New Vacuum Swing Adsorption Cycles for Air Purification with the

Simple equilibrium theory-based formulations were derived and used to investigate the feasibility of complete cleanup in and compare the performances ...
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Ind. Eng. Chem. Res. 1998, 37, 1970-1976

New Vacuum Swing Adsorption Cycles for Air Purification with the Feasibility of Complete Cleanup James A. Ritter,* Yujun Liu, and Dharmashankar Subramanian Department of Chemical Engineering, Swearingen Engineering Center, University of South Carolina, Columbia, South Carolina 29208

Simple equilibrium theory-based formulations were derived and used to investigate the feasibility of complete cleanup in and compare the performances of pressure swing adsorption (PSA) and vacuum swing adsorption (VSA) air purification processes. Three representative contaminants were investigated (dimethyl methylphosphonate, benzene, and butane), all on activated carbon. For these systems, complete cleanup during every cycle was always possible in a VSA process; and it was also possible in a PSA process, but only for the two less strongly adsorbed systems and only when their feed mole fractions were less than some specific value. Otherwise, a subatmospheric purge pressure was required by PSA no matter how high the feed pressure. The pressure ratio required for complete cleanup by PSA was generally several times higher than that required by VSA for the same feed mole fraction, except for the two less strongly adsorbed systems at very low feed mole fractions. For VSA and PSA processes with incomplete cleanup, VSA processed more feed than PSA; this advantage became more pronounced with stronger adsorbates and higher feed concentrations. The superiority of VSA over PSA also became more pronounced with higher pressure ratios and lower purge-to-feed ratios. Introduction There has been a great deal of interest recently in the design and development of pressure swing adsorption-air purification (PSA-AP) systems (Ritter and Yang, 1991a,b; White, 1988; White and Barkley, 1989; Friday et al., 1993; Mahle et al., 1996), especially for use in chemical defense systems where specific concerns have been raised pertaining to the residual contaminants that remain in PSA-AP beds (Tevault, 1995). This so-called “heel” within the beds is characteristic of PSA processes, since PSA beds are never meant to be completely regenerated. What this means is that PSA-AP systems used in defense applications would continuously desorb contaminant vapors from the beds even after the contaminant is no longer being exposed to them. This makes it rather difficult for a military vehicle to return to the base, for example, after being exposed to the contaminant vapor in the field, because toxic vapors would be continuously desorbed from the AP system as long as it is operating; this desorption could persist for some time. Even if the AP system is turned off, a significant amount of contaminant vapor would still remain in the beds, which is undesirable for many obvious reasons. For example, special protective equipment and facilities would be required for personnel to service the vehicle. Thus, the objective of this communication is to introduce new vacuum swing adsorption (VSA) cycles for AP that augment the desorption of strongly adsorbed contaminants, including the possibility of complete regeneration of the beds during every cycle. Several advantages of these new VSA-AP cycles over conventional PSA-AP cycles are revealed using simple expressions derived from nonlinear wave propagation * To whom correspondence should be addressed. Phone: (803) 777-3590. Fax: (803) 777-8265. E-mail: Ritter@ sun.che.sc.edu.

theory. The first case considered is that of finding and contrasting VSA and PSA cycle conditions for complete cleanup of the beds during every cycle. The second case considered is that of comparing the performance of conventional PSA-AP cycles with new VSA-AP cycles, both with incomplete cleanup. The purpose of this second case is to emphasize the superiority of VSA cycles over PSA cycles even when complete cleanup is not desired. Theory LeVan (1995) used physical arguments to develop an equilibrium theory for purification and enrichment by PSA, where closed form expressions were obtained for the direct determination of the periodic state. Using nonlinear wave propagation theory, Subramanian and Ritter (1997) further extended LeVan’s theory and obtained analytic expressions for the PSA process performance, such as the heavy component enrichment, and the solvent vapor recovery and light product impurity when breakthrough occurred. The analytic results of Subramanian and Ritter (1997), in terms of the characteristic invariant nomenclature, are adopted here to determine the condition for complete cleanup of the adsorption column during the purge step of every cycle. This relation is then used to investigate the feasibility of complete cleanup in PSA and VSA processes. These expressions are also used to compare the performance of PSA and VSA processes when complete cleanup is not desired. The system considered consists of the purification of a nonadsorbing carrier gas containing a small concentration of an adsorbing impurity (contaminant). A fourstep, Skarstrom-type cycle with cocurrent high-pressure feed, countercurrent blowdown, countercurrent purge and countercurrent light product pressurization is considered, but with adoption of the frozen solid-phase assumption which allows the pressure transient steps

