Effects of Nonisobaric and Isobaric Steps on O2 Pressure Swing

equation related to the loading ratio correlation isotherm model. The LDF coefficients ... The pressure swing adsorption (PSA) process plays an import...
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Ind. Eng. Chem. Res. 2002, 41, 4383-4392

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Effects of Nonisobaric and Isobaric Steps on O2 Pressure Swing Adsorption for an Aerator† Jeong-Geun Jee, Hae-Jun Park, Seung-Joo Haam, and Chang-Ha Lee* Department of Chemical Engineering, Yonsei University, Shinchon-dong, Seodaemun-gu, Seoul 120-749, Korea

The effects of nonisobaric and isobaric steps on a two-bed O2 pressure swing adsorption (PSA) packed with zeolite 5A were investigated. In addition, the operating conditions in the O2 PSA were studied to supply the various O2 concentrations to the oxygen aerator efficiently. Because the velocity variation along the bed and the related Mass Transfer Zone (MTZ) shape at the isobaric and nonisobaric steps were affected by the diffusion rate, the concentration-dependent rate parameter in a modified linear driving force (LDF) model was evaluated from the Darken equation related to the loading ratio correlation isotherm model. The LDF coefficients had a significant effect on the prediction of the O2 purity and recovery at the low flow rate region. However, the higher the feed flow rate, the lower the LDF parameter effect. It was also noted that the effects of each step time in the isobaric and nonisobaric steps on the PSA performance were subtle in the O2 purity and recovery except for the blowdown step. Also, there was the optimum step time to maximize the O2 purity and recovery in the adsorption and pressurization steps, while the increase of O2 purity and recovery with the pressurization equalization step time showed asymptotic curvature. The idle time at the pressurization step had a negative effect on the PSA performance, while the short idle time at the pressure equalization step led to improved product purity. However, it was negligible for the effect of the idle time at the blowdown step on the PSA performance. The successive variation between high and low P/F ratios caused the continuous variation of O2 purity and recovery to nearly the same extent as the results under each constant P/F ratio condition. Therefore, to save the operating cost of the oxygen aerator system, the desired oxygen concentration for the aerator can be supplied simply by controlling the feed rate or purge rate. Introduction The pressure swing adsorption (PSA) process plays an important role in the commercial application of the adsorptive generation of oxygen from air.1 Through a new development in terms of improving the process and the quality of the zeolite, it brings an economically beneficial increase in the capacity of oxygen PSA plants and a higher market share of oxygen from PSA units.2 In addition, the field of application for oxygen generated in PSA plants has widened considerably.3 As a result, numerous modified adsorption cycles were developed and have been vigorously studied until recently. In particular, it was reported that the Vacuum Swing Adsorption (VSA) process produced oxygen with both high purity and high productivity.4,5 However, the O2 PSA still has an advantage in specific systems such as the oxygen aerator system to treat wastewater because of the water pressure drop. Moreover, the oxygen cost in the oxygen aerator system to treat wastewater is one of the most important factors. Because of the limitation of oxygen saturation in the water, it needs to supply the proper O2 concentration from the PSA to the aerator to save the oxygen cost. The efficiency of the PSA cycle can be optimized through an understanding of the adsorption and desorption dynamics related to pertinently adopted step and step times.6 Furthermore, another way of improving †

This paper was presented at the AIChE meeting in 2001. * To whom correspondence should be addressed. Tel.: +822-2123-2762. Fax: +82-2-312-6401. E-mail: [email protected].

the utilization of the system is to modify the operating variables of the process, such as the pressure ratio, the purge-to-feed ratio, the cycle time, the particle and column diameters, and so on.7 It was reported that the effects of adsorption pressure and feed flow rate on the O2 purity and recovery were systemically changed by the variation of the P/F ratio at a small-scale medical oxygen PSA unit.8 Moreover, the reduced cycle time and small-size adsorbents caused high purity as well as high productivity. Farooq et al.9 introduced a variable diffusivity model to a zeolite-based kinetically controlled PSA separation process. They pointed out that the Darken equation with the binary Langmuir isotherms predicted the experimental data better than the constant diffusivity model. Mendes and co-workers10 reported that the higher pressurization rate decreases the product purity and recovery, whereas the pressure lowering rate during the blowdown step has almost no effect. Furthermore, they pointed out that the production pressure has a complex effect on the product purity and recovery. In this study, the effects of nonisobaric and isobaric steps on the adsorption dynamics were investigated in the six-step two-bed O2 PSA packed with zeolite 5A. In the case of the nonisobaric steps, such as the pressurization and blowdown steps, the PSA performances under the same total cycle time conditions were compared by the variation of the flow rate during the step time. However, in the case of the pressure equalization step, the effects of total step time as well as the flow rate during this step on the PSA performance were

