2418
Znd. Eng. Chem. Res. 1993,32, 2418-2429
Steam Regeneration of Solvent Adsorbers Thomas A. J. Schweigert and M. Douglas LeVan' Department of Chemical Engineering, University of Virginia, Charlottesville, Virginia 22903-2442
We report results of modeling and experimental studies on steam regeneration of activated carbon beds with adsorbed n-hexane. Experiments are performed using a well instrumented pilot-scale apparatus with a nearly adiabatic adsorption column. We vary the initial loading of n-hexane, the steam flow rate, and the flow direction, and measure temperature profiles within the bed and effluent concentrations and flow rate. Experiments indicate the presence of a sharply condensing steam flow with drastic changes in velocity in the bed, the development of liquid phases within the bed, and a wave character with fronts separated by plateau regions. Mathematical models are developed based on finite differences and orthogonal collocation on finite elements. The models predict the observed velocity variations, the development of the liquid phases, and the wave character of the process.
Introduction Steam regeneration of an adsorbent bed is carried out by passing live steam through a bed of exhausted adsorbent, usually activated carbon with adsorbed solvent. It is commonly used industrially, yet little fundamental research of either a theoretical or experimental nature has been performed to improve our understanding of the process. Unoptimized steam requirements for solvent recovery systems have been found to vary from 0.77 to 20 kg of steam per kilogram of solvent recovered (LeVan and Schweiger, 1991). Improved understanding can be expected to lead to improved design methods and optimization of existing processes through minimization of steam requirements. Also, better understanding is important because regeneration fixes the state of the adsorber when it is placed in service. This means regeneration determines the capacity of the adsorber to recover solvent and also, because of residual solvent loading, contributes to the level of solvent emissions during service. Steam is an effective regenerating agent for activated carbon adsorbers used for solvent recovery in temperature swing cycles because, with its high heat content, it quickly raises the temperature of the adsorbent to desorb the solvent. Further, adsorbed water competes with the solvent for pore volume of the adsorbent to enhance desorption. The flow of steam purges from the adsorber the desorbed solvent, which is easily condensed and purified for reuse. After steaming and perhaps drying, the carbon is ready for service again. While many models for adsorption and desorption by a pressure reduction or by purge with a hot inert gas have been developed, steam regeneration has been given little attention. The principal reason for this is most likely that models for steam regeneration require the treatment of adsorption equilibrium for hydrocarbon-water mixtures, which is not well understood, and the treatment of fluid velocity for a condensing flow. With steam regeneration, the condensing steam flow results in interstitial velocities that drop from the inlet value to almost zero during the initial part of the cycle step. Most past studies have fitted experimental regeneration data with empirical equations or used overly simplified mathematical models; e.g., the adsorber is preheated to avoid condensing flow (El-Rifai et al., 1973; Anikeeva et al., 1976; Dubinin et al., 1978;
* Author to whom correspondence should be addressed.
t Present address: Du Pont de Nemours, (Luxembourg) S.A., Grand Duchy of Luxembourg.
Scamehorn, 1979; Lukin and Egorov, 1979,1984; Kisarov et al., 1980;Subbotin and Kashnikov, 1980; Capelle et al., 1983; Jedrzejak and Paderewski, 1988). Other contributions have involved both theoretical and experimental efforts. Schork and Fair (1988) present experimental results for a small-scale adsorber. The wall of their apparatus is massive and the steam flow rate is fast; thus, their resultssuggest the adsorber can be modeled as a single, well-stirred tank. Ustinov and co-workers (Ustinov et al., 1982,1985; Ustinov, 1986) simplified the mathematics by treating steam as a gas which condenses, rather than adsorbs, on the carbon; with this model they explain the fronts of condensing vapors that emerge from an adsorber during regeneration. They present no experimental results. Models and experimental results for steam regeneration of an adsorber uniformly loaded with n-hexane were recently presented by the authors (LeVan and Schweiger, 1991). We extend that work here, showing more experimental results, presenting an alternative numerical solution, and improving significantly the adsorption equilibria in light of new data. These new data (Rudisill et al., 1992)allow quantitative prediction of water adsorption in the presence of adsorbed n-hexane. The goal of this work is to enable simulation of industrial solvent recovery adsorption systems that use steam regeneration.
