Pressure Drop Models of Seepage Catalytic Packing Internal for

May 16, 2012 - National Engineering Research Center for Distillation Technology, Tianjin 300072, China ... (3-7) In the design of the catalytic packin...
0 downloads 0 Views 2MB Size
Download PDF
Research Note pubs.acs.org/IECR

Pressure Drop Models of Seepage Catalytic Packing Internal for Catalytic Distillation Column Xin Gao,†,‡ Xingang Li,†,‡ Rui Zhang,† and Hong Li*,†,‡ †

School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072, China National Engineering Research Center for Distillation Technology, Tianjin 300072, China

‡

ABSTRACT: A seepage catalytic packing internal (SCPI) consisting of catalyst containers with avert-overflow baffles and corrugated metal sheets was developed for a catalytic distillation column. By changing the width ratio (Rcc/cms) of the catalyst containers (CC) relative to corrugated metal sheets (CMS), the SCPI developed in this work can be suitable to various reaction and separation zones in different catalytic distillation processes. The influence of the Rcc/cms, a significant factor influencing the pressure drop, also was studied. The flooding behaviors and pressure drop were evaluated using cold model experiments in the column (600 mm in diameter × 1500 mm height); the results were compared with that of the catalytic packing typically used in catalytic distillation. A model for predicting the pressure drop of SCPI was developed and compared with experimental results. Results show that the pressure drop was decreased with decreases of Rcc/cms. The results from this work are valuable in the design and scale-up of SCPI in catalytic distillation columns. metal sheets (CMS) at various gas and liquid flow rates are measured in a 600 mm diameter poly(methyl methacrylate) (PMMA) column. An air/water system is used for simulation of gas/liquid flow. To calculate the pressure drop of the SCPI, a model has been developed with a better understanding of the operation mechanism of SCPI. The results of this work provide important information for the design and scale-up of SCPI used in CD columns with heterogeneous catalysis.

1. INTRODUCTION Catalytic reaction and distillation separation are two important operations involved in most chemical processes. They are typically conducted in different sections of the plant using various equipments. The catalytic distillation (CD) technology can successfully combine these two operations in one piece of equipment, and holds great potential for improving conversion, reducing capital expenditure, reducing energy consuming, improving selectivity, and decreasing environmental emissions.1 One major challenge in CD technology is that the small catalyst particles used to improve catalytic efficiency are too small to meet the operating conditions of CD columns. The installation of small solid particle catalysts inside a distillation column without any packing internal can induce an enormous pressure drop even flooding along the height of the column. The flooding boundary of a randomly packed bed of these particles is well below the required gas and liquid fluxes for large-scale operations.2 In addition, the loose catalyst bed results in a low separation efficiency of the column, so the randomly loose catalyst bed cannot be used in the CD column. The separation efficiency and permissible flow rates decrease as the pressure drop increases; thus this pressure drop is one important parameter of the CD column internal. The method of catalyst packing in a CD column is an alternative to address this drawback. In recent years, catalytic packing has been gaining increasing attention in both industrial practice and scientific research.3−7 In the design of the catalytic packing internal for CD columns, two main factors need to be considered: (1) efficient contact between the liquid phase and the solid catalyst with sufficient residence time; (2) efficient separation by distillation with a high capacity or low pressure drop.8 In this work, characterization of the seepage catalytic packing internal (SCPI) is developed based on the factors discussed above. Pressure drops of three SCPI with different width ratios (Rcc/cms) of the catalyst containers (CC) relative to corrugated © 2012 American Chemical Society

2. SEEPAGE CATALYTIC PACKING INTERNAL (SCPI) The SCPI was developed by the National Engineering Research Center for Distillation Technology in China,9 combining crossflow plates and a fixed-bed reactor. A picture of a laboratory scale component device with five catalyst containers is shown in Figure 1. The SCPI consists of corrugated metal sheets and

Figure 1. Laboratory scale element of SCPI-I (left) with five catalysts containers and SCPI-III (right) with five catalysts containers.

Received: Revised: Accepted: Published: 7447

July 31, 2011 April 7, 2012 May 16, 2012 May 16, 2012 dx.doi.org/10.1021/ie201686y | Ind. Eng. Chem. Res. 2012, 51, 7447−7452

Industrial & Engineering Chemistry Research

Research Note

The ratio of the separation to reaction sections can be varied according to different catalytic distillation process requirements.

catalyst containers with avert-overflow baffles. The corrugated metal sheets, serving as the separation section, are the metallurgic orifice corrugated packing widely used in industrial distillation columns. The catalyst containers, serving as the reaction zone, are closed boxes filled with catalyst particles with avert-overflow baffles. To allow the liquid seepage to flow through the closed box, the wire meshes are installed in the top and bottom surfaces of the closed box to fix the catalysts particles. The arrangement of catalyst containers and corrugated metal sheets in the experimental column is shown in Figure 2. An integral element of SCPI is its arrangement of

3. EXPERIMENTAL APPARATUS AND METHOD The system used for pressure drop measurements is shown in Figure 3. The column is a PMMA tube of 600 mm i.d. An air/

Figure 2. The schematic for an integrated element of SCPI: (1) corrugated metal sheets; (2) catalyst particles; (3) liquid layer; (4) gas flow; (5) liquid flow; (6) metal mesh; (7) avert-overflow baffle.

