Comparison of Radial-and Axial-Flow Rapid Pressure Swing

Compared to axial-flow rapid pressure swing adsorption (RPSA) processes, ... innovative coordinate transformation, the governing equations of both rad...
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1998

Ind. Eng. Chem. Res. 2003, 42, 1998-2006

Comparison of Radial- and Axial-Flow Rapid Pressure Swing Adsorption Processes Wen-Chun Huang* Department of Chemical Engineering, Kao Yuan Institute of Technology, Lu-Chu, Kaohsiung, Taiwan 821, ROC

Cheng-tung Chou Department of Chemical and Materials Engineering, National Central University, Chung-Li, Taiwan 320, ROC

Compared to axial-flow rapid pressure swing adsorption (RPSA) processes, radial-flow RPSA processes can have the larger cross section for the same volume of adsorbers. Radial-flow RPSA processes, thus, may have the advantage of a low-pressure drop for the same volumetric flow and a small particle size of the adsorbent can be used for the same pressure drop. After an innovative coordinate transformation, the governing equations of both radial- and axial-flow RPSA processes carry a similar form. Therefore, only a simulation program is needed and is developed to simulate the dynamics of the adsorbers for both systems. The simulation results of an axial-flow RPSA were compared with the experimental data in the literature. For the modeling of radial-flow RPSA processes, the parameter of effective length is equivalent to the length of the packed bed of axial-flow RPSA processes. For the same feed pressure and the same amount of adsorbent, the separation performance of the radial-flow RPSA processes would be better than that of axial-flow RPSA processes if small adsorbent particles and long effective lengths were used. The effects of the particle size of the adsorbent, feed pressure, production rate, and feed direction on the performance of radial-flow RPSA were also explored. Introduction Pressure swing adsorption (PSA) is an important industrial process for separation and purification of gas mixtures. When the high-pressure mixture enters the adsorber from the feed end, adsorption occurs and a product of enriched weakly adsorbed components is obtained at the production end. Before breakthrough of the adsorber, regeneration of the adsorbent is preceded by desorption at low pressure and a gas stream with enriched strongly adsorbed components is obtained. By the alternate operations of adsorption and desorption, a cyclic process is designed to produce products with the desired concentration continuously. The detailed introduction for this kind of process can be obtained in work by Ruthven1 and Yang.2 PSA processes may be divided into multibed and single-bed processes according to the number of adsorbers. Single-bed PSA usually has the shorter cycle time compared to that of multibed PSA and is called rapid PSA (RPSA) generally. The larger pressure drop is another characteristic of RPSA processes. RPSA processes were originally proposed by Turnock and Kadlec3 and Klower and Kadlec4 and became commercial processes after the improvement of Jones et al.5 and Jones and Keller.6 Pitchard and Simpson,7 Verelst and Baron,8 Doong and Yang,9 Jianyu and Zhenhau,10 Hart and * To whom correspondence should be addressed. Present address: Advanced Lithography Technical Department, Micropatterning Technology Division, Taiwan Semiconductor Manufacturing Co., Ltd., No. 6, Li-Hsin Rd 6, Science-Based Industrial Park, Sin-Chu, Taiwan 300-77, ROC. E-mail: [email protected]. Tel: 886-3-5636688 ext. 5856. Fax: 886-3-5637386.

Thomas,11 Alpay et al.,12,13 Sircar and Hanley,14 Suzuki et al.,15,16 and Betlem et al.17 also studied RPSA processes. These studies explored the effects of cycle time, feed pressure, production rate, particle size of the adsorbent, pressure drop, and slop recycling on the separation performance of axial-flow RPSA processes. Rota and Wankat18 proposed the radial-flow PSA first. The radial-flow RPSA could provide the larger flowing cross section for the same volume of adsorbers compared to axial-flow RPSA and has, thus, the smaller pressure drop for the same volumetric flow because of the slower velocity. Therefore, an adsorbent of smaller particle size and shorter cycle time can be applied to obtain higher productivity or the quantity of adsorbent and the volume of adsorbers can be reduced for the same productivity. In addition, the scale-up of a radial-flow RPSA is easier because such a process can remove the restriction of height. LaCava et al.19 mentioned that, “As competitive pressures are driving companies to operate their PSA units with high superficial velocities and short masstransfer zones, radial bed designs are becoming more and more popular.” The radial-flow RPSA is a potential process, although studies about this kind of process are few. Rota and Wankat18 proposed the idea of radial flow, and Chiang and Hong20 did the experimental study of a radial-flow RPSA process. A three-step RPSA process for separating air by 5A zeolite was studied, as shown in Figure 1. A mathematical modeling that is suited for simulations of both radialand axial-flow RPSA processes was developed. The simulation results for the axial-flow RPSA were compared to the experimental results of Pitchard and Simpson,7 and good agreement between these two

