputed isotherm

constants) are taken and simulated. The simula-

tion results are shown in Fig. 7a and b. It is

Fig. 5. Effect of adsorption pressure on product purity with

yf �/(0.99, 0.01). (a) System 1 and 2. (b): System 3. (c): Systems

4 and 5 (purification process).

Fig. 6. Effect of pressure ratio on power requirement.

Fig. 7. Effect of pressure on bed performance for varying

selectivity. System A: Having same properties as system 2 of

Fig. 6 except equilibrium selectivity. System B: Having same

properties as system 2 of Fig. 6 except equilibrium selectivi-

tyand kinetic selectivity. The kinetic data are: k1�/0.002 s�1,

k2�/0.00018 s�1. (a): Selectivity. (b): Product purity.

33

illustrated that the product purity is maximum atthe pressure where the selectivity is also maximum.

3.4. Selection of adsorption time

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 bymonitoring the concentration of the effluent.

Breakthrough occurs when the effluent concentra-

tion reaches a specific value. The adsorbate con-

centration 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 balanceequations for both the bed and adsorbent parti-

cles, 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 be

near the breakthrough time. This time dependsupon isotherm, diffusivity and residence time of

the feed in the bed.

From simulation studies, it can be observed that

beyond a certain value of the adsorption time, the

change in product purity becomes insignificant.

The product purity decreases as the adsorption of

less adsorbable species increases. Fig. 8 shows how

the change in the adsorption time affects theproduct purity. It can be seen that the time of

Fig. 8. Effect of adsorption time on product purity. (System 2:

PH�/4 atm, PL�/1 atm, purge/feed�/2).

Fig. 9. Effect of distribution of total adsorption time on bed

performance. (a): Product purity. (b): Product recovery.

Fig. 10. Effect of distribution of total adsorption time on bed

performance for purification process (a): Product purity. (b):

Product recovery.

34

the adsorption step should be where the productpurity is maximum. This is the time when break-

through occurs.

3.5. Effect of distribution of adsorption time

In a two-bed, four-step PSA system, adsorption

takes place in both the pressurization and adsorp-

tion steps. The apportion of the total adsorptiontime to these two steps affects the performance of

PSA. Figs. 9 and 10 show the simulation results

corresponding to different time allocations to these

two steps. In Fig. 10, where the results shown are

those of purification processes, it can be seen that

as the ratio of the pressurization time and the

adsorption time increases, the product recovery

will decrease, but its purity will increase. With ahigher time ratio, less product will be obtained. At

the same time, higher time ratio improves product

quality. Moreover, it can be seen from the simula-

tion results that the rate of the decrease of product

recovery is much greater than the rate of the

increase of product purity. Thus, the change in

recovery is a dominating factor to determine the

adsorption time apportion. Having these twoopposite effects and taking the fact that the

recovery effect is more dominant, the ratio of the

pressurization time to the adsorption time should

be low. The upper limit should be 0.2, according to

the simulation results.

3.6. Effect of purge-to-feed ratio

The purge step in PSA is a desorption step thatregenerates adsorbents by desorbing the adsorbed

species. In a PSA process, saturated adsorbents are

regenerated by lower pressure, thus a low pressure

purge step is required. Generally, from the product

vessel with the raffinate at a high pressure, a

fraction of the product stream is withdrawn to

purge the bed and expended to a low pressure. The

volume required in the purge step affects theproduct quality as well as its recovery. As the

purge volume increases, purging becomes more

effective, providing a regenerated bed with adsor-

bents of less loading and leading to an increased

product purity. In principal, the bed should be

fully regenerated with adsorbents completely un-

saturated, thus more purging is necessary. At the

same time, since purging is done by utilizing the

product, increase in the purge volume decreases

the product recovery. Generally, the purge volume

specification for PSA is given by the purge-to-feed

volume ratio.Simulation was made with different values of

the purge-to-feed volume ratio. The results are

presented in Fig. 11. The effect of this ratio on

product purity and recovery is shown for two

cases. It can be seen that as this ratio increases, the

product purity increases as well, but the recovery

decreases. The rate of the increase in purity is

much slower than the rate of the decrease in

recovery. From these results, one may infer that

the purge-to-feed ratio should be neither too low

nor too high. A guideline regarding this ratio from

the simulation results is that it should be between

1.0 and 2.0, if purging is done by product. These

are volumetric ratios. It should be noted that,

although the volume of purge used is more than

Fig. 11. Effect of purge/feed ratio on bed performance (a):

Product purity. (b): Product recovery.