Figure 3. Schematic drawing of the cold model experimental apparatus: (1) air blower; (2) pitot tube flowmeter; (3) U-tube manometer; (4) liquid distributor; (5) SCPI; (6) catalysts; (7) column; (8) liquid rotometer; (9) gas distributor; (10) liquid level meter; (11) water tank; (12) pump.

two different catalytic layers with alternating zones of catalyst containers and corrugated metal sheets and two layers of corrugated metal sheets. In the Z2 catalytic layer, five catalyst containers and four blocks of corrugated metal sheets are held tightly together in an alternating sequence. The Z4 catalytic layer consists of four catalyst containers and five blocks of corrugated metal sheets, and is staggered parallel relative to Z2 catalytic layers. Z3 layer of corrugated metal sheets with suitable heights is sandwiched between the above-mentioned two adjacent catalytic layers Z2 and Z4 to improve the separation efficiency of SCPI. The catalytic layer Z2 and its adjacent Z1 and Z3 layers of corrugated metal sheets are bent gradually to 90° with respect to the horizontal to enhance mixing and spreading of the liquid. The gas and liquid flow behavior in the SCPI is also shown in Figure 2. Driven by gravity, the liquid flows uniformly downward through the corrugated metal sheets and catalyst containers. Driven by a pressure gradient, gas flows upward, though only through the corrugated sheets, which avoids contact between gas and liquid in the catalyst particles bed. This results in a significantly decreased pressure drop in the column compared with conventional catalyst bale packing. The main features of SCPI are as follows: (1) The catalyst is uniformly distributed in the catalytic distillation column. (2) The avert-overflow baffle ensures that the liquid seepage flow through the catalyst container driven by its own gravitational force, which avoids the slow catalyst surface renewal caused by the liquid’s transverse diffusion. (3) The corrugated metal sheets between each catalyst container provide appropriate conditions for countercurrent vapor−liquid mass transfer. (4)

water system was chosen as the model gas and liquid, forming countercurrent flow in the SCPI bed. The air stream produced by the blower entered the column through the gas distributor located at the bottom of the column, flowed upward through the SCPI bed, and finally vented out from the top of the column. The water was transferred from a storage tank to the liquid distributor by a centrifugal pump, passed through the SCPI bed, discharged at the bottom of the column, and was collected in a recycling tank. The flow rates of gas and liquid were monitored by Pitot tube flowmeter and rotameter, respectively. A water-filled U-tube manometer with a scale of 0.5 mm was used to measure the pressure drop across the bed with the accuracy of 20 Pa. The dry pressure drop is the pressure drop of the SCPI when there is only a single-phase gas flow through the dry SCPI; the irrigated pressure drop is the pressure drop of the SCPI when there is two-phase counter-current gas and liquid flow. After the dry pressure drop experiments, the air/water system testing was conducted at a high liquid flow rate for about 15 min to completely wet the SCPI bed. The experimental pressure drop data was recorded after the column operation reached steady state. The liquid spray density varied from 0 to 31.25 m3/ (m2h), and the gas F-factor increased to the flooding of the SCPI bed. For the optimization of the catalytic distillation performance of the SCPI, a narrower container width and increased number of containers per catalytic layer should be used. However, 7448

dx.doi.org/10.1021/ie201686y | Ind. Eng. Chem. Res. 2012, 51, 7447−7452

Industrial & Engineering Chemistry Research

Research Note

excessive containers within each layer result in manufacturing difficulty; so an optimal trade-off must be established. Table 1

Table 2. Main Geometric Parameters of the Metallurgic Orifice Corrugated Packing

Table 1. Main Geometric Parameters of the Three SCPI geometric parameters

SCPI-I

SCPI-II

SCPI-III

specific surface area, a (m2/m3) volume fraction of the catalysts in the column, FCC (m3/m3) width ratio of catalyst container to corrugated metal sheets, Rcc/cms volume fraction of the corrugated metal sheets in the column, FCMS (m3/m3) height of catalysts bed of catalysts container, hC (m) height of avert-overflow baffle of catalysts container, hA (m) height of corrugated metal sheets of Z1,Z3 section, Z1,Z3 (m) width of catalysts container in catalytic layer with four catalyst containers, W4cc (mm) width of corrugated metal sheets in catalytic layer with four catalyst containers, W4cms (mm) width of catalysts container in catalytic layer with five catalyst containers, W5cc (mm) width of corrugated metal sheets in catalytic layer with five catalyst containers, W5cms (mm) cross sections area ratio of catalysts container and corrugated metal sheets in an integrated element, Acc/cms

260 0.111

218 0.134

180 0.151

1:1

3:2

2:1

0.611

0.533

0.481

0.1

0.1

0.1

0.25

0.25

0.25

0.1

0.1

0.1

66.67

81.82

92.31

66.67

54.55

46.15

66.67

78.26

85.71

66.67

52.17

42.86

1:1

1.4:1

1.95:1

geometric parameters

value

corrugation length (mm) corrugation height (mm) specific geometric area (m2/m3) corrugation angle (deg) void fraction (%) corrugation sheet thickness (mm) corrugation sheet height (mm)

18 10 298.7 45 97 0.2 350/100

rendering it unavailable for reaction. Because of this, the value of Rcc/cms can not be less than 1.

