Pressure Swing AdsorptionâSolvent Vapor Recovery: Process

Ind. Eng. Chem. Res. 1996, 35, 2299-2312

2299

SEPARATIONS Pressure Swing Adsorption-Solvent Vapor Recovery: Process Dynamics and Parametric Study Yujun Liu and James A. Ritter* Department of Chemical Engineering, Swearingen Engineering Center, University of South Carolina, Columbia, South Carolina 29208

A comprehensive study of the periodic state process dynamics and performance of a pressure swing adsorption (PSA)-solvent vapor recovery (SVR) process was carried out by computer simulation. An investigation of the process dynamics showed that temperature swings, velocity changes, and their effects were significant in these kinds of systems and must be accounted for in simulation studies. Also, the rigorous model showed that the frozen solid and gas phase assumption was valid during the pressurization step but not the blowdown step and that the temperature and concentration waves propagated together during the adsorption step. Nine parameters were investigated to ascertain their effects on the process performance. The trends from the parametric study showed that the process performance was affected significantly by all of these parameters and that the nonidealities included in the rigorous model, in most cases, had a marked effect on the process performance, beyond that which could be explained by an idealized, isothermal, equilibrium PSA model. Introduction Pressure swing adsorption (PSA) has been studied extensively, and many of its applications have been commercialized since its invention (Skarstrom, 1959). Reviews on the theory and practice of PSA have been given by Tonduer and Wankat (1985), Ruthven (1984), Yang (1987), and most recently in the comprehensive monograph by Ruthven et al. (1994). However, PSA for solvent vapor recovery (SVR), a relatively new commercial application of PSA, has received comparatively little attention in the literature (Lovett and Cunnuff, 1974; Parmele et al., 1979; Contrell, 1982; Ritter and Yang, 1991a,b; Kikkinides et al., 1991; Hall and Larrinaga, 1993; LeVan, 1995). Lovett and Cunnuff (1974), Parmele et al. (1979), Contrell (1982), and Hall and Larrinaga (1993) all described similar commercial solvent vapor recovery (SVR) processes that utilized a heatless vacuum regeneration cycle. However, only Hall and Larrinaga (1993) made it clear that they were operating a true PSA process, i.e., their dual column process was allowed to come to a unique periodic state that depended solely on the process conditions and characteristics. The other SVR processes were operated more like steam regeneration plants, where one of the columns was kept on line until trace breakthrough occurred; it was then taken off line and vacuum regenerated. This apparent delay in the commercialization of PSA for SVR may have been due to PSA technology being developed almost exclusively for the purification and recovery of the light component, where the heavy component was considered a waste gas. The recent works by Ritter and co-workers (Ritter and Yang, 1991a,b; Kikkinides et al., 1991) appear to have been the first PSA studies to address * To whom correspondence should be addressed. Phone: (803) 777-3590. Fax: (803) 777-8265. E-mail: ritter@ sun.che.sc.edu.

S0888-5885(96)00114-5 CCC: $12.00

the simultaneous light component purification and heavy component enrichment and recovery both experimentally and theoretically. They showed that PSA can be used effectively for enriching and recovering a heavy component from a fairly dilute feed stream, while at the same time producing a high-purity light product. Following their work with dimethyl methylphosphonate (DMMP) and hexane vapors, PSA researchers began investigating heavy component enrichment and recovery from a variety of feed gases, including CO2 from flue gas (Kikkinides and Yang, 1993a; Chue et al., 1995), CO2 from air (Diagne et al., 1994, 1995), SO2 and/or NOx from flue gas (Kikkinides and Yang, 1991, 1993b), H2S and CO2 from natural gas (Kikkinides et al., 1995), and hydrogen from helium (Ruthven et al., 1994). However, no one has advanced the work done by Ritter and coworkers on traditional PSA-SVR. PSA-SVR differs from conventional PSA purification and separation processes in that the heavy (desired) product is the most strongly adsorbed component, though in most applications a certain light product purity is also required. Therefore, an additional design constraint is imposed on PSA-SVR processes: in addition to considering the light product purity and heavy product recovery (in lieu of the light product recovery), the heavy product enrichment must also be considered. Moreover, a unique characteristic of PSA-SVR, even compared to those aforementioned heavy component enrichment and recovery processes, is that a very high interaction or affinity generally exists between the solvent vapor and the adsorbent; thus, the isotherms tend to be rectangular in shape and, in general, a vacuum desorption step is necessary. Another characteristic is that when the feed concentration is 5-10 vol % or greater the PSA-SVR process is comparable to a bulk PSA separation process; i.e., the temperature and velocity variations are important to the process perfor© 1996 American Chemical Society

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Ind. Eng. Chem. Res., Vol. 35, No. 7, 1996

mance. However, in previous PSA-SVR studies that included computer simulations (Ritter and Yang, 1991a; Kikkinides et al., 1991), the PSA processes were based on isothermal and/or constant velocity conditions; therefore, these important effects were neglected. The recent equilibrium theory analysis presented by LeVan (1995) also neglected these effects. The objective of this study was to investigate by computer simulation the PSA-SVR process under realistic operating conditions to determine the effects of important process parameters on the process performance; i.e., on the light product purity (yp), the solvent vapor recovery (R) and enrichment (E), and the bed capacity factor (BCF). The effects of the purge to feed ratio (γ), pressure level (p), pressure ratio (R), feed flow rate (Vf), feed concentration (yf), heat transfer coefficient (h), cycle time (tc), adsorption step time (ta), and bed dimensions (L/db) were studied to obtain a relatively comprehensive understanding of the PSA-SVR process. In all cases, commercially relevant PSA-SVR process conditions were employed for the recovery of benzene vapor from nitrogen using an activated charcoal. Moreover, all of the simulations accounted for finite heat and mass transfer resistances and pressurization and blowdown effects, as well as velocity variation during the cycle. PSA-SVR Process Description The PSA-SVR process simulated in this study consisted of two interconnected beds each undergoing four cycle steps in tandem. The four steps were cocurrent feed pressurization (I); high-pressure adsorption with feed gas (II); countercurrent blowdown (III); and countercurrent low-pressure desorption with light product purge (IV). The solvent vapor (heavy component) was enriched and recovered in steps III and IV, whereas the light component (nitrogen or inert carrier gas) was purified during step II. In step IV the purge gas used in one bed came directly from the other bed as the light product of step II. The amount of the light product that was used for purge was determined by γ, which was simply the ratio of the purge gas velocity at PL to the feed gas velocity at PH since the adsorption and purge step times were equal. A unique feature of this two-bed, four-step PSA process was that during feed pressurization (step I) the light product end of the bed was closed; thus, during part of the cycle, no light product was withdrawn. However, the heavy product was withdrawn continuously. Compared to most conventional PSA processes, which have been designed to deliver a continuous light product at or near PH, this feature was favorable from both economic and operational points of view. The PSA-SVR process performance at the periodic state was judged mainly by R and E of the heavy component (solvent vapor), which were defined as follows:

