High Recovery Cycles for Gas Separations by Pressure-Swing

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Ind. Eng. Chem. Res. 2006, 45, 8117-8133

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High Recovery Cycles for Gas Separations by Pressure-Swing Adsorption Kyle P. Kostroski and Phillip C. Wankat* School of Chemical Engineering, Forney Hall of Chemical Engineering, Purdue UniVersity, 480 Stadium Mall DriVe, West Lafayette, Indiana 47907-1283

Cycling-zone pressure-swing adsorption (CZPSA) and combination PSA-CZPSA cycles have been developed to increase the high-pressure product recovery of the Skarstrom PSA cycle. CZPSA uses a low-pressure feed as purge, whereas the combination PSA-CZPSA cycles use both a low-pressure feed gas and a product gas as purge. Extensive parametric studies were simulated using ADSIM for the model system of dilute benzene in nitrogen on activated carbon to determine how process performance was affected by flow scheme, purge sequence, penetration distance, feed and purge pressures and velocities, and pressurization procedure. For example, a nitrogen product purity of yB,prod/yB,feed ) 0.05 and a high-pressure nitrogen recovery of P/F1 ) 0.46 were obtained using the Skarstrom cycle, whereas the CZPSA cycle achieved values of yB,prod/yB,feed ) 0.18 and P/F1 ) 0.58. Air drying with activated alumina and air separation with zeolite 13X were also modeled. The Skarstrom cycle produced dry air with a dew point of -71 °C and P/F1 ) 0.58, whereas the CZPSA cycle produced dry air with a dew point of -11 °C and P/F1 ) 0.99. For air separation with pressure equalization, the modified Skarstrom cycle produced an oxygen product purity of yN,prod/yN,feed ) 0.15 (∼88% O2) and P/F1 ) 0.11 (44% O2 recovery), whereas the CZPSA cycle achieved yN,prod/yN,feed ) 0.36 (∼72% O2) and P/F1 ) 0.22 (75% O2 recovery). For all three systems, the combination cycles performed between the Skarstrom limits and the CZPSA limits. The combination and CZPSA cycles increase the recovery of highpressure product while maintaining productivity, making them alternatives to the Skarstrom cycle when lower product purities are acceptable. Introduction Gas-separation processes include cryogenic distillation, pressure- and temperature-swing adsorption, and membrane technology. In this spectrum, adsorption often falls midrange between the high-capacity cryogenic processes and the small-scale membrane units. The ultimate selection of the separation process is dependent on feed conditions, product conditions, property differences that may be exploited, and characteristics of the separation operation.1 Pressure-swing adsorption (PSA) has been extensively applied to air drying, air separation for oxygen or nitrogen enrichment, and hydrogen purification.2 PSA typically uses a bed of solid particles that has an affinity for the solute (waste) gas to separate it from its carrier (product) gas. One of the first PSA cycles developed, the Skarstrom cycle, is composed of four steps: bed pressurization with feed, adsorption and production of product, bed depressurization or “blowdown,” and desorption or purge.3 Usually, product gas is used as the purge gas. The Skarstrom cycle,4 including many modifications,5,6 has become a common PSA cycle. It produces a product of high purity because purging is done with product, which is equivalent to reflux, but product recovery can be low. Because compression is the major operating cost, a process that can achieve almost the same purity while increasing highpressure product recovery would be useful. A similar problem that involves temperature-swing adsorption (TSA) and the reduction of hot solvent liquid and hot carrier gas use in desorption was investigated previously.7,8 Analogues to these TSA processes were used for initial development of the new PSA processes (which are referenced as “combination cycles”) presented here, which are also an extension of earlier work.9 The objective is to maximize the recovery of the high-pressure feed as high-pressure product. * To whom correspondence should be addressed. Tel.: 765-4940814. Fax: 765-494-0805. E-mail: [email protected].

Figures 1 and 2 schematically show the PSA cycles. The new high-recovery “combination cycles” combine two limiting cases. One limiting case is the well-known Skarstrom cycle, which achieves high purity but has low recovery of high-pressure product. The opposite limiting case is the cycling-zone pressureswing adsorption (CZPSA) cycle, which uses a continuous flow of feed material, with adsorption and desorption occurring as a result of pressure changes of the feed.4,9,10 As first developed,4 CZPSA (Skarstrom did not use this name) was conceptualized as a Skarstrom cycle that used low-pressure feed as the purge gas. This process, as expected, achieves a lower purity but higher recovery of pressurized product. Both the combination and CZPSA cycles have the potential for increasing high-pressure product recovery beyond that of the Skarstrom cycle while maintaining reasonably high purity. Figures 1A and 1B show the processes operating with co-flow and counter-flow of purge gas flow, relative to feed gas flow, respectively. The combination cycles in these figures are operated with purge sequence A: purge with recycled product gas, followed by low-pressure feed, which is analogous to the TSA processes.7 Figures 2A and 2B show operation of the combination cycles with purge sequence B: purge with low-pressure feed, followed by recycled product. From a process point of view, the combination and CZPSA cycles are not much more complex than the Skarstrom cycle. A blower is required for the low-pressure feed. Because the pressure drop along the bed will be relatively small, a compressor should not be necessary. A parametric study (Figure 3) was constructed to fully elucidate the parameter space as a function of operating variables. The first model system was a feed of 0.003 mole fraction benzene vapor in nitrogen at 363 K adsorbed on Sorbonorit B activated carbon. The relatively high operating temperature was chosen to reduce the adsorption of the strongly adsorbed benzene, so that the adsorbent could be regenerated

10.1021/ie060566h CCC: $33.50 © 2006 American Chemical Society Published on Web 10/21/2006

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Figure 1. Combination cycles developed following purge sequence A, with the Skarstrom cycle and CZPSA as limiting cases: (A) co-flow schemes and (B) counter-flow schemes. Pressurization and blowdown steps are not shown.

Figure 2. Combination cycles developed following purge sequence B: (A) co-flow schemes and (B) counter-flow schemes. Pressurization and blowdown steps are not shown.

in a PSA process. The combination cycles and CZPSA were later extended to two additional model systems. An air feed (0.004 mole fraction water in 0.21 mole fraction oxygen and 0.786 mole fraction nitrogen) was dried with activated alumina. In addition, air (0.21 mole fraction oxygen and 0.79 mole fraction nitrogen) was separated with zeolite 13X. All three model systems used data from the literature (Table 1).7,11-14

Figure 3. Map of parameter space for exploration of the benzene-nitrogen system.

∂qji ∂ci ∂cji,pore + Fs(1 - e)(1 - p) + e + Kdi(1 - e)p ∂t ∂t ∂t ∂(Vfci) ∂2ci e - eEZ 2 ) 0 (1) ∂z ∂z During blowdown, the appropriate boundary conditions for concentration and velocity are2

Theory The equations that are used to describe nonisothermal fixed bed adsorption are the mass and energy balances, the mass and energy transfer equations, and the equilibrium isotherm. For the mass balance, it is assumed that radial gradients are negligible, no chemical reactions occur, and mass transfer follows a linear driving force model. The mass balance is15

∂ci | )0 ∂z z)0

(2a)

∂ci | )0 ∂z z)L

(2b)

Vf|z)0 ) 0

(2c)

Ind. Eng. Chem. Res., Vol. 45, No. 24, 2006 8119 Table 1. Data for Benzene-Nitrogen System, Air-Drying System, and Air-Separation System parameter

benzene-nitrogen system carbon8,11,12

air drying system

air separation system

alumina13,18

13X14,18

adsorbent L D i p Fb Rp kMTCsolid isotherm parameters

activated 102 cm 8.8 cm 0.44 0.67 0.40 g/cm3 0.077 cm benzene: 0.001 s-1 benzene,eqs 18 and 19; m1 ) 2.889 mmol/g; m2 ) 5.429× 10-7 K; b1 ) 79.11 kPa-1; b2 ) 5292 K

activated 100 cm 20 cm 0.4 0 0.720 g/cm3 0.0355 cm water: 8.33 × 10-4 s-1 water; eqs 21 and 22; K0 ) 7.57 m3/kg at T0; Q0 ) 5.19× 104 J/mol; T0 ) 303 K

Cp,solid heat of adsorption hp ap bottom Ptop ) H (PH bottom Ptop ) L (PL

470 J/(kg K) benzene: -56 000 kJ/kmol 100 W/(m2 K) 3896.1 m-1 5 bar (4.9 bar) 1.1 bar (1.0 bar), 0.3 bar (0.2 bar) 363 K 0.3 m/s (0.6 m/s), 0.1 m/s (0.2 m/s), see Table 3 for others