10.1021/ie020129c CCC: $25.00 © 2003 American Chemical Society Published on Web 03/27/2003

Ind. Eng. Chem. Res., Vol. 42, No. 9, 2003 1999

Based on these assumptions, the governing equations are Total material balance

∂C 1 -  ∂ 1 ∂ + (n + nB) ) (Cur) ∂t  ∂t A r ∂r

(1)

Material balance for component A

∂(Cy) 1 -  ∂nA 1 ∂ 1 ∂ ∂y + )(Cyur) + rDrC (2) ∂t  ∂t r ∂r r ∂r ∂r

(

Figure 1. A three-step RPSA process.

)

Applying the ideal gas law, C ) P/RT, eqs 1 and 2 become

1 ∂ ∂P 1 -  ∂ + RT (nA + nB) ) (Pur) ∂t  ∂t r ∂r

(3)

∂nA ∂(yP) 1 -  ∂y 1 ∂ 1 ∂ rDrP + RT )(yPur) + ∂t  ∂t r ∂r r ∂r ∂r (4)

[

]

The relation between the velocity and pressure drop is described by the Blake-Kozeny equation

u)Figure 2. Diagram for the radial adsorber with anoutward feed.

results was obtained. For the radial-flow RPSA process with outward flowing, the diagram of an adsorber is shown in Figure 2. For the modeling of radial-flow RPSA processes, the parameter of effective length that is equivalent to the length of the packed bed of axial-flow RPSA processes is introduced. For the same feed pressure and the same amount of adsorbent, the separation performance of the radial-flow RPSA would be better than that of the axial-flow RPSA if small adsorbent particles and long effective lengths were used. The effects of the particle size of the adsorbent, feed pressure, production rate, and feed direction on purity, recovery, and productivity of radial-flow RPSA were also explored. Mathematical Modeling A. Radial-Flow Processes. Governing Equations. To simplify the calculation, the following assumptions were used to model radial-flow RPSA. (1) A local equilibrium model that neglects mass transfer between the adsorbent and the adsorbate is assumed. (2) An ideal gas law is applicable. (3) Extended Langmuir isotherms can be used to describe the adsorption behavior. (4) The concentration gradient and pressure drop in the axial direction should be neglected. (5) The Blake-Kozeny equation can be used to describe the relation between the velocity and pressure drop. (6) The system is isothermal. (7) The flow pattern is described by the radially dispersed plug flow. (8) The dispersion coefficient is inversely proportional to pressure.

dp22

∂P 150(1 - ) µ ∂r

(5)

2

An innovative dimensionless radial position η is defined as

η)

r2 - Ri2 Ro2 - Ri2

w

{ [( ) ] }

r2 ) Ri2 η

Ro Ri

2

- 1 + 1 ) Ri2(aη + 1)

where Ri and Ro are the inner radius and the outer radius, respectively (referring to Figure 2), and

a ) (Ro/Ri)2 - 1 The dimensionless pressure, φ, and dimensionless adsorption amounts, NA and NB, are defined as

φ)

1 -  RT 1 -  RT P , NA ) n , NB ) n P0  P0 A  P0 B

where P0 is the reference pressure, 1 atm. The dispersion coefficient is inversely proportional to the pressure

Dr0 ) Drφ The effective length, Leff, and two time constants, tµ and td, are defined as

aRi 150(1 - )2µLeff2 Leff2 , tµ ) , td ) (6) Leff ) 2 Dr0 2d 2P p

0

Therefore, eqs 3 and 4 become

∂φ ∂ 1 ∂ ∂φ + (N + NB) ) (aη + 1)φ ∂t ∂t A tµ ∂η ∂η

[

]

