1084
I n d . Eng. Chem. Res. 1990,29, 1084-1090
Carver, M. B. FORSIM, A Fortran Package for the Automated Solution of Coupled Partial and/or Ordinary Differential Equation Systems; Atomic Energy of Canada Ltd.: Chalk River Nuclear Laboratories, Canada, 1974. Finlayson, B. A. The Methods of Weighted Residuals and Variational Principles; Academic Press: New York, 1972. Kaguei, S.; Yu, Q.; Wakao, N. Thermal Waves in an Adsorption Column. Chem. Eng. Sci. 1985, 40 (7), 1069. Lapidus, L.; Amundson, N. R. Mathematics of Adsorption in Beds VI. The Effect of Longitudinal Diffusion in Ion Exchange and Chromatographic Columns. J . Phys. Chem. 1952,56, 984. Leavitt, F. W. Non-isothermal Adsorption in Large Fixed Beds. Chem. Eng. Prog. 1962,58 (81,54. Levenspiel, 0.;Bischoff, R. B. Aduances in Chemical Engineering; Academic Press: New York, 1963; Vol. 4. Marcussen, L. Comparison of Experimental and Predicted Breakthrough Curves for Adiabatic Adsorption in Fixed Bed. Chem. Eng. Sci. 1982, 37, 299. Pan, C. Y.; Basmadjian, D. Constant-Pattern Adiabatic Fixed-Bed Adsorption. Chem. Eng. Sci. 1967,22, 285.
Pan, C. Y.; Basmadjian, D. An Analysis of Adiabatic Sorption of Single Solutes in Fixed Beds: Pure Thermal Wave Formation and its Practical Implications. Chem. Eng. Sci. 1970, 25, 1653. Raghavan, N. S.; Ruthven, D. M. Dynamic Behaviour of an Adiabatic Adsorption Column-11. Chem. Eng. Sci. 1984, 39, 1201. Ruthven, D. M.; Garg, D. R.; Crawford, R. M. The Performance of Molecular Sieve Adsorption Columns: Non-Isothermal Systems. Chem. Eng. Sci. 1975,30, 803. Sircar, S.; Kumar, R.; Anselmo, K. J. Effects of Column Nonisothermality of Nonadaiabaticity on the Adsorption Breakthrough Curves. Ind. Eng. Chem. Process Des. Deu. 1983,22, 10. Villadsen, J. V.; Stewart, W. E. Solution of Boundary-Value Problems by Orthogonal Collocation. Chem. Eng. Sci. 1967,22,1483. Yoshida, H.; Ruthven, D. M. Dynamic Behaviour of an Adiabatic Adsorption Column-I. Chem. Eng. Sci. 1983, 38 (6), 877.
Receiued for reuiew June 6, 1989 Reuised manuscript received October 17, 1989 Accepted November 10, 1989
Heat Effects in Adsorption Column Dynamics. 2. Experimental Validation of the One-Dimensional Model Shamsuzzaman Farooq a n d Douglas M. Ruthven* Department of Chemical Engineering, University of New Brunswick, P.O. Box 4400, Fredericton, New Brunswick, Canada E3B 5A3
The effect of thermal gradients on the dynamic response of an adsorption column has been investigated experimentally by measuring adsorption and desorption breakthrough curves and corresponding temperature profiles (both radial and axial) in a series of adsorption columns with intemal diameters ranging from 0.77 to 7.9 cm. The departure from isothermal conditions becomes more pronounced as the column diameter is increased, and this leads to a corresponding broadening of the experimental breakthrough curves. Desorption is almost isothermal, and as a result, the response is practically independent of the column diameter. It is shown that the major resistance to heat transfer is a t the column wall, and a simple one-dimensional model with all heat-transfer resistance concentrated a t the column wall provides a good representation of the experimentally observed behavior. In the preceding paper (Farooq and Ruthven, 1990),it was shown theoretically that, even under the extreme conditions of a linear isotherm and negligible film resistance to heat transfer at the column wall, the one-dimensional model provides a good representation of nonisothermal adsorption column dynamics, particularly under conditions leading to the formation of a combined temperature and concentration wave. Under conditions of pure thermal wave formation, there is some difference between the one- and two-dimensional models. However, for a favorable isotherm system, the effect of temperature excursions on the concentration profile is, for a given heat of adsorption, less pronounced than for a linear system. Furthermore, heat-transfer resistance at the column wall brings the radial temperature profile closer to that of the idealized one-dimensional model (uniform temperature across the central core with a temperature change at the wall). One may therefore expect that, for most practical systems, the one-dimensional model should provide an adequate representation of the column dynamics, regardless of the relative velocities of temperature and concentration fronts. In order to verify this conclusion, an experimental study was undertaken using columns of various diameter with different heat-transfer conditions at the wall. The results, which are reported here, confirm the validity
* Author to whom correspondence should be addressed. 0888-5885/90/ 2629-1O84$O2.5O/O