10.1021/ie020088k CCC: $22.00 © 2002 American Chemical Society Published on Web 07/19/2002

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investigated. Also, based on the PSA experiments, the operating condition to produce the various O2 concentrations from time to time was studied because the desired oxygen concentration in the aerator was changed by the wastewater concentration from the upstream process. The adsorption dynamics at each step and the experimental PSA results were predicted by the mathematical model incorporated with mass and energy balances. Moreover, the concentration-dependent rate parameter obtained from the Darken equation with the loading ratio correlation (LRC) model was applied to the linear driving force (LDF) model.

To understand the dynamic behaviors of the adsorption bed during the PSA running, the mathematical models were developed on the basis of the following assumptions: (i) the gas phase behaves as an ideal gas mixture, (ii) radial concentration and temperature gradients are negligible, (iii) thermal equilibrium between adsorbents and bulk flow is assumed, (iv) the flow pattern is described by the axially dispersed plug-flow model, (v) the mass-transfer rate is represented by a LDF model and a modified LDF model, (vi) constant heat of adsorption is assumed,11 (vii) the heat capacities are constant and the heat capacity of the adsorbed phase is negligible,12 and (viii) the pressure drop along the bed is negligible.13,14 The assumption of neglecting the radial gradient was widely accepted by numerous studies, and the others are also common assumptions in simulating the adsorption process.7,8,15 The component and overall mass balances for the bulk phase in the adsorption column are given by

∂2Ci ∂z

2

∂2 C

-DL

∂z2

+u

+u

∂Ci ∂Ci 1 -  ∂qi + + Fp )0 ∂z ∂t  ∂t

∂C ∂z

(

+

∂C ∂t

)

( )∑

+ Fp

1-

n

∂qi



i)1

∂t

)0

∂P

+P

∂t

∂u ∂z

[

+ PT -DL

+

∂z2 T

∂ 1

∂t T

FpRT

+u

( )]

∂ 1

( )∑ n

∂qi



i)1

∂t

+

) 0 (4)

Another characteristic of the adsorption process is the temperature variation caused by the heat of adsorption. In this system, the energy balance for the gas phase also includes the heat transfer to the column wall: 2

∂T ∂u ∂T +T + -KL 2 + FpCpg u ∂z ∂z ∂z

(

)

(tFgCpg + FBCps)

(5)

∂Tw ) 2πRBihi(T - Tw) ∂t 2πRBoho(Tw - Tatm) (6)

where Aw ) π(RBo2 - RBi2). If the system is near isothermal condition, eqs 5 and 6 can be neglected to save calculation time. The boundary and initial conditions of mass and energy balances are presented below. The well-known Danckwerts boundary conditions are applied.16

Boundary conditions for feed pressurization and adsorption steps -DL -KL

( )| ∂yi ∂z

) u(yi|z)0- - yi|z)0+);

z)0

(∂T∂z )|

z)0

( )| ∂yi ∂z

z)L

)0 (7-1)

(∂T∂z )|

) FgCpgu(T|z)0- - T|z)0+);

z)L

)0 (7-2)

Boundary conditions for purge and pressurizing pressure equalization steps

∂z T

1-

(T - Tw) ) 0 RBi

(2)

)

() ()

∂2 1

2hi

where yi|z)0- means the feed composition for component i.

