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Hydrodynamics of Ceramic Sponges in Countercurrent Flow Julia Grosse* and Matthias Kind Institute of Thermal Process Engineering, Karlsruhe Institute of Technology(KIT), Kaiserstrasse 12, D-76131 Karlsruhe, Germany ABSTRACT: A broad range of ceramic sponge types regarding porosity, pore size, and material was investigated experimentally in order to determine liquid holdup as well as wet pressure drop and operation limits. The observed values for the holdup are higher than those for state-of-the-art random and structured packings. The onset of flooding occurs at relatively low gas loads, but the operation range can be significantly enlarged by using a sponge with a cone-shaped bottom as drainage enhancer. Effects of stacking can be shown especially for the static liquid holdup. Possible applications are, for example, reactive rectification, where the continuous solid and the ceramic material as catalyst carrier are of advantage. The experimental values are compared with established correlations from the literature for conventional column internals. In general, those are able to describe the behavior of sponge structures, although the deviations are bigger than observed for other column internals.
1. INTRODUCTION Solid sponges are a new class of material in chemical engineering. They possess a monolithic network structure with two continuous phases and have thus a continuously accessible void space. The void fraction of solid sponges can vary in a wide range between 0.7 and 0.95 with pore numbers between 5 and 75 ppi (pores per linear inch). They show a pressure drop and specific surface areas in the same range as structured packings,1 and they can be produced from a variety of metals as well as inert ceramic materials such as silicate, aluminum oxide, and silicon carbide. The standard production process for commercially available ceramic sponges is a replication of a polymer precursor, the socalled Schwartzwalder process,2 where reticulated polymer foams are coated with a ceramic suspension and afterward sintered to remove the polymer. The inner cavities caused by the polymer precursor can be infiltrated to reduce the microporosity of the material. Ceramic sponges were originally developed as filters for molten metal, but are now explored in a broad range of applications in chemical engineering such as porous gas burners and solar receivers or as a catalyst support in exhaust and waste gas purification, reforming, and partial and preferential oxidation, as well as Fischer-Tropsch synthesis. Reviews on these topics have been provided by different authors.3,4 However, little research was done on two-phase flow in sponge structures, although the fundamental characterization in multiphase flow is necessary to judge the potential of sponges compared with conventional packed beds or structured packings as catalyst support or in mass transfer columns. Stemmet et al. performed investigations on the use of metal sponges of one porosity and several pore sizes as packing concerning holdup in countercurrent flow5,6 as well as modeling of mass transfer in countercurrent flow6 and experimental investigations on mass transfer in cocurrent flow.7,8 Calvo et al.9 used X-ray radiography to determine the liquid holdup and its local distribution as well as radial dispersion in one type of metal sponges. Leveque et al.10 performed measurements of holdup and mass transfer in distillation columns for a single type of ceramic sponges. All these works are limited to a very small range r 2011 American Chemical Society
of sponge parameters or even restricted to a single sponge type. The range of investigated sponge parameters such as material, porosity, and pore size in the literature is thus still too small to judge the applicability of established correlations for column internals. The aim of this work is hence to broaden the investigated range of sponge parameters and to present hydrodynamics for sponges of different material, porosity, and pore sizes as well as to describe the influence of sponge element and total packing height on these parameters in two-phase countercurrent flow. A comparison with selected correlations established in the literature will also be performed to enable prediction of hydrodynamic performance of sponge structures. The sponge element height is an important parameter for sponge packings, as thoroughly open-celled sponges can often only be produced with a limited element height of 25-30 mm. All higher elements normally suffer from a minor quality, as mainly inside the sponge the cells are not thoroughly open. A stacking of sponge elements will be thus indispensable for all applications.
2. SPONGE PARAMETERS The sponges used in this study are commercially available and are made of different materials and by different manufacturers. The sponges from Vesuvius, Becker & Piscantor, Grossalmeroder Schmelztiegelwerke, Germany, are made from 99% pure aluminum oxide with total porosities ranging between 0.75 and 0.85 and pore numbers of 10-30 ppi. Sponges made of silicon carbide infiltrated with pure silicon (SiSiC) are manufactured by Erbicol SA, Switzerland, with a total porosity of 0.88 and pore numbers of 10 and 20 ppi. Furthermore, a new sponge type is used, which is provided by Johann Jacob Letschert Sohn, Germany, who developed a prototype with thoroughly opened Received: July 15, 2010 Accepted: February 18, 2011 Revised: February 3, 2011 Published: March 09, 2011 4631
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Table 1. Overview of the Characteristics of All Sponges Used in This Study
a
sponge ID
manufacturer
material
nominal porosity
ppi
V 85 10 25 V 85 10 50 V 75 10 25 V 75 10 50 V 85 20 25 V 85 20 50 V 75 20 25 V 75 20 50 V 85 30 25 V 85 30 50 V 75 30 25 V 75 30 50 E 88 10 25 E 88 20 25 L 91 10 100/L 91 10 100 Cb
Vesuvius
Al2O3
0.85
10
0.75
10
0.85
20
0.75
20
0.85
30
0.75
30
Erbicol
SiSiC
0.88
Letschert
silicate
0.91
10 20 10
element height, mm 25 50 25 50 25 50 25 50 25 50 25 50 25 100/125
outer porosity
specific surface area, m2/m3
amount of closed faces
0.81a
630a
0.69a
640a
0.81a
970
0.72a
1000
0.79a
1330
0.70
1330
some many some many some many many most many most many most little little very little
0.86 0.88
a
470a 660a 700
Data from Grosse et al.12 b “C” symbolizes the cone-shaped bottom.