35

the volume of feed, the mass of purge is less thanthe mass of feed or product, since the pressure of

purging is much lower than the feed pressure.

3.7. Residence time determination

The residence time of species in a bed is the ratio

of the bed holdup to the volumetric feed rate.

Sufficient residence time should be provided, so

that the desired product purity can be achieved.

For species with lower diffusivities, greater resi-

dence time is required. The choice of residence

time is critical in adsorption, since if the residencetime is too short, there will be no significant

adsorption. Increase in residence time can be

made by reducing the feed rate or by increasing

the bed volume. Since the feed rate is decided by

the desired capacity of the unit, required residence

can be achieved by changing the bed volume.

However, in an existing unit, residence time can be

altered only by adjusting feed rate or feed pressureor both.

Simulations were made to study the effect ofresidence time on bed performances. Fig. 12 shows

the effect of residence time and feed composition

on the product purity for system 2 (refer Appendix

A). Similar profiles can be obtained for other

systems too. For different systems, the shape of

profiles remains the same. The main features of

these plots are that, at low residence time, no high

product purity can be obtained, and the relation-ship between feed composition and product com-

position is linear. When keeping the feed

composition constant, product purity can be

increased by increasing residence time. If the feed

composition of the desired species is high, product

purity will increase linearly with residence time.

Fig. 13 shows the effect of the decrease in

diffusivity with a factor of 0.1 for the highlyadsorbing species. Comparing Fig. 13 with Fig.

12, it can be observed that for the same residence

time, a decrease in diffusivity leads to a decrease in

product purity. This means that for the same

product purity, more residence time is needed for

systems with lower diffusivity. To calculate the

residence time for a given system and a given

product purity, the concept of the minimumresidence time is introduced in the following.

3.7.1. The minimum residence time

A PSA process reaches its cyclic steady state

after a certain number of cycles of operation. A

steady state PSA model can be developed using the

same assumptions as stated before. The governing

equations may be obtained as follows. First, by

combining Eqs. (1) and (4) and letting the time-

differential terms be zero, the following equationcan be gained

Fig. 12. Effect of residence time and feed composition on

product purity. System 2: PH�/3 atm, PL�/1 atm, tads�/

tpurg�/40 s, tpres�/tblow�/5 s, L�/0.65 m. (a): Effect of

residence time. (b): Effect of feed composition.

Fig. 13. Effect of residence time and feed composition on

product purity for system 2 by decreasing diffusivity of the

highly adsorbing species with a factor of 0.1.

36

�o

(1 � o)

dCi

ki(qi�� qi)�

dz

v(25)

If the maximum driving force is applied, i.e. bytaking qi �/ 0 in the above equation, one has

�o

(1 � o)

dCi

kiqi��

dz

v(26)

The boundary condition for this equation is the

same as given in Eq. (6). It is easy to solve this

equation, and the solution for the highly adsorbedcomponent will give the residence time for a

system under the conditions of a constant velocity

and the maximum driving force. Therefore, the

solution of Eq. (26) gives the minimum residence

time for a given feed and desired product compo-

sition. Initially, one may expect the existence of

certain relationship between the ratio of the actual

and the minimum residence time, with the kineticparameters and separation factor. These relations

are shown in Figs. 14 and 15. Fig. 14 gives the

relationship between the separation factor and the

time ratio. As the separation factor increases, the

required ratio of actual-to-minimum residence

time also increases. The results of actual-to-mini-

mum residence time versus the mass transfer

coefficient ratio are shown in Fig. 15. But thisrelation is less clear. As an explanation, one may