∂yi ∂yi RT 1 -  ∂qi + + Fp ) 0 (3) -DL 2 + u ∂z ∂t P  ∂t ∂z

(

+

(1)

When the ideal gas law (Ci ) Pyi/RT and C ) P/RT) is applied to eqs 1 and 2, the component and overall mass balances can be represented as follows:

∂2yi

∂qi

∑ i)1 ∂t

where t is the total void fraction [) + (1 - )R] and FB is the bed density [)(1 - )Fp]. To consider heat loss through a wall and heat accumulation in the wall, another energy balance for the wall of the adsorption bed was used

FwCpwAw

Mathematical Model

-DL

n

-FB(-∆Hi)

∂T ∂t

-DL -KL

( )| ∂yi ∂z

(∂T∂z )|

) u(yi|z)L+ - yi|z)L-);

z)L

z)L

( )| ∂yi ∂z

) FgCpgu(T|z)L+ - T|z)L-);

z)0

(∂T∂z )|

)0 (8-1)

z)0

)0 (8-2)

where yi|z)L+ means a volume-averaged composition of the effluent stream during the adsorption step for the purge step and a temporal effluent’s composition during a depressurizing pressure equalization step for the pressurizing pressure equalization step, respectively. The fluid velocity is inherently negative during these steps.16

Depressurizing pressure equalization and countercurrent depressurization steps

( )| ( )| ∂yi ∂z

)

z)0

∂T ∂z

z)0

) 0;

( )| ∂yi ∂z

z)L

)

( )| ∂T ∂z

z)L

) 0 (9)

Also, the boundary conditions for the interstitial velocity in each step are presented below.

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Boundary conditions for the interstitial velocity u|z)0 ) 0 (depressurizing and pressurizing pressure equalization steps) u|z)N ) 0 (pressurizing and blowdown steps) u|z)0 ) ufeed (adsorption step) u|z)N ) upurge (purge step)

(10)

In this study, the pressure history obtained during a PSA experiment at the product end was fitted by the following polynomials used as a boundary condition for the overall mass balance.

P ) at + bt2 + ct3 + dt4

(11)

The multicomponent adsorption equilibrium was predicted by the following LRC model:

qi )

qmiBiPini

(12)

n

1+

BjPj ∑ j)1

nj

where qmi ) k1 + k2T, Bi ) k3 exp(k4/T), and ni ) k5 + k6/T. The sorption rate into an adsorbent pellet is described by the LDF model with a single lumped mass-transfer parameter:17

KDei ∂qi ) ωi(q/i - qi), ωi ) 2 ∂t r

Table 1. Equilibrium/Rate Parameters and Heat of Adsorption of N2 and O2 for Zeolite 5A6,18,19 k1 × 103 (mol/g) k2 × 105 (mol/g‚K) k3 × 104 (1/atm) k4 (K) k5 k6 (K) heat of adsorption, -∆H h (cal/mol) LDF coefficient, ωi (s-1)

N2

O2

6.210 -1.270 1.986 1970 2.266 -396.5 5470 0.05

7.252 -1.820 54.19 662.6 -1.101 656.4 3160 0.15

Table 2. Characteristics of Adsorbents and the Adsorption Bed adsorbent type normal pellet size [mesh] average pellet size, Rp [cm] pellet density, Fp [g/cm3] heat capacity, Cps [cal/g‚K] particle porosity, R bed density, FB [g/cm3]

zeolite 5A sphere 4-8 0.157 1.16 0.32 0.65 0.795

Adsorption Bed length, L [cm] inside radius, RBi [cm] outside radius, RBo [cm] heat capacity of the column, Cpw [cal/g‚K] density of column, Fw [g/cm3] internal heat-transfer coefficient, hi [cal/cm2‚K‚s] external heat-transfer coefficient, ho [cal/ cm2‚K‚s] axial thermal conductivity, KL [cal/cm‚s‚K] axial dispersion coefficient, DL [cm2/s]

100 1.1 1.275 0.12 7.83 9.2 × 10-4 3.4 × 10-4 6.2 × 10-5 1.0 × 10-5

(13)

c

However, in this system that has a very slow flow pattern at the nonisobaric and isobaric steps, it is necessary to use a more accurate rate model. Therefore, the modified LDF model combining the Darken equation with the LRC model was presented as the adsorption rate model.