Figure 1. Left: different sponges: alumina with 10 ppi and element heights 25 and 50 mm (white); silicon-infiltrated silicon carbide with 10 and 20 ppi and element height 25 mm (black); silicate with 10 ppi and element height 100 mm (gray). Second from left: silicate sponge element with cone-shaped bottom. Second from right: cut alumina sponge with porosity 0.85, 10 ppi, and height 50 mm. Right: cut alumina sponge with porosity 0.75, 20 ppi, and height 50 mm.
cells in elements of 100 mm height. These are not yet commercially available and are made of silicate ceramics with a porosity of 0.91 and a pore number of approximately 10 ppi. A sponge element with a cone-shaped bottom (90° cone angle) was also provided. This variety makes a comparison of parameters such as porosity, pore number, and material as well as characteristics such as more or fewer closed cells possible. All sponge elements are cylinders of 100 mm diameter with different element heights. An overview of all sponge types used in this study with their characteristics is given in Table 1. A sponge identification which consists of manufacturer, porosity, pore number, and element height is introduced for better identification. By inserting “XX” at one position in the sponge identification, the sponges can be grouped by common characteristics, such as V 85 XX 25 for all sponges of Vesuvius with a porosity of 0.85 and an element height of 25 mm, but different pore numbers. The commercially available sponges were thoroughly characterized in previous work with different methods such as light microscopy, pycnometry, and volume imaging in order to determine the face and strut diameters, the porosity, and the specific surface area. The methods used for these characterizations and parts of the obtained data are described in detail
in previous publications.11,12 Here only the values for the outer porosity and specific surface area are given in Table 1. These surface area values only consider the outer surface area; surfaces inside hollow struts or due to the porous sintered ceramic material are not taken into account. In analogy to that, the outer porosity does not consider the void phase inside the hollow struts or the porosity of the sintered material. It is thus the porosity value which is relevant for fluid dynamics. The nominal porosity value provided by the manufacturer corresponds approximately to the total porosity value and takes all void spaces into account. Photographs of the sponges are shown in Figure 1. One sponge of each type was cut into pieces and was inspected visually concerning the amount of closed faces. A classification was thus possible and is given in Table 1.
3. EXPERIMENTAL APPROACH Several characteristics must be determined for the ceramic sponges in order to evaluate their performance as column internals. This work focuses on the determination of static and dynamic liquid holdup as well as wet pressure drop and flooding behavior. This should offer the possibility to compare ceramic sponges with structured packings or monoliths. The influence of 4632
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Figure 2. Experimental setup for the determination of total liquid holdup and pressure drop.
the stacking height and the number of intersections is investigated for all characteristics. The main investigated characteristic of packing structures is the liquid holdup, the volume fraction of a packing filled with liquid. The static liquid holdup of a packing structure is the holdup remaining in a packing after wetting the structure completely and allowing it to drain afterward. The sponge elements are placed into a Plexiglas device with adjustable height in order to determine this parameter, which allows them to drain under similar conditions as in a column. They are completely dipped in water for 5 min and afterward drained in water-saturated air for 15 min. The times needed to ensure complete and reproducible wetting and draining are determined by varying both until the holdup is constant. Reproducibility is investigated by repeating the experiment several times both with the same element and with an element of the same sponge type. The behavior of the sponges during column operation is investigated in addition to the static liquid holdup, especially the total liquid holdup, the wet pressure drop, and the operation limits. The total liquid holdup is the sum of static and dynamic liquid holdup and corresponds to the liquid volume fraction in the sponge during operation. The experimental setup chosen allows determining the total liquid holdup, the wet pressure drop, the loading point, and the onset of flooding. It consists of a DN 100 column in which the sponge elements are placed, as shown in Figure 2. Its adjustable height allows investigations on variable packing heights under the same inlet and outlet conditions, as top and bottom configurations as well as the distances of inlet and outlet to the packing are similar in all experiments. Air and water are chosen as the standard test system. All experiments are carried out at ambient conditions. The sponge elements are wrapped in cellophane film in order to fit properly in the column and avoid bypass.