Models In our recent paper (LeVan and Schweiger, 1991), we presented two models for steam regeneration of a carbon bed based on discretizing the bed length into stages (or mixing cells). One model assumedlocal equilibrium, while the other added mass-transfer resistances. We observed that mass transfer imposes no significant limitation since the propagation of changes in concentration and temperature is slow. Furthermore, it has been identified that fluid mechanics, through flow maldistribution, can be more significant than mass- and heat-transfer resistances in determining observed rate behavior (Schweiger, 1991). Thus, in the formulation of our current models, we assume local equilibrium. Two models are presented here, the original equilibrium stage model and a model solved by orthogonal collocation on finite elements. Both models treat an adsorber as a column containing a fixed bed and well-mixed unpacked volumes at the inlet and outlet. The conservation equations are material and energy balances for the fluid and stationary phases. The energy balance contains a term for energy loss through the wall of the
QSSS-5885/93/2632-2418$Q4.QOlQ 0 1993 American Chemical Society
Ind. Eng. Chem. Res., Vol. 32, No. 10,1993 2419 packed bed, and the heat capacity of the wall is lumped with that of the column packing. The two models differ in how spatial derivatives are treated. The stage model writes spatial derivatives by backward finite differences, which is mathematically equivalent to describing the fixed bed as a cascade of wellmixed cells. The orthogonal collocation model fits variables to polynomial functions in the axial direction, which are differentiated to obtain the spatial derivatives. As a consequence, the conservation equations for the two methods differ on two points. First, the stage model is first order, whereas the collocation model has second derivativesin the form of an axial dispersion term to allow implementation of two boundary conditions, which the method requires. Second, the stage model solves directly for velocity at constant pressure, whereas our collocation model includes pressure as a variable and requires an additional equation to link pressure and velocity. Conservation and Rate Equations. For the collocation model, the material and energy -- balances are the following. adsorbate material balance:
voidage e’ is the local void fraction in the bed including intraparticle pore volume. It is calculated from = €0 + (1 - eo)X - Pb(6A + 6W) (9) where x is the particle porosity and 6, and 6w are specific volumes of n-hexane and water in the stationary phase. For the collocation model, the pressure gradient is used to determine the velocity in the packed bed through the Blake-Kozeny equation e’
For the stage model, the material and energy balances are given by eqs 1-4 but without the dispersion terms on the right-hand sides. Also, rather than use pressure as a variable in the stage model, we assume that at any time the bed is at a constant pressure throughout and solve for velocity directly as described below. The wall of the end tanks, on which water and solvent may condense and in which energy accumulates and through which it is transferred, is assumed to be in contact with the bulk vapor through a mass- and heat-transfer film. For both models, rate equations for this process are the following. condensation of adsorbate:
water material balance:
condensation of water: overall material balance:
accumulation and transfer of energy: energy balance:
u,u(Twd
u, = ( c p , b &
dqd -
XW(qA,qW’,Tref)
(13)
Boundary Conditions. The boundary conditions at the column ends arise from the material and energy balances for the end tanks. For the collocation model, we stipulate that concentration, temperature, and fluxes are continuous across the boundary between well-mixed end tanks and the packed bed (Ramkrishna and Amundson, 1974;Parulekar and Ramkrishna, 1982,1984).At the bed inlet, 2 = 0, we have
+ qACpAJ + qWCpW,l)(T - Tref) -
J ,XA(qA’,o,Tr&)
- Tmb)
dqw‘ (7)
Since internal energy is a state variable, usis calculated by following a thermodynamic path. The above equation is for a path in which the solvent and then the water are adsorbed at a reference temperature and then heated to the current system temperature. XA(qA, qw, 2“) and Xw(qA, qw, T )are the isosteric heats of adsorption of the solvent and water. For the solvent, this is calculated from ita adsorption isotherms using
evaluated at Tmf. The latent heat of adsorption of water is taken to be independent of loading (Dubinin, 1980)and set equal to the heat of vaporization of water. Liquid heat capacities are used for the adsorbed components. The
gz=o- 150p(l=
d;e3
e)2 ULO
where uIZ=ois obtained from the overall material balance
2420 Ind. Eng. Chem. Res., Vol. 32, No. 10, 1993
WA and WW, the amount of adsorbate and water condensate in the tank respectively, are restricted to nonnegative values. At the bed outlet, z = lb, we write
where ulout is obtained from the overall material balance:
The pressure at the outlet is fixed. For the stage model, flux is continuous across the bed inlet and outlet planes. The boundary conditions serve as the equations for a tank at the inlet emptying into the adsorber and for a tank at the outlet into which the adsorber empties, respectively. At the column inlet, z = 0, we have (23)
and at the column outlet, z =
lb, we
write