KDci Dci Dei ∂qi 1 ) ω′i(q/i - qi), ω′i ) 2 , ) 2 2 ∂t n (1 rc rc rc i - θi) (14) This model depicts the adsorption rate as a function of the sorbate concentration.9 The adsorption isotherm parameters and LDF coefficients of N2 and O2 on zeolite 5A are also shown in Table 1. The adsorbed amounts of N2 and O2 on the zeolite 5A in this study were similar values compared with the published equilibrium data.6,18,19 A process simulator uses only one bed to simulate this two-bed process. To describe bed connectivities during a pressure equalization step, temporal effluent arrays (flow, pressure, composition, and temperature) from a depressurizing pressure equalization step were retained and used later when the bed underwent a pressurizing pressure equalization step.20 In this study, a finite difference method was used to solve a mathematical model, which consisted of coupled partial differential equations. A three-point backward finite difference approximation was used for temporal differential terms in order to improve temporal accuracy and a secondorder central and backward difference for the secondand first-order space derivatives, respectively. Then, all

Figure 1. Schematic diagram of the apparatus for a two-bed O2 PSA process.

of the partial differential equations were converted into algebraic equations to form a tridiagonal matrix. The 100 nodes in this system were employed to discretize the spatial domain, whereas the time step was 0.02 s. Experimental Section A schematic diagram of the two-bed PSA unit is shown in Figure 1. The adsorption beds were made of stainless steel pipe with a length of 100 cm, an i.d. of 2.2 cm, and a wall thickness of 0.175 cm. The beds were packed with zeolite 5A. The characteristics of the adsorbent and adsorption beds are listed in Table 2. Three calibrated resistance temperature detectors (RTD, Pt 100 Ω) were installed at the positions of 10,

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Table 3. Operating Conditions for PSA Experiments run no. 1 2 3 4 5 6 7 8 9 10 11 12 13 14

studied variables

isobaric step

adsorption step

nonisobaric step

pressurization step pressure equalization step blowdown step P/F ratio

50, and 80 cm from the feed end and at the center of the radial position in order to measure the temperature variations inside the bed. The two pressure transducers were located at the feed and product ends in order to measure the bed pressure variation. The feed and purge flow rates were controlled by a mass flow controller (Hastings 202D-799). A surge tank of the same size as the adsorption bed was equipped to prevent flow fluctuation. The total amount of feed flow and the flow rate of each step were measured by a wet gas meter. To keep the pressure in the adsorption bed constant, an electric back-pressure regulator was installed between the adsorption bed and the product bed. The concentration variations of the influent and effluent were analyzed by a portable oxygen analyzer (Teledyne Analytical Instruments 320B/RC-D). The oxygen analyzer has its own error in the range of (0.25% at every run. Therefore, to reduce this error range within (0.1%, calibration by a mass spectrometer (Balzers QME 200) was conducted at every run. The system was fully automated by a personal computer with a developed control program, and all measurements including pressure, temperature, and O2 purity were saved on the personal computer through the AD converter. The binary mixture (N2/O2 ) 79/21 vol %) was used as a feed gas for the PSA experiments. The adsorbent was regenerated at 613 K overnight. The bed packed with the adsorbent was kept at a 1.5 atm pure O2 (99.9+%) condition to prevent contamination from the outside air. Prior to each experimental run, the adsorption bed was vacuumed up to 10-3 mmHg for 2 h. Before each experiment, the adsorption bed was pressurized at 6 atm using pure oxygen and was kept for 1 h. The temperatures of the feed, bed, and surroundings as the initial experimental temperature were kept in the range of 298-299 K. The PSA performances were studied in the range of cycle time of 160-220 s under an adsorption pressure of 6 atm and a feed flow rate of 2.2 L(STP)/ min. Therefore, the high and low pressure limits in this study were fixed as 6 atm for the adsorption step and ambient pressure for the blowdown step, respectively. Also, the P/F ratio was fixed as 0.5 except for the study of the variable P/F ratio condition. The more detailed operating conditions are shown in Table 3. In this study, the pressurization and blowdown step times consisted of real step time and idle time to study the PSA performance based on the same total cycle time. In Table 3, the word “real” means the period of time that the flow exists. The idle time implies the duration from the end of the real step time to the total step time without the flow.

step time [s] (PR-AD-DPE-BD-PU-PPE) 30-20-30-30-20-30 30-30-30-30-30-30 30-40-30-30-40-30 30-50-30-30-50-30 (20 + 10)-30-30-30-30-30 (25 + 5)-30-30-30-30-30 30-30-30-30-30-30 30-30-20-30-30-20 30-30-25-30-30-25 30-30-30-30-30-30 30-30-30-(7 + 23)-30-30 30-30-30-(11 + 19)-30-30 30-30-30-(15 + 15)-30-30 30-30-30-30-30-30

remark

(real PR time + idle time) nonidle time (real BD time + idle time) P/F ratio (0.5-0.32-0.5)