(7)

2000

φ

Ind. Eng. Chem. Res., Vol. 42, No. 9, 2003

∂NA ∂NB ∂y + (1 - y) -y ) ∂t ∂t ∂t ∂φ ∂y 1 ∂ ∂y 1 (aη + 1)φ (aη + 1) (8) + tµ ∂η ∂η td ∂η ∂η

[

]

For extended Langmuir isotherms, the amounts of equilibrium adsorption can be expressed as

n/A

)

n/B )

φ(η,t)0) ) 1; y(η,t)0) ) yfeed; Ni(η,t)0) ) N/i (at yfeed, feed temperature, and 1 atm) (i ) A, B) (13)

aAPy 1 + bAPy + bBP(1 - y) aBP(1 - y)

When eqs 7-13 are solved, concentration and pressure profiles within the adsorber could be obtained. B. Axial-Flow RPSA Processes. Governing Equations. The assumptions used for the modeling of axialflow RPSA are the same as those for the radial-flow process except that radially dispersed plug flow is replaced by axially dispersed plug flow and neglecting axial concentration and pressure gradients is replaced by neglecting radial gradients. Based on these assumptions, the following governing equations could be obtained:

1 + bAPy + bBP(1 - y)

Therefore, the dimensionless form is

N/A )

aAφy 1 -  RT  P0 1/P0 + bAφy + bBφ(1 - y)

N/B )

a2φy 1 -  RT  P0 1/P0 + bAφy + bBφ(1 - y)

For the local equilibrium model, we have

NA ) N/A, NB ) N/B

Total material balance

∂C 1 -  ∂ ∂ + (n + nB) ) - (Cu) ∂t  ∂t A ∂z

(9)

Boundary Conditions and Initial Conditions. Boundary conditions for pressure are from the BlakeKozeny equation

tµq0 ∂φ )∂η (aη + 1)Vbedφ

where q0 ) flow rate in m3/s (1 atm and 298 K), Cv ) valve flow coefficient, SG ) specific gravity of gas (air at 1 atm and 294.4 K ) 1), T ) absolute temperature of flowing gas (K), P1 ) upstream pressure (atm), and P2 ) downstream pressure (atm). Initial conditions are beds saturated with gas at feed composition, feed temperature, and 1 atm,

(η ) 0, 1)

(10)

Material balance for component A

∂(Cy) 1 -  ∂nA ∂y ∂ ∂ DC + ) - (yCu) + ∂t  ∂t ∂z ∂z z ∂z

(

)

∂φ ∂ 1 ∂ ∂φ + (N + NB) ) φ ∂t ∂t A t′µ ∂η′ ∂η′

( )

At the inlet end (from Danckwert’s boundary condition:

∂y/∂r ) -u(yfeed - yin)/Dr) (11)

(15)

Similar to the manipulations in the radial-flow RPSA, eqs 14 and 15 become

Boundary conditions for the mole fraction are

td(yfeed - yin)q0 ∂y )∂η (aη + 1)Vbed

(14)

φ

(16)

∂NA ∂NB 1 ∂φ ∂y ∂y 1 ∂ ∂y + (1 - y) -y ) φ + ∂t ∂t ∂t t′µ ∂η′ ∂η′ t′d ∂η′ ∂η′ (17)

( )

where η′ is the dimensionless axial position and t′µ and t′d are two time constants.

At the outlet end

∂y )0 ∂η

(12)

where yfeed is the mole fraction of A in the feed, yin is the mole fraction at the feed end of the adsorber, and Vbed is the volume of the adsorber. The flow rate through the valve at reference pressure and operation temperature, q0, can be calculated by the valve equation that is recommended by Fluid Controls Institute, Inc.,21

[

]

1/2

P12 - P22 q0 ) 8.406E - 2Cv SG × T

for P2 > 0.53P1

or

q0 ) 7.129E - 2CvP1

[SG1× T]

1/2

for P2 e 0.53P1 (critical flow)

