Ind. Eng. Chem. Res. 1998, 37, 2783-2791
2783
Tapered Pressure Swing Adsorption Columns for Simultaneous Air Purification and Solvent Vapor Recovery James A. Ritter* and Yujun Liu Department of Chemical Engineering, Swearingen Engineering Center, University of South Carolina, Columbia, South Carolina 29208
The performance of a tapered pressure swing adsorption (PSA) column is investigated on the basis of rigorous nonisothermal numerical modeling, for simultaneous nitrogen purification and butane vapor recovery. The results indicate that the tapered column improves the process performance when feeding from the wider end of the column and purging from the narrower end. An optimum taper angle (5°) is also found for the constant length and volume system investigated with an order of magnitude increase in the light product purity. The favorable effects are manifested through complex temperature variations and corresponding local concentration wave velocity variations associated with heating and cooling effects that are caused by adsorption and desorption of the butane vapor. The favorable effects of a tapered PSA column also improve as the heat effects become more pronounced. Introduction During the 1980s, pressure swing adsorption (PSA) gained widespread commercial acceptance (Ruthven, 1984; Yang, 1987; Ruthven, et al., 1994), and the growth in research and development, and commercialization, of PSA has been rather spectacular in the last 2 decades. The key reason for this outstanding progress is that PSA technology can provide a very flexible and efficient means of gas separation and purification, and for many applications, it can reduce the energy and cost of separation compared to conventional separation processes such as absorption and distillation. Nowadays, PSA processes are widely used on a very large scale for hydrogen and carbon dioxide recovery from steammethane reformer off-gas, carbon dioxide and carbon monoxide production from blast furnace flue gas and other waste gases from the steel industry, air separation for producing oxygen and nitrogen enriched gases, gas drying, and recovery of methane from landfill gas (Sircar, 1989). Environmental and defense applications of PSA represent two relative new areas, however, with major potential for growth. For example, the recovery of small amounts of organic vapors from chemical processes, storage tanks, and other gaseous vents, as well as from solvent painting, purging and cleaning operations are increasing (Keller, 1983; Baron, 1994), as are air purification needs in defense applications (Tevault, 1995). Specific environmental issues related to adsorption science and technology where PSA processes have either recently been commercialized or shown some promise for commercialization include local environmental problems, such as solvent vapor recovery (SVR) (Gerard, 1989; Ritter and Yang, 1991; Holman and Hill, 1992; Graham and Ramaratram, 1993; Hall and Larrinaga, 1993; Liu and Ritter, 1996; Pezolt et al., 1997; Subramanian and Ritter, 1997), solvent vapor fractionation, and SOx and * To whom correspondence should be addressed. Phone: (803) 777-3590. Fax: (803) 777-8265. E-mail: Ritter@ sun.che.sc.edu.
