I n d . E n g . Chem. Res. 1995,34,2084-2093
2084
SEPARATIONS
Modeling of a Packed Column Contactor Abu Bakr S. H. Salem* Chemical Engineering Department, King Fahd University of Petroleum & Minerals, Dhahran 31261.Saudi Arabia
Mohammad S.H. Al-Fandery and Abdul Al Haq M. Abdul Al Latif Department of Chemical Engineering & Technology, College of Technological Studies, Kuwait
A 5.5 cm diameter and 125 cm long glass column, packed with 10 mm glass Raschig rings was used as a liquid-liquid contactor. The contactor performance was investigated by the system acetic acid-toluene-water a t 25 "C.The data obtained have been compared with previous works using mixer-settler contactors with the same test system. A new modeling approach is used to simulate extraction in packed columns. This approach is based on dividing the packing section into a number of strips simulating the stages in tray contactors. A nonequilibrium stage model is developed in which equilibration of the phases is not necessarily attained. Material balance relationships have to be only strictly observed. The model results are in excellent agreement with the experimental data. An extraction efficiency parameter similar to the vaporization efficiency developed by 'Holland is introduced. This parameter is given by the ratio of the actual composition of the extract to that of the raffinate phases obtained from the contactor divided by the equilibrium ratios. The extraction efficiency is in effect the fractional equilibrium achieved in a n actual situation. Using the nonequilibrium stage model may result in better simulation of the actual performance of the commercial contactors and in the design of this equipment.
Introduction Various types of liquid-liquid extraction contactors have been developed during the past few decades. The user is faced with a critical choice between contactors. Gourdon et al. (1991) proposed an objective criterion t o be used for comparison of two types of mechanically agitated extraction columns. These criteria are based on the local effects (transport, breakup) that the drops undergo and the effects determining the residence time, the interfacial area, and, therefore, the global efficiency of the contactor involved. A logical criterion for comparing different types of contactors may be obtained by using these contactors in performing a certain extraction duty. In such a case, the test system, the residence time, and the output raffinate stream specified for each contactor should be the same. The performance of each contactor can be evaluated by using a suitable model. Molstad et al. (1942,1943) adopted a similar approach in investigating the performance of drip-point grid packing compared with other types of packing. However, in this connection, many older liquid-liquid extractors are being reevaluated to take advantage of newer, more efficient contacting devices. This has created a need for more reliable flooding and mass transfer correlations for commercial scale columns, since previous correlations have been verified only with data from small diameter columns. Large commercial contactors are characterized by a low surface area to volume ratio. Under these conditions, the type of drop movement may deviate substantially from that occurring in smaller diameter laboratory columns. Accord-
* Author to whom correspondence
should be addressed.
ingly, significant differences in efficiency can arise, which might not be predicted by presently available mathematical models. The present work is aimed at developing a mathematical model to simulate the behavior of packed column extractors. The packing bed is divided into a number of elements of equal height. This number is assumed to be equivalent to the number of stages usually included in a tray column. Equilibrium conditions are not necessarily attained. An extraction efficiency parameter is proposed to account for the behavior of liquids used, the design of the stage, or the packing section and the prevailing operating conditions. In other words, the simulation technique is based on adopting a nonequilibrium stage model where partial equilibrium is only achieved. This is usually expected in commercial contactors. An experimental study using a packed column is presented. The model results obtained were in excellent agreement with the experimental findings. A comparison between the packed column contactor and mixersettlers is discussed.
Experimental Equipment A flow diagram for the extraction unit UOP 5 used in this investigation is shown in Figure 1. The equipment is mounted on a floor-standing welded steel frame fitted with adjustable feet. This unit includes an extraction column, a distillation unit for the solvent recovery, and a control panel. The extraction column consists of a Pyrex glass tube of 55 mm internal diameter, and 1250 mm height. The column is fitted with a top and bottom enlarged sections of glass bulbs of about 380 mm diameter. These bulbs serve as
0888-5885/95/2634-2084$09.0QlO 0 1995 American Chemical Society
Ind. Eng. Chem. Res., Vol. 34,No. 6, 1995 2085
12
4
I
$1
8
I
2
I
4
1:Extraction Column
2,3:Feed tank
: 8:
4
-8-
I
E x t r a c t Receiver
5 : Metering Pump
Raffinate Receiver
9,10, I I , 12
6:CentrifugaI Pump
7 : Solvent tank
13: Solenoid Valve
1 4 , l S : S w i t c h intheControl Panel.
