A Capacitance Probe and a New Model To Identify ... - ACS Publications

Jan 27, 2001 - A new probe based on the measurement of the electrical capacitance has been developed to measure liquid holdup in columns equipped with...
0 downloads 0 Views 127KB Size
Download PDF
Ind. Eng. Chem. Res. 2001, 40, 1205-1212

1205

A Capacitance Probe and a New Model To Identify and Predict the Capacity of Columns Equipped with Structured Packings Elisabetta Brunazzi, Alessandro Paglianti,* and Sandro Pintus Department of Chemical Engineering, Industrial Chemistry and Materials Science, University of Pisa, I-56126 Pisa, Italy

A new probe based on the measurement of the electrical capacitance has been developed to measure liquid holdup in columns equipped with structured packings. The main advantages of this new probe are that it is nonintrusive, it allows fast and online measurements, and it can be used for laboratory-scale columns as well as for industrial applications. The probe is designed to measure local liquid holdup and it can therefore be used to evaluate the presence of the liquid hold-up gradient inside each packing element in the column. Evaluation of the liquid hold-up gradient is helpful to identify locations inside the packing element where flooding begins and to suggest packing design modifications. The relation between electrical capacitance and liquid holdup closely follows the predictions obtained using simple electrical models. The experimental results obtained with the probe have enabled a simplified model to be tuned to predict capacity limits of columns equipped with structured packings. 1. Introduction Liquid holdup is the key parameter for the proper description of the behavior of packed columns working in steady state and batch conditions. As pointed out by several authors (Brunazzi et al.,1 Nardini et al.,2 and Engel et al.3), the knowledge of liquid holdup allows the fluid dynamics and the mass-transfer performances to be described and therefore allows the prediction of pressure drop, capacity, and separation capacity of a packing to be made. Notwithstanding the importance of liquid holdup, the experimental data available are only related to the average liquid holdup inside the column and, to our knowledge, no experimental data are available in the open literature on local liquid holdup inside a column. This is probably due to the lack of probes that permit simple and accurate measurements to be made of local liquid holdup inside a column. Many different techniques have been proposed for the measurement of liquid holdup in columns equipped with structured packings. These techniques can be classified into three main categories according to the physical effects they use: (1) radiometric measurements, (2) volumetric measurements, and (3) electrical impedance measurements. The radiatiometric technique is extensively used to measure the void fraction in two-phase flow transport pipelines and in fluidized beds. It is based on the increase of γ-ray absorption when there is a void fraction decrease in the test section. Suess and Spiegel4 have used this technique with good results to measure liquid holdup in columns equipped with structured packings. Difficulties arising using this technique are that the measurement can be uncertain because of the natural statistical fluctuation of photons; the measurement can be affected by void distribution on the test section, and it cannot be used in industrial columns because of the safety implications associated with the use of radiation. Volumetric measurements are taken of the amount of liquid drained from the packing after the liquid flow rate * Author to whom correspondence should be addressed. Fax: +39-050-511266.Phone: +39-050-511225.E-mail: paglianti@ ing.unipi.it.

has been stopped. This has been used by McNulty and Hsieh,5 Billet and Mackowiak,6 Brunazzi et al.,1 and Nardini et al.,2 among others. This approach is simple and economic and can be used in laboratory-scale experiments. On the other hand, this technique requires the liquid load to be stopped, and therefore it cannot be used in industrial applications. Moreover, the only measurements achievable with this approach are related to the average liquid holdup in the columns. In fact, the presence of liquid hold-up gradients cannot be measured with this technique. Finally, the electrical impedance method is extensively used for the measurement of liquid holdup in two-phase gas-liquid systems. Details on this technique can be found in work by Hewitt.7 More precisely, either capacitance or conductance is determined, depending on the working fluids present. The main problem of this method is the calibration of the probe. In fact, as pointed out by Andreussi et al.,8 these types of probes are extremely sensitive to a change of flow pattern and probe geometry, so that different calibration curves are necessary if different flow patterns are present in the test section. The impedance method can be used both to predict the local void fraction in stirred tank reactors (Takenaka and Takahashi9) and in transport pipelines (Andreussi et al.10) and to measure the mean liquid holdup across the test section in transport pipelines (Andreussi et al.8). In the field of structured packings, this technique has been used by Engel et al.3 to measure the liquid holdup as an average across a packing element. In the present work, a probe based on this technique has been developed and some measurements of the local liquid holdup in a column equipped with a structured packing will be presented. These measurements show that large liquid hold-up gradients build up inside the packing when the column works close to the loading point. When the loading point is approached, the liquid holdup at the edge between two successive packing elements is much larger than the average liquid holdup of the column. Reducing this stagnation of liquid, which is probably caused by the concentrated pressure drop (Brunazzi and Paglianti11) in the zone between two

10.1021/ie000546u CCC: $20.00 © 2001 American Chemical Society Published on Web 01/27/2001

1206

Ind. Eng. Chem. Res., Vol. 40, No. 4, 2001

Figure 1. Schematic diagram of the experimental loop.

