1046
Ind. Eng. Chem. Res. 1991, 30, 1046-1054
Recycled Thermal Swing Adsorption: Applied to Separation of Binary and Ternary Mixtures Michael J. Matzt and Kent S. Knaebel* Department of Chemical Engineering, The Ohio State University, Columbus, Ohio 43210
Research has been conducted on a process that is an offshoot of the liquid-phase parametric pumping and cycling zone adsorption processes. The shortcomings of those processes were the former could achieve high overall separation factors (ao= ch/cl) onIy when operated in the batch mode and the latter never achieved high separation factors. The present recycled thermal swing adsorption process appears to overcome those problems. Experimental and theoretical results are presented for a multisolute system. The separation of aromatic solutes from aliphatic solvents, specifically toluene and xylene from n-heptane, was studied. The theory was based on local equilibrium and traveling-wave thermal cycling and was solved via hodograph transformation. Experiments showed that the purified product concentration depends strongly on the feed concentration. For a feed of 1300 ppm toluene, the product was less than 0.5 ppm. For a feed of loo00 ppm, the product concentration was 810 ppm. The enriched product concentrations were typically 3-5 times that of the feed, regardless of the feed concentration. Thus, overall separation factors ranged from a. = 37 to over 10 000.
Introduction The original liquid-phase thermal swing adsorption (TSA) processes were parametric pumping (PP) and cycling zone adsorption (CZA). The former was invented by Wilhelm and co-workers (1966) and was perceptively analyzed by Pigford and co-workers (1969a). The latter was both invented and analyzed by Pigford and co-workers (Pigford et ai., 1969b; Baker and Pigford, 1971). The early contributions spurred efforts by others toward variations on the original themes. Wankat (1986) reviewed virtually all of those studies. Both PP and CZA employed fixed-bed adsorbers to which fluid was fed and temperature was cycled synchronously. PP also required a shift in flow direction that was coupled to the temperature shift. CZA was envisioned as a simplification of PP because it involved no flow reversal. Despite their auspicious beginnings, liquid-phase TSA processes have been regarded as laboratory curiosities since their inception. For example, there was inordinate attention paid to the manner by which heat was transferred. The direct (or standing-wave) mode of operation transferred heat through the column wall, so that the temperature shift was instantaneous along the axis of the adsorber. Conversely, the recuperative (or traveling-wave) mode of operation employed heat exchangers to shift the temperature of the feed to the adsorber. The former cannot be applied to adsorbers with diameters larger than about 4 cm. In contrast, even for small-scale systems the latter offers distinct advantages over the former in terms of separation performance. Applications of liquid-phase TSA processes in the laboratory were directed toward solvent cleanup, most commonly removing a single solute from a solvent. Performance was judged by the overall separation factor (Le., the ratio of time-averaged product concentrations), the solvent recovery ratio (i.e., the quantity of pure product per unit of solvent in the feed), and for batchwise PP systems the time required to reach cyclic steady state. Examples of experimental separation factors were 2.3 for continuous PP (Gregory and Sweed, 1972), 243.0 for batchwise PP (Rice and Foo, 1981),and a range of 2.6 (Shih and Pigford, 1975) to 9.3 (Knaebel and Pigford, 1983) for CZA systems. Unfortunately, batchwise PP was not feasible because the
* To whom correspondence should be addressed.
Present address: Dow Chemical Company, Midland, MI. 0888-5885/91/2630-1046$02.50/0
times to reach cyclic steady state were typically hundreds of hours (Rice and Foo, 1981). Similarly, staging of CZA systems did not appear promising, due to isotherm curvature and kinetic effects (Knaebel, 1982). A simple variation of CZA involved recycling a portion of one or both products to be fed synchronously to the adsorbent bed, as shown in Figure 1. This process has been referred to as recycled thermal swing adsorption (RTSA). A version of this process was studied by Rieke (1973) in Pigford’s group at Berkeley. His report of experiments indicated that the additional process complexity might not be worthwhile (Rieke, 1984). That observation was probably an inevitable result of the relatively high concentration of solute in the feed solution. In a subsequent study of RTSA, high separation factors (e.g., in the range of 80-300) were obtained for fairly dilute solutions by Kayser and Knaebel (1987). The ideal RTSA cycle proceeds as follows: cold feed is admitted to a fully regenerated bed, i.e., with hot, pure solvent in the interstitial voids. Contacting the clean adsorbent with cold feed results in uptake of the solutes, depending on the adsorbent’s selectivity and capacity. As a result, multiple self-sharpeningfronts (shocks) propagate through the column. When the bed has been loaded, the feed to the column is shifted to hot, pure solvent. The composition shift due to the imposed temperature shift results in a slug of hot, concentrated solution characterized by a diffuse wave. When this wave has traversed the column length, the cycle is complete. Subtle variations on this ideal cycle are possible by allowing one or both steps to be incomplete, which permits higher productivity though possibly diminished separation. The purpose of this report is to describe further work on RTSA. It examines more variables for separation of a single solute from a solvent, it extends the theory to apply to two or more solutes, and it presents experimental evidence that validates that theory. Additional information concerning the adsorbent properties that are relevant for RTSA applications has been presented elsewhere (Matz and Knaebel, 1989). Those results are summarized in Table I.