The six-step PSA process was employed to obtain high-purity oxygen from air. A six-step, two-bed PSA cycle was employed to obtain oxygen from a binary (N2/ O2 ) 79/21 vol %) mixture. The six-step process used is as follows: (I) cocurrent feed pressurization (PR) of a partially pressurized bed by a previous pressurizing pressure equalization step (PPE); (II) high-pressure adsorption (AD) step; (III) cocurrent depressurizing pressure equalization (DPE) step; (IV) countercurrent depressurization (DP) step; (V) countercurrent purge with a light product, O2 (PU) step; (VI) countercurrent PPE step. A cyclic sequence of a typical six-step, twobed PSA process can be found in the previous works.7,21 O2 purity was defined as the volume-average O2 mole fraction of the product in the adsorption step. O2 recovery was defined as follows:

O2 recovery (%) ) total O2 moles in the product × 100 total O2 moles in the feed Results and Discussion Effect of the Rate Model and Rate Parameters. Figure 2 shows the effect of the LDF parameters of N2 and O2 on the O2 purity and recovery in the cyclic PSA process at the low feed flow rate condition, 2.2 L(STP)/ min. As can be seen in Figure 2, an increase of the LDF coefficient of N2 caused the improvement of O2 purity, while that of O2 had relatively little effect on the O2 purity. However, the effect of the LDF parameters on the O2 recovery showed itself to be totally different from that on the O2 purity. The change in the LDF parameters of O2 and N2 led to a meaningful change in the O2 recovery, but the effect of the LDF parameter of O2 on the O2 recovery was more significant than that of N2. As shown in Figure 2, the higher diffusivity of N2 led to faster adsorption and desorption rates of N2 in the adsorption step. Because it eventually caused an increase in the adsorption amount of N2 as well as a decrease in that of O2 in this step, the purity became high. However, the recovery was slightly increased because the desorbed O2 amount in the purge step was larger than that in the blowdown step. Higher diffusivity of O2 led to higher recovery in Figure 2 because the purge gas with a high O2 mole fraction remained at the adsorbed phase in the purge step regardless of the increase of the desorbed O2 amount in the blowdown step. It was noticeable that the rate parameters had a great effect on the process performance. This implies that, under the slow flow rate condition in nonisobaric

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Figure 2. 3D plots of (a) O2 purity and (b) O2 recovery to the variation of LDF coefficients at 6 atm and 2.2 L(STP)/min.

Figure 4. Cyclic variation of experimental and predicted O2 concentration curves at 6 atm and 2.2 L(STP)/min.

Figure 3. Comparison of O2 concentration profiles along the bed at 6 atm and 2.2 L(STP)/min using (a) a LDF model and (b) a modified LDF model.

and isobaric steps, kinetic selectivity by mass-transfer resistance and equilibrium selectivity acted as key factors in determining the total selectivity between N2 and O2. However, the effect of the rate parameters on the simulated result of the O2 PSA performance was significantly weakened with an increase in the flow rate.11,12 Figure 3 shows the effect of adsorption rate models on the concentration variation of each step in the cyclic process. There was no noticeable difference between the

two cases. The only prominent difference was shown at the pressurizing pressure equalization step. At this step, the MTZ predicted by the modified LDF model showed a higher O2 mole fraction at the feed end than that predicted by the LDF model. Also, the MTZ moving velocity at the nonisobaric step predicted by the modified LDF model was slightly faster than that predicted by the LDF model. As a result, the predicted recovery by the modified LDF model was about 5-7% higher than that predicted by the LDF model at all operating conditions. Therefore, the modified LDF model should be considered in terms of the recovery in the experimental range in this study. The comparison of the predicted results by both models with the experimental results is presented in a later section. Dynamic Characteristics of the O2 PSA Process. Figure 4 shows a representative cyclic behavior by comparing the experimental effluent O2 concentration with the predicted one. In the predicted results, the effluent O2 concentrations at the adsorption, depressurizing pressure equalization, and pressurization steps were obtained at the product end, while those at the purge, pressurizing pressure equalization, and blow-

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Figure 6. Effect of adsorption step time on the O2 purity and recovery at 6 atm and 2.2 L(STP)/min.