Figure 2. Schematic drawing of the impedance probe. Measures are in millimeters.

successive packing elements, could enable the column capacity to be increased (Moser and Kessler12). 2. Experiments 2.1. Experimental Apparatus. Figure 1 shows a schematic drawing of the pilot-scale column designed and built for the experimental characterization of the hydraulic packing performance. The test rig is situated at the Department of Chemical Engineering, Industrial Chemistry and Materials Science, University of Pisa, Pisa, Italy. The column is 6700 mm high and has an inner diameter of 400 mm. It is equipped with Mellapak 250 Y elements made from polypropylene, arranged to give packing with an overall height of 3150 mm. A centrifugal pump circulates the liquid to the top of the column, with specific liquid loads of up to 40 m3/h/m2. Air at room conditions is driven by a fan, which permits flow rates of up to 2500 Nm3/h to be reached. The gas flow rate is measured with an orifice meter and adjusted by acting on the inverter of the fan motor. The pressure drop across the packing is measured both by a differential pressure transmitter and by a U-tube-type manometer. Figure 2 shows a schematic drawing of the packing element containing the probes developed and used in these experiments. The figure shows that two similar probes have been used in this work, one located in the middle of a packing element and the other positioned on the bottom. This type of capacitance probe is very

simple and nonintrusive; it is composed of aluminum electrodes fixed with acrylic glue onto successive corrugated layers. The probe was only tested with water solutions and air, but it could also be used with different working fluids by simply changing the material of the electrodes. The probe can be used in both laboratoryscale and industrial-scale columns if plastic packings are used. Nevertheless, it is important to point out that the experimental results, which allow the complex fluid dynamics phenomena responsible for flooding to be understood, can also be used to tune mechanistic models developed to predict the capacity of columns equipped with both plastic and metal packings. The probe functions by measuring the capacitance of the medium between the two electrodes, and through the use of a simple electric model, it will be shown that the local liquid holdup can be evaluated. This probe presents interesting possibilities because it permits the local liquid holdup to be measured, it is extremely cheap, it can be used in large-scale equipment, it does not need complex calibration, and it does not present any safety problems. The value of this probe stands out when it is compared to the only other technique that so far permits the same measurements to be made; the γ densitometer. This other instrument is expensive, it cannot be used in industrial plants because of safety problems associated with the use of radiation, and it requires complex calibration procedures. A Boonton Electronics capacimeter model 72BD was used to measure the capacitance. The capacimeter and the differential pressure transmitter readings are stored simultaneously on a data acquisition system developed with LabView software. Liquid holdup was evaluated using both the present capacitance probe and a common volumetric technique. Particular care was used to ensure that steady state was reached before each measurement. When volumetric measurements were made, the liquid feed line was shut off rapidly using gate valves, and the liquid drained from the packing was collected and measured. 2.2. Experimental Data. The probe used in this work allows capacitance to be measured across a single channel formed by two adjacent corrugated sheets. The measured capacitance is then used to derive the dielectric value of the capacitor, which is in turn related to the amount of liquid phase. The capacitance-type probe is highly sensitive to a change in the flow pattern. This was pointed out by Andreussi et al.8 using capacitance probes for transport pipelines and by Engel et al.3 using capacitance probes for packed columns. Therefore, the equivalent electric circuit has to be identified to enable the liquid holdup to be evaluated from the dielectric value of the capacitor. The dielectric consists of three phases: the packing material and the liquid and gas phases. Using the simple case of a plate capacitor, these phases can be schematically arranged to give the equivalent electric circuits shown in Figure 3. The capacitance is proportional to the permittivity, /. The permittivity can be evaluated by considering the liquid holdup in the channel and the permittivities of the three phases. For the case in Figure 3A, the permittivity can be evaluated as

/ )

1 1-e e + PP G

(

)

(1)

Ind. Eng. Chem. Res., Vol. 40, No. 4, 2001 1207

Figure 5. Dimensionless capacitance vs liquid holdup. Comparison between experimental data and the two equivalent electrical models labeled as B and C in Figure 3 (static measurements; airwater system). Figure 3. Equivalent electric circuits.

