Ind. Eng. Chem. Res. 2006, 45, 1085-1096
1085
Optimization of Medical PSA Units for Oxygen Production
J. C. Santos, A. F. Portugal, F. D. Magalhães, and A. Mendes*
LEPAEsDepartamento de Engenharia Quı́mica, Faculdade de Engenharia, UniVersidade do Porto Rua Dr.
Roberto Frias, 4200-465 Porto, Portugal
A dynamic model, a simulator, and an optimization procedure were developed for small oxygen pressure
swing adsorption units with different equalization configurations, top-to-top equalization (TE), bottom-tobottom equalization (BE), and cross equalization (CE), and three different commercial adsorbents, Oxysiv 5
and Oxysiv 7 from UOP and Sylobead MS S 624 from Grace Davison. These units’ cycles have the peculiarity
of having the pressure history dependent on the product flow rate, which makes them more difficult to simulate
and optimize than the classic Skarstrom cycle. The units’ performances (product recovery and power
consumption) using each adsorbent and equalization type were compared for cycles with the same pressure
ratio. The simulation results were shown to be in agreement with the experimental data obtained with Oxymat
3, an oxygen concentrator from Weinmann. The optimization procedure lead to an improvement of the unit’s
performance.
Introduction
The pressure swing adsorption (PSA) technology has experienced many developments since 1932 when Finlayson and
Sharp developed the first PSA single-bed process. Ten years
later, Khale released a German patent describing a two-bed PSA
process. Back then, only modest separations could be obtained
because of the low separation factor between oxygen and
nitrogen on the available zeolites.1 In the following years, this
technology and the adsorbents used went through many
developments. From 1949 to the early 1950s, Milton and Breck
discovered the commercially significant zeolites. In 1960,
Skarstrom developed several PSA cycles. Most applications
were for air-drying. In 1964 (U.S. Patent 3,142,547), Skarstrom
proposed an equalization step which allowed the decrease of
the power consumption.2 In this step, some of the gas inside
the column that was producing is used to pressurize the other
column, in this way increasing the recovery.
Zeolites experienced enhancements in terms of nitrogen
capacity and selectivity, which resulted in improvements in
pressure swing adsorption processes for oxygen production.
Zeolites such as NaX made possible the development of the
first economical PSA process for oxygen production.3 In 1964
(U.S. Patent 3,140,931), McRobbie, from Union Carbide
Corporation, specified a zeolite for O2 PSA plants. In 1966 (U.S.
Patent 3,237,377), a patent was filled by Skarstrom describing
a PSA unit for producing oxygen from air, in a two-bed process
with an equalization step and using a 13X-type zeolite.2
These developments allowed, in 1970, the commercialization
of pressure swing adsorption units for separating oxygen from
air. However, the goal of decreasing the power consumption
even more was still being pursued. In 1982 (G. B. Patent
2,091,121), Armond and Deverell proposed the use of smaller
particles, claiming that this allowed reduced power consumption,
bed size, and cycle times.2 Other developments have been made
in the zeolite field, such as the decrease of the quantity of the
inert inorganic material that binds the zeolite crystallites (binderzeolites for equilibrium air separations contain ∼20% of this
material). This modification in the zeolite structure was aimed
* Corresponding author. Tel.: +351 22 5081695. Fax: +351 22
5081449. E-mail: [email protected].
at increasing the adsorption capacity and, consequently, the
performance of the PSA units.4 New adsorbents, such as LiX,
used commercially since 1997, together with process improvements, allowed the reduction of both capital and operating costs.3
Many applications have been found for PSA units, such as
the production of oxygen for medical use. In 1975, these units
became widely used in hospitals for treating patients with
respiratory illness, providing 2-4 L/min of 85-95% oxygen.
Also in this year, Ruder and Isles patented a PSA unit to produce
enriched air for use onboard jet aircraft (U.S. Patent 3,922,149).
One year later, Armond described an electric-powered, compact
PSA apparatus (DE Patent 2,559,120) using zeolite molecular
sieve to generate breathing air for medical use. In 1984 (U.S.
Patent 4,477,265), Kratz and Sircar patented a medical oxygen
generator for domiciliary use which generated a product with
90% of oxygen.2 Currently, ∼500 000 of these units are sold
per year worldwide.
For economical reasons, the cycle and configuration of these
units differ from the ones proposed in the simple and widely
known, even though rarely used in practice, Skarstrom’s cycle:
the solenoid on-off valves used for controlling the pressurization step are replaced by check valves, and this step will become
dependent on the volume of the storage tank and on the
production flow rate. The units that incorporate an equalization
step operate in four stages: one stage that begins with
pressurization and finishes at the end of production, one
equalization stage, one stage that begins with depressurization and finishes at the end of purge, and another equalization
stage.
One of the consequences of using these units and cycles is
that the pressure history during a cycle depends on the product
flow rate, while it is independent when using the Skarstrom
cycle. For this reason, the first cycle is more difficult to simulate
and optimize, and thumb rules valid for Skarstrom cycles are
not applicable.