R)

moles solvent leaving during steps III and IV moles solvent entering during steps I and II (1) E)

steps III and IV avg solvent vapor conc (2) solvent vapor feed conc

Under the most ideal conditions (i.e., when heat and mass transfer and velocity effects are ignored and when the gas and adsorbed phases are frozen during steps I

and III), equilibrium theory predicts that when the bed is long enough to contain the adsorption wave front at the end of step II, the maximum E that can be obtained occurs at the critical purge to feed ratio, i.e., γ ) 1 (LeVan, 1995). It is easy to show that the maximum possible E is then given by

EI )

ye PH ) yf P L

(3)

This ideal case gives a convenient reference point to compare the effect of the process conditions on E. The relative enrichment was defined for this purpose as

ER )

E EI

(4)

However, in practice, E would always be less than EI since using a γ equal to unity is not generally possible because as γ decreases the length of bed required to maintain the adsorption wave within the column increases (LeVan, 1995). Nevertheless, ER has more meaning than E when comparing the process performance at different process conditions. Equally important to the PSA-SVR process performance was yp, as PSA-SVR processes typically vent the light product (usually air with traces of solvent vapor) to the atmosphere. Thus, the composition of this vent gas must necessarily meet all the current environmental regulations. To a lesser extent, another important PSASVR process performance indicator was the throughput (τ), defined as the cubic meters of feed gas at STP (including step I) processed per hour per kilogram of adsorbent. Finally, another new process performance indicator, the bed capacity factor (BCF), was defined as

BCF )

∫0Lq dz/q*f L

(5)

BCF represented the capacity of the bed that was used at the periodic state (measured at the end of step II) compared to the maximum capacity of the bed at the feed conditions. It is akin to the familiar “LUB” in fixed bed adsorption processes and is used here in a similar fashion. Mathematical Model The model used in this study was similar to that used previously in the simulation of bulk-gas PSA processes (Ruthven et al., 1994). It was derived on the basis of the following assumptions: inert carrier gas and adsorbent, single component feed, negligible column pressure drop, ideal gas behavior, no radial gradients, and no axial dispersion and heat conduction, thermal equilibrium between gas phase and adsorbent, and temperature-independent gas and adsorbent properties. Mass and heat transfer were accounted for by using, respectively, the linear driving force (LDF) approximation, and an overall heat transfer coefficient. The total and component mass balances were given by

(1 - ) RT ∂q ∂y ∂y +u + (1 - y) F )0 ∂t ∂z P s ∂t ∂u 1 ∂T 1 ∂P u ∂T (1 - ) RT ∂q + + F )0 ∂z T ∂t P ∂t T ∂z P s ∂t

(6) (7)

Ind. Eng. Chem. Res., Vol. 35, No. 7, 1996 2301

where ∂q/∂t was based on the LDF approximation as

∂q ) k(q* - q) ∂t

(8)

The mass transfer coefficient, k, for the benzene vaporactivated charcoal system was estimated from k ) 15De/ rp2, with De approximated from correlations given in theliterature (Yang, 1987). The energy balance was written as

(F C g

Pg

+

∂u 1- ∂T ∂T FC + FgCPg u +T + s Ps ∂t ∂z ∂z 1 - ∂q 2h F + (T - T0) ) 0 (9) ∆H s ∂t rb

)

(

)

where the last term was included to account for heat transfer between the column wall and the surrounding ambient atmosphere. Temperature-dependent adsorption equilibria for the nitrogen-benzene vapor-activated charcoal system were obtained from the literature (James and Phillips, 1954). This system was represented by eqs 10 and 11; and the corresponding isotherms are displayed in Figure 1.

q* ) b)

qsbPy 1 + bPy

b0 RxT

(

exp -

(10)

∆H RT

)

(11)

These isotherms have been used by numerous investigators to study fixed bed adsorption processes (Rhee et al., 1970; Friday and LeVan, 1982; Wheelwright and Vislocky, 1984). A unique feature of this system was that all of the isotherms, covering the temperature range of interest, were nearly rectangular in nature, becoming horizontal at around 5 kPa. This system was therefore indicative of a solvent vapor that was very strongly adsorbed and consequently very difficult to remove from the adsorbent simply by decreasing its partial pressure. Furthermore, benzene vapor represents one of the heavy vapor components in gasoline filling operations (Tolles, 1995). Thus, the isotherms depicted in Figure 1 were ideally suited for carrying out the first comprehensive study of PSA-SVR under realistic process conditions. The initial and boundary conditions are listed below; they were applied to every cycle: step I:

at t ) 0: at z ) 0: at z ) L: step II: at t ) 0: at z ) 0: step III: at t ) 0: at z ) L: step IV: at t ) 0: at z ) L:

y ) yIV, y ) yf,

T ) TIV, T ) Tf

q ) qIV,

y ) yI, y ) yf, y ) yII, ∂y/∂z ) 0 y ) yIII, y(t) ) yII(t),

u)0 T ) T I, q ) qI, T ) T f, u ) uf T ) TII, q ) qII, u)0 T ) TII, T ) TIII, q ) qIII, T(t) ) TII(t), u ) uP

for all z for all t for all t for all z for all t for all z for all t for all z for all t

Note that for step IV, previous investigators used either the volume-averaged or the isothermal instantaneous step II light product composition from one of the beds to purge the other bed. In this study, the inlet purge gas had the same composition and temperature as the step II light product at all times. Also, the pressure history was required as input to the PSA model. The pressure history was represented by a linear function of time during steps I and III; and it was held constant at PH and PL during steps II and IV, respectively. The bed characteristics, together with the fixed operating

Figure 1. Adsorption equilibrium isotherms of benzene vapor on activated charcoal (James and Phillips, 1954). Table 1. Base Case Bed Characteristics, Fixed Process Conditions, and Physical Properties bed diameter (db) bed length (L) bed void fraction () bed density (Fs) heat capacity of adsorbent (CPs) feed flow rate (Vf) feed mole fraction (yf) feed temperature (Tf) ambient temperature (T0) total cycle time (tc) cycle step time (ts) I and III II and IV gas phase density (Fg) gas phase heat capacity (CPg) heat of adsorption (∆H) mass transfer coefficient (k) qs b0

