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Multiplicity Behavior of Trickle Flow Liquid-Solid Mass Transfer Rita Joubert and Willie Nicol* Department of Chemical Engineering, UniVersity of Pretoria, Pretoria, South Africa
Dissolution as well as electrochemical techniques confirmed the existence of multiplicity. The commonly accepted upper multiplicity branch (achieved by Kan liquid prewetting) outperformed the lower branch (achieved by Levec prewetting) by as much as 1.6 times in Sherwood numbers. Although similar trends were observed for the two measurement techniques, the dissolution measurements were significantly lower than the electrochemical measurements. It was further shown that the multiplicity behavior of liquid-solid mass transfer is not linked solely to liquid hold-up and wetting efficiency variations, indicating major differences in flow structures between the multiplicity modes employed. In addition, a decrease in Sherwood numbers with bed depth was observed for both multiplicity modes. 1. Introduction Research on the complex hydrodynamic phenomena occurring in trickle bed reactors (TBR) has been prominent in chemical engineering literature for more than 50 years. Recently there has been a renewed interest in the multiplicity behavior of the low-interaction regime (trickle flow regime). Although the existence of multiplicity had been established as early as 1978,1 in-depth investigation of the causes and application possibilities of this phenomenon is relatively new to TBR literature. The ongoing development of nonintrusive visualization techniques has led to improved images of trickle flow structures.2-5 In a recent study by Van der Merwe and Nicol,6 high definition X-ray tomography results were used to analyze the flow structure differences between various hydrodynamic multiplicity modes. The study highlighted the importance of capillary effects in pore necks (small channels between larger pore openings) and proposed a mechanism where capillary blocking (or the absence thereof) in pore necks was used to account for multiplicity. Apart from a fundamental understanding of multiplicity, there has also been interest in the application of multiplicity in TBRs operating at industrially relevant conditions. Van der Merwe et al.7 showed major productivity differences between the multiplicity modes for the hydrogenation of R-methylstyrene in a bench-scale reactor and contemplated the potential impact on commercial reactors. In this study, reverse trends were observed for gasand liquid-limited scenarios and it was speculated that the difference in the multiplicity behavior of gas-liquid mass transfer and liquid-solid mass transfer could account for the counterintuitive results. In the classical studies, multiplicity was typically represented as pressure drop and liquid hold-up hysteresis loops.1,8-12 These loops did not always represent the extreme cases (or boundaries) of the multiplicity envelope, implying that lower or higher values of the specific hydrodynamic parameter (e.g., pressure drop) might be possible at the specific gas/liquid velocities. The focus was therefore shifted to rather define limiting cases that are characterized by a preconditioning or prewetting procedure.11 Unfortunately no single procedure defines the upper or lower extremes of multiplicity for all the hydrodynamic variables. As a good approximation, the Levec mode11 is generally used to define the lower boundary (nonwetted beds are mostly excluded in multiplicity studies) whereas the Kan liquid mode11 is used for the upper boundary. * To whom correspondence should be addressed.
Today multiplicity data are available on gas-liquid mass transfer,11-13 external catalyst wetting,14 and other nondirect hydrodynamic parameters such as liquid maldistribution.15 Information about liquid-solid mass transfer (LSMT) is scarce, and only the limited study by Sims et al.16 reports a hysteresis loop on liquid-solid mass transfer using an unconventional packing. The results from Sims et al.16 are in direct conflict with the suggestion by Van der Merwe et al.7 that LSMT in the Levec prewetting mode might exceed that of the Kan liquid mode owing to the higher average interstitial velocity in the Levec bed. The need for a thorough study on LSMT multiplicity under trickle flow conditions is therefore evident. Furthermore, one would like to perform the measurements on a system where the other hydrodynamic parameters have been well quantified in order to investigate the interdependencies of the different hydrodynamic parameters. This study quantifies the differences in LSMT for the Levec and Kan liquid prewetting modes, using an aqueous-air-3 mm glass bead system. Both the electrochemical and dissolution techniques were employed, though a single packing element electrode as well as a multiple packing electrode was used for the electrochemical method. Previously published data on liquid hold-up and wetting efficiency on a similar system were used to analyze the LSMT data. In addition, the influence of column height on LSMT was also investigated. 2. Experimental Section A diagram of the experimental apparatus is shown in Figure 1. The 3 mm glass bead packing has a height of 800 mm (id 63 mm). A detailed description of the system appears in the article by Loudon et al.11 All experiments were performed with only the Levec or Kan liquid prewetting procedures. In Levec prewetting the column is flooded and left to drain for 20 min, and then liquid flow is then reintroduced into the column. Kan liquid prewetting requires operation in the pulsing regime for 15 s, after which the liquid flow is set to the desired operating flow rate. A detailed description of the prewetting procedures is given in Loudon et al.11 After preconditioning, the liquid flow was set at the lowest value and then incrementally increased. The dissolution experiments were carried out at liquid velocities of 2, 3, 4, 5, and 8 mm/s, whereas the electrochemical experiments were carried out at 2, 3, 4, and 5 mm/s (8 mm/s was not feasible as this would have been at the
