Dynamic Liquid Saturation in a Trickle Bed Reactor Involving

Mar 9, 2009 - Dynamic liquid saturation is an important hydrodynamic parameter that ... dynamic liquid saturation, by using Newtonian liquid phase, in...
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Ind. Eng. Chem. Res. 2009, 48, 3341–3350

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Dynamic Liquid Saturation in a Trickle Bed Reactor Involving Newtonian/ non-Newtonian Liquid Phase Ajay Bansal,*,† R. K. Wanchoo,‡ and S. K. Sharma‡ Department of Chemical Engineering, National Institute of Technology, Jalandhar, India 144011, and Department of Chemical Engineering and Technology, Panjab UniVersity, Chandigarh, India 160014

Dynamic liquid saturation is an important hydrodynamic parameter that affects the performance of a trickle bed reactor. The parameters that affect the dynamic liquid saturation, by using Newtonian liquid phase, include gas and liquid flow rates, surface tension and viscosity of the liquid phase, and bed configurations. Additional rheological parameters affecting dynamic liquid saturation, in case of non-Newtonian viscoinelastic liquids, are observed to be flow consistency index K and flow behavior index n. The effect of viscoelasticity, in case of non-Newtonian viscoelastic fluids, was investigated in terms of Weissenberg number. A set of 20 correlations were selected from the literature to see the applicability of these correlations under varied conditions of bed configurations and liquid-phase properties as studied in the present investigation. It was observed that the correlations are valid only for a restricted range of parameters and none of the correlations seem to be applicable over the entire range of parameters as investigated in the present study. On the basis of the experimental data obtained, correlations are first developed for Newtonian liquids. These correlations could reproduce the literature data satisfactorily to (20%. Further, the correlations developed are extended to predict dynamic liquid saturation for viscoinelastic and viscoelastic liquid phases. 1. Introduction With the continuous evolution of the products relying on TBR technology to meet concomitantly environmental regulations and economical constraints, any slight modification in the design or performance of these reactors can result into substantial benefits. According to Trambouze,1 the annual processing capacity of TBRs for petroleum sectors alone was estimated at 1.6 billion metric tons. With the increasing market needs for light oil products such as middle distillates and decreasing demands for heavy cuts, the refiners have to keep improving their processing units for upgrading heavy oil and feedstock (Trambouze).2 This stimulates continued research efforts aimed at improving TBR operation and performance. Any improvement in the understanding of physio-chemical phenomena taking place within a TBR may be vital for the accomplishment of better product quality, cost reduction, and environmentally sustainable technologies. Process design of a TBR is based on both hydrodynamic and interfacial parameters. One of the main hydrodynamic parameters, the liquid hold-up or liquid saturation, affects the reactor performance because it is closely interlinked with two-phase pressure drop, reaction conversion, selectivity, and power consumption. Extensive work has been carried out on liquid saturation, and a detailed literature review has been given by Saroha and Nigam.3 Most of the literature studies correspond to air-water system. Sai and Varma4 studied dynamic and total liquid saturation for different packings. They also attempted to correlate the data for viscoinelastic non-Newtonian liquid phase by using flow consistency index. A few investigators (Xiao et al.5 and Iliuta et al.6) have made some experimental studies with viscoinelastic non-Newtonian aqueous CMC solutions, whereas * To whom correspondence should be addressed.Tel.: +91 181 2690301, +91 181 2690302, +91 181 2690453, and +91 181 2690603Ext (399). Fax:+91 181 2690320, +91 181 2690932. E-mail: [email protected]. † National Institute of Technology. ‡ Panjab University.

many chemical and biochemical applications are expected to involve the liquid phases with non-Newtonian behavior which may not always be characterized by viscoinelastic character of the aqueous CMC solutions. Non-Newtonian liquids may show considerable yield stress (and/or viscoelastic character). No experimental studies involving these kinds of liquid phases are reported in the literature so far (Iliuta and Larachi).7 Therefore, it seems worthwhile to have a systematic study elucidating the effect of bed configurations and liquid-phase properties ranging from simple water as fluids to rheologically complex viscoinelastic and viscoelastic liquids on dynamic liquid saturation. 2. Experimental Section Experiments were carried out on a 7.4 cm diameter glass column, packed to a height of 50 cm. Entry for gas and liquid phases was provided at the top of the column. The detailed description of the experimental set up is given elsewhere (Bansal et al.).8 The dynamic liquid saturation was measured when liquid and gas phases flowed concurrently downward over a bed of packing and by allowing the liquid to drain out for 30 min. An average of the three repeated runs, under identical conditions, was taken to minimize the experimental error. Different liquid phases, as listed in Table 1, ranging from simple Newtonian to viscoelastic non-Newtonian fluids were investigated in the present study. Different bed configurations corresponding to various packings, as listed in Table 2, were used. 3. Results and Discussion On the basis of experimental observations, the results, categorized on the basis of the nature of the fluid handled in the TBR, are discussed below. 3.1. Newtonian Liquid Phase. 3.1.1. Effect of Liquid Flow Rate. The void space in the TBR is shared by the two phases flowing downward. When liquid flow rates are small, more space is occupied by the gas, and if liquid flow rate is increased, the liquid will occupy a higher volume fraction of the voids available, which in turn should be reflected as