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A gravimetric measurement method is used to determine the total holdup, as can be found for metallic sponges in the literature.5 The liquid is circulated from the storage tank through the column with a gear pump and distributed over the packing by a pipe distributor with approximately 1000 drip points/m2 of approximately 1 mm in diameter. This high value is chosen to avoid liquid maldistribution due to an insufficient radial distribution of liquid inside the sponge. The liquid level in the storage tank is kept constant due to an overflow. An additional liquid flow of about 10% of the total liquid flow is created by a peristaltic pump from the small vessel placed on the balance. This allows weighing the amount of water in the column, as the overflow from the storage tank is connected to the small vessel. It is ensured that the liquid circuit is completely filled with water before each experiment. The system with tank and vessel is chosen due to more stable operation condition, as the storage tank with its enlarged surface area serves as a buffer for fluctuations in the liquid flow. The total liquid flow is measured by a Krohne H250 flow meter based on the float principle. A siphon at the liquid outlet avoids gas breakthrough at the column bottom. The gas is taken from the pressurized air supply and saturated with water before entering the column. The dry gas flow is measured by a Krohne H250 flow meter based on the float principle. A Bronkhorst mass flow controller F203AV is used for higher gas flow rates above 14 Nm3/h. The gas is inserted into the column by an inlet pipe with a downward opening of 50 13 mm, which leads the air toward the bottom of the column before it flows upward through the packing in countercurrent flow to the liquid. This ensures a better gas distribution for side-fed gas compared with an undirected gas flow. The pressure drop over the packing is measured with a Betz differential pressure gauge with an accuracy of 0.01 mbar. The balance and the two flow meters are read out with a PCI data acquisition device and a Labview data acquisition program. The experiments are carried out separately for each liquid load starting with a dry packing, as a hysteresis effect up to 20% could be observed by first increasing and then decreasing the liquid load without gas load. This effect was also observed by Calvo et al.9 for metal sponges. The dry packing is thus thoroughly wetted at constant liquid load without gas load until it reaches a steady state. Then the gas load is gradually increased. By weighing the amount of water remaining in the liquid circuit with and without sponges, it is possible to determine the amount of water remaining in the sponge online. The operation limits determined are the loading point and the onset of flooding. Loading is reached when pressure drop and total liquid holdup increase significantly stronger with increasing gas flow than before. Operation in countercurrent flow is still possible but might be less stable at the loading point, as the packing is partially filled with liquid. Flooding is reached when countercurrent operation is no longer possible as either the liquid forms a significant bubbling region above the packing which leads to heavy entrainment or the liquid no longer drains out of the packing. Thus a different hydrodynamic regime is obtained and the pressure drop starts to fluctuate heavily.
4. EXPERIMENTAL RESULTS AND DISCUSSION The range of investigated sponge types varies for the determined hydrodynamic parameters. The static liquid holdup of a single sponge element is investigated for all sponge types. Several sponge types lead to instantaneous flooding under gas load when 4633
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Figure 3. Experimental results for the static liquid holdup of one sponge element per sponge type as a function of the specific surface area. Sponge types are grouped by porosity and element height. Error bars indicate the standard deviation.
column operation is investigated, so the range of experiments is limited for those investigations. Therefore stacking of sponge elements for the static liquid holdup is investigated on selected sponge types only. Additionally the contact angle of water in air on the different sponge surfaces is determined with a Kruess G10 contact angle measurement device based on a static sessile drop, where the tangent is manually adjusted to the three-phase contact point. Measurement of the contact angle was tried for the alumina sponges on an even surface of the sponge, where a closed face leads to a sufficiently big plate of solid material. The alumina sponge directly absorbed all the liquid due to its capillarity, even if the sponge was filled with water before. Thus a perfect wetting of the surface and a contact angle of 0° is assumed. The same observation is made for the silicate sponges. For the sponges made of silicon-infiltrated silicon carbide, a plate made of the solid material is provided by the manufacturer. The contact angle measured on this plate is between 20° and 40° depending on the surface preparation, so the liquid is still wetting the surface, but no complete wetting was observed as for the other sponges. 4.1. Static Liquid Holdup. The static liquid holdup is measured with one element per sponge type. Experimental results for all sponge types are depicted in Figure 3. In this plot the static holdup is shown as a function of the specific surface area and the sponge types are grouped by porosity and element height. In general, the static liquid holdup increases with increasing specific surface area, i.e., with increasing pore number and decreasing pore size. At the same time the amount of closed faces increases with increasing pore number, which also contributes to an increasing holdup. An influence of porosity is also visible for the alumina sponges: the values for the sponges with porosity of 0.85 are always lower than those for sponges with lower porosity (V 85 XX 25 and V 85 XX 50 vs V 75 XX 25 and V 75 XX 50). The influence of the material or manufacturer is also clearly visible. For the sponges made of silicon-infiltrated silicon carbide (E 88 XX 25) the holdup values are lower. This can be due to three different reasons: first, the contact angle is higher than for the alumina sponges, second, the porosity is slightly higher than for the alumina sponges, and, third, the amount of closed faces is significantly lower for the 20 ppi sponges, and still lower for the 10 ppi sponges. This leads to a better drainage and thus to lower
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Figure 4. Static holdup and holdup profile for stacked sponge elements with a stacking height of 200 mm. The mean value for the stack is given as well as the individual holdup values for the different positions in the stack. Note the different numbers of elements per stack due to the different element heights. Error bars were omitted for the sake of clarity, but were in same range as shown in Figure 3.
