Chemical Engineermg Science, Vol. 45, No. 3. pp. 759-763, Printed in Great Britain
Liquid
1990.
CKW-2509190 $3.00 + 0.00 % 1990 Pergamon Press plc
holdup and dispersion
(Received6 February
1989;
acceptedfor publication
INTRODUCTION
In real flow systems the flow pattern is intermediate to the two extremes of plug flow and backmixed (CSTR) behaviour. A dispersion model is frequently used to describe the flow behaviour of real systems which do not drastically deviate from plug flow. It is well known that the liquid phase flow pattern in a packed column does not deviate drastically from plug flow and therefore the dispersion model has been widely used to describe it (Carberry and Bretton, 1958; Sater and Levenspiel, 1966; van Swaaij et al., 1961; Bennett and Goodridge, 1970; Kan and Greenfield, 1983; Schubert er al.. 1986). The liquid holdup in a packed column is comprised of two major regions (Shulman et al., 1955; Hoogendoorn and Lips, 1965; Kan and Greenfield, 1983): (a) the relatively fast moving or dynamic liquid holdup, h,, which accounts for the major solute transfer; and (b) the relatively stagnant or static liquid holdup, h,, which exchanges mass with the surrounding dynamic liquid phase through a convective-type diffusion process. The relative proportions of h, and h, are important to the designer inasmuch as it gives the extent of effective liquid holdup for mass transfer. From the above it is clear that a complete description of the liquid phase flow in a packed column requires a knowledge oE (a) total, dynamic and static respectively; (b) dispersion effects.
liquid
holdup,
h,, h, and h,,
Shulman et al. (1955) were the first investigators who differentiated between h, and h,. Shulman et al. determined h,, h, and h, by the weighing method. They found that the static holdup is constant over the entire range of liquid flow rate. van Swaaij et al. (1969) used impulse tracer approach to study the hydrodynamics and concluded that static holdups measured by the tracer method and draining method are equivalent, and that all the liquid holdup is accessible to the tracer. However, it can be argued that for the impulse tracer the total period between tracer entry and exit may not be sufficient to cause interaction of the short lived tracer with the static holdup. The response to an impulse input thus may not include static holdup regions. On the other hand the step decrease tracer approach seems more versatile as far as static holdup is concerned. Bennett and Goodridge (1970) and Schubert et al. (1986) used this step decrease method to investigate static and dynamic holdup. It was shown by these authors that the static holdup determined by tracer methods is lower than that found by the draining method. The basic difference between the tracer methods and the draining method is that in tracer experiments the column hydrodynamics are not disturbed as during the draining method. Secondly, the draming method measures the liquid which remains trapped in packing interstices and joints as well as the liquid which is held on the packings due to surface forces. Under irrigated condition a significant part of this latter liquid may start moving, thereby reducing the static CES
153.11
in packed columns 12 July
1989)
holdup. The step decrease method can differentiate between these two liquid portions and is therefore best suited for this purpose. Bennett and Goodridge (1970) and Schubert et al. (1986) obtained the liquid phase axial dispersion characteristics along with h, and h, in a packed column using the step decrease method. These workers however. used relatively small sized ( < 0.0095 m) packings (Raschig rings, Berl saddles) in very small ( < 0.075 m diameter) columns. The lowest nominal packing size used industrially is 0.025 m. Further, highly open packings like Pall rings are used in modern plants rather than the closed Raschig rings. In view of this it was thought desirable to obtain the above-mentioned characteristics using a metal Pall ring (MPR). For comparison with Shulman et al., data were also obtained for a 0.025-m ceramic Raschig ring (CRR). The characteristics of the packings used are given in Table 1. for describing the Various models have been used nonideality of flow in a packed column. The mixing cell model postulates flow through a number of perfectly mixed cells in series. The flow between any two consecutive cells is assumed to be piston-like. This model has only one parameter, i.e. number of perfectly mixed cells (Sater and Levenspiel, 1966). The drawback of this model is that it is far from reality and does not represent the physical picture of the flow in a packed bed. A two-parameter model which is more realistic is the piston exchange (PE) model, which assumes piston flow through dynamic holdup and exchange with the static holdup. There are a number of variations of the PE model. All these versions are termed crossflow models (Patwardhan, 1978a). In a series ofarticles Patwardhan (1978a,b, 1979, 1980, 1981) proposed an extended crossflow model wherein the exchange between static and dynamic holdup is depicted by convective-type transport. He applied this model to various cases of mass transfer with chemical reaction to mathematically evaluate the effectiveness of static holdup in mass transfer compared to dynamic holdup, and elegantly brought out the applicability of the extended crossflow model even for second-order kinetics and reactions where gas phase transfer is rate-controlling. Like all other crossflow models this model also assumes piston flow in the dynamic holdup. From the foregomg discussion it is evident that the static holdup is that part of the total holdup which attains a dynamic equilibrium with its surroundings and exchanges mass with the dynamic holdup through a convective-type process. This description correctly defines the static holdup and its coexistence with the dynamic holdup from mass transfer viewpoint. The PDE model proposed by van Swaaij er al. (1969) is a modification of the crossflow model. It is a three-parameter model which accounts for the axial dispersion taking place in dynamic holdup. This model is better than the previous models since it represents the reality more closely. Bennett and Goodridge (1970) have given the details of the model and solved the equations using the Laplace transform method. These authors have reported that this solution con759
Shorter
Communications Table
Packing 25-mm metal Pall ring 25-mm ceramic Raschig
ring
1.