New pressure swing adsorption cycles and adsorbents are still
being developed: Sequal Technologies, Inc., developed a
portable multicolumn pressure swing adsorption unit for medical
oxygen production5 which makes use of a rotary valve;6 a
LiLSX-type zeolite was developed, having a large nitrogen
capacity and a high selectivity; Air Products and Chemicals,
10.1021/ie0504809 CCC: $33.50 © 2006 American Chemical Society
Published on Web 01/04/2006
1086
Ind. Eng. Chem. Res., Vol. 45, No. 3, 2006
Inc., patented an AgLiLSX-type zeolite in 2002 (U.S. Patent
6,432,170) and in 2003 (U.S. Patent 6,544,318) patented a PSA
cycle that makes use of it, which allows the production of highpurity oxygen (>95%).
In this paper, we present simulation and optimization results
of small pressure swing adsorption units operating under three
different equalization cycles: top-to-top, bottom-to-bottom, and
crossed equalization. The performance of these units with each
of these steps is compared with three different commercially
available zeolites: Oxysiv 5 and Oxysiv 7 from UOP and
Sylobead MS S 624 from Grace Davison. The simulation results
are compared with the actual performance of a commercial
oxygen concentrator, Oxymat 3 from Weinmann.
Unit Description
The pressure swing adsorption (PSA) unit is composed of
two fixed adsorbent beds, a storage tank, solenoid valves and
calibrated orifices to control the feed, purge, and equalization
and vent streams. It operates with four stages (six steps):
pressurization/production, equalization, depressurization/purge,
and equalization again. Pressurization and production occur in
stage 1. Simultaneously, stage 3 (depressurization and purge)
takes place in the other column. Stages 2 and 4 (equalization)
occur after stages 1 and 3, respectively.
Three different equalization steps may be considered: (1)
bottom-to-bottom equalization (BE)sthe equalization stream
exits from the bottom of one of the columns and enters at the
bottom of the other; (2) crossed equalization (CE)sthe equalization stream exits from the top of one of the columns and
enters at the bottom of the other; (3) top-to-top equalization
(TE)sthe equalization stream exits from the top of one of the
columns and enters at the top of the other. Figure 1 illustrates
these small pressure swing adsorption units with different
equalization steps. Table 1 presents, for the units shown in
Figure 1, the valve positions for each of the operation stages.
Because of the units’ configuration, in the equalization step
there is always gas passing through the purge orifice from one
column to the other. Therefore, in the units with a bottom-tobottom equalization and those with a crossed equalization, the
tops of the columns are always connected and so, in addition
to these equalizations, a sort of top-to-top equalization will also
occur. The ratio between the purge-orifice coefficient and the
equalization-orifice coefficient will determine which of these
equalizations will have the most influence.
Another particularity is that, because of the use of check
valves before the storage tank (ST in Figure 1), whenever the
pressure inside the storage tank is lower than the pressure inside
one of the columns, there will be gas entering the tank, coming
from one of the columns, regardless of the stage the unit is at.
The pressure history inside the columns, during the unit’s
operation, is presented in Figure 2.
By following, in Figure 2, the pressure history inside column
1 (C1 in Figure 1), at the beginning of stage 1, one can see that
this column is being pressurized while column 2 is depressurizing. When point B is reached, column 1 starts producing. This
happens because of the presence of a check valve before the
storage tank: while the pressure inside the columns is lower
than that inside the tank, the valves are “closed”. Before point
A is reached, the gas goes from column 2 to column 1, which
can be seen as a complement to the equalization step. Afterward,
column 2 is purged with the gas coming from column 1.
In stage 2, the equalization step will take place. One may
notice the different slopes of the equalization, pressurization,
and depressurization. This is due to different equalization,
pressurization, and vent orifices coefficients.
Mathematical Model
Some assumptions were made in order to derive the governing
equations of the theoretical model. These include perfect gas
behavior, axially dispersed plug-flow, uniform cross-sectional
void fraction, uniform adsorbent properties throughout the bed,
negligible radial gradients, instantaneous temperature equilibrium between gas, adsorbent, and column wall, ideal distribution
of the gas entering the adsorption column, and negligible
pressure drop. Cruz et al.7 showed that isothermal operation is
a reasonable hypothesis for oxygen separation from air, so this
was also considered here.
Considering the theoretical model, the following dimensionless equations can be written as follows.
Interparticle Total Mass Balance.
∂P*
) -P*
∂θ
∂u*
nc
- T*
∂x
N/i
∑
i)1
(1)
Interparticle Partial Mass Balance.
∂yi
∂θ
) -u*
∂yi
∂x
+
2
1 ∂ yi
Pe ∂x
+
2
nc
T*
N/j - N/i ),
∑
j)1
P*
(yi
i ) 1, nc
(2)
where P* is the dimensionless total pressure, P* ) P/Pref, and
P is the column pressure; the subscript “ref” denotes the
reference state; θ is the dimensionless time variable, θ ) t/θref,
where t is the time variable and θref is the bed time constant
defined as θref ) L/uref, where uref is the reference interstitial
velocity; u* is the dimensionless interstitial velocity, u* ) u/uref;
x is the dimensionless spatial coordinate, x ) z/L, where z is
the spatial coordinate and L is the adsorption column length;
T* is the dimensionless temperature, T* ) T/Tref, where T is
the operating temperature; N/i is the ith component dimensionless molar flow rate, N/i ) Niθref/(crefb), where Ni is the molar
flow rate; cref is the reference fluid-phase concentration, cref )
Pref/RTref, where R is the universal gas constant; b is the bed
void fraction; yi is the molar fraction in the gas phase; Pe is the
Peclet number for mass transfer, Pe ) urefL/Dax, where Dax is
the effective axial dispersion coefficient; and nc is the number
of components in the mixture.