holdup values. The same effect can be observed for the silicate sponges (L 91 10 100), where the holdup is in the same range as for the silicon-infiltrated silicon carbide sponges, thus also lower than for the alumina sponges. Here, a higher porosity and fewer closed faces can be the reason. As can be seen in Figure 3, the static holdup of the alumina sponges with an element height of 25 mm (V 85 XX 25 and V 75 XX 25) is approximately twice the holdup of the alumina sponges with an element height of 50 mm (V 85 XX 50 and V 75 XX 50). This indicates that the total amount of water in both sponge types is approximately the same. A reason for this effect could be a vertical holdup profile inside the sponge element with a significant part of the liquid remaining at the lower end of the element. Therefore a closer examination of stacking of sponge elements seems necessary. 4.2. Stacking Effects on Static Liquid Holdup. Several experiments on stacking of sponge elements are performed. The results presented in Figure 4 are restricted to sponge types which can be used for dynamic holdup experiments. A stacking height of 200 mm is chosen for all experiments, and the number of sponge elements used is adapted to the element height. Stacking of more or fewer sponge elements leads to similar results which are therefore not shown here. The holdup observed for the sponge element at the bottom of the stack is always up to 3 times bigger than for the elements in the center or at the top. The lowest value is found for the element at the top of the stack. The holdup of the silicon-infiltrated silicon carbide sponges (E 88 10 25) is lower than the values found for the alumina sponges (V 85 10 XX). For the alumina sponges with the same nominal parameters but different element height (V 85 10 25 vs V 85 10 50), the holdup decreases with increasing element height which corresponds to a decreasing number of intersections. The silicate sponge (L 91 10 100) has the lowest average holdup value as was observed for the single elements (compare Figure 3). The influences of the pore number (E 88 10 25 vs E 88 20 25) and porosity (V 85 10 25 vs V 75 10 25) are also as observed for the single elements. It is thus assumed that the higher holdup especially in the bottom of the stacks is due to a drainage problem of the sponge structure. The influence of the drainage problem on flooding is discussed in the following sections. 4634
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Figure 5. Comparison of total liquid holdup as a function of gas load for sponges made of silicon-infiltrated silicon carbide with 10 ppi and 200 mm stacking height at different liquid loads. O: Last operating point before onset of flooding.
Figure 6. Comparison of total liquid holdup as a function of gas load for different sponge types with stacking height 200 mm and constant liquid load. O: Last operating point before onset of flooding.
4.3. Total Liquid Holdup. The total liquid holdup is measured with different stacking heights and at different liquid loads for most sponges. The alumina sponges with higher pore number (V 85 20 XX, V 75 20 XX, V 85 30 XX, and V 75 30 XX) led to instantaneous flooding when the gas flow was started and are thus not presented in the following sections. A comparison of different liquid loads for the sponges made of silicon-infiltrated silicon carbide with 10 ppi (E 88 10 25) is shown in Figure 5. It is evident that the loading region and the onset of flooding depend on the liquid load. Instantaneous flooding without a loading region was observed for the highest liquid load. A comparison of the different sponge types at constant liquid load is shown in Figure 6. Here the early onset of flooding without a loading region for sponge types with higher pore numbers (E 88 20 25) as well as many closed faces and lower porosities (V 85 10 XX and V 75 10 XX) is also observed. A loading region could be observed only for sponge types with thoroughly open faces and low pore numbers (E 88 10 25 and L 91 10 100). The total liquid holdup is lower for the sponge types with a bigger contact angle and a lower specific surface area (E 88 10 25). The highest value for the total liquid holdup is found for the sponge types with the lowest porosity (V 75 10 25), which corresponds to the results for the static liquid holdup. The higher
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Figure 7. Comparison of total liquid holdup as a function of gas load for alumina sponges with porosity 0.85 and 10 ppi at different stacking heights and constant liquid load. O: Last operating point before onset of flooding.