interaction between solvent and water in the adsorbed phase is significant, with adsorbed water able to displace solvent. Our principal concern for the adsorption equilibria correlation is for accurate prediction over the path found in the steam regeneration experiments. As we will show, this path begins at room temperature with moderate solvent loading, passes through moderate temperatures with high solvent and low water loading, and finishes at high temperatures with low solvent and moderate to high water loading. The correlations used, based on pore filling concepts, are given in the Appendix. For mixed adsorbates, we assume that the apparent pore volumes filled determine the equilibrium partial pressures. Because we expect the n-hexane to occupy the highest energy sites, particularly a t low loading, we include an empirical scaling of the effect of water on the volatility of the solvent at low solvent loading. While the form of our scaling function lacks a theoretical basis, it allows representation of the available data fairly well and is numerically efficient in the steam regeneration models. Solution Method. For both models, time derivatives were expanded using the chain rule to write them in terms of time derivatives of QA, QW,T, and, for the collocation model, P. For the collocation model, we used 11 equal length finite elements. Interior elements had three interior collocation points. End elements had two interior collocation points and one boundary collocation point, at z = 0 on the first element and at z = lb on the last element. Trial functions were written fOrYA,YW, T,andP. Variables and their first derivatives were made continuous between elements. Interior collocation points were located on the finite elements at the roots of the shifted Chebyshev polynomial of the second kind. For the stage model, for each of the stages the set of conservation equations was solved to obtain the time derivatives and u. The time derivatives were then integrated numerically. For both models, the equation set was integrated using the Gear's method solver LSODE (Hindmarsh, 1980). Experiments
where uIZ=o and ulout are again obtained from overall material balances given by eqs 18 and 22. Numerical values of parameters used in the model are given in the Appendix. Adsorption Equilibria. A mathematical description of adsorption equilibria over wide ranges of temperature and composition is needed. For the pure components, n-hexane and water, we have used correlations of the data of Rudisill et al. (1992). All of these data were measured for the same lot of Calgon Type BPL activated carbon that was used in the adsorber for the steam regeneration experiments reported here. Rudisill et al. (1992) identified two important trends in their data that we take into account in constructing an empirical representation of adsorption equilibria. These trends were not included in the adsorption equilibrium model used in our previous paper (Schweiger and LeVan, 1991). First, the shape of the water isotherm changes with temperature. Specifically, as temperature increases, the normally sharp upturn in water adsorption becomes blunt and occurs a t higher relative pressures. Second, the
To determine behavior during steam regeneration and to test the accuracy of the predictions of the mathematical models, experimental breakthrough curves were collected under various loading and steaming conditions. Properties of industrial-scale adsorbers are reproduced in the apparatus design and are reflected in the experimental conditions. The apparatus, shown in Figure 1,provides reliable measurements and rapid data sampling. It consists of an adsorption column, feed makeup sections for solvent vapor and steam, and analytical equipment for temperature, concentration, and flow rate measurement. The adsorption column is a thin-walled tube fabricated from phenolic-impregnated cloth and capped at both ends with plates of the same material. Phenolic-impregnated cloth is lightweight, has a low thermal conductivity and heat capacity, is thermally stable, and is resistant to most solvents. The column is 740 mm long and 72 mm in diameter, and is packed to a depth of 580 mm with type BPL activated carbon (Calgon Carbon Corp.; Lot No. 4814J, 6 X 16 mesh), leaving an 80-mm space at each end. A fixed, wire mesh screen supports the carbon on the bottom, and a floating screen retains the carbon on the top. The column is well insulated using wraps of Dacron insulation and metalized Mylar film and has a low heat-transfer coefficient for energy loss to the surroundings. The
* Ind. Eng. Chem. Res., Vol. 32, No. 10, 1993 2421
Sparging Vessels
r
Gild Chromatograph
I
Recorder
Figure 1. Apparatus for steam regeneration.
effective heat capacity of the entire adsorption column is 50% greater than the heat capacity of the adsorbent alone. Temperatures in the bed are measured with thermocouples located at one-quarter bed length intervals, with the thermocouples located at the radial position where the area of the inner cylindrical region equals the area of the outer annular region (i.e., at r/rwd = 1 / 4 2 ) . Two thermocouples are placed at midlength, one positioned to give the core temperature and one positioned to give the wall temperature. (Radial temperature gradients were found to be small.) An additional thermocouple is installed in the feed line to measure the temperature of the column feed. The thermocouples for which temperature breakthrough curves are reported below are just upstream of the retaining screens, near the top of the column for upflow and near the bottom for downflow. All thermocouples are connected to a multipoint recorder and temperatures are measured continuously. Mostly, flows are downward for loading the bed with hydrocarbon and upward for steaming, and the apparatus is easily modified to reverse the flow directions. The steam flow rate from an electric steam generator is set with a needle valve and metered with a rotameter mounted in a thermostated hot oil bath to prevent condensation. The bath also houses a second rotameter for measurement of the flow rate of the effluent. All lines carrying steam or concentrated solvent vapors are heat-traced using electrical heating tapes to prevent condensation. The carbon is dried prior to loading with solvent, and dry air is used in the feed makeup. Gas samples are continuously drawn from the column outlet and analyzed using a gas chromatograph with a thermal conductivity detector. Effluent concentration measurement is automated with sampling every 2.5 min. The column heat capacity and wall heat-transfer coefficient were determined experimentally by heating the column with an inert gas. Axial dispersion coefficients for the adsorber were estimated from tracer experiments. Additional details concerning the apparatusand operating procedures are given by Schweiger (1989).