Piece density (No./m3)
Geometric surface area (m-l)
Voidage (%)
48,000 45,500
188 180
94 73
verges too slowly for high values of the Peclet number (Pe > 25) to be satisfactory and that the partial differential equation can be better solved using the Crank-Nicholson procedure for the entire range of parameters. Bennett and Goodridge also proposed an innovative graphical method of estimating parameters from the obcharacteristics of the response curves on served a semilogarithmic scale. This method was used by Patwardhan and Shrotri (1981) to find the exchange coefficient between the static and dynamic holdup by analysing the tail portion of the response curve. In the present work a computer program was written to solve the model equations and to estimate the model parameters directly from the experimentally obtained response curves. The constrained programming was adopted to simplex method of nonlinear obtain the best match between the experimental and predicted response curves for the step decrease. The graphical method of Bennett and Goodridge was used to arrive at the preliminary guesses required for the computer program.
TREATMENT
OF EXPERIMENTAL
DATA
The input to the computer program is required to be in the form of dimensionless concentration vs dimensionless time. The experimentally obtained concentration values were made dimensionless on the basis of the conductivity of inlet water. The area under the c vs t curve was calculated numerically to find k,. The area under the curve up to “D” (Fig. 1) is equal to the mean residence time of the dynamic liquid phase. Based on td the time axis was made dimensionless for further parameter estimation. To find the characteristics of the response curve., a plot of In (c) YS l was made. The slopes of the first and second linear portions and the intercept of the extrapolated second linear portion were measured. Using the method of graphical solutions of Bennett and Goodridge (1970) the preliminary estimates of Pe, k,/k, and q were found. These estimates were fed to the computer program which minim&d the sum of squares due to residuals between experimental and predicted response curves. The results of the computer program were more accurate than the graphical estimates.
48 160
too
Fig.
1. Transformed experimental response I/, = 0.0889 x lo-‘m/s.
EXPERIMENTAL The experimental set-up used in the present work was similar to that of Bennett and Goodridge (1970). A perspex column of 0.2 m diameter and 1.5 m height was used. A ladder-type liquid distributor was used to distribute the liquid. A conductivity probe (cell constant 0.104, time lag < 0.1 s) was fixed in the column outlet to measure the conductivity of the outlet solution. The procedure used was akin to that of Bennett and Goodridge. Schubert rt al. (1986) used preflooded columns, which is an unlikely situation in industrial applications. In the present work no attempt was made to wet the packings by flooding the column before commencing an experiment. Also, the liquid velocity was increased for each successive run to incorporate the effect of improvement in packing surface coverage on the holdup as liquid velocity increases. The liquid velocity was varied from 0.0005 to 0.006 m/s. Since it is well known that the gas velocity has no effect on the liquid holdup in the preloading region, no gas was introduced in the column.
Packing factor (F)
RESULTS
curve
for MPR:
AND DISCUSSION
Table 2 summarises the correlations the packings investigated.
for Pe and k,/k,
for
Total holdup, h,
The total liquid holdup obtained is shown in Fig. 2. The data obtained for a 0.025 m CRR by Shulman et al. are also shown in Fig. 2. The total holdups obtained by the present method are 15-20%higher than those obtained by Shulman et al. This difference may be attributed to the difference in the two procedures employed. ratio, h,/h, Figure 3 shows the values of the holdup ratio determined by the present method. It has been observed that k, is a much stronger function of V, than k, and therefore k,/k, decreases with Vi. Holdup
h, Figure 4 shows the variation of static holdup with liquid velocity. The static holdup for 0.025-m CRR reported by Shulman et al. (1955) is also shown for comparison. The following observations can be made: The static holdup determined by the present method is much less compared to the values reported by Shulman et al. (1955). A similar observation has been made by Schubert et al. (1986). This difference can be attributed not only to the different methods of measurement used but also to the definiStatic holdup,
Table (a) MPR:
(b) CRR:
2.