Adsorption Equilibrium For binary mixtures, i.e., a single solute in a nonadsorbing solvent, isotherm shape is critical to RTSA process performance. As opposed to conventional adsorption 0 1991 American Chemical Society
Ind. Eng. Chem. Res., Vol. 30, No. 5, 1991 1047 Feed
Feed
Cf Tf
Heater
Cf
-
Tf
0.06
01
&-&-;:
\
2
I
I
I
I
I
I
Temp. 1°C) Solute -0.0 Toluene
Symbol
0.05
-
0
-
Xylene Toluene Xylene
0.0 80.0 80.0
*
X
U PI
n
L
Intermediate Product Recycle Tank
Pure Product Recycle Tank
0.04
m m
0
0.03
0.02 Enriched Product ch
Th
Heating Half-Cvcle
Pirified Product
0.01
c, TI Cooling Half-Cvcle
0.00
Figure 1. Flow sheet of the dual recycle thermal swing adsorption process (after Kayser and Knaebel, 1987). Table I. Experimentally Measured Properties of t h e Adsorbent, Solvent, and Solutes a t 25 "C" property, Units value
0.000
0.002
0.004
C = Concentration
0.006 (g/g)
Figure 2. Pure-component isotherms of toluene and xylene in nheptane on silica gel at 0 and 80 "C.
-
0.025
OI
\ OI
0.020 U
5
I
PI
n
L 0
m
0.41 22.0 7.5 x lo*
's = solid = silica gel; f = fluid = n-heptane; eff = effective value in fluid-filled pores of the solid; T = toluene.
systems, higher favorability of the isotherm actually decreases the separation capacity as feed concentration increases. For RTSA processes the maximum feed concentration at which pure solvent can be obtained is determined by the intersection of the Henry's law portion of the high-temperature isotherm with the low-temperature isotherm. Thus, systems that exhibit Freundlich isotherms or rectangular isotherms cannot yield a pure solvent product by RTSA. Similarly, systems that have Henry's law coefficients which are not strongly affected by temperature are unlikely candidates for RTSA. As a result, when kinetics, durability, cost, and thermal-exchange capacity are considered, adsorbent selection can be quite involved. The binary mixtures considered here are toluene or xylene in n-heptane. The relevant equilibrium data have been correlated with the Langmuir isotherm. A(T)ci 9i* = (1) 1 + B(T)Ci where units for 9i* and ciare g(solute)/g(solid) and g(solute)/g(solution), respectively. Parameters for both solutes for temperatures of 0,30,35,and 80 "C are listed in Table 11. Typical isotherm data are shown in Figure 2. For applications involving more than one solute, it is natural to asaume that species compete for adsorption sites. If nonlinear effects exist, the isotherm parameters ( A and B ) may depend on concentration as well as temperature. In order to apply the thermal swing coherence theory presented later, isotherm parameters must be independent of composition. Consequently, experiments were performed to verify this assumption for two solutes present in the solution. Figure 3 shows data collected for toluene
0.015
U
Q >I U . i
U C
0.010 0
J
a I
SOLUTE SOURCE --+ Toluene B i n a r y
SYMBOL
I
0.005
u
0.000 0.0000
I
*
X 0 I
Toluene Xylene Xvlene I
0.0020 C = Concentration
Ternary Binary Ternark' I
0.0040 (g/g)
Figure 3. Isotherms of toluene in the presence of xylene, and xylene in the presence of toluene, both in n-heptane on silica gel at 30 "C. Table 11. Langmuir Isotherm Constants for Xylene (1) and Toluene (2) with Silica Gela 0 "C 30 "C 35 "C 80 "C A, 22.36 12.03 6.28 2.01 A, 17.46 7.77 5.16 1.23 Bl 348.0 327.0 113.0 121.0 Bz 390.0 177.0 159.0 0.0 "In (A,) = -38.299 + 22245.6/(T/K) - 2988320/(T/K)2. In (Az) = -42.441 + 24421.7/(T/K) - 3297912/(T/K)'. B1 = 20.3AI. Bz = 23.142.
adsorption in the presence of xylene and xylene adsorption in the presence of toluene. Within experimental error, it appears that the assumption is valid. In the subsequent treatment, isotherms are expressed in the mixed Langmuir form, viz.