of the one-dimensional model. Experimental Study A schematic diagram of the experimental setup is shown in Figure 1. A series of stainless steel columns with different diameters and lengths, packed with 5A zeolite adsorbent, was used. One of the larger columns was fitted with a Teflon liner in order to alter the heat-transfer boundary condition at the column wall. The columns were immersed in a large water tub that acted as a constanttemperature bath. The sorbate concentration in the exit gas was monitored continuously by a Gow-Mac thermal conductivity detector (Model 40-001),which had previously been calibrated with mixtures of known composition. Temperatures were measured during the experimental runs in the large-diameter columns (run 10 and run 11) at different axial and radial positions, as well as at the column exit using copper-constantanthermocouples. The thermocouples were introduced into the bed through stainless steel sheaths. The thermocouple monitoring the temperature of the exit gas was placed bare into the gas stream through a Teflon seal. The readings of these thermocouples were collected and printed at preassigned intervals with an Apple (IIe) microcomputer using a Sciemetric Instruments (Model 901) data acquisition interface. The gas flow to the column was controlled by a Matheson flow controller which was precalibrated against 0 1990 American Chemical Society
Ind. Eng. Chem. Res., Vol. 29, No. 6, 1990 1085 Ref.
;; %
I
f
I
0
Oesorption
xO
0
0
0
b
.6
t OFM ct
I
c a FC FI(
IoDlUr 8
-
ffi W
-
Fid
w
t f l a mntmller l f l a matar
Adsorptlon
OL
Q
0
0
2
Q
.4
Q
o x
0
o
x
o
x
0
"n Y
t.
r 7
3imensionless T 1 m e . r
Figure 2. Reproducibility of the experimental adsorption and desorption breakthrough curves.
I
Figure 1. Schematic diagram of the experimental setup.
a wet test meter (a soap bubble meter was used at very low flow rates) covering a wide range of flow rates under experimental temperatures and pressures. Prior to an experiment, the column was activated (or regenerated) by purging overnight with helium at 250 "C. With the regenerated column in place, the required flow and corresponding column pressure were adjusted with helium and a sufficiently long time was allowed for the TCD base line to stabilize and the column temperature to become uniform with the bath temperature. The flow of helium was then replaced by the feed (a mixture of 1% ethylene in helium) through switching of valves. Compared to the duration of the experiment, this could be considered as a step change. The adsorption breakthrough was completed, i.e., the bed was completely saturated with the feed, and thermal equilibrium was established for the saturated column. The feed was then cut off, and the desorption curve was measured using a helium purge. The experimental adsorption and desorption data thus obtained were very reproducible, as may be seen from Figure 2.
Theoretical Model In order to develop a theoretical model to analyze the experimental results, the following approximations are introduced. 1. The feed consists of a small concentration of a single adsorbable component, and the frictional pressure drop through the bed is negligible so that the linear velocity through the bed may be considered constant. 2. The equilibrium relationship for the adsorbing component is represented by the Langmuir isotherm, and the Langmuir constant shows the normal exponential temperature dependence. 3. The flow pattern is described by the axial dispersed plug flow model. 4. Thermal equilibrium is assumed between fluid and adsorbent particles. 5. Bulk flow of heat and conduction in the axial direction are considered in the heat balance equation. An overall heat-transfer coefficient has been used to account for heat loss from the system, and the temperature of the
column wall is assumed to be the same as the feed temperature. This implies a uniform temperature across the column radius with all heat-transfer resistance concentrated at the wall. 6. The mass-transfer rate is represented by a linear driving force rate expression. 7. The temperature dependence of gas and solid properties is neglected. With these assumptions, the equations describing the system are mass balance
heat balance
1 - t aq 2h (-AH)- - ( T - To) = 0 at t~ +
(2)
mass-transfer rate
aq/at = k(q* - q ) adsorption equilibrium
(3)
(4)
temperature dependency of b
boundary conditions
(7)
Equations 6 and 7 are the correct boundary conditions for mass flow for a dispersed plug flow system as discussed by Wehner and Wilhelm (1956). Boundary conditions for heat flow (eqs 8 and 9) have been written assuming an analogy of mass and heat transfer in a dispersed plug flow system.