150(1 - )2µL2 L2 z , t′ ) η′ ) , t′µ ) d L Dz0 2d 2P p

0

Boundary Conditions and Initial Conditions. Boundary conditions for pressure are from the BlakeKozeny equation

t′µq0 ∂φ )∂η′ Vbedφ

(η′ ) 0, 1)

(18)

Boundary conditions for the mole fraction are At the inlet end (from Danckwert’s boundary condition)

t′d(yfeed - yin)q0 ∂y )∂η′ Vbed

(19)

Ind. Eng. Chem. Res., Vol. 42, No. 9, 2003 2001

At the outlet end

∂y )0 ∂η′

Table 1. Parameters Used in the Axial-Flow RPSA of Pitchard and Simpson7

(20)

Initial conditions are beds saturated with gas at feed composition, feed temperature, and 1 atm,

φ(η′,t)0) ) 1; y(η′,t)0) ) yfeed; Ni(η′,t)0) ) N/i (at yfeed, feed temperature, and 1 atm) (i ) A, B) (21) Comparison with the Radial-Flow RPSA. In a comparison of eqs 16 and 17 with eqs 7 and 8, when the effective length and radial dispersion coefficient for the radial-flow RPSA were replaced by the length of the adsorber and axial dispersion coefficient for the axialflow RPSA and coefficient a was allowed to be zero, the form of governing equation of the radial-flow RPSA became exactly the same as the form of the governing equation of the axial-flow RPSA. The boundary conditions and initial conditions for the radial-flow RPSA are also similar to those of the axial-flow RPSA by allowing coefficient a be zero. Therefore, the simulation program for the radial-flow RPSA can be applied to solve axialflow RPSA by adjusting the parameters accordingly. C. Numerical Method. The numerical method used is the method of lines with adaptive grid points,21 and the integrator used is LSODI of ODEPACK.

feed gas composition adsorbent feed pressure axial dispersion coefficient column length column diameter bed porosity temperature particle size of the adsorbent particle density of the adsorbenta isotherm constant aAa isotherm constant aBa isotherm constant bAa isotherm constant bBa a

air (21% O2 and 79% N2) 5A zeolite 1.52-1.80 atm 1.58 × 10-5 m2/s 6.1 × 10-1 m 3.8 × 10-2 m 0.32 298 K 2.11 × 10-4 m (60-80 mesh) 1.20 × 103 kg/m3 1.8901 × 10-4 kg‚mol‚atm-1‚ (m3 of solid)-1 3.8716 × 10-4 kg‚mol‚atm-1‚ (m3 of solid)-1 5.5133 × 10-2 atm-1 1.5022 × 10-1 atm-1

At 298 K, Chou and Huang.22

Table 2. Comparison of Simulation Results with Experimental Data of Pitchard and Simpson7

run

feed pressure (atm)

exptl

simulation

exptl

simulation

1 2 3 4 5

1.52 1.59 1.66 1.72 1.80

68.7 80.6 86.9 93.2 97.8

67.96 78.35 87.44 94.37 100

19.28 16.89 17.65 17.67 17.56

16.88 17.09 16.98 16.43 15.56

purity (%)

recovery (%)

Results and Discussion In this study, all simulation results are based on the same amount of adsorbent, the same porosity, and the same cycle times. When the bed length of axial-flow RPSA or the effective bed length of radial-flow RPSA was changed, the diameter of the adsorber would be adjusted accordingly. The performance of PSA processes is usually expressed by purity, recovery, and productivity. Purity is defined as the ratio of the amount of oxygen in the product to the amount of total product here. Recovery is defined as the ratio of the total amount of oxygen in the product to the total amount of oxygen fed during a whole cycle at cyclic steady state. Productivity is defined as the amount of oxygen per unit mass of adsorbent per unit time. For the discussion that follows, when the production rate was maintained, productivity is proportional to purity; therefore, only purity and recovery were discussed. A. Simulation of the Axial-Flow RPSA Process. Comparison with Experimental Data. The simulation results of axial-flow RPSA were compared with the experimental data of Pitchard and Simpson.7 The process simulated is a three-step process, as shown in Figure 1. During the feed step, the air at high pressure was fed into the adsorber from the feed end and the product with enriched oxygen was obtained from the production end. The feed end, then, was closed, and the product was drawn continuously from the production end during the delay step. During the exhaust step, the feed end was opened to the atmosphere to vent desorbed nitrogen-rich gas and the product was drawn continuously. The physical parameters used are listed in Table 1. The constants of the Langmuir isotherm are the same as those of Chou et al.22 For the following simulations of axial-flow RPSA, the parameters would be the same as those listed in Table 1 if they were not described