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Ind. Eng. Chem. Res., Vol. 37, No. 5, 1998 1971

to be omitted. In other words, the concentration profiles in the gas and solid phases do not change during the pressurization and blowdown steps (Ritter and Yang, 1991a,b). This reduces the analysis to a two-step VSA or PSA process, composed only of feed and purge steps, similar to LeVan (1995) and Subramanian and Ritter (1997). Other usual assumptions involved in the development of the equilibrium theory include isothermal operation, no axial dispersion, no axial pressure gradients, and instantaneous local equilibrium. The low mole fraction of the adsorbing impurity permits velocity changes in the column to be neglected (Subramanian and Ritter, 1998). High partition ratios between the solid and bulk phases allow the rate of accumulation of the adsorbing species in the gas phase to be neglected with respect to the rate of adsorption. The countercurrent purge is done by pure carrier gas, which emanates from an adjacent bed during the high-pressure adsorption step. A detailed development of the equilibrium theory and analytic expressions for the periodic state process performance have been given elsewhere (Subramanian and Ritter, 1997). Only the results that are necessary to facilitate the forthcoming discussions are presented below. The dimensionless periodic penetration of the contaminant vapor concentration wave, ζa, was derived by Subramanian and Ritter (1997) as

ζa )

(1 - R)(γV - 1) + γV - 2x(1 - R)(γV - 1)γV (1) R

q)

(2)

with L defined as

L)

vtf qf Fb cf

()

(3)

a(c* i) )

q*i )

c* i R + (1 - R)c* i

(4)

where

q*i )

qi qf

(5)

c*i )

ci cf

(6)

A one-to-one correspondence exists between the constant separation factor isotherm (eq 4) and the Langmuir adsorption isotherm through

1 1 + bPHyf

with the Langmuir isotherm given by

(7)

(9)

is invoked. The characteristic invariant that reaches the exit of the bed (ζ ) 0) during the purge step is expressed as (Subramanian and Ritter, 1997)

a* ) -

x

γV ζaR

(10)

where the condition for complete cleanup in the purge step requires that

a* ) a(c* i ) 0)

(11)

Applying eqs 9, 10, and 1 to eq 11 leads to a quadratic in the volumetric purge-to-feed ratio, γV. Solving this quadratic leads to the γV required for complete cleanup as

γVc )

1 R

(12)

which is the physically relevant root beyond which purging becomes irrelevant. Equation 12 is readily adapted to yield the critical pressure ratio, Rc, that must be applied in the process to affect complete cleanup in terms of the actual (or molar) purge-to-feed ratio, γM, as

1 γ R

(13)

γV ) γMR

(14)

M

by noting that

where R is the pressure ratio (R ) PH/PL). According to the definition of R (eq 7), eq 13 becomes

Rc )

R)

1 (c* i R - R - c* i)

Rc )

which is the penetration of the shock wave in the very first feed step. The constant separation factor isotherm is given by

(8)

For favorable Langmuir adsorption isotherms, the range of R is restricted to 0 < R < 1.0. To determine the process conditions required for complete cleanup of the bed at the end of the purge step, the characteristic invariant defined by Subramanian and Ritter (1997) as

where the subscript on ζ indicates a periodic state variable. ζ is given by

ζ ) z/L

qSbPy 1 + bPy

(1 + bPHyf) γM

(15)

For the case of incomplete cleanup, the above development is also used to readily compare the performance of VSA with PSA under similar process conditions. Clearly, any one of the process or bed dimension parameters is determinable using eqs 1-8 if all of the other parameters are known. For example, for a given system of known bed dimensions (Lb and db) and adsorption isotherm (b and qs), the volumetric feed flow rate for a selected periodic bed penetration, La, is calculated using the following procedure. First, the ideal gas law is used to calculate cf from the known yf, PH, and T. Then eq 8 is used to calculate qf and eq 7 is used to calculate R. Now, eq 1 is used to calculate ζa in terms of the calculated R and a selected purge-to-feed