Figure 4. Schematic diagram of the setup for the static measurements.

where e is the packing void fraction. For the case in Figure 3B, the permittivity can be computed as

1 e(1 HL,m) eHL,m 1-e + + PP G L

(

/ )

)

(2)

where HL,m is the channel liquid holdup, whereas for the case in Figure 3C

/ )

1 1-e e + PP (1 - HL,m)G + HL,mL

(

)

(3)

A more complicated relation is needed for the case in Figure 3D; more details can be found in works by Maxwell13 or Bruggeman.14 3. Results and Discussion 3.1. Static Measurements. The key idea of the present work is that the previously described probe follows the theoretical behavior of a capacitor formed from parallel plates. The calibration of the probes was performed by taking both static and dynamic measurements. The static measurements were performed on a bench, with the corrugated sheets of the packing and the probe placed horizontally. The packing was gradually filled with measured quantities of liquid (see Figure 4). These measurements are referred to as static, because the liquid is not flowing across the surface of the packing. The experimental results are plotted in Figure 5, and they show that the experimental behavior of the probe can be predicted in this case by using the equivalent electric circuit shown in Figure 3B.

Figure 6. Dimensionless capacitance vs liquid holdup. Comparison between experimental data and the two equivalent electrical models labeled as B and C in Figure 3 (dynamic measurements; air-water system).

The results shown in Figure 5 are of interest because they indicate that it is possible to use a simple electric equivalent circuit to interpret the experimental behavior of the probe suggested in the present work. Nevertheless, it is important to point out that a dynamic calibration is also required. The dynamic calibration is necessary to investigate and interpret the experimental behavior of the probe when it is installed inside a column operated under common working conditions. In this case, the liquid moves across the packing surface, mainly flowing as a film or in discrete rivulets. 3.2. Dynamic Measurements without Gas Load. Figure 6 shows a comparison between dynamic liquid holdup, evaluated using volumetric measurements, and dimensionless capacitance, C*, evaluated using the two probes suggested in this work (see Figure 2). The dimensionless capacitance was evaluated as

C/ )

C - Cstatic Cliquid - Cstatic

(4)

where Cstatic is the capacitance measured after liquid collection has been performed when only static holdup is present in the column and Cliquid is the capacitance of the probe when it is fully filled with the liquid phase. The experimental results shown in Figure 6 were obtained using water as the working liquid and without a gas load. Figure 6 shows that at a fixed liquid load the two probes give about the same experimental values

1208

Ind. Eng. Chem. Res., Vol. 40, No. 4, 2001

Figure 7. Dimensionless capacitance vs liquid holdup. Comparison between experimental data and the two equivalent electrical models labeled as B and C in Figure 3 (dynamic measurements; air-low surface tension mixture system).

of dimensionless capacitance. This simple observation allows us to assume that no significant liquid gradient is present when a column works in the absence of a gas load. Another important result can be obtained if the experimental results are compared with the theoretical ones derived using the equivalent electric circuits shown in Figure 3B,C. The results obtained from the static measurements showed that the liquid holdup can be evaluated by measuring the capacitance and using the equivalent electric circuit labeled as part B in Figure 3. The dynamic measurements show, however, that the liquid holdup can be evaluated by measuring the capacitance of the dielectric and using the equivalent electric circuit labeled as part C in Figure 3. This change in the configuration of the dielectric can be explained as the result of the behavior of the liquid and the different way the packing is wetted in the two types of measurements. In fact, the liquid position in static measurements is similar to a stratified flow between two electrodes, with one electrode partially wetted and the other completely dry (see Figure 4), and can therefore be described using the electrical circuit labeled in Figure 3B. Whereas the liquid arrangement in dynamic measurements is like rivulets wetting both of the electrodes, therefore the type of electric circuit that most closely reflects this real behavior is the circuit in Figure 3C. This result was confirmed using a working liquid with physical properties different from those of water. Figure 7 shows a comparison between the experimental results obtained with water and those obtained with a special liquid mixture used as working fluids. The special mixture has the following physical properties: FL ) 1000 kg/m3, µL ) 1.2 cP, and σ ) 0.030 N/m. Therefore, it can be used to evaluate the effect of a change of the surface tension. Figures 6 and 7 show that only one calibration curve has to be introduced to evaluate liquid holdup from the measurements of capacitance, independent of the surface tension of the working liquid; in fact, the mean square errors of the two sets of data are comparable and have the values of 10.5% and 13.1% for water and the special mixture, respectively. 3.3. Dynamic Measurements with Gas Load. One of the most important design factors of a packed column is the capacity. The gas capacity of a column is limited by the onset of flooding. Flooding conditions can be defined in different ways: (a) when the slope of the pressure drop curve goes to infinity, (b) when the