10.1021/ie9002552 CCC: $40.75 2009 American Chemical Society Published on Web 08/17/2009
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Figure 1. Experimental setup. Table 1. Physicochemical Properties of Electrolytic Solution property
value
units
density viscosity diffusion coefficient
1200 1.02 × 10-3 5.50 × 10-9
kg/m3 poise (P) m2/s
trickle-pulse transition boundary). All runs were done at 20 °C, atmospheric pressure, and a gas flow rate of 30 mm/s. Three different methods were used to determine LSMT coefficients. Two electrochemical techniques (method A using a single packing electrode and method B a multiple packing electrode) and one dissolution technique (method C). The measurement at each liquid velocity was repeated three times for each of the three methods employed. Repacking was performed before each repeat experiment. All the repeat runs had a variation of less than 2%, indicating excellent repeatability for each of the methods employed. The method described by Sims et al.16 was followed for the electrochemical technique. Distilled water was used as the solvent, and a mixture of 0.003 M potassium ferricyanide and 0.02 M potassium ferrocyanide was used as the electrolyte. Sodium hydroxide (1 M) was used as a current carrier. The physicochemical properties of the electrolytic solution are given in Table 1. The cathode consisted of a single 3 mm spherical nickel particle soldered to an isolated wire (system A) or a group of the nickel spheres (4 cm in axial length) in close contact (system B), while the supporting sieve acted as the anode. The placement of the electrodes is shown in Figure 2. A voltage of 1000 mV was applied (determined to be the midpoint of the diffusion plateau). The measured current was converted to the LSMT coefficient by means of eq 1: Ilim ) FklsAec
(1)
The method described by Specchia et al.18 was used for the dissolution technique. The 10 cm active section, glass spheres coated with benzoic acid, was placed in the middle of the column (see Figure 2). Steady state in the effluent concentration was ensured, and a plug flow assumption was used to calculate the LSMT coefficient (see eq 2). The physicochemical properties of the effluent are given in Table 2. klsa )
[
Ul cs - cf ash cs - ce
]
(2)
In order to compare the results from the single and multiple packing electrodes, additional experiments were performed where smaller increments in liquid velocity were used within the defined range. Only the Levec mode was used for the comparative study. The results can be seen in the form of a parity plot (see Figure 3). As all data points lie well within a 5% deviation, only the measurements taken with the single electrode (system A) are used in the rest of the discussion in this article. 3. Results and Discussion It is clear from Figure 4 that the electrochemical LSMT measurements are approximately double the magnitude of the dissolution measurements. Apart from the difference in magnitude, the multiplicity bounds exhibit similar trends for both measuring techniques. The Sherwood numbers obtained in the Kan liquid operating mode were as much as 1.6 times more than the corresponding Levec mode number, confirming the trend found by Sims.16 Figure 5 clearly indicates that the measurements fall within the lower range of accepted trickle flow correlations. There is
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Figure 2. Placement of single packing electrodes and multiple packing electrode for electrochemical technique (systems A and B) and active section for the dissolution technique (system C). Table 2. Physicochemical Properties of Effluent in Dissolution Technique property
value
units
density viscosity diffusion coefficient
1000 1.0 × 10-3 1.0 × 10-9
kg/m3 poise (P) m2/s
good agreement with the correlation by Mochizuki and Matsui19 developed at zero gas flow. It is well established that both liquid hold-up and external wetting efficiency exhibit multiplicity11,15 behavior. Since liquid hold-up is related to the average interstitial velocity and wetting efficiency to the area available for liquid-solid interaction, both variables will influence overall LSMT. In order to quantify the effect of these two parameters on LSMT, the results from prior studies on a similar system11,14 were used (see Table 3). Figure
6 represents the specific mass transfer coefficient, calculated for the estimated wetted exchange area, as a function of the average interstitial velocity. The Levec mode interstitial velocities are higher than those for the Kan liquid mode, due to the smaller liquid hold-up. The mode differences in Figure 6 suggest that flow structure plays an important role in LSMT. It is well accepted that multiplicity is associated with different liquid morphologies4,5 and it can be argued that higher liquid stagnancy (or more stagnant or slower flowing zones) in the Levec mode causes poor refresh rates and therefore the lower Sherwood numbers. The capillary gate theory posed by Van der Merwe and Nicol6 could be used to elaborate on the speculative argument, but the focus should rather be on the fact that the total external liquid hold-up and wetting differences cannot account for the LSMT multiplicity behavior.