Figure 5. Experimental and predicted temperature curves at the position of (a) 10 cm, (b) 50 cm, and (c) 80 cm from the feed end at 6 atm and 2.2 L(STP)/min.

down steps were at the feed end. After approximately 16-18 cycles, the concentration variation reached a cyclic steady state. Also, the predicted concentrations at the adsorption step agreed well with the experimental results. As the concentration wave front of N2 and O2 propagated along the bed, the heat of adsorption caused a temperature rise in the bed. Temperature histories at 10, 50, and 80 cm from the feed end under 6 atm and 2.2 L(STP)/min are presented in Figure 5. The ranges of the temperature swing were about 8 K near the feed end, which was higher than the results from previous studies.7,8 Because the difference of the predicted purity between nonisothermal and isothermal conditions by this thermal effect was about 0.5 vol %, the energy balance needed to predict the PSA performance more accurately in this study. In Figure 5, the temperature at the initial cycle showed a relatively small excursion of temperature due to the O2 saturated condition as an initial condition. The cyclic temperature variation reached a steady state after about 16 cycles, which agreed with the result in Figure 4. Also, the temperature variation at the product end was relatively small because that part of the bed was kept at a high O2 concentration condition. Figure 6 shows the effects of the adsorption step time on the O2 purity and recovery. The purge step time also changed with the variation of the adsorption step time in order to maintain cyclic symmetry. As shown in Figure 6, the modified LDF model predicted the recovery better than the LDF model even though there was no distinct difference in the prediction of the purity between both models. Therefore, the modified LDF model was applied to the simulation in this study. In Figure 6, up to 20 s, the increased adsorption step time, that is an isobaric step, showed a negligible change in purity even with the large change in recovery. However, over 20 s in the adsorption step time, the breakthrough of N2 had a detrimental effect on the O2 purity because of

Figure 7. Effect of adsorption and purge step time on the O2 concentration profiles along the adsorption bed of (a) AD and (b) PU steps at 6 atm and 2.2 L(STP)/min.

the breakthrough of N2.22 Also, the recovery increased almost linearly with the increase of the adsorption step time. These results were confirmed in Figure 7. In Figure 7a, the O2 mole fraction at the product end was kept constant at about 20 s regardless of the proceeding of O2 MTZ. However, after 30 s, the product end was significantly contaminated because the N2 breakthrough noticeably proceeded at the product end. Figure 7b shows the effect of the purge step time on the MTZ. As the purge step time increased, the O2 concentration at the feed end was increased because of the continuous

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Figure 8. Effect of pressurization step time on the O2 purity and recovery at 6 atm and 2.2 L(STP)/min.

desorption of N2. However, the O2 concentration at the product end drastically decreased from the 30 s purge step time because the O2 concentration of the purge gas from the other bed was decreased. Therefore, the MTZs near 25-30 s in the purge step time showed the crossover near the product end. Figure 8 shows the effects of the pressurization step, which is a nonisobaric step, on the O2 purity and recovery. In the experiments, the step time was fixed at 30 s, but the real step time was controlled by the flow rate with the idle time in Table 3. As could be expected, the increased real pressurization step time led to an increase in O2 purity and recovery.10 This implies that the lower flow rate led to an increased contact time between the gas and adsorbent. Also, the pressurization step shows the maximum purity in the case of the lowest flow rate during the step without the idle time. This is because the convex-shaped MTZ is formed at the pressurization step as shown in Figure 3. Although the MTZs at 35-40 s were slightly farther from the product end than the MTZ at 30 s, the product end was more contaminated at these longer pressurization step times. As a result, the pressure rise through the entire pressurization step time without idle time could be considered as an effective method for improving the O2 purity in the experimental range, but the prolonged pressurization step time over 30 s was not profitable to produce the high purity. Therefore, as shown in Figure 8, the evolution length during the pressurization step must be optimized to minimize the evolution length during the adsorption step because the mole fraction profile at the end of the pressurization step is the mole fraction profile at the beginning of the adsorption step.23 Figure 9 shows the effect of the pressure equalization step time on the O2 purity and recovery. The longer the pressure equalization step time, the higher the O2 purity. However, both the O2 purity and recovery approached the limiting value with an increase in the pressure equalization step time, which was different from the results of the pressurization step time effect in Figure 8. Therefore, in terms of the productivity and purity, the optimum pressure equalization step time could be determined at 30-35 s in this study. These results were confirmed in Figure 10. In Figure 10a, the slower flow rate at the depressurizing pressure equalization step caused the steeper O2 MTZ. Moreover,