Figure 8. Experimental capacity data for Mellapak 250 Y represented in a Wallis diagram.

efficiency goes to zero, (c) when mean liquid holdup increases by a factor of 2-3. As pointed out by Spiegel and Meier,15 the onset of flooding is really difficult to measure; therefore, they suggested using the concept of a capacity limit, which is defined simply as the point of operation where pressure drops equal 10-12 mbar/m. According to Spiegel and Meier,15 the capacity limit is 5-10% lower than the flooding point. The capacity of a column can be represented on Souders-type or Wallis-type diagrams depending on the dimensionless parameters used. The approach suggested by Wallis has been used in the present work, and the two parameters used to plot the data are

( (

) )

CG ) USG

FG FL - FG

1/2

CL ) USL

FL FL - FG

1/2

(5)

(6)

where USG and USL are respectively the superficial gas and liquid velocities expressed in m/s and FG and FL are the gas and liquid densities, respectively. Figure 8 shows the comparison of the present experimental data, experimental data by Spiegel and Meier,15 and experimental data by Sulzer.16 Figure 8 shows that the present experimental data of the capacity limit agree with the data by Spiegel and Meier15 relative to water as working fluids. Moreover, the data plotted in the figure also show that by decreasing the liquid surface tension, the capacity of the packing slightly decreases; this experimental behavior agrees with the experimental observation by Spiegel and Meier.17 The liquid holdup distribution over the element of packing when gas and liquid flow countercurrently inside the column is analyzed below. Suess and Spiegel4 showed that liquid holdup has a vertical profile along the column and that flooding starts where two elements of packing touch each other. They showed that the liquid holdup becomes a local property of the packing above the loading point. They used a γ-densitometer to measure the local liquid holdup. This gives very accurate measurements, but it is extremely expensive and can only be used for laboratory equipment. Figure 9 shows the mean capacitance values, measured with the two capacitance probes used in the present work, versus the F factor. The data refer to a liquid load of 40 m3/h/m2. A vertical line is drawn on the same figure, showing the column capacity limit computed according to Spiegel

Ind. Eng. Chem. Res., Vol. 40, No. 4, 2001 1209

Figure 9. Comparison between the present experimental data and the Spiegel and Meier15 approach.

Figure 11. Present experimental data of capacitance measured by the bottom probe.

bottom probe starts to increase. Finally, it is possible to assume that the criterion suggested by Spiegel and Meier15 simply identifies the loading point of the packing. 4. New Approach To Evaluate the Packing Capacity

Figure 10. Comparison between the present experimental data of capacitance and pressure drop and the Spiegel and Meier15 approach for evaluating loading conditions.

and Meier.15 The experimental data show that capacitance, and therefore liquid holdup, is not particularly influenced by the gas load up to a F factor of Fl ) 2.1 m/s‚(kg/m3)0.5. Above this critical value, the capacitance measured by the probe on the bottom of the element increases, whereas the capacitance measured by the probe located in the middle of the element remains approximately constant. Another key value is Ff ) 2.5 m/s‚(kg/m3)0.5; above this critical F factor value, the capacitance measured by the bottom probe reaches a maximum, whereas the capacitance measured by the middle probe starts to increase. This experimental behavior indicates that below Fl the gas load does not have practically any influence on the capacitances measured by both of the probes, and therefore on the liquid holdup in the column. For this reason, it could be assumed that the gas load Fl identifies the loading conditions. Finally, Figure 9 shows that capacity limit identified by the present probes agrees with results obtained using Spiegel and Meier’s method. Short-cut methods to design columns equipped with structured packings usually assume that working conditions are 70-85% of the capacity limit (Spiegel and Meier15). Figure 10 compares the present experimental data of capacitances, measured using the two probes, and the present experimental data of pressure drop as suggested by Spiegel and Meier,15 i.e., Fwork ) 0.75Ff. The figure shows that the working conditions suggested by Spiegel and Meier,15 and identified by Fwork, simply represent the conditions where the capacitance of the

