Lee. H.. Cummings, W. P., Chem. Eng. Progr. Symp. Ser.. 63, No. 74, 42 (1967). Lezin, S..Russ. J . Phys. Chem., 42 [7], 922 (1968). Lychkin. I . P., Rizov, 2 . M . , Todes, 0. M., Zh. Priki. Khim.. 34 [6], 1225 (1961). Nordon, P., Banks, P. J.. “Interacting Heat and Mass Transfer,” Invited Review, First Australasian Conference on Heat and Mass Transfer, Monash University, May 23-25, 1973. Pan, C. Y . , Ph.D. Thesis, Universityof Toronto, 1970.
Pan, C. Y . , Basmadjian. D., Chem. Eng. Sci.. 26,45 (1971). Rhee. H.. Amundson, N . R., Chem. Eng. J . , 1, 279 (1990). Rhee, H., Amundson, N. R . , Chem. Eng. .I.. 3, 121 (1972). Young, P. L . , Gas, 44 [7], 49 (1968). Zwiebel, I,, Gariepy, R. L . , Schnitzer, J. J . , A.I.Ch.E. J . . 16, 1139 (1972).
Received for reuieu: December 23, 1974 Accepted March 24, 1975
Nonisothermal Desorption by Gas Purge of Single Solutes from Fixed-Bed Adsorbers. II. Experimental Verification of Equilibrium Theory Diran Basmadjian* and K. Dan Ha Department of Chemical Engineering, University of Toronto, Toronto Ontario M5S 7 A 4
David P. Proulx Pioctor and Gambie, Hamilton Ontario L8N 3L5
The results are reported of an experimental study of the desorption by gas purge of single gases from a 5’/z ft long, 31/2 in. diameter fixed-bed adsorber. Breakthrough curves were measured for the systems c02-N~5 A molecular sieves, COZ-He-carbon and C2HG-He-carbon over a wide range of regenerant temperatures (80-450°F). Nonuniform initial bed loadings caused by adsorption transfer zones and plateaus, as well as uniformly saturated beds were used. The data are in all qualitative respects in agreement with the predictions of equilibrium theory detailed in Part I . In particular, it was confirmed that the desorption time i s independent of pure regenerant temperature when the initial bed loading is located in the region ( I ) of the q - Y diagram. Quantitative predictions of desorption time and gas consumption are satisfactory to excellent for uniformly saturated columns yielding two-zone desorption profiles. The predictions are also good for the important case of columns loaded with low concentration feed to breakthrough only (partial saturation). In the severest test of the theory involving a low-temperature purge yielding a single unstable solute zone, the predicted desorption time was approximately 5 0 % of the measured value over a 3.6 ft length of column.
In Part I of this series (Basmadjian et al., 1975) equilibrium theory was applied to analyze the desorption by constant pressure gas purge of single gaseous components from a fixed-bed adsorber. The heat effects associated with the process were seen to give rise to a variety of equilibrium profiles whose shape for a given isotherm depended primarily on the initial bed loading, system pressure, and the temperature, concentration, and heat capacity of the regenerant gas. ?he most common type of profile was found to consist of two zones separated by plateaus of constant concentration and temperature. The zones could be of the stable (shock) or unstable type, with plateau conditions most often higher than the initial bed values. Single zone solute profiles followed by a pure temperature wave are also possible, and arise when pure gas is used to purge a bed loaded in the so-called region (I)of the q-Y diagram. In actual operations one can expect some deviations in column behavior from the predictions of simple equilibrium theory, since the latter postulates adiabatic operation and uniform initial bed conditions, as well as local equilibrium between the two phases. A departure from these conditions affects the bed performance in the following manner. ( a ) Heat and Mass T r a n s f e r Resistances. These two 340
Ind. Eng. Chem., Process Des. Dev., L’ol. 14, No. 3, 1975