Figure 8. Comparison of total liquid holdup as a function of gas load for silicate sponges with the normal configuration (filled symbols) and with the drainage enhancer (C, open symbols) at different stacking heights and constant liquid load. O: Last operating point before onset of flooding.
elements and thus the stacks with fewer intersections lead to similar total holdup values and onset of flooding (compare V 85 10 50 with V 85 10 25). The tendency of all these results can also be observed at higher liquid loads. The early onset of flooding is a phenomenon also reported for sponges in the literature.10 In this work it was observed for high liquid loads BL and sponge types with many closed cells together with no significant loading region. It could be due to the drainage problem already observed in the static liquid holdup hstat, as a continuous liquid layer at the lower end of the packing might cause the onset of flooding already at comparatively low gas loads. In general, the observed values are higher than those for state-of-the-art random and structured packings. 4.4. Stacking Effects. The results for different stacking heights L of alumina sponges with different element heights (V 85 10 XX) are shown in Figure 7. A higher holdup was observed for lower stacking heights, which corresponds to the data collected for the static liquid holdup. The onset of flooding is mostly identical except for the single element of 50 mm height. As no significant difference was shown for stacks of 150-300 mm, a good reproducibility of the experiment is given. The selection of 200 mm stacking height for the comparison of the sponge 4635
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Figure 9. Wet pressure drop as a function of gas load for different sponge types of stacking height 200 mm at constant liquid load. O: Last operating point before onset of flooding.
types was due to a limited number of elements for several sponge types and the fact that the low pressure drop of the sponges could be measured with more accuracy than at lower stacking heights. Further results for the stacking of silica sponges (L 91 10 100) are shown in Figure 8. Here an increase of the total liquid holdup and especially earlier flooding can be observed with increasing stack height. For 300 mm stack height an immediate flooding was observed, while the other stack heights could be operated longer in the loading region. The problem of stacking of monolithic structures and the early flooding due to exit effects at the lower end of the packing is also reported in the literature. Lebens13 and Heibel14 have investigated the flooding of honeycomb monoliths and suggested different stacking and outlet configurations for improvement of flooding performance. A beveled monolith as lower packing end was used by Lebens. In analogy to this, a sponge with a coneshaped bottom was chosen as drainage enhancer for the silicate sponges. The results are depicted in Figure 8. The total liquid holdup decreased with increasing stack height as was observed without drainage enhancer. It was unfortunately not possible to observe loading or flooding with the chosen experimental setup for the configuration with drainage enhancer due to the limits of the operation range adapted to the conventional sponge elements. The operation range is thus at least twice as big with drainage enhancer, as the liquid accumulated at the bottom of the packing no longer prevents the countercurrent gas flow from entering the packing. It is properly drained instead. 4.5. Wet Pressure Drop. The wet pressure drop was also observed during the experiments, as this is one of the relevant parameters for column operation. Some of the presented literature correlations use the wet pressure drop to predict the total liquid holdup with gas flow. In Figure 9 some selected results for the wet pressure drop are shown. The generally assumed dependence on the square of the gas load can be observed for all sponge types. Similar results were obtained for all other experiments.