: Flawmeters
Figure 1. Flow diagram of the extraction system.
receivers for the input streams and also for disengaging the raffinate and extract phases. The truncated sections of the bulbs are closed by stainless steel plates. The lower plate is bolted to the framework to support the column. The column proper and the two end plates are all fastened together with flanges. The joints between the sections of the column are sealed with molded PTFE gaskets. The column was filled with packing rings supported on a perforated stainless steel plate which is fitted between the bottom enlarged portion and the lower section of the column. This plate contains 20 holes of 7 mm diameter. A layer of 0.37L of 10 mm Raschig rings was placed on the top of a smaller layer of 0.1 L of 15 mm rings. The two layers form the packing bed in the column. Three stainless steel storage tanks for the liquids are mounted on the same framework. The light phase was allowed to flow from its supply tank by using a centrifugal pump through an air bleed valve, a flow control valve, and a flowmeter to an injector. The injector was mounted on the baseplate. The exit of the injector delivers the liquid at about 150 mm above the plate. This phase leaves the top of the column through a pipe and is collected in a polythene receiver tank. The heavy phase supply tank provides the feed through a diaphragm meter pump. The pumping rate of this type is varied by a stroke adjustment knob. A digital readout shows this rate as a percentage of the maximum flow. The pumped liquid enters the top of the column via an injector similar to that fitted at the base of the column for the light liquid. A cock for sampling and draining is fitted in the liquid feed line. The heavy liquid is withdrawn from the bottom of the column and returned t o a receiver vessel via a pipeline which is fitted with a solenoid valve and a sampling cock. The level of the light-heavy phase interface in the column is determined by the operation of a solenoid valve in the heavy phase outlet pipeline. The operation of this valve is controlled by two sets of water-sensing
electrodes; one is fitted to the top plate and the other is fitted to the bottom one. The system control panel is provided with a switch which selects the electrodes in use and hence determines whether the interface is at the top or the bottom of the column. Each set consists of three stainless steel electrodes. One bare earth electrode makes continuous contact with the light liquid. The two other electrodes are insulated up to 5 mm apart from their ends. These insulated electrodes are set to heights differing by 5 mm t o produce a liquid level differential of 5 mm. The purpose of this arrangement is to avoid frequent opening and closing of the solenoid valve which would occur with a simple single-electrode system. The electrical sensing system operates at a low ac voltage which provides a small value of the conduction current through the light liquid. The latter being translated into a solenoid-operating voltage by a plugin module behind the control panel. The distillation column boiler mounted behind the extraction column is fitted at such a height that liquid may be drained into it from the highest of the three tanks and can be drained from it into the lowest one. A valve controls the release of the solvent into the boiler. The boiler, pipework, valves, and fittings are constructed in stainless steel. Heating is provided by means of two 500 W cartridge elements inserted at the base of the boiler. The boiler temperature is indicated on a thermometer. The boiler lid is perforated for fitting the distillation column. The distillation column proper is made up of a glass section containing four sieve plates. The glass reflux divider is bolted to the column top and to a stainless steel condenser through flanges, and all the sections are sealed together with molded PTFE gaskets.
Experimental Procedure and Results The toluene-water system was used for the nonmass-transfer flooding and holdup studies.
2086 Ind. Eng. Chem. Res., Vol. 34, No. 6, 1995 Table 1. Solubility and Equilibrium Data of the System Water-Acetic Acid-Toluene at 25 OC (a) Solubility Data toluene-rich phase
water-rich phase
toluene, wt %
acetic acid, wt %
water, wt %
RI
water, wt %
acetic acid, wt %
toluene, wt %
RI
100 89.30 85.52 80.13 77.12 70.32 65.32 58.49 52.18 47.97 42.67"
0 10.63 14.39 19.72 22.70 29.25 33.90 40.71 44.98 47.84 51.85"
0 0.07 0.09 0.15 0.18 0.43 0.60 0.80 2.84 4.19 5.48"
1.4900 1.4837 1.4787 1.4728 1.4694 1.4612 1.4561 1.4483 1.4428 1.4401 1.4356
100 86.651 80.502 74.314 68.252 60.552 55.511 49.139 38.940 33.870 22.520
0 13.304 19.440 26.618 31.672 39.352 44.387 50.011 59.205 63.210 70.160
0 0.045 0.058 0.068 0.076 0.096 0.102 0.850 1.855 2.920 7.32
1.33 1.3436 1.3474 1.3512 1.3551 1.3602 1.3634 1.3671 1.3728 1.3752 1.3794
(b) Equilibrium Data water phase
a
toluene phase
RI
Y, %
RI
x, %
1.3472 1.3493 1.3516 1.3557 1.3585 1.3621 1.3664 1.3708 1.3772 1.3823 1.3827
19.50 22.54 26.36 32.36 36.56 41.69 47.86 54.33 63.52 70.54 71.07
1.4941 1.4936 1.4927 1.4918 1.4898 1.4886 1.4872 1.4848 1.4802 1.4792 1.4754
1.58 1.78 2.52 3.60 4.41 5.52 7.08 8.81 12.59 21.59 24.60
Plait point.