1260 J/(kg K) water: -51 900 kJ/kmol estimated with kez ) 0.026 W/(m K) 8450.1 m-1 5 bar (4.9 bar) 1.1 bar (1.0 bar)

Zeolite 50 cm 5 cm 0.39 0.21 0.713 g/cm3 0.07 cm nitrogen: 0.197 s-1; oxygen: 0.62 s-1 nitrogen, oxygen; eqs 23 and 24; k1 x 103 ) 12.52, 6.705 mol/g; k2 x 105 ) -1.785, -1.435 mol/(g K); k3 x 105 ) 2.154, 3.253 atm-1; k4 ) 2,333, 1,428 K; k5 ) 1.666, -0.3169; k6 ) -245.2, 387.8 K 0.32 cal/(g K) nitrogen: -4390 cal/mol; oxygen: -3060 cal/mol estimated with kez ) 0.026 W/(m K) 4,285.7 m-1 4 bar (3.9 bar) 1.1 bar (1.0 bar)

303 K, 323 K 0.1 m/s (0.2 m/s)

293 K 0.02 m/s (0.04 m/s)

Tfeed Vfeed (Vpurge)

During the pressurization, adsorption, and purge steps, the appropriate boundary conditions on concentration are2

∂ci EZ |z)0 ) -Vf|z)0(ci|z)0- - ci|z)0) ∂z

(3a)

∂ci | )0 ∂z z)L

(3b)

PL (ci|z)0-)purge ) (ci|z)L)adsorption PH

(3c)

The boundary conditions on velocity for the pressurization, adsorption, and purge steps are, respectively,2

Vf|z)0 ) V0(P)

(4a)

Vf|z)0 ) Vfeed

(4b)

Vf|z)0 ) Vpurge

(4c)

The initial conditions for a clean bed and saturated bed, respectively, are2

ci(z,0) ) 0

(5a)

qji(z,0) ) 0

(5b)

ci(z,0) ) c0i

(5c)

qji(z,0) ) q0i

(5d)

The adsorption beds were initially clean. Thus, the beds were initially charged with 100% N2, 100% dry air (79% N2, 21% O2), and 100% O2 for the benzene-nitrogen, air-drying, and air-separation systems, respectively. The initial amount adsorbed was calculated based on the equilibrium isotherms. The assumptions for the energy balance are that radial gradients are negligible, heat transfer follows a linear driving force model, and the bed is adiabatic. The energy balance is15

FfCP,fe

∂T ∂T h* + FfCP,fp(1 - e) + FsCP,s(1 - p)(1 ∂t ∂t ∂T hs ∂(VT) ∂2T  e) + FfCP,fe - Ez,TFfCP,fe 2 ) 0 (6) ∂t ∂z ∂z

During blowdown, the appropriate boundary conditions for temperature are2

∂T | )0 ∂z z)0

(7a)

∂T | )0 ∂z z)L

(7b)

During the pressurization, adsorption, and purge steps, the appropriate boundary conditions on temperature are2

EZ,T

∂T | ) -Vf|z)0FfCp,f(T|z)0- - T|z)0) ∂z z)0

(8a)

∂T | )0 ∂z z)L

(8b)

(T|z)0-)purge ) (T|z)L)adsorption

(8c)

The initial condition for temperature is2

T(z,0) ) Tfeed

(9)

The bed temperatures were initially 363, 303 (or 323), and 293 K for the benzene-nitrogen, air-drying, and air separation systems, respectively. The transfer equations with linear driving forces written in terms of the solid phase for mass and heat transfer are12,15

∂qji ) kMTCsolid(q*i - qji) ∂t

(10)

∂Ts ∆Hads ∂q ap (T - Ts) ) hHTC ∂t Cp,fFp f Cp,f ∂t

(11)

The mass- and heat-transfer coefficients were assumed to be constant.

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Typically, the volumetric purge-to-feed ratio (γ) must be greater than 1.0 to achieve bed regeneration during purge.2,3 In this work, two values of γsγTotal and γpuresare defined:

γTotal )

Vpurge VpurgetpurgeAc Vpurgetpurge ) ) Vfeed VfeedtfeedAc Vfeedtfeed

(12)

Vpurge,pure Vpurgepuretpurgepure ) Vfeed Vfeedtfeed

(13)

γpure )

In the combination cycles, purge gas is part relatively pure product and part low-pressure feed. At the CZPSA limit, γpure ) 0, no product is used as purge, and high-pressure product recovery is at a maximum; the twobed system is decoupled, because only low-pressure feed is used as purge. In contrast, at the Skarstrom limit (γpure ) γTotal), purge is done exclusively with product, and high-pressure product recovery is at a minimum. As γpure (and γTotal) approach zero for the Skarstrom cycle, the blowdown cycle limit is reached; because there is no purge step, all desorption occurs during blowdown. The two-bed system is decoupled at the blowdown cycle limit and resembles the Basmadijan configuration for onebed systems with no purge.5 γpure can be changed by adjusting the pure purge time at constant pure purge velocity (mode 1) and by adjusting the pure purge velocity at constant pure purge time (mode 2). Mode 1 operation results in an idle period with a step time tidle in which no gas flows through the bed. As defined, γpure is effectively a measure of high-pressure product recovery: large values of γpure indicate low high-pressure product recovery and vice-versa. Thus, an inverse one-to-one correspondence exists between γpure and high-pressure product recovery. The penetration distance (ZPD) is the distance a solute wave front moves through the adsorption bed during the high-pressure adsorption step plus the pressurization with feed step, if that step is used. This distance can also be linked to a critical value of the purge-to-feed ratio.16,17 Assuming local equilibrium between the solid and gas phases and infinitely fast mass transfer, local equilibrium theory can be used to predict the penetration distance. For linear isotherms, qi ) Kci, and ZPD is16

( () )

ZPD ) Zpressurization + Zadsorption ) L - L

PH PL

-βA

+ ustfeed

e + (1 - e)p + (1 - e)(1 - p)FsRTKinert e + (1 - e)p + (1 - e)(1 - p)FsRTKi

kMTCsolid )

60 Ds dp2

(15)

For the air-drying system, which follows a linear isotherm, eqs 14 and 15 are used to calculate the penetration distance.13 This result is discussed later and compared to the actual simulation results. For nonlinear isotherms, such as those used for the benzene-nitrogen and air-separation systems, the penetration distance calculations become more complex.16,17 The extremes of short and long penetration distances for both co- and counterflow directions at varying values of γpure were investigated for the benzene-nitrogen system. In evaluating cycle performance, product purities were measured in terms of the relative concentration of more strongly adsorbing species i in the product: yi,prod/yi,feed. The high-pressure product recovery P/F1 and overall recovery, P/(F1 + F2), are

(16)

and, typically,12

E Ds ) Ds0 exp RT

( )

(17)

Yun et al.12 reported a best-fit value of Ds0 ) 3.8 × 10-4 cm2/ s, a heat of adsorption of ∆H ) 45-56 kJ/mol, and a value of E ≈ 0.45∆H for a nonpolar adsorbent, such as activated carbon. From these data, the linear lumped parameter mass-transfer coefficient based on the solid driving force (kMTCsolid) is ∼0.001 s-1 for ∆H ) 45 kJ/mol. The heat-transfer coefficient (hHTC) for the benzene-nitrogen system was reported to be 100 W/(m2 K).12 The equilibrium data7,11,12 for the benzene-nitrogen system can be fit with the Langmuir isotherm:

qi )

m(T)b(T)Pyi 1 + b(T)Pyi

(18)

where

( ) ()

m(T) ) m1 exp

m2 T

(19a)

b(T) ) b1 exp

b2 T

(19b)

(14)

where

βA )

also reported. For the concentrated system, air separation, the high-pressure product and overall product recoveries of the less strongly adsorbed oxygen are also reported (PyO2,prod/(F1yO2,feed) and PyO2,prod/[(F1 + F2)yO2,feed], respectively). Productivities were calculated based on the number of moles of the nonadsorbed (or less strongly adsorbed) component j in the high-pressure feed to the system per second per unit mass adsorbent, (tpr + tfeed)VfeedAccj,feed/(tcyclemads). All cycles that process the same feed, regardless of type, and have the same timing and the same highpressure feed velocity Vfeed will have the same productivity, and productivities for different processes can be directly compared. Benzene-Nitrogen System. For the benzene-nitrogen system, Schorck and Fair11 reported several expressions for determining the mass-transfer coefficient, kMTCsolid, based on film transfer, pore diffusion, surface sorption, and surface diffusion. They concluded that surface diffusion was the dominant masstransfer mechanism. When surface diffusion is dominant,15

The values of m1, m2, b1, and b2 are listed in Table 1. Air Drying System. For air drying with activated alumina, the overall volumetric mass-transfer coefficients (values of Ksav) were reported to be 0.2 and 1.0 kg/(m3 s) at 5.0 and 1.0 bar, respectively.13 To simplify the computations, an average value of 0.6 kg/(m3 s) was used to determine the linear lumped parameter mass-transfer coefficient based on the solid driving force (kMTCsolid), where the two coefficients are related by bed density (kMTCsolid ) Ksav/Fb). Thus, kMTCsolid ) 8.33 × 10-4 s-1. The constant heat-transfer coefficient was estimated based on the thermal conductivity (kez)18 of the gas phase (21% O2, 79% N2, 1 atm, 298 K) and the Colburn j-factor:19

hHTC ) jCp,fνfFfPr-2/3

(20)

where j ) 1.66Re-0.51 if Re < 190 and j ) 0.983Re-0.41 otherwise.