The dimensionless adsorbent molar flow rate, N/i , can be
written as follows,8
N/i ) ζa
∂qj/i
∂cj/i
+ ζp
∂θ
∂θ
(3)
where ζa is the adsorbed-phase capacity factor, ζa ) Fs[(1 b)/b][qref/cref], where Fs is the adsorbent apparent density; qj/i
is the ith component dimensionless average concentration in
the adsorbed phase, qj/i ) qi/qref; q/i is the ith component
dimensionless concentration in the adsorbed phase, q/i )
qi/qref; qref is the reference component concentration in the
adsorbed phase at reference conditions, qref ) q(Pref,Tref); and
ζp is the fluid-phase capacity factor, ζp ) p(1 - b)/b, where
p is the particle void fraction and cj/i is the ith component
dimensionless average concentration in the intraparticle fluid
phase, cj/i ) cji/cref, cj/i is the ith component dimensionless
concentration in the fluid phase, c/i ) ci/cref, and cref is the
reference component concentration in the interparticle fluid
Ind. Eng. Chem. Res., Vol. 45, No. 3, 2006 1087
Figure 1. Sketch of PSA units with three different equalization steps: (a) crossed, (b) top-to-top, and (c) bottom-to-bottom.
phase at reference conditions, cref ) Pref/(RTref). Instantaneous
equilibrium was considered between the inter- and intraparticle
gas phases: ∂cj/i /∂θ ) ∂c/i /∂θ.9
For the intraparticle mass transfer, the linear driving force
(LDF) model10 was used. This simple model corresponds to a
first-order delay in mass transfer and can be deduced considering
a parabolic profile inside the particle.11 This assumption is only
valid for long cycles.12 The use of such a simple model is
justified when modeling this type of system: for equilibriumdominated separations, the use of more-complex models usually
leads to only inconsequential differences in the results and would
augment the computational time.13 The linear driving force
1088
Ind. Eng. Chem. Res., Vol. 45, No. 3, 2006
valve
stage 1
stage 2
stage 3
stage 4
VF
VE
V1
V2
on
off
1f2
1f3
off
on
1f2
1f2
on
off
1f3
1f2
off
on
1f2
1f2
1.179
f(P/u,P/d,T*,M)
(4)
where RDi is the ratio between the LDF kinetic coefficients, k,
of the ith and reference components, RDi ) ki/kref, and Rbp is the
ratio between the bed time constant, θref, and the particle
diffusion time constant, 1/kref, Rbp ) krefθref.
Adsorption Column Mass Balance. A mass balance of
the adsorption column will allow one to obtain its pressure
history,14
u/inP*
)
u/outP*
+
∂P*
+ T*
∂θ
∫0 ∑N/i dx
i)1
LT ∂PT*
L ∂θ
x ) 0:
u/in
x ) 1:
{
CFv H /
) / f(P *,P1,T*,M)
P1
T*
CPv / /
uT*
in P
f(P
,P
,T*,M)
+
, P/1 g P/2
1
2
P/1
bP/1
CPv
u* ) - / f(P/2,P/1,T*,M)
, P/1 < P/2
P1
u* )
Column 2
x ) 0:
T
T
yi,out
∂yi,out
∂PT*
L T T*
T
) T(yi,in
, i ) 1, nc
uin - yi,out
uT*
)
out
T*
∂θ
∂θ
L
P
(7)
u*P* )
Cvf(P/u,P/d,T*,M)
(8)
where P/u and P/d are the dimensionless upstream and downstream pressures, respectively, T* is the dimensionless temperature, M is the molecular weight of the gas passing through the
nc
orifice and it was considered to be given by M ) ∑i)1
yiMi,
and Cv is the dimensionless orifice coefficient, given by
Tref
P0
K
Cv ) (2.035 × 10-2)
0 v
bAuref xPrefT
(9)
where Kv is the orifice coefficient and the superscript “0”
stands for standard temperature and pressure conditions (STP).
(10)
1 ∂yi
) u/in(yi - yi,in)
Pe ∂x
u* ) -
where yTi is the ith component molar fraction of the gas
entering or exiting the tank.
Pressure Drop Model In Orifices. The molar velocity across
a valve or a calibrated orifice was considered to be given by14,15
P/d e 0.53P/u
T*
∂yi
, P/1 g P/2
)0
∂x
1 ∂yi
/
/
) u*(yi - yi|x)1,column2) , P1 < P2
Pe ∂x
{
(6)
T*
where the superscript “T” stands for storage tank, uT*
in and uout
are the dimensionless velocities of the gas entering or exiting
the tank, respectively, and LT is the storage tank length. This
equation is obtained assuming that the adsorption column and
the tank have the same diameter, which is rather usual in
commercial units.