10.1021/ie801399u CCC: $40.75  2009 American Chemical Society Published on Web 03/09/2009

3342 Ind. Eng. Chem. Res., Vol. 48, No. 7, 2009 Table 1. Properties of Liquid Phases Newtonian Fluids FL, kg m-3

liquid phase tap water 6 ppm surfactant (sodium lauryl sulfate) 12 ppm surfactant (sodium lauryl sulfate) 60% glycerol (w/w) 77% glycerol (w/w)

µL, Pa s

σL, mN m-1

T, °C

70.00 59.10 55.00 64.35 63.24

22.0 16.0 16.0 32.0 32.0

-4

9.60 × 10 11.13 × 10-4 11.13 × 10-4 5.93 × 10-3 27.04 × 10-3

997.6 999.5 999.5 1148.0 1192.7

Non-Newtonian (Viscoinelastic) Fluids liquid phase

FL, kg m-3

K, Pa sn

n

σL, mN m-1

T, °C

CMC 0.15% CMC 0.30% CMC 0.40% PEO 0.80% PEO 1.6%

997.6 997.8 998.5 998.1 1000.5

0.00252 0.01633 0.34145 0.00230 0.01360

1.0000 0.9157 0.8909 1.0000 1.0000

62.72 59.40 56.89 56.91 54.99

30.0 30.0 30.0 29.0 30.5

a

Non-Newtonian (Viscoelastic) Fluids liquid phaseb PAA PAA PAA PAA PAA PAA a

0.04% (tap water) 0.08% (tap water) 0.12% (tap water) 0.05% (distilled water) 0.075% (distilled water) 0.10% (distilled water)

FL, kg m-3

K, Pa sn

n

K1, Pa sm

m

σL, mN m-1

T, °C

λt, s

1000.7 1000.6 1000.9 1000.1 1000.20 1000.7

0.0340 0.0640 0.141 0.0776 0.1833 0.2387

0.673 0.644 0.564 0.601 0.502 0.466

0.0319 0.0699 0.2346 0.1860 0.5700 0.8250

0.8265 0.8131 0.7422 0.7879 0.6888 0.6513

67.67 67.04 65.85 68.00 66.70 66.09

18.0 17.0 15.0 23.0 23.0 23.0

1.40 2.60 6.47 14.90 19.54 23.09

Molecular weight of CMC ) 1 × 105. Molecular weight of PEO ) 3 × 105. b Molecular weight of PAA ) 8.7 × 106.

Table 2. Types of Packing Used type of packing

packing size, mm

dp, mm

E1/E2/ε

sphericity, φs

glass beads-I glass beads-II ZnO catalyst pellets, d × h solid cylinders, d × h raschig rings di × do × h

3.337 14.840 4.522 × 7.677 6.083 × 27.047 6.336 × 9.130 × 10.274

3.337 14.840 5.302 11.450 3.690

225/1.58/0.376 350/0.419/0.441 200/2.29/0.406 245/1.50/0.479 242/3.20/0.686

1.000 1.000 0.850 0.716 0.423

enhancement in dynamic liquid saturation. However, there should be an upper limit to this increase in βd, because the void space is finite and βd cannot be greater than unity. Hence, βd is expected to approach asymptotically to a maximum value but to be less than one. This maximum value is expected to be dependent on fluid and bed properties. To study the effect of liquid flow rates, the dynamic liquid saturation, βd, is plotted against liquid flow rates at different gas flow rates corresponding to different packings (Figures 1, 2, 3, 4, and 5). It is observed that with an increase in liquid flow rate, the dynamic liquid saturation increased for all the packings. Corresponding to air-water system on glass beads-I (ε ) 0.376), it is observed that the dynamic liquid saturation rises gradually at lower liquid flow rates and has a tendency to move asymptotically at higher

liquid flow rates. Similar observations were recorded for catalyst pellets (ε ) 0.406). For other packings, that is solid cylinders, glass beads-II, and Raschig rings (ε ) 0.479, 0.441, and 0.686, respectively), the dynamic liquid saturation was observed to be following a gradual rise. This is because these packings have comparatively large bed porosities which allow more liquid to be accommodated in the voids. A similar effect of liquid flow rate on liquid saturation has been observed by Charpentier and Favier;9 Goto and Smith,10 Morsi et al.,11 Rao et al.,12 Levec et al.,13 Sai and Varma,4 and Iliuta et al.6 It is important to mention that no abrupt change in dynamic liquid saturation βd is observed corresponding to the shift of flow regime from low to high interaction (unlike the two-phase pressure drop, discussed elsewhere Bansal et al.)14

Figure 1. Effect of gas flow rate on dynamic liquid saturation (glass beads-I).

Figure 2. Effect of gas flow rate on dynamic liquid saturation (catalyst pellets).

Ind. Eng. Chem. Res., Vol. 48, No. 7, 2009 3343

Figure 6. Effect of bed porosity on dynamic liquid saturation. Figure 3. Effect of gas flow rate on dynamic liquid saturation (solid cylinders).

Figure 4. Effect of gas flow rate on dynamic liquid saturation (glass beads II).

Figure 5. Effect of gas flow rate on dynamic liquid saturation (raschig rings).