Figure 3. Effect of the particle size of the adsorbent for axialflow RPSA.

specifically. The cycle times for feed, delay, and exhaust are 1.0, 0.5, and 4 s for all calculations. At fixed product flow rate, 4.2 × 10-3 STP L/s, purity and recovery were obtained for different feed pressures. The simulation results were compared with the experimental results of Pitchard and Simpson,7 as shown in Table 2. The maximum relative errors in purity and recovery are about 2% and 12%, respectively. Reasonable agreement was obtained between simulation and experimental results. Effect of the Particle Size of the Adsorbent. For various lengths of the adsorber, the effect of the particle size of the adsorbent on the performance was studied. The range of length of the adsorber is 0.5-1.5 m. Figure 3 shows the result with the length of 0.5 m. When the particle size of the adsorbent increased from 1.77 × 10-4 m (80 mesh) to 3.54 × 10-4 m (35 mesh), the recovery decreased gradually and a maximum would exist for the purity. Alpay et al.13 showed a similar tendency for the two-step RPSA process. Pressure drop within the adsorber is an important factor for the RPSA process. Very

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Figure 5. Effect of the adsorber length for axial-flow RPSA.

Figure 4. Pressure profiles within the axial-flow adsorber: (a) adsorber length ) 0.5 m and particle size of the adsorbent ) 3.54 × 10-4 m; (b) adsorber length ) 1.5 m and particle size of the adsorbent ) 2.11 × 10-4 m.

small particles reduced the separation capacities by the ineffective pressure swing of most of the bed near the production end. For large particles carrying negligible pressure drop, high concentration was difficult to maintain inside the bed after the delay and exhaust steps, which caused a low-purity product at the following production step. Hence, an optimal particle size that gave the maximum average product purity exists. When the particle size increased, the total feed amount increased owing to the reduction of the flow resistance for the same valve opening, which made the recovery decrease gradually. For illustrating the difference of pressure distribution, Figure 4 shows the pressure profile within the adsorber at different stages for two cases. For the operation of Figure 4a with an adsorber length of 0.5 m and a particle size of 3.54 × 10-4 m, the pressure at the outlet end changes from 1.07 to 1.34 atm and the maximum pressure drop is about 0.2 atm. A relatively higher concentration cannot be maintained in the adsorber after the exhaust step. For the operation of Figure 4b with an adsorber length of 1.5 m and a particle size of 2.11 × 10-4 m, the pressure at the outlet end is maintained almost at 1.04

atm and the region with ineffective pressure swing exists. The maximum pressure drop is about 0.5 atm. The existence of a maximum pressure during the exhaust step can help maintain the higher concentration in the adsorber. Effect of the Length of the Adsorber. The effect of the length of the adsorber on the performance was explored while keeping the same adsorbent amount. Figure 5 shows the effects of the adsorber length on purity and recovery. The particle size used is 3.54 × 10-4 m. When the length of the adsorber increased from 0.5 to 1.5 m, a maximum product purity appeared and the recovery increased with an increase of the length of the adsorber. An optimal bed length would give the maximum purity for the same particle size. The reason for the existence of an optimal bed length is the difference of the pressure distribution within the adsorber that also explains the appearance of an optimal particle size in the preceding section. The longer adsorber that generated a larger pressure drop would decrease the feed amount and increase the recovery. B. Simulation of the Radial-Flow RPSA Process. The operating steps for radial-flow RPSA are the same as those in Figure 1, and the radial-flow adsorber replaces the axial adsorber. Relative to the axial-flow RPSA, the feed direction and the ratio of the outer radius to the inner radius are additional process parameters. The effective length, defined in eq 6, depends on the inner radius and the outer radius. For the simulations of the radial-flow RPSA, the effects of the effective length, feed direction, particle size of the adsorbent, feed pressure, and production rate on the performance were explored. Transient profiles reaching the cyclic steady state were also studied. Table 3 lists the parameters used in the simulation of the radial-flow RPSA. Effect of the Particle Size of the Adsorbent. The effects of the particle size of the adsorbent on purity and recovery of the radial-flow RPSA are shown in Figure 6. The feed direction is inward, the inner radius is 3.05 × 10-2 m, and the outer radius is 1.95 × 10-1 m. When the particle size increased from 3.7 × 10-5 to 2.11 × 10-4 m, maximum product purity appeared and recovery decreased gradually. The tendency of change was similar to that of axial-flow RPSA. However, the optimal particle size occurred at a smaller particle size compared with that of the axial-flow RPSA (Figure 3). For the same amount of adsorbent, the adsorber with radial and inward flowing provided more cross section to flow and