Local Equilibrium Theory A variety of theories have been proposed for TSA processes that embody the assumption of instantaneous, local
1048 Ind. Eng. Chem. Res., Vol. 30, No. 5, 1991
equilibrium. Most employed the method of characteristics in applications involving a single solute (Baker and Pigford, 1971; Knaebel and Pigford, 1983; Kayser and Knaebel, 1987). Conversely, Camero and Sweed (1976) included multisolute analysis in their study of PP. They employed the approach of Rhee et al. (1972). Their system was restricted to the direct (standing-wave) mode, however, so that temperature shifts were instantaneous. Therefore, effects of temperature were straightforward. In the present work, the approach of Knaebel and Pigford (1983) was applied to predict the performance of single-solute systems. The details are not repeated here, for the sake of brevity. Rather, the remainder of this section deals with a more comprehensive treatment. The coherent wave theory of Helfferich and Klein (1970) was extended here to TSA applications involving two (or more) solutes, the recuperative (traveling-wave) mode of operation, and allowing for nonstoichiometric adsorption. In an adsorption column, the continuity equation for a solute i may be written
processes, because it may clarify the synchronization of the composition shifts driven by thermal shifts. In the present version, the effects of the thermal wave are considered later. The composition velocity can be expressed in terms of dimensionless variables, as uc,
= u/[l
Pbqi
=
Ei
cpC[
+ (1 - cp)Ppqi*
= Pbqi(1 - cb)/cb
(4)
(5)
A simpler continuity equation can be stated in terms of both the interstitial fluid and the intraparticle concentration, which comprises the capacity of the adsorbent including its pore volume. a[ci + Ei]/dt + u(dci/az) = 0 (6) In order to obtain positive velocities in the direction of flow, composition velocities can be defined via the triple product rule as UCi =
(ez/at)c,= -(ac,/at),/(ec,/az),
pxi
= (az/a~),; = (axi/ayi)z
uci =
./[ + q ] 1
The following dimensionless variables allow the continuity equation to be expressed more compactly as xi
= c ~ / C=CciBi[/(Ai ~ - 5)
(9)
and yi = Ei/Cc'i = qi/Cqi = qiBi/(Ai - F )
(10)
where C$lxi = 1.0 and CLlyi = 1.0 and
5 = (1 - cb)Pb(Cqi/CCi)/fb
(11)
Transforming time to be relative to the movement of the fluid simplifies the subsequent analysis. 7- = ( U / W - z / u ) (12) Equation 12 is similar to the transformation used by Knaebel and Pigford (1983) except that their distancevelocity lag term was based on the thermal wave velocity. That version helps to visualize the operation of TSA
(14)
These velocities are related as follows: UCi
= u/[l
+ t/PXi]
(15)
In addition, eq 6 can be rewritten in dimensionless terms since the velocity of a specific composition does not change under isothermal conditions. The result implies that solute lost by the interstitial fluid is gained by the adsorbent within the column.
+ (dyi/a7)z = 0
Equation 14 can be arranged to give for i =1, n - 1 dyi = (l/px,) axi = Xi axi
(16) (17)
where Xi are the eigenvalues of the system of equations. For an n-component system (including the solvent and solutes), n. - 1 composition changes should occur as the multicomponent feed passes through a column. The coherence condition is that the velocity determined via eq 14 is identical for all solutes (at a given position and time). A result of coherence is that changes in concentrations of separate species occur at the same time. If the system exhibits constant component separation factors, aij (as defined below), along with coherence, the so-called hodograph transformation results:
5[xi/(ali
i=l
-
h)] = 0
(18)
with n - 1 roots given by h = pyl/xl, and at a specific temperature aij
(7)
Combining eqs 6 and 7 yields
(13)
The corresponding dimensionless composition velocity is:
(exi/az), (3) where c[ represents the pore fluid concentration, which is at equilibrium with the solid at qi*. In addition, since the interstitial concentration, ci, is taken as identical with that in the pore fluid, it is appropriate to lump the concentrations as follows:
+ [(dyi/dxi)I
(Yixj)/(Yjxi)
(19)
Note that component 1 is the most strongly adsorbed solute. The component separation factors, aij, are not to be confused with the overall separation factor mentioned previously. According to mixed Langmuir capacity isotherms, given by eq 2, ai; is constant in the respective isothermal regions of the column; viz. aij(TJ = Ai(TJ/Aj(TJ
and aij(Th) = Aj(Th)/A;(Th) for the cold and hot steps, respectively. This result also implies that only n - 1 independent binary equilibrium isotherms (i.e., for all species more strongly adsorbed than the solvent) are necessary. In addition, since Langmuir coefficients and aiis depend on temperature, their values change when a temperature wave passes, resulting in a shift in both the adsorbed-phase and fluid-phase compositions. The time at which the shift occurs at a specific position is given by Tt
= ( u / f ) ( t - z/ut)
Thus, the resulting material balances incorporate coher-
Ind. Eng. Chem. Res., Vol. 30, No. 5, 1991 1049 ence theory with the effects of thermal cycling, and the equations are coupled to prevent accumulation at the respective thermal and composition fronts. This approach is applicable to shock waves usually associated with uptake (Le., the cold step). Diffuse waves that are normally associated with regeneration (Le., the hot step) are noncoherent and are discussed further below. Nonstoichiometric adsorption with multiple solutes requires an nth pseudo-component to be introduced. The value of x, is always defined as n-1
x , = [l - CXi] i=1
As a result, ain= A i / [ . The value of [ is arbitrary according to Helfferich and Klein (1977), since actual column composition velocities are independent of [, though Tien et al. (1976) argued otherwise. In this paper the only constraint observed is that [ must be less than the smallest Ai value. The n - 1 roots of eq 18 can be calculated from the specified (constant) influent composition, based on an initially clean column. For composition waves traveling ahead of the feed wave in the adsorption column, the h roots are successively replaced by alkwhere k represents each species not present in the fluid phase. For example, in a three-component system, two h roots are determined. One root falls between all and a12,and another lies in the interval etl2 to aI3,where the order of decreasing adsorbability is 1,2, and 3. If component 1is missing, hl becomes etl1 (=1)and hz remains the same, or if both components 1 and 2 are not present in the fluid, h2 becomes a12and hl remains at unity. The following equation can be used to determine the composition of all species present in the effluent. Waves are denoted by the components that vanish at the respective fronts.