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The equilibrium data for air drying on activated alumina can be correlated with a linear isotherm:13

qi ) K(T)ci where

K ) K0 exp

{

∆Hads

R[(1/T) - (1/T0)]

(21)

}

(22)

The values of K0, T0, and ∆Hads are listed in Table 1. Ruthven et al.2 stated that the equilibrium isotherm for water vapor on activated alumina is less strongly curved than the corresponding isotherms for zeolite adsorbents, and for air of low to medium relative humidity, the isotherm is predominately linear.2 The use of this linear isotherm is justified with simulation results later in this work. Air-Separation System. For air separation, linear lumped parameter mass-transfer coefficients of 0.197 and 0.62 s-1 for nitrogen and oxygen, respectively, were reported.14 As in the air-drying system, the heat-transfer coefficient was estimated based on the thermal conductivity of the gas phase, kez,18 and the Colburn j-factor.19 The equilibrium data for air separation on 13X zeolite can be predicted by the extended Langmuir-Freundlich isotherm: 14

qi )

qmiBiPini (23)

n

1+

BjPjnj ∑ j)1

where

qm ) k1 + k2T

(24a)

B ) k3 exp

() k4 T

(24b)

ni ) k5 +

k6 T

(24c)

Euler integration with a variable step size of 0.01-5 s. The use of 100 grid points was sufficient for the dilute systems, because their solute waves moved slowly and nonlinear shocks were not severe. The dynamics inside the 102- and 100-cm adsorption beds, respectively, were accurately captured with a spacing of ∼1 grid point per centimeter. For the third model system, the bed length was 50 cm, giving a spacing of 2 grid points per centimeter. This decreased spacing was required because solute waves moved quickly and shocks were sharp, especially during nonisobaric steps. Variables that change with axial distance, such as velocity, amount adsorbed, etc., are discretized along the length of the bed and, thus, are calculated at each of the grid points. Thus, any changes in velocity due to adsorption effects are automatically included. This is especially important in gas systems, because large density changes (and, thus, velocity changes) can occur. A pressure drop (∆P ) Ptop - Pbottom) across the bed was specified. For the three systems studied in this work, a value of ∆P ) 0.1 bar gave the desired gas velocities. The pressure and velocity values used are given in Table 1. Based on the literature,12,13,20 axial dispersion effects were assumed to be negligible for all three chemical systems. This simplification decreased the computation time significantly. To justify this simplifying assumption, axial dispersion was included for air separation, which, as the most concentrated system, should have the greatest axial dispersion effects. These results, which are discussed later, show that axial dispersion was negligible. Step timing is listed in Tables 2-5. All of the processes were simulated dynamically until a cyclic steady state was attained. For the dilute systems, sometimes, thousands of cycles were required to attain a cyclic steady-state and mass-balance closure, especially at short penetration distances. The concentrated system attained a cyclic steady state much faster. Results and Discussion

Values of k1, k2, k3, k4, k5, k6, and ∆Hads are listed in Table 1. Equation 23 accurately describes the competitive adsorption of oxygen and nitrogen on zeolite 13X. Simulations ADSIM, from Aspen Technology, Inc., was used to solve the differential mass and energy balances, in conjunction with the accompanying boundary and initial conditions, the mass and energy transfer equations, and the equilibrium isotherms presented previously. The following assumptions have been made in developing the solutions: (1) Mass and heat transfer can be modeled by linear lumped parameter equations; (2) The bed is adiabatic; (3) No reactions other than adsorption occur; (4) Axial dispersion is negligible; (5) The momentum balance follows the Karman-Kozeny equation; and (6) Ideal gas behavior is assumed. ADSIM solves the governing equations directly via numerical integration, using the method of lines. For all model systems, 100 grid points, discretized by the first-order upwind differencing scheme (UDS1), were used in conjunction with implicit

Benzene-Nitrogen System. The dilute benzene-nitrogen system was chosen as a model system to determine whether the newly developed combination cycles were feasible. Because of the strongly adsorbing nature of benzene, temperatureswing7,11,12 and vacuum-swing adsorption are more commonly used techniques for benzene separation. To make PSA a moreviable separation method for our model system, we increased the feed temperature to 363 K. The conditions in Table 1 were chosen based on PSA design heuristics.2,15,17 With the base case operating conditions that have been chosen, a case study was completed to show how the combination cycles behaved under diverse operating conditions. The cycles were first examined with co-flow schemes and short penetration distances. Under this scenario, all the processes at short penetration distances used a feed step time of 14 s and achieved a value of yB,prod/yB,feed > 0.7, which is a poor result. Because of the short penetration distance, the mass-transfer zone was in the column for many cycles before it exited the product end, which caused significant spreading. A co-flow scheme with a much longer feed time (3600 s) has a long penetration distance, and the longer purge time can be used to push the mass transfer zone out of the bed more fully. The long penetration results are shown in Figure 4. The best dimensionless relative product concentration of benzene was ∼0.47. Note that the combination cycles can use significantly less product purge gas with a small purity penalty. After low purities were obtained for the co-flow processes, counter-flow schemes were studied. Figure 4 includes the long

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Figure 4. Relative concentration of benzene in nitrogen product (yB,prod/yB,feed) as a function of pure volumetric purge-to-feed ratio (γpure) at long penetration distances for co- and counter-flow schemes and purge sequences A and B. Conditions: PH ) 5 bar, PL ) 1 bar, Vfeed ) 0.3 m/s, Vpurge ) 0.6 m/s. See Table 2 for details. Table 2. Cycle Operating Conditions and Results for the Benzene-Nitrogen System at Long Penetration Distancea run

cycleb

1 2 3 4 5 6 7g 8 9 10 11g 12g 13g 14g 15g 16g 17g 18g 19 20 21 22 23 24 25 26

Skarstrom combination combination combination combination CZPSA Skarstrom combination combination combination combination combination combination CZPSA Skarstrom Skarstrom Skarstrom blowdown Skarstrom Skarstrom Skarstrom Skarstrom blowdown Skarstrom combination CZPSA

symbolc

purge sequenced

PRe

Vpurgef (m/s)

tpurge,pure (s)

tidle (s)

γpure

γTotal

yB,prod/yB,feed

yB,waste/yB,feed

P/F1

P/(F1 + F2)

) ) ) ) 0 ) + ( ( ( + + + + × × × × 4 4 4 4 4 none none none

N/A A A A B N/A N/A A A A B B B N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A B N/A

F F F F F F F F F F F F F F F F F F F F F F F P P P

0.6 0.6 0.6 0.6 0.6 0.6 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6 -0.41 -0.34 -0.23 -0.16 0.0 -0.60 -0.60 -0.60

3600 2700 1800 900 1800 0 3600 2700 1800 900 2700 1800 900 0 2700 1800 900 0 3600 3600 3600 3600 3600 3580 1790 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 900 1800 2700 3600 0 0 0 0 0 0 0 0

2.0 1.5 1.0 0.5 1.0 0.0 2.0 1.5 1.0 0.5 1.5 1.0 0.5 0.0 1.5 1.0 0.5 0.0 1.36 1.13 0.78 0.52 0.0 2.0 1.0 0.0

2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 1.5 1.0 0.5 0.0 1.36 1.13 0.78 0.52 0.0 2.0 2.0 2.0

0.47 0.52 0.56 0.59 0.53 0.62 0.29 0.37 0.44 0.51 0.32 0.39 0.46 0.54 0.47 0.62 0.81 0.99 0.48 0.55 0.65 0.73 0.99 0.29 0.39 0.54