0.027 m 0.29 m 0.43 480 kg/m3 1.05 kJ/(kg‚K) 0.0005 m3/min 5 vol % 293 K 293 K 20 min 2 min 8 min 1.308 kg/m3 1.006 kJ/(kg‚K) -43.5 kJ/mol 0.086 1/s 4.4 mol/kg 3.88 × 10-8 m3/(mol‚K0.5)

conditions and physical properties, are given in Table 1; the remaining parameters are given in Table 2. Equations 6-11, the coupled partial differential and algebraic equations, were cast into a finite difference form and solved together with the initial and boundary conditions. A Newton-Raphson procedure, based on Newman’s algorithm (Newman, 1991) was used to solve the set of nonlinear equations. At each time step, the equations at each spatial node point were solved simultaneously. When the convergence criteria were satisfied at all the spatial node points, the procedure was advanced to the next time step. This process was repeated cycle by cycle until the periodic state was attained. The periodic state was defined as that state which produced essentially no changes in the temperature and gas and adsorbed phase bed profiles from cycle to cycle. It was determined that 101 spatial node points and a time step of 0.01 s produced a fairly accurate representation of the solution to this system of model equations. The PSA process simulation can be started from any of the four steps; in all the simulations, the process was started from the beginning of step II with a clean bed. It should be noted that a few of the runs covering a wide range of conditions were also started from a completely saturated bed to check for multiple periodic states (Croft

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Table 2. Values of the Parameters Used in Each Simulation run no.

ta (min)

tc (min)

R

PH (kPa)

γ

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22a 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44

8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 2 4 6 9 7 6 5 8 8 8 8 8

20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 5 10 15 20 20 20 20 20 20 20 20 20

20 20 20 20 20 20 20 20 20 20 20 10 15 25 30 15 25 30 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20

152 152 152 152 253.25 202.6 177.28 141.83 131.69 121.56 111.43 152 152 152 152 114 190 227.97 152 152 152 152 152 152 152 152 152 152 152 152 152 152 152 152 152 152 152 152 152 152 152 152 152 152

2 1.75 1.25 1 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5

a

h (kJ/(s‚m2‚K)) 0.02092 0.02092 0.02092 0.02092 0.02092 0.02092 0.02092 0.02092 0.02092 0.02092 0.02092 0.02092 0.02092 0.02092 0.02092 0.02092 0.02092 0.02092 0.0 0.0004184 0.004184 0.02092 0.04184 10.0 0.02092 0.02092 0.02092 0.02092 0.02092 0.02092 0.02092 0.02092 0.02092 0.02092 0.02092 0.02092 0.02092 0.02092 0.02092 0.02092 0.02092 0.02092 0.02092 0.02092

Vf × 106 (m3 STP/min)

yf (%)

L/db

500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 300 400 600 700 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500

5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 0.5 1 2.5 10 5 5 5 5 5 5 5 5 5 5 5 5

10.74 10.74 10.74 10.74 10.74 10.74 10.74 10.74 10.74 10.74 10.74 10.74 10.74 10.74 10.74 10.74 10.74 10.74 10.74 10.74 10.74 10.74 10.74 10.74 10.74 10.74 10.74 10.74 10.74 10.74 10.74 10.74 10.74 10.74 10.74 10.74 10.74 10.74 10.74 15.00 7.500 5.000 2.500 1.250

Base case.

and LeVan, 1994; Kikkinides et al., 1995). In all cases tested, only one unique periodic state was exhibited. Typically, 70-3000 cycles were required to reach the periodic state, depending on the process conditions. A variety of computer systems was used to carry out the parametric study in a timely fashion. These included a VAX/VMS version V5.5-2, VAX 6000 model 440, Sun SparcStation 10/40, and Paragon OSF/1. For reference purposes, it took 8 min of CPU time per cycle on the Sun SparcStation 10/40 for the base case run (no. 22). Results and Discussion Process Dynamics. A good understanding of the bed dynamics during the periodic state PSA cycle is quite helpful to understanding the process performance. Therefore, the bed dynamics of the base case run (no. 22) are presented first prior to analyzing the process performance in terms of the parametric study. This base case was designed so that at the end of the adsorption step only traces of benzene broke through the bed and contaminated the light product. Therefore, it was operated at a BCF very close to unity and very near to the critical γ, but only with respect to yp, not with respect to yp and E (see above and LeVan, 1995). The results of this run are presented in Figures 2-4,

and Table 3. Figure 2 shows the variations of the gas phase temperature (T), benzene vapor concentration (y), adsorbed phase benzene loading (q), and gas phase interstitial velocity (u) at three different positions in the bed over a complete cycle at the periodic state. These curves essentially represent breakthrough curves occurring at different positions in the bed. The same variables are plotted in Figures 3 and 4, but in terms of the bed profiles at various times during the adsorption and desorption steps, respectively. Table 3 summarizes the results in terms of the process performance. A. Step I: Pressurization. During pressurization, Figure 2 shows that T increased as a result of the energy released due to adsorption and energy brought in with the feed used to pressurize the bed. It was not due to compression effects, as they were thought to be negligible and not accounted for in these simulations. Figure 2 also shows that y decreased rapidly during pressurization and approximately as inversely proportional to R throughout the bed. This is seen very clearly in Figure 4b, curve 5, and Figure 3b, curve 1, which respectively show the gas phase bed profiles just before and just after pressurization. Also, since the pressure increased with time, and the flow rate was not con-


Figure 2. Run no. 22 periodic state temperature (a), concentration (b), benzene loading (c), and velocity (d) variations at three different positions in the bed. Dash: z ) 5.22 cm. Solid: z ) 14.5 cm. Dot dash: z ) 25.23 cm.

trolled in this step, u and thus the amount of benzene vapor fed into the bed decreased with time. The benzene vapor was also quickly adsorbed near the feed end. Thus, pressurization occurred within the column as if no benzene vapor was present in the feed; and q remained essentially frozen, which agreed very well with the assumptions made by Ritter and Yang (1991a) in their modeling study. Ritter and Yang (1991a) assumed that for strongly adsorbed gases or vapors the pressurization step may

Figure 3. Run no. 22 periodic state temperature (a), concentration (b), benzene loading (c), and velocity (d) profiles at the end of the adsorption step. Curves 1, 2, 3, 4, and 5 correspond to profiles at ta ) 0, 2, 4, 6, and 8 min, respectively.

be approximated by freezing the solid and gas phases, which necessarily and ideally implies that the gas phase concentration bed profile decreases as inversely proportional to the change in pressure. In fact, it can be shown from equilibrium theory (e.g., see Knaebel and Hill, 1985) that for a very favorable, linear isotherm, the mole fractions change exactly as inversely proportional to the pressure ratio during pressurization, which is essentially what eq 3 indicates. This can also be argued from the isotherm relationship when the solid phase is frozen. For example, it is seen from eq 10 that at constant T, when q* is constant and P changes, y must change as