factors combine to give a n elongation or dispersion of the theoretical transfer zones. The shock-type temperature and concentration “jumps” elongate into S-shaped transfer zones which retain their shape-as do the theoretical discontinuities-in the direction of flow (“constant-pattern” or stable zones). Unstable, expanding transfer zones predicted by the theory also become more elongated and continue to expand as they travel through the bed. An exception is the pure temperature fronts which, when they arise, are invariably unstable in practice while the theory predicts shock-type discontinuities. The elongation of the transfer zones is usually accompanied by an erosion and even a decline of the plateau zones. A recent parametric simulation study by Cooney (1974) shows these effects quite clearly for the case of twozone adsorption profiles. Their magnitude generally tends to diminish with increasing bed length. (b) Heat Exchange with Column Wall a n d Surroundings. Departure from adiabatic conditions affects primarily the plateau levels and, to a minor degree, the length of the transfer zones. In desorption at ambient conditions, for example, the temperature plateau initially drops below the ambient level due to the heat of desorption. Under adiabatic equilibrium conditions. it should stay at that level, but instead shows a gradual rise in the direction of
S
gnometer
~
P G
3e,
* Rotameter
THERMOCOUPLES Thermal
Rotameter
COz NP Cyhxkr Cylinder
Figure 1. Schematic diagram of experimentalapparatus
flow due to heat leaks from the surroundings. This rise is accompanied by an increase in the concentration plateau level and the regeneration process becomes more efficient. In high temperature regeneration, the reverse occurs, plateau concentrations drop because of heat leaks to the surroundings, and the regeneration process loses efficiency. In industrial columns, this trend is often counteracted by insulating the interior of the column wall. The more favorable volume to surface area ratio of these larger beds compared to laboratory columns helps to reduce the effect of heat leaks in industrial operations. ( c ) Nonuniform Initial Bed Conditions. This factor is of little importance in the adsorption step, which usually takes place on a fairly uniform, regenerated, and cooled bed. In desorption, the initial bed loading is determined by the adsorption profiles at breakthrough time. These are inevitably nonuniform due to the presence of transfer zones and plateaus, and the variations in both temperature and concentration can be fairly severe in short columns and systems with high transport resistances. The effect will tend to be less serious in the longer columns used in industrial operations since the transfer zones there occupy a proportionately smaller fraction of the total bed length if they are stable. Laboratory columns are thus generally more susceptible to the distorting influences of nonideal factors than the larger industrial beds. We will show, however, that even for the smaller size columns used in this work, the theory provides an excellent qualitative description of actual behavior and yields near quantitative estimates of some important desorption parameters. The experimental data presented here consist of desorption temperature and concentration breakthrough curves which were measured a t various column positions and under a variety of purge gas and initial bed conditions using three different systems. The domain of adsorber behavior covered includes the formation of single and two-zone solute profiles, self-sharpening and unstable zones. and plateaus of various levels. Regenerant temperatures ranged from ambient to 450°F. Nonisothermal breakthrough curves of this type have not so far been reported in the field of desorption. In the related area of drying of beds of solids, much experimental work has been done, but the results are usually reported in terms of average drying rates and weight loss, or
are incomplete in some way which rules out a comparison with equilibrium breakthrough curves. A rare exception is the limited data reported by Nordon and Bainbridge (1971) on the drying of beds of terylene. The single temperature breakthrough curve given by those authors shows a characteristic low-temperature plateau, flanked by a first leading transfer front and a much slower rear zone. Reasonable agreement was reported with the predictions of equilibrium theory. Experimental Section The desorption experiments were carried out in semipilot scale columns at slightly above atmospheric pressures (78-86 cm Hg). Purge gas velocities were in the range 500-1700 SCF/hr ft2, which is of the same order as the velocity of 4000 SCF/hr f t 2 reported for a natural gas dehydrator (Thomas and Clark, 1967). The operating conditions and systems investigated were as follows: (I) Low-temperature purge (Pan, 1970). Carbon dioxide-helium and ethane-helium on Pittsburgh Activated Carbon Type BPL, 4 x 10 mesh. Full column saturation and helium purge at ambient temperatures ( 7 ~ 3 4 ° F ) .