Results Results of five experiments are reported here. The initial conditions and feeds are given in Table I. We vary the
Table I. Experiments initial condition T qAa qwo P: (K) (mol/kg) (moVkg) 1 basecase 0.1 302 3.03 0.008 2 high flow 0.1 300 3.04 0.008 3 downflow 0.1 298 3.05 0.008 4 low load 0.01 302 2.45 0.008 5 highload 0.8 300 3.56 0.008 Predicted. experiment
feed
G
Ti.
(ds) 0.021 0.041 0.020 0.0205 0.021
(K) 384 390 388 400 400
initial loading of n-hexane on the carbon, the steam flow rate, and the flow direction. Flow of steam was upward except for experiment 3. In all experiments the steam fed to the column was at atmospheric pressure and slightly superheated. We show breakthrough curves predicted by the stage model using 50 stages for all experiments and predictions of the collocation model for selected experiments. Velocities predicted by both models oscillate with time and will be shown for only selected experiments. For the first three experiments, the bed was loaded by passing air 10% saturated with n-hexane (i.e., PA PA/;p"A = 0.1)through the column a t ambient temperature untd equilibrium was reached. For experiment 1,the base case, steam was then passed upward through the column a t atmospheric pressure and at a flow rate of 0.021 g/s, corresponding to 0.85 superficial bed volumes of steam per minute at feed conditions. Bed profiles predicted for experiment 1,obtained using the collocation model after 35 superficial bed volumes of steam have been passed into the column, are shown in Figure 2. The bed profiles show various fronts and plateaus; these will be more sharply defined in stage model predictions. Note the plateau at 334 K, which will be described in detail below. The front at { = 0.7 that precedes this plateau removes the inert gas from the bed. Experimental breakthrough curves for experiment 1are shown in Figure 3. Plotted as a function of time are solvent and water effluent mole fractions from the column and temperature at the outlet thermocouple just inside the bed. The solid lines are predictions of the stage model, and the points are experimentalresults. The breakthrough curves show the emergence of two principal zones. At first the conditions a t the outlet are the initial conditions,
* 8K--
2422 Ind. Eng. Chem. Res., Vol. 32, No. 10, 1993
lo
--
4
400 380
. '\
0.8
T
\
\
360
z
h
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Y
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4
c
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0
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0
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c
150
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3
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3401
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0.4
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0
0
1
4
P
300
0.2
0.4
0.6
0.8
1.o
4
280 0
50
100
150
200
t (min)
Figure 2. Bed profides for experiment 1 (base case) predicted by collocationmodel. (top)Loadingeand temperature. (bottom)Vaporphase mole fractions and velocity.
Figure 3. Breakthrough curvea for experiment 1 (base case). Predictions by stage model. (top) Vapor-phase mole fractions at column outlet. (bottom) Temperature at bed outlet.
with a gentle purge of inert. After about 60 min of steaming, a wave of desorbed solvent emerges at a temperature of 334 K. After about 110 min, when most of the solvent has been desorbed, the solvent concentration drops rapidly. Note, however, that the second wave here is not as sharp as predicted; the thermocouples positioned along the bed showed this wave to be relatively sharp at { = 0.75,only becoming diffuse a t the bed outlet (Schweiger, 1989). A third, very slow moving wave is predicted to still be in the bed near its inlet; it is this wave that essentially fills the pores of the carbon with water. For experiment 2 the steam flow rate was 1.7superficial bed volumes per minute, double the base-case flow rate, with the direction of steam flow still upward. Figure 4 shows bed profiles predicted by the stage model using 100 stages after 40 bed volumes of steam have been passed into the column. Three distinct regions are apparent. Beginning at the bed inlet, the first region contains residual solvent and steam at high temperature, with the pores of the carbon nearly filling with water very close to the bed inlet. In the second region, between { = 0.4 and 0.76,the solvent has rolled up to a great extent and forms a plateau. The void fraction of the bed is 0.4.On this plateau, e', the total local voidage of the bed, including that within the particles, is only 0.38;thus, the volume of the solvent and water exceed the pore volume of the carbon and some of the n-hexane and water exist as bulk liquid in the
interstitial voids of the packing. In fact, in the simulations and throughout the experiments, we will continue to find this plateau with a temperature of 334 K. This is the temperature at which the sum of the pure componentvapor pressures of n-hexane and water equals atmospheric pressure, in effect giving a steam distillation in this region. The front of this wave, a t { = 0.76,purges all of the inert gas from the column at a low velocity. Further down the bed, in the third region, the adsorbent has yet to be influenced by the steaming and thus preserves the initial condition. Breakthrough curves for experiment 2 are shown in Figure 5 with comparison to stage model predictions and in Figure 6 with comparison to collocation model predictions. The transition zones are much sharper than for the base case. Mole fractions are predicted with resonable accuracy, and the steam distillation plateau is readily apparent. Dimensionless flow rates, u* (ratio of flow rate at column outlet to column inlet), are shown in the figures for this experiment. A very low velocity occurs for the first 30 min as inert gas is purged from the bed along with small amounts of n-hexane and water. The velocity rises to a reasonably constant value on the steam distillation plateau, with the predicted value oscillating for reasons discussed below. With the emergence of the second wave from the bed, temperature continues to increase with slightly superheated steam leaving the bed.