3.1.2. Effect of Gas Flow Rate. As discussed earlier, the void space is shared by both liquid and gas phases. Therefore, an increase in gas flow rate should result in a decrease in the dynamic liquid saturation. However, different correlations available in the literature do not always consider the effect of gas flow rate on the dynamic liquid saturation. Many investigators have proposed correlations independent of gas flow rate (Otake and Okada,15 Buchanan,16 Hochman and Effron,17 Satterfield and Way,18 Wijffels et al.,19 Charpentier and Favier,9 Goto and Smith,10 Colombo et al.,20 Specchia and Baldi,21 Morsi et al.,11 and Matsura et al.22). On the other hand, many investigators have observed that with an increase in gas flow rate, the dynamic liquid saturation decreases. These authors deemed it necessary to take into account the gas flow rate while proposing correlations for dynamic liquid saturation (Turpin and

Huntington,23 Clements and Schmidt,24 Blok et al.,25 Rao et al.,12 Sai and Varma,4 Burghardt et al.,26 and Xiao et al.5). The experimental results on air-water system corresponding to different packings are shown in Figures 1, 2, 3, 4, and 5. A typical behavior of the effect of gas flow rate is represented by air-water system on glass beads-I (Figure 1). Corresponding to an increase in gas flow rate, a decrease in dynamic liquid saturation is observed. Corresponding to catalyst pellets (ε ) 0.406, φs ) 0.850; Figure 2), the effect of gas flow rate is observed to be less prominent at low liquid flow rates; but for high liquid rates, an increase in gas flow caused a significant decrease in dynamic liquid saturation. Observations corresponding to other packings were somewhat different. The packings of solid cylinders (ε ) 0.479, φs ) 0.716), glass beads-II (ε ) 0.441, φs ) 1.000), and Raschig rings (ε ) 0.686, φs ) 0.423) showed little effect of the gas flow rate on dynamic liquid saturation. It is felt that bed porosity is an important parameter, and probably, there exists some critical value of porosity (between 0.406 and 0.441) below which saturation is affected by gas flow rate and above which the effect of gas flow rate is negligible. Our observations in respect of the effect of effect of gas flow rate are in agreement with that of Goto and Smith,10 who observed that there exists a critical particle size at which hold-up change takes place, and it ranges somewhere between 0.3 and 0.40 cm (0.371 < ε < 0.441). The present observations also indicate that the critical bed porosity is in the range 0.406 < ε < 0.441. 3.1.3. Effect of Bed Porosity. With the foregoing discussion on effect of gas flow rate, some aspects of bed porosity are already discussed implicitly. The effect of bed porosity is rather controversial in the literature; Sai and Varma4 have reported that an increase in effective particle diameter or bed voidage increases the liquid hold-up. On the contrary, Sato et al.27 and Clements and Schmidt24 report that larger particles (larger voidage) resulted in a lower liquid hold-up. To elucidate the effect of bed porosity, ε, two different packings, viz. glass beads-I and glass beads-II, having widely different diameters of 3.337 and 14.840 mm, respectively, with bed porosities of 0.376 and 0.441, respectively, were chosen. The dynamic liquid saturations corresponding to these packings under identical conditions are shown in Figure 6. It is observed that largerdiameter particles with larger bed porosity resulted into smaller dynamic liquid saturations. It appears that higher saturation corresponding to smaller particles, that is glass beads-I, could be due to larger specific area of 1176 m2/m3 of the packed bed, compared to 280 m2/m3 of the packed bed for the larger particles, that is glass beads-II. A large surface area is expected to provide more contact points for liquid to adhere. The observation is in agreement with the findings of Sato et al.,27 Blok et al.,25 and Rao et al.12

3344 Ind. Eng. Chem. Res., Vol. 48, No. 7, 2009

Figure 7. Effect of bed configuration on dynamic liquid saturation.

Figure 9. Effect of viscosity on dynamic liquid saturation.

Figure 8. Effect of surface tension on dynamic liquid saturation.

Figure 10. Effect of rheological parameters K and n on dynamic liquid saturation.

3.1.4. Effect of Particle Sphericity. The dynamic liquid saturation as observed corresponding to different packings is plotted in Figure 7. It is noted that the dynamic liquid saturation corresponding to identical conditions is maximum for glass beads-I (dp ) 3.337 mm, ε ) 0.376, φs ) 1.000) followed by catalyst pellets (dp ) 5.302 mm, ε ) 0.406, φs ) 0.850), and then, the rest of the packings, that is, glass beads-II (dp ) 14.840 mm, ε ) 0.441, φs ) 1.000), solid cylinders (dp )11.450 mm, ε ) 0.479, φs ) 0.716), and Raschig rings (dp )3.690 mm, ε ) 0.686, φs ) 0.423). The role of bed porosity appears to dominate, and no significant observations could be made on the effect of the particle sphericity. 3.1.5. Effect of Surface Tension. Dynamic liquid saturations corresponding to low surface tension solutions of 6 ppm (σL ) 59.1 m Nm-1) and 12 ppm surfactant (σL ) 55.0 m Nm-1) in water are shown in Figure 8. The solutions are foaming in character in high-interaction regime, but no foaming was noticed in the low-interaction regime. At gas mass velocity, G ) 0.042 kg m-2 s-1, the critical value of liquid flow at transition was as 4.924 and 4.885 kg m-2 s-1 for 6 ppm and 12 ppm solutions, respectively. Below these values of L, that is, in trickle or lowinteraction regime, a decrease in surface tension is found to give rise to a higher dynamic liquid saturation. Similar observations are also reported by Morsi et al.,11 Sai and Varma,4 and Ellman et al.28 This is probably due to better spreading of liquid with lower surface tension (Adamson).29 There was a reversal in the effect of surface tension for foaming solutions when the regime changed (Figure 8) from low- to high-interaction regime. This has led to a dip in the curve at the onset of transition. Foaming solutions have been found to behave differently in the literature as well (Larkins et al.,30 Midoux et al.,31 and Sai and Varma4), need separate treatment in terms of correlation development, and have not been included while correlating the data in the following sections.