In the non-mass-transfer mode, the organic light phase feed was introduced and dispersed near the bottom of the extractor in the heavy continuous water phase. The light phase was collected at the top of the column to the raffinate receiver. The heavy continuous phase was fed near the top of the column. The operating interface was maintained at the top of the extractor by the solenoid valve. In the mass-transfer mode, acetic acid solute was blended with the organic toluene feed to give a feed mixture in the vicinity of 15.0 w t % solute. Water was used to extract the acid from toluene using different phase ratios and residence times. Toluene, 99 mol % pure, QZO = 0.866 kgL, and acetic acid, 99.75 mol % pure, QZO = 1.049 kg/L, were obtained from the Fisher Scientific Co. Distilled deionized water used was produced in the department. The solubility data for the system used were determined at 25 "C by the titration method which is described elsewhere (Salem, 1991). The equilibrium data were also determined at 25 "C. Equal amounts of water and toluene were stirred with a certain weight of solute for 2 h. The mixture was then allowed t o settle overnight in jacketed Smith-Bonner cells kept a t 25 "C. The phases were separated and the solute content in each phase was determined by refractometry using calibration graphs obtained from the solubility data. Compositions of the phases were determined by using an Abbe Mark 2 digital refractometer and the calibration graphs of the respective phases. The solubility and equilibrium tie lines data are given in Table 1. The distribution ratios for the system components are given in Table 2. Hydrodynamics The liquid holdup in a packed column is comprised of two major parts (Kan and Greenfield, 1983): the
Table 2. Distribution Ratios of the Components of the System Acetic Acid (1)-Toluene (2)-Water (3)at 25 "C acid concn in raffinate phase XI, wt % 0.500 0.700 0.980 1.250 2.300 2.700 3.800 5.600 7.300 8.500 10.200 11.500 12.590
distribution coeff
Ki 35.770 27.130 20.797 17.402 11.690 10.640 8.940 7.370 6.300 5.930 5.350 5.030 4.950
1 0 4 ~ ~ 5.056 5.209 5.417 5.670 6.459 6.838 7.567 8.253 9.125 10.234 11.341 12.129 13.215
K3 82.615 84.281 86.905 89.513 101.117 106.304 108.450 112.670 114.430 117.560 120.780 124.290 128.350
relatively fast moving or dynamic liquid holdup, hd, which accounts for the major solute transfer; and the relatively stagnant or static holdup, h,, which exchanges mass with the surrounding dynamic liquid phase through a convective-type diffusion process. The relative proportions of h d and h, are important to the designer in as much as they give the extent of effective liquid holdup for mass transfer. The liquid holdups in packed towers are generally measured by either the drainage method (Shulman et al., 1955) or by the tracer methods (Schubert et al., 1986). Kushalkar and Pangarkar (1990) reported that the static holdup determined by the tracer technique is less than that obtained by the drainage method. They also reported that each type of the liquid holdup increases with the increase of the superficial liquid velocity while the holdup ratio h&d decreases with the increase of that velocity. The total liquid holdup in this present work was measured by the drainage method (Bonnet, 1982). In this method the valves in the feed and exit lines were
Ind. Eng. Chem. Res., Vol. 34, No. 6, 1995 2087 Table 3. Holdup of the Solvent Phase (Water) in the Column ~ S C mass ,
no. 1 2 3 4 5 6 7 8
flow rate, kglmin F S
t,min
2.73 2.73 2.73 2.73 5.45 5.45 5.45 5.45
0.9140 0.7290 0.6440 0.4380 0.5398 0.4310 0.3806 0.2580
mass fraction
@SF,
0.3400 0.5480 0.6440 0.8760 0.2025 0.3240 0.3806 0.5170
0.8
-
0.27 0.43 0.50 0.67 0.27 0.43 0.50 0.67
no packing without with mass transfer mass transfer
SIF, kg/kg 0.375 0.750 1.000 2.000 0.375 0.750 1.000 2.000
0.270 0.310 0.350 0.370 0.680 0.700 0.710 0.740
fraction using packing without with mass transfer mass transfer
0.300 0.330 0.351 0.353 0.700 0.710 0.740 0.760
0.29 0.33 0.36 0.39 0.71 0.72 0.76 0.78
0.304 0.350 0.375 0.400 0.774 0.806 0.830 0.860
With packing X Wifhout pocking
0.7C
.-c X
-
0.6-
2
0.5-
L
ul
I 8 0.4-
0.3
-
0.27
I
I
rapidly and simultaneously closed. The phases were discharged, collected, and weighed. The fractional holdup of the dispersed phase (toluene) was measured after complete separation of the phases. The solvent (water) holdup was obtained by difference. The holdup measurements were conducted with and without mass transfer using different phase ratios and residence times. The results in case of using packing and without packing are shown in Table 3. Figure 2 shows the solvent phase holdup at different phase ratios and different residence times. Flooding in packed towers occurs when true countercurrent flow no longer exists. Examples of flooding situations include entrainment of drops by the continuous heavy phase. The dispersed light phase will be unable to penetrate packing, resulting in a buildup of light phase below the packing support, and phase inversion may occur (Seibert et al., 1990). None of these phenomena should be tolerated since they will eventually upset downstream processes. In this investigation phase inversion was observed just when flooding was about to start. Figure 3 shows the values of the superficial velocities of the two phases at flooding conditions. Discussion The holdup of the solvent phase in the column, ~ S C , and that in the feed, ~ S F are , shown in Table 3. The table includes the values obtained in case of mass transfer and without mass transfer, in the presence and
1
I
c
E
' 3 1
0 5 : 01
, 0 2
.