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Ind. Eng. Chem. Res., Vol. 35, No. 7, 1996 Table 3. Simulation Results in Terms of the Process Performance run no. yp (ppm) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22a 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 a

Figure 4. Run no. 22 periodic state temperature (a), concentration (b), benzene loading (c), and velocity (d) profiles at the end of the purge step. Curves 1, 2, 3, 4, and 5 correspond to profiles at tp ) 0, 2, 4, 6, and 8 min, respectively.

inversely proportional to P. In other words, freezing the adsorbed phase necessarily freezes the partial pressure in the gas phase during pressure changing steps. B. Step II: Adsorption. Figure 2 shows that during step II (adsorption), the in-bed T, y, q, and u breakthrough curves tracked each other, indicating that their wave velocities were similar. This result suggested that temperature front sensing may be used to monitor the concentration wave front (Cen and Yang, 1986; Matz and Knaebel, 1987). Figures 2 and 3 also

32.58 129.0 8632.5 13206.0 13990.0 9883.8 6826.8 377.77 266.27 191.94 146.42 8081.8 924.32 398.9 316.3 190.14 6526.5 9385.5 13314.0 544.5 81.65 0.690 0.000 34.96 10399.4 14544.6 0.000 0.000 0.000 57721.3 0.000 0.060 41.20 7333.0 135.8 43.51 8.270 389.77 792.24 1253.71 6868.06 8750.78

R (%) 99.946 99.782 84.506 75.887 75.428 82.565 87.962 99.349 99.541 99.669 99.748 86.856 98.443 99.303 99.442 99.681 88.327 83.064

E

ER

τ (m3 STP/(h‚kg)) BCF (%)

5.356 0.268 0.252 5.631 0.282 0.252 6.273 0.314 0.252 6.715 0.336 0.252 5.218 0.261 0.257 5.542 0.277 0.254 5.726 0.286 0.253 6.011 0.301 0.252 6.091 0.305 0.251 6.168 0.308 0.251 6.244 0.312 0.251 3.765 0.377 0.252 4.972 0.331 0.252 6.723 0.269 0.252 7.384 0.246 0.252 5.264 0.351 0.251 6.425 0.257 0.254 6.829 0.228 0.256 condensation occurred condensation occurred 76.244 5.161 0.258 0.252 99.061 5.934 0.297 0.252 99.860 6.179 0.309 0.252 99.999 6.353 0.318 0.252 100.00 6.359 0.318 0.154 99.941 6.303 0.315 0.203 81.443 5.584 0.279 0.301 73.867 5.307 0.265 0.351 100.00 10.101 0.505 0.252 100.00 9.515 0.476 0.252 100.00 8.095 0.405 0.252 48.434 3.220 0.161 0.252 100.00 6.092 0.305 0.272 99.9999 6.344 0.317 0.260 99.930 6.275 0.314 0.255 86.980 6.183 0.309 0.283 99.768 5.643 0.282 0.222 99.926 5.325 0.266 0.191 99.986 4.920 0.246 0.160 99.329 5.980 0.299 0.252 99.061 5.934 0.297 0.252 98.632 5.882 0.294 0.252 87.854 5.683 0.284 0.252 84.480 5.562 0.278 0.252

99.334 99.589 99.959 99.973 99.987 99.975 99.960 99.712 99.653 99.586 99.504 99.953 99.824 99.732 99.707 99.555 99.964 99.971 99.953 99.692 99.610 95.644 86.152 99.345 99.964 99.976 7.817 18.905 57.595 99.996 56.597 90.438 99.349 99.962 99.592 99.351 98.276 99.740 99.795 99.829 99.917 99.920

Base case.

show that the peak T was increasing with z because the light product end of the bed was cleaner, due to the effects of the countercurrent purge used during step IV. This gave rise to a greater change in q as z increased (see Figure 3c), thus more energy was released due to adsorption. In addition, heat convected from the feed end of the bed contributed to the higher T at the light product end of the bed. At the end of the adsorption step (Figure 3, curve 5), the y wave had just reached the light product end of the bed, T peaked at about 310 K, and the T wave had just broken through the bed. This result, again, indicated the usefulness of temperature front sensing. Note that when T increased, u also increased significantly, which clearly showed that velocity changes were sometimes coupled with the temperature changes. C. Step III: Blowdown. Figure 2 shows that during the blowdown step, y increased slowly at first but then very rapidly near the end of the step. It also increased very uniformly over the entire bed, as seen in Figure 4, curve 1. Figures 2-4 also show very clearly that q remained essentially frozen during this step. However, since cooling due to gas expansion was not included in the model, some desorption definitely occurred because T decreased over most of the bed. Also, the significant changes in u that occurred during step III were caused by benzene desorbing. By the end of


step III, the u profile in the bed was linear and ranged from zero at the closed end to nearly 4 times uf at the feed end, which showed that the velocity changes can be significant. Also, at the end of step III, E just barely exceeded 11. Instilling the assumption made by Ritter and Yang (1991a) would have predicted an initial E of 20, i.e., y would have increased as inversely proportional to R, as occurred during step I and predicted by eq 3. Ritter and Yang’s assumption assumed that blowdown occurred as if all the benzene in the gas phase remained frozen in place and only the inert carrier gas exited the bed in the exhaust stream. In subsequent work, Ritter and Yang (1991b) showed that this was valid for a very strongly adsorbed vapor (DMMP). The reason why the assumption was valid in their case, and 11 instead of 20 was obtained for E in this case, was due to the rectangular nature of the isotherm coupled with slight changes in loading. For example, q* was equal to 4.363 mol/kg at the feed conditions; at these conditions and for ideal blowdown, E would be equal to 20. Back calculating for an E equal to 11 gives a q* of 4.345 mol/kg, which corresponded to the conditions at the end of the blowdown step. Clearly, E was very sensitive to the changes in q that occurred most likely due to the self-purging effects associated with benzene desorbing. D. Step IV: Purge. During step IV, Figures 2 and 4 show that benzene continued to desorb because the purge gas lowered the partial pressure of benzene vapor by sweeping through the void spaces in the column. At the beginning of the purge step, y was uniform and relatively high throughout the bed. As desorption continued, however, the slight changes in q that occurred produced drastic changes in y because of the rectangular nature of the benzene isotherms. Thus, y decreased sharply in the first few minutes of the step; thereafter, the y profiles became fairly flat. The sharp decrease was primarily due to the rapid changes that occurred initially in u, whereas the leveling off of y was caused by the concentration velocities decreasing dramatically as the knee of the isotherm was approached. In effect, this PSA-SVR process exhibited hardly any change in q at the periodic state (note the expanded ordinate scale in Figure 3c); nevertheless, the change was enough to contain and distribute the moles of adsorbate in the feed that entered and exited the bed during each cycle. At the beginning of the step, T also decreased; but after about 1 min, T at all positions began to rise with time, as seen in Figures 2 and 4. The decrease in T was caused by desorption cooling, whereas the increase was caused by the energy brought in with the purge gas, which came directly from the light product of the other bed; recall that the light product had a relatively high temperature at the end of step II. Also, during the entire purge step, T throughout the bed was below the ambient temperature (293 K), except at the light product end, which was heated by the incoming purge gas. Clearly, the cooling effect due to desorption was being overcome in time by the energy being convected in with the purge. This produced a very uniform bed temperature over about 70% of the bed. Finally, the u profiles varied considerably in time, and u/uf was generally much higher than it would have been if constant u was assumed (i.e., u/uf ) 1.5). Since higher velocities should have the same effect as increasing γ (see below), this increase in u probably contributed to the leveling off of y. The u profiles were also essentially