Storage Tank Partial Mass Balance.
1
P/dM
Column 1
(5)
where u*in and u*out are the dimensionless interstitial velocities
of the gas entering and exiting the column, respectively.
Storage Tank Total Mass Balance. The storage tank total
mass balance equation may be written in dimensionless form
as follows,
T*
T* T*
uT*
in P ) uoutP +
x
x
/2
P/2
/
/
u - Pd
T* Pd > 0.53Pu
/
PdM
Boundary Conditions. The boundary conditions, considering
that column 1 is pressurizing/producing and column 2 is
depressurizing/purging, are as follows:
nc
1
)
P/u
model in the dimensionless form is given by
∂qj/i
/
) Rbp RDi (qs,i
- qj/i )
∂θ
{
Function f is expressed as follows:
Table 1. Valve Positions for Each Operation Stage
x ) 1:
{
∂yi
)0
∂x
CVv / L
f(P2,P *,T*,M)
P/2
∂yi
, P/2 g P/1
)0
∂x
1 ∂yi
/
/
) u*(yi - yi|x)1,column1) , P2 < P1
Pe ∂x
{
u* ) u* )
CPv / /
f(P1,P2,T*,M)
P/2
, P/1 g P/2
T*
CPv / /
uT*
in P
f(P
,P
,T*,M)
+
, P/1 < P/2
2 1
/
/
P2
bP 2
PH* and PL* are the dimensionless high and low pressures,
respectively, and yi,in is the molar fraction of the gas entering
the column, in this case, air.
Every time the pressure inside the storage tank is higher
T* T
than inside the columns, uT*
in ) 0. Otherwise, uin P * )
T
T
Cv f(P*,P *,T*,M).
Afterward, in the equalization step, there will be gas coming
from column 1 to column 2. In this step, the boundary conditions
Ind. Eng. Chem. Res., Vol. 45, No. 3, 2006 1089
for each equalization type are as follows:
Column 1
x ) 0, x ) 1:
dy
)0
dx
Top-to-top equalization (TE) or crossed equalization (CE)
x ) 0: u* ) 0
x ) 1: u* )
T
CEv / /
uT*
CPv / /
in P *
f(P
,P
,T*,M)
+
f(P
,P
,T*,M)
+
1 2
1 2
P/1
P/1
bP/1
Bottom-to-bottom equalization (BE)
x ) 0: u* ) -
CEv / /
f(P1,P2,T*,M)
P/1
Figure 2. Pressure history inside the adsorption columns and the storage
tank.
T*
CPv / /
uT*
in P
x ) 1: u* ) / f(P1,P2,T*,M) +
P1
bP/1
Initial Conditions. It was considered that, in the beginning,
the columns and the storage tank are filled with air at
atmospheric pressure, which corresponds to the low pressure,
PL. Thus, P* ) PL* and yi ) yTi ) yi,in, ∀x.
Column 2
Top-to-top equalization (TE)
Numerical Solution
dy
x ) 0:
)0
dx
u* ) 0
x ) 1:
u* ) -
1 ∂yi
) u*(yi - yi|x)1,column1)
Pe ∂x
CEv / /
CPv / /
f(P
,P
,T*,M)
f(P1,P2,T*,M)
1 2
P/2
P/2
Crossed equalization (CE) or bottom-to-bottom
equalization (BE)
x ) 0:
1 ∂yi
) u*(yi - yi|x)0,column1)
Pe ∂x
u* )
x ) 1:
CEv / /
f(P1,P2,T*,M)
P/2
Simulation and Optimization Data
1 ∂yi
) u*(yi - yi|x)1,column1)
Pe ∂x
CPv / /
u* ) - / f(P1,P2,T*,M)
P2
For medical oxygen pressure swing adsorption units, it is
important that the unit never stops producing and keeps a stable
product flow rate, Q0prod. For this reason, the dimensionless
T*
storage tank output molar velocity, uT*
outP , is assumed to be
constant and equal to
T*
uT*
outP )
Q0prod T P0
Auref T0 Pref
The coupled system of 2(nc - 1) partial differential equations
and 2(nc + 1) + nc ordinary differential equations resultant from
two adsorption columns was solved using a numerical technique
which combines the use of high-resolution schemes (such as
SMART16) with an adaptive mesh technique inspired by wavelet
theory. This method is based on an adaptive multiresolution
approach which ensures numerical stability, accuracy, and small
computational times.17
Cyclic Steady-State Convergence. The cyclic steady state
is reached when, after a certain time, the process starts exhibiting
periodically identical dependent-variable values and these
recurrences occur in a constant cycle time. In this work, the
cyclic steady state was considered to be reached when the purity
and recovery did not change, in two consecutive cycles, more
than 0.01% (absolute). Nevertheless, it was verified that, using
a larger number of cycles, no change was observed in the
simulation results.
(11)
where A is the column cross-sectional area and the superscript
“0” stands for standard temperature and pressure conditions
(STP).