k = 0.1024 l’~“.5z’ a’= 0.0408 v-o.597 Pe = 43.034 b1.0s3 I
(SD = 5.74%) (SD = 7.39%) (SD = 8.75%)
h = 0.1088 V”.4887 aI= 0.0852 i+J67 Pe = 18.011 Y0.‘ I s5
(SD = 5.07%) (SD = 9.8%) (SD = 7.4%)
Shorter
I
0.01
I
0
1
0.2
Fig.
2.
/
I
LIQUID VELOCITY, VL(10-2m.i’)
0.5
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1
--
Variation of total holdup with liquid velocity: (0) CRR, (0) MPR, (A) Shulman et al.
the liquid held up in the packed bed. A significant portion of this held up liquid may have been a part of the dynamic holdup before stoppage of flow. As against this in the present method only that part of the held up liquid which exchanges mass slowly with the dynamic holdup has been determined as the static holdup. The static holdup shows a clear increase with liquid velocity. At higher liquid velocities it attains a constant value. As liquid velocity increases more and more surface is covered by the flow of liquid due to increased radial liquid spreading. Correspondingly, the static holdup, which is also dependent upon the wetted surface, is found to increase with liquid velocity. As mentioned earlier in the present work the packings were not preflooded or prewetted. Thus, the static holdup was not a function of the history of the packing surface. In the method using preflooding (Schubert et al., 1986) all the packing is prewetted and therefore the effect of liquid velocity on static holdup is not noticed. Previous workers obtained a constant value for the static holdup while determining it by the draining or tracer method (Shulman et al., 1955; Bennett and Goodridge, 1970; Schubert et al., 1986). These investigators deduced h, by extrapolating the plot of h, vs 4 to V! = 0. Obviously h, vs y plot is unique for each packing and its intercept on the Y-axis has also a unique value. Therefore this method can not differentiate h, for different liquid velocities. Indeed the value obtained by the extrapolation procedure is h, at V, = 0 or under non-irrigated conditions. It is probably this lacuna which led these investigators to believe that h, is constant. In the case of the Pall rings also liquid pools can build at contact points of two packings. However, because of the slotted geometry of the Pall ring a larger number of these pools may interact with the dynamic liquid than in the case of the Raschig ring. Thus, the MPR exhibits a very low static holdup as defined by Bennett and Goodridge. holdup, h, Figure 5 shows the dynamic holdup data obtained for the packings investigated The data of Shulman et al. are also shown in Fig. 5. The h, values determined by the tracer method are again much higher (about 60%) than the values of Shulman et al. In both methods h, is determined from a knowledge of h, and h,: Dynamic
Fig.
3.
Variation
of holdup ratio with (Cl) MPR, (0) CRR.
liquid
velocity:
h,=h,-hh,.
(1)
As discussed earlier, h, and h, values obtained by the tracer method are higher and lower, respectively, than those obtained by the draining method. Consequently, h, values obtained from eq. (1) show considerable diflerence. Peclet number, Pe Figure 6 shows the variation of Pe with V,. The increasing trend of Pe with V, is similar to that observed by Bennett and
0012 0011 o-010 0009
0 08
0.008 0 007 0.006 OW5 0004
0.002 0
Fig.
4.
04
0.2 LMJn
VELoctlY,
v, m’m
6’ 1 -
Variation of static holdup with (A) Shulman et al., (0) CRR, (0)
liquid MPR.
velocity:
0
04 LtQUtD
tion of static holdup which is different in the two cases. The static holdup obtained by the draining method is simply all
Fig.
“EtoctTV”,:,~ld2~.i’)
-
5. Variation of dynamic holdup with liquid velocity: (0) CRR, (El) MPR, (A) Shulman et al.
762
Shorter Communications ition region data for pipe flow (Levenspiel, 1969) where the following approximate proportionality can be derived: Pe D a. Re’-‘.
(8)
The exponents on Re in eqs (7) and (8) are not significantly different. It can therefore be concluded that dispersion in packed beds is equivalent to that in pipe flow when the Peclet and Reynolds numbers are defined with respect to the dynamic liquid region. It is likely that eq. (7) may also hold for other random packings. This possibility, however, needs td be tested with more extensive data.