Ind. Eng. Chem. Res., Vol. 32,No. 10,1993 2423 lo
-
l.oL',l,l,,,ll,,,,l,,,, 1
( , , , , ( I , , , A
400
c -----T --
A
'
A'
1380
\ I I
1360 0.2
of1 ' ' ' 0
I
L---
' ' ' ' I ' ' ' '
0.2
I
' '
0.6
0.4
0.8
280 1.o
0 20
0
60
40
5
80
100
120
t (min) 4 0 0 ~ I1 I
I
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1
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h
Y F
320 -
-
300'-
-
0.3
0 0
0.2
0.6
0.4
0.8
1.o
5 Figure 4. Bed profiles for experiment 2 (high velocity) predicted by stage model. (top)Loadings and temperature. (bottom)Velocity and total voidage.
Experiment 3 used the initial conditions and steam feed and flow rate of the base case, but the steam flow was downward. The flow direction was changed to determine if the liquid phase formed is immobile or if it trickles downward through the packing. Breakthrough curves are shown in Figures 7 and 8 with stage and collocationm d e l predictions, respectively. The transitions for this experiment are much sharper than those observed for steaming the bed with upflow in the base case, and the outlet velocity on the steam distillation plateau is slightly higher. Wave fronts predicted by the stage model are smoother than those obtained with the collocation model. The velocity oscillations characteristic of our models are readily apparent. For experiments 4 and 5 the bed was equilibrated at ambient temperature with air 1 % and 80% saturated with n-hexane, respectively. Experimental measurements and stage model predictions are shown in Figures 9 and 10. For the lower loading, the steam distillation plateau is relatively short and shows some variation in measured temperature and concentration, although the quantity of adsorbate and liquid that develops is still predicted to be enough to overflow the pore structure. For the higher loading, this plateau is extended because of the greater quantity of solvent removed; the solvent rollup quickly overflows the pore structure of the adsorbent. Velocities predicted for these experiments (not shown) show oscillations on the steam distillation plateau that are less than
>
0
0
0
20
40
60
80
100
120
t (min)
Figure 5. Breakthrough curves for experiment 2 (high velocity). Predictions by stage model. (top) Vapor-phase mole fractione at column outlet. (middle) Temperature at bed outlet. (bottom) Velocity at column outlet.
average for the low initial loading and greater than average for the high initial loading. For experiments 4 and 5, despite the large difference in initial loading of n-hexane, 2.45 mollkg compared to 3.56 mol&, the solvent residue (or 'heel") remaining on the carbon after regeneration is essentially the same. Stage model predictions of these are shown in Figure 11 after regeneration with 260 bed volumes of steam. Experiment
2424 Ind. Eng. Chem. Rea., Vol. 32,No. 10, 1993 1.o
0.8
E
0.6
x
L
x
0.2
0.2
0
0 0
20
60
40
80
100
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100
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xI-
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320
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120
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t (min) 1
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1.0
150
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h
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t (rnin)
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150
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~
t (min) 1
1
O
,
,
~
,
,
,
,
~
,
,
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,
l 0.8
0
>
-
0.4
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-I I
0 0
20
40
60
80
100
120
0 0
t (rnin)
Figure 6. Breakthrough curves for experiment 2 (high velocity). Predictions by collocationmodel. (top)Vapor-phase mole fractions at column outlet. (middle) Temperature at bed outlet. (bottom) Velocity at column outlet.
5, which began with more n-hexane adsorbed, finishes with less. The small difference between the curves is due to the water competing with the solvent for pore volume; more water must condense to provide the heat to desorb the larger quanitity of solvent at the high initial loading. In the experiments, approximately 15% more water is predicted to adsorb for the higher initial n-hexane loading.
50
100
t (min)
Figure 7. Breakthrough curves for experiment 3 (downflow). Predictions by stage model. (top) Vapor-phaee mole fractions a t column outlet. (middle) Temperature at bed outlet. (bottom) Velocity at column outlet.