,
03
,
, 0 4
. ,
05
,
,
,
06
Superficial Velocllyof DiSc8rsed pnaae
,
07
,
1 08
cmh
Figure 3. Flooding of the packed column contactor.
absence of packing. Figure 2 shows the variation of 4sc compared to SF against the solvent to feed ratio at different residence times. This figure shows that at z = 2.73 min the change of dsc without packing assumes the same trend with a slight change from about 0.27 to 0.37 for a change of phase ratio from 0.375 to 2.0. In the same range of phase ratios, ~ S changes F from 0.27 to 0.67. This shows clearly that correlation between 4sc and SF is not a straightforward one. The figure also shows that when the residence time was doubled, the values of 4sc were also doubled but assuming the same trend of change. It can be seen also that the presence of packing has resulted in an increase about 5%in the holdup values of &c. The data in case of mass transfer will show the same trend as that
2088 Ind. Eng. Chem. Res., Vol. 34, No. 6, 1995 Table 4. Results of Extraction in the Packed Column input flow toluene, kgimin
water, kgimin
SIF, kgkg
5.45 5.45 5.45 5.45 2.73 2.73 2.73 2.73
0.457 0.653 0.322 0.218 0.914 0.729 0.644 0.438
0.1700 0.2750 0.3220 0.4375 0.3400 0.5480 0.6440 0.8760
0.375 0.750 1.000 2.000 0.375 0.750 1.000 2.000
5.45 5.45 5.45 5.45 2.73 2.73 2.73 2.73
0.5398 0.4310 0.3800 0.3500 1.0700 0.8480 0.7600 0.5160
0.2025 0.324 0.38 0.517 0.403 0.648 0.760 1.033
0.375 0.750 1.000 2.000 0.375 0.750
res time min
t,
1.000
2.000
mass fraction
XO,
outflow x , mass
fraction
(a) With Packing 0.15 0.019 0.15 0.016 0.007 0.15 0.15 0.005 0.15 0.040 0.15 0.032 0.15 0.025 0.023 0.15 (b) Without Packing 0.15 0.025 0.021 0.15 0.013 0.15 0.15 0.009 0.042 0.15 0.040 0.15 0.030 0.15 0.15 0.025
observed in Figure 2. Inspection of these data shows that the mass-transfer mechanism has resulted in about 10%increase in the holdup values of +sc. Comparison of +sc with +SF indicates whether or not the heavy solvent phase is accumulated in the column. If the value of ~ S is C approximately the same as that of +SF, it can be assumed that the column is in continuous smooth operation. Cases in which +sc is less than +SF indicate that the solvent is not allowed to have a proper residence time in the column. This can result in lower mass transfer rates. On the other hand, when 4sc is greater than +SF, the solvent will stay in the column for longer periods. This may have a relatively positive effect on the mass transfer rate. It may also delay supplying fresh solvent to the column resulting in solvent dead pockets, discrepancies in the hydrodynamics leading to lower efficiencies of extraction. Inspection of the data in Table 3 may highlight this discussion point. At t = 2.73 min, and phase ratio of 1, +SC values with or without packing are less than ~ S = C 0.5. At t = 5.45 min, the values of +sc at the same phase ratio are greater than +SF. This may indicate that operating the column at t = 4.5 min allows no accumulation in the column and hence better separation efficiency will be achieved. Figure 3 shows the flooding characteristics of the packed column contactor used. This figure shows that at low values of dispersed organic phase superficial velocity of about 0.15 c d s flooding of the column occurs at a continuous water phase velocity of about 1.2 c d s . On the other hand increasing the dispersed phase velocity to about 0.75 c d s allows flooding to take place at smaller rates of continuous phase of about 0.55 c d s. However, the flooding velocities are functions of the system physical properties, the design parameters of the column, and the porosity of the packed section. The values indicated by this figure determine the velocities which should not be exceeded for safe operation of the column without flooding. For example if the superficial velocity of the organic phase is around 0.4 c d s , flooding will not take place in this column if the water phase velocity is kept usually below 0.85 c d s . However, reference should be made here t o the works of Molstad et al. (1942,1943)on the loading and flooding characteristics of a packed absorber using different types of packing. There, the loading point was defined as that point at which the rate of change of pressure
c/o
PR, 9%
12.85 13.18 16.40 15.40 9.50 10.00 11.90 11.10
99.00 99.70 100.00 100.30 97.30 98.15 98.40 99.00
87 89 95 98 73 78 83 86
14.00 16.30 16.60 15.70 10.00 10.00 13.00 13.79
92.5 92.8 97.2 97.9 90.7 90.1 91.0 93.3
83 86 91 94 70 73 80 83
y, mass fraction
x * , mass
fraction
K
23.0 20.7 11.5 8.5 35.0 30.0 28.5 23.5
0.0179 0.0157 0.0070 0.0055 0.0370 0.0300 0.0240 0.0210
21 18 15 11 32 28 24 22