To perform the simulation work, it was necessary to specify
the model parameters and the characteristics of the three
adsorbents studied: Oxysiv 5, a 13X (NaX)-type zeolite14
commercialized by UOP; Oxysiv 7, a LiX-type zeolite18 from
the same company; and Sylobead MS S 624, a binderless 5Atype zeolite from Grace Davison.
The theoretical work, W, (J/m3STP) done by a single-stage
compressor is given by19
W)
( ) [( )
γ
T PH
P0 0
γ - 1 T Patm
((γ-1)/γ)
-1
]
(12)
where γ is the ratio between the specific heat capacity at constant
pressure and the specific heat capacity at constant volume (for
air, γ ) 1.4) and the superscript “0” stands for standard
temperature and pressure conditions (STP).
The power consumption per product unit flow rate, Ψ,
expressed as MJ/m3, is given by
1090
Ψ)
Ind. Eng. Chem. Res., Vol. 45, No. 3, 2006
∫0θ
1/2 cycle
{
[( )
]}
γ
P H*
P*Prefbu/in / γ-1/γ - 1
10-1
γ-1
Patm
Table 2. Reference Variables Used in the Simulations
dθ
(13)
where θ1/2 cycle is the dimensionless half cycle time (θ1/2 cycle
) θpress/prod + θequalization).
Since the bed length is 100 times larger than the adsorbent
diameter and the bed diameter is 30 times larger than the
adsorbent diameter, it is reasonable to consider the wall effects
to be negligible.20 Thus, assuming a packaging of small identical
spherical particles, one can use the value of b ) 0.36 for the
bed void fraction.
This methodology has the advantage of being independent
of the product flow rates, and in this way, the velocity does not
need to be previously known. This implies that the correlations
to predict the Peclet number cannot be used, as they are a
function of the velocity. However, for small-scale units, the
values for Peclet number vary from 500 to 1000. No noticeable
changes on the process performance are verified for Peclet
numbers >600;13 therefore, this value was used.
In small medical oxygen pressure swing adsorption units, a
special certificate is required for using pressures >0.3 MPa, so
this was the high pressure, PH, value used in the simulations.
The low pressure was considered to be the atmospheric pressure
(0.1 MPa).
The particle diameter and void fraction, the average pore
diameter, the particle diameter, the pure-component adsorption
parameters of oxygen, nitrogen, and argon, and the LDF kinetic
coefficients, for the three adsorbents, were presented in a
previous work.21 For Oxysiv 5 and MS S 624, the multicomponent adsorption was predicted by the multicomponent
Langmuir-Freundlich equation:22
nc
bjyjP)1/n- 1
∑
j)1
biyiP(
qi ) Qmax
nc
1+(
(14)
bjyjP)1/n
∑
j)1
For Oxysiv 7, the multicomponent adsorption was predicted
by the ideal adsorption solution theory (IAST), because the
maximum capacities, Qmax, and the Langmuir-Freundlich
equation parameter n are not the same for the three pure
components. The use of this equation would reveal a thermodynamic inconsistency.22
As referred before, the feed of the unit was air, which has
the approximate composition of 78% nitrogen, 21% oxygen,
and 1% argon. However, for simulation purposes, the feed was
considered to be a pseudobinary mixture of 78% nitrogen and
22% oxygen because of the similitude of the oxygen and argon
adsorption isotherms.
The reference variables adopted in the simulations are defined
in Table 2.
Optimization Variables
The unit’s performance is influenced by the following
variables:
• θpress/prod ) dimensionless pressurization/production time;
• θequalization ) dimensionless equalization time;
• L/LT ) ratio between the adsorption column and storage
tank lengths;
•CFv ) feed orifice parameter;
reference pressure: Pref (Pa)
reference temperature: Tref (K)
reference fluid velocity: uref (m/s)
reference component
PH
293.15
uprod
nitrogen
•CTv ) storage tank orifice parameter;
•CPv ) purge orifice parameter;
•CEv ) equalization orifice parameter; and
•CVv ) vent orifice parameter.
The dimensionless pressurization/production time, θpress/prod,
represents the duration of stages 1 and 3, when pressurization
and production take place for both columns. Along with the
feed orifice parameter, CFv , the storage tank orifice parameter,
CTv , the vent orifice parameter, CVv , the purge orifice parameter,
CPv , and the ratio between the storage tank and column lengths,
L/LT, this variable will highly influence the unit’s performance,
because it will determine the amount of the bed’s adsorption
capacity effectively used. These last variables affect the pressurechanging rate, influencing, in this way, the product purity and
recovery.23 Considering Figure 2, CFv will alter the pressurization rate and CVv will alter the depressurization rate. Point A
will be reached sooner or later, as these parameters are,
respectively, higher or lower. After this point is reached, column
2 will start being purged. Production will start after point B is
reached. The values of CFv and L/LT determine when and at
which pressure this will happen (higher L/LT values will result
in a slower decrease of the pressure inside the storage tank).
The storage tank and purge orifice parameters will influence
the amount of gas that exits the adsorption bed.