3.1.6. Effect of Viscosity. Viscosity is a measure of flow resistance: the higher the viscosity of a fluid, the higher the resistance experienced in its flow. It means that under identical conditions, high-viscosity liquid will take more time to flow through a flow channel than low-viscous solution. Likewise, the residence time of a fluid with higher viscosity is expected to be higher. Therefore, a highly viscous solution will lead to more liquid retention inside the flow channel (packed bed), which is nothing but the liquid saturation. Dynamic liquid saturation corresponding to tap water, 60% glycerol, and 77% glycerol having viscosities of 7.53 × 10-4, 5.93 × 10-3 and 27.0 × 10-3 Pa s, respectively, are plotted in Figure 9. At the same liquid flow rate, the dynamic liquid saturation corresponding to tap water with least viscosity (µL ) 7.53 × 10-4 Pa s) is noticed to be the lowest. However, 77% glycerol with maximum viscosity of 27.0 × 10-3 Pa s resulted into the highest dynamic liquid saturation. The observations are in agreement with those of Morsi et al.,11 Clements and Schmidt,24 and Sai and Varma.4 3.2. Non-Newtonian Liquid Phase. 3.2.1. Viscoinelastic Liquid Phase. Effect of Rheological Parameters K and n. The viscoinelastic fluids investigated in the present study were described by Ostwald-de Waele power law model, τ ) K˙γn, whereas Newtonian fluids are described by τ ) µLγ. Therefore, the effect of K is expected to be similar to that of µL. But with an increase in K, a simultaneous decrease in n is expected. Therefore, only the cumulative effect of parameters K and n could be elucidated. Two concentrations of CMC, 0.15 and 0.40%, are plotted in Figure 10. It was observed that the dynamic liquid saturation was maximum for 0.40% CMC (K ) 3.41 × 10-1 Pa sn, n ) 0.891) followed by 0.15% CMC (K ) 2.52 × 10-3 Pa sn, n ) 1.000) and water (µL ) 7.53 × 10-3 Pa sn, n ) 1.000). Therefore, it may be concluded that, with anincrease in flow consistency index (accompanied by a

Ind. Eng. Chem. Res., Vol. 48, No. 7, 2009 3345 31

Figure 11. Effect of viscoelasticity on dynamic liquid saturation.

decrease in flow behavior index, n), the dynamic liquid saturation increases. This observation is in agreement with those of Sai and Varma4 and Iliuta et al.6 3.2.2. Viscoelastic Liquid Phase. Effect of Viscoelasticity. Viscoelastic fluids have the tendency to behave like solids. This solid-like character is imparted to fluids by the force acting in a direction normal to the shear force. For the flow of viscoelastic fluids past solid spheres, the normal force is expected to favor the dynamic liquid saturation. The dynamic liquid saturation corresponding to aqueous 0.40% CMC solution and aqueous 0.075% PAA are shown in Figure 11. Aqueous 0.40% CMC solution is a viscoinelastic fluid (λt ≈ 0 s) with K ) 3.41 × 10-1 Pa sn and n ) 0.891, whereas 0.075% PAA solution is viscoelastic (λt ) 19.54 s) with K ) 1.83 × 10-1 Pa sn and n ) 0.502. The value of K corresponding to 0.40% CMC is higher, and because the effect of K is already known, 0.40% CMC should have resulted in higher dynamic liquid saturations owing to higher values of K, but experimental observations indicate that the dynamic liquid saturation was higher for 0.075% PAA. This could be due to significant viscoelasticity shown by PAA solution (λt ) 19.54 s). Similar results were also obtained for solutions of 0.40% CMC and 0.10% PAA (λt ) 23.09 s). 4. Comparison with Literature Correlations A large number of correlations are available in the literature, each of them predicting the data of the investigating authors reasonably, but the data of others is usually not described properly. This could be because the correlations are mainly applicable in the conditions for which they are originally developed. Hardly any of the correlations seem to be applicable over a wide range of bed characteristics and fluid-phase properties (ranging from simple water-like Newtonian fluids to rheologically complex viscoelastic fluids) as investigated in the present study. A set of the 20 most widely used correlations were selected for the comparison with the present data and to see their applicability under varying fluid and bed characteristics. For the ease of comparison, the performances (in terms of MRQE) of various literature correlations and models are given in Table 3. The results are discussed in different sections in Table 3: Table 3A, air-water system (different packings, Table 3A), different Newtonian liquid phases (Table 3B), and nonNewtonian (viscoinelastic, Table 3C, and viscoelastic, Table 3D) liquid phases. For air-water systems on different packings (Table 3A), it was observed that various correlations predicted results reasonably well for some particular type of packing but resulted in high MRQEs for other packings. The correlations obtained by Larkins et al.,30 Charpentier et al.,9 Sato et al.,27 Midoux et