1086 Ind. Eng. Chem. Res., Vol. 29, No. 6, 1990
The experiments conducted and described in the previous section satisfy the following initial conditions: adsorption C(Z,O)
= 0; q(z,O) = 0; T(%,O)= T,
(10)
= co; q(z,O) = q*; T(%,O)= To
(11)
desorption C(%,O)
Equations 1-9 are written in dimensionless form as follows:
(17)
-
L -.-__-.
(18) For adsorption, the dimensionless initial conditions are E(x,O) = 0; Q ( X , O ) = 0; T(x,O) = 1 (19) For desorption, the dimensionless initial conditions are
E(x,O) = 1; Q ( X , O ) = 1; T(x,O) = 1 (20) The simultaneous solution of eqs 12-18 gives breakthrough and corresponding temperature profiles e = f(7) and T = f ( ~with ) Pem, Peh, Peh', 7f, 71, r 2 , r3, 6, and X as parameters. Equations 12-18 were first reduced to a set of ordinary differential equations by the method of orthogonal collocation. The ordinary differential equations were then integrated numerically in the time domain by using the Gear's stiff (variable-step) integration algorithm with full Jacobian analysis, as provided in the FORSIM package (Carver, 1974). Seven to 15 discretization points were used depending on the parameter values. Details of the collocation form of these equations are discussed elsewhere (Farooq, 1988).
Estimation of Model Parameters for Experimental Response Curves In order to match the experimental response curves, numerical values for the dimensionless groups listed in a previous section are required. Heat capacities and densities of the fluid and solid and the heat of adsorption were specified from the available physical properties. The contribution of the adsorbed phase to the heat capacity is quite small and is therefore neglected. Bed voidage, bed length, fluid velocity, feed temperature, and feed concentration are directly measurable operating variables. A simple material balance of the adsorption column yields (21)
zq"
,
L...--__Iu
1
, 3 JDC
Lli
jd~e-,.or
ecs
1
5300 i
Figure 3. Experimental beakthrough curves showing the effect of column diameter. (a) Adsorption. (b) Desorption.
The mean residence time, E, is determined by integration of the breakthrough curve when c/co is plotted as a function of time. qo/c, was therefore easily obtained from the experimentally observed breakthrough curves. Dispersion coefficients of mass and heat and the linear driving force rate constants were estimated from available correlations. The axial dispersion coefficients for the different experimental runs were estimated from the correlation given by Hsu and Haynes (1981): 3.33 -1- -- 0.328 (22) Pe' ReSc 1 0.59(ReSc)-' +
+
The above correlation follows from experiments in a column packed with 0.72-mm (diameter) particles in the range 0.08 < ReSc < 1. In the present study, 0.707-mm particles were used and ReSc for the different runs varied from 0.0869 to 0.3846. In view of this close agreement in the experimental conditions, eq 22 was chosen among many other correlations put forward in the literature for estimating the axial dispersion coefficient. The effective axial thermal conductivity of the fluid follows from the similarity assumed between the mechanism of fluid-phase mass and heat transfer (Pem = Peh'). The effective axial bed thermal conductivies were estimated from the correlation given by Yagi et al. (1960). The adsorbent thermal conductivity used includes the contribution from the adsorbed phase. The overall effective linear driving force rate constants for the experimental runs were estimated from the following correlation:
Ind. Eng. Chem. Res., Vol. 29, No. 6, 1990 1087
4 ,
0'
C
"
"
"
2002
Dimensionless Time. t
"
"
'
4. ,
"
4330 Tine, T
6030
2:nensio-isss
, 0
U
.4
I I
Run: 1 (d=3. 50" 0
'
0
"
'
'
'
2000
'
"
"
'
~
4000
x"/
,
Run: 10 ( c ~ 6 . 2 5 ~ ~ )
>
X
I
I
6000
Dimensionless Time,
k
Run: 1 1 (d=7. 88cm)