Fig. 6. Variation
of Peclet number with (El) MPR, (0) CRR.
liquid
velocity:
d
= 0.038 x 10’4.93” lo-‘L’)
A similar correlation Pe
d
(2)
was derived from the present data:
= 0.0185 x 10’2.15 x 10_4L’)
(3)
The Pe, values obtained in the present work are considerably higher than those of Dunn rr ~1. It should be noted that the model used by Dunn et al. neglected the static holdup and therefore the consequent slow exchange of the tracer material in h, with h,. This latter phenomenon causes an increase in the spread of the distribution. Dunn er al. included this additional spread in the dispersion in the dynamic region and therefore obtained lower Pe,. The values of Pe, obtained in this work are, however, in the same range as those of 0.065- and 0.095-m Raschig rings used by Bennett and Goodridge. The two packings used here have different geometries. Whereas the CRR is a closed packing, the MPR has a highly open geometry. The beds formed by these packings and the liquid flow in them is therefore expected to be considerably different. In the model used for our data analysis the dispersion is solely restricted to the dynamic region. Based on the treatment of dispersion in pipe tlow it was thought that dispersion in packed beds can also be similarly treated if a relevant Reynolds number, Re,, for the dynamic region is used: Re, A modified fined as
= d, ~‘,P,/P,
(9
where V, = Y/h,
(6)
and d, is the diameter of the dynamic liquid stream having a cross-sectional area A, = Q,/k’,. The above definition of Re, is expected to incorporate the effect of packing characteristics and the effect of bed geometry due to the inclusion of h, which is characteristic of the particular packing for a given K. Data for both the packings were subjected to regression analysis and the following correlation was obtained: PP,
= 2.195 x 10-6(Re,)‘.46 correlation
MPR:
kd,, kd,,
CRR: where
(SD = 15%).
can be compared
(7)
with the trans-
= 3.843 = 4.83
x lo-“‘Reg
699
x 10-8Re~.571
(SD = 3.7%)
(10)
(SD = 7.6%)
(11)
d., = 6(1 - ~),/a~, c: = dry-bed voidage, ap = geometric surface area of the packing (mZ/m3).
‘.Or------
region was de-
Pe, = V,d,/D,
The above
(9)
It was observed that k increases with V,. This behaviour can be explained by the fact that as liquid velocity increases the level of turbulence in the dynamic holdup increases and therefore the rate ofexchange of mass between the static and dynamic holdup increases. The k values obtained for the CRR are in the same range as those reported by Bennett and Goodridge (1970). It can be argued that k is decided jointly by the turbulence in the bed and the location of the static liquid regions. Both these factors are in turn governed by the packing shape and bed geometry. For instance, the CRR with its closed geometry and continuous surface can build liquid prisms, unlike the MPR. This difference has been discussed earlier. It is therefore unlikely that a single correlation on the same lines as that of Bennett and Goodridge can be obtained for the MPR and CRR. Indeed, all attempts at a single correlation satisfying both the MPR and CRR failed. This failure can be attributed to the reasons discussed above and implies that further characterisation of the static holdup locations and the local turbulence for different packings is needed. The presently available information is insufficient for this purpose. Therefore the following separate correlations for the MPR and CRR are proposed (Fig. 8):
(4)
Peclet number for the dynamic
coeficient, T, program yields values of the dimensionless coefficient, q, which can be converted into value, k, as follows: k = TJtd.
Goodridge. The present data for the CRR can be compared with the literature data of Dunn et al. (1977) who also used a step input to obtain axial dispersion characteristics of et al. correlated 0.025-m CRR and Berl saddles. Dunn Peclet number with the liquid mass velocity as follows: Pe
Liquid exchange The computer liquid exchange the dimensional
I
B
1/ 0
O-1
0 0, 100
0
1
1000
101 30
Reo -
Fig. 7. Variation
of Peclet number with Reynolds (0) CRR, (0) MPR.
number:
Shorter 0.02
.
O-01
-
k L L Pe
/
,~,,,,
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exchange coefficient between static and dynamic holdup, l/s length of the packed bed, m liquid flow rate, ib/h/ft2 Peclet number based on the length of the bed
CLV,lD,)
0,005
P%i
Peclet
number
based on the size of packing
Cd,b/D, )
Peclet number defined by eq. (5) volumetric liquid flow rate, m’/s liquid phase Reynolds number defined by eq. (4) liquid exchange coefficient between static and dynamic liquid holdups (kc,) time, s mean residence time of dynamic liquid phase, s liquid velocity in the dynamic holdup as defined by eq. (6), m/s superficial liquid velocity (Q,/A), m/s
0001
OJX05 0002 100 ;
,
r;ldoo
0
,
o-a03
-3
Fig. 8. Variation
of kd,,
with Re,:
( q ) CRR, (0)
MPR.