al., Hochman and Effron,17 Wijffels et al.,19 Otake and Okada,15 Yang et al.,31 Blok et al.,25 Ellman et al.,28 and Fu et al.33 were found to result in MRQEs greater than 25% and, in certain cases, as high as 200%. The correlation obtained by Charpentier at al.,9 which had MRQE ) 0.343 for glass beadsI, lead to MRQE as high as 3.851 for glass beads-II. The correlation obtained by Rao et al.12 could predict the dynamic saturation for catalyst pellets with MRQE ) 0.175, but it was high for Raschig rings (MRQE ) 0.987). Similarly, the correlations obtained by Sai and Varma4 and Larachi et al.34 could predict results well for glass beads-I with MRQEs of 0.128 and 0.199, respectively, but yielded very high MRQEs (>1) for Raschig rings. The predictions corresponding to the correlation obtained by Specchia and Baldi21 were reasonable for most of the packing with MRQE < 25% but predicted the data on catalyst pellets with MRQE > 25%. Table 3B contains the statistical comparison for different Newtonian liquid phases. Correlations obtained by Larkins et al.,30 Charpentier at al.,9 Hochman and Effron,17 Wijffels et al.,19 Otake and Okada,15 Yang et al.,32 and Blok et al.25 predicted the present data with MRQEs > 30%. In certain cases, the correlation was as high as 100%. The correlation obtained by Specchia and Baldi21 responded well to the high-viscosity solutions of 60 and 77% glycerol but lead to MRQE of 35.3% for low-surface-tension solution of 12 ppm surfactant in water. The correlation obtained by Larachi et al.,34 which could predict results well for air-water systems, lead to high errors for highviscous (MRQE > 40%) and low-surface-tension solutions (MRQE > 25%). The correlation obtained by Ellman et al.28 could predict results well for low-surface-tension solutions but could not predict results satisfactorily for high-viscous solutions (MRQE ) 0.607 and 0.729, respectively). The correlation obtained by Fu et al.,33 which lead to high MRQE for air-water systems, was able to predict well the data on highly viscous solutions with MRQEs of 0.193 and 0.150 for 60 and 77% glycerol, respectively. The MRQEs corresponding to viscoinelastic non-Newtonian liquid phases are presented in Table 3C. The correlations obtained by Turpin and Huntington,23 Sato et al.,27 Midoux et al.,31 Morsi et al.,35 Rao et al.,12 Hochman and Effron,17 Wijffels et al.,19 Clements and Schmidt,24 Xiao et al.,5 Larachi et al.,34 and Fu et al.33 are observed to show an increasing trend in MRQE with an increase in concentrations of CMC and PEO, whereas the correlations obtained by Larkins et al.30 and Charpentier et al.9 were observed to give high errors at low concentrations of CMC and PEO; but, as the concentration increased, the correlations appear to predict results better with lower MRQE. The MRQEs corresponding to viscoelastic liquid phases are presented in Table 3D. It is worth mentioning that no studies in the literature include the viscoelastic systems for the correlation development, and consequently, the viscoelasticity is not taken into account. However, for 0.05% PAA solution, the correlation obtained by Larkins et al.30 appears to predict results reasonably. Most of the correlations show an increase in MRQE with an increase in concentration of PAA, that is, an increase in the Weissenberg number. The MRQEs corresponding to the Hochman and Effron27 correlation is >100%. 5. Correlation for Dynamic Liquid Saturation, βd 5.1. Newtonian Liquid Phase. The experimental data for dynamic liquid saturation corresponding to different bed geometries involving air and water as the two phases were initially considered. By using an approach similar to the one

3346 Ind. Eng. Chem. Res., Vol. 48, No. 7, 2009 Table 3. Statistical Comparison of Literature Models with Present Dynamic Liquid Saturation Data (MRQE Values) A. Air-Water system (Different Packings) packing type ref

glass beads-I

catalyst pellets

solid cylinders

glass beads-II

Raschig rings

Larkins et al. Charpentier et al.9 Turpin and Huntington23 Sato et al.27 Midoux et al.31 and Morsi et al.35 Rao et al.9 Hochman and Effron17 Wijffels et al.19 Otake and Okada15 Yang et al.32 Specchia and Baldi21 and Wammes et al.38 Clements and Schmidt24 Blok et al.25 Sai and Varma4 Xiao et al.5 Ellman et al.28 Larachi et al.34 Fu et al.33 present correlation

0.474 0.343 0.163 0.219 0.249 0.224 0.608 0.578 0.648 0.334 0.192 0.217 0.381 0.128 0.288 0.337 0.199 0.431 0.078

0.350 0.541 0.170 0.297 0.549 0.175 0.506 0.849 0.604 0.680 0.265 0.238 0.606 0.169 0.237 0.232 0.426 0.552 0.160