Table 4. Summary of the Parametric Studya effect on the PSA-SVR process performance parameter vγ vp vR vVf vyf vh vtc vta vL/db

by VPL by vPH

R

E

ER

yp

BCF

v V v V V V v V V v

V V v v V V v vV v v

V V V V V V v vV v v

V v V v v v V v v V

V v V v v v V v v V

a Arrows imply the following: v, increasing; V, decreasing; vV, increasing then decreasing.

linear over the entire bed. This last result may be used to simplify the set of governing equations if the u profile is a priori linearized during step IV. Parametric Study. Forty-four simulations were carried out to investigate the effects of the nine parameters on the process performance. Four to eight runs were used to show the effect of each parameter, where in each run, only one of the nine parameters was changed from the base case run (no. 22). The values of the varied parameters are given in Table 2, whereas Table 1 lists the remaining fixed process conditions and model parameters. The simulation results are listed in Table 3, summarized in Table 4, and displayed in Figures 5-13, in terms of the process performance, i.e., in terms of yp, R, E (and ER), τ, and BCF. An idealized PSA process was also defined by invoking the following assumptions beyond those utilized in this study. Heat effects and velocity variation were considered negligible, and the solid and gas phases were frozen during steps I and III (Ritter and Yang, 1991a); further, mass transfer effects were ignored (LeVan, 1995). Under these conditions, LeVan (1995) developed a simple equilibrium theory that described the periodic state of this idealized PSA process. His theory was adopted in this work to state whether the performance trends observed in the parametric study were dominated by equilibrium effects or the coupled effects associated with the aforementioned nonidealities. A. Effect of Purge to Feed Ratio (γ). In PSA systems, γ is always selected as one of the more important design variables, as it controls both the purity and recovery of the light component. The effect of γ on the performance of a PSA-SVR process was investigated by Ritter and Yang (1991a) and Kikkinides et al. (1991), but under isothermal and/or constant velocity conditions. Therefore, five runs (nos. 1-4 and 22) were performed to investigate the effect of γ on the process performance under more realistic conditions. γ was varied from 1 to 2 by increasing the purge flow rate; all of the other parameters were fixed (see Tables 1 and 2). The results of these runs are shown in Figure 5, and Tables 3 and 4. Increasing γ decreased yp and BCF and increased R, because the higher purge rate lowered the partial pressure of the solvent vapor, which resulted in a larger stripping effect. This created a more highly regenerated zone near the light product end of the bed, which was critical to preventing the solvent vapor from breaking through the bed during the adsorption step. However, increasing γ decreased E because of the diluting effect of the purge gas on the solvent vapor effluent during step IV. These trends were also observed by Ritter and Yang (1991a) and Kikkinides et al. (1991); however, the

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Figure 5. Effect of purge to feed ratio (γ) on the process performance, in terms of yp, R, E, and ER.

Figure 6. Effect of pressure level (p) on the process performance, in terms of yp, R, E, and ER.

maximum in the E-γ plane that was reported in the later reference was not observed here because γ’s < 1 were not explored as they lead to low R. The idealized PSA model also predicted the same trend as that shown in Figure 5, including the convex shape, which indicated that the effect of γ on the process performance was controlled largely by equilibrium effects. Overall, the effects of γ on yp and R were significant, while the effect on E (or ER) was only moderate. Also, within an acceptable yp operating region (say, e.g., 500 ppm or less), ER was rather low (∼0.27), indicating that there was much room for improvement in the process performance. B. Effect of Pressure Level (p). The p is an important design variable to consider when examining PSA-SVR operations at constant R and γ, to determine whether step II compression or step IV evacuation is more advantageous. However, only Ritter and Yang (1991a) investigated p, but under very limited conditions. Therefore, eight simulations (nos. 5-11 and 22) were used to evaluate the effect of p on the process performance. In these runs, the pressures (PH and PL) were either increased or decreased compared to the base case, while R and all the other parameters were kept fixed (see Tables 1 and 2). PH ranged from 111.43 to 253.25 kPa when PL ranged from 5.57 to 12.66 kPa. The results of these runs are plotted in Figure 6 in terms of PL; they are also tabulated in Table 3 and summarized in Table 4. Decreasing p at constant γ not only increased the linear velocities, it also decreased the partial pressure of benzene during both the adsorption and desorption steps. Intuitively, it seemed that these changes should have affected the process performance, especially the partial pressure effect, since this would have allowed the process to take advantage of operating more toward the knee of the isotherm. In fact, Figure 6 and Table 3 show that as p decreased, the process performance improved, i.e., yP and BCF decreased, and R and E (or ER) increased. However, the idealized PSA model