NOx removal from flue gas (Kikkinides and Yang, 1991), and global environmental problems, such as emission control of greenhouse gases (CO2, CH4, N2O, etc.) (Chue et al., 1995; Sasaki et al., 1993), recovery of chlorofluorocarbons (CFCs) in emission control of ozone depletion gases (Suzuki, 1995), and contaminant removal in defense applications (Ritter et al., 1997). Measures of the PSA process performance differ for different applications, but the process throughput as an indicator is common to all applications. In environmental applications of PSA, the light product purity is the most important process performance indicator, with the solvent vapor recovery and enrichment as secondary indicators (Liu and Ritter, 1996). Considerable research has been done on improving the PSA process performance, with a major part of this effort directed toward improving the process economy by enhancing the light product recovery (Yang, 1987). Two of the most important developments involve adding a cocurrent blowdown step between the adsorption and countercurrent blowdown steps to increase the light product recovery and adding a pressure equalization step between the adsorption and blowdown steps to minimize the energy losses and increase the light product recovery (Berlin, 1966). The development of new adsorbents has also been given credit for improving the PSA process performance (Haag and Blystone, 1994; Tsuchiai et al., 1996)), and so has the use of layered beds that take advantage of the properties of different adsorbents in a single column (Greenbank, 1990; Shirley and LaCava, 1995; Pigorini and LeVan, 1997). In contrast, the use of tapered columns in adsorption processes have received essentially no attention, although their use is ubiquitous throughout the chemical process industries; typical examples include tapered fluidized beds, cyclone contactors and separators, circulating beds, and sprouted beds as catalytic reactors (San Jose et al., 1996). One exception, however, is the recent work by Subramanian et al. (1997), where an isothermal equilibrium theory analysis of a tapered PSA column interestingly resulted in exactly the same analytic expressions for the process
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2784 Ind. Eng. Chem. Res., Vol. 37, No. 7, 1998
performance as those obtained from an equivalent analysis of a cylindrical PSA column (LeVan, 1995; Subramanian and Ritter, 1997). In light of the no effect results obtained by Subramanian et al. (1997), the objective of this study is to further investigate whether tapered columns improve the performance of PSA-SVR processes based on a rigorous, nonisothermal, numerical modeling study. This objective is achieved via comparison between the process performances obtained from tapered and cylindrical PSA columns having the same volume and thus adsorbent inventory. Realizing that many different geometric configurations exist for tapered and cylindrical columns that have the same volume, only those that have the same length are investigated. In this way, the effect of the column length is eliminated when comparing the PSA process performance. The PSA system for the recovery of n-butane vapor from nitrogen using Westvaco’s BAX activated carbon is selected and commercially relevant process conditions are used. The effects of feed direction, taper angle, heat- and masstransfer coefficients, and cycle time are investigated.
Table 1. Values of the Parameters Used in the Rigorous Numerical Model parameters for the gas-phase heat capacity, Cpg (kJ/(mol‚K)) A × 102
B × 104
C × 107
D × 1011
0.948 3.112
3.310 -0.136
-1.107 0.268
-0.282 1.167
n-butane nitrogen
parameters for the three-process Langmuir model qm process 1 n-butane-BAX process 2 (ARE: 3.0%) process 3 process 1 nitrogen-BAX process 2 (ARE: 3.96%) process 3
b0
6.4627 2.6820 0.7305 1.2163 2.1379 0.0189