Figure 3. Parity plot of mass transfer coefficients measured with single and multiple packing electrodes. (Only the Levec mode was employed.)
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Figure 4. Multiplicity behavior of Sherwood numbers for both the dissolution and electrochemical techniques.
Figure 5. Comparison of experimental results with accepted trickle flow correlations. Table 3. Wetting Efficiency and Total External Liquid Hold-up Measurementsa wetting efficiency
total liquid hold-up
superficial liquid velocity (mm/s)
Levec
Kan liquid
Levec
Kan liquid
2 3 4 5
0.58 0.62 0.64 0.70
0.71 0.73 0.76 0.81
0.060 0.085 0.097 0.106
0.123 0.147 0.153 0.161
a
those taken at the bottom of the bed. This is most likely also linked to differences in liquid flow morphology.
As taken from Van Houwelingen et al.14 and Loudon et al.11
Finally, a gradual decrease in Sherwood number, as a function of bed depth, was observed (Figure 7). This coincides with the findings by Trivizadakis and Karabelas17 that the mass transfer coefficient decreases down the bed. The measurements taken close to the top of the column were up to 1.4 times higher than
4. Conclusions As expected, the study confirms the existence of multiplicity in LSMT under trickle flow conditions. The conventional upper boundary of the multiplicity envelope represented by the Kan liquid prewetting mode also proved to be the upper boundary for LSMT when compared to the lower boundary of the Levec mode. The Kan liquid mode has Sherwood numbers approximately 1.6 times the magnitude of the corresponding Levec mode numbers. The Sherwood numbers obtained from the dissolution method are almost half of the corresponding Sherwood numbers obtained from the electrochemical method, although the multiplicity trends are similar. Compared to
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Figure 6. Specific mass transfer coefficient (based on estimated wetted area) as a function of average interstitial velocity.
Figure 7. Sherwood number as a function of bed depth (using the electrochemical technique and single packing electrodes).
accepted trickle flow LSMT correlations, the results tend to be on the lower side of the spectrum. By use of liquid hold-up and external wetting data from a prior study on a similar system, it was shown that the multiplicity behavior of LSMT is not linked solely to the multiplicity behavior of these variables. When correcting for the wetted external area on the packing, the specific mass transfer coefficient (in meters per second) is still higher for the Kan liquid mode, despite the lower average interstitial velocities in this mode. This indicates a major difference in flow structure and it can be argued that higher liquid stagnancy (or more stagnant or slower flowing zones) in the Levec mode causes poor refresh rates and therefore the lower Sherwood numbers. This argument concurs with the capillary gate theory posited by Van der Merwe and Nicol,6 where blocked openings (or pore necks) cause some pores to be filled with liquid without any flow passing through the pore. The work also confirms a gradual decrease in the Sherwood number as a function of bed depth, accentuating the importance of hydrodynamic changes as flow progress through a TBR. The mentioned decrease occurred for both the Kan liquid and the Levec modes. Finally, it was shown that, when used properly, a single packing element electrode gives readings very similar to those
for a multiple packing element electrode. Despite the repacking of the bed, the LSMT measured on both electrodes remained almost the same. Nomenclature a ) effective area for mass transfer (m2/m3) as ) total external surface area of particles per unit volume of packing (m-1) av ) geometrical area per unit of bed volume, 6(1 - ε)/dp (m-1) Ae ) electrode area (cm2) c ) concentration (mol/cm3) cs ) solubility of benzoic acid (g/L) D ) diffusivity (m2/s) dp ) catalyst particle diameter (m) F ) Faraday constant (C/mol) h ) packing height (m) H ) total external liquid hold-up (m3/m3) Ilim ) limiting current (A) kls ) solid-liquid mass transfer coefficient (m/s) Ul ) volumetric liquid flow rate (m3/s) uinterstitial ) interstitial velocity (mm/s) Vl ) superficial liquid velocity (m/s) Rel ) liquid Reynolds number, FldpVl/µl (unitless)
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Sc ) Schmidt number, υ/D Sh ) Sherwood number, klsdp/D (unitless) ε ) void fraction in catalyst bed φ ) fractional wetting of packing or electrode, as/av F ) density (kg/m3) µ ) dynamic viscosity (Pa · s) υ ) kinematic viscosity (m2/s)
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ReceiVed for reView February 18, 2009 ReVised manuscript receiVed July 14, 2009 Accepted August 1, 2009 IE9002552