0.015 0.011 0.009 0.007 0.032 0.028 0.018 0.016
EMR,
drop with a change of gas velocity abruptly increases. The phenomenon of flooding occurs when the gas velocity is increased past the loading point until the liquid is seen to begin building up above the top of the packed space. These authors suggested that the loading point is more significant than the flooding point as a guide in the design of towers using the drip-point grid packing. Table 4 shows the results obtained when the column was used t o extract acetic acid from toluene by using water as a solvent at ambient temperature. Part a of the table shows the data obtained when the column was packed; part b shows the data obtained in absence of packing. Two values of residence times, z, were used in each case as shown in that table. Four different phase ratios, SIF,starting from 0.375 to 2.0 were used with a fured value of t. The corresponding flow rates for the two phases are shown in the table. The feed concentration was kept constant at 0.15 w/w. The mass fraction of the raffinate and extract streams are included. The value of the raffinate stream concentration at equilibrium with the outlet extract stream, x * , and the equilibrium ratios of the acid are also given in the same table. From these values, the Murphree efficiency of the raffinate stream can be estimated assuming that the packed bed can be considered as a single theoretical stage. Hence,
Table 4 shows that the efficiency of the unpacked column at z = 2.73 min has a maximum value of 93.3% at a phase ratio of 2. Packing increased this value to 99%. At t = 5.45 min the efficiency has increased by packing the column from 97.9 t o about 100%. Hence it can be assumed that the packed section height of 125 cm is equivalent to one theoretical stage. The percentage recovery, PR, calculated as PR=-
xo - x
x
100
XO
is also included in Table 4. The table shows that the increase in recovery due to packing is only about 8%at t = 5.45 min. This relatively small increase in the recovery reveals that the presence of packing has little
Ind. Eng. Chem. Res., Vol. 34, No. 6, 1995 2089 100 a With pocking
x
without pocking
B u
0,
+
I
I
0.0
1
I
0.50
I
I
I
I
1.50
1.00 Phase Ratio
2.00
W F1
Figure 4. Percentage recovery vs phase ratio ( S I F ) at different residence times.
effect on the mass transfer rate since the system used has a high distribution ratio and large interfacial tension. Figure 4 shows the relation between the percentage recovery and phase ratio. The figure indicates that appreciable increase in the percentage recovery of about 30% can be obtained by using packing and doubling the residence times. Treybal(1973) suggested using the following formula to calculate the overall number of transfer units in a packed column contactor based on raffinate phase concentrations.
Symbol
x @
NTU
HT U
1-0
1-0
273
N
2-0
2-b
273
V
3-0
3-b 4-b
545 5 45
N
4'0
'imin
Pocking
Y
1
I
700
NTU =
where xo is the initial feed concentration and XO* is the raffinate phase concentration at equilibrium with the outlet extract phase. K is the slope of the equilibrium line in the very dilute solution. R is the total flow rate of the raffinate phase leaving the column, and S is the total flow rate of the solvent entering the column. Equation 3 was used to calculate the NTU using the values in Table 3. The data obtained are shown in Figure 5 plotted vs the phase ratios used. Curves l-a and 2-a are obtained at t = 2.73 min while curves 3-a and 4-a are those a t z = 5.45 min. The maximum value of NTU obtained was about 3.5 at S I F = 2 for the packed tower when t was 5.45 min. In a perfectly mixed tray, the point efficiency would be equal to the Murphree efficiency of the tray. In this case, the Murphree efficiency can be estimated using the overall number of transfer units, NTU. According to Holland (19751, Dribika and Biddulph (1987), and Koziol and Mackowiak (1992) the Murphree efficiency, EMis given by E M
= 1 - exp(-NTU)
(4)
For a value of NTU = 3.5, EMR will be 0.97, which can be considered to be in good agreement with the values given in Table 4 with a certain error tolerance. The height of transfer unit, HTU, was calculated by dividing the height of the packed section by the NTU.
15
05
Pnore Ratio 1S/FI
Figure 5. Number of transfer units and height of transfer units vs phase ratio.
The values obtained are shown in Figure 5 on curves l-b through 4-b. The minimum HTU obtained was about 340 mm at a phase ratio of 2 for the tower operating at t = 5.45 min. It can be said that four transfer units are required for such separation. Each unit has about 300 mm packing height if 10 mm Raschig rings are used.