coefficients for the isosteric heat of adsorption, ∆H (kJ/mol) butane nitrogen
c0
c1
c2
c3
c4
-53.879 -44.105
14.466 55.222
-4.753 366.376
0.744 -1706.729
-0.041 1831.544
Mathematical Model
The energy balance is given by
The rigorous, nonisothermal, multicomponent mathematical model developed for a tapered PSA column accounts for finite heat- and mass-transfer resistances, integration of the pressurization and blowdown steps, and gas-phase velocity variations due to geometric and adsorption/desorption effects. It also accounts for temperature-dependent gas-phase physical properties, loading-dependent heat of adsorption, and the heat capacity of the adsorbed phase, which has been shown to have a significant effect on simulation results (Liu and Ritter, 1998). Other assumptions used to derive the model include the ideal gas law, negligible column pressure drop, thermal equilibrium between gas and solid phases, negligible axial and radial dispersions, negligible axial heat conduction, and temperature-independent adsorbent properties. Also, mass- and heat-transfer resistances are accounted for, respectively, by the linear driving force (LDF) approximation and an overall heattransfer coefficient. It is noted that rf always represents the cross sectional radius of the feed end of the bed, and rp represents that of the purge end. The total mass balance is given by
∂(uCpg)
∂u ∂z
-
1 ∂T T ∂t
+
1 ∂P P ∂t
-
u ∂T T ∂z
+
2(rp - rf) rL
N
u+
Si ) 0 ∑ i)1
(1)
∂z
+
1-R
P
(
Cpg ∂P
∂t
+u
∂yi ∂z
Sj + Si ) 0 ∑ j)1
ai
+
∂t
P ∂t
+
2uCpg(rp - rf)
+
rL R
rb cos(θ) P
(T - T0) ) 0 (5)
with the gas-phase heat capacity represented by N
Cpg )
yiCp ∑ i)1
(6)
gi
where
Cpgi ) Ai + BiT + CiT2 + DiT3
(i ) 1, 2, ..., N) (7)
The single- and mixed-gas equilibrium amounts adsorbed are represented by the three-process Langmuir model (Drago et al., 1996; Liu and Ritter, 1998), which is modified here for mixtures and given by
∑ j)1
s qi,j bi,jPyi
i ) 1, 2, ..., N
N
1+
(8)
bi,jPyi ∑ i)1
( )
0 exp bi,j ) bi,j
i ) 1, 2, ..., N - 1 (3)
i ) 1, 2, ..., N
where
where ∂qi/∂t is based on the LDF approximation as
∂qi ) ki(qi* - qi) ∂t
1 - R ∂T
2h
(2)
N
- yi
∂t
+ FpCpp
qi(Cp T + ∆Hi)] ∑ i)1
Fp
q*i ) i ) 1, 2, ..., N
)
∂Cpg
N
3
The component mass balances are given by
∂yi
P ∂t
+
∂[
where
1 - RTFp ∂qi Si ) P ∂t
B
1.5091 × 10-8 3968.5822 7.2187 × 10-8 4653.4317 5.3529 × 10-8 6009.3764 6.8751 × 10-5 720.8872 -8 4.2256 × 10 2552.3570 2.0223 × 10-33 21347.0611
(4)
Bi,j T
(9)
The isotherm model parameters are obtained from regressed experimental data for nitrogen and butane adsorbed on BAX activated carbon (Liu et al., 1997); the parameters are given in Table 1, along with the absolute relative error (ARE) of the correlations. The heat of
Ind. Eng. Chem. Res., Vol. 37, No. 7, 1998 2785 Table 2. Cylindrical Column Characteristics and Base-Case Operating Conditions column characteristics db (m) Lb (m) rp (m) Fp (kg/m3) Cpp (kJ/(kg‚K)) Cpa (C4H10) (kJ/(mol‚K)) Cpa (N2) (kJ/(mol‚K)) k (C4H10) (s-1) k (N2) (s-1) h (kJ/m2‚s‚K)
Table 3. Cylindrical and Tapered Column Dimensions with the Same Volume and Lengtha
operating conditions
0.0747 0.2724 0.001 05 0.391 550.0 1.046 9.86 × 10-2 2.84 × 10-2 0.026 99 0.026 99 0.000 67
yf (vol %) PH (kPa) PL (kPa) PH/PL Vf (SLPM) γM tc (min) tpb (min) (I, III) tfp (min) (II, IV) Tf (K) T0 (K)
35.0 151.6 15.16 10.0 7.5 0.15 10.0 1.0 4.0 295.0 295.0
θ (deg)
0
1
3
5
7
9
rf or rp (m) rp or rf (m)
0.0387 0.0387
0.0411 0.0363
0.0457 0.0314
0.0500 0.0262
0.0542 0.0208
0.0583 0.0151
a
The column length is 0.2724 m.