j#m
Since various plateaus of composition can be determined, it is important to calculate the concentration velocity of the fluid. Two velocities can be defined representing upstream (u) and downstream (d) conditions of the kth wave. P l = (hE)2Pk
(21)
Note: h i = a l k . If p i > p i , a diffuse (i.e., proportionate or simple) wave, which elongates as it propagates, is created. p i cannot be greater than p i as this would form a crest (or multiplicity) on the composition wave, which would violate continuity. Therefore, the velocity of the self-sharpening (or shock) front is calculated via PP = [Plri11’2
(24)
Evaluation of the diffuse waves encountered in TSA is more complicated than for self-sharpening fronts because a unique velocity exists for each composition. In addition, the situation is inherently noncoherent. In previous studies in which noncoherence was addressed, the phenomenon arose as a consequence of gradual feed composition variation, such as accompanying the influx of a regenerant, or from interference of coherent waves. In the present case, however, temperature rather than composition drives the
cyclic sorption phenomena. In this situation, the hk roots reduce to alk values, which are presumed to be in the reverse order of shock fronts (i.e., h2 decreases to a12before hl falls to all = 1). The path of each composition can be determined from the dimensionless velocity (Helfferich, 1984) as
To summarize the application of these concepts to RTSA: when feed is admitted to a fully regenerated bed, i.e., with hot, pure solvent in the interstitial voids, the analysis proceeds as above for the coherent case; conversely, when the bed has not been fully regenerated, the analysis is slightly more involved because the composition shift of the residual material due to the imposed temperature shift must be determined, as follows. In that case and for the regeneration step, the values of aij must be adjusted for the new temperature, and the composition within the column must be calculated so that the h roots upstream and downstream of each wave front can be determined. The results in multisolute RTSA separations will be a centered diffuse (simple) wave during the hot step and multiple self-sharpening fronts (shocks) during the cold step.
Column Experiments The experimental portion of this study looked at bench-scale TSA performance via two types of experiments; these revealed the effects of operating conditions on process performance. Breakthrough experiments involved no recycle and employed steps in which feed solution at ambient temperature or pure solvent at an elevated temperature was admitted to the adsorbent bed. In particular, at the outset, cold feed was introduced into a hot bed, and following breakthrough, the regeneration step was begun 45 min after the experiment began. The breakthrough experiments yielded concentration histories as affected by temperature, particle size, and velocity. Continuous cyclic experiments involved recycle of both the purified solvent, which was obtained in the low-temperature (feed) step, and the enriched solution, which resulted from the high-temperature (regeneration) step. Part of the purified solvent was required for use as regenerant, and the remainder was combined with the enriched solution and returned to the feed tank. In this manner closure of the material balance was assured. Some of the results are expressed in terms of the feed separation factor (aF= ?h/cF), since the overall separation factor (ao = Eh/El) is not as meaningful. The latter loses significance for dilute feed solutions because ?, approaches zero experimentally and is identically zero in theory. Materials and Apparatus. The solutions were toluene in n-heptane and both toluene and xylene in n-heptane. The adsorbent was Davison silica gel (grades 408,12, and 923). For both breakthrough and cyclic studies, the same apparatus was used, and it is shown in Figure 4. A variable-stroke piston-type metering pump supplied the hydrocarbon feed to the column. The column (61-cm length; 5.1-cm id.) was made of glass, and it contained 805 g of silica gel. The bottom of the column was a sintered glass plate. This plate and a 60-pm in-line filter in the effluent line minimized passage of particulates. The composition of the column effluent was measured continuously with a Hewlett-Packard UV spectrophotometer (Model 8452), via a flow-through cell. A Pelton wheel flowmeter with maximum capacity of 605 mL/min was used to measure the effluent flow rate. Type K thermocouples (0.159-cm diameter) were inserted
1050 Ind. Eng. Chem. Res., Vol. 30, No. 5, 1991
-a E
Q
C 0 .-I +J
m L u C
ar
U
C 0
U II
u
distributor
0
30
t
filter
temperature shift of 30
'
L
= Time
90
120
150
(min)
Figure 6. Breakthrough profiles for lo00 ppm toluene feed at a
llow meter
PURE PRODUCT
60
O C
for various particle sizes of silica gel.
3200
CONCENTRATED PRODUCT
Figure 4. Diagram of the experimental dual recycle thermal swing adsorption process used in this work.
-aa E
u u
= 10 c m / m i n
u
=
= 35
"
70
2400
C
5000
I
I
1
I
I
0
I
.A
U
m
E
-
P P
L U
C
1600
al
4000
U
C
0
u
C
I
.r(
3000
u
ROO
L
U C
U
c
2000 0
U
0
II
u
4
8
V = Volume
1000
12
16
20
(liters)
Figure 7. Breakthrough profiles for lo00 ppm toluene feed and 40-60-mesh silica gel particles at a temperature shift of 55 OC, indicating the effect of interstitial velocity.