The dimensionless equalization time, θequalization, represents
the duration of the equalization step (stages 2 and 4). Along
with the equalization orifice parameter, CEv , this variable will
influence the equalization step and, in this way, the unit’s
performance. The higher the pressure level attained in the
equalization step, the lower will be the amount of feed gas
needed to achieve the intended operating pressure. Therefore,
the higher will be the recovery. However, if the equalization
time is too long, or if the equalization orifice parameter is too
high, the product purity, as well as the recovery, will decrease.
Optimization Results
For small pressure swing adsorption units, the investment
costs are much higher than the operating costs; therefore, the
optimization may be directed toward the maximization of
recovery, Rec.21 This approach has the advantage of being
independent of the adsorbent, columns, valves, storage tank,
and energy prices.
The optimization was carried out using a successive quadraticprogramming algorithm (SQP)24 developed in a previous work.7
The following restriction was imposed to the product purity
(purity of oxygen plus argon): Pur ) 0.99, ∼94.5% in oxygen.
The optimization results for the three adsorbents considered
are presented in Figures 3-8 as a function of Rbp (Rbp ) krefL/
uref). In view of the fact that the adsorption kinetic coefficients,
kref, do not differ significantly among the adsorbents, Rbp
basically relates the unit size and the product flow rate.
Figure 3 presents the maximum product recovery for each
cycle and adsorbent studied. As referred before, in the next
figures, BE, CE, and TE denote, respectively, bottom-to-bottom,
cross, and top-to-top equalizations, and NE denotes no equalization.
Ind. Eng. Chem. Res., Vol. 45, No. 3, 2006 1091
Figure 3. Maximum product recovery.
Figure 4. Power consumptions.
Oxysiv 7 yields higher recoveries for the imposed product
purity. This adsorbent also allows the use of lower Rbp values,
i.e., smaller units or higher product flow rates. However, it is
the most expensive, so economical judgment should be taken
into account when selecting the unit’s adsorbent.
Figure 3 shows that the unit recovery is always improved
when an equalization step is added to the original cycle. In
addition, it can be seen that top-to-top equalization presents
better results for all the absorbents studied. Bottom-to-bottom
and crossed equalizations display quite similar performances.
In addition, it must be noted that top-to-top and bottom-tobottom equalizations are more economical, since they need
fewer valves than crossed equalization (crossed equalization
needs five more valves than the others).
Besides the higher recovery and the lower unit cost, top-totop equalization also has another advantage: in bottom-tobottom equalization as well as in crossed equalization steps,
the gas enters the column that is being pressurized from the
bottom. This flux can drag the contaminants eventually accumulated at the bottom of the adsorption column. This effect
is certainly avoided by using top-to-top equalization. The use
of this type of equalization will result in a delay of the adsorbent
contamination and, consequently, in an extension of the equip-
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Ind. Eng. Chem. Res., Vol. 45, No. 3, 2006
Table 3. Optimum Feed, Equalization, Storage Tank, and Vent
Orifices Parameters
Oxysiv 5
Oxysiv 7
MS S 624
CFv
CEv
CTv
CVv
NE
TE
CE
BE
199
205
238
238
28.46
0.63
1.26
73.4
47.9
58.0
55.0
228
424
423
423
NE
TE
CE
BE
220
360
232
232
15.57
3.68
3.83
62.0
4.76
5.28
4.05
307
440
316
316
NE
TE
CE
BE
155
257
216
201
18.15
3.53
3.50
70.0
43.7
1.70
1.70
282
466
423
361
ment lifetime. Therefore, top-to-top equalization appears to be
the best choice for oxygen separation from air.
A decrease on the product recovery is noticeable for small
Rbp values. This strong variation is verified in almost all the
variables optimized, which shows that this region is unstable,
and little variations in the operating conditions result in
significant variations in the unit performance. For this reason,
it is advisable to avoid this region.
The unit’s power consumptions for the different adsorbents
and cycles studied are presented in Figure 4.
It can be seen that the introduction of an equalization step
reduces the unit’s power consumption, and once again, top-totop equalization gives the best results.
Figures 5-8 present, respectively, the optimum values for
the unit’s ratio between the column and storage tank lengths,
the pressurization/production time, the equalization time, and
the purge orifice parameter. The optimum feed, equalization,
storage tank, and vent orifices parameters were shown to be
independent of the unit size and product flow rate, and their
values are presented in Table 3.
Cycles without equalization require larger storage tanks
(Figure 5). This feature causes the unit to take longer to reach
the steady state, which is undesirable in oxygen concentrators.
Figure 5. Optimum ratio between the column and storage tank lengths.
It is very important that the unit starts producing oxygen with
purity >82% in a short time. Even in cycles with equalization
steps, for small Rbp values, the ratio between the column and
the storage tank lengths starts to decrease strongly, so this zone
should be avoided.
As can be seen in Figure 6, when an equalization step is used,
the pressurization/production times do not differ significantly
among adsorbents. However, units without equalization require
longer pressurization/production times.
Top-to-top equalization needs a shorter equalization time, but
it has a higher CEv (Table 3), which implies a higher gas flow
rate during equalization or, in other terms, the energy stored
inside the column in the form of pressure is more efficiently
used. Top-to-top is also the equalization type that allows the
lower CPv , which means that less product is wasted for the
purge. In Table 3, it can be seen that, except for Oxysiv 5, the
values of CFv and CVv in top-to-top equalization are high, which
means that this type of equalization needs a low-pressure drop
in the feed and vent.