argue that the ratio of actual-to-minimum resi-

dence time depends on the total amount of gas

adsorption, rather than the kinetic selectivity (the

ratio of diffusivities). Basis for this argument is

that in the calculation of the minimum residence

time, the maximum driving force is considered

(taking qi �/0), but this is not the case of the actual

residence time. The difference arises due to the

difference in driving force, which is the adsorbed

phase concentration in a practical cycle. The

concentration in the adsorbed phase depends on

the mass transfer of each component, which relies

on the individual mass transfer coefficient. In this

way, the total effect on the adsorbed phase

concentration depends on the sum of the mass

transfer coefficient, rather than the kinetic selec-

tivity. To test this argument, in Fig. 16, the time

ratio is plotted against the sum of the mass

Fig. 14. Effect of adsorption separation factor on the ratio of

actual-to-minimum residence time for k1�/k2�/0.0055 in sys-

tem 2. PH�/4 atm, PL�/1 atm, tads�/tpurg�/40 s, tpres�/

tblow�/5 s, vf�/0.007 m s�1, L�/0.65 m.

Fig. 15. Effect of kinetic separation factor on the ratio of

actual-to-minimum residence time for system 2. PH�/4 atm,

PL�/1 atm, tads�/tpurg�/40 s, tpres�/tblow�/5 s, vf�/0.007 m

s�1, L�/0.65 m.

Fig. 16. Effect of summation of mass transfer coefficients on

the ratio of actual-to-minimum residence time. PH�/4 atm,

PL�/1 atm, tads�/tpurg�/40 s, tpres�/tblow�/5 s, vf�/0.007 m

s�1, L�/0.65 m, feed composition (0.21, 0.79).

Fig. 17. Relation between (k1�/k2)(K1/K2) and the ratio of

actual-to-minimum residence time.

37

transfer coefficients. A more obvious relationshipbetween these two quantities can be seen.

In Fig. 17 an attempt is made to combine the

relations of Figs. 14 and 16, from which the

relation between (K1/K2)(k1�/k2) and the ratio of

actual-to-minimum residence time can be ob-

served. It should be noted that this ratio also

depends on the feed composition, but this relation

is not so clear. This is because in calculation of theminimum residence time, the assumption of a

constant velocity is taken, which is invalid if the

concentration of the highly adsorbing species is

high in the feed. If the concentration of the highly

adsorbing species in the feed increases, the product

flow rate will be low as compared with the feed

flow rate, and the minimum residence time will be

much less than the actual residence time. Thus theratio of actual-to-minimum residence time will

also depend on feed composition. This relation is

illustrated in Fig. 18, in which various cases

(including systems 1, 2 and 3) are tested. It is

seen that all these data fit a straight line, which can

be approximated with the following relation

tact

tmin

�1�100(k1�k2)

�K1

K2

�yf1 (27)

Most of the systems have (k1�/k2)(K1/K2)yf1B/

0.015, where the value of the time ratio is in

between 1 and 2. From this result, a quick

estimation of the bed size can be made.

The bed volume is determined based on the

required residence time. To specify the bed size, i.e.

the bed diameter and bed height, some criteria

should be kept in mind. The choice of the beddiameter depends on the fluidizing velocity, which

is the minimum velocity required to fluidize a bed.The maximum velocity in the bed should not

exceed 70% of the minimum fluidizing velocity

[9]. For velocities greater than this value, entrain-

ment of adsorbents in effluent stream may occur

and also the pressure drop in the bed would be

very high. After determining the fluidizing velo-

city, the bed diameter can be calculated. Another

important criterion for bed specifications is thecrushing strength of the solids. The height should

be such that no crushing occurs in the bed.

3.8. Pressure equalization

The first improvement over Skarstrom’s cycle is

the introduction of a pressure equalization step, as

shown in Fig. 19. After the first bed has been

purged and the second bed has completed its high-

pressure adsorption step, instead of blowing downthe second bed directly, the two beds may be

connected to each other through their product

ends in order to equalize their pressures. The first

bed is thus partially pressurized with gas from the

outlet region of the second bed. After the pressure

equalization, the two beds are disconnected and

the first bed is pressurized with feed gas while the

second bed is vented to complete the blowdown.The pressure equalization step conserves energy,

because the compressed gas from the high-pressure

bed is used to partially pressurize the low-pressure

bed. Since this gas is partially depleted of the

strongly adsorbed species, the degree of separation

is conserved and the blowdown losses are reduced.

Based on these considerations, a pressure equal-

Fig. 18. Relation between (k1�/k2)(K1/K2)yf1 and the ratio of

actual-to-minimum residence time. Fig. 19. Pressure equalization step in a PSA process.