0
0
10
20
30
t
40 =
50
Time
60
70
80
90
(min)
Figure 5. Breakthrough profiles for lo00 ppm toluene feed and 40-60-mesh silica gel particles at various temperature shifts.
at the inlet, inside (i.e., 1/4 bed length), and at the outlet of the adsorption column. The flow rate, UV absorbance, and temperatures at various points were digitized by a Hewlett-Packard data acquisition unit (Model 3421), which transmitted the results to a Hewlett-Packard Vectra personal computer. To maintain the high temperature of the regenerant, heating tape (1000 W) was wrapped around the hot product tank, and it was controlled by a Yellow Springs, Inc., temperature controller (Model 63RC) which sensed the temperature of the contents of the tank. Feed and product streams were stored in 20-L glass bottles. Temperature Effects. Breakthrough curves for experiments having a range of temperature swings (but all with 40-60-mesh silica gel, lo00 ppm toluene feed, and 240 mL/min volumetric flow rate) are shown in Figure 5. As the temperature difference between the hot and cold steps increases, the peak concentration increases and the time
necessary for regeneration decreases. It is obvious that, for a given feed temperature, a smaller temperature swing diminishes performance because less pure product is produced, and that is accompanied by an increase in the required regenerant. The sharpness of the concentration front is dependent on the sharpness of the thermal wave moving through the column. Sample temperature profiles taken by three thermocouples placed along the axis of the bed showed that radial heat losses, along with axial conduction and dead volume within the column and fittings, detracted from the sharpness of the thermal wave. Further comments regarding the factors that affect thermal-wave sharpness are given by Matz and Knaebel (1990). Particle Size and Velocity Effects. Three different particle size ranges were investigated to determine the effect on concentration wave sharpness. Davison silica gel grades 408,12, and 923 had 18-20-, 40-60-, and 100-120mesh particle sizes, respectively. Figure 6 shows the composition histories for experiments at different particle sizes. For a given temperature swing and feed concentration, the peak concentration increased as particle size decreased from 18-20 to 40-60 mesh. In addition, the
Ind. Eng. Chem. Res., Vol. 30, No. 5, 1991 1051 3.2 0 .-I
U
m
2.8
I -
a C
*
2.4
-
2.0
-
U
m
L U C C
1.6
0 U
II
Cf =
I
I
I
I
I
1000 ppm
C f = 10000 ppm
I
I
I
I
U m U
ri C d
U
m
L
m a W
In
P)
U
I
1.2
-
U W W
LL
-
I 9-
y.
0.8
-
0.4
-
u
\ 0
0.0
u
\
r
0
1
[T ( h o t )
-
-
T ( c o l d ) 1 / [T (hot max)
T (cold) I
Figure 9. Theoretical and experimental feed separation factors as Figure 8. Breakthrough profiles for different levels of toluene in the
a function of dimensionless temperature shift.
feed at a temperature shift of 32 "C with particle sizes of 100-120 meah silica gel.
amount of pure product required for regeneration decreased. Further reduction in particle size to 100-120-mesh particles, however, failed to further sharpen concentration fronts inside the adsorption column. In fact, the composition histories were practically indistinguishable. In Figure 7, breakthrough data are shown for three different flow rates (with 40-60 mesh particles, 1OOO ppm toluene feed, and a temperature swing of 30 "C). The breakthrough curves are slightly sharper for lower flow rates, and the peak concentrations are higher. Although equilibrium behavior should be more closely approached as interstitial velocity decreases, velocity has a small effect on performance since the axial dispersion coefficient increases in proportion to velocity. This topic has also been discussed by Matz and Knaebel (1990). Concentration Effects. The base case feed concentration was 1000 ppm toluene. Additional experiments were conducted in which the feed concentration was 10OOO and 40O00 ppm toluene, respectively, with other conditions fixed (i.e., 100-120-mesh particles and volumetric flow rate of 265 mL/min). In these experiments, at the outset cold feed was admitted to the column, which contained hot regenerant, and then the hot step was started 20 min later. Resulting breakthrough profiles are shown in Figure 8 for both 1000 and 10000 ppm toluene feed. Note that the ordinate is the concentration ratio c/cF. Though the profiles are similar, it can be seen that the peak concentration ratio is lower and that the breakthrough time is shorter at the higher feed concentration. The results of a breakthrough experiment with 40 OOO ppm toluene feed were similar. The similarity of the breakthrough profiles should not be construed to mean that RTSA operation is feasible: constraints exist that cannot be inferred directly from breakthrough behavior. For example, as feed concentration increases, the amount of purified product required for regeneration increases. Obviously, the fractional product recycle must be less than unity for RTSA to be feasible. In addition, LYF (the feed separation factor) decreases with increasing feed Concentration. Equilibrium Theory Predictions. To exploit TSA separations, it is necessary to understand their capabilities and limitations. Minimizing dissipative effects, e.g., by employing small adsorbent particles to reduce the diffusion time constant, allows one to test the predictions of the simple theory. It also exposes the drawbacks associated
3000
E
Q
a
I
1
I
theory
2400
Th Tc Oc Oh
C
--
---
100
0
I
-r\
51.7'C 22.6OC 272 ml/min 250 ml/min 120 mesh
d
4-l
1800
L U
C P)
0
c
1200
U
I
0
600
I
0 0
10 t
I
I
I
J
20
30
40
50
-
Time
(min)
Figure 10. Typical experimental and theoretical breakthrough profiles for toluene in a TSA system. Note that the theory overpredicts the step time for uptake but accurately predicts the extremes of concentration, as well as the general shape of the profile.