predicted essentially no effect whether breakthrough occurred or not. Counter to the idealized model, Figure 6 shows that E (or ER) continued to increase even when yp approached zero and R approached 100%. But the increase was moderate over the p range investigated (at about 6%), which suggested that, for the most part, the effect of p on the process performance was equilibrium controlled. However, there was clearly some lumped effect of the nonidealities that provided a positive influence on the process performance. Also, within the acceptable yp operating region, ER increased only slightly, ranging from 0.261 to 0.312, compared to that obtained while varying γ, again indicating that improvements in the performance were possible. C. Effect of Pressure Ratio (r). The R is a critical design parameter in conventional PSA processes because a higher R allows less purge to be used at constant γ, thereby increasing the recovery of the light product. However, this positive aspect of increasing R is offset by an increase in the level of compression or evacuation that is required. Both Ritter and Yang (1991a), and Kikkinides et al. (1991) investigated the effect of R on the process performance, but under more idealized conditions. Therefore, two sets of simulations were used to investigate the effect of R. In one set (nos. 12-15 and 22), R was changed by varying PL with PH constant. In the other set (nos. 16-18 and 22), R was changed by varying PH with PL constant. Overall, R was varied from 10 to 30 with all the other parameters fixed (see Tables 1 and 2). The results of these runs are shown in Figure 7 and Tables 3 and 4. Increasing R by decreasing PH decreased the feed velocity, since Vf (at STP) was fixed during the adsorption step, and since γ was constant, the purge gas velocity also decreased. Also, increasing PH at constant yf increased the feed gas partial pressure. On the other hand, increasing R by decreasing PL did not change the purge velocity, since PH (and the feed velocity) did not change, nor did it change the feed gas partial pressure. But it did change the partial pressure of benzene during


Figure 8. Effect of feed flow rate (Vf) on the process performance, in terms of yp, R, E, ER, and τ. Figure 7. Effect of pressure ratio (R) on the process performance, in terms of yp, R, E, and ER.

desorption. Intuitively, it seemed that these changes should have affected the process performance, especially the velocity and partial pressure effects. However, according to the idealized PSA model, these changes only affected E. In terms of the other process performance indicators, when R was increased by decreasing PL, the idealized PSA model predicted no effect whether breakthrough occurred or not, and when R was increased by increasing PH, the idealized PSA model predicted no effect when yp was equal to zero and a very slight but completely opposite effect, compared to the rigorous model, when breakthrough occurred. The rigorous model showed that increasing R by decreasing PL always improved the process performance (i.e., R and E increased and yp and BCF decreased), whereas increasing R by increasing PH only improved E (both yp and BCF increased and R decreased). In both cases, the idealized PSA model predicted similar trends for E whether yp was equal to zero or not, indicating the effects of R on the process performance (in terms of E, only) were largely controlled by equilibrium effects. However, in terms of the other process performance indicators, the nonidealities included in the rigorous model, compared to the idealized model, caused some surprising differences. It was also intriguing that, as

E increased, ER decreased (but this trend was easily rationalized according to eqs 3 and 4); thus, within an acceptable yp operating region, a very low ER of 0.25 was obtained, which suggested that an optimum R (and thus PL) may exist and that decreasing PL without bound does not necessarily lead to an important process performance. D. Effect of Feed Flow Rate (Vf). A 40% increase or decrease in Vf is not unusual in some PSA-SVR operations, especially for large gasoline tank filling operations. However, the effect of Vf on the PSA-SVR process performance has not been studied. Therefore, five simulations (nos. 25-28 and 22) were used to evaluate the effect of Vf on the process performance. In these runs, Vf ranged from 3 × 10-4 to 7 × 10-4 m3 STP/ min with the base case set at 5 × 10-4 m3 STP/min. All the other parameters were fixed (see Table 2). Figure 8 and Tables 3 and 4 display the results of these runs. Increasing Vf (and thus τ) had a detrimental effect on the process performance, i.e., it decreased R and E (or ER) and increased yp and BCF. In fact, a considerable amount of benzene breakthrough occurred at Vf above the base case, because there simply was not enough adsorbent to contain all or most of the benzene brought in with the feed during each cycle. This is seen clearly from the range of the BCFs. It was first thought that the observed trend was caused by the purge velocity

2308


Figure 9. Effect of feed concentration on (yf) the process performance, in terms of yp, R, E, and ER.

Figure 10. Effect of heat transfer coefficient (h) on the process performance, in terms of yp, R, E, and ER.

increasing with Vf (recall γ was held constant); however, the idealized model indicated that there was no effect of Vf on E unless benzene breakthrough occurred. Once breakthrough occurred, it agreed qualitatively with the trends shown in Figure 8. Clearly, the nonidealities caused the subtle, yet intriguing, differences between the idealized and rigorous models. Also, within the acceptable yp operating region, ER (at 0.32) was similar to all of the ER’s that have been discussed so far, indicating that an ER of 0.3 may be all that can be expected for this specific PSA-SVR process. E. Effect of Feed Concentration (yf). A PSA-SVR process must be designed to handle the highest yf expected; and similarly to Vf, large variations can be anticipated. The effect of yf on the PSA-SVR process performance was investigated by Ritter and Yang (1991a), but only with an emphasis on yp and under unusual conditions (i.e., γ < 1). Therefore, five runs (nos. 29-32 and 22) were made to study the effect of yf on the process performance. yf was varied from 0.5 to 10 vol %, with all the other parameters fixed (see Tables 1 and 2). The results of all these runs are shown in Figure 9, and Tables 3 and 4. Increasing yf had the same effect on the process performance as did increasing Vf; i.e., as yf increased, yp and BCF increased, and R and E (or ER) decreased. The idealized model also predicted the same trends as those discussed with respect to Vf; therefore, the ideal versus nonideal conclusions were the same. However, yf had the largest effect on the process performance among all the variables investigated, suggesting that there were subtle differences between changing yf and Vf. Intuitively, as yf decreased, more ideal operating conditions should have been approached, i.e., isothermality and constant velocity should have prevailed. The large changes that occurred in the BCF’s, ranging from 8% to nearly 100%, suggested that this may have been the case. The large changes that occurred in ER and the magnitude of ER reaching as high as 0.50 were also consistent with this statement. This result suggested

that either a very low BCF, ideal conditions, or both were conducive to significantly increasing ER. F. Effect of Heat Transfer Coefficient (h). Heat effects in PSA-SVR processes are largely unknown as previous studies assumed that isothermal conditions prevailed for dilute feeds (Ritter and Yang, 1991a; Kikkinides et al., 1991). Therefore, six runs (nos. 1924) were carried out to evaluate the effect of h on the process performance. A large h (10 kJ/(s‚m2‚K)) was used in run no. 24 to approximate isothermal conditions, and an h equal to zero was used to simulate adiabatic conditions (see Table 2). All the other parameters were fixed (see Tables 1 and 2). The results of these runs are shown in Figure 10, and Tables 3 and 4. When the operating conditions approached isothermal conditions, the process performance improved significantly. The yp and BCF decreased, and R and E (or ER) increased with an increase in h. However, in the acceptable yp operating region, ER was again on the order of 0.3, and it began to level off as h increased and yp approached zero, which indicated that breakthrough had more pronounced effects on ER than h. In contrast, as adiabatic conditions were approached, the performance became very poor, as indicated very clearly from the BCFs. The decrease in the process performance with decreasing h was initially caused by the elevation and depression of the bed temperature relative to feed temperature during the adsorption and desorption steps, respectively. However, as h decreased further, a net cooling effect persisted over more than 80% of the bed (except near the boundaries) throughout the entire periodic cycle (Liu and Ritter, 1994). Figures 2-4 show the periodic state heating and cooling effects during the adsorption (steps I and II) and desorption (steps III and IV) portions of the cycle for the base case. Clearly, during adsorption the capacity was reduced causing the wave front to move further down the bed compared to the isothermal case, and during desorption the capacity was increased causing