0.596 2.674 1.459 1.426 2.401 0.769 0.226 0.908 0.315 2.742 0.156 1.175 2.119 0.734 2.863 1.392 2.114 0.440 0.266

0.738 3.851 1.656 1.315 2.784 0.697 1.165 0.948 0.627 3.056 0.122 1.460 2.039 0.608 3.351 1.288 2.336 0.581 0.216

0.668 2.891 1.609 1.749 2.574 0.987 0.476 0.924 0.722 2.933 0.185 0.730 2.498 1.026 3.239 2.190 2.365 0.245 0.141

30

B. Different Newtonian Liquid Phases different Newtonian liquid phases (packing: glass beads-I) ref

water

6 ppm surfactant

12 ppm surfactant

60% glycerol

77% glycerol

Larkins et al. Charpentier et al.9 Turpin and Huntington23 Sato et al.27 Midoux et al.31 and Morsi et al.35 Rao et al.9 Hochman and Effron17 Wijffels et al.19 Otake and Okada15 Yang et al.32 Specchia and Baldi21 and Wammes et al.38 Clements and Schmidt24 Blok et al.25 Sai and Varma4 Xiao et al.5 Ellman et al.28 Larachi et al.34 Fu et al.33 present correlation

0.474 0.343 0.163 0.219 0.249 0.224 0.608 0.578 0.648 0.334 0.192 0.217 0.381 0.128 0.288 0.337 0.199 0.431 0.078

0.437 0.446 0.140 0.294 0.333 0.136 0.783 0.705 0.719 0.447 0.295 0.135 0.551 0.233 0.193 0.161 0.262 0.375 0.064

0.421 0.491 0.107 0.325 0.360 0.096 0.797 0.738 0.734 0.492 0.353 0.116 0.609 0.211 0.143 0.103 0.298 0.373 0.048

0.362 0.504 0.284 0.532 0.613 0.260 0.963 0.382 0.748 0.599 0.170 0.341 0.731 0.205 0.389 0.607 0.481 0.193 0.083

0.307 0.308 0.409 0.474 0.634 0.217 1.000 0.759 0.814 0.438 0.191 0.329 0.565 0.147 0.450 0.729 0.428 0.150 0.115

30

C. Non-Newtonian Viscoinelastic Liquid Phases different non-Newtonian liquid phases (packing: glass beads-I) ref

0.15% CMC

0.30% CMC

0.40% CMC

0.80% PEO

1.60% PEO

Larkins et al. Charpentier et al.9 Turpin and Huntington23 Sato et al.27 Midoux et al.31 and Morsi et al.35 Rao et al.9 Hochman and Effron17 Wijffels et al.19 Otake and Okada15 Yang et al.32 Specchia and Baldi21 and Wammes et al.38 Clements and Schmidt24 Blok et al.25 Sai and Varma4 Xiao et al.5 Ellman et al.28 Larachi et al.34 Fu et al.33 present correlation

0.403 0.384 0.214 0.333 0.400 0.155 0.906 0.510 0.719 0.425 0.224 0.219 0.544 0.156 0.299 0.281 0.305 0.264 0.102

0.269 0.374 0.289 0.534 0.674 0.197 0.985 0.876 0.739 0.540 0.159 0.263 0.638 0.119 0.345 0.719 0.510 0.182 0.146

0.240 0.273 0.325 0.946 1.210 0.670 1.006 21.423 0.599 0.421 0.591 0.264 0.526 0.591 0.348 1.123 0.972 1.892 0.133

0.418 0.433 0.210 0.356 0.382 0.107 0.940 0.745 0.810 0.514 0.417 0.136 0.653 0.187 0.232 0.269 0.308 0.336 0.134

0.292 0.313 0.340 0.460 0.600 0.149 0.994 0.594 0.790 0.464 0.236 0.253 0.597 0.121 0.372 0.669 0.430 0.109 0.119

30

Ind. Eng. Chem. Res., Vol. 48, No. 7, 2009 3347 Table 3. Continued D. Non-Newtonian Viscoelastic Liquid Phases different non-Newtonian liquid phases (packing: glass beads-I) ref

0.05% PAA in water

0.075% PAA in water

0.10% PAA in water

Larkins et al. Charpentier et al.9 Turpin and Huntington23 Sato et al.27 Midoux et al.31 and Morsi et al.35 Rao et al.9 Hochman and Effron17 Wijffels et al.19 Otake and Okada15 Yang et al.32 Specchia and Baldi21 and Wammes et al.38 Clements and Schmidt24 Blok et al.25 Sai and Varma4 Xiao et al.5 Ellman et al.28 Larachi et al.34 Fu et al.33 present correlation

0.070 0.495 0.119 0.632 0.934 0.310 1.068 0.924 0.756 0.327 0.197 0.103 0.814 0.406 0.204 0.564 0.608 0.175 0.037

0.247 0.265 0.354 0.437 0.680 0.203 1.070 0.623 0.855 0.221 0.457 0.308 0.597 0.074 0.473 0.545 0.381 0.145 0.061

0.233 0.466 0.363 0.751 1.054 0.421 1.113 0.563 0.927 0.461 0.457 0.279 1.007 0.128 0.427 1.051 0.635 0.335 0.046

30

adopted by Clements and Schmidt,24 Rao et al.,12 and Sai and Varma,4 the dependence of dynamic liquid saturation, βd, on various system parameters may be expressed as P2 P3 βd ) P1[ReL,M ReG,M asP4εP5]

(2)

By using the Nelder and Mead nonlinear regression technique, the constants of the above equation for the experimental data on an air-water system involving various packings have the following values: P1 ) 2 × 10-4 ( 5.15 × 10-6 P2 ) 0.500 ( 0.10 P3 ) -0.150 ( 0.001 P4 ) 0.750 ( 0.018

Figure 12. Parity plot for dynamic liquid saturation (different packings).