adsorption of each component is assumed to be the same as that of the corresponding single component, and the loading dependency of the heat of adsorption is calculated from the adsorption isotherms (Valenzuela and Myers, 1989) and then regressed into a polynomial of the form
∆Hi ) c0 + c1q + c2q2 + c3q4 + c4q5
(10)
The polynomial coefficients are also given in Table 1. The adsorbed-phase heat capacities of butane and nitrogen are approximated by the corresponding gasphase heat capacities, on the basis of results obtained from thermodynamic correlations derived from the adsorption isotherms for several hydrocarbons adsorbed on BAX carbon (Liu et al., 1997). The pressure history is also required as input to the PSA model. The pressure is held constant at PH and PL during the adsorption and purge steps, respectively; and it is approximated by linear functions of time during the blowdown and pressurization steps. The initial and boundary conditions are step I
at t ) 0 at z ) 0 at z ) L
y ) yIV u)0 y)0
T ) TIV
q ) qIV
for all z for all t for all t
step II
at t ) 0 at z ) 0
y ) yI y ) yf
T ) TI T ) Tf
q ) qI u ) uf
for all z for all t
step III
at t ) 0 at z ) L
y ) yII u)0
T ) TII
q ) qII
for all z for all t
step IV
at t ) 0 at z ) L
y ) yIII y)0
T ) TIII T ) T0
q ) qIII u ) uP
for all z for all t
T ) T0
Equations 1-10, along with the set of initial and boundary conditions, represent the comprehensive mathematical model of a PSA process utilizing tapered columns. The model is solved using a finite difference scheme starting from step II and a clean bed. Details of the solution method are given elsewhere (Liu and Ritter, 1996; Liu et al., 1998). Results and Discussion In this study, the performances of tapered and cylindrical PSA columns are compared at the same process conditions, and with the same length and volume. Also, the molar purge-to-feed ratio, not the volumetric purge-to-feed ratio, is kept the same (i.e., the same amount of carrier gas is used to purge both types of columns). The cylindrical bed characteristics and the base case operating conditions are given in Table 2. A basic, four-step, Skarstrom-type cycle is used in this rigorous numerical modeling investigation, which includes countercurrent carrier gas pressurization (step I), cocurrent high-pressure feed (step II), countercurrent
Figure 1. Periodic-state performance of PSA columns with different taper angles and feed directions.
blowdown (evacuation) (step III), and countercurrent low-pressure pure inert carrier gas purge (step IV). Heavy-component (solvent vapor) adsorption and light product purification are accomplished during step II; heavy-component desorption and concentration are accomplished during steps III and IV. The process performance is judged by the light product purity (yp), heavy-component recovery (R) and enrichment (E), and the bed capacity factor (BCF) which is defined as the ratio of the actual amount of the heavy component adsorbed at the end of the adsorption step to the equilibrium amount that can be adsorbed by the entire bed of adsorbent corresponding to the feed conditions (Liu and Ritter, 1996). For fixed process conditions, a larger BCF indicates a larger portion of the bed has been contaminated, which leaves less adsorbent as a guard against heavy-component breakthrough during the adsorption step; thus, this behavior corresponds to a poorer process performance. Effects of the Feed Direction and Taper Angle. A tapered PSA column can be fed from either the wide or narrow end during step II; correspondingly, it can be purged from the narrow or wide end during step IV, respectively. Using the base case operating conditions, the results from 10 simulations are presented that show the effect of the feed direction for different taper angles ranging from 0° to 9°. The process conditions are given in Table 2, the column dimensions are given in Table 3, and the simulation results are given in Figures 1-4. Figure 1 displays the periodic-state performance of the PSA columns with different taper angles for both feed directions. When the column is fed from the wide end (rf g rp), the periodic-state time-averaged butane
2786 Ind. Eng. Chem. Res., Vol. 37, No. 7, 1998
Figure 2. Periodic-state (a) gas-phase concentration, (b) loading, (c) temperature, and (d) gas-phase velocity profiles at the end of the adsorption step for PSA columns with different taper angles and fed from the wide end.
Figure 3. Periodic-state (a) gas-phase concentration, (b) loading, (c) temperature, and (d) gas-phase velocity profiles at the end of the purge step for PSA columns with different taper angles and fed from the wide end.