Comparison between Simulation and Experimental
Results
A small medical oxygen pressure swing adsorption unit from
Weinmann (Oxymat 3) was tested for different production flow
rates. The experimental results obtained were compared with
the simulation ones.
The unit operates between 0.1 and 0.3 MPa with a bottomto-bottom equalization step, and the adsorption columns were
first packed with Oxysiv 5 from UOP. The unit characteristics
are presented in Table 4.
The purge valve parameter, KPv , was measured experimentally. The storage tank, the vent, and the equalization valve
parameters, KTv , KVv , and KEv , respectively, could not be determined experimentally because of the configuration of the unit.
These were, therefore, estimated, for one product flow rate, by
fitting the simulated to the experimental pressure histories. It
was then verified that the simulation results obtained with these
Ind. Eng. Chem. Res., Vol. 45, No. 3, 2006 1093
Figure 6. Optimum pressurization/production time.
Figure 7. Optimum equalization time.
parameters also yielded very good agreement with the experimental data for the other flow rates.
With the intent of optimizing this unit, the feed flow rate
given by the unit’s compressor was experimentally determined,
to incorporate this information in the optimization procedure.
It was found to be given by the following correlation:
u/inP* )
10-3P0T
[0.0731(P*Pref)3 +
0
60 AT uref‚Pref
(-0.288)(P*Pref)2 - 6.517P*Pref + 91.370] (15)
For using eq 15, the production flow rate must be known and
it must be kept in mind that the high pressure is not limited.
The pressure drop along the bed was measured and verified to
be negligible, validating the assumption made in the formulation
of the model.
Experimental and simulation curves of purity and recovery
as a function of the production flow rate are presented in Figure
9 and are in good agreement.
The simulated pressure histories, inside the columns, for each
operating condition tested were also in agreement with the
experimental results, as can be seen in Figure 10.
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Ind. Eng. Chem. Res., Vol. 45, No. 3, 2006
Figure 8. Optimum purge orifice parameter.
Table 4. Physical Characteristics and Operating Conditions of the
Unit Tested
L
(cm)
D
(cm)
LT
(cm)
tpress/prod
(s)
tequalization
(s)
KPv
KTv
KVv
KEv
29.5
8.0
12.5
7.0
1.0
0.0394
0.15
0.55
0.90
To better evaluate the performance of the simulator, Oxysiv
5 was replaced with MS S 624, and some experimental runs
were carried out at different product flow rates and with the
same operating conditions used with Oxysiv 5 (Table 4). The
experimental and simulation results using MS S 624 are
presented in Figure 11. The pressure histories obtained from
the simulations were also in agreement with the experimental
results, for each operating condition tested with this adsorbent.
A batch of fresh adsorbent was used for all these experiments.
Since untreated air was being fed to the columns, to check for
possible water or CO2 contamination effects, at the end of the
experiments the first run (see Figures 9 and 11) was repeated.
Since both runs agreed, it was concluded that there was no
Figure 9. Comparison between simulated and experimental purity and
recovery achieved on the unit studied using Oxysiv 5 (] experimental purity,
s simulation purity, + simulated optimum purity, O experimental optimum
purity, 4 experimental recovery, - - - simulation recovery, × simulated
optimum recovery, and 0 experimental optimum recovery).
Figure 10. Comparison between simulated and experimental pressure
history, inside the columns, achieved on the unit studied for a production
flow rate of 2 LSTP/min, using Oxysiv 5 (s simulation and 0 experimental).
contamination. Figures 9-11 confirm that the developed
simulator is able to very accurately represent the performance
of a real unit.
The optimization procedure described above was used for
optimizing the commercial PSA unit, with Oxysiv 5, with a
top-to-top equalization. A flow rate of 4.3 LSTP/min (Rbp )
244.15) was chosen, because it is the maximum flow rate that
allows the production of the pseudocomponent (oxygen plus
argon) with a purity of 0.99.
Comparing the unit’s physical characteristics with the optimization results presented before, it is possible to conclude that
the storage tank and vent orifices parameters are in agreement
with these results, because their values are already high, which
means a low-pressure drop in the orifices. Simulations with L/LT
in the range from 1 to 5 with high Rbp revealed no significant
difference in the unit’s performance. For this reason, this
variable may be excluded from the optimization variables.
These units have a legislated limit for the maximum operation
pressure. Above this limit, a special certificate is required. For
this reason, it is important to ensure that this limit is not
Ind. Eng. Chem. Res., Vol. 45, No. 3, 2006 1095
The simulator was able to faithfully represent a real commercial unit. Using the optimization strategy, it was possible
to attain new operating conditions and design characteristics
that improved the unit’s performance. The developed tools
should make easier the design and optimization of oxygen
concentrators and expedite the selection of adsorbents and
operation configurations.