1972 Ind. Eng. Chem. Res., Vol. 37, No. 5, 1998

ratio, γV; eq 2 is used to calculate L, noting that z ) La and ζ ) ζa. Once L is obtained, the superficial feed velocity, v, is calculated from eq 3 from the selected feed step time, tf. Finally, the volumetric feed flow rate at STP is calculated using the ideal gas law, in terms of the bed dimensions and PH. However, it must be pointed out that physically unrealistic results may be obtained for the incomplete cleanup case, depending on the process conditions. Physically unrealistic results may occur when a chosen set of process conditions does not satisfy the requirement of incomplete cleanup. In other words, the process conditions result in an over-regeneration of the column during the specified purge step duration, where complete cleanup occurs before the end of the purge step. These mathematically correct but physically unrealistic results occur with these analytic expressions because the mass balance is inherently satisfied. These anomalous results are not a concern, however, because they are readily identified by analyzing the adsorbed-phase concentration profiles at the end of the purge step, as outlined below. The periodic adsorbed phase concentration profile at the end of the adsorption step is simply a shock wave that covers the bed from ζ ) 0 to ζ ) ζa. The adsorbedphase concentration profile at the end of the purge step is an expansive wave (heel). This heel extends from the bed entrance to a certain position ζ ) ζ0, where ζ0 is the dimensionless axial position reached by the dimensionless concentration c* i ) 0 (and thus q* i ) 0) when it travels countercurrentlly. The adsorbed-phase concentration profile at the end of the purge step is obtained from (Liu et al., 1998)

q* i )

ζ - ζa + xγVR(ζa - ζ) (1 - R)(ζ - ζa)

(16)

Table 1. Bed Characteristics and Process Conditions Used in the VSA-AP and PSA (or PVSA)-AP Processes a. Bed Characteristics bed length, Lb (m) bed diameter, db (m) bulk adsorbent density, Fb (kg/ m3)

b. Process Conditions for Investigating the Feasibility of Complete Cleanup feed pressure, PH (kPa) PSA 506.5 VSA 101.3 operating temperature, T (K) 298.15 M molar purge-to-feed ratio, γ 0.5 La/Lb 0.6 feed mole fraction, yf (ppm) varieda c. Process Conditions for VSA and PSA with Incomplete Cleanup PH of VSA and PL of PSA (kPa) 101.3 feed step time, ta (min) 8 purge step time, tp (min) 8 molar purge-to-feed ratio, γM varieda La/Lb 0.6 feed mole fraction, yf (ppm) varieda pressure ratio, R varieda a

Refer to Figures 2, 3, 4, or 5.

any PSA model constrains the pressure ratio that can be employed for a given feed mole fraction or vice versa, as argued by Subramanian and Ritter (1997). For the case of complete cleanup, this feature limits the applicability of the equilibrium theory-based analytic expressions to feed mole fractions constrained by

yf e

ζ0 ) ζa - RγV

(17)

The corresponding gas-phase concentration profile is obtained from eq 16 through the adsorption isotherm. The physically unrealistic results are indicated by a negative expansive wave starting position (ζ0) and negative adsorbed-phase concentrations. Therefore, according to eq 17, the following inequality must be satisfied to obtain physically realistic results:

RγV < ζa

(18)

Once a set of process conditions are chosen, eq 18 is used to ensure that they represent physically meaningful results. Another possibility of obtaining physically impossible results also exists, but only when the analytic expressions are used to design PSA processes (e.g., they may occur in the determination of the bed dimensions for a certain set of process conditions and specified process performance (Liu et al., 1998)). In this case, the unrealistic results are indicated when some of the adsorbed-phase concentrations exceed the adsorbedphase concentration corresponding to the feed condition. These anomalous concentrations can also be identified by examining the bed profiles given by eqs 16 and 17, as shown by Liu et al. (1998). It must also be pointed out that the frozen solid-phase assumption applied to the pressure transient steps in

γM (1 + bPHyf)

(19)

which upon solution gives

e ymax f

and ζ0 is given by

0.25 0.052 517.97

x1 + 4bPHγM - 1 2bPH

(20)

This again is the physically relevant root. For the case of incomplete cleanup, Subramanian and Ritter (1997) showed that

e ymax f

1 R

(21)