vapor mole fraction in the light product stream, yp, is 5520 ppm (Figure 1a) for the cylindrical column. However, when a small taper is applied to the column, yp decreases dramatically (i.e., the light product purity improves significantly). With a further increase in the taper angle of the column, yp continues to decrease until an optimum taper angle is reached. Under the conditions investigated, this optimum angle is 5°. Beyond this optimum angle, further increasing θ causes a slight increase in yp. In contrast, when the column is fed from the narrow end (rf e rp), after an initial drop in yp for a small taper, yp increases with further increases in θ; and for all θ’s, yp is always higher for the column fed from the narrow end than from the wide end. However, the other process performance indicators (BCF, R, and E) are nearly independent of both θ and the feed direction, although the small differences realized in the BCF, E, and R always produce favorable results when feeding from the wide end. Therefore, feeding from the wide end of a tapered column is superior to feeding from the narrow end, especially in terms of the light product purity. The favorable effect of a taper over the “no effect” result predicted by the isothermal equilibrium theory (Subramanian et al., 1997) is manifested through complex temperature variations associated with heating and cooling effects that are caused solely by adsorption and desorption phenomena. To illustrate these effects, the periodic-state butane vapor mole fraction, adsorbedphase loading, temperature and gas-phase velocity
profiles at the end of the adsorption step are displayed in Figure 2 for tapered columns with different angles and fed from the wide end. Figure 3 shows the same information, but at the end of the purge step. Note that the significantly shorter penetration depths of the concentration waves (y and q in Figure 2a,b) do not correspond with the slight changes in the BCF (see Figure 1) because of the tapered shape of the column (i.e., the BCF depends on volume). Figures 2c and 3c show that, with an increase in θ, the temperatures in the mass-transfer regions decrease at the end of the adsorption step and increase at the end of the purge step. The lower temperatures in these regions during the adsorption step result in more adsorption capacity, which causes the penetration depth of the solvent vapor to decrease (see Figures 1, 2a, and 2b). Similarly, the higher temperatures in these regions during the purge step result in more desorption. The overall effect is a greater periodic capacity, which corresponds to less periodic penetration depth and thus less breakthrough. To illustrate why feeding from the wide end compared to the narrow end produces a higher light product purity, the bed profiles of the four dependent variables at the end of the adsorption and purge steps are displayed in Figure 4 for two 5° tapered PSA columns fed from different ends. Figure 4c shows that the temperatures in the column fed from the wide end (rf > rp) are lower than those in the column fed from the narrow end (rf < rp) near the light product end of the column (z/Lb > 0.7) and higher everywhere else during
Ind. Eng. Chem. Res., Vol. 37, No. 7, 1998 2787
Figure 5. Periodic-state performance of tapered (θ ) 5°) and cylindrical PSA columns for systems with different heat-transfer coefficients: s, tapered; - -, cylindrical.
Figure 4. Periodic-state (a) gas-phase concentration, (b) loading, (c) temperature, and (d) gas-phase velocity profiles at the end of the adsorption (solid lines) and purge (dash lines) steps for two 5° tapered PSA columns fed from different ends.
both the adsorption and purge steps. Moreover, as pointed out by Liu and Ritter (1998), the lower temperatures during the purge step are more detrimental to the PSA process performance than the higher temperatures during the adsorption step. The higher adsorption step temperatures near the light product end and the lower purge step temperatures everywhere else that occur in the column fed from the narrow end result in less capacity at the end of the adsorption step and less regeneration at the end of the purge step (see Figure 4b). These coupled effects of temperature cause the concentration wave to cover more of the column (Figure 4a,b), which in turn causes earlier solvent vapor breakthrough and a lower light product purity in the tapered column fed from the narrow end. Effect of the Heat-Transfer Coefficient. The effect of the overall heat-transfer coefficient (h) on the performances of tapered and cylindrical PSA columns is investigated to further verify the preceding arguments and to disclose subtle effects of the heat-transfer characteristics of tapered and cylindrical PSA columns in PSA-SVR processes. Eight h’s from 0.0 to 10.0 kJ/ (m2‚s‚K) (0.0, 6.7 × 10-4, 2.5 × 10-3, 9.89 × 10-3, 5.23 × 10-2, 0.2, 0.5, and 10.0 kJ/(m2‚s‚K)) are selected to cover the entire range from adiabatic to isothermal conditions. The tapered column fed from the wide end with the optimum taper angle (i.e., θ ) 5°) is also used in this investigation. The other conditions are the same as those used in the base case. The PSA process conditions are given in Table 2, the column dimensions
Figure 6. Periodic-state temperature profiles at the end of the (a) adsorption and (b) purge steps for PSA columns with different heat-transfer coefficients (h1 ) 0.0, h3 ) 0.0025, h5 ) 0.0523, h7 ) 0.5 kJ/(m2‚s‚K)): s, tapered; - -, cylindrical.