Acknowledgment
Figure 11. Comparison between simulated and experimental purity and
recovery achieved on the unit studied using MS S 624 (] experimental
purity, s simulation purity, 4 experimental recovery, and - - - simulation
recovery).
exceeded. The θpress/prod value directly influences the operating
pressure, because further increasing it will imply a higher
pressure ratio (PH/PL) as the compressor continues to pressurize
the column, up to its maximum operation pressure. Although
this should correspond to higher purity and recovery,23 for the
reason pointed before, this is not desirable. The pressurization/
production time value was found to be at its optimum value,
and the only optimization parameters left are θequalization, CEv ,
and CPv .
For these operating conditions and for the purity constraint,
the maximum recovery obtained was 34.1%, with tequalization )
1 s, KEv ) 0.6700, and KPv ) 0.0162. However, because of the
existence of small outlet holes in the top of the column, the
maximum equalization orifice parameter possible for this unit
was found to be KEv ) 0.1100, quite below the optimum value.
Since the optimization results pointed to a high equalization
orifice parameter, a new optimization was performed with a
KEv set to 0.1100. The new maximum recovery, presented in
Figure 9, was 31.9%, achieved with the optimum values of
tequalization ) 1 s and KPv ) 0.0392.
From the optimization results, it is possible to conclude that
the performance of the commercial unit can be improved with
the use of a top-to-top equalization. Further improvements could
be achieved if larger outlet holes were used in the top of the
columns.
Conclusions
A simulator and an optimization procedure were developed
for small oxygen pressure swing adsorption units with different
equalization configurations. A design procedure was proposed,
making it easier to size these units and to choose the right
adsorbent and equalization types to use.
Oxysiv 7 was revealed to allow the best performance,
followed by MS S 624 and Oxysiv 5. Oxysiv 7 is the adsorbent
that allows the use of smaller units or higher product flow rates,
considering that the adsorption kinetics do not differ significantly
among the adsorbents.
Top-to-top equalization was shown to be the best configuration, because it allows higher recoveries, allows lower power
consumption, requires a low number of valves, and avoids
dragging the contaminants from the bottom of the adsorption
column into the rest of the adsorbent bed. Bottom-to-bottom
equalization and crossed equalization were shown to give small
differences between themselves. Nevertheless, the use of any
of these three types of equalization will result in a significant
increase of the unit’s performance.
The work of J.C.S. was supported by FCT: Grant SFRH/
BD/6817/2001. The work of A.F.P. was supported by project
Growth GRD1-2001-40257. This research was also supported
by funds from FCT project POCTI/EQU/38067/2001. The
authors would like to thank the company Weinmann GbmH as
well as Dr. Ulrich Palm for their support and for offering the
oxygen concentrator. The authors would like to acknowledge
Dr. Roger D. Whitley from Air Products and Chemicals for
reviewing this manuscript.
Nomenclature
c ) concentration in the fluid phase, mol/kg
cref ) reference fluid-phase concentration, cref ) Pref/RTref
Cv ) orifice parameter
Dax ) effective axial dispersion coefficient, m2/s
F ) volume flow rate, m3/s
k ) LDF kinetic coefficient, s-1
L ) column length, m
LT ) storage tank length, m
N ) molar flow rate, mol/(kg‚s)
N* ) dimensionless molar flow rate, N* ) Nθref/(Crefb)
nc ) number of components in the mixture
qj ) average concentration in the adsorbed phase, mol/kg
q ) concentration in the adsorbed phase, mol/kg
P ) total pressure, Pa
Pe ) Peclet number for mass transfer, Pe ) urefL/Dax
R ) universal gas constant, (Pa‚m3)/(mol‚K)
Rbp ) ratio between the bed time constant and the particle
diffusion time constant, Rbp ) krefθref
t ) time variable, s
T ) temperature, K
u ) interstitial molar velocity, m/s
u* ) dimensionless interstitial velocity, u* ) u/uref
uT* ) dimensionless velocity of the gas entering or leaving the
storage tank
V ) molar velocity, m/s
V ) volume, m3
x ) dimensionless spatial coordinate, x ) z/L
y ) molar fraction in the gas phase
z ) spatial coordinate, m
Greek Symbols
RDi ) ratio between the diffusivity coefficients, RDi ) ki/kref
b) bed void fraction
p ) particle void fraction
γ ) ratio between the specific heat capacity at constant pressure
and the specific heat capacity at constant volume
Fs ) adsorbent apparent density, kg/m3
θ ) dimensionless time variable, θ ) t/θref
θref ) bed time constant, θref ) L/uref
ζa ) adsorbed-phase capacity factor, ζa ) Fs[(1 - b)/b][qref/
cref]
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Ind. Eng. Chem. Res., Vol. 45, No. 3, 2006
ζp ) fluid-phase capacity factor, ζp ) p(1 - b)/b
Ψ ) power consumption per product unit flow rate, MJ/m3
Subscripts
i ) ith component
ref ) reference
T ) total
Superscripts
* ) dimensionless
d ) downstream
E ) equalization
F ) feed
H ) high
L ) low
P ) purge
T ) storage tank
u ) upstream
V ) vent
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ReceiVed for reView April 22, 2005
ReVised manuscript receiVed November 9, 2005
Accepted November 30, 2005
IE0504809