Comparison with Mixer-Settlers Mixer-settler contactors are usually preferred in most cases t o packed towers due to their high throughputs and higher extraction efficiency obtained. A comparison between the performance and design parameters of the packed column contactor used in this present investigation with two previously published works (Salem, 1991, 1993) in which a single-stage mixer-settler was used is given in Table 5. The same
2090 Ind. Eng. Chem. Res., Vol. 34, No. 6, 1995 Table 5. Comparison between the Packed Column Contactor and Single-Stage Mixer-Settlers Using the Same System single-stage mixer-settler mixer capacity settler capacity total stage capacity 5
phase ratio, S I F feed concentration EMR
Salem (1991)
Salem (1993)
packed column contactor present work
two cylindrical sections each of 5.5 cm diam, 12.0 cm height 0.55 L vertical tube 0.36 L 0.85 L 3-6 min 0.375-2.3 0.15 wlw 0.99 at 2000 rpm
cylindrical vessel of 5.5 cm diam, 18 cm height 0.31 L same 0.395 L 0.705 L 4.67 min 0.5-3.5 0.15 wlw 1.00 at 1200 rpm
column of 5.5 cm diam, 125 cm packed section, 0.47 L packing vol, 3.72 L operating capacity with packing, 4.40 L without packing, bed vol 1.85 L, void vol 1.38 L, void fraction 0.75
test system acetic acid-toluene-water was used in these studies. The performance in the published studies shows that the mixer-settler in both cases acted as an ideal stage. According t o the analysis shown in Table 4,the packed column in the case of using a phase ratio of 2 at 5.45 min residence time can be also considered as an ideal stage. In this case, 125 cm packing height is equivalent to a theoretical stage if 10 mm glass Raschig ring packing is used. However, t o pursue the analysis, another modeling approach is tried using the concept of an actual stage.
A Mathematical Model Approach Holland (1975, 1981) proposed that the packing bed in a packed column used for distillation or absorption can be divided into N sections or elements numbered down from the top or vice versa. If equilibrium conditions are attained in these sections, then N is said to be equivalent to the number of theoretical plates, NTP, in a column containing plates. The height of each packing section is, therefore, equivalent to that of a theoretical plate, HETP (Rubac, 1968). In actual operation, stages rarely, if ever, operate at equilibrium despite attempts to approach this condition by proper design of the stage and choice of the operating conditions. The usual way of dealing with departures from equilibrium is by incorporating stage eficiency into the equilibrium relations. Krishnamurthy and Taylor (1985) indicated that it is with the introduction of this stage efficiency parameter that the problems begin. The first problem is that there are several different definitions of stage efficiency: Murphree (19251, Hausen (19531, generalized Hausen (Standart, 19651, vaporization (Holland, 19811, and others. There is by no means a consensus on which definition is best. The Murphree efficiency, although the least soundly based, is the one most widely used because it is easily combined with the equilibrium equation. In a c component system there are c - 1independent component efficiencies, which for lack of anything better have usually been taken t o be the same for all components (King, 1980). Toor (1964) stated that the efficiencies of the different components are rarely equal simply because of their varying behavior in the mass-transfer mechanisms. This results due to coupling between the individual concentration gradients, interaction effects, reverse diffusion, and osmotic diffusion phenomena. A n interesting consequence of such effects is that the individual point efficiencies of different species are not constrained to lie between 0 and 1. Instead they may be found any where in the range from --m to +-m. Horvath (1985) and Salem and Sheirah (1990) reported experimental extraction stage efficiency to reach 1.3 in some cases and 1.7 in others.
flow rate 0.627-1.55 kglmin 2.73-5.45 min 0.375-2.0 0.15 wlw 1.00 with 125 cm HETP
In the present work, a nonequilibrium stage model is developed which will rely only on material balances and summation equations. Equilibrium relations are assumed to be not applicable. However, other functional relations between the yi and xi will be deduced as for example
where mi,n is the functional relation between the composition of i in the two phases. If equilibrium is attained, mi,,,= Ki+,otherwise it is only a fraction of it. In this sense, it is possible t o assume an extraction efficiency, similar t o the absorption efficiency proposed by Edmister (1949) and the vaporization efficiency proposed by Holland (19811, which can be calculated from
The parameter &,n embodies the effects of stage design variables, the operating variables, and the system variables. In actual packed towers, the number of packing sections, N , is that equivalent to the number of actual stages, NAS. The height of the packing section is the height equivalent to an actual stage, HEAS. The algorithm which is used in this model assumes that the number of actual stages is known.
Simulation of a Packed Column Extraction Using a Nonequilibrium Stage Model A sketch of a typical packed column contactor is shown in Figure 6. The packed bed is divided into N sections from bottom to top. The notation employed in the description of this column corresponds to that used in the treatment of columns with plates. The bottom element of packing is assigned the number 1, and the top element is given the number N . n represents any element of packing of a height, HEAS. The feed mixture containing the solute is introduced below the bottom section if it is the light phase. The heavy solvent phase is introduced from the top of the tower and flows countercurrently to the light phase. The flow rate and composition of these two streams are represented by Fo, xi,o, L N + ~and , yi~v+l,respectively. The corresponding outlet raffinate and extract phase flow rates and concentrations are represented by FN, xi&, L I , and yi,1, respectively. The raffinate phase is collected from the top while the extract phase is discharged from the bottom of the contactor. f i , ~f ,i ~ v ,l i ~ v + land l i , ~are the flow rates of component i in the corresponding streams. Usually in liquid extraction design problems the values of Fo, xi,^, L N + ~and , yi&+l, are given and the
Ind. Eng. Chem. Res., Vol. 34, No. 6, 1995 2091 (Treybal, 1986).