are given in Table 3, and the simulation results are given in Figures 5 and 6. Figure 5 shows that under isothermal conditions, the tapered and cylindrical columns essentially result in the same process performance, which agrees completely with the isothermal equilibrium theory results reported
2788 Ind. Eng. Chem. Res., Vol. 37, No. 7, 1998
by Subramanian et al. (1997), even though a finite rate of mass transfer is used here (k ) 0.026 99 s-1). However, when the PSA process becomes nonisothermal, a tapered column always improves the process performance compared to a cylindrical column, except for E. Above a certain h, the cylindrical column gives a higher E than the tapered column, and vice versa below this value. Nevertheless, the favorable difference in yp in the tapered column compared to the cylindrical column is quite significant under nonisothermal conditions; this difference continues to increase as the adiabatic condition is approached. The improvements in the other performance indicators are relatively small, however. Interestingly, the BCF, yp, and E all go through a maximum and R goes through a minimum in both the tapered and cylindrical columns when the conditions vary from being adiabatic to isothermal. The maximum BCF and yp, and the minimum R (all indicative of the worst process performance) occur at h ) 0.0523 kJ/(m2‚s‚K), while the maximum E occurs at h ) 0.2 kJ/(m2‚s‚K). That the maximum E occurs at a larger h than the other performance indicators verifies once again that the maximum enrichment in a PSASVR process occurs at the onset of significant solvent vapor breakthrough (Liu and Ritter, 1996). This maxima/minimum phenomena is the result of complex temperature variations, as explained recently by Liu and Ritter (1998) and briefly below in terms of the temperature profiles. Figure 6 displays the periodic-state temperature profiles at the end of the adsorption and purge steps for both the tapered and cylindrical columns for different h’s. Except for the isothermal case, the tapered column generally results in lower temperatures during the adsorption step (Figure 6a) and higher temperatures during the purge step (Figure 6b), which again improves the performance over cylindrical columns. Also, a smaller h results in higher temperatures during both the adsorption and purge steps due to a larger heattransfer resistance. The maxima/minimum that occurs in the process performance indicators is caused by competition between the beneficial effects of higher purge step temperatures and the detrimental effects of higher adsorption step temperatures which change as the heat-transfer resistance changes, as explained in detail by Liu and Ritter (1998). To further prove that the temperature variations cause the differences in the process performances of tapered and cylindrical PSA columns, the bed profiles of the four dependent variables at the end of the adsorption and purge steps are displayed in Figure 7 for a 5° tapered PSA column fed from the wide end and for a cylindrical PSA column, both under the adiabatic (h ) 0 kJ/(m2‚s‚K)) equilibrium (k ) 10 s-1) condition. The other conditions are the same as those used in the base case (Table 2). Figure 7 shows very clearly that even when the rates of mass and heat transfer are infinite and zero, respectively, the tapered column still performs better than the cylindrical column in terms of the axial positions of the concentration wave fronts (or BCF) (Figure 7a,b). For example, the yp for this tapered PSA column process is 0.0 ppm, whereas that for the cylindrical PSA column process is 160 ppm; the corresponding BCFs are 0.546 and 0.629, respectively. So, in contrast to the isothermal equilibrium condition, where tapered and cylindrical columns perform the
Figure 7. Periodic-state (a) gas-phase concentration, (b) loading, (c) temperature, and (d) gas-phase velocity profiles at the end of the adsorption (solid lines) and purge (dash lines) steps for tapered (5°) and cylindrical PSA columns under the adiabatic equilibrium condition.