with striving for local equilibrium behavior, e.g., high pressure drop (due to small particle size) or unusual equipment design (to achieve sharp thermal waves). The equilibrium theory was employed here to examine trends in RTSA performance as affected by feed concentration, temperature swing, and multiple solutes in the feed. For example, aFis independent of concentration according to the equilibrium theory, but higher concentrations lead to mass-transfer effects that hinder performance. To compensate for the deleterious effect of high feed concentration, it is possible to increase the magnitude of the temperature swing. Both of these trends are shown in Figure 9. Notice that as the temperature swing increases, the effect of high feed concentration increases. In addition, the separation at a given temperature swing diminishes as the feed concentration increases. Single-solute RTSA breakthrough profiles can be simulated by equilibrium theory as shown in Figure 10. The concentration extremes do not quite reach the theoretical limits, nor do they remain at the respective plateaus for as long as predicted. These deviations are probably primarily due to dissipative effects, incomplete regeneration, and errors in the isotherm parameters. Nevertheless, the
1052 Ind. Eng. Chem. Res., Vol. 30, No. 5, 1991 6000
I
I
I
I
I
1
6000
-aa E
n
I
THEORETICAL PREDICTION
I
C
BOTH SOLUTES
4000
0
d
d
U 0 L
U
c
U
2
I
3 5 4 5
6
I
5000
I
4000
step:
m L
c,
3000
C
OI U C
3000
al
1
U
C 0
0
u
2000 I
I
u
0
I000
I
2000
I
I000
0 0
20
10
t
-
30 Time
40
150
50
155
pure-product concentration was actually less than 0.5 ppm toluene, which was certainly not “zeronthough it was purer than the reagent-grade n-heptane used as the solvent. It was not possible to measure the pure-product concentration with greater accuracy using the available instruments (UV spectrophotometer and GC-mass spectrometer). Furthermore, the peak concentration attained during regeneration was predicted within about 4 % , as was the total regeneration time. Multisolute breakthrough curves, i.e., for both toluene and xylene, are shown in Figure 11. Both concentration shifts and breakthrough times are predicted with good accuracy by the equilibrium theory. Toluene, the less strongly adsorbed component, broke through first and exhibited roll-up, followed by xylene. After 30 min of the feed step, the regeneration step was started. The peak concentration of toluene was greater than that of xylene (for the same initial concentrations) due to its less favorable isotherm. Again, the theoretical predictions deviated slightly from the experimental results, i.e., by overestimating ultimate concentrations and step times. Nevertheless, understanding the concentration shifts that are induced by temperature shifts, as revealed by multicomponent equilibrium theory, can lead to optimal operation of RTSA systems. Continuous Cyclic Experiments. Four experiments are discussed here: a base case, a high-recycle case, a high feed concentration case, and a dual-solute case. The same basic apparatus used in the breakthrough experiments was employed in the continuous experiments, though some alterations were made. For these experiments, both the pure product (beyond the amount required for regeneration) and the enriched product were recycled to the feed tank. Although this caused minor fluctuations of the feed composition, it conserved solvent and solute. In addition, heat exchangers were installed between the effluent-end solenoid valves and corresponding recycle tanks to minimize fluctuations of temperature in the feed and product-recycle tanks. To ensure consistent results, data were recorded only after achieving cyclic steady state. From that point, the RTSA process was operated for 12 h while data were being collected. Typically, the duration of the RTSA cycles was 30 min. The cycle consisted of six time intervals, as shown in Figure 12 (from the base case). These are described
165
t = Time
(min)
Figure 11. Typical experimental and theoretical breakthrough profiles for toluene and xylene in a TSA system. The theory predicts with good accuracy the step times for uptake for both components as well as the extremes of concentrations.
160
170
175
I80
(min)
Figure 12. Experimental breakthrough profile for toluene in a RTSA system with step times superimposed. The steps represent different influent and effluent concentrations and temperatures, as follows: 1, feed = cF, TI,product = cl, TI; 2, feed = cI, Th,product = cl, TI;3, feed = cl, Th,product = ci, Th;4, feed = cI, Th,product = ch, Th;5, feed = CI,Th,product = ci, Th; 6, feed = CF, TI, product = ci, T b
-
5000
7
7
E
n a
C 0 .rI
+I
m
L U C
al
0 C 0
u I U
0
30
60
t
-
90 Time
120
150
180
(minl
Figure 13. Experimental breakthrough profiles of toluene and xylene for six cycles in a RTSA system.