1.70 1.72 1.75 1.80 1.80 1.85 1.94 1.95 1.95 1.95 2.02 2.04 2.05 2.02 2.13 2.35 2.54 1.99 2.21 2.35 2.84 3.18 1.99 1.90 2.04 2.02

0.57 0.67 0.78 0.89 0.80 0.99 0.57 0.67 0.78 0.89 0.67 0.78 0.89 0.99 0.67 0.78 0.89 0.99 0.70 0.75 0.84 0.89 0.99 0.56 0.78 0.99

0.57 0.60 0.63 0.66 0.63 0.69 0.57 0.60 0.63 0.66 0.60 0.63 0.66 0.69 0.68 0.78 0.89 0.99 0.70 0.75 0.84 0.89 0.99 0.56 0.63 0.69

a For all runs, t ) t ) 10 s, P ) 5 bar, P ) 1 bar, V b pr bd H L feed ) 0.3 m/s, and tfeed ) 3600 s. Refer to Figure 6 for timing schematic. Productivity for all cycles is 0.06 mol nitrogen/(kg s). c Symbols correspond with data points in Figure 4. d N/A indicates that the purge sequence is not applicable, because only one source of purge gas is used. e Note that positive and negative values of Vpurge indicate co- and counter-current flow schemes, respectively. f PR designates pressurization with feed (F) or product (P). g Data points also appear in Figures 7 and 8.

penetration distance results for the Skarstrom cycle, combination cycles, and CZPSA with different purge sequences. The operating conditions and product and waste purities are given in Table 2. Figure 4 shows that counter-flow operation of the combination cycles provides better separation than co-flow operation. This is expected because operating in the counter-

flow mode leaves the product end clean. The combination cycles using purge sequence B are more favorable than those using purge sequence A, because purging with low-pressure feed, followed by product, will leave the bed cleaner than purging in the opposite sequence. Figure 4 also shows that both modes of the Skarstrom cycle suffer a rapid loss of purity as γpure

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decreases; however, a longer purge time with smaller purge velocity (mode 2) facilitates more desorption. To obtain lower values of yB,prod/yB,feed, the penetration distance was reduced. Shortening the penetration distance required changing the feed step time to tfeed ) 14 s, making the total cycle time 48 s. Operating conditions and product and waste purities for the counter-current short penetration cycles are summarized in Table 3. The shortened penetration distance yielded higher product purities and more-concentrated waste gas (see Table 3 and Figure 5). Because commercial PSA processes use counter-flow, short penetration operation, this is expected. Another variation that is used to achieve a high-purity product is to pressurize with product instead of feed. This has the advantage of pushing the adsorption wave front farther away from the product end during counter-flow pressurization with product; however, it requires a slight change in cycle timing (see Figure 6 and Table 3). However, for this very dilute system, product purities obtained by pressurizing with product did not differ significantly from those obtained by pressurizing with feed (see Table 3, compare runs 27 and 31 vs 66 and 67). Pressurization with product also had no significance for the long penetration case (see Table 2; compare runs 7, 12, and 14 vs 24, 25, and 26). Vacuum purge was investigated to achieve lower values of yB,prod/yB,feed. Changing the purge step pressure to 0.2 bar requires that the step times be changed to accommodate time required to reach the vacuum pressure (see Figure 6 and Table 3). The blowdown step had to be increased from 10 s to 15 s, and the purge step was decreased accordingly. Figure 7 illustrates that, as expected, changing the purge pressure from 1 bar to 0.2 bar with a constant feed pressure of 5 bar yielded significant increases in product purity. To amplify the product purity even further, PH was increased from 5 bar to 10 bar with a PL value of either 1 or 0.2 bar. The timing was adjusted as shown in Table 3. For a pressure ratio of 5/1, Table 3 shows that the Skarstrom and CZPSA limits achieved products with yB,prod/ yB,feed ) 0.15 (run 27) and 0.33 (run 31), respectively. For a pressure ratio of 10/1, the Skarstrom and CZPSA limits achieved products with yB,prod/yB,feed ) 0.12 (run 46) and 0.31 (run 47), respectively. The last variable investigated to maximize product purity was feed velocity. Slowing the feed velocity allows more time for mass transfer but reduces productivity (see Table 3). The superficial feed velocity was reduced from 0.3 m/s to 0.1 m/s and the superficial purge velocity was reduced from 0.6 m/s to 0.2 m/s to maintain the same total purge-to-feed ratio of 2. The feed pressure was maintained at 10 bar and purge pressures at 1 and 0.2 bar were investigated. For the vacuum cycle, the blowdown time had to be increased from 7 s to 12 s (see Figure 6 and Table 3). Figure 5 and Table 3 show that the reduction in velocity resulted in higher purities at short penetration distances for the counter-flow scheme with purge sequence B. The best purity overall for this model system, yB,prod/yB,feed ) 0.01, was obtained with reduced velocity and vacuum purge at short penetration and counter-flow with purge sequence B (see Table 3, runs 57 and 68). Pressurization with product was also examined (see Table 3, compare runs 57 and 60 vs runs 68 and 69); however, again, the improvement was very small. The CZPSA limit achieves the most concentrated benzene waste for all cycles at the same value of γTotal (see Tables 2 and 3). The low-pressure feed used as purge gas at the CZPSA limit has an enriching effect on the waste stream, unlike the Skarstrom cycle, in which purge has a diluting effect. As the Skarstrom cycle reaches the blowdown cycle limit (γTotal ) 0.0),

yB,waste/yB,feed decreases (see Tables 2 and 3). Because purge is only accomplished by blowdown, the amount of benzene desorbed and released as waste gas is less than that if a purge step was used. Figures 4 and 5 (and Tables 2 and 3) show that the CZPSA limit performs better than the blowdown cycle limit. Both of these cycles occur at γpure ) 0.0. Thus, using lowpressure feed as purge gas is better than not using a purge step at all. Figure 4 shows that, with long penetration distances, the bed became saturated with benzene at the blowdown cycle limit, because blowdown alone cannot provide adequate bed cleanout. At short penetration distances, the blowdown and pull vacuum steps do provide some bed cleanout. Figure 7 shows the high-pressure product recovery, P/F1, and product purity for the cycles of interest. The combination cycles always achieve larger high-pressure product recoveries than the Skarstrom cycle at the same product purities. The opposite is also true: the combination cycles always achieve higher product purities at the same high-pressure product recovery. However, the purest product at a given value of γtotal is obtained at the Skarstrom cycle limit (γtotal ) γpure). Shorter penetration distances result in decreased values of P/F1, but with a purer product. For example, compare run 14 (Table 2) to run 31 (Table 3). Because shorter penetration distances require shorter cycle times, blowdown and pressurization occur more frequently than they would with long penetration distances. This increased frequency of blowdown and pressurization causes more gas to be lost to waste during these steps; thus, high-pressure product recovery is lower. Unfortunately, the high-recovery operation (long penetration distances) suffers from significantly lower purity (Figure 7). Figure 8 shows the overall product recovery, P/(F1 + F2), which includes the amount of low-pressure feed used as purge. A slightly different trend is evident here: the Skarstrom cycles have almost the same or slightly better overall product recovery than the combination cycles at the same purity. The savings realized in recovering all of the high-pressure product gas (Figure 7) comes at the expense of using a low-pressure feed to purge. For a plentiful, inexpensive, and essentially free lowpressure feed, the loss of low-pressure feed when it is used as purge gas is unimportant. Overall product recovery becomes moot and one will want to recover as much high-pressure product as possible. On the other hand, if low-pressure feed is valuable, cycles with high overall product recoveries are probably desirable. Clearly, the choice of which cycle and set of operating parameters to use is dependent on the characteristics of the separation and other factors,1 such as complexity. Because the combination and CZPSA cycles add little complexity, they are viable alternatives to the Skarstrom cycle. The combination and CZPSA cycles also maintain the productivity of the Skarstrom cycle. Overall, for the benzene-nitrogen system, the combination cycles and CZPSA cycles have higher recoveries of highpressure product than the Skarstrom cycle. Although the operating conditions shifted the product purity, the trends are the same: (i) at the same value of γpure, the combination cycles and CZPSA can obtain a product of higher purity than the Skarstrom cycle, and (ii) at the same value of γTotal, the combination cycles and CZPSA obtain higher values of P/F1 than the Skarstrom cycle but with lower product purities. The results show that the combination cycles and CZPSA can increase the high-pressure product (nitrogen) recovery, P/F1, under diverse operating conditions. These results also indicate that PSA can be an alternative to TSA and VSA for the separation of a strongly adsorbed species, such as benzene, if