Discussion Thermal regeneration of an adsorption bed using steam is qualitatively different than thermal regeneration using a hot noncondensible purge gas. Heat losses from a vessel undergoing regeneration with a noncondensible gas are manifested by a temperature drop and lower final temperature reached, whereas with steam regeneration, the
Ind. Eng. Chem. Res., Vol. 32, No. 10, 1993 2425 1.o
0.8
0.6
3
2.
k
x
l
0.4
0.2
0
50
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300
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4"- 1
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>
0.41 0.2
0
0
50
100
50
100
150
200
t (rnin)
t (rnin)
0.6
280 0
4
150
200
.
t (mini \"".',
Figure 8. Breakthrough curves for experiment 3 (downflow). Predictions by collocationmodel. (top) Vapor-phase mole fractions at column outlet. (middle) Temperature at bed outlet. (bottom) Velocity at column outlet.
temperature is not affected significantly but condensation occurs within the vessel a t the walls. The velocity of the effluent also differs considerably. With hot purge gas regeneration, the carrier leaves the bed throughout the heating step with roughly the same molar flow rate that it entered the bed. In contrast, with steam regeneration, the steam adsorbs and condenses in the bed. Only a slow
Figure 9. Breakthrough curves for experiment4 (lowinitial loading). Predictions by stage model. (top) Vapor-phase mole fractions at column outlet. (bottom) Temperature at bed outlet.
purge of inert gas with solvent and water at initial condition values leaves the bed until many bed volumes of steam have been fed to the bed, at which point the first front leaving the bed effectively sweeps all inert gas from the bed. Of course, there are also other obvious qualitative differences between steam and hot purge gas regeneration such as the added competition for adsorbent pore volume by adsorbed water, the large latent heat effecte for condensing steam, etc. Most of the energy provided by the steam goes to heat the carbon, the vessel, and any residues of solvent and water. Only about one-fourth to one-third of the total energy goes to desorb solvent. Specifically, for our base case. with steam fed to the bed until iust after the steam distillation plateau has been removed,"approximately52% ' of the energy has gone into heating theckbon (excluding the vessel), 32 96 has gone toward desorbing n-hexane, and 16% has gone into warming the solvent residue (ignoring any preadsorbed water). If the heat capacity of the vessel is included in the calculations, then the percentage of the energy used to desorb the solvent drops to 26%. From the standpoint of an energy analysis, the amount of water that adsorbs and condenses can be thought of as being determined largely by energy needs. Indeed, if water did not adsorb but only condensed, we would observe some of the same qualitative behavior, especially the early trends. The effect of water adsorption is most influential
2426 Ind. Eng. Chem. Res., Vol. 32, No. 10, 1993 1.01
I
I
I
I
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I
I
t
I
I
I
I
I
I
I
J--
I
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0.2
0 0
100
50
150
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t (min)
3801 - t 4 0 0 ~ 1I
I
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1
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I
I
,
I
il
360
+
340
1
320
1
300
t 50
0
150
100
200
t (rnin)
Figure 10. Breakthrough curves for experiment 5 (high initial loading). Predictions by stage model. (top) Vapor-phase mole fractions at column outlet. (bottom) Temperature at bed outlet.
4
12.5
L
1
"I
- 2.5 O
0
-
"
~ 0.2
'
~
~ 0.4
~
'
0.6
'
~
' 0.8
'
'
~0 1.o
~
~
i Figure 11. Residual loadings of n-hexane (A) and water (W) in bed at end of heating with 260 bed volumes of steam as predicted by stage model for experiment 4 (low initial loading) and experiment 5 (high initial loading).
after the steam distillation zone has passed. In particular, treatment of water adsorption gives a more accurate prediction of final profiles of bed temperatures and loadings. Its inclusion in models is necessary for quantitative prediction.
'
The wave character of steam regeneration observed experimentally is predicted by the models, including velocity variations and the formation of a liquid phase within the bed. Both models give fairly good predictions of the behavior and their results differ only a little. Of the two models, the stage model is the faster computationally. An explanation for why the solvent heel after regeneration is essentially independent of initial loading is quite simple. During regeneration the solvent rollup overflows the pore structure, substantially erasing any link to the initial loading. All of the cases we considered have nearly identical steam distillation plateaus; solvent and water loadingsare approximately 4.5and 0.5mol&, respectively, and the temperature is 334 K. If this is considered as the initial condition for the remainder of the regeneration step, then it is unremarkable that one should see little variation in the solvent heel between cases. The initial loading will determine somewhat the amount of water adsorbed, and will determine the length of the steam distillation plateau. The amount of solvent residue at a point should be essentially a function of the amount of steam fed to the bed since the steam distillation plateau was eluted. The quality of predictions of our models is better than for our previous model (LeVan and Schweiger, 1991) and reasonable considering the complexity of the problem. The principal reason for the improved prediction is a better understanding and mathematical description of adsorption equilibria for water and for n-hexane and water based on new data (Rudisill et al., 1992). In our previous model, we assumed that the shape of the water isotherm, plotted as qw vs P I P , was independent of temperature, and as a consequence our simulations predicted higher bed temperatures during steaming than we observed in the experiments. Rudisill et al. (1992) show that the shape of the water isotherm changes with temperature, and the isotherm used here reflects this dependence. Viewing the amount of water adsorbed from the standpoint of energy needs with the relative pressure of water fixed by its isotherm, if the isotherm is incorrectly sharp in the model, then the loading of adsorbed water determined by energy needs gives too low a relative pressure, which results computationally in a high bed temperature because the sum of the partial pressures of solvent and water is fixed. In our previous paper, we assumed that adsorbed water has no effect on the quantity of solvent adsorbed. The higher bed temperature predicted in our previous work corrected for this omission by increasing the volatility of the adsorbed solvent. Condensate Flow. The most notable difference between the experimental and predicted breakthrough curves is the difficulty the models have in matching the transition after the steam distillation plateau for experiment 1. In experiment 2,performed at a higher steam flow rate, and in experiment 3, with steam downflow, the transition was much sharper. These anomalies can be explained only by and ' the' formation ~ ' ' ~ ~ downward trickling of condensate in the column. As mentioned previously, for experiment 1 thermocouples at other locations in the bed (e.g., = 0.75) showed the wave to be much sharper prior to reaching the top of the bed (Schweiger, 1989). In experiment 2, the increase steam flow rate reduced the time for heat losses and for condensation and trickling to become severe. The sharpening of the wave with increasing velocity is contrary to conventional mass-transfer models, occurring only when axial molecular diffusion is controlling, which is not the case here. In experiment 3, downward flow facilitates drainage, rather than the refluxing and flow maldistribution that are likely occurring with upflow.