Ind. Eng. Chem. Res., Vol. 42, No. 9, 2003 2003 Table 3. Parameters Used in the Radial-Flow RPSA. feed gas composition adsorbent feed pressure radial dispersion coefficient effective length ratio of the outer diameter to the inner diameter inner radius bed porosity temperature particle size of the adsorbent particle density of the adsorbenta isotherm constant aAa isotherm constant aBa isotherm constant bAa isotherm constant bBa a

air (21% O2 and 79% N2) 5A zeolite 1.52-1.80 atm 1.58 × 10-5 m2/s 6.1 × 10-1-1.8 m 1.05-9 3.05 × 10-2-3.0 × 10-1 m 0.32 298 K 3.7 × 10-5 m (400 mesh) to 3.54 × 10-4 m (42 mesh) 1.20 × 103 kg/m3 1.8901 × 10-4 kg‚mol‚atm-1‚ (m3 of solid)-1 3.8716 × 10-4 kg‚mol‚atm-1‚ (m3 of solid)-1 5.5133 × 10-2 atm-1 1.5022 × 10-1 atm-1

At 298 K, Chou and Huang.22 Figure 7. Pressure profiles within the radial-flow adsorber for the particle size of the adsorbent ) 7.4 × 10-5 m.

Figure 6. Effect of the particle size of the adsorbent for radialflow RPSA.

the pressure drop was reduced for the same particle size and the same flow. For the same pressure drop, the smaller particle size could be used for radial-flow RPSA. This is the reason the optimal particle size shifts from a large particle size for axial-flow RPSA to a small particle size for radial-flow RPSA. Figure 7 shows the pressure profiles within the adsorber for the run with optimal particle size for producing maximum purity in Figure 6. For a particle size smaller than this optimal particle size, the constantpressure zone with an ineffective pressure swing near the product end would appear (refer to Figure 4b). The zone with an ineffective pressure swing would reduce the effective utilization of adsorbents. For a particle size larger than this optimal particle size, the pressure drop within the adsorber is smaller and would not maintain a relatively high purity at the production end to enrich oxygen at the next cycle after the operation of the exhaust step (refer to Figure 4a). Effect of the Feed Direction. The effects of the feed direction on purity and recovery were compared at the same production rate. Figure 8 shows the results for the effective length of 1.5 m. When the particle size increased from 1.05 × 10-4 to 3.54 × 10-4 m, the product purity for inward feed operation is always higher than that for outward feed operation and the oxygen recovery for inward feed operation is always lower than that for outward feed operation. Chiang and Hong20 employed 3 µm particles of 5A zeolite to do the experiments of

Figure 8. Effect of the feed direction for radial-flow RPSA.

radial-flow RPSA; product purity for the outward feed operation is always lower than that for inward feed operation too. In radial-flow geometry, most of the flow resistance was located near the center. The relatively small pressure gradient at the feed end enabled a better adsorbent utilization for the inward operation. Figure 9 shows the pressure profiles within the adsorber for a run with outward feed and a particle size of 2.11 × 10-4 m. Owing to the fact that the cross section increases gradually in the feed direction, with the pressure drop concentrated at the feed end, the zone of relatively high pressure is less than that for inward feed operation. This large flow resistance at the feed end caused the ineffective utilization of adsorbent. Hence, a low product purity was obtained. The large flow resistance also caused a decrease of the feed amount, and high recovery was obtained. Effect of the Effective Length. Effects of the effective length of the adsorber on purity and recovery of radial-flow RPSA for different particle sizes of adsorbent were investigated. Figure 10a shows the results with a particle size of 3.70 × 10-5 m. The inner radius was maintained at 4.0 × 10-2 m, and the outer radius was varied to obtain different effective lengths of the adsorber. The changing tendency is similar to that in Figure 3. The recovery decreased gradually, and a maximum appeared for the purity.