9 9 9 9 9 0 0 0 0 b b b b b O O O O O none none 2 2 2 2 2 4 4 4 4 ( ( ( ( ) ) ) ) ) none none none none

symbolb

F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F P P P P

PRc 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.3 0.3 0.1 0.1

Vfeed (m/s) 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.93 0.93 0.93 0.93 0.93 0.93 0.93 0.93 0.93 0.93 0.6 0.6 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.31 0.31 0.31 0.31 0.31 0.31 0.31 0.31 0.31 3.6 3.6 2.1 2.1

Vpurge (m/s) 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 24 24 21 21

tfeed (s) 14.0 10.5 7.5 3.5 0.0 10.5 7.0 3.5 0 9.0 6.75 4.5 2.25 0.0 6.75 4.5 2.25 1.13 0 14.0 0.0 14.0 10.5 7.0 3.5 0.0 10.5 7.0 3.5 0 9.0 6.75 4.5 0.0 6.75 4.5 2.25 1.13 0 4.0 0.0 2.0 0.0

tpurge,pure (s) 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 10 10 7 7

tpr (s) 10 10 10 10 10 10 10 10 10 15 15 15 15 15 15 15 15 15 15 7 7 7 7 7 7 7 7 7 7 7 12 12 12 12 12 12 12 12 12 10 10 12 12

tbdd (s) 0 0 0 0 0 3.5 7.0 10.5 14.0 0 0 0 0 0 2.25 4.5 6.75 7.87 9.0 0 0 0 0 0 0 0 3.5 7.0 10.5 14.0 0 0 0 0 2.25 4.5 6.75 7.87 9.0 0 0 0 0

tidle (s) 2.0 1.5 1.0 0.5 0 1.5 1.0 0.5 0 2.0 1.5 1.0 0.5 0.0 1.5 1.0 0.5 0.25 0 2.0 0.0 2.0 1.5 1.0 0.5 0.0 1.5 1.0 0.5 0 2.0 1.5 1.0 0.0 1.5 1.0 0.5 0.25 0 2.0 0.0 2.0 0.0

γpure 2.0 2.0 2.0 2.0 2.0 1.5 1.0 0.5 0 2.0 2.0 2.0 2.0 2.0 1.5 1.0 0.5 0.25 0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 1.5 1.0 0.5 0 2.0 2.0 2.0 2.0 1.5 1.0 0.5 0.25 0 2.0 2.0 2.0 2.0

γTotal 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 5 5 10 10

PH (bar) 1 1 1 1 1 1 1 1 1 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 1 1 1 1 1 1 1 1 1 1 1 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 1 1 0.2 0.2

PL (bar) 0.15 0.18 0.22 0.28 0.33 0.28 0.42 0.61 0.87 0.03 0.04 0.06 0.09 0.12 0.12 0.20 0.40 0.53 0.67 0.12 0.31 0.05 0.08 0.11 0.15 0.18 0.14 0.28 0.47 0.70 0.01 0.02 0.03 0.05 0.04 0.10 0.23 0.32 0.45 0.14 0.33 0.01 0.05

yB,prod/yB,feed 1.78 1.85 1.92 1.92 1.96 1.92 2.03 2.05 1.59 3.26 3.24 3.30 3.34 3.26 3.26 3.40 3.13 2.77 2.32 1.95 2.13 1.81 1.82 1.82 1.85 1.85 1.83 1.78 1.65 1.41 2.07 2.11 2.09 2.12 2.08 2.06 1.90 1.83 1.67 1.79 1.93 2.07 2.12

yB,waste/yB,feed 0.48 0.56 0.64 0.73 0.82 0.56 0.64 0.73 0.82 0.70 0.72 0.75 0.78 0.80 0.72 0.75 0.78 0.79 0.80 0.52 0.82 0.46 0.49 0.52 0.55 0.58 0.49 0.52 0.55 0.58 0.52 0.53 0.54 0.55 0.53 0.54 0.54 0.55 0.55 0.48 0.81 0.52 0.55

P/F1 0.48 0.51 0.54 0.56 0.59 0.56 0.64 0.73 0.82 0.70 0.70 0.71 0.72 0.72 0.72 0.75 0.78 0.79 0.80 0.52 0.62 0.46 0.47 0.48 0.50 0.51 0.49 0.52 0.55 0.58 0.52 0.53 0.53 0.54 0.53 0.54 0.54 0.55 0.55 0.48 0.58 0.52 0.54

P/(F1 + F2)

0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.12 0.12 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.06 0.06 0.04 0.04

productivity (mol N2/(kg s))

Refer to Figure 6 for timing. b Symbols correspond to data points in Figures 5, 7, and 8. c Pressurization (PR) is with feed (F) or product (P). d Blowdown time; includes time to vacuum when PL ) 0.2 bar.

Skarstrom combination combination combination CZPSA Skarstrom Skarstrom Skarstrom blowdown Skarstrom combination combination combination CZPSA Skarstrom Skarstrom Skarstrom Skarstrom blowdown Skarstrom CZPSA Skarstrom combination combination combination CZPSA Skarstrom Skarstrom Skarstrom blowdown Skarstrom combination combination CZPSA Skarstrom Skarstrom Skarstrom Skarstrom blowdown Skarstrom CZPSA Skarstrom CZPSA

27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69

a

cycle

run

Table 3. Cycle Operating Conditions and Results for the Benzene-Nitrogen System at Short Penetration Distance, Counter-current Flow, and Purge Sequence Ba

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Figure 5. Relative concentration of benzene in nitrogen product (yB,prod/yB,feed) as a function of pure volumetric purge-to-feed ratio (γpure) at short penetration distances with counter-flow schemes and purge sequence B. See Table 3 for details.

Figure 6. Timing for different operating cycles. PR refers to pressurization, BD to blowdown, PV to pull vacuum, DPE to depressurization equalization, and RPE to repressurization equalization. Not to scale. Refer to Tables 2-5 for details.

higher feed temperatures are used. For the same separation of benzene, Natarajan and Wankat7 obtained values of ypure/yF on the order of 0.01 in their TSA cycles. This is comparable to the values of yB,prod/yB,feed achieved by the combination cycles with short penetration distances and high pressure ratios. Air-Drying System. The air-drying data (Table 1) and process operating conditions (Table 4) are taken from Chihara and Suzuki,13 who studied air drying via the Skarstrom cycle. Their operating conditions are assumed to be reasonable, and the Skarstrom cycle is used as the base case. High and low

pressures were set at 5 and 1 bar, respectively; vacuum purge was not used, and pressurization was with feed. The combination cycles used counter-flow with purge sequence B to obtain the highest purities possible. The superficial feed and purge velocities, 0.1 and 0.2 m/s, respectively, were relatively slow to facilitate mass transfer. A four-step cycle was used: the pressurization and blowdown steps were 10 s each, whereas the feed and purge steps were 530 s each. Because of strong adsorption and a dilute feed gas, the 530 s feed time produced a relatively short penetration distance with minimal blowdown and pressurization losses. Equations 14 and 15 were used with the air-drying data in Table 1 to calculate a theoretical ZPD ≈ 0.98 cm, which is ∼1% of the bed length. The ADSIM simulation results are shown in Figures 9 and 10 and Table 4. The Skarstrom limit (Table 4, run 1) achieves very dry air (yW,prod/yW,feed ) 2.2 × 10-4, dew point18 ≈ -71 °C) at a modest value of high-pressure product recovery (P/F1 ) 0.58). Chihara and Suzuki13 obtained a dew point of -55 °C for the nonisothermal Skarstrom cycle. The CZPSA cycle, under the same conditions (Table 4, run 3), produced air with a dew point of approximately -11 °C and P/F1 ) 0.99. A comparison of the CZPSA and blowdown cycle limits (see Figures 9 and 10 and Table 4) indicates that purge with a low-pressure feed step (the CZPSA limit) is better than no purge step at all (the blowdown cycle limit). Clearly, the Skarstrom cycle is best when very low dew points are required, despite its low recovery of high-pressure product. Based on these simulation results, one can deduce that the actual penetration distance is larger than the theoretical penetration distance of ZPD ≈ 0.98 cm. The difference between the theoretical and actual penetration distances can be attributed to finite mass-transfer rates. As illustrated by the simulation results in this work, the combination and CZPSA cycles have the added advantage of increasing the recovery of high-pressure product, which will significantly lower compression costs when products with higher dew points are acceptable.

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Figure 7. Relative concentration of benzene in nitrogen product (yB,prod/yB,feed) as a function of high-pressure product recovery (P/F1). All cycles operate counter-flow with purge sequence B and use short penetration distances unless marked. See Tables 2 and 3 for details.