(11) High-temperature purge (Proulx. 1972). Carbon dioxide-nitrogen on LINDE SA molecular sieves, l/g-in. pellets. Loading to breakthrough only. i.e.. column partially saturated. Nitrogen purge at 200-450°F and cocurrent to loading step. Equilibrium isotherms for the first two systems were determined in separate experiments (Pan, 1970. p 119). For the molecular sieve system, equilibrium data supplied by the manufacturer was used. Analytical expressions were fitted to the data by multiple linear regression as outlined in Part I. These expressions, along with the pertinent equilibrium and thermal data. appear in the Appendix. The agreement between the analytical and experimental isotherms was within 670 of the q values over most of the range, with a few larger deviations of up to 357" occurring in the sensitive low temperature and concentration range. The relatively poor fit in this region made an accurate prediction of total desorption times difficult. particularly for profiles with long trailing rear zones. The experimental apparatus is essentially that described in the original work of Pan (1970) and by Pan and Basmadjian (1970), suitably modified for the high-tempInd. Eng. Chem., Process Des. Dev., Vol. 14, No. 3, 1975
341
erature experiments by the addition of heaters (Proulx, 1972). A diagram of the latter apparatus appears in Figure 1. Two columns, constructed of 0.05-in. metal shim, were used, both 3Ih in. in diameter, approximately 6 ft long, and packed to a depth of 5Ih f t . The material of construction was brass for the low-temperature runs and stainless steel for the hot gas purge. Gas temperatures and compositions were measured a t 1-ft intervals along the columns by means of iron-constantan thermocouples (&0.5”F), and by diverting minute sample streams into a calibrated Gow-Mac thermal conductivity cell with an analytical accuracy of *2%. The readings were monitored continuously on a Barber-Coleman multi-point recorder. Column temperatures in the cold purge runs were never more than 40-60°F below ambient and heat leaks were relatively easy to contain with a 1 in. thick layer of Fibreglas insulation. Over a 3-ft section of the column, the maximum rise in plateau levels due to heat leaks was about 10°F. The high-temperature column was insulated with a 3-in. layer of Fibreglas wool (optimum thickness). The heat leak in these experiments was considerably higher and its most drastic effect was on the effluent temperature which attained asymptotic values 50-100°F below the inlet value. Plateau values were less affected, declining by 15-35°F over a 4-ft section. In comparable industrial columns, temperature drops due to heat leaks are generally about 50-75°F over the entire length of the bed. No adsorptioh profiles were measured in these experiments, but good estimates of the prevailing distributions a t the start of the desorption step could be made on the basis of equilibrium theory and the adsorption breakthrough curves presented by Pan and Basmadjian (1970). Calculations The procedure for calculating desorption times, from which breakthrough curves are derived, was given in Part I. We limit ourselves here to a summary of the relevant equations: Characteristic ODE’s
where
the bracketed portions of eq 1, 2, and 5 ) can be calculated for various concentrations or temperature levels. The values for p are then substituted into the general relation desorption t i m e t,,
=
height of bed Z velocity of propagation fl
(6 )
Sectional shocks did not arise in this study and need not be considered. Results Representative experimental breakthrough curves, along with those calculated from equilibrium theory, appear in Figures 3 and 4 for the low-temperature runs, and in Figures 5 to 7 for regeneration a t elevated temperatures. In Figure 8 we present experimental proof that the desorption time is independent of regenerant temperature when purging a bed loaded in region (I) with clean gas. Relevant portions of the hodographs for the three systems appear in Figure 2. In the low-temperature runs, material and time limitations made it difficult to achieve total regeneration of the entire bed. Complete desorption curves are consequently given for the 0.6 and 1.6 f t positions only, while those for the 3.6 ft position are approximately 90% complete. The