which considers macropore, micropore, and film resistances to mass transfer. Molecular diffusivity was estimated from the Chapman-Enskog equation. Linde 5A molecular sieves have a wide distribution of macropore size. An average pore radius of 2500 A was used to estimate the Knudsen diffusivity. A tortuosity factor of 3 and particle porosity of 0.33 were assumed. qo/covalues obtained from different runs were very close and in good agreement with the gravimetric data of Derrah (1971). An average value was used in the rate expressions. Micropore resistance, estimated with a crystal diffusivity of 1.0 X cm2/s and an average crystal radius of 1.8 pm (representative of Linde 5A),was found to be insignificant with respect to macropore resistance. The experiments were conducted in a very low Reynolds number regime, and the external film resistance was found to be approximately one-third of the macropore resistance. The external mass-transfer coefficients were estimated from the correlation of Wakao and
-%,,I
~
,
,
Funazkri (1978), which has been corrected for axial dispersion contribution and has been shown to provide a consistent representation of extensive mass-transfer data from many sources:
Sh = 2.0 + l.lReo.6S~0.33
(24)
Thus, only the two parameters X and h remained to be estimated by matching the theoretical and experimental breakthrough and temperature curves. Adsorbent properties and common experimental conditions are given in Table I. Other parameter values used for computing the theoretical curves are summarized in Table 11.
Results and Discussion The adsorption and desorption breakthrough curves obtained from different experimental runs are shown in Figure 3. The experiments were conducted under near-
1088 Ind. Eng. Chem. Res., Vol. 29, No. 6 , 1990 Table I. Adsorbent Properties and Common Experimental Conditions feed 1 % ethylene in helium adsorbent Linde 5A zeolite 0.0707 d , cm 0.206n cal/(g "C) 1.14" P,, g/cm3 K,, cal/(cm s "C) 1.385 X AH,cal/mol -8000.0* 1.24 1.66 X lo-' (at atmospheric pressure) 3.64 X IO-' 10 21. f 1
6,
i
Desorption
-5
t
i I
-101
'Ruthven et al. (1975). *Haasan (1985). CKagueiet al. (1987).
1
Run: 10
~
'
0
'
I "
'
"
I5CC
1003 TIME
equilibrium conditions, and the L / v ratio varied in such a way that the Peclet number varied between 100 and 250. For such parameter values, the breakthrough curves plotted on a time axis made dimensionless with respect to v j L are expected to be more or less coincident under isothermal conditions. It is clear from Figure 3a that the spread of the mass-transfer zone during adsorption increases with increasing column diameter. This additional spreading of the mass-transfer zone is therefore associated with heat effects since the surface area available for heat transfer (per unit column volume) decreases with increasing column diameter. On the other hand, for a favorable adsorption isotherm, desorption is a much slower process and the associated heat effects are therefore less pronounced. This is evident from Figure 3b. The experimental adsorption and desorption breakthrough curves for several experimental runs are compared in Figure 4 with the theoretical curves calculated according to the one-dimensional nonisothermal model using the parameters given in Tables I and 11. The theoretical isothermal curves are also shown for comparison. For adsorption, the deviation of the experimental breakthrough curve from the isothermal prediction increases with increasing column diameter. This trend is correctly predicted by the nonisothermal model. For a system with a favorable isotherm, desorption is essentially equilibrium controlled. Since desorption under these conditions is slow, it is practically isothermal, and there is therefore very little difference between the theoretical curves derived from the isothermal and nonisothermal models. Both theoretical curves show semiquantitative agreement with the experimental desorption curves; the deviation between theory and experiment no doubt reflects the inadequacy of the Langmuir model in providing a quantitatively accurate representation of the equilibrium isotherm. Temperatures measured at the column exit during adsorption and desorption, for some experimental runs, are compared with the model predictions in Figure 5. The contribution af the thermocouple probes associated with
1I
'
"
500
(M i - )
___
3eso-?t,an
E
-3
4
t
FLT
__ 2323
,'OC
3;::
7 i V E ( 4 d
Figure 5. comparison of experimental and theoretical temperature profiles at the column exit. The theoretical curves shown by continuous lines are calculated using the parameters given Tables I and 11.