From eq 11the values ofL, up to LN cail be estimated. Then an overall material balance on the column gives
N
LN+1+
Fo = L 1 +
FN
(12)
This equation can be rearranged and written as
.1
I Fn
Ln+1
LN+,
H.E.A.S
- F N = L1 - Fo= A
(13)
Another equation representing an overall material balance on the tower section between stage n and the top stage N can be written as
n
7-
Fn
+ L N +=~FN + L n + 1
(14)
Rearranging eq 14 using eq 13 gives the value of the flow rate, F,, from any stage n as follows:
F, = Lnil
I
f
F o , f i , o , Xi,o
Lt,li,l, Yi,l
-
recoveries or the final raffinate compositions for a certain component are specified. It is required to find the number of stages and the raffinate and extract flow rates and compositions of each stage. Since liquid-liquid extraction equipment is operated frequently in an adiabatic manner, the isothermal sum rates (ISR) method developed by Tsuboka and Kateayama (1976) can be applied. This method essentially assumes values for N , determines the exit raffinate composition, xi&, and compares it with the specified composition until convergence. In the present approach, N is initially assumed and L1 can be roughly estimated assuming that the two solvents are immiscible, hence FN can be estimated from
- xi'o O 1 -xip
A
(15)
The value of F N obtained from eq 15 is to be compared with that estimated from eq 7. If the two values for F N do not agree in a certain tolerance, the new value obtained from eq 15 has to be used in another round of calculation until convergence is achieved. The flow rates li,n of the components of the extract stream can be calculated by an equation similar to eq 11 as follows:
Figure 6. Diagram of a packed extraction column.
FN=F-
-
i = solute under consideration (7)
The values of yi,,, the compositions of these streams can be calculated using Yi,n = li,nlLn
(17)
However, it can be checked that
The flow rates fi,, and compositionsxi,, of the raffinate streams can be calculated by applying a component balance on each stage n, where fi,n =
+ li,n+l - li,n
(19)
Then a component balance on the tower gives C
Ll Yi,l
=L N f l
Yi,N+1
+ Fdci,O - FN%,N
(8)
Equation 8 can be also written in terms of components flow rates as follows:
1.1 , l = 1.l,NNfl+ fi,o - f i &
(9)
The total stream flow rate, L1, and its composition,y i , l can be estimated from
The other stream flow rates from any stage n, L,, can be estimated using the Edmister group relationship
(20) The values of xi& obtained from eq 20 are to be compared with the assumed specifications of the outlet raffinate stream. If these specifications are not met, a new value of N has to be assumed. The calculation is repeated until this condition is satisfied within a specified convergence limit. Once the value of N is fixed, through which the values of L,, F,, yi,,, and xi,, are determined, the values of mi,, and the extraction efficiency EL,, can be estimated. (21)
2092 Ind. Eng. Chem. Res., Vol. 34, No. 6, 1995
Table 6. Simulation Results for the System Acetic Acid (1)-Toluene (2)-Water (3) n i 1 Y f X m 0
1
2 3
3
1 2 3
0.015615 0.00017 0.437325 0.45311
0.06770 0.00028 0.93202 1.00000 0.05120 0.00032 0.94846 1.00000 0.03446 0.00038 0.96516 1.00000
4
1 2 3
5
1 2 3
0.007737 0.000190 0.437303 0.44523 0.00000 0.00022 0.43728 0.43750
0.01740 0.00040 0.98220 1.00000 0.0000 0.0005 0.9995 1.0000
1
2
1 2 3 1
2 3
0.03177 0.00013 0.43737 0.46927 0.023616 0.000149 0.437347 0.461112
0.032700 0.185191 0.000109 0.218000 0.024546 0.185210 0.000086 0.209842 0.016540 0.185231 0.000064 0.201840 0.008667 0.185251 0.000420 0.193960 0.00093 0.18528 0.00019 0.18623
It is also possible t o estimate the Murphree stage efficiency for the raffinate phase, EMR.