38

ization step is often incorporated in the PSA

process.

Simulation results are presented in Table 2

indicating the PSA performance with and without

a pressure equalization step. It can be seen that a

pressure equalization step favors product recovery.

But if the pressure swing is sufficiently low, the

inclusion of a pressure equalization step may be

impractical. Otherwise, the pressure equalization

step should always be incorporated in the PSA

process.

3.8.1. Selection of the intermediate pressure

The intermediate pressure is the pressure after

the pressure equalization step. As the intermediate

pressure increases, the degree of saturation of the

highly adsorbed species increases in the bed, which

is unfavorable. If it is higher than a certain value,

this saturation causes decrease in product purity

and recovery. Simulation results for different

intermediate pressures are shown in Fig. 20. Itcan be seen that once the intermediate pressure is

increased beyond a threshold value, both the

product recovery and purity are adversely affected.

This means that the intermediate pressure should

be below this threshold value. If the intermediate

pressure is denoted as PI, then the following

relation holds approximately

PI

PL

�(0:5 to 0:8)PH

PL

(28)

3.9. Vacuum swing adsorption

Vacuum swing adsorption (VSA) is also aSkarstrom cycle in which the low-pressure purge

step is replaced by a vacuum desorption. The

product end of the bed is kept closed and the

vacuum is applied through the feed end, as shown

in Fig. 21. In a VSA process, using the same high

operation pressure as a Skarstrom cycle and for

the same product purity, the loss of the less

favorably adsorbed species in the evacuation stepis normally less than the corresponding loss in the

purge. The gain in raffinate recovery is achieved at

the expense of the additional mechanical energy

required for the evacuation step. A significant

Table 2

Comparison of PSA process with and without pressure equal-

ization step for air separation on CMS

Product

purity

Recovery without pres-

sure equalization

Recovery with pressure

equalization

0.914 0.418 0.532

0.945 0.374 0.51

0.96 0.348 0.488

0.972 0.325 0.469

Fig. 20. Effect of intermediate pressure (after purge) on

product purity and product recovery (a):System 1: Feed

composition: (0.4, 0.6), PH�/5 atm, vf �/0.007 m/s, L�/0.6

m, purge/feed�/1.5. (b): System 2. Feed composition: (0.21,

0.79), PH�/5 atm, vf �/0.007 m/s, L�/0.65 m, purge/feed�/1.5. Fig. 21. The sequence of VSA cycle (only one bed is shown).

39

amount of energy can be saved, if the adsorptiontakes place slightly above the atmospheric pressure

and the desorption is done at a very low pressure.

A VSA cycle will, therefore, be advantageous over

a normal Skarstrom cycle, if a low-pressure

product is acceptable.

In kinetically controlled separation, a major

disadvantage using a normal Skarstrom cycle is

that the slowly diffusing raffinate product wouldbe continuously adsorbed during the purge step.

This problem can be avoided by using VSA. In

kinetically controlled processes there is a little

difference in isotherms of feed components (e.g.

nitrogen separation from air using zeolite 4A) but

a large difference in diffusivity. In such a system,

purging with the product to remove the highly

diffusing species from the bed is undesirable. Thisis so because apart from wasting product (a certain

fraction of nitrogen), the raffinate gas will be

adsorbed during this step, thereby reducing the

capacity for oxygen during the next adsorption

step. For such type of systems a VSA process is

worth considering.

Simulation is performed for the nitrogen separa-

tion from air using carbon molecular sieve (CMS).The results are shown in Table 3, which illustrate

that the recovery of nitrogen is greater in a VSA

process than in an ordinary Skarstrom cycle. From

the results and the above explanation, it can be

concluded that for kinetically controlled processes,

VSA is a better choice over a normal Skarstrom

cycle.

4. Two case studies

Heuristics developed in the previous section

have been tested using two case studies. Rajasree

and Moharir [16] discussed simulation based

synthesis, design and optimization of PSA pro-

cesses. The system used was air separation using

Zeolite 5A. The data are given in Table A1 in theAppendix A with system 6. Table 4 compares the

results in [16] with the results obtained using our

heuristic rules. In [16] the pressure equalization

step was used for some cases. They showed that

product (oxygen) recovery increases from 28.5 to

32.8% when pressure equalization step is included.