less regeneration compared to the isothermal case. Ultimately, as h decreased, the net cooling effect materialized, and more of the bed became contaminated with benzene, thereby reducing the portion of the bed that was necessarily used as a guard against breakthrough (Ritter and Yang, 1991a). Although under these net cooling conditions, the capacity clearly increased during adsorption, apparently desorption dominated the process dynamics because the process performance continued to deteriorate. Moreover, the magnitude of the temperature excursion increased as the operating conditions approached adiabatic conditions; thus, the net cooling effect became more pronounced. In fact, when the system was operated adiabatically or near adiabatic conditions (run nos. 19 and 20), the benzene vapor condensed in the bed during the repressurization and adsorption steps prior to reaching the periodic state. This marked effect of h on the process performance was unexpected, as the periodic state temperature swings were not very large. For example, for the base case (which was moderately non-isothermal), Figure 2 shows that most of the bed experienced only 10-15 °C swings (the much larger swings that occurred at the light product end of the bed were considered inconsequential, on the basis of continuing work). Nevertheless, these relatively small temperature swings that increased as h decreased produced dramatic changes in the process performance, especially in terms of the BCF. G. Effect of Cycle Time (tc). tc is one of the more important design variables in PSA processes, as it sets the column size. Clearly, if tc is too long, breakthrough would occur, and if it is too short, the adsorbent would be underutilized (low BCF). Nevertheless, very few studies have investigated the effect of tc on the process performance. Two exceptions were the works by Chihara and Suzuki (1983) and Ritter and Yang (1991a); but they were both concerned only with yp. Therefore, four runs (nos. 33-35 and 22) were used to investigate the effect of tc on the process performance. tc was changed from 5 to 20 min while all the other parameters were fixed (see Tables 1 and 2). When tc was decreased compared to that of the base case, the cycle step times were scaled-down in proportion to the decrease. For example, for a tc of 10 min, the durations of steps I, II, III, and IV were respectively 1, 4, 1, and 4 min. The results of these runs are shown in Figure 11, and Tables 3 and 4. As tc increased, τ changed slightly due to pressurization with feed. However, the actual amount of feed that entered the column during step I was, for the most part, constant and set by R; this change was therefore neglected. Increasing tc also increased the amount of benzene vapor fed into the bed during a cycle. Consequently, BCF increased and eventually benzene breakthrough occurred, which necessarily increased yp and decreased R. This trend was also exhibited in the studies by Chihara and Suzuki (1983) and Ritter and Yang (1991a); however, neither study addressed the effect of tc on E (or ER). Figure 11 shows that a maximum in E (or ER) occurred essentially at the onset of breakthrough. This result suggested that the maximum E (or ER) that can be obtained for a given set of process conditions occurs at a tc corresponding to a BCF of unity, i.e., just at the onset breakthrough. In contrast, the idealized model indicated that there was no effect of tc on E prior to breakthrough; and thereafter, E decreased with increas-

Figure 11. Effect of cycle time (tc) on the process performance, in terms of yp, R, E, ER, and τ.

ing tc, as exhibited in this work. Thus, the nonidealities included in the model in this study caused the maximum in E. Moreover, the maximum ER was similar to those found with the other parameters, indicating that improvement was still possible. H. Effect of Adsorption Step Time (ta). The blowdown (or evacuation) time in a PSA-SVR process is set by the working capacity of the vacuum pump. This time depends on the size of the column, which, in turn, depends on τ, which, in turn, depends on ta. These three factors together set tc. Therefore, it was instructive to investigate the effect of ta on the process performance at a fixed tc. Five runs (nos. 36-39 and 22) were made by setting tc at 20 min and by setting the combined times for steps I and II and steps III and IV at 10 min each. Also, in all cases, the times for steps I and III were equal, as were those for steps II and IV. For example, run no. 38 step times were 4, 6, 4, and 6 min, respectively, for steps I, II, III, and IV. The results of these runs are shown in Figure 12, and Tables 3 and 4. Increasing ta increased the amount of benzene fed into the bed during a cycle, similarly to increasing tc. However, in this case, τ increased linearly with ta because tc was fixed, and the feed gas used to pressurize the column was also fixed by R. At a ta of 5 min, the light product contained only 8.27 ppm of benzene, whereas at a ta of 9 min, significant benzene break-

2310


Figure 13. Effect of length to diameter ratio of the bed (L/db) on the process performance, in terms of yp, R, E, and ER.

Figure 12. Effect of adsorption step time (ta) at fixed cycle time (tc) on the process performance, in terms of yp, R, E, ER, and τ.

through occurred. Therefore, in terms of yp, R, and BCF, the explanations were the same as those given for the effects of tc; however, this was not the case for E (or ER). Figure 12 shows that a marked increase in E (or ER) occurred with an increase in ta whether breakthrough occurred or not. This was in contrast to the effect of tc on E, where a maximum occurred (see Figure 11), and it was contrary to the idealized model. The idealized model treated ta and tc the same because steps I and III were frozen; accordingly, the predicted trends were the same as those given for tc. These results showed that steps I and III had a significant and rather surprising effect on the process performance. In other words, if the effects of steps I and III were negligible, changing ta would have been equivalent to changing tc. Clearly, this was not the case, as evidenced by the marked differences in the performance trends. In fact, within the acceptable yp operating range, the ER’s in this case were the lowest among all the parameters investigated. I. Effect of Bed Length to Diameter Ratio (L/ db). The L/db in industrial PSA-SVR processes generally ranges from 1.0 to 1.5 to minimize pressure drop (Tolles, 1995). However, the effect of L/db on the process performance is largely unknown, especially under realistic conditions. Therefore, six simulations (nos. 40-