The stage recovery of each component can be estimated as follows:
This nonequilibrium stage model has been used to simulate the extraction of acetic acid from toluene using water solvent in the packed column used in this study. The flow rates and compositions of the inlet streams are Fo = 0.218 kglmin and L N +=~ 0.4375 kglmin, i = 1 = acid, i = 2 = toluene, i = 3 = water. q o = 0.15, XZ,O = 0.8495, and X3,O = 0.0005 mass fractions. y1,”+1 = 0.0, ypail = 0.0005, and y 3 , ~ + 1 =0.9995 mass fractions. The raffinate output stream compositions are those obtained actually using a packed column operating at z = 5.45 min and solvent t o feed ratio of 2 to 1. The specified value was 3 ~ 1=, ~0.005. The equilibrium ratios for the system components, Ki,are obtained from the experimental data shown in Table 2. Initially the number of packing sections assumed was N = 3. This gave x l , = ~ 0.0096, which did not match the experimental results. The calculation was repeated using N = 4. Two rounds of calculations were needed t o get to the specifications required. The final results are given in Table 6. The table shows the values of stream flow rates Zi,n and fi,,, the functional and their concentrations yi,,, and relationships mi+,the extraction efficiencies &,n, and the Murphree efficiency for the raffinate EMRfor each component in each section. Values for &,n greater than 1 are obtained especially for the water component while negative values of EMRare also shown. However, for the acid component 1, which is the solute under consideration, it can be seen that EMRhas assumed the values around 24.0, 32.0, 48.0, and 90% for the four
0.1500 0.8495 0.0005 1.0000 0.1170 0.8826 0.0004 1.0000 0.0820 0.9177 0.0003 1.0000 0.04460 0.95518 0.00022 1.00000 0.0050 0.9949 0.0001 1.0000
6
EMR
0.5786 3.17 10-4 2.33 103
0.1155 0.2641 18.7900
0.242 -0.054 -0.014
0.6244 3.49 10-4 3.16 103
0.1037 0.3558 27.008
0.3227 -0.0643 -0.013
0.7726 3.98 10-4 4.39 103
0.09840 0.42277 39.90900
0.4814 -0.0858 -0.01
3.48 4.02 x 10-4 9.82 x 103
0.0973 0.7950 118.864
0.8977 -0.2561 -0.01
stages (or sections) from the feed entrance at the bottom to the solvent entrance at the top. This present model shows that it is possible to develop the extraction efficiency from operational data. Once a data bank is available for this parameter, it will be possible to correlate it for possible use in the design of new contactors. In fact, no attempt was made to fit the extraction efficiency using the operating parameters due to the complexity of some of them and also the lack of simple quantification of others. The number of sections, four, is also limited, which does not allow for a sound correlation. However, reference can be made to the works of Molstad et al. (1942, 1943) in this context.
Conclusion
A packed column was used for removing acetic acid from toluene by water solvent. A 125 cm packed bed using 10 mm glass Raschig rings was successful in obtaining 98% acid recovery. Data analysis using equilibrium stage model proved that this contactor is almost identical t o an ideal stage. Comparison with data obtained from single-stage mixer-settlers tested with the same system at approximately the same residence times shows full agreement between the performances obtained. Analysis of the packed column with the conventional number of transfer units indicated that four of such units each of about 300 mm HTU are required for this particular extraction duty. A new modeling approach based on the nonequilibrium stage model is used also for the analysis of the data obtained in this study. Four actual stages or packed sections each of 300 mm height are obtained using this simulation model. The Murphree efficiencies of these stages are low at the feed-entering sections and become larger as the raffinate phase flows to the outlet top section. The new modeling approach allows analysis of actual existing equipment without the assumption of a hypothetical stage efficiency which may produce biased information. The nonequilibrium stage model, on the other hand, produces the actual flow rates and composition profiles through the tower based only on the
Ind. Eng. Chem. Res., Vol. 34, No. 6, 1995 2093 material balance considerations. The efficiencies can then be estimated based on the actual performance. For testing commercial scale equipment, this model requires a set of fitted efficiencies which can be obtained from operational data. The extraction efficiency can be used to provide a correlating parameter for nonequilibrium stages. However, no attempts have been made to correlate it from the data obtained in this work since the number of experimental points is not sufficient to produce a sound correlation.
Nomenclature EMR= Murphree efficiency of the raffinate phase, fractional F = feed flow rate, kglmin
fi
= flow rate of a component i in the feed phase, kglmin FR, = fractional recovery of component i HEAS = height equivalent to an actual stage HETP = height equivalent to a theoretical plate HTU = height of a transfer unit hd = dynamic holdup h, = static holdup i = component L = solvent phase flow rate, kglmin I, = flow rate of a component i in the solvent phase, kgl min K, = distribution ratio of component i at equilibrium m, = functional relation between the actual values of y, and x, N = number of stages or sections n = stage or section number NAS = number of actual stages NTU = number of transfer units R = raffinate phase flow rate leaving the column, kglmin RI = refractive index S = solvent phase flow rate entering the column, kglmin x = feed or raffinate phase composition, mass fraction y = solvent or extract phase composition, mass fraction C = sum
Greek Letters = density at 20 "C,kgL = holdup of the solvent in the column, mass fraction @SF = holdup of the solvent in the feed, mass fraction [(SI e20
@SC
F) + SI, k@g A = constant defined by eq 13 t
E
= residence time, min = extraction efficiency defined by eq 6
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Received for review November 21, 1994 Revised manuscript received February 27, 1995 Accepted March 15, 1995@ IE9406916 @
Abstract published in Advance A C S Abstracts, May 1,
1995.