Ind. Eng. Chem. Res., Vol. 32, No. 10, 1993 2427 Moreover, flow direction through the development of the liquid phase affects transitions differently. For steaming upward, trickling of the liquid phase would affect the second transition zone, where mostly n-hexane would fall into a hot region. There, it would quickly vaporize and be pushed back up into the bed. For steaming downward, the trickling would affect the first transition zone, where n-hexane would fall into a cold region. There it would tend to be wicked into the pore structure of the carbon and be adsorbed. We expect trickling to be most pronounced at the wall, where heat transfer to the vessel wall promotes the formation of additional condensate. Also, in comparison with a large industrial bed, our apparatus has a large wall area compared to its volume. For the larger beds, trickling at the wall may be of lesser importance. Our models assume that condensate in the bed is stationary. It is not allowed to trickle; instead, it moves by vaporization and recondensation. The possibility that condensate in the top end region was dripping back into the bed in the base-case experiment and causing the broadening of the second transition was investigated by modifying the stage model. The model was changed to let 80% of the liquid condensate drip back into the last stage. The results of this test showed no significant difference in the breakthrough curves, indicating that the observed effects of condensation and trickling are due to condensation and trickling in the bed and not predominantly in the outlet region. From the standpoint of overall energy analysis the energy to heat residues, particularly of water, can become large. We predict if an adsorbent has a significant water residue that is not removed before regeneration, water may continue to accumulate with successivecycles as more and more steam adsorbs and condenses to heat the residue. With upflow steaming, significant trickling and refluxing can be expected to occur, and the adsorber may effectively flood. By implication, the relative humidity of the feed is important in determining the water residue, as is the operating temperature. If the regenerating steam is near saturation, the carbon on the steam-feed step will fill with water as it reaches equilibrium with the feed. Although this wave propagates through an adsorber slowly, it deposits water which may cause flooding problems later if it is not removed. Velocity Oscillations. Our models predict that the velocity on the steam distillation plateau is reasonably constant as shown in the bed profiles in Figures 2 and 4. However, this velocity rises and falls with time as shown in Figures 5-8. The number of oscillations is proportional to the number of stages or collocation points. The stage model, with no upstream propagation of effects, shows a large spike in the velocity as the steam distillation plateau exits the adsorber. This spike is due to the rapid expansion of gas and vaporization of condensed solvent in the end mixing cell as it is heated by the wave of steam. Similar expansion effects cause the prior oscillations as the second transition, ending the steam distillation plateau, passes through stages or past collocation points.
Conclusions We have reported experimental data for steam regeneration obtained using an apparatus designed to enable measurement of concentrations, temperatures, and flow rates under flexible operating conditions. We know of no other data of this kind. Two mathematical models, a stage model and an orthogonal collocation on finite elements model, have been
used to analyze the experimental results. Both are of the local equilibrium type; rate models give similar results (Schweiger, 1989; LeVan and Schweiger, 1991)since rates of intraparticle mass and heat transfer are fast. The models require no fitted parameters and predict breakthrough curves that are in reasonably good agreement with experimental breakthrough curves. Three zones are predicted and observed under normal operating conditions: a plateau on which the initial condition including inert gas is purged a t low flow rate from the bed, a plateau on which steam distillation of the water-immiscible solvent occurs, and a largely steam purge leading ultimately to the feed condition. Most of the solvent is removed during the elution of the second zone. The vapor-phase concentration of solvent drops rapidly after this steam distillation plateau has passed, signaling the end of effective regeneration. As a practical consideration, in experiments only a weak dependence on flow direction was found, indicating that the primary mechanism for movement of solvent is vaporization with downstream adsorptiordcondensation rather than any bulk flow caused by trickling. The extent of regeneration is determined by the quantity of steam passed through the adsorber. The solvent heel remaining in a well-regenerated adsorber at the end of steaming is largely independent of the initial loading. For models for steam regeneration of activated carbons to predict performance representative of a real system, the adsorption equilibrium relations, and particularly the interaction between adsorbed water and solvent, must be reasonably accurate. While the current adsorption equilibria improves on our previous work, it remains a critical point to the usefulness of the model.