data are nevertheless sufficient to reveal all features of importance and to afford a meaningful comparison with the predictions of equilibrium theory. Both single solute zone (pure thermal wave) and two-zone desorption behavior are demonstrated in these experiments. The high-temperature desorption runs pose greater difficulties of interpretation since they are performed under conditions of both nonuniform initial loading and substantial heat losses to the surroundings. To convey some idea of column performance in the absence of these effects, several detailed breakthrough curves for the 1 ft position are presented in Figure 5. The proximity to the gas inlet of this section of column ensures complete saturation and a minimum of heat losses. In Figures 6 and 7 desorption breakthrough curves measured over the entire bed length are shown. In both these experiments the bed was loaded to breakthrough only. The adsorber feed was located in region (11) in one case, run 9, and outside it for run 12. This choice was made in order to examine the effect of two types of nonuniform initial distributions which arise in practice: those resulting from single solute zone adsorption profiles, which are the more common variety, as well as those arising from two-zone adsorption profiles associated with high concentration feeds. Beds treating such feeds are usually regenerated by depressurization and their thermal desorption behavior is thus largely of theoretical interest only. Discussion
Equilibrium Equation
Algebraic Shock Equation
(5) As indicated in Part I, the equilibrium isotherm (4)is solved with combinations of the ODE’s and shock equation to obtain the q-Y “characteristics.” Once these are (in known, the profile propagation velocities P I , 1911, or
os
342
Ind. Eng. Chem., Process Des. Dev., Vol. 14, No. 3, 1975
I. Low Temperature Purge. (a) System COz-He-Carbon. Single Desorption Solute Zone. A feed of Y = 0.22 mol of COz/mol of He, T = 81.3”F, was used in this run, locating the loaded bed in the region (I) of the hodograph, Figure 2. A purge with pure helium gas should, according to equilibrium theory, lead to a single solute zone followed by a pure thermal wave. The predicted behavior is in excellent agreement with the measured results (Figure 3). The concentration curve is, in fact, of the single zone type and is unstable as required by the curvature of the I characteristic [cf. Part I, Table 1111. The leading zones are succeeded by well-defined temperature plateaus which gradually rise in the downstream direction because of heat leaks from the surroundings. The most noticeable deviation from theory occurs as expected with the rear pure
n
SYSTEM SYSTEM C02-He-C C02-He-C RUN E - 3
/
/--I
/
I
' 0 0
0
..-. ..-. H/'
- G,"?
Loading Y .022 T '813.F
0
0 05
01
015
Y
02
Initial Loading
30t
SYSTEM
0
RUN 12
T =825.F ,
O W
008
Y
Figure 2. q-Y diagrams (hodographs)for the systems studied.
SYSTEM COz-He-Carbon 015
/Equilibrium
Theory
Derorptm complete, 1611 ,Theorttdcol * ,
EKpenrnenml
I
0
80 Tp F
70
60
50
40
L
0
'0 20 30 40 50 Minutes Figure 3 . Experimental and theoretical ( - - -1 breakthrough curves. Run B-3 (Pan, 1970). Feed: Y = 0.22 mol of COp/mol of He, Purge: Gb = 3.08 Ib-mol of He/hr f t 2 . ~
temperature zone which is unstable in practice because of finite heat transfer rates while equilibrium theory predicts a shock jump from plateau to inlet temperature. The quantitative agreement was expected to be less satisfactory because of the anticipated low heat and mass transfer rates. Their effect should be particularly notice-
able since the entire solute transfer takes place in a single unstable zone. The results d o in fact show a n elongation of the transfer zone over the predicted shape, but what is surprising is the degree to which equilibrium considerations still dominate the course of desorption. At the higher concentrations, the equilibrium zone follows the Ind. Eng. Chem., Process Des. Dev.. Vol. 14, No. 3, 1975
343
Y
h,
0.20 7
SYSTEM CZi+HHe
-Carbon
0 I5
010 End of Derorpflon, 1611 Theoretical
005
n
80
60
40
I
20
I
20 40 60 0o Minutes 100 Figure 4. Experimental and theoretical ( - - -) breakthrough curves. Run D-1 (Pan, 1970). Feed: Y = 0.204 mol of CzH,j/mol of He. Purge: Gb = 4.33 lb-mol of He/hr ft2. 0
SYSTEM c 0 2 - N ~ -JAMS (111)
T w 260 O F
no4
-
002
001
T:Fl
T4F
253
300
-
t
1
100
I 530
M
,
u)
€0
83
loo!