5. COMPARISON WITH CORRELATIONS FROM THE LITERATURE In the literature a broad range of theoretical or adapted correlations for the description of the liquid holdup of structured and random packings can be found. The five most recent
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correlations based on a broad data range are selected for this work. In general, the correlations assume either a maximum holdup at the flooding point and interpolate between the liquid holdup at no gas load and the flooding holdup, or the wet pressure drop is used for the adaption of the holdup values. The correlations presented in detail of Mackowiak,15 Billet and Schultes,16 as well as Bornhuetter17 belong to the first category, while those of Stichlmair18 and Engel19 belong to the second category. 5.1. Correlations from the Literature. Mackowiak15 presents a correlation for random packings and structured Y-packings with a liquid load of ReL g 2. He derives a value for the total liquid holdup without gas flow (eq 1). The total holdup at the flooding point is calculated according to eq 2 for uL/uG,Fl < 0.03. He assumes a constant liquid holdup of hL,0 before loading, predicts the onset of loading at uG = 0.65 uG,Fl, and interpolates for the loading region according to eq 3. !1=3 uL 2 ageo ð1Þ hL, 0 ¼ 0:57 g
hL, Fl
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi !2 ! u u u u u uL L L L t1:44 þ 0:8 1- 1:2 uG, Fl uG, Fl uG, Fl uG, Fl ! ¼ uL 0:4 1 uG, Fl ð2Þ vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u 0 u 12 G u - 0:65 u u B C BuG, Fl C hL ¼ hL, Fl - ðhL, Fl - hL, 0 Þu A t1 - @ 0:35 for uG g 0:65uG, Fl
ð3Þ
where ReL is the Reynolds number of the liquid, uL is the nominal liquid velocity, uG is the nominal gas velocity, uG,Fl is the nominal gas velocity at flooding, ageo is the specific surface area, g is the gravitational acceleration, hL is the total liquid holdup, hL,0 is the total liquid holdup below the loading region, and hL,Fl is the total liquid holdup at flooding. Billet and Schultes16 proceed in a similar way. The total liquid holdup below the loading point is calculated for ReL g 5 according to eq 4. Ch is a specific constant and is found for a structured ceramic packing (Impuls Ceramic Packing) to be approximately 1.9.16 At the flooding point, the total liquid holdup is calculated according to eq 5. Then, the gas velocity is used to interpolate (eq 6). The onset of loading is not predicted. !1=3 12 2 νL uL ageo hL, 0 ¼ g 0 !0:25 !0:1 1 2 2=3 u a u L geo L @0:85Ch A ð4Þ ageo νL g hL, Fl ¼ 2:2hL, 0 4636
νL ν H2 O
0:05 ð5Þ
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uG hL ¼ hL, 0 þ ðhL, Fl - hL, 0 Þ uG, Fl
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2
!13 ð6Þ
where νL is the kinematic viscosity of the liquid, νH2O is the kinematic viscosity of water, and Ch is a specific dimensionless constant for a packing type. Bornhuetter17 concentrates his work on liquid viscosities νL < -4 10 m/s and calculates the total liquid holdup without gas according to eq 7. For random packings with ageo < 200 m2/m3 and ε < 0.8, he predicts the total liquid holdup at the flooding point (eq 8) and interpolates (eq 9). !1=3 10:85 !0:095 0 2 νL 2 ageo 3 u a L geo @ A hL, 0 ¼ 1:56 ð7Þ g gε4 0 hL, Fl
uL σL ¼ 0:62ε@ uG, Fl ðFL - FG Þg
!1=2
11=4 ageo A ε
uG hL ¼ hL, 0 þ ðhL, Fl - hL, 0 Þ uG, Fl
ð8Þ
!7 ð9Þ
where ε is the outer porosity, FL is the density of the liquid, FG is the density of the gas, and σL is the surface tension of the liquid. Stichlmair18 predicts the total liquid holdup without gas flow according to eq 10 and uses the pressure drop for the adaption of the holdup values up to the flooding point (eq 11). !1=3 uL 2 ageo ð10Þ hL, 0 ¼ 0:555 gε4:65 2 Δp=L hL ¼ hL, 0 41 þ 20 FL g
!2 3 5
ð11Þ
where Δp is the pressure drop and L is the packing length. Engel19 has developed a correlation according to Stichlmair, but he fitted it to a much broader data range. He described the total liquid holdup as the sum of static and dynamic holdup (eq 12) and used dimensional analysis to determine the dimensionless number for the equations of the static and dynamic liquid holdup without gas flow (eqs 13 and 14). The exponents were fitted to the experimental data. He then adapted the dynamic holdup with the pressure drop (eq 15). hL ¼ hstat þ hdyn
hstat ¼ 0:033 exp -0:22
ageo 0:5 uL hdyn, 0 ¼ 3:6 g 0:5
!0:66
hdyn
ageo 1:5 νL g 0:5
!0:25
ð15Þ
The equivalent drop diameter is described for structured packings according to eq 17. sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 6σ L dL ¼ 0:8 ð17Þ ðFL - FG Þg The packing-specific friction constant ψ in eq 16 was calculated by comparing coefficients between the dry pressure drop equation of Engel and the quadratic term from the universal pressure drop correlation of Dietrich,1 which was developed for sponges of the same manufacturer as used in this project. The determination of the dynamic liquid holdup was then performed numerically for simplicity reasons, as dynamic holdup and wet pressure drop depend on each other. The Engel correlation also predicts flooding. The wet pressure drop at the flooding point is derived from the assumption of an infinitely increasing slope of the wet pressure drop with the gas velocity and calculated according to eqs 18 and 19. The dynamic holdup at the flooding point is then derived with eq 20, and the corresponding gas velocity is derived with eq 21. When flooding is reached, eqs 15 and 16 can no longer be solved numerically. ΔpFl ¼ L
FL g ½249hdyn, 0 ðX 0:5 - 60ε - 558hdyn, 0 - 103dL ageo Þ0:5 2988hdyn, 0 ð18Þ X ¼ 3600ε þ 186480hdyn, 0 ε þ 32280dL ageo ε þ 191844hdyn, 0 2 þ 95028dL ageo hdyn, 0 þ 10609dL 2 ageo 2 ð19Þ
!