According to the proposed heuristics, recovery

increases if pressure equalization is considered.

Air separation using CMS was considered by

Nilchan [15]. The author discussed optimization

approach for PSA processes. The objective func-

tion used in the case study is minimizing the power

requirement. The data are given in Table A1 in the

Appendix A with system 2. Table 5 compares the

results in [15] using optimization study with the

results obtained using the heuristic rules proposed

in this study.

Both the case studies show that the results

obtained using the heuristics are close to the

results obtained using optimization. It demon-

strates that heuristics based synthesis is useful for

preliminary design and screening of PSA pro-

cesses. In addition, in both case studies the flow

to be separated is air, but the adsorbent is different

(in case 1 Zeolite 5A, and in case 2 CMS), due to

different product requirement. In the first case

oxygen is the desired component, and in the

second case nitrogen is the desired component.

The separation factor for nitrogen in the second

case is 41, while in the first case it is 0.16. If

nitrogen is the desired component from air, CMS

adsorbent should be used rather than Zeolite 5A.

The heuristic rule proposed for this case also

suggests using the adsorbent with a higher separa-

tion factor.

Table 3

Performance comparison of VSA cycle with ordinary Skar-

strom cycle

Product purity

for nitrogen in %

% Recovery of nitro-

gen in Skarstrom cycle

% Recovery of ni-

trogen in VSA cycle

89.5 56.4 88.3

92.5 53.7 83.3

94.2 49.7 77.6

95.1 42.1 72.5

98.2 21.6 60.1

The blowdown pressure used is 1 atm and the vacuum

pressure used is 0.25 atm.

40

5. Conclusions

In PSA design and operation, heuristics devel-

oped in this study may be summarized as follows:

Rule 1 : Adsorbent, which gives the largest

separation factor, should be used.

Rule 2 : Bed porosity should be in the range

0.3�/0.5. Particle size distribution and shape

should be such that bed porosity is within these

limits.Rule 3 (a ): For systems whose isotherms are

given either by the Henry’s Law or by the

extended Langmuir isotherm expression, the

adsorption pressure should be as high as

possible, subjected to the power requirement

constraint.

Rule 3 (b): For systems with pressure dependent

selectivity, adsorption pressure should be the

pressure, which gives maximum selectivity.

Rule 4 (a ): The adsorption time should be near

the adsorption breakthrough time.

Rule 4 (b): For a two bed PSA process, the

adsorption and desorption time should be

equal.

Rule 5 : The maximum limit for the ratio of the

pressurization time to the adsorption time

should be 0.2.

Rule 6 : The ratio of purge-to-feed volume

should be in the range 1.0�/2.

Rule 7 (a): The bed diameter should be such

that the velocity within the bed does not exceed

70% of the minimum fluidizing velocity.

Rule 7 (b ): Bed height should not cross the

crushing strength of adsorbent particles.

Table 4

Comparison of results by the heuristic rules and optimization (Case Study 1)

Purity of oxygen 87.8% and

recovery is 36.8%

From Rajasree and

Moharir [16]

Using heuristic rules proposed

o 0.376 0.3�/0.5

PH (atm) 6 Heuristic suggests to use high pressure to obtain higher purity

P /F 6.125 1.0�/2.0

tads 65 Both are equal

tdes (s) 65

tpress/tads 0.077 0.0�/0.2

tmin (s) 104.00 104.00

tactual (s) 270.0 316.0

Table 5

Comparison of results by the heuristic rules and optimization (Case Study 2)

Purity of nitrogen 87.1% and

recovery is 67.6%

From Nilchan [15] Using heuristic rules proposed

o 0.4 0.3�/0.5

PH (atm) 2.36 Power requirement decides the adsorption pressure

P /F Purging was not

considered

Zero purge results in high impurity in the product. As in the case study,

without purge consideration high impurity (12.89%) was achieved

tpress/tads 0.086 0.0�/0.2

tmin (s) 18.2 18.2 (solution of Eq. (26))

tactual (s) 21.2 19.3

41

Rule 7 (c ): The Ratio of actual-to-minimumresidence time should be in the range 1�/2. Eq.