A
,
10
;o
&
4
Minuter
Figure 5 . Experimental and theoretical ( - - -) breakthrough curves. Run 3. Feed: Y = 0.075 mol of COz/mol of Nz. Purge: G b = 2.13 lb-mol of Nz/hr ftz. Run 15. Feed: Y = 0.018 mol of COz/mol of Nz, G b = 4.46 Ib-mol of Nz/hr ft2, (Proulx, 1972). experimental data quite closely and it is only at the low trailing edge levels that serious deviations occur. Part of this may in fact be attributable to the relatively poor fit of the equilibrium isotherm equation in this region. As a result, the predicted breakthrough time is about one-third of the measured value at the 1.6 f t position, and approximately 50% at the 3.6 ft position. 344
Ind. Eng. Chem., Process Des. Dev., Vol. 14, No. 3. 1975
The predicted temperature plateau of 35.3"F is in good agreement with the value measured closest to the inlet, 38.7"F, but heat leaks cause modest deviations further downstream. In general, however, this rather severe test of the equilibrium theory shows a surprising degree of agreement between experimental and equilibrium breakthrough curves. (b) System CzHs-He-Carbon. Two-Zone Desorption Behavior. The adsorber was in this instance loaded outside region (I) and should consequently give rise to twozone desorption curves. This is confirmed by the experimental results (Figure 4 ) . The leading zones are again unstable as required by the shape of the I characteristics (Figure 2) and are followed by combined concentration and temperature plateaus. The rear temperature zones appear to be constant pattern, but the data are not sufficiently extensive to verify unequivocally the predicted rear zone stability. The quantitative agreement with theory is better here than in the preceding case because of the substantial contribution of the plateaus which are a t near equilibrium conditions. The predicted desorption time is thus a much improved 77% of the observed value at 1.6 ft and even closer agreement can be expected for greater column lengths as the relative contribution of the transfer zones diminishes. The experimental concentration plateau also agrees well with the predicted value of Y = 0.013 while the temperature minimum at 0.6 ft is only 4" higher than the theoretical level. Breakthrough curves of this type, with a plateau lower than the initial loading, arise quite generally in the low temperature gas purge of beds, which is used extensively in the drying of heat-sensitive materials. The same type of curve has been obtained for example in the drying of beds of terylene with air at 70°C (Nordon and Bainbridge, 1971). 11. High-Temperature Purge. System COz-Nz-SA Molecular Sieves. (a) Uniformly S a t u r a t e d Bed Section. In these exploratory experiments, a 1 ft long section
T,'F I
400
300
200
IO0
0
20
40
60
80
Minutes
100
120
Figure 6. Experimental and theoretical ( - - - ) breakthrough curves. Run 9 (Proulx. 1972) Feed: Y = 0.02 mol of COz/mol of Nz,Purge: = 4.32 Ib-mol of Nn/hr f t 2
L
O0
20
Figure 7 . Experimental a n d theoretical (---, ----) Purge: G h = 4.44 lb-mol of XZ/hr ft2.
40
60
Minutes
loo
(;b
120
breakthrough curves. Run 12 (Proulx, 1972). Feed. Y = 0.089 mol of COz/mol of N2,
below the inlet was fully saturated at feed conditions and purged a t different temperatures. Heat and mass transport resistances were thus expected to be the only major factor causing deviations from equilibrium behavior. The results of the runs, together with the equilibrium breakthrough curves, are shown in Figure 5. Bed loading
and purge temperatures were chosen so as to yield two different types of two-zone desorption curves. The bed saturated with a high concentration feed of Y = 0.075 and purged at 260°F results in a desorption profile made up of an unstable leading zone, followed by a low-leuel plateau and a stable rear zone. For the bed with a low initial loadInd. Eng. Chem., Process Des. Dev., Vol. 14, No. 3, 1975
345
SYSTEM C@-Ns-S&MS
Y
0 12
Trq
C
160.F
0 4ylT
\
O
008O
h
\o
0021
-
0
0
1
10
20 2
30 3
40 4
50 5 MINUTES
60
6
T2 7
80
90 2.411
0
9Z.lft
Figure 8. Desorption of bed loaded in region (I) with clean gas a t different temperatures. Regeneration time independent of purge, gas temperature.