2
ð13Þ
ageo 2 σL gFL
!2 3 5
where hstat is the static liquid holdup and hdyn is the dynamic liquid holdup. For this correlation type it is possible to use the measured or a predicted pressure drop. Engel uses the same type of equation for the prediction of the wet pressure drop as Stichlmair does. A detailed evaluation with the predicted pressure drop was therefore only performed for the correlation of Engel, as this was developed on a broader data range but based on the same assumptions. The dry pressure drop and wet pressure drop according to this correlation can be calculated following eq 16. The dynamic holdup value is set to zero for the calculation of the dry pressure drop. Δp ψ 6hdyn FG u G 2 ¼ þ ageo ð16Þ L 8 dL ðε - hdyn Þ4:65
ð12Þ gFL ageo 2 σL
Δp=L ¼ hdyn, 0 41 þ 36 FL g
hdyn, Fl
!0:1 uG, Fl 2 ¼ ð14Þ 4637
!2 3 Δp=L 5 ¼ hdyn, 0 41 þ 6 FL g
ð20Þ
ageo hdyn, Fl 4:65 8ε4:65 ΔpFl 1ð21Þ ψFG ageo L 6hdyn ε þ ageo dL dx.doi.org/10.1021/ie101514w |Ind. Eng. Chem. Res. 2011, 50, 4631–4640
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Figure 10. Parity plot for the static liquid holdup predicted by the correlation of Engel (eq 12) and experimentally determined values for one sponge element (black and gray filled symbols) and the sponge stacks (open symbols).
where ΔpFl is the pressure drop at flooding, hdyn,0 is the dynamic liquid holdup without gas load, hdyn,Fl is the dynamic liquid holdup at flooding, and X is an auxiliary quantity. The outer porosity is used in calculations for all correlations, which is determined with mercury intrusion porosimetry and is given in Table 1. 5.2. Static Liquid Holdup. The only correlation mentioned above that also predicts the static liquid holdup is the correlation of Engel.19 The other correlations neglect the static holdup or concentrate on the total holdup. A parity plot is used for the correlation evaluation and shown in Figure 10. It is obvious that the correlation will not fit the measured data very well, as Engel predicts a maximum value of 0.033 for the static holdup and as most of the values determined experimentally are significantly higher than 0.033. Engel mentions in his work that the values found for ceramic material do not fit his correlation properly and may exceed the predicted values significantly. He explains the fact with the porous and hydrophilic ceramic material, which leads to bigger values as liquid is absorbed inside the solid volume. Furthermore, he states that this amount of liquid can be neglected due to stagnation. This observation can only be confirmed partly, as the lowest values were found for the silicate sponges, which exhibit a better wettability than the sponges made of silicon-infiltrated silicon carbide but also a bigger porosity value. At the same time, the difference between nominal porosity and total porosity is even bigger than the static holdup value measured for those sponges. The absorption of liquid in the porous structure of the solid material can thus not be the only reason for higher holdup values. The amount of closed cells seems to be of the same importance, as those hinder the liquid drainage of the sponge structure. It can be seen in Figure 10 that the values for the sponge stacks (unfilled symbols) are only partly better represented than those of the single elements. 5.3. Total Liquid Holdup. The general agreement of measured and calculated values for the total liquid holdup of sponges is not expected to be very good, as the correlations used were not developed for structures exhibiting holdup values in the range of those observed for sponges. Nevertheless, a parity plot was generated for all correlations presented here with the data of all sponge types and liquid loads at 200 mm packing height. The
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proper representation of the experiments with the sponge with cone-shaped bottom is not possible for all correlations. They are therefore not considered in the parity plots. The results for the correlations of the first type together with the deviation interval of (40% are presented in Figure 11. Here it can be seen that the correlation of Mackowiak underestimates both the holdup value without gas flow and the increase of holdup with increasing gas flow. The correlation of Bornhuetter is able to describe the holdup value at low gas flows but is not able to describe the increase in holdup for increasing gas velocity. The correlation of Billet and Schultes both overestimates and underestimates the holdup values depending on the sponge type. The influence of increasing gas velocity is not represented well. These three correlations rely on the same principle concerning the prediction of holdup values with gas flow or above the loading point. The correlation of Stichlmair shown in Figure 12 slightly underestimates the holdup at low gas flow rates, but is able to predict the increase of holdup with increasing gas flow and after loading due to the use of the measured pressure drop. Therefore, a closer study of the correlation of Engel, which represents a further development of the Stichlmair correlation type, is performed. The parity plots for the Engel correlation using the measured pressure drop as well as the predicted pressure drop are also shown in Figure 12. It is clearly visible that the Engel correlation strongly overestimates the increase of the holdup with onset of loading up to impossible values above the value of the outer porosity ε when the experimentally determined pressure drop is used. When the calculated pressure drop is used, the increase of holdup is slightly underestimated. Nevertheless, the holdup at low gas velocities is represented properly. For this diagram it should be noted that due to the different gas loads measured and calculated for the onset of flooding only total holdup values up to the lower value of the measured or calculated flooding gas load values were considered. The gas load for the onset of flooding is mostly underestimated, but is represented properly in general, as can be seen in Figure 13. The flooding of the sponges at comparatively low gas velocities compared with established structured packings and packed beds agrees with the prediction of flooding as predicted by Engel. The fact that the static liquid holdup is underestimated while the total holdup does agree well with the results could be due to the fact that a part of the static liquid holdup measured is caused by poor drainage and will become part of the dynamic liquid holdup in operation. Thus the total liquid holdup is better represented than the static liquid holdup. In general, most established correlations are able to represent the total holdup values at low gas loads. The correlations of Billet and Schultes as well as Engel lead here to the best results. For the prediction of holdup values at higher gas velocity the correlations of Stichlmair and Engel based on the pressure drop are better suited. Nevertheless, the deviations between measured and predicted values are up to over 40%.