44 and 22) were carried out to determine the effect of L/db on the process performance. In these runs, the volume of the bed was not changed, i.e., the amount of adsorbent packed into the bed was fixed. Also, the L/db was varied from 1.25 to 15.00 to ensure that a broad range was covered, including bench-scale systems. The results of these runs are displayed in Figure 13, and Tables 3 and 4. A decrease in L/db had a negative effect on the process performance, i.e., yp and BCF increased, and R and E (or ER) decreased. It was first thought that the decrease in both the feed and purge velocities that occurred with a decrease in L/db caused the poor performance (recall that these runs were performed at a fixed Vf at STP and constant γ). However, the idealized model predicted that there was no effect of L/db on the process performance whether breakthrough occurred or not. Thus, the poor performance was caused by the coupled effects of the nonidealities included in the rigorous model used here. These results were intriguing since they also have some interesting ramifications from a process design point of view. Typically, PSA processes are scaled-up from bench to pilot to full scale simply on the basis of τ. This necessarily implies that the process performance only depends on the volume of the column and is independent of L/db. However, as the scale decreases the L/db of the PSA system usually increases. Thus, on the basis of the results of this study, using τ for scale-up may lead to undersized columns. This problem is exascterbated by the fact that heat effects also typically decrease with scale, i.e., bench scale systems, because of their larger L/db, typically operate closer to isothermal conditions than full scale systems. This study showed that heat effects can be significant in PSA-SVR processes, which, if ignored, would make the scale-up from τ even worse. Conclusions PSA-SVR was studied at the periodic state by computer simulation using a benzene vapor-nitrogen-


activated charcoal system. A four-step, Skarstrom-type cycle was implemented, but with vacuum in lieu of compression to effect pressure changes. The rigorous model accounted for heat and mass transfer resistances, velocity changes, and pressurization and blowdown effects. Also, realistic process parameters and conditions were used in all cases to study both the process dynamics and performance. An investigation of the process dynamics showed that under moderately non-isothermal conditions, temperature swings can be significant and have a marked effect on the velocity profiles. Also, temperature front sensing can be used to monitor the concentration front since the two waves may propagate together during the adsorption step. The rigorous model also showed that the frozen solid and gas phase assumption can be used to approximate fairly accurately the pressurization step of a PSA-SVR process operated under realistic conditions, but not the blowdown step; very slight changes in loading may cause the assumption to breakdown during blowdown. Finally, velocity changes can be significant, during both the blowdown and evacuation steps due to the considerable amount of vapor desorption that occurs. Overall, this study showed that these temperature and velocity changes must be accounted for to accurately model the process dynamics and performance of a PSA-SVR process. A comprehensive parametric study also examined the effects of γ, p, R, Vf, yf, h, tc, ta, and L/db in terms of four process performance indicators, i.e., yp, BCF, R, and E (or ER). Increasing γ improves the process performance, except for E which decreases. Increasing R by increasing PH and increasing ta both have the same negative effects on the process performance, except for ER which increases. On the other hand, increasing R by decreasing PL and increasing h and L/db all have the same positive effects on the process performance. Negative effects on the process performance result when increasing p, yf, Vf, and tc; however, when increasing tc, E may exhibit a maximum at the onset of breakthrough. All of these trends were compared qualitatively to trends predicted by an idealized PSA model, which showed that in almost all cases, the coupled effects of heat and mass transfer resistances, velocity changes, and pressurization and blowdown effects have significant and rather interesting effects on the process performance. Moreover, at near the adiabatic condition, vapor condensation may occur prior to reaching the periodic state, indicating that heat effects can be very pronounced in PSA-SVR systems. Acknowledgment The authors gratefully acknowledge financial support from the National Science Foundation under Grants CTS-9410630 and OSR-9108 772-004 and from the Westvaco Charleston Research Center. Nomenclature BCF ) bed capacity factor, defined in eq 5 b, b0 ) isotherm parameters, m3/(mol‚K0.5) CP ) heat capacity, kJ/(kg‚K) db ) bed diameter, m De ) effective diffusion coefficient, m2/s E ) enrichment ∆H ) heat of adsorption, kJ/mol h ) overall heat transfer coefficient, kJ/(s‚m2‚K) k ) mass transfer coefficient, 1/s

L ) bed length, m LDF ) linear driving force LUB ) length of unused bed P ) pressure, kPa PSA ) pressure swing adsorption q ) amount adsorbed, mol/kg q* ) equilibrium amount adsorbed, mol/kg rp ) pore radius, m R ) gas constant or recovery STP ) standard temperature and pressure SVR ) solvent vapor recovery T ) temperature, K T0 ) ambient temperature, K t ) time, s u ) interstitial velocity, m/s V ) volumetric flow rate, m3/s y ) gas phase mole fraction z ) axial position, m Greek Symbols R ) pressure ratio F ) density, kg/m3 ) bed void fraction γ ) purge to feed ratio p ) pressure level τ ) throughput, m3 STP/(h‚kg) Subscripts a ) adsorption b ) bed c ) cycle or critical e ) exhaust f ) feed g ) gas phase H ) high I ) ideal L ) low P ) purge p ) light product R ) relative s ) solid phase or step I, II, III, IV ) step numbers

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Ritter, J. A.; Yang, R. T. Pressure Swing Adsorption: Experimental and Theoretical Study on Air Purification and Vapor Recovery. Ind. Eng. Chem. Res. 1991a, 30, 1023. Ritter, J. A.; Yang, R. T. Air Purification and Vapor Recovery by Pressure Swing Adsorption: A Comparison of Silicalite and Activated Carbon. Chem. Eng. Commun. 1991b, 108, 289. Ruthven, D. M. Principles of Adsorption and Adsorption Processes; John Wiley & Son: New York, 1984. Ruthven, D. M.; Farooq, S.; Knaebel, K. S. Pressure Swing Adsorption; VCH Publishers: New York, 1994. Skarstrom, C. W. Use of Adsorption Phenomena in Automatic Plant-type Gas Analyzers. Ann. N. Y. Acad. Sci. 1959, 72, 751. Tolles, E. D. Westvaco Charleston Research Center, Charleston, SC, personal communication, 1995. Tondeur, D.; Wankat, P. C. Gas Purification by Pressure Swing Adsorption. Sep. Purif. Meth. 1985, 14 (2), 157. Wheelwright, S. M.; James, M. V. Adiabatic Adsorption with Condensation: Prediction of Column Breakthrough Behavior Using the BET Model. In Fundamentals of Adsorption; Myers, A. L., Belfort, G., Eds.; Engineering Foundation: New York, 1984; p 721. Yang, R. T. Gas Separation by Adsorption Processes; Butterworth: London, 1986.

Received for review February 29, 1996 Revised manuscript received April 9, 1996 Accepted April 9, 1996X IE960114C

X Abstract published in Advance ACS Abstracts, June 1, 1996.

Pressure Swing AdsorptionâSolvent Vapor Recovery: Process

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