ing [ Y = 0.018] and a purge gas temperature of 385"F, equilibrium theory predicts roll-up, and in this case both front and rear zones are expected to be stable. Zone stability cannot be verified from the single breakthrough curves shown here, but all other features of importance are confirmed both qualitatively and to a large degree quantitatively as well. Predicted temperature plateaus agree within 5" with experimental values, concentration plateaus within 0.001 mole ratio unit. More significantly. predicted desorption times are now within 80-8570 of the experimental values, a considerable improvement over the results obtained in the low-temperature runs. (b) Nonuniform Initial Loading. Adsorber Feed in Region (11). A clean bed taking a feed located in region (11) generally gives rise to a single solute adsorption zone preceded by a pure thermal wave. The feed conditions for this run, Y = 0.02, T = 87"F, fall within that region (see hodograph Figure 2) and give a theoretical pure adsorption temperature plateau value of 172°F. Assuming equilibrium behavior, the loaded bed can thus be expected to contain a single solute zone ranging in temperature from 172" a t the exit to 87" at some location in the bed, and a section further upstream which is fully saturated a t feed conditions. In practice the loaded bed profile will be distorted to some extent by heat losses during the adsorption step and the interphase transport resistances, but the essential features of the above profile are retained. We have no direct measurements of these profiles, but the experimental adsorption results reported by Pan and Basmadjian (1970, Figure 6) indicate that the transfer zone will be of considerable length. Figure 6 shows the detailed desorption breakthrough curves obtained for this case. The theoretical curves based on equilibrium theory were calculated assuming the bed to be fully saturated a t feed conditions. The data exhibit the two-zone behavior with some roll-up which was already noted in the similar saturation run shown in Figure 5. The most striking feature here is the general decline in concentration plateau values with bed length, while the corresponding temperature plateaus show an increase in the same direction. The effluent plateau a t the 4 ft position, in fact, emerges with a temperature about 50°F higher than that crossing the 1 ft position and shows a decline due to heat loss only in the latter half of the breakthrough curve. Its level is some 40°F higher than the equilibrium value calculated on the basis of full bead saturation a t 87°F. These differences are quite evidently due to the heat picked up by the purge gas during its passage through the 346
Ind Eng. Chem., Process Des. Dev., Vol 14, No. 3, 1975
nonisothermal, adsorption solute zone. The change in concentration plateau values is likewise to be attributed to the nonuniform solute distribution on the bed, rather than to heat leaks which would have led to a decline in temperature plateau levels. At the 1 f t position there is good agreement between experimental and equlibrium breakthrough curves and desorption times which is to be expected in view of the nearsaturation conditions in this section of the bed. With length of passage, the two sets of curves diverge increasingly and the measured concentration plateau eventually drops to less than one-half the value predicted by equilibrium theory. It therefore comes as somewhat of a surprise that the theoretical desorption time is within 5% of the experimental value: 115 vs. 122 min. The explanation lies in the relative insensitivity of the regeneration time to bed loading in region (11) which has already been noted in Part I. The hodograph Figure 2 shows that the slope of the rear shock chord FP, which is inversely proportional to desorption time, is 0.045 Ib-mol of gas/lb of bed a t full bed saturation and drops only moderately to 0.037 if the bed is assumed uniformly loaded midway between adsorption plateau and feed conditions ( Y = 0.01, T = 130°F). The desorption time would change by only 17% for nearly a 2.5-fold change in loading. One can thus expect the nonuniform distribution, even if it occupies a substantial portion of the bed, to have no more than a marginal effect on the length of the desorption process. Simple equilibrium theory can be used in these cases to arrive a t close estimates of desorption time and purge gas consumption even though the initial bed loading has a substantial degree of nonuniformity. (c) Nonuniform Initial Loading. Adsorbed Feed Outside Region (11). With the adsorber feed located outside region (II), a t Y = 0.089, T = 83"F, the loaded bed profile now consists of a leading zone ranging in temperature from that of the clean bed to the plateau value of 205°F. The plateau itself is followed by an unstable rear zone with a temperature range 205-83°F and a section saturated in feed conditions. This wide range of concentration and temperature distributions make predictions