Figure 8. Relative concentration of benzene in nitrogen product (yB,prod/yB,feed), as a function of overall product recovery (P/(F1 + F2)). All cycles use a short penetration distance unless marked. See Tables 2 and 3 for details.

An interesting result shown in Figure 9 is the crossoVer point. The Skarstrom cycle at a feed temperature of 303 K is able to achieve higher product purities (drier air) than the combination cycles at γpure values greater than ∼1.0. For γpure values less than ∼1.0, the Skarstrom cycle purity declines rapidly and the result is that much drier air is produced by the combination cycle at the same γpure value. Figure 10 shows corresponding trends in high-pressure product recovery. The exact location of the crossover point helps to determine the relative competitive-

ness of the combination, CZPSA, and Skarstrom cycles. To move the crossover point, the feed temperature was varied. At feed temperatures of 303, 313, and 323 K, the corresponding crossover points were located at γpure ≈ 1.0, 1.25, and 1.5, respectively (see Figures 9 and 10). Increasing the temperature causes a decrease in adsorption strength, causing yW,prod/yW,feed to increase. The results indicate that the temperature increase and concomitant decreased adsorption strength has a more drastic effect on the Skarstrom cycle than on the combination

Ind. Eng. Chem. Res., Vol. 45, No. 24, 2006 8127 Table 4. Cycle Operating Conditions and Results for the Air-Drying Systema

run

cycle

symbolb

tpurge,pure (s)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Skarstrom combination CZPSA Skarstrom combination combination combination combination CZPSA Skarstrom Skarstrom Skarstrom blowdown Skarstrom Skarstrom Skarstrom Skarstrom blowdown

9 9 9 2 2 2 2 2 2 0 0 0 0 4 4 4 4 4

530.0 265.0 0.0 530.0 463.75 397.5 265.0 132.5 0.0 397.5 265.0 132.5 0 463.75 397.5 265.0 132.5 0

tidle (s) 0 0 0 0 0 0 0 0 0 132.5 265 397.5 530 66.25 132.5 265 397.5 530

γpure γTotal 2.0 1.0 0.0 2.0 1.75 1.5 1.0 0.5 0.0 1.5 1.0 0.5 0 1.75 1.5 1.0 0.5 0

2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 1.5 1.0 0.5 0 1.75 1.5 1.0 0.5 0

feed product temperature dew productivity (K) yW,prod/yW,feed yW,waste/yW,feed P/F1 P/(F1 + F2) point (°C) (mol dry air/(kg s)) 303 303 303 323 323 323 323 323 323 303 303 303 303 323 323 323 323 323

2.2 x 10-4 0.12 0.23 0.04 0.07 0.09 0.15 0.20 0.25 0.01 0.11 0.55 0.99 0.06 0.10 0.24 0.57 0.99

2.38 2.63 2.80 2.33 2.40 2.48 2.58 2.70 2.84 3.20 4.35 4.64 1.99 2.60 2.91 3.69 4.48 1.99

0.58 0.79 0.99 0.58 0.63 0.68 0.78 0.89 0.99 0.69 0.79 0.89 0.99 0.63 0.68 0.78 0.89 0.99

0.58 0.65 0.70 0.58 0.60 0.62 0.65 0.68 0.71 0.69 0.79 0.89 0.99 0.63 0.68 0.78 0.89 0.99

-71.07 -15.97 -10.54 -24.81 -20.60 -18.31 -14.15 -11.62 -9.74 -39.46 -17.00 -2.87 2.32 -21.68 -18.07 -9.97 -2.52 2.32

0.014 0.014 0.014 0.013 0.013 0.013 0.013 0.013 0.013 0.014 0.014 0.014 0.014 0.013 0.013 0.013 0.013 0.013

a For all cases, V b feed ) 0.1 m/s, Vpurge ) 0.2 m/s, PH ) 5 bar, PL ) 1 bar, tfeed ) 530 s, tpr ) tbd ) 10 s, and pressurization with feed were used. Symbols correspond to data points in Figures 9 and 10.

Figure 9. Relative concentration of water in product dry air (yW,prod/yW,feed), as a function of pure volumetric purge-to-feed ratio (γpure) at various feed temperatures. See Table 4 for details.

cycles and CZPSA: this causes the crossover point to move to the right, toward the Skarstrom limit. Increasing the temperature even more would further shift the crossover point to the right while increasing yW,prod/yW,feed; thus, the behavior of the airdrying system approaches that of the benzene-nitrogen system. The overall recovery of dry air (P/(F1 + F2)), shown in Table 4, is essentially moot, because low-pressure humid air is essentially free and the cost associated with using it as purge is very low, because only a blower is required. However, one practical issue associated with drying air is that, depending on the relative humidity and the pressure ratio, some water may be removed as condensate after compression and cooling. Thus, the mole fraction of water in the compressed air being fed to

the process can be less than the mole fraction of water in ambient air. In these cases, there will not be a source of low-pressure feed that has the same mole fraction of water as the highpressure feed. This issue is characteristic of any system in which the vapor becomes saturated during compression. The validity of the linear isotherm was checked for the adsorption of water vapor on activated alumina. The highest concentrations of water in the bed occurred during the blowdown and purge steps, when large amounts of water desorbed and were purged from the system as waste. The most concentrated waste had a value of yW,waste/yW,feed ) 4.64 (see Table 4, run 12). This amounted to a water concentration of ∼0.02 mole fraction, which had a relative humidity of ∼43% at 303 K and

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Figure 10. Relative concentration of water in product dry air (yW,prod/yW,feed), as a function of high-pressure product recovery (P/F1) at various feed temperatures. See Table 4 for details. Table 5. Cycle Operating Conditions and Results for the Air-Separation Systema run

cycleb

symbolc

tpurge,pure (s)

tidle (s)

1 2 3 4 5 6 7 8 9 10

Skarstrom combination combination combination CZPSA Skarstrom Skarstrom Skarstrom Skarstrom blowdown

2 2 2 2 2 4 4 4 4 4

10.0 7.5 5.0 2.5 0.0 7.5 5.0 2.5 1.25 0

0 0 0 0 0 2.5 5 7.5 8.75 10

b

γpure γTotal yN,prod/yN,feed yN,waste/yN,feed P/F1 P/(F1 + F2) PyO,prod/F1yO,feed PyO,prod/ (F1 + F2)yO,feed 2.0 1.5 1.0 0.5 0.0 1.5 1.0 0.5 0.25 0

2.0 2.0 2.0 2.0 2.0 1.5 1.0 0.5 0.25 0

0.15 0.19 0.23 0.29 0.36 0.23 0.30 0.39 0.45 0.52

1.11 1.12 1.14 1.16 1.16 1.12 1.13 1.14 1.15 1.14

0.11 0.13 0.16 0.19 0.23 0.13 0.16 0.19 0.21 0.23

0.11 0.13 0.15 0.18 0.20 0.13 0.16 0.19 0.21 0.23

0.46 0.53 0.62 0.70 0.78 0.51 0.58 0.63 0.64 0.65

0.46 0.53 0.58 0.66 0.68 0.51 0.58 0.63 0.64 0.65

a For all cases, V feed ) 0.02 m/s, Vpurge ) 0.04 m/s, PH ) 4 bar, PL ) 1 bar, tfeed ) 10 s, tpr ) tbd ) 4 s, tdpe) trpe ) 4 s. Entering air is bone dry. Productivity for all cycles is 0.0008 mol oxygen/(kg s). c Symbols correspond to data points in Figures 11-13.

atmospheric pressure.18 This relative humidity is within the linear range of the isotherm of activated alumina, as shown by Ruthven et al.2 Thus, the use of a linear isotherm is acceptable for our simulations. For air drying, the combination and CZPSA cycles can increase the recovery of high-pressure dry air product (P/F1) at the cost of the product being less dry. The productivity of the Skarstrom cycle is also maintained in the combination and CZPSA cycles. Based on the robustness of the combination cycles illustrated in the benzene-nitrogen case study, one can conclude that the combination and CZPSA cycles should behave favorably under operating conditions that differ from the literature-based13 operating conditions used here. Air-Separation System. The air separation data (see Table 1) and process operating conditions (given in Table 5) are taken from Jee et al.,14 who studied air separation using the six-step Skarstrom cycle with pressure equalization. Therefore, for the purposes of this work, the operating conditions used by Jee et al.14 are assumed to be reasonable. The six-step Skarstrom cycle with pressure equalization is used as the base case for comparison to the combination cycles and CZPSA developed in this work. In this cycle, after the adsorption step of bed 1

(purge step of bed 2), the feed to bed 1 is turned off and the product ends of both beds are connected; bed 1 is partially depressurized co-flow and bed 2 is partially pressurized counterflow. Blowdown and pressurization with feed steps accomplish the remainder of the pressure changes. This cycle is common in commercial practice, because the pressure equalization steps significantly improve product recovery.2 Modest pressures were used: the feed was at 4 bar with purge at 1 bar. The feed gas was bone dry. Relatively slow superficial feed and purge velocities of 0.02 and 0.04 m/s, respectively, were used to facilitate mass transfer. The feed step occurred for 10 s, followed by a 4-s pressure equalization step, and a 4-s blowdown to 1 bar. The other half of the cycle consisted of a 10-s purge step, pressure equalization for 4 s, and pressurization with feed for 4 s. For this concentrated system, there was extensive solute movement during the feed step and pressurization with feed. This made the penetration distance fairly long. However, the counter-flow pressure equalization step kept the solute wave sufficiently far from the end of the column, to prevent breakthrough. The counter-flow scheme with purge sequence B was used to obtain the highest purities possible.