below in terms of the column effluent and the column influent. During the first and second, pure product was produced. The third, fifth, and sixth intervals yielded effluent having intermediate concentration, to be recycled and mixed with the feed. Only during the fourth interval was concentrated product collected. The feed solution was admitted to the column during the first and sixth intervals. During the second through fifth steps hot regenerant (i.e., pure product) was fed to the column. The times allotted varied depending on the feed concentration and the desired pure-product concentration: generally they were 10,6,2.5, 2, 3.5, and 6 min, respectively, for the first through sixth intervals. For the first experiment, the so-called base case, the cycle employed a product recycle of 66%. Since the feed concentration fluctuated slightly, samples were taken at 2-min intervals and yielded an average of 1312 ppm toluene. The average peak concentration was 5310 ppm, and the pure-product concentration profile had an unexpected,
Ind. Eng. Chem. Res., Vol. 30,No. 5, 1991 1053 very small secondary peak in each cycle (cf. Figure 12 at time = 150 min and Figure 13 at time intervals of 30 min). The time-averaged pure-product concentration was about 10 ppm. Thus, the overall separation factor was at least 500, and the feed separation factor was 4.05. By increasing the pure-product recycle in the second experiment to 75%, however, the small secondary peak was eliminated, and the pure product concentration was reduced to less than 0.5 ppm. The lower limit was examined by both UV spectrophotometry and GC/MS, but it could not be resolved accurately, though it apparently was greater than 0.1 ppm. The average peak concentration was 5220 ppm, and the feed concentration was 1300 ppm. The resulting overall separation factor was about 10000, and the feed separation factor was 4.02. In the third experiment, with a feed concentration of 9620 ppm toluene and 90% recycle of the pure product for regeneration, the average product compositions were 810 and 30000 ppm, respectively. The resulting overall separation factor was 37.0,and the feed separation factor was 3.11. The fourth experiment demonstrated RTSA with two solutes, and the breakthrough curves are shown in Figure 13. Toluene and xylene were each present at 500 ppm in the feed. The peak concentration of toluene was higher than that of xylene, due to its less favorable isotherm. Again, the sum of both solutes exceeded 4000 ppm during each cycle. A fractional product recycle of 0.64was used in this experiment. Accordingly, a small secondary peak was again observed, as in the base case. The average total pure-product concentration was about 1 ppm. Hence, the overall separation factor was about 4000,and the feed separation factor was 4.00.
Conclusions Thermal swing adsorption with recycle has been investigated with primary emphasis on separations of dilute aromatics from aliphatics. In particular, toluene and xylene as solutes and n-heptane as the solvent have been studied in temperature swing experiments in a column of silica gel adsorbent. Adsorbent requirements are suitable thermal-exchange capacity, minimal intraparticle masstransfer resistance, and adequate thermal properties. In addition, the shapes of the pertinent isotherms are extremely important to the successful application of the process. Bench-scale studies of the TSA studied effects of flow rates, temperature extremes, step times, feed concentration, recycle ratio (of the pure product for regeneration), and presence of two solutes. Experimental separation factors were affected by virtually all of the operating conditions except flow rate. A peak overall separation factor exceeding 10000 was obtained. For different operating conditions, the overall separation factor was dramatically affected. For example, increasing the feed concentration by an order of magnitude reduced it by over 2 orders of magnitude, due to the strong dependence on the pure-product concentration. Another scale of performance, the feed separation factor, was not nearly as sensitive. For the same change of feed concentration, it changed by only 23% . The impact of the second solute was minor: neither the overall separation factor nor the feed separation factor was affected much. The absence of serious effects was probably due to the relatively small adsorbent selectivity between them. Theoretical analyses for single-solute and multiple-solute systems have also been conducted. These yielded good agreement with actual concentration profiles. The multiple-solute theory developed here is unique because it
incorporates thermal wave behavior along with the coherence theory developed by Helfferich. In particular, the significant features are assessing concentration shifts resulting from thermal swings and the presumption that the h roots determined during uptake are inverted during regeneration. In relation to its predecessors (Le., parametric pumping and cycling zone adsorption), RTSA offers superior performance. The future of the RTSA process is promising in the area of purification. It is essential, however, that a suitable temperature-sensitive adsorbent be found and that the adsorbates exhibit appropriate sorption kinetics.
Acknowledgment We express our gratitude for the following contributions. This material is based on work supported by the National Science Foundation under Grant No. CBT-8617680.Additional funds for instrumentation were provided by Ammo Oil Company. The adsorbent was provided by the Davison Chemical Division of W. R. Grace & Co.
Nomenclature A = Langmuir isotherm constant E = Langmuir isotherm constant c = fluid concentration Ei = adsorbed-phase concentration E = time-averaged fluid concentration C, = heat capacity Deff= effective diffusivity of solute in adsorbent pores h = root of hodograph transform k = thermal conductivity P = defined by eq 23 q* = amount adsorbed per unit particle mass t = time T = temperature u = interstitial velocity x = dimensionless fluid composition y = dimensionless adsorbed-phase composition z = column position Greek Symbols a = separation factor or adsorbent selectivity aeff= effective thermal diffusivity X = eigenvalue p = density T = transformed time p = dimensionless concentration velocity f = ratio of total solute in adsorbed phase to that in fluid phase e = void fraction y = ratio of specific heats
Subscripts b = bed c = composition eff = effective f = fluid F = feed h = high i = refers to species i or intermediate (Figure 12) j = refers to species j k = refers to absent species 1 = low
Ind. E n g . C h e m . Res. 1991, 30, 1054-1060
1054
m = refers to present species n = number of components p = particle pore = pore
d = downstream sh = shock wave u = upstream
Adsorption; Liapis, A. I., Ed.; New York: Engineering Foundation: 1987. Knaebel, K. S. Multistage cycling zone adsorption for purification of binary mixtures. AZChE Symp. Ser. 1982, 78 (No. 219), 128. Knaebel, K. S.; Pigford, R. L. Equilibrium and dissipative effects in cycling zone adsorption. Znd. Eng. Chem. Fundam. 1983,22,336. Matz, M. J.; Knaebel, K. S. Criteria for selection of an adsorbent for a thermal swing adsorption process: Applied to purification of aliphatic solvent contaminated with aromatic solutes. Sep. Sci. Technol., in press, 1989. Pigford, R. L.; Baker, B.; Blum, D. E. An equilibrium theory of the parametric pump. Znd. Eng. Chem. Fundam. 1969a, 8 , 144. Pigford, R. L.; Baker, B.; Blum, D. E. Cycling Zone Adsorption, A New Separation Process. Znd. Eng. Chem. Fundam. 196913,8,848. Rhee, H. K.; Aris, R.; Amundson, N. R. On the theory of multicomponent chromatography. Philos. Trans. R. SOC.London 1972,
Literature Cited
Rice, R. G.; Foo, S. C. Continuous desalination using cyclic mass transfer on bifunctional resins. Znd. Eng. Chem. Fundam. 1981,
sh = shock t = thermal Superscripts
’ = within pores * = on particle surface N
= lumped solid
- -- average
A267, 419.