Acknowledgment is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for the support of this research. Nomenclature A = cross-sectional area of column, m2 c = fluid-phase concentration, m0l/m3 C, = heat capacity, J/(mol K) Cp,bsd = heat capacity of adsorption bed, J/(kg K) C,,u = heat capacity of end mixing cell, J/K d, = diameter of adsorbent particle, m D = column diameter, m D L = axial dispersion coefficient, m2/s G = mass flow rate of feed to column, g/e hf = enthalpy of fluid phase, J/m3 h = heat-transfer coefficient, 5-1 k = mass-transfer coefficient, ms/(kg s) lb = bed length, m M = molecular weight, kg/mol P = pressure, Pa Pe = Peclet number for mass dispersion, couoldDL PeT = Peclet number for energy dispersion, eovol,,/XL q = adsorbed/condensed phise concentration, mol/kg t = time, s T = temperature of fluid phase, K uf= internal energy of fluid phase, J/m3 us = internal energy of stationary phase, J/kg U = wall heat-transfer coefficient, J/(m2s K) U,U = end mixing cell wall heat-transfer coefficient, J/(K e) v = interstitial fluid velocity, m/s u* = dimensionless flow rate, eu/(c,pb) V,, = volume of end mixing cells, m3 w = condensate in mixing cell, mol y = fluid-phase mole fraction z = axial coordinate, m
2428 Ind. Eng. Chem. Res., Vol. 32, No. 10, 1993
Greek Letters t
Pure water:
= volumetric gas fraction in interstices of bed
60
= void fraction of packing
t'
= total volumetric gas fraction including pore volume
{ = dimensionless axial coordinate, d l b 0 = fractional loading, 4/@ h = heat of desorption, J/mol
lnPw(MPa)=A'A' = A
+ In ,e + al(i - e,) + a2(ia,(l- e,l3
XL = thermal diffusion/dispersion coefficient, m2/s p
B + b,(i - e,) C+T
for ,8 I 1 (31)
+
+ a,(i -
(32)
= viscosity of fluid phase, kg/(m s)
Pb = bulk density of bed, kg/m3 PI = liquid density, kg/m3
4 = volume adsorbed based on liquid density, qM/pl, mVkg x = particle porosity Subcripts
A = solvent f = fluid phase I = inert gas in = feed value 1 = adsorbate/liquid W = water
In Pw(MPa) = A - - for e, 2 1 (33) C+T with A = 9.38086, B = 3816.41, C = -46.13, = 0.6856, a2 = 4.8123, a3 -7.5767, a4 = 5.9743, and bl = 438.165. 4; = 406.0 X lV m3/kg. pwj = 997.01 - 0.5221(T - Tref). Mixtures: The equations above are used to predict partial pressures empirically using values of eA and Ow given by
Superscripts
r = relative to saturation s = saturation
Appendix Model Parameters lb
= 0.584 m
D = 0.073 m Vceu= 0.000 32 m3 U = 0.944 J/(m2s K) V, = 0.0174 J/(s K) d, = 2.67 mm pb = 480 kg/m3 0.4 = 0.5 k = 1 m3/s h = 6.4 X 104 kJ/(m3 s) Pe = 60 PeT = 60 to
x
Tamb= 298-303 K Trer= 298 K C p , w = 1.52 X 103 J/(kg K) Cp,cel= 127.0 J/K Cp~,= f 158.0 J/(mol K) C P , f = 36.9 J/(mol K) Cp, = 29.24 J/(mol K) C p ~ ,=l 216.0 J/(mol K) C P , l = 75.4 J/(mol K) XW = 4.07 X lo" J/mol = 9.4 X 1o-B kg/(m s) at 105 "C pw = 12.7 X 108 kg/(m s) at 105 OC I ~ I= 21.9 X 1o-S kg/(m s) at 105 "C
Adsorption Equilibria. Pure n-hexane (Hacskaylo, 1987):
In PA (MPa) = A - - for 8, 2 1 (30) C+T with A = 6.98946,B = 2737.59, C -46.87, and b l = 3356.89. 4: = 477.4 X 10-8 m3/kg. PAJ = 654.71 - 0.9735(T - T&.
(35)
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Received for review February 24, 1993 Revised manuscript received June 24, 1993 Accepted July 2,1993. Abstract published in Advance ACS Abstracts, September 15, 1993.