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Figure 11. Effect of the feed pressure for radial-flow RPSA.

Figure 9. Pressure profiles for a radial-flow run with an outward feed.

Figure 12. Effect of the production rate for radial-flow RPSA.

Figure 10. Effect of the effective length of the adsorber for radialflow RPSA: (a) inner radius ) 4.0 × 10-3 m, particle size of the adsorbent ) 3.70 × 10-5 m; (b) inner radius ) 6.0 × 10-3 m, particle size of the adsorbent ) 2.11 × 10-4 m.

Figure 10b shows the results with a particle size of 2.11 × 10-4 m and an inner radius of 6.0 × 10-2 m. When the effective length increased from 0.6 to 1.8 m,

both product purity and recovery increased gradually. The longer effective length causing a larger pressure drop achieved a better separation performance. The gradual increase in the product purity indicated that these effective bed lengths used in Figure 10b were smaller than that with the maximum purity. If the effective length of the adsorber increased further, a maximum in purity was expected. The increasing effective length that generated the larger pressure drop would reduce the feed amount. The increase of the product purity and the decrease of the total feed caused the gradual increase of recovery. Effects of the Feed Pressure and Production Rate. When the feed pressure increased from 1.52 to 1.80 atm, purity increased and recovery decreased slightly, as shown in Figure 11. The effective length was fixed at 0.61 m, and the particle size was 3.70 × 10-5 m. When the production rate increased from 4.2 × 10-3 to 8.4 × 10-3 L/s, the purity decreased and recovery increased, as shown in Figure 12. The effective length was fixed at 1.5 m, and the particle size was 1.25 × 10-4 m. The effects of the feed pressure and production rate on the purity and recovery of the radial-flow RPSA are similar to those for the axial-flow RPSA that has been discussed in many literary works. C. Comparison of Performance. The productivity is defined as SLPM O2/(kg of adsorbent) in this study. Table 4 lists some simulation results for specific runs. Run A is the same as run 1 in Table 2, and the operation conditions are the same as those of an experimental run of Pitchard and Simpson.7 Run B is the run with the

Ind. Eng. Chem. Res., Vol. 42, No. 9, 2003 2005 Table 4. Comparison of the Performance for the Axial- and Radial-Flow RPSAa run

adsorber type

(effective) length of the adsorber (m)

particle size (m)

production rate (STP L/s)

average feed rate (STP L/s)

purity of O2 (%)

recovery of O2 (%)

productivity (SLPMc/kg of adsorbent)

A B C D

axial axial radialb radialb

0.61 0.5 1.80 1.50

2.11 × 10-4 2.97 × 10-4 2.11 × 10-4 1.25 × 10-4

4.20 × 10-3 4.20 × 10-3 4.20 × 10-3 6.30 × 10-3

8.05 × 10-2 1.37 × 10-1 1.68 × 10-1 1.15 × 10-1

68 84 97 69

17 12 12 18

0.30 0.37 0.42 0.46

a For all runs, feed pressure ) 1.52 atm, porosity ) 0.32, weight of adsorbent ) 0.5645 kg, and volume of adsorber ) 0.692 L. b Feed direction is inward. c Standard liter per minute, STP L/min.