Ind. Eng. Chem. Res., Vol. 45, No. 24, 2006 8129

Figure 11. Relative concentration of nitrogen in product oxygen (yN,prod/yN,feed), as a function of pure volumetric purge-to-feed ratio (γpure). See Table 5 for details.

Figure 12. Relative concentration of nitrogen in product oxygen (yN,prod/yN,feed), as a function of high-pressure product recovery (P/F1). See Table 5 for details.

The results are shown in Figures 11 and 12 and in Table 5. The Skarstrom limit (see Table 5, run 1) achieved the purest oxygen-enriched air (yN,prod/yN,feed ) 0.15; ∼88% O2) at a highpressure product recovery of P/F1 ) 0.11, and a recovery of the high-pressure oxygen of PyO,prod/F1yO,feed ) 0.46. The

CZPSA limit produced oxygen-enriched air at yN,prod/yN,feed ) 0.36 (∼72% O2), P/F1 ) 0.23, and a recovery of the highpressure oxygen of PyO,prod/F1yO,feed ) 0.78. The combination cycles performed between these limits. Figures 11 and 12 (and Table 5) also show that the CZPSA limit again performs better

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Figure 13. Relative concentration of nitrogen in product oxygen (yN,prod/yN,feed) as a function of high-pressure product recovery of oxygen (PyO,prod/F1yO,feed). See Table 5 for details.

than the blowdown cycle limit. From these results, the Skarstrom cycle is best when high-purity oxygen product is required, despite its low recovery of high-pressure oxygen product. When lower oxygen product purities are acceptable, the combination and CZPSA cycles will increase the recovery of high-pressure oxygen product and, thus, have lower compression costs, which might make the combination and CZPSA cycles competitive with membranes and other PSA cycles.21 Figure 13 and Table 5 show the recovery of high-pressure oxygen. The Skarstrom cycle achieved ∼88% O2 recovery with PyO,prod/F1yO,feed ) 0.46. This is comparable to the findings of Jee et al.,14 which reported that the Skarstrom cycle achieved ∼90% O2 recovery at PyO,prod/F1yO,feed ) 0.50. On the other end of the purity-recovery spectrum, CZPSA achieved ∼72% O2 recovery with PyO,prod/F1yO,feed ) 0.78. Figure 13 is more similar to Figures 7 and 10 than Figure 12 is, because Figure 13 adjusts for the product gas (oxygen) not being the major component of the feed gas (as was the case in the dilute systems). Table 5 also lists two overall recoveries: the overall highpressure product recovery, P/(F1 + F2), and the overall oxygen recovery, (PyO,prod)/(F1 + F2)yO,feed. Figure 14 shows the overall oxygen recovery results. Comparing Figures 13 and 14, one can see that, because low-pressure air is used as purge, the overall recoveries of oxygen are less than the high-pressure product recoveries of oxygen. As with air drying, the overall recoveries are moot, because low-pressure air is essentially free and the cost associated with using it as purge is low, because only a blower is required. However, in most practical applications, the high- and low-pressure feeds will contain water. These feed streams must be dried before they are fed to the zeolite 13X beds. To dry the high-pressure feed, desiccant layers should be added to the feed ends of both zeolite 13X beds; also, a desiccant bed should be put in place to supply low-pressure

dry air to the zeolite 13X beds for use as purge gas. Somewhat complicated flow arrangements may be required to purge the desiccant bed used to dry the feed of low-pressure air.9 The commonly made assumption of negligible axial dispersion12,13,20 was examined for air separation. The Edwards and Richardson correlation22 for axial dispersion of gases in packed beds was used to calculate the axial dispersion coefficient, Ez. Based on the molecular diffusivities of oxygen and nitrogen as calculated from the Chapman-Enskog equation19 at an average pressure of 2.5 bar, an average interstitial velocity of 0.077 cm/ s, a particle radius of 0.07 cm, and a temperature of 293 K, the average value of the axial dispersion coefficient was determined to be 0.37 cm2/s. Two simulations (runs 11 and 12) were completed, and the results are shown in Table 6. Comparing the runs that included axial dispersion effects (see Table 6, runs 11 and 12) to the corresponding runs that neglected axial dispersion effects (see Table 6, runs 1 and 5), it is clear that there are no significant effects of axial dispersion for these conditions. Differences in the results were detected in the third decimal place, which is not significant, compared to the numerical accuracy of the simulations. Thus, the assumption of negligible axial dispersion is justified. For air separation, the combination and CZPSA cycles increase the high-pressure product recovery (P/F1) and, therefore, the high-pressure oxygen product recovery (PyO,prod/ F1yO,feed) at the cost of lower oxygen product purity. The combination and CZPSA cycles also maintain the productivity of the Skarstrom cycle. As with the air drying system, one can conclude that the combination cycles and CZPSA should behave favorably under operating conditions that differ from the literature-based14 operating conditions used here. This conclusion is based on the robustness of the combination cycles illustrated in the benzene-nitrogen case study.

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Figure 14. Relative concentration of nitrogen in product oxygen (yN,prod/yN,feed), as a function of overall product recovery of oxygen (PyO,prod/(F1 + F2)yO,feed). See Table 5 for details.

Table 6. Cycle Operating Conditions and Results for the Air-Separation System with and without Axial Dispersion Effectsa run

cycleb

Ez (cm2/s)

tpurge,pure (s)

tidle (s)

γpure

γTotal

yN,prod/yN,feed

yN,waste/yN,feed

P/F1

P/(F1 + F2)

PyO,prod/F1yO,feed

PyO,prod/(F1 + F2)yO,feed

1 5 11 12

Skarstrom CZPSA Skarstrom CZPSA

0.0 0.0 0.37 0.37

10.0 0.0 10.0 0.0

0 0 0 0

2.0 0.0 2.0 0.0

2.0 2.0 2.0 2.0

0.15 0.36 0.16 0.35

1.11 1.16 1.12 1.15

0.11 0.23 0.11 0.23

0.11 0.20 0.11 0.20

0.46 0.78 0.46 0.79

0.46 0.68 0.46 0.69

b

a For all cases, V feed ) 0.02 m/s, Vpurge ) 0.04 m/s, PH ) 4 bar, PL ) 1 bar, tfeed ) 10 s, tpr ) tbd ) 4 s, tdpe) trpe ) 4 s. Entering air is bone dry. Productivity for all cycles is 0.0008 mol oxygen/(kg s).