Results and Discussion Three air purification systems were chosen to study the feasibility of complete cleanup in VSA and PSA processes and to compare the performance of VSA and PSA processes with incomplete cleanup. The dimethyl methylphosphonate (DMMP)-BPL activated carbon, benzene-Westvaco BAX activated carbon, and butaneWestvaco BAX activated carbon systems were chosen for this purpose; they are representative of AP processes having significantly different levels of affinities between the contaminant vapors and the adsorbent. The magnitudes of the affinities decrease in the following order: DMMP > benzene > butane. The contaminant vapor concentration levels, physical characteristics of the column, and AP process conditions were similar to those used by Friday et al. (1993); the operating temperature was set at 298.15 K. All of this information is tabulated in Table 1. The adsorption isotherm for DMMP on BPL activated carbon was taken from Ritter (1989), and the adsorption

Ind. Eng. Chem. Res., Vol. 37, No. 5, 1998 1973 Table 2. Adsorption Isotherm Parameters Used in the VSA-AP and PSA (or PVSA)-AP Processes and AREa Values system

DMMP-BPL carbon

benzene-BAX carbon

butane-BAX carbon

b (kPa-1) qs (mol/kg) ARE (%)

8732.1 3.83 7.51

438.3 1.24 15.30

29.5 0.89 17.20

a

Defined by eq 22.

Figure 1. Low-pressure adsorption isotherms of DMMP on BPL activated carbon (Ritter, 1989), benzene, and butane on BAX activated carbon (Tolles, 1996). Symbols are experimental data, curves are Langmuir model correlations, and the arrows point to the Henry’s law constants.

isotherms for benzene and butane on BAX activated carbon were provided by the Westvaco Charleston Research Center (Tolles, 1996). Since the simple equilibrium theory was developed exclusively for the two parameter Langmuir model, which does not fit isotherm data very well over broad pressure ranges, only the lowpressure data that adequately covered the concentration ranges of interest were used to regress the Langmuir isotherm parameters. The resulting best fit values of these parameters are given in Table 2, along with the absolute relative errors (ARE) defined as

ARE% )

100 N N

∑ i)1

(

abs

)

qexp,i - qcal,i qexp,i

(22)

Figure 1 compares the model predictions with the experimental data for all three systems. The Langmuir model correlated well with the subsets of the experimental data, especially when considering that the limited pressure ranges still spanned 3-5 orders of magnitude. Feasibility of Complete Cleanup during Every Cycle. The feasibility of complete cleanup in these three air purification systems using VSA and PSA cycles was investigated through the comparison of the required critical pressure ratio, Rc. Equation 15 shows that Rc depends only on the feed pressure (PH), feed mole fraction (yf), Langmuir isotherm parameter (b, the Henry’s law constant) at the operating temperature, and molar purge-to-feed ratio (γM); it is completely indepen-

Figure 2. Critical pressure ratios (a) and purge pressures (b) required for complete cleanup by VSA and PSA (or PVSA) for all three systems. Refer to Table 1b for the process conditions; note that ymax e 336, 1498, and 5750 ppm in PSA, and 751, 3344, and f 12765 ppm in VSA for DMMP, benzene, and butane, respectively (refer to eq 20).

dent of other process parameters and bed dimensions. The trends predicted by eq 15 are also intuitive in that Rc required for complete cleanup at the end of the purge step increases with an increase in PH, yf, and b, but decreases with an increase in γM. The only subtle parametric effect is the influence of PH on Rc: increases in PH are consistent with increases in the periodic bed penetration depth with decreases in R, as shown by Subramanian and Ritter (1997), and Liu and Ritter (1996). However, this effect is not so obvious from the expressions developed here because changes in PH affect R, qf, v, and γV (for constant γM), which are needed to calculate La. By definition, the PSA process in this study always has a purge pressure (PL) that is equal to or greater than atmospheric pressure (101.3 kPa), whereas the VSA process always has a PH that is equal to atmospheric pressure. Any process that has a superatmospheric feed pressure and subatmospheric purge pressure is referred to here as PVSA. A PH of 506.5 kPa for PSA (or PVSA) and a γM of 0.5 for both VSA and PSA (or PVSA) were used to investigate the feasibility of complete cleanup at different yf’s. These conditions are listed in Table 1. Rc’s for both VSA and PSA (or PVSA) processes are displayed in Figure 2a; the corresponding PL,c’s at the condition of complete cleanup are displayed in Figure 2b. As expected from eq 15, Rc increased with increases in yf and b. What was surprising, however, were the marked differences between the Rc’s required by VSA and PSA (or PVSA). They were consistently several times higher for PSA (or PVSA) than VSA, except for the very low yf’s in the butane system. With Rc determined, the required PL,c’s were readily calculated. PL,c decreased with an increase in yf because of the