based on simple equilibrium theory rather more difficult than in the previous cases. The approach taken in Part I was to assume uniform loading at adsorption plateau conditions. This condition is closely approached in longer beads which provide sufficient contact time for the two transfer zones to pull apart and create a substantial plateau region. In the relatively short columns used here, this will only be partially achieved and the nonuniform initial distribution will remain reflected to a substantial degree in the desorption breakthrough curves. This is evident in the results shown in Figure 7. The theoretical equilibrium curves given there are based on initial column loadings at both feed and adsorption plateau conditions. At the 1 ft position the former condition prevails and the measured values are closer to the prediction based on saturation with feed. At bed positions further downstream, the breakthrough curves tend increasingly toward the conditions predicted on the basis of bed loading at plateau conditions. At the 4 ft position the concentration plateau has dropped to Y = 0.015, compared to 0.013 predicted on this basis. Equilibrium loading at feed conditions overestimates the desorption time while saturation at adsorption plateau conditions underestimates it by 30%. As bed lengths increase, these differences may be expected to diminish. For the shorter beds used here, use can be made of a prediction method proposed by Proulx (1972) in which the desorption time is calculated from an average zone propagation velocity $ composed of the velocities of the plateau and the fully saturated sections.
111. Uniform Initial Loading Inside Region (I). The type of profile which results in this case was previously demonstrated in a general way with the system C02-Hecarbon (Figure 3). The main purpose of the runs described here was to verify that the desorption time is independent of purge gas temperature. In order to locate the operation in region (I), the adsorber containing 5A molecular sieves was initially heated to 310°F and saturated a t that temperature with a gas stream of Y = 0.11 mol of COz/mol of SZ.Two widely different purge gas temperatures of 160 and 45O"F were then used to regenerate the bed. The resulting solute desorption curves, measured a t 1 and 4 ft from the inlet, are shown in Figure 8. Breakthrough times were found to be identical, within experimental error, for the two feed temperatures used and present striking conformation of the results predicted by equilibrium theory. The possibility of exploiting this phenomenon by regenerating with cold gas was previously discussed in Part I. Conclusions Experimental desorption breakthrough curves, obtained on three different systems under semi-adiabatic conditions and over a wide range of initial loadings and purge gas temperatures, have been used to confirm the essential qualitative and quantitative predictions of equilibrium theory. Stable and unstable zones, single and two-zone profiles, as well as plateaus of various levels occur as predicted by theory. Desorption times were shown to be independent of regeneration temperature when purging a bed loaded in region (I) with clean gas. In the low-temperature purge of uniformly loaded beds, predicted plateau levels agree well with measured values and for two-zone desorption the calculated desorption time is within an acceptable percentage (>77%) of the experimental result. Single solute zone curves agree well with theory at the higher concentrations, but trail off much more slowly than the calculated values. The prediction of desorption times of such profiles is perhaps the least amenable to equilibrium theory. a t least a t low regeneration temperatures. The high-temperature purge of uniformly loaded beds having only modest heat losses is well described by the theoretical equilibrium breakthrough curves. In the more interesting case of a bed loaded to breakthrough only using feed located in region (11), desorption times are also well predicted by equilibrium theory although the bed may have a substantial section with a nonuniform initial distribution. The rather surprising success of the theory in this case is due to the relative insensitivity of bed behavior to initial loading levels. In the TSA regeneration of a bed loaded to breakthrough outside region (II)-a relatively rare occurrence in practice-quantitative predictions are hampered by the wide range of initial temperature and concentration distributions in the bed. It was verified, however, that the desorption breakthrough curves approach those calculated on the basis of uniform bed saturation at adsorption plateau conditions a t sufficient bed lengths. Acknowledgments The authors gratefully acknowledge the financial assistance of the National Research Council of Canada in support of this work. They were again much aided by several discussions with Messrs. B. Glover and J . Cripps of the LINDE Division, Union Carbide Canada Ltd.