6. CONCLUSIONS Ceramic sponges qualify as column internals in gas-liquid countercurrent flow, although their operation range is limited compared with conventional structured packings or packed beds. Only thoroughly open-celled sponges exhibit a loading region before the onset of flooding. Stacking of sponge elements has an 4638
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Figure 11. Parity plots for the prediction of the total liquid holdup by the correlations of Billet and Schultes, Bornhuetter, and Mackowiak.
Figure 12. Parity plots for the prediction of the total liquid holdup by the correlations of Stichlmair (left) and Engel (middle) using the experimentally determined pressure drop for both correlations. Parity plot for the Engel correlation using the theoretically calculated pressure drop (right). Note the differing axis scaling.
Figure 13. Parity plot for the prediction of the flooding gas load by the Engel correlation.
influence on operation range and flooding, but no significant influence on the total liquid holdup value at relevant packing heights. The static liquid holdup exhibits a profile over the sponge stack with high holdup values at the bottom and low holdup values at the top. This indicates that drainage is the main
problem for limited operation ranges. A sponge with a coneshaped bottom can be used as drainage enhancer for enlarging the operation range. Thus at least twice the gas load can be realized without flooding of the sponges. The observed values for sponges are in general higher than those for state-of-the-art random and structured packings. The operation range is also restricted except for the configuration with drainage enhancer. Therefore the possible applications as column internals are special applications such as reactive rectification or highly corrosive systems. There the continuous and inert solid matrix could enhance heat transfer or reduce corrosion. Furthermore, the possibilities to coat the sponges with a catalytically active layer or to integrate the catalyst in the material of the sponge exhibit an additional advantage. The hydrodynamic behavior of sponges can be described by using established correlations for column internals, although the accuracy is not as good as for the column internals to which the correlations were adapted. The correlation of Engel proved to be the most suited correlation discussed for all gas load values and the test system air-water. The prediction of the flooding performance of this correlation is also in sufficient agreement with the experimental values. The limited operation range was thus confirmed. The results for the sponges with drainage enhancement could not be reproduced with most correlations. 4639
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’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT The authors thank the German Research Foundation (Deutsche Forschungsgemeinschaft) for the financial support of Research Unit 583 “Solid Sponges—Application of Monolithic Network Structures in Process Engineering” and Johann Jacob Letschert Sohn, Germany, for the provision of the silicate sponge prototypes. ’ NOMENCLATURE AC = column cross-sectional area, m2 BL = liquid load, m3/m2/h ageo = specific surface area of the structure, m2/m3 Ch = specific dimensionless constant for a packing type dL = equivalent drop diameter, m F = gas load (F = uGFG1/2), Pa0.5 g = gravitational acceleration, m/s2 hdyn = dynamic liquid holdup value, m3/m3 hL = total liquid holdup value, m3/m3 hstat = static liquid holdup value, m3/m3 L = packing length, m Δp = pressure drop, Pa ReL = Reynolds number of the liquid (ReL = uL/(ageoνL)) u = nominal velocity (u = V_ /AC), m/s V_ = volume flow rate, m3/s X = auxiliary quantity Greek Symbols
ε = outer porosity, m3/m3 ν = kinematic viscosity, m2/s F = density, kg/m3 σ = surface tension, N/m ψ = packing-specific dimensionless friction constant Subscripts
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0 = without gas flow Fl = at the flooding point G = gas L = liquid
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