Conclusions The combination pressure-swing adsorption (PSA) cycles and cycling-zone pressure-swing adsorption (CZPSA) use lowpressure feed as part or all of the purge gas. The results for the benzene-nitrogen system indicated that the best operating conditions use a counter-flow purge that consists of low-pressure feed, followed by product gas. Short penetration distances and large pressure ratios were also favorable. For this very dilute system, pressurization with feed and product were essentially identical. Blowdown and pressurization reduced the highpressure product recoveries with short penetration distances but had little effect on the long penetration distance runs. The results for air drying indicated that the feed temperature controlled the crossover point of the Skarstrom and combination cycles. The results for air separation using cycles with pressure equalization showed that the combination and CZPSA cycles are also applicable for concentrated gas separations. The CZPSA cycle performed better than a cycle with blowdown but no purge step. Compared to the Skarstrom cycle, the combination and CZPSA cycles increased the recoveries of high-pressure product while maintaining the productivity. Thus, these cycles are viable high-recovery alternatives when lower product purities are acceptable. For all three model systems, the combination cycles

and CZPSA have larger high-pressure product recoveries but lower product purities than the Skarstrom cycle at the same total purge-to-feed ratio (γTotal), and the combination cycles (and CZPSA limit) can achieve higher product purities than the Skarstrom cycle (and blowdown cycle limit) at the same pure purge-to-feed ratio (γpure). Acknowledgment The authors gratefully acknowledge Dr. Andrew Stawarz (Aspen Technology, Inc.) for his technical support, Dr. JeungKun Kim for his assistance with ADSIM, and the National Science Foundation (through Grant No. CTS-0327089) for providing part of the funding for this research. Nomenclature ap ) external surface area per volume (m2/m3) b ) isotherm parameter B ) extended Langmuir-Freundlich isotherm parameter (atm-1) ci ) concentration of solute i in fluid (kmol/m3) cji,pore ) average concentration of solute i in pore cf ) concentration (or molar density) of feed (mol/m3) Cp,f ) fluid-phase heat capacity (J/(kg K))

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Cp,s ) solid-phase heat capacity (J/(kg K)) dp ) particle diameter (cm) Ds ) surface diffusion coefficient (cm2/s) DS0 ) reference value of surface diffusion coefficient (cm2/s) ∆Hads ) heat of adsorption (kJ/kmol) E ) activation energy (kJ/mol) Ez ) axial dispersion coefficient (cm2/s) Ez,T ) thermal axial dispersion coefficient (cm2/s) F1 ) high-pressure feed (mol) F2 ) low-pressure feed (mol) hHTC ) heat-transfer coefficient (W/(m2 K)) j ) j-factor for calculating the heat-transfer coefficient in eq 20 kj ) extended Langmuir-Freundlich isotherm parameters K) linear isotherm parameter Ki ) equilibrium constant for species i Kinert ) equilibrium constant for inert species Kdi ) fraction of the interparticle volume that species i can penetrate kez ) thermal conductivity of gas phase (W/(m K)) kMTCsolid ) linear lumped parameter mass-transfer coefficient (m/ s) Ksav ) overall volumetric mass-transfer coefficient (kg/(m3 s)) L ) bed length (m) m ) isotherm parameter mads ) mass of adsorbent in bed (kg) n ) extended Langmuir-Freundlich isotherm parameter P ) high-pressure product (mol) P/F1 ) high-pressure product recovery P/(F1 + F2) ) overall product recovery Pyj,prod/F1yj,feed ) high-pressure product recovery of the less strongly adsorbed species j Pyj,prod/((F1 + F2)yj,feed) ) overall product recovery of the less strongly adsorbed species j PH ) high (feed) pressure (bar) PL ) low (purge) pressure (bar) Pr ) Prandtl number; Pr ) µCp,f/kez Pyi ) partial pressure of species i (bar) Re ) Reynolds number; Re ) 2rpFfνf/µ qi ) amount of solute i adsorbed (kmol/kg adsorbent) qj ) average amount of solute adsorbed q*i ) equilibrium amount adsorbed of species i qi ) amount of solute i adsorbed (kmol/kg adsorbent) qi ) average amount of solute i adsorbed qm ) extended Langmuir-Freundlich isotherm parameter (g/ mol) R ) universal gas constant t ) time (s) tbd ) time of blowdown step (s) tcycle ) total cycle time (s) tdpe ) time of depressurization equalization step (s) tfeed ) time of feed step (s) tpr ) time of pressurization step (s) tpurge ) time of purge step (s) tpurge,pure ) time of purge step using pure product gas (s) trpe ) time of repressurization equalization step (s) T ) temperature (K) T* ) average equilibrium temperature (K) Ts ) solid-phase temperature (K) Ts ) average solid-phase temperature (K) us ) solute velocity (m/s) Vf ) bulk fluid velocity (m/s) Vfeed ) superficial velocity of feed stream (m/s) Vpurge ) superficial velocity of purge stream (m/s)

Vpurge,pure ) superficial velocity of purge stream of pure product gas (m/s) Vfeed ) volume of feed gas processed per cycle (m3) Vpurge ) volume of purge gas processed per cycle (m3) yi ) mole fraction of solute i yi,prod/yi,feed ) dimensionless relative concentration of adsorbing species i in the product yi,waste/yi,feed ) dimensionless relative concentration of adsorbing species i in the waste z ) axial distance (m) Zadsorption ) axial distance moved during adsorption step (m) Zpressurization ) axial distance moved during pressurization step (m) ZPD ) penetration distance (m) Greek Symbols βA ) solute movement parameter for species A defined in eq 15 e ) external porosity (m3 void/m3 bed) p ) internal porosity (m3 pore/m3 particle) µ ) viscosity (N s/m2) γ ) general (or total) purge-to-feed ratio defined in eq 12 γpure ) purge-to-feed ratio, using pure product purge gas, as defined in eq 13 γTotal ) maximum value of purge-to-feed ratio, using pure product purge gas Fb ) bed density (g/cm3) Fs ) solid-phase density (kg/m3) Ff ) fluid phase density (kg/m3) Literature Cited (1) Seader, J. D.; Henley, E. J. Separation Process Principles; Wiley: New York, 1998. (2) Ruthven, D. M.; Farooq, S.; Knaebel, K. Pressure Swing Adsorption; Wiley: New York, 1994. (3) Skarstrom, C. W. Use of Adsorption Phenomena in Automatic PlantType Gas Analyzers. Ann. N. Y. Acad. Sci. 1959, 72 (13), 751. (4) Skarstrom, C. W. Oxygen Concentration Process. U.S. Pat. No. 3,237,377, 1966. (5) Tondeur, D.; Wankat, P. C. Gas Purification by Pressure Swing Adsorption. Separ. Purif. Methods 1985, 14 (2), 157. (6) Babicki, M.; Hall, A. PSA Technology Hits the Fast Lane. Chem. Process. 2003, 66 (8), 39. (7) Natarajan, G.; Wankat, P. C. Thermal-Adsorptive Concentration. Adsorption 2003, 9, 67. (8) Natarajan, G. Thermal-Adsorptive Concentration. M.S. Ch.E. Thesis, Purdue University, West Lafayette, IN, 2001. (9) Wankat, P. C. Feed Purge Cycles in Pressure Swing Adsorption. Sep. Sci. Technol. 1993, 28 (17&18), 2567. (10) Wankat, P. C.; Dore, J. C.; Nelson, W. C. Cycling Zone Separations. Separ. Purif. Methods 1975, 4 (2), 215. (11) Schork, J. M.; Fair, J. R. Parametric Analysis of Thermal Regeneration of Adsorption Beds. Ind. Eng. Chem. Res. 1988, 27, 457. (12) Yun, J.-H.; Choi, D.-K.; Moon, H. Benzene Adsorption and Hot Purge Regeneration in Activated Carbon Beds. Chem. Eng. Sci. 2000, 55, 5857. (13) Chihara, K.; Suzuki, M. Simulation of Nonisothermal Pressure Swing Adsorption. J. Chem. Eng. Jpn. 1983, 16 (1), 53. (14) Jee, J.-G.; Lee, J.-S.; Lee, C.-H. Air Separation by a Small-Scale Two-Bed Medical O2 Pressure Swing Adsorption. Ind. Eng. Chem. Res. 2001, 40, 3647. (15) Wankat, P. C. Rate-Controlled Separations; Kluwer: Amsterdam, 1990; Chapters 6 and 8. (16) Chan, Y. N. I.; Hill, F. B.; Wong, Y. W. Equilibrium Theory of a Pressure Swing Adsorption Process. Chem. Eng. Sci. 1981, 36, 243. (17) Yang, R. T. Gas Separation by Adsorption Processes; Imperial College Press: London, 1997; Chapter 8. (18) Perry, R. H.; Green, D. W.; Maloney, J. O. Perry’s Chemical Engineers’ Handbook, 6th Edition; McGraw-Hill: New York, 1984; Sections 3 and 12.

Ind. Eng. Chem. Res., Vol. 45, No. 24, 2006 8133 (19) Bird, R. B.; Stewart, W. E.; Lightfoot, E. N. Transport Phenomena; Wiley: New York, 1960; Chapter 21. (20) Kumar, R.; Dissinger, G. R. Nonequilibrium, Nonisothermal Desorption of Single Adsorbate by Purge. Ind. Eng. Chem. Process Des. DeV. 1986, 25, 456. (21) Sircar, S.; Kratz, W. C. A Pressure Swing Adsorption Process for Production of 23-50% Oxygen-Enriched Air. Sep. Sci. Technol. 1988, 23 (4&5), 437.

(22) Ruthven, D. M. Principles of Adsorption and Adsorption Processes; Wiley: New York, 1984; Chapter 7.

ReceiVed for reView May 5, 2006 ReVised manuscript receiVed September 5, 2006 Accepted September 18, 2006 IE060566H