Baker, B.; Pigford, R. L. Cycling zone adsorption: Quantitative theory and experimental results. Znd. Eng. Chem. Fundam. 1971, 10, 283.
Camero, A. A.; Sweed, N. H. Modeling multicomponent parametric pumping separations. AZChE J . 1976, 22, 369. Gregory, R. A.; Sweed, N. H. Parametric pumping: Behavior of open systems, 11. Experiment and computation. Chem. Eng. J. 1972, 4 , 139.
Helfferich, F. G. Conceptual view of column behavior in multicomponent adsorption or ion-exchange systems. AZChE Symp. Ser. 1984,80 (No. 233), 1. Helfferich, F. G.; Klein, G. Multicomponent Chromatography; Dekker: New York, 1970. Helfferich, F. G.; Klein, G. Application of h-transformation to multicomponent adsorption in fixed beds. AZChE J. 1977, 23,
20, 150.
Rieke, R. D. Ph.D. Dissertation, University of California, Berkeley, CA, 1973. Rieke, R. D. Cycling zone adsorption: Variable feed mode of operation. Sep-Sci.Yechnol. 1984, 19, 261. Shih. T. T.: Pieford. R. L. Rec. Deu. S e n Sci. Li. N. N.. Ed.: CRC Press: ClevGland; OH, 1975. Tien, C.; Hsieh, J. S. C.; Turian, R. M. Application of the h-transformation for the solution of multicomponent adsorption in fixed bed. AZChE J. 1976,22, 498. Wankat, P. C. Large Scale Adsorption and Chromatography; CRC Press: Boca Raton, FL, 1986; Vol. 1. Wilhelm, R. H.; Rice, A. W.; Bendelius, A. R. Parametric pumping: a dynamic principle for separation of fluid mixtures. Znd. Eng. Chem. Fundam. 1966,5, 141. I
,
Received for review May 29, 1990 Revised manuscript received September 4, 1990 Accepted September 25, 1990
407.
Kayser, J. C.; Knaebel, K. S. Recycled thermal swing adsorption: Processes for separation of binary mixtures. Fundamentals of
Constant Pattern Behavior for Adsorption Processes with Nonplug Flow Edgar N. Rudisill and M. Douglas Levan* Department of Chemical Engineering, University of Virginia, Charlottesville, Virginia 22903-2442
Adsorption of a dilute solute from fluid in nonplug flow through a porous structure of arbitrary but constant cross section is treated. Mass transfer is determined by diffusion in transverse and axial directions in both fluid and solid phases. A general existence criterion is developed for the constant pattern concentration wave. The criterion is applied to systems with cocurrent and countercurrent flow. T h e results pertain to fixed-bed adsorbers and adsorptive membrane systems.
Introduction The concept of the constant pattern is well developed for fixed-bed adsorption with nonlinear isotherms. The constant pattern is the asymptotic shape to which a concentration wave will spread in a bed of infinite extent. It corresponds to the maximum breadth of the wave and is therefore useful in the conservative design of adsorption systems. For fixed beds with plug flow, considerable effort has been devoted to constant pattern behavior. Different isotherms have been considered, and the theory is well understood for general isotherms. Existence, uniqueness, and stability criteria have been developed. The masstransfer mechanisms of axial dispersion, external mass transfer, pore diffusion, surface diffusion, and reaction kinetics have been considered individually and in some combinations. Treatments have also been carried out for multicomponent adsorption, nontrace systems, and adiabatic adsorption. Reviews that collectively summarize this previous work are available (Vermeulen, 1958; Vermeulen 0888-5885/91/2630-1054$02.50/0
et al., 1984; Ruthven, 1984; LeVan, 1989). This paper is concerned with constant pattern behavior when an allowance is made for deviations from plug flow. Such deviations exist in real adsorption beds and in other devices in which adsorption plays a role. In packed beds, they are created by (i) the randomness of a packing, (ii) a lower packing density near the column wall, and (iii) local velocity profiles between particles. Experiments using laser-Doppler anemometry to measure velocity profiles at the outlet of fixed beds reveal higher velocities near the wall and gross deviations from plug flow in the central core of a packing (Vortmeyer and Schuster, 1983; Volkov et al., 1986). In comparison with the large number of previous studies of constant pattern behavior with plug flow, very little research has been carried out on constant pattern behavior with deviations from plug flow. A Graetz-type problem has been considered in which a solute is adsorbed on the wall of a cylindrical channel through which fluid flows (Sartory, 1978; Tereck et al., 1987). These studies show 0 1991 American Chemical Society