same and a simple volumetric argument can be used to explain the behavior (Subramanian et al., 1997), the adiabatic equilibrium condition produces widely different results for tapered and cylindrical columns and no simple volumetric argument holds. An explanation for this behavior is similar to that given previously and can be understood by referring to Figure 4c. The higher temperatures exhibited during the adsorption step and lower temperatures during the purge step in the cylindrical column compared to that in the tapered column give rise to a decreased periodic capacity, as explained previously. Effect of the Mass-Transfer Coefficient. The effect of the mass-transfer coefficient (k) on the performance of a tapered PSA column fed from the wide end is investigated using five k’s ranging from 0.001 to 0.5 s-1 (0.001, 0.005, 0.026 99, 0.1, and 0.5 s-1). The optimum taper angle (i.e., θ ) 5°) is also selected. The other conditions are the same as those used in the base case. The PSA process conditions are given in Table 2, the column dimensions are given in Table 3, and the simulation results are given in Figures 8 and 9. Figure 8 shows that for a system with a very small k, the PSA process performances of tapered and cylindrical columns is the same. In this case, the very large masstransfer resistance (i.e., very small k) results in marked breakthrough; essentially all of the adsorbent is contaminated in both types of columns. However, in systems with larger k’s, the advantages of the tapered
Ind. Eng. Chem. Res., Vol. 37, No. 7, 1998 2789
Figure 8. Periodic-state performance of tapered (θ ) 5°) and cylindrical PSA columns for systems with different mass-transfer coefficients: s, tapered; - -, cylindrical.
Figure 9. Periodic-state temperature profiles at the end of the (a) adsorption and (b) purge steps for PSA columns with different mass-transfer coefficients (k1 ) 0.001, k3 ) 0.02669, and k5 ) 0.5 s-1): s, tapered; - -, cylindrical.
column become very apparent, especially in terms of yp (Figure 8a). For example, at k ) 0.1 s-1, the tapered column with θ ) 5° exhibits no breakthrough (yp ) 0), whereas the cylindrical column exhibits a yp ) 580 ppm. The BCF also decreases with an increase in k in the tapered column, as shown in Figure 8a, but the effect of k on the differences in E and R is essentially negligible (Figure 8b).
Figure 10. Periodic-state performance of tapered (θ ) 5°) and cylindrical PSA columns using different cycle times: s, tapered; - -, cylindrical.
The favorable effect of a tapered column is again caused by the complex temperature variations as shown in Figure 9, which displays the periodic-state temperature profiles at the end of the adsorption and purge steps for both the tapered and cylindrical columns for different k’s. Figure 9a clearly shows that at k ) 0.001 s-1, the temperature waves are completely removed from both the tapered and cylindrical columns at the end of the adsorption step, resulting in the same flat temperature profiles, but for the larger k’s, the cylindrical column results in higher temperatures in the wave front region compared to those in the tapered column, which results in a better process performance for the tapered column. Effect of the Cycle Time. The effect of cycle time (tc) on the performance of a tapered PSA column fed from the wide end is investigated by varying tc from 5 to 20 min (5, 10, 15, and 20 min). The time of each step is also scaled up or down according to the base case cycle and step times, and the optimum taper angle (i.e., θ ) 5°) is again chosen. The other conditions are the same as those used in the base case. The PSA process conditions are given in Table 2, the column dimensions are given in Table 3, and the simulation results are given in Figures 10 and 11. When using a short cycle time (e.g., tc ) 5 min) in the butane-nitrogen-BAX carbon system, tapered and cylindrical columns result in almost the same process performance. As tc increases, however, the performance of the tapered column consistently improves over the performance of the cylindrical column within the range of the tc’s investigated. The tapered column not only improves yp (Figure 10a) but also R and E (Figure 10b), even though there is not much difference in the BCF (Figure 10a). Interestingly, at tc ) 10 min, both the tapered and cylindrical columns exhibit maximum in E essentially at the onset of breakthrough; this maximum has also been reported elsewhere (Liu and Ritter, 1996).