Figure 9. Effect of pressure equalization step time on the O2 purity and recovery at 6 atm and 2.2 L(STP)/min.

Figure 10. Effect of pressure equalization step time on the O2 concentration profiles along the adsorption bed of (a) DPE and (b) PPE steps at 6 atm and 2.2 L(STP)/min.

the higher purity oxygen at this step was delivered in the other bed, as shown in Figure 10b. It also led to a higher O2 recovery because the lower amount of oxygen was vented at the blowdown step. Therefore, it caused both the steep MTZ in the pressurization step and the high purity in the adsorption step. However, the extents of the MTZ change with an increase in the depressurizing pressure equalization step time and pressurizing pressure equalization step time became smaller. Therefore, the PSA performance in Figure 9 was asymptotically improved with the change of the pressure equalization step time.

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Figure 12. Effect of blowdown step time on the (a) O2 purity and recovery and (b) O2 concentration profiles along the adsorption bed of the BD step at 6 atm and 2.2 L(STP)/min.

Figure 11. Effect of idle time on the (a) O2 purity and (b) O2 MTZ at DPE steps at 6 atm and 2.2 L(STP)/min.

Figure 11 shows the effect of the idle time at the pressure equalization step on the PSA performance. The total pressure equalization step time was fixed at 40 s with the idle time. Compared to Figure 9, the prolonged idle time at the same real purge step time led to improved product purity. However, as shown in Figure 11a, an increased real pressure equalization time up to 35 s caused the increase of O2 purity, while a real pressure equalization time over 35 s had a negative effect on the O2 purity, which was different from the result in Figure 9. Figure 11b shows the effect of idle time on the O2 MTZ at the end of the pressure equalization step time. The shortened idle time at the pressure equalization step caused the steep and slowly moving O2 MTZ up to 35 s. However, it was noticeable that the O2 MTZ at the depressurizing pressure equalization step which consisted of 35 s real pressure equalization time with 5 s idle time moved more steeply and slowly to the product end than that at the pressure equalization step with a 40 s step time without the idle time. This implies that the short idle time at the pressure equalization step is helpful to stabilize the O2 MTZ at the pressure equalization step and to improve the process performance. Figure 12 shows the effect of the blowdown step on the O2 purity and recovery. The total blowdown step time was fixed at 30 s with the change of the flow rate. The variation of the real blowdown step time had little effect on the O2 purity, recovery, and O2 MTZ shape, which were different from the results of the other

Figure 13. Cyclic variation of O2 purity at (a) a constant P/F ratio and (b) variable P/F ratio conditions at 6 atm and 2.2 L(STP)/ min.

nonisobaric steps such as the pressurization and pressure equalization steps. Mendes et al.10 also pointed out that the dispersion by the pressure decrease between adsorption pressure and blowdown pressure was the main factor which determined blowdown efficiency. Therefore, varying the diffusion rate by controlling the interstitial velocity at the blowdown step had little effect on the total process performance.