The previous paragraph described a new probe to evaluate packing capacity. It has been shown that local liquid holdup can be evaluated from the measurements of electrical capacitance. In Figure 11 the mean values of the electrical capacitance measured by the bottom probe are shown as a function of the F factor. The figure shows that the capacity limit, independently from the liquid load and according to the definition given in the previous paragraph, occurs when the electrical capacitance of the bottom probe assumes a critical value of about 140 pF. All of the data related to working conditions above the capacity limits are contained in the range of 130-150 pF with the exception of the datum at the lowest liquid load when the F factor is greater than 4 m/s‚(kg/m3).0.5 This behavior is due to physical reasons; in fact, in this condition the liquid phase did not flow downward but was dragged upward by the gas phase, and therefore the probe was dried. If the simplified electrical circuit shown in Figure 3C can be used, the capacitance of 140 pF corresponds to a liquid holdup in the channel of about 0.7. The hydraulic scheme used in the present work is based on the assumption that a capacity limit occurs when a motionless liquid plug with vertical height equal to S is formed between two adjacent elements. If the pressure drops due to the change in the gas direction at the bottom of the element are evaluated as shown by Brunazzi and Paglianti,11 the force balance on the liquid phase at the capacity limit conditions assumes the following form:

(

)

2 Le FG USG SAHL,bg(FL - FG) ) 4f A (7) de 2 e sin ϑ(1 - HL,m)

where A is the area of the channel, HL,b the liquid holdup in the plug measured by the bottom probe, g acceleration due to gravity, f the friction factor, Le the equivalent channel length of each bend, de the characteristic dimension of the flow channel, USG the superficial gas velocity, HL,m the mean liquid holdup in the

1210

Ind. Eng. Chem. Res., Vol. 40, No. 4, 2001

Table 1. Characteristics Data of the Structured Packings Tested packing type

material

f∞

e

ag [m2/m3]

Le/de

Mellapak 250 Y Mellapak 125 Y Mellapak 250 Y Mellapak 350 Y Mellapak 500 Y Mellapak 250 X

plastic metal metal metal metal metal

0.023 0.0178 0.0178 0.0178 0.0178 0.0178

0.9 0.987 0.975 0.965 0.95 0.98

250 125 250 350 500 250

35 35 35 35 35 25

Figure 13. Comparison between computed and measured values of capacity (experimental data by Spiegel and Meier;15 air-water system; metal Mellapak packings).

Figure 12. Comparison between computed and present measured values of capacity (air-water system; plastic Mellapak 250 Y).

channel, e the void fraction of the packing, and ϑ the inclination of the channel with respect to the horizontal. The friction factor, f, can be evaluated using the Brunazzi and Paglianti11 model or simplified equations. Because the aim of this work is to suggest a simple equation to compute the column capacity, a simplified form to compute f was used. Wallis18 suggested the following equation to evaluate the friction factor in pipes working in annular regime

f ) f∞(1 + 75HL,m)

(8)

where f∞ is the friction factor at a very high Reynolds number. In the present work, eq 8 is simplified by neglecting 1 with respect to 75HL,m, therefore close to the flooding points:

f ) f∞(75HL,m)

(9)

where f∞ depends on the geometric characteristics of the packing. Values for f∞ and Le/de were taken from Brunazzi and Paglianti11 and are shown in Table 1. Therefore, eq 7 assumes the following form: 2 2 HL,m 1 FL - FG e (sin ϑ) USG2 ) SHL,bg f∞(Le/de) (1 - HL,m)2 150 FG

(10)

The liquid holdup in the plug, as shown in Figure 11, can be assumed to be constant and was measured to be equal to the critical value of 0.7 for the Mellapak 250 Y made in plastic. It was assumed that the plug height, S, was constant in this work. From the analysis of both these experimental data and experimental data available in the open literature for aqueous solutions, an empirical value of S ) 20 mm was derived. Figure 12 shows a comparison between the present model, the Kister and Gill19 relation, and the present experimental data performed on an air-water test system and related to the identification of capacity limit conditions. The figure shows that the simplified model