Appendix The equilibrium isotherm for the following systems takes the classical Langmuir form
where
+
A [ T I = exp[a,
1
B [ T ] = exp[a,
+
a5T
+
31 a5T2]
PY # = I C Y P i n cm Hg, q in lb/100 lb of adsorbent, and T i n O R . (1) System COz-He-Carbon. Isotherm constants: a1 = 0.465872 X a2 = -0.586828 X lo4; a3 = 0.278254 X io7; U 4 = 0.344481 x 10'; a5 = -0.131064; a6 = 0.111114 X W 3 .Thermal data: Cpa = 8.62; C p b = 5.0; C,, = 0.2; AH' = -0.1364 x 105 + 748q. (2) System CzH6-He-Carbon. Isotherm constants: a1 = 0.129823 X a2 = -0.581829 X lo4; a3 = 0.310454 X lo7; a4 = 0.30629 X lo2; a5 = -0.103438; a6 = 0.758712 X W4. Thermal data: C p a = 11.6; C p b = 5.0; ClIs = 0.2; AH' = -0.130842 X lo5 457.8q. The bed density j)b for both systems is 34.1 Ib/ft3. Data for the system COZ-NZ-~A MS were given in Part I .
+
Notation Cp, = heat capacity of adsorbate, Btu/lb-mo1"F c p b = heat capacity of the carrier gas, Btu/lb-mo1"F CDb = C p b YCpa heat capacity of gas mixture, Btu/lbmo1"F C,, = heat capacity of the adsorbent, Btu/lb"F Cps = C p s + qCpa Gb = superficial flow rate of the carrier gas, lb-mol/hr ft2 AH = l / q AH' dq mean integral heat of adsorption Btu/lb-mol of adsorbate AH' = differential (isosteric) heat of adsorption, Btu/lbmol of adsorbate q = solid phase adsorbate concentration Ib-mol/lb of adsorbent q* = equilibrium function. defined by eq 4 q*)-;1. = partial derivatives of the equilibrium function t d e s = time, hr Y = mole ratio of gaseous adsorbate to carrier gas Z = bed length, ft
+
Greek Letters $ = propagation velocity, ft/hr $1.11 = propagation velocity of concentrations and tem-
peratures in unstable front (I) and rear (11) zones. ft/hr
& = propagation velocity of shock. ft/hr A = = definedbyeq3 = bulk density of the adsorbent bed, lb/ft3
Subscripts j = refers to feed or initial conditions I, II = refers to the I and I1 characteristics
Literature Cited Basrnadjian. D , Ha. K-D.. Pan. C . Y . , Ind Eng C h e m . Process Des. Dev.. 1 4 , 328 (1975). Gooney, D 0 . . I n d Eng C h e m . Process Des. Dev.. 13, 368 (1974) Nordon; P.. Eainbridge. N. W . , A p p / .Poiym. Symp.. 18, 1111 (1971). Pan. C. Y . . Ph.D. Thesis. Universityof Toronto, 1970. Pan, C. Y.. Basrnadjian, D.. Chem Eng S o . 25, 1653 (1970) Proulx, D . P.. M . A Sc. Thesis. University of Toronto. 1972 Thomas, T. L.. and Clark. E L . . Oii G a s J . . 65 [3]. 112 (1967)
R e c e i c e d f o r recieu. December 23. 1974 i i c c e p t e d M a r c h 24. 19it5
Ind. Eng. Chem., Process Des. Dev., Vol. 14, No. 3, 1975
347