maximum purity for axial-flow RPSA while changing the particle size of the adsorbent and the length of the adsorber. The range of the particle size is 3.7 × 10-53.54 × 10-4 m, and that of the length is 0.5-1.5 m. Run C is the run with the maximum purity for radial-flow RPSA while changing the particle size of the adsorbent and the effective length of the adsorber. The range of the particle size is 3.7 × 10-5-3.54 × 10-4 m, and that of the effective length is 0.6-1.8 m. Run D is the operation for the radial-flow RPSA with about the same purity as run A for the axial-flow RPSA. From runs A and B, reducing the length of the adsorber and increasing the particle size of the adsorbent would improve the purity and productivity and would reduce the recovery for the same production rate. However, a large particle size would increase the masstransfer resistance. In a comparison of runs C and A, it was found that the purity increased from 68% (axial flow) to 97% (radial flow), the productivity increased from 0.30 (axial flow) to 0.42 (radial flow) SLPM O2/(kg of adsorbent), and the recovery decreased from 17% (axial flow) to 12% (radial flow) for the same production rate. In a comparison of runs D and A at about the same purity, it was found that the recovery increased from 17% (axial flow) to 18% (radial flow) and the productivity increased from 0.30 (axial flow) to 0.46 (radial flow) SLPM O2/(kg of adsorbent). The radial-flow RPSA can utilize a smaller particle size of the adsorbent and a longer effective length to achieve a better separation performance compared to the axial-flow RPSA. Although the radial-flow RPSA would obtain a better performance than the axial-flow RPSA, there exists a practical limit. If a longer effective length wants to be obtained for the same adsorber volume, the inner radius or the ratio of the outer radius to the inner radius should be increased. The height of the adsorber, therefore, should be reduced and would become too short to be practical in some cases. In this study, the recovery is not very high. Improvement of the recovery is needed for commercial application and would be our next topic for radial-flow PSA. Cycle steps and cycle times are the possible candidates for improving recovery. Conclusions A simulation program has been developed to simulate the dynamics of the adsorbers for the radial- and axialflow RPSA processes. The simulation results of an axialflow RPSA were compared with the experimental data of Pitchard and Simpson,7 and good agreement was presented. For the modeling of the radial-flow RPSA processes, the parameter of effective length that is equivalent to the length of the packed bed of the axial-flow RPSA process was introduced. Effective length depends on the ratio of the outer radius to the inner radius and the

inner radius. For the same feed pressure and the same amount of adsorbent, the separation performance of the radial-flow RPSA is better than that of the axial-flow RPSA by utilizing a smaller particle size of the adsorbent and a longer effective length for the radial-flow RPSA. The feed direction is an important factor for the radial-flow RPSA too. The operations with an inward feed always generate higher purity and productivity than the operations with an outward feed that is owing to the difference of the pressure profile within the adsorber. Acknowledgment The authors are grateful for financial support of this work by the National Science Council, Taiwan, ROC, under Grant NSC89- 2214-E-224-001. Notation a ) defined as (Ro/Ri)2 - 1 aA, aB ) isotherm constants [kg‚mol‚atm-1‚(m3 of solid)-1] bA, bB ) isotherm constants (atm-1) C ) total molar concentration in the gas (kg‚mol/m3) Dr ) radial dispersion coefficient (m2/s) Dr0 ) radial dispersion coefficient at the reference pressure (m2/s) Dz ) axial dispersion coefficient (m2/s) Dz0 ) axial dispersion coefficient at the reference pressure (m2/s) dP ) particle size of the adsorbent (m) L ) length of the axial adsorber (m) Leff ) effective length of the radial adsorber (m) nA, nB ) amounts of adsorption of O2 and N2 on the adsorbent (kg‚mol/m3 of adsorbent) P ) absolute pressure (atm) P0 ) reference pressure (atm) q0 ) flow at the reference pressure (1 atm) and operation temperature (298 K) (m3/s) Ro ) outer radius of the radial adsorber (m) Ri ) inner radius of the radial adsorber (m) r ) radial position (m) t ) time (s) T ) absolute temperature (K) u ) interstitial velocity (m/s) VBED ) volume of an adsorber (m3) y ) mole fraction of A in the gas yfeed ) mole fraction of A in the feed yin ) mole fraction at the feed end of the adsorber z ) axial position (m)  ) void fraction of the adsorber µ ) viscosity (kg‚s-1‚m-1) η ) dimensionless radial position η′ ) dimensionless axial position φ ) dimensionless pressure

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Received for review February 12, 2002 Revised manuscript received December 10, 2002 Accepted January 20, 2003 IE020129C