Figure 14. Comparison between computed and measured values of capacity at high liquid loads (experimental data by Spiegel and Meier;17 air-water system; metal Mellapak packings).

suggested in the present work agrees both with the empirical equation by Kister and Gill19 and with the present experimental data. The present model can also be used to predict the capacity limit if different structured packings are used. Figures13 and 14 show comparisons between computed data and experimental data performed by Spiegel and Meier15,17 related to the Mellapak family of packings fabricated from metal. The channel liquid holdup, HL,m, was computed using the Brunazzi and Paglianti11 model:

HL,m ) H/e

(11)

where H is the mean liquid holdup computed using the equation suggested by Suess and Spiegel.4 In all cases the liquid holdup in the plug, HL,b, was assumed to be equal to the value measured for the plastic Mellapak 250 Y. Figure 13 shows a comparison between experimental data by Spiegel and Meier15 related to structured packings of the Mellapak family and the present relation. The simplified model suggested in the present work seems to predict the experimental data with sufficient accuracy. It is important to point out that the model derives from a force balance on the liquid plug and that

Ind. Eng. Chem. Res., Vol. 40, No. 4, 2001 1211

probe is absolutely nonintrusive and allows online measurements to be performed without requiring any special attention to calibration. Evaluation of liquid holdup from the measurements of the capacitance can be performed using very simple electric models. The experimental data obtained with the probe show that, at the capacity limit conditions, the liquid holdup is constant in the zone where two packing elements touch each other. This experimental observation suggested a simple model to permit the easy evaluation of the capacity limit conditions in structured packings. The model allows both the experimental data performed in the present work and also other experimental data available in the open literature to be evaluated. Acknowledgment Figure 15. Comparison between computed and measured values of capacity (experimental data by Billet;20 air-water system; metal Mellapak packing 250 Y and metal Montz packing B1-300).

only one empirical parameter, the plug height S, has been introduced. The adjustable parameter, S, does not depend on either the specific surface area or the angle of inclination of the channels, and all of the other parameters used in the model derive either from measurements, such as the liquid holdup HL,b, or from a previous mechanistic model developed for predicting the pressure drop in structured packings (Brunazzi and Paglianti11). Figure 14 shows a comparison between the present model and the experimental data by Spiegel and Meier17 obtained using Mellapak 250 X and Mellapak 250 Y packings made from metal, at very high liquid loads. The simplified model suggested in the present work seems to predict the capacity with sufficient accuracy even under these working conditions. Finally, Figure 15 shows the experimental data obtained by Billet20 using Mellapak 250 Y and Montz B1-300 packings, both made from metal, and it compares them to the results obtained using both the present model and the Billet and Schultes21 model. The liquid holdup, HL,m, for the structured packing B1-300, was computed for the present model as suggested by Billet and Schultes.21 Moreover, considering the similarity between the Montz B1-300 packing and the Mellapak types listed in Table 1, the values for f∞ and Le/de were assumed to be equal to 0.0178 and 35, respectively. The other geometrical characteristics, ag and e, were taken from Billet and Schultes.21 Figure 15 highlights that both the present simplified model and the model by Billet and Schultes21 satisfactorily reflect the experimental capacity limit data. Finally, it can be concluded that the simplified model shown in the present work accurately predicts the capacity limit conditions measured in the same work just as well as some data available from the open literature, obtained under different working conditions and with different structured packings. 5. Conclusions The impedance method could become a very attractive method for measuring liquid holdup in packed columns. In the present work, a new probe to measure the local liquid holdup has been designed and tested. The probe presented in this paper can be used not only in laboratories but also on large-scale equipment. In fact, the

The authors thank Dr. L. Spiegel and Dr. P. Bomio from Sulzer ChemTech for having provided the Mellapak packings and Ing. K. Bandini and Ing. E. Favilli for their help with the experimental work. Financial support from CNR (Consiglio Nazionale delle Ricerche) under grant 97.02732.CT03 is gratefully acknowledged. Notation A ) area of a channel [m2] ag ) packing specific surface area [m2/m3] C ) electrical capacitance [pF] C* ) dimensionless capacitance CG ) gas parameter in the Wallis equation [m/s] CL ) liquid parameter in the Wallis equation [m/s] de ) characteristic dimension of the flow channel [m] e ) packing void fraction f ) friction factor F ) F factor, USGxFG [Pa0.5] Ff ) F factor at the capacity limit [Pa0.5] Fl ) F factor at the loading point [Pa0.5] g ) acceleration due to gravity [m/s2] H ) mean liquid holdup in the packing HL,b ) liquid holdup at the bottom element HL,m ) mean liquid holdup in the channel Le ) equivalent channel length of each bend [m] S ) geometrical parameter [m] USG ) superficial gas velocity [m/s] USL ) superficial liquid velocity [m/s] Greek Letters  ) permittivity [F/m] /) overall permittivity of the probe [F/m] µ ) viscosity [N m] ϑ ) channel inclination [deg] σ ) surface tension [N/m] F ) density [kg/m3] Subscripts G ) gas phase L ) liquid phase PP ) polypropylene