1974 Ind. Eng. Chem. Res., Vol. 37, No. 5, 1998

increase of Rc with yf. For the butane system, complete cleanup in a true PSA process was possible only when yf was less than about 100 ppm; for the benzene system, it was possible only when yf was less than 10 ppm; for the DMMP system, even at a yf of 1 ppm, complete cleanup in a true PSA process was not possible. This result indicates that if complete cleanup is desirable for a system with a very high adsorbate-adsorbent affinity (i.e., large b), PL,c must be below atmospheric pressure (i.e., a VSA or PVSA process is needed). Figure 2b also shows that the required PL,c’s for complete cleanup in the PVSA process, in all cases, approached those of the VSA process as yf increased; as the adsorbate-adsorbent affinity increased (b), this agreement between the VSA and PVSA processes occurred at markedly lower yf’s. For example, the PL,c’s became essentially the same when yf exceeded 5000, 1300, and 20 ppm, in the butane, benzene, and DMMP systems, respectively. These results clearly indicate the superiority of VSA over PSA (or PVSA) for complete cleanup, especially for systems with high adsorbateadsorbent affinities and feed concentrations. It should be noted that increasing PH to increase R does not help to increase PL,c above atmospheric pressure: increasing PH also increases Rc, as indicated by eq 15. The DMMP system serves as a good example to illustrate this point. For a yf of 300 ppm, when PH was increased to 3039 kPa (30 atm), Rc increased to 7962 (i.e., 3 times higher than that required at a PH of 506.5 kPa (5 atm)). The required PL,c’s were essentially the same, however, for these two PH’s (i.e., PL,c ) 0.191 and PL,c ) 0.190 kPa, respectively). Comparison of VSA and PSA with Incomplete Cleanup. For the case of incomplete cleanup, the performances of VSA and PSA processes were compared using the volumetric feed flow rate at STP (Vf) (or equivalently the feed throughput) that was processed by VSA and PSA while all of the other conditions were held constant. The comparisons were made at different yf’s, R’s, and γM’s for a fixed La of 0.15 m (i.e., at 60% of the bed length (Lb)). PL of PSA and PH of VSA were also fixed at 101.3 kPa; so, PVSA was not considered. These conditions are listed in Table 1; the procedure used for this study was described above. Figure 3a compares Vf,vsa/Vf,psa for different yf’s; the actual amounts processed are shown in Figure 3b. These results were calculated using R ) 5 and γM ) 0.5, which corresponded to γV ) 2.5 (see eq 14). It is noted at the onset that in each case, a yf existed below which physically impossible results were obtained (i.e., a negative ζ0 and negative adsorbed-phase concentrations were obtained at the end of the purge step). For example, the yf was about 1 ppm for the VSA-DMMP system, 10 and 50 ppm for the PSA-benzene and VSAbenzene systems, respectively, and 200 and 600 ppm for the PSA-butane and VSA-butane systems, respectively. Figure 3 shows that VSA always performed better than PSA (i.e., VSA processed more feed than PSA). Moreover, as the adsorbate-adsorbent affinity increased, Vf,vsa/Vf,psa increased for the same yf. This result indicates that it is more advantageous to use VSA in systems with high adsorbate-absorbent affinities. The performances of PSA and VSA processes were also judged in terms of La at a fixed Vf. Actually, it is easy to show using the equilibrium theory-based correlations that La,vsa/La,psa at constant Vf is equal to Vf,psa/ Vf,vsa at constant La for a feed with the same mole

Figure 3. VSA to PSA ratios (a) and actual values (b) of the volumetric feed flow rates (at STP) processed by VSA and PSA processes as a function of the feed mole fraction. Refer to Table 1c and the text for the process conditions; note that ymax e f 200 000 ppm for the butane and benzene systems (refer to eq 21) max and yf e 320 and 1600 ppm in PSA and VSA, respectively, for the DMMP system (saturation limitations).