2790 Ind. Eng. Chem. Res., Vol. 37, No. 7, 1998
using a very short time cycle, a tapered PSA column has almost the same process performance as a cylindrical PSA column. For a system operating under nonisothermal conditions or having a large mass-transfer coefficient, a tapered PSA column improves the process performance, especially in terms of the light product purity. For a system using a longer cycle time, a tapered PSA column not only improves the light product purity but also improves the butane vapor recovery and enrichment. The favorable effects of a tapered PSA column over a cylindrical PSA column are manifested through complex temperature and thus local concentration wave velocity variations associated with heating/cooling that is caused by adsorption/desorption phenomena. Because the favorable effects of a tapered column are associated with heat effects, systems with more pronounced heat effects (like PSA-SVR processes) are expected to show more improvement over cylindrical columns. In these systems, for the same adsorbent inventory, a slight taper guards more against breakthrough, or for the same process performance, the bed size (i.e., adsorbent inventory) is reduced. Acknowledgment
Figure 11. Periodic-state temperature profiles at the end of the (a) adsorption and (b) purge steps for PSA columns using different cycle times: s, tapered; - -, cylindrical.
The explanation for the favorable effects of increasing tc in a tapered PSA column is similar to those given previously for the effects of θ, h, and k. Figure 11 shows the periodic-state temperature profiles at the end of adsorption (Figure 11a) and purge (Figure 11b) steps for both tapered and cylindrical columns for different tc’s. Clearly, the same arguments based on the effects of complex temperature variations cause the improvement in the performance of the tapered column over the cylindrical column. Conclusions The performance of a tapered PSA column is studied at the periodic state by using rigorous nonisothermal numerical modeling. The rigorous model utilizes a fourstep, Skarstrom-type cycle and accounts for heat- and mass-transfer resistances, pressurization and blowdown effects, and velocity variations caused by the column geometry, adsorption/desorption, and heating/cooling. The performances of tapered and cylindrical PSA columns are evaluated based on columns of the same length and volume (i.e., amount of adsorbent) that use the same molar purge-to-feed ratio and process conditions. Based on the n-butane-nitrogen-BAX activated carbon system, the results indicate that slightly tapered columns improve the PSA process performance, especially in terms of the light product purity. The results also show that feeding from the wide end of the column is superior to feeding from the narrow end and that an optimum taper angle (5°) exists where an order of magnitude increase in the light product purity is obtained compared to the cylindrical column. For a system operating under isothermal conditions, or having a very small mass-transfer coefficient, or
The authors gratefully acknowledge financial support from the National Science Foundation under Grant CTS-9410630 and from the Westvaco Charleston Research Center. Nomenclature A: coefficient for the gas-phase heat capacity B: coefficient for the gas-phase heat capacity BCF: bed capacity factor b, b0: adsorption isotherm parameters, kPa-1 C: coefficient for the gas-phase heat capacity Cpg: gas-phase heat capacity, kJ/(mol‚K) Cpp: solid-phase (pellet) heat capacity, kJ/(kg‚K) D: coefficient for the gas-phase heat capacity E: solvent vapor enrichment h: overall heat-transfer coefficient, kJ/(m2‚s‚K) ∆H: isosteric heat of adsorption, kJ/mol k: mass-transfer coefficient, s-1 P: pressure, kPa PH: feed (high) pressure, kPa PL: purge (low) pressure, kPa qi: adsorbate loading, mol/kg qi*: equilibrium amount adsorbed, mol/kg rf: radius of the feed end of the tapered column, m rp: radius of the purge end of the tapered column, m R: gas constant, or solvent vapor recovery Si: defined by eq 2 t: time, s T: temperature, K T0: ambient temperature, K u: interstitial velocity, m/s uf,c: interstitial feed velocity in cylindrical column, m/s Vf: feed volumetric flow rate, m3/min y: gas-phase mole fraction yp: time-averaged solvent vapor mole fraction in the light product z: axial position in the column, m Greek Letters Fp: pellet density, kg/m3 : interstitial void fraction in the column
Ind. Eng. Chem. Res., Vol. 37, No. 7, 1998 2791 γ: volumetric purge-to-feed ratio θ: taper angle, deg
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Received for review January 12, 1998 Revised manuscript received April 27, 1998 Accepted May 5, 1998 IE980019Z