P5 ) -1.000 ( 0.039

so as to yield P6 ) -2 ( 0.026 (correlation coefficient R2 ) 0.86). This correlation predicts the data with low-surface-tension solutions as studied in the present investigation to with in (10%. Similarly, the data corresponding to highly viscous solutions of 60 and 77% (w/w) glycerol in water were considered to introduce the effect of viscosity in the correlation developed. The viscosity dependence was included in eq 4 in the following form:

With these values, the correlation assumes the following form: βd ) 2 × 10-4

0.50 3/4 ReL,M as

(3)

0.15 ReG,M ε

It was observed that the correlation predicts the present data to within (15% (Figure 12). To include the effect of surface tension, the data corresponding to 6 and 12 ppm surfactant in water were considered. These solutions were found to cause foaming in the high-interaction regime, but no appreciable foam was noticed in the low-interaction regime. It is reported in the literature that the foaming solutions behave differently (Larkins et al.30 and Midoux et al.31) and, hence, need separate consideration. In the present study, only the data corresponding to nonfoaming conditions are considered. Thus, to include the effect of surface tension in the correlation, the data corresponding to 6 and 12 ppm surfactant solutions (under nonfoaming conditions only) were subjected to a nonlinear regression technique to estimate the constant P6 in the following expression, βd ) 2 × 10-4

( )

0.50 3/4 ReL,M as σL 0.15 Re ε σw G,M

P6

(4)

βd ) 2 × 10-4

( ) ( )

0.50 3/4 ReL,M as σL 0.15 Re ε σw G,M

-√2

µL µw

P7

(5)

By using the data on 60 an 77% glycerol systems, the exponent P7 is found to be 2/3 ( 0.003 (correlation coefficient R2 ) 0.91). It was observed that the data remained within (15%. The parity corresponding to the data available in the literature for various systems obtained by using eq 5 are shown in Figure 13, and the correlation is found to predict the literature data within (20%. 5.2. Non-Newtonian Liquid Phase. 5.2.1. Viscoinelastic Liquid Phase. The dynamic liquid saturations corresponding to different concentrations of CMC were predicted by using correlation eq 6 with the dynamic liquid viscosity, µL, being replaced by the apparent viscosity, µa, so that

3348 Ind. Eng. Chem. Res., Vol. 48, No. 7, 2009

Figure 15. Parity between present viscoinelastic data and correlation for viscoinelastic liquid phase.

βd ) 2 × 10-4

G,M

Figure 13. Parity between literature data and predicted dynamic liquid saturation.

( ) ( )

0.50 3/4 ReL,M as σL 0.15 Re ε σw

-√2

µa µw

2/3 Q1ln(n)

where Q1 is evaluated by regressing the data on 0.30 and 0.40%CMC solutions to yield Q1) 0.900 + 0.0024 (correlation coefficient R2 ) 0.80). The parity between predicted and experimental dynamic liquid saturations for non-Newtonian viscoinelastic liquid phases is shown in Figure 15. The correlation developed is found to predict data to within (20%. 5.2.2. Viscoelastic Liquid Phase. The dynamic liquid saturation data corresponding to different concentrations of PAA in distilled water under high-interaction regime was used for the development of the correlation. Different concentrations of PAA are known to exhibit a viscoelastic character which has a force component normal to the shear force applied and tries to behave like a solid, thus resisting the motion of fluid. To consider the viscoelastic effect, the Weissenberg number, Wi, was considered to represent the viscoelastic character shown by the different concentrations of the PAA solutions. The Weissenberg number was calculated by using the method described by Abdel-Khalik et al.36 Details areavailable elsewhere (Bansal et al.).8 The data could be correlated as βd,ve T2 ) (1 + T1ReL,M WiT3) βd,vi

Figure 14. Parity between present viscoinelastic data and correlation for Newtonian liquid phase.