Greek letters a
ratio
of static
holdun
to
dvnamic
holdup
Wk,) PI P’r
Comparing the power index of Re, in the above equations it can be concluded that the mechanism of liquid exchange is similar in both cases. CONCLUSIONS (a) The data obtained by the present method indicate that the static holdup so determined is less than that obtained by the draining method. This observation is in agreement with the conclusions of Bennett and Goodridge (1970) and Schubert et al. (1986). (b) The static holdup is found to be a function ofthe liquid velocity below a certain liquid velocity unlike the findings of previous investigators. A rational explanation has been given in support of this observation. (c) The present work provides more meaningful holdup and dispersion data for larger packed columns using commercial sizes of packings, especially at low liquid flow rates. Acknowledgement-One of the authors (KBK) wishes to thank MS Kevin Enterprise, Bombay, for sponsoring him for the research work. K. B. KUSHALKAR V. G. PANGARKAR Department of Chemical Technology University of Bombay Matunya, Bombay 400019, India
AD % C CO c
‘Author
NOTATION cross-sectional area of dynamic stream, mz geometric area of packings, l/m concentration of tracer in the dynamic liquid phase, kmol/m3 initial concentration of the tracer in the dynamic liquid phase, kmol/m3 dimensionless concentration of the tracer in the dynamic liquid phase (C/C,,) liquid phase axial dispersion coefficient, r&/s nominal packing size, m equivalent diameter of packing as defined by eq. (1% m total, dynamic and static Liquid phase holdup, respectively
to whom correspondence
may be addressed.
density of the liquid, kg/m3 viscosity of the liquid, kg m/s
REFERENCES Bennett, A. and Goodridge, F., 1970, Hydrodynamics and mass transfer studies in packed absorption columns. Trans. Instn them. Engrs 48, T232. Carberry, J. J. and Bretton R. H., 1958, Axial dispersion of mass in flow through fixed beds. A.I.Ch.E. J. 4, 367. Dunn, W. E., Vermeulen, T., Wilke, C. R. and Word, T. T., 1977, Longitudinal dispersion in packed gas-absorption columns. Ind. Engng Chem. Fundam. 16, 116. Hoogendoorn, C. J. and Lips, J., 1965, Axial mixing of liquid in gas-liquid flow through packed beds. Can. J. chern. Engng 43, 125. Kan. K. M. and Greenfield, P. F., 1983, A residence-time model for trickle-flow reactors incorporating incomplete mixing in stagnant regions. A.I.Ch.E. J. 29, 123. Levenspiel, O., 1969, Chemical Reaction Engineering. Wiley Eastern, New Delhi. Patwardhan, V. S., 1978a, Effective interfacial area in packed beds for absorption with chemical reaction. Can. J. them. Engng 56, 56. Patwardhan, V. S., 1978b, Gas-liquid reactions in a packed bed: some implications of the extended crossflow model. Can. J. them. Engng 56, 558. Patwardhan, V. S., 1979, The effectiveness of static hold-up for absorption with a chemical reaction in a packed trickle bed: general order kinetics. Can. J. them. Engny 57, 582. Patwardhan, V. S., 1980, Gas-liquid reactions in packed beds: regimes of reaction in the static hold-up. Can. J. them. Engng 58, 454. Patwardhan, V. S., 1981, Gas-liquid reactions in packed beds: the effectiveness of static hold-up in presence of gas side resistance. Can. J. them. Engng 59, 483. Patwardhan, V. S. and Shrdtri, V. R., 1981, Mass transfer coefficient between the static and dynamic holdups in a packed column. Chem. Engng Commun. 10, 349. Sater, V. E. and Levenspiel, O., 1966, Two phase flow in packed beds. Ind. Engng Fundam. 5, 89. Schubert, C. N., Lindner, J. R. and Kelly, R. M., 1986, Experimental methods for measuring static liquid holdup in packed columns. A.I.Ch.E. J. 32, 1920. Shulman, H. L., Ullrich, C. F. and Wells, N., 1955, Performance of packed columns. 1: Total, static, and operating holdups. A.I.Ch.E. J. 1, 247. van Swaaij, W. P., Charpentier, J. C. and Villermaux, J., 1969, Residence time distribution in the liquid phase of trickle flow in packed columns. Chem. Engng Sci. 24.1083.