fraction. This relation is expressed as

( ) ( ) La,vsa La,psa

)

vf,stp

Vf,psa Vf,vsa

La

)

ζa,vsa PH,psa Rpsa ζa,psa PH,vsa Rvsa

(23)

Equation 23 indicates that under conditions with incomplete cleanup, VSA either processes more feed than PSA at the same La or it needs a shorter column than PSA at the same Vf. Figure 4a compares Vf,vsa/Vf,psa for different R’s; the actual amounts processed are displayed in Figure 4b. PH of PSA and PL of VSA were varied with γM ) 0.5, La ) 0.15 m, and yf ) 0.01 for the benzene and butane systems, and yf ) 50 ppm for the DMMP system. R was varied from 5 to 30, which corresponded to γV varying from 2.5 to 15 for the selected γM (see eq 14). Also, to avoid condensation during compression, the range of PH (and thus R) was limited by the saturation pressure of the contaminant vapor (for a fixed yf), especially for DMMP which has a vapor pressure of 0.16 kPa at 25 °C. This was the basis for using a lower yf in the DMMP system. Figure 4a shows that Vf,vsa/Vf,psa increased with an increase in R for all three systems and the values were always above unity (i.e., the performance of VSA was always better than PSA and it improved with increasing R). Figure 4a also shows that Vf,vsa/Vf,psa increased with the adsorbate-adsorbent affinity, and this increase was more pronounced at higher R’s. The Vf,vsa/Vf,psa values for the DMMP system fell in between those of the butane and benzene systems, because a much lower yf was used due to the saturation limitation. The advantage of VSA over PSA was also less pronounced at a lower yf, as shown in Figure 3a.

Ind. Eng. Chem. Res., Vol. 37, No. 5, 1998 1975

Figure 4. VSA to PSA ratios (a) and actual values (b) of the volumetric feed flow rates (at STP) processed by VSA and PSA processes as a function of the pressure ratio. Refer to Table 1c and the text for the process conditions; note that ymax e 33 333 f ppm for the butane and benzene systems (refer to eq 21) and ymax f e 53 and 165 ppm in PSA and VSA, respectively, for the DMMP system (saturation limitations), for the worst condition at R ) 30.

Figure 5. VSA to PSA ratios (a) and actual values (b) of the volumetric feed flow rates (at STP) processed by VSA and PSA processes as a function of the molar purge-to-feed ratio. Refer to Table 1c and the text for the process conditions; note that ymax e f 200 000 ppm for the butane and benzene systems (refer to eq 21) and ymax e 320 and 1600 ppm in PSA and VSA, respectively, for f the DMMP system (saturation limitations).

Figure 4b shows that the actual amounts processed by PSA increased with an increase in R, but the increases were small. Clearly, the amount adsorbed quickly approached the saturation limit with increasing R (PH), especially for the systems with stronger adsorbate-adsorbent affinities, such as DMMP. In contrast, in the VSA systems significant increases in Vf occurred with increases in R. Clearly, the decreases in PL with increasing R generated a cleaner bed and thus provided a larger adsorption capacity for the ensuing adsorption step. Figure 5a compares Vf,vsa/Vf,psa for different γM’s; the actual amounts processed are shown in Figure 5b. A yf ) 300 ppm for the DMMP system and a yf ) 5000 ppm for the butane and benzene systems were used with La ) 0.15 m and R ) 5. Note that the lowest γM used was 0.2, which corresponded to a γV of unity for the selected R (see eq 14). Below this γV, equilibrium theory predicts that no periodic state exists with complete or partial containment of the contaminant vapor during the feed step (Subramanian and Ritter, 1997). The highest γM used was unity, which corresponded to a γV of 5 for the selected R (see eq 14). Figure 5a shows that under the conditions in question, increasing γM always decreased Vf,vsa/Vf,psa; this decrease became more pronounced with less strongly adsorbed systems (e.g., the butane system). For more strongly adsorbed systems, this decrease became almost invisible (e.g., the DMMP system). Very similar decreases in Vf,vsa/Vf,psa were observed with the benzene and DMMP systems because a much higher yf was used for the benzene system compared to the DMMP system. Figure 5b shows that the actual amount processed by both VSA and PSA increased greatly with an increase in γM, most likely because a higher γM resulted in more