(27) may be used to calculate the ratio.

Rule 8 (a ): For processes with high swing in

pressure, a pressure equalization step should be

included.

Rule 8 (b ): The ratio of intermediate pressure to

the low pressure should be in the range 0.5�/0.8

of the ratio of the high pressure to the lowpressure.

Rule 9 : For a kinetically controlled process,

VSA should be considered.

The work for developing heuristics for PSA has

been initiated in this paper. Some rules could

appear obvious or trivial, considering the accumu-

lated knowledge on PSA at this stage. More

detailed models and more extensive simulation

studies in future would help modify the rules

proposed here and develop more elaborate heur-istics. Moreover, the study of interactions between

individual decision parameters is also part of the

further work.

Appendix A: Systems considered in the simulation

studies

Table A2: Purification systems

Number 4 5

System CO2�/He�/Silica

Gel [13]

H2O�/Air�/Alu-

mina [13]

Component

1

CO2 1% H2O 1%

Component

2

He 99% Air 99%

K1 9084 52.7

k1 (s�1) 2.583 e-4 4.67 e-2

References

[1] D.M. Ruthven, S. Farooq, K.S. Knaebel, Pressure Swing

Adsorption, VCH Publishers, New York, 1994.

[2] R.T. Yang, Gas Separation by Adsorption Processes,

Butterworth Publishers, Boston, 1987.

[3] P.L. Cen, R.T. Yang, AIChE Symposium Series 80 (1985)

68.

[4] E. Alpay, D.M. Scott, Chemical Engineering Science 47

(1992) 499.

[5] N.S. Raghavan, D.M. Ruthven, The American Institute of

Chemical Engineers Journal 31 (1985) 385.

[6] N.S. Raghavan, D.M. Ruthven, The American Institute of

Chemical Engineers Journal 31 (1985) 2017.

Table A1: Bulk separation systems

Number 1 2 3 6

System CH4�/N2�/CMS

[14]

Air separation�/CMS

[15]

Hypothetical

system

Air separation�/Zeolite

5A [16]

Composition of compo-

nent 1

N2 40% O2 21% 40% N2 79%

Composition of compo-

nent 2

CH4 60% N2 79% 60% O2 21%

qs1 (mol cm�3) 0.00182 0.00264 0.0033 0.0258

qs2 (mol cm�3) 0.00255 0.00264 0.00065 0.00344

b1 (atm�1) 0.26 0.14 0.161 0.0155

b2 (atm�1) 0.62 0.154 0.164 0.057

k1 (s�1) 9.99 e-4 2.7 e-3 0.002 0.0098

k2 (s�1) 4.82 e-6 5.9 e-5 0.0018 0.0032

42

[7] M.H. Chahbani, D. Tondeur, Separation and Purification

Technology 20 (2000) 185.

[8] H.M. Kvamsdal, T. Hertzberg, Chemical Engineering

Science 50 (1995) 1203.

[9] Z.P. Lu, J.M. Loureiro, M.D. LeVan, A.E. Rodrigues, The

American Institute of Chemical Engineers Journal 38

(1992) 857.

[10] Z.P. Lu, J.M. Loureiro, M.D. LeVan, A.E. Rodrigues,

Gas Separation and Purification 6 (1992) 15.

[11] Z.P. Lu, J.M. Loureiro, M.D. LeVan, A.E. Rodrigues,

Industrial Engineering and Chemical Research 32 (1993)

2740.

[12] Z.P. Lu, J.M. Loureiro, A.E. Rodrigues, M.D. LeVan,

Chemical Engineering Science 48 (1993) 1699.

[13] W.L. McCabe, J.C. Smith, Unit Operations of Chemical

Engineering, fifth ed., McGraw-Hill, New York, 1993.

[14] A.I. Fatehi, K.F. Loughlin, M.M. Hassan, Gas Separation

and Purification 9 (1995) 199.

[15] S. Nilchan, The optimization of periodic adsorption

processes, Ph.D. Thesis, Department of Chem. Tech.,

Imperial College of Science, Technology and Medicine,

London, 1997.

[16] R. Rajasree, A.S. Moharir, Computers and Chemical

Engineering 24 (2000) 2493.

43