Literature Cited (1) Brunazzi, E.; Nardini, G.; Paglianti, A.; Petarca, L. Interfacial area of Mellapak Packing, Absorption of 1,1,1-trichloroethane by Genosorb 300. Chem. Eng. Technol. 1995, 18, 248. (2) Nardini, G.; Paglianti, A.; Petarca, L.; Viviani, E. Sulzer BX gauze: Fluodynamics and Absorption of Acid Gases. Chem. Eng. Technol. 1996, 19, 20. (3) Engel, V.; Stichlmair, J.; Geipel, W. A new model to predict liquid hold-up in packed columnssUsing data based on capacitance measurement techniques. Inst. Chem. Eng. Symp. Ser. 1997, 142, 939. (4) Suess, P.; Spiegel, L. Hold-up of Mellapak structured packings. Chem. Eng. Process. 1992, 31, 119.

1212

Ind. Eng. Chem. Res., Vol. 40, No. 4, 2001

(5) McNulty, K. J.; Hsieh, C. Hydraulic performance and efficiency of Koch Flexipac structured packings. AIChE Annual Meeting, 1982. (6) Billet, R.; Mackowiak, J. Application of modern packings in thermal separation processes. Chem. Eng. Technol. 1988, 11, 215. (7) Hewitt, G. F. Measurements of two phase flow parameters; Academic: New York, 1978. (8) Andreussi, P.; Di Donfrancesco, A.; Messia, M. An impedance method for the measurement of liquid hold-up in two phase flow. Int. J. Multiphase Flow 1988, 14, 777. (9) Takenaka, K.; Takahashi, K. Local gas hold-up and recirculation rate in an aerated vessel equipped with a Rushton impeller. J. Chem. Eng. Jpn. 1996, 29, 799. (10) Andreussi, P.; Paglianti, A.; Silva, F. Dispersed bubble flow in horizontal pipes. Chem. Eng. Sci. 1999, 54, 1101. (11) Brunazzi, E.; Paglianti, A. A mechanistic pressure drop model for columns containing structured packings. AIChE J. 1997, 43, 317. (12) Moser, F.; Kessler, A. Increased capacity thanks to improved geometry Sulzer Tech. Rev. 1999, 3, 24. (13) Maxwell, J. C. A treatise on electricity and magnetism; Clarendon Press: Oxford, U.K., 1881. (14) Bruggeman, D. A. G. Calculation of different physical constants of heterogeneous substances. Ann. Phys. 1935, 24, 636.

(15) Spiegel, L.; Meier, W. Correlations of the performance characteristics of the various Mellapak types. Inst. Chem. Eng. Symp. Ser. 1987, 104, A203. (16) Sulzer. Separation Columns for Distillation and Absorption; Publ. No. 22.15.06; Sulzer: Winterthur, 1991. (17) Spiegel, L.; Meier, W. Capacity and pressure drop of structured packings at very high liquid loads. AIChE Spring National Meeting, 1994; Paper 91C. (18) Wallis, G. B. One-dimensional two-phase flow; McGrawHill: New York, 1969. (19) Kister, H. Z.; Gill, D. R. Flooding and Pressure drop prediction for structured packings. Inst. Chem. Eng. Symp. Ser. 1992, 128, A109. (20) Billet, R. Packed Column Analysis and Design; Department of Thermal Separation Processes, Ruhr-Universita¨t Bochum: Bochum, Germany, 1989. (21) Billet, R.; Schultes, M. Prediction of mass transfer columns with dumped and arranged packings. Updated summary of the calculation method of Billet and Schultes. Chem. Eng. Res. Des. 1999, 77, 498.

Received for review June 5, 2000 Accepted November 17, 2000 IE000546U