βd ) 2 × 10-4

( ) ( )

0.50 3/4 ReL,M as σL 0.15 Re ε σw G,M

-√2

µa µw

2/3

where µa ) K˙γn-1. It is observed that the data corresponding to 0.15% CMC were within (20%, but the data corresponding to 0.30 and 0.40% CMC solutions showed significant deviation (Figure 14). It is observed that the dynamic liquid saturation corresponding to 0.30 and 0.40% CMC solutions were overpredicted. This could be due to the drag reduction character of the CMC because of which the viscosity was probably reduced, and the experimental dynamic liquid saturation was lower than the predicted. To include this effect on apparent viscosity, the term (µa/µw) is modified as

(6)

This kind of dependence has already been used by Bansal et al.8 and Carlos et al.37 It has the advantage that when the fluid is not viscoelastic, that is, Wi f 0, the expression reduces to the one applicable for viscoinelastic systems, that is, as Wi f 0, βd,ve f βd,vi. The data corresponding to different viscoelastic systems for the high-interaction regime lead to the correlation coefficients as, T1 ) 0.112 ( 0/012 T2 ) -0.671 ( 0.010 T3 ) 2.774 ( 0.084 with final form of the expression for the dynamic liquid saturation for viscoelastic systems βd,ve as βd,ve ) βd,vi(1 + 0.112

Wi2.774 ) 0.671 ReL,M

(correlation coefficient R2 ) 0.97). The parity of the predicted and experimental values of the dynamic liquid saturation corresponding to the viscoelastic liquid phase was within (10%

Ind. Eng. Chem. Res., Vol. 48, No. 7, 2009 3349

liquid saturation for rheologically complex viscoinelastic and viscoelastic liquid phases. Acknowledgment Financial support from All India Council for Technical Education, Government of India, New Delhi under Grant number F.NO. 8017/RDII / R&D-617 / 1999-2000 is gratefully acknowledged. Appendix

NOTATION as Figure 16. Parity between present viscoelastic data and correlation for viscoelastic liquid phase.

(Figure 16). However, there seems to be plenty of room for testing the model developed on other viscoelastic fluids. 6. Conclusion An important hydrodynamic parameter, the dynamic liquid saturation, βd, is thoroughly investigated in the present study. The parameters affecting the dynamic liquid saturation corresponding to rheologically simple Newtonian liquid phase included gas and liquid flow rates, surface tension, and viscosity of the liquid phase and bed characteristics including porosity and particle sphericity. Additional rheological parameters affecting dynamic liquid saturation in the case of rheologically complex non-Newtonian viscoinelastic liquids are flow consistency index K and flow behavior index n, whereas the case of the viscoelastic fluid effect of viscoelasticity is investigated in terms of Weissenberg number. At the same gas flow rate, an increase in liquid flow rate increased the dynamic liquid saturation, whereas with an increase in gas flow rate, a decrease in dynamic liquid saturation was observed for glass beads-I. It was observed that bed porosity was an important parameter, and there probably existed some critical value of porosity between 0.406 and 0.441 below which dynamic liquid saturation was affected by gas flow rate and above which the effect of gas flow rate was negligible. Larger-diameter particles with larger bed porosity were found to give smaller liquid saturations. It was observed that the dynamic liquid saturation in trickle regime increased with a decrease in surface tension. Highly viscous solutions were found to result in increased dynamic liquid saturation. For non-Newtonian viscoinelastic fluids, with an increase in flow consistency index K, the dynamic liquid saturation was observed to increase. The viscoelastic aqueous solutions were found to give higher dynamic liquid saturations in comparison to viscoinelastic solutions. No abrupt change was observed in dynamic liquid saturation (for nonfoaming solutions) corresponding to regime shift from low to high interaction, and the correlations obtained are based on data for low- as well as high-interaction regimes. A set of the 20 most widely used correlations were selected from the literature to see the applicability of these correlations under varied conditions of bed configurations and liquid-phase properties. It was observed that the correlations are valid only for a restricted rage of parameters, and none of the correlations seem to be applicable over the entire range of parameters investigated in the present study. However, the correlations developed for dynamic liquid saturation could predict the literature data for Newtonian liquid phase to (20%. Further, the correlations developed are extended to predict the dynamic

dp G K L n ReL,G ReL,M Wi

) specific surface area of packing [6(1 - ε)]/dp + [4/de] [m-1] ) effective particle diameter [m] ) gas superficial mass velocity [kgm-2 s-1] ) flow consistency index [Pa sn] ) liquid superficial mass velocity, [kg m-2 s-1] ) flow behavior index [-] ) modified Reynolds number, dpG/µG(1-ε)Rw [-] ) modified Reynolds number, dpL/µL(1-ε)Rw [-] ) Weissenberg number [-]

GREEK SYMBOLS βd ˙γ σL ε φs λt µL µa µa FR τ

) ) ) ) ) ) ) ) ) ) )

dynamic liquid saturation [-] shear rate [s-1] surface tension of liquid-phase [N m1-] bed void fraction [-] sphericity of packing particles [-] time constant of material [s] viscosity of liquid phase [Pa s] apparent viscosity of liquid phase [Pa s] K˙γn-1 density of R-phase [kg m-3] shear stress, K˙γn [Pa]

SUBSCRIPTS G L ve vi w R

) ) ) ) ) )

gas phase liquid phase viscoelastic liquid phase viscoinelastic liquid phase water fluid phase, liquid or gas

ABBREVIATIONS CMC MRQE PAA TBR

) carboxymethylcellulose ) mean relative quadratic error, calculated as N [(Exp-Preed)/Exp]2}/[N - 1] {√ ∑ i)1 ) polyacrylamide ) trickle bed reactor

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ReceiVed for reView September 17, 2008 ReVised manuscript receiVed January 17, 2009 Accepted January 27, 2009 IE801399U