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The oxygen cost in the oxygen aerator system to treat the wastewater is one of the most important factors. Because of the limitation of oxygen saturation in the water, it needs to supply the proper concentration of oxygen to the aerator to save the oxygen cost. Figure 13 shows the comparison of cyclic performances at constant and variable P/F ratio conditions. Under both operating conditions, the cyclic steady state approached between 16 and 18 cycles. When the two P/F ratios in Figure 13a were applied to the PSA continuously, almost the same purity at the cyclic steady-state condition was obtained from each P/F ratio in Figure 13b. As a result, the PSA process with variable P/F ratio in Figure 13b showed very similar dynamic behavior to each process that had a constant P/F ratio in Figure 13a. Therefore, the desired oxygen concentration for the aerator can be supplied simply by controlling the feed rate or purge rate. Conclusions The effects of nonisobaric and isobaric steps on adsorption dynamics were investigated in the six-step, two-bed O2 PSA with zeolite 5A. In addition, on the basis of the PSA experiments, the operating condition needed to produce the various O2 concentrations from time to time was studied with regard to the oxygen aerator system. The modified LDF model that depicts the adsorption rate as a function of the sorbate concentration showed slightly better calculated results than the Gluekauf LDF model at the low flow rate region. Also, the LDF parameter of O2 influenced the calculated result of O2 purity, while that of N2 had a great effect on that of O2 recovery. This implies that the diffusion rates as well as the adsorption equilibria are important in the low flow rate region. In the adsorption step, even though the increased adsorption step time generally caused a decrease in O2 purity and an increase in O2 recovery, the improvement of the product purity by the decrease of the adsorption step time was negligible up to a certain step time (up to 20 s in this study), but the product recovery decreased drastically. At both nonisobaric steps in pressurization and pressure equalization steps, the increased step times led to an increase in purity and recovery. This implies that a lower flow rate caused increased contact time between gas and adsorbent. However, the pressurization step shows a maximum purity with the change in the step time because the proceeding N2 contaminated the product end. The purity and recovery at the pressure equalization step approached the limiting value. In particular, the depressurizing pressure equalization step had a great effect on the O2 purity and the pressurizing pressure equalization step on the O2 recovery. Furthermore, the idle time at each nonisobaric step had a different effect on the process performance. The pressurization step without idle time showed a better performance than that with idle time, while a short idle time at the pressure equalization step was needed to improve the process performance. However, the idle time at the blowdown step had little effect on the process performance. The PSA performances at the variable P/F ratio condition showed dynamic behavior similar to that at each constant P/F ratio condition. Therefore, to supply the proper concentration of oxygen to the aerator to save the oxygen cost, the desired oxygen concentration for

the aerator can be supplied simply by control of the feed rate or purge rate in the PSA operation. Acknowledgment The financial support of the Korea Institute of Industrial Technology and Daesung Sanso Corp. is gratefully acknowledged. Notation Aw ) cross-sectional area of the wall (cm2) B ) equilibrium parameter for the Langmuir-Freundlich model (atm-1) Ci ) i component concentration in the bulk phase (mol/ cm3) Cpg, Cps, Cpw ) gas, pellet, and wall heat capacities, respectively (cal/g‚K) De ) effective diffusivity defined by the solid diffusion model (cm2/s) Dc ) intracrystalline diffusivity (cm2/s) DL ) axial dispersion coefficient (cm2/s) hi ) internal heat-transfer coefficient (cal/cm2‚K‚s) ho ) external heat-transfer coefficient (cal/cm2‚K‚s) -∆H h ) average heat of adsorption (cal/mol) k ) parameter for the LRC model K ) proportionality parameter for the LDF model KL ) axial thermal conductivity (cal/cm‚s‚K) L ) bed length (cm) n ) equilibrium parameter for the Langmuir-Freundlich model P ) total pressure (atm) q, q*, q j ) amount adsorbed, equilibrium amount adsorbed, and average amount adsorbed, respectively (mol/g) qm ) equilibrium parameter for the Langmuir-Freundlich model (mol/g) R ) gas constant (cal/mol‚K) Rp ) radius of the pellet (cm) RBi, RBo ) inside and outside radii of the bed, respectively (cm) t ) time (s) Tatm ) temperature of the atmosphere (K) T, Tw ) pellet or bed temperature and wall temperature, respectively (K) u ) interstitial velocity (cm/s) yi ) mole fraction of species i in the gas phase z ) axial distance in the bed from the inlet (cm) Greek Letters R ) particle porosity , t ) voidage of the adsorbent bed and total void fraction, respectively Fg, Fp, FB, Fw ) gas density, pellet density, bulk density, and bed wall density, respectively (g/cm3) ω ) LDF coefficient (s-1) θ ) dimensionless adsorbed amount ()qi/qmi) Subscripts B ) bed i ) component i p ) pellet g ) gas phase s ) solid w ) wall

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Received for review February 1, 2002 Revised manuscript received May 20, 2002 Accepted May 30, 2002 IE020088K