-10 I:
I
-15
'
;I
'
.\
i -4
'
'
-i5
'
'
0
'
~~
c
v, cm/s crolca h
Pem k , s-' KZIK, h, cal/(cm s "C)
1
5 35.0 3.5 0.315 4.05 2650.0 0.9 223.0 0.086 2.31 1.0 x lo-'
'I
these runs was duly accounted for in computing the theoretical curves by including the thermal capacity and conductivity of the probes in the heat balance. Some ~
run 35.0 3.5 0.315 5.7 2671.0 0.9 247.0 0.086 2.34 1.0 x 10"
'
Figure 6. Experimental radial temperature profiles.
Table 11. Parameters Used in the Calculation of Theoretical Curves parameters L, cm d, cm
'
.5
ri4
6 15.6 0.77 0.334 7.48 2640.0 0.9 100.0
0.086 2.385
1.0 x lo"
" The column used for this rung was internally lined with Teflon.
7 15.8 1.38 0.33 6.2 2643.0 0.9 103.0 0.086 2.352 1.0 x lo-'
104 35.0 6.25 0.338 3.3 2676.0 0.9 215.0 0.086
2.306 1.0 x 10-4
11 35.0 7.88 0.32 1.21 2698.0 0.9 119.0 0.086 2.27 1.0 x 10-4
200-
,
,
,
,
I
,
,
1
,
I
,
,
.
1
I
< Run: 10
150-
\ \
\ \
E
\
100-
\ \ \
2
i If i
Oh
d i
ii
'
i2co ':
I
400
600 TIME(Min)
k
i
r.
,
aoo
50 t-
K\ x '
%\
1
,
1000
Figure 7. Comparison of nonisothermal adsorption breakthrough curves with isothermal, axial dispersed plug flow model. The equivalent Peclet numbers corresponding to the enhanced dispersion coefficients giving the best fit (-) to the experimental points are given on the diagram. Other parameter values are the same as in Tables I and 11.
representative radial temperature profiles are shown in Figure 6. The experimental results clearly reveal that a radial temperature gradient exists in the column, but the inside wall film resistance to heat transfer is more important. I t is important to note that the same value of heattransfer coefficient gives a good fit of the experimental data obtained with or without the Teflon liner. The thermal conductivity of steel is 2 orders of magnitude greater than that of Teflon. This result therefore implies that the major resistance to heat transfer is at the inner surface of the column wall. In part 1 of our study, it was shown that for a linear system the form of the breakthrough curve under nonisothermal conditions can be adequately represented by the isothermal, dispersed plug flow model using an enhanced dispersion coefficient. I t was also shown that the enhancement of axial dispersion is a regular function of dimensionless radial thermal Conductivity. The experimental adsorption breakthrough curves obtained here are similarly matched with an isothermal model, and the results are shown in Figure 7. Clearly, an isothermal, dispersed plug flow model using an enhanced dispersion coefficient provides an adequate representation of the heat effects on the experimental adsorption breakthrough curves. The corresponding Peclet numbers are plotted against the dimensionless group RuC,'/hL in Figure 8, which shows a regular trend. In principle, it is possible to represent the heat effect on the desorption curve by an isothermal, dispersed plug flow model, but this was not attempted here since the desorption steps in the present study were very nearly isothermal.
Conclusions The nonisothermal one-dimensional model developed here broadly represents the experimentally observed adsorption and desorption behavior of the ethylene-helium5A system. This model is currently being used to study the dehydration of ethanol-water azeotrope, using 3A zeolite. Although the temperature rises in this system are very much greater than the present study, the preliminary results show that the agreement between theory and experiment is quite satisfactory over a wide range of flow rates (Rojo, 1988). This model should therefore prove useful in extracting reliable kinetic and equilibrium information from experimental breakthrough curves as well
as for predicting the performance of larger, near-adiabatic industrial adsorbers.