desorption, which in turn resulted in a cleaner bed at the end of the purge step and also a broader masstransfer zone for a fixed periodic bed penetration. Conclusions Simple equilibrium theory-based formulations were developed and used to investigate the feasibility of complete cleanup at the end of the purge step and to compare the performances of VSA and PSA processes for air purification. Several interesting features were revealed. The results showed that complete cleanup was always possible in a VSA process; it was also possible in a PSA process (i.e., a process with a purge pressure not less than atmospheric pressure, but only for systems with weaker adsorbate-adsorbent affinities and then only when the feed mole fraction was less than some specific value). Otherwise, a subatmospheric purge pressure was required for complete cleanup (i.e., a PVSA process was needed) no matter how high the feed pressure. The critical pressure ratio required for complete cleanup increased with the feed pressure, feed mole fraction, and adsorbate-adsorbent affinity. The critical pressure ratio required for complete cleanup by PSA (or PVSA) was also several times higher than that required by VSA for the same feed mole fraction, except for systems with weaker adsorbate-adsorbent affinities and then only at very low feed mole fractions. The periodic performances of VSA and PSA processes were also compared with incomplete cleanup. VSA always processed more feed than PSA at the same pressure ratio and bed penetration. This advantage of VSA over PSA became more pronounced with stronger adsorbate-adsorbent affinities and higher feed concentrations. The superiority of VSA over PSA also became

1976 Ind. Eng. Chem. Res., Vol. 37, No. 5, 1998

more pronounced with higher pressure ratios and lower purge-to-feed ratios, especially in systems with less stronger adsorbate-adsorbent affinities. Overall, this study showed that complete cleanup during every cycle of a VSA process is possible even for very strongly adsorbed contaminants and that VSA cycles are superior to PSA. These new VSA cycles are thus applicable to a wide variety of air purification needs. These needs include VSA-air purification processes for chemical defense systems, VSA-air prepurification processes for air fractionation plants, and simultaneous VSA-air purification and solvent vapor enrichment processes for solvent vapor recovery. Langmuir isotherm parameters and hypothetical process conditions are all that are needed to rapidly carry out feasibility studies of such processes using the analytic expressions provided in this work. Acknowledgment The authors gratefully acknowledge financial support from the National Science Foundation under Grant CTS-9410630 and from the Westvaco Charleston Research Center. Nomenclature a ) characteristic invariant defined by eq 9 a* ) characteristic invariant at σ ) 0 b ) Langmuir isotherm parameter, kPa-1 ci ) fluid-phase concentration of species i, mol/m3 c* i ) dimensionless fluid-phase concentration cf ) (fluid-phase) feed concentration, mol/m3 db ) bed diameter, m L ) penetration of the square profile in the very first step, m La ) periodic bed penetration, m Lb ) bed length, m N ) number of data points Patm ) atmospheric pressure, kPa PH ) high pressure of the feed step, kPa PL ) low pressure of the purge step, kPa PL,c ) critical purge pressure for complete cleanup, kPa qi ) adsorbed-phase concentration of species i, mol/kg q* i ) dimensionless adsorbed-phase concentration qexp,i ) experimental adsorbed-phase concentration of species i, mol/kg qcal,i ) calculated adsorbed-phase concentration of species i, mol/kg qf ) adsorbate concentration in equilibrium with the feed concentration cf, mol/kg R ) constant separation factor isotherm parameter t ) time, min tf ) feed-step duration, min tp ) purge-step time, min Vf ) volumetric feed flow rate at STP, SLPM v ) superficial velocity, m/s yf ) feed mole fraction ) maximum feed mole fraction constrained by model ymax f limitations z ) axial coordinate, m

Greek Letters R ) pressure ratio Rc ) pressure ratio required for complete cleanup  ) void fraction of the packing γV ) volumetric purge-to-feed ratio γVc ) critical volumetric purge-to-feed ratio required for complete cleanup γM ) molar purge-to-feed ratio FH ) bulk density of the packing, kg/m3 ζ ) dimensionless axial coordinate ζa ) dimensionless periodic penetration of the shock wave at the end of the feed step ζ0 ) dimensionless periodic axial position reached by q*i ) 0 at the end of the purge step

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Received for review September 22, 1997 Revised manuscript received February 9, 1998 Accepted February 17, 1998 IE970685K