Nomenclature b (bo) = Langmuir constant at T (at To) c = sorbate concentration in the gas phase co = sorbate concentration in the feed E = dimensionless gas concentration, c / c o C, (C ') = heat capacity (volumetric)of the gas C, = heat capacity of the adsorbent d = column diameter d , = particle diameter D, = micropore diffusivity DL = axial dispersion coefficient D, = molecular diffusivity D, = particle diffusivity h = overall effective coefficient of the wall heat transfer AH = heat of adsorption k = effective mass-transfer coefficient kf = film mass-transfer coefficient K g = thermal conductivity of the gas K L = effective thermal conductivity of the gas in the axial direction K , = thermal conductivity of adsorbent Kz = effective bed thermal conductivity in the axial direction L = bed length m = (1- € ) / e Peh = uL(p,C + mp,C,)/Kz Peh' = (uLpgeg)/KL Pem = Peclet number, uL/DL Pe' = particle Peclet number, ud,/DL q = sorbate concentration in the solid phase q* = value of q at equilibrium with c at T qo = value of q at equilibrium with co at 2'0 q8 = saturation constant Q = dimensionless solid-phase concentration, 4 / 4 0 re = crystal radius R = column radius Re = Reynolds number, dptupg/p R, = gas constant R, = particle radius Sc = Schmidt number, p / ( p Sh = Sherwood number, 12 ,/Dm t = time T = mean residence time T = bed temperature To = feed temperature T = dimensionless temperature, T / To u = interstitial velocity z = dimensionless axial distance, t / L z = distance from bed inlet
P'
1090 Ind. Eng. Chem. Res., Vol. 29, No. 6, 1990
0 (0-) = position just inside (just outside) the column Greek L e t t e r s
6 = (-aH)/(RT) e = bed voidage = particle voidage X = nonlinearity parameter, qO/qe pg = density of gas ps = density of adsorbent T = dimensionless time, t u / L 7 = dimensionless mean residence time, Ev/L tp
= viscosity
Literature Cited Carver, M. B. FORSIM, A Fortran Package for the Automated Solution of Coupled Partial and/or Ordinary Differential Equation Systems; Atomic Energy of Canada Ltd.: Chalk River Nuclear Laboratories, Canada, 1974. Derrah, R. I. Adsorption and Diffusion in 5A zeolite. M.Sc. Thesis, University of New Brunswick, Canada, 1971. Farooq, S. A Study of Pressure Swing Adsorption Systems. Ph.D. Thesis, University of New Brunswick, Canada, 1988.
Farooq, S.; Ruthven, D. M. Heat Effects in Adsorption Column Dynamics. 1. Comparison of One- and Two-Dimensional Models. Znd. Eng. Chem. Res. 1990,preceding paper in this issue. Hassan, M. M. Theoretical and Experimental Studies of Pressure Swing Adsorption Systems. Ph.D. Thesis, University of New Brunswick, Canada, 1985. Hsu, L.-K. P.; Haynes, H. W. Effective Diffusivity by the Gas Chromatography Technique: Analysis and Application to Measurements of Diffusion of Various Hydrocarbons in Zeolite NaX. AZChE J. 1981,27,81-91. Kaguei, S.; Nishio, M.; Wakao, N. Parameter Estimation from Constant Pattern Thermal Waves in an Adsorption Column. Chem. Eng. Sci. 1987,42 (12),2964-2966. Rojo, J. C. Ph.D. Dissertation, University of Valladolid, Spain, 1988. Ruthven, D. M.;Garg, D. R.; Crawford, R. M. The Performance of Molecular Sieve Adsorption Columns: Nonisothermal Systems. Chem. Eng. Sci. 1975,30,803-810. Wakao, N.; Funazkri, T. Effect of Fluid Dispersion Coefficientson Fluid-to-Particle Mass Transfer Coefficients in Packed Beds. Chem. Eng. Sci. 1978,33,1375-1384. Wehner, J. F.; Wilhelm, R. A. Boundary Conditions of Flow Reactor. Chem. Eng. Sci. 1956,6, 89. Yagi, S.;Kunii, D.; Wakao, N. Studies on Axial Effective Thermal Conductivities in Packed Beds. AZChE J. 1960,6, 543.
Received for review June 6 , 1989 Revised manuscript received October 17, 1989 Accepted November 10, 1989