4. RESULTS AND DISCUSSION 4.1. Dry Pressure Drop. The dry pressure drop across the packed section is measured when only air flows through the SCPI bed. Figure 4 illustrates the relationship between dry

shows a selection of appropriate sizing and number of containers for simplified production. The catalyst fill is determined by the reaction rate, and will vary according to the residence time demands of the CD process desired. The filling height of catalyst in each container determines that container’s residence time, while the total amount of catalyst in all catalyst containers determines the residence time of the entire reactive distillation section. It follows that increasing the amount of catalyst leads to an increased residence time when needed for a particular application. There are two methods of changing the amount of catalyst in the CD column. The first is to change the Rcc/cms, which is the ratio of the widths of one catalyst container and that of one block of corrugated metal sheets. In this paper, three SCPI with different Rcc/cms are investigated to confirm the relationship between Rcc/cms and the hydrodynamics of the SCPI. The second method is to change the filling height of the catalyst in the container, leaving the Rcc/cms constant. For example, the height of hC can be increased, the height of hA decreased, and the height of Z4 left unchanged; this maintains the hydrodynamics of SCPI because the structure, figure, and volume fraction of structured packing in the CD column is not changed. Table 1 gives an overview of the three SCPI with different Rcc/cms used in this work, and Table 2 shows the basic dimensions of the metallurgic orifice corrugated packing used. Notably, another possibility for arranging the packing would be to decrease the Rcc/cms further and increase the filling height of catalyst in each container. As a result, more corrugated metal sheets would fit and the specific surface area would be increased while keeping the catalyst amount constant. This would result in a decrease of the horizontal cross-sectional area of the catalyst containers, leading the cross-sectional area of all containers in the SCPI to be less than that of the column. Thus some liquid would not flow through the catalyst containers,

Figure 4. Dry pressure drop of three SCPI with different Rcc/cms.

pressure drop per unit of SCPI bed height and the gas F-factor when three SCPI are added to the column. It can be seen that the dry pressure drop of the three SCPI increased when the gas F-factor increased from about 0.4 to 1.8. The resistance of the gas is mainly caused by the twists and turns of the corrugated metal sheets channels. The SCPI-III with Rcc/cms of 2:1 had the narrowest channels, so the dry pressure drop of SCPI-III was highest. The dry pressure drop difference between SCPI-I and SCPI-II is larger than that between SCPI-II and SCPI-III; this illustrates the direct proportional relationship between the dry pressure drop and the sum of the metal sheets’ cross-sectional areas in one integrated element. 4.2. Irrigated Pressure Drop. Results of the irrigated pressure drop (Figures 5, 6, and 7) indicated that the pressure behavior in SCPI was similar to that of traditional packed beds.10 Interpolation lines connecting the data points at a constant liquid sprayed density are shown. From these figures, the pressure drop of three SCPI is increased with an increasing F-factor at a constant liquid load. The pressure drop was found to undergo biphasic dynamics; a slow increase followed by a sharp increase. The transition point of these two phases is equivalent to the liquid load value obtained when the maximum liquid flow rate was reached in the catalyst containers and the excess liquid overflowed the avert-overflow baffle to the corrugated metal sheets. The sharp rise of the pressure drop 7449

dx.doi.org/10.1021/ie201686y | Ind. Eng. Chem. Res. 2012, 51, 7447−7452

Industrial & Engineering Chemistry Research

Research Note

m3/(m2h) liquid loads are shown in Figure 8 and Figure 9, respectively. The data of KATAPAK-SP 12 from Behrens12 was

Figure 5. Pressure drop of SCPI-I at different liquid sprayed density. Figure 8. Comparison of pressure drop for catalyst bundles,2 KatapakSP12,10 and SCPI I−III (catalyst bundle, L = 20 m3/(m2h); KatapakSP12, L = 20 m3/(m2h); SCPI I−III, L = 20.31 m3/(m2h)).

Figure 6. Pressure drop of SCPI-II at different liquid sprayed density.

Figure 9. Comparison of pressure drop for Katapak-SP 11,11 KatapakSP 12,11 and SCPI I−III (Katapak SP11−12, L = 30 m3/(m2h); SCPI I−III, L = 31.25 m3/(m2h)).

measured using a column of 450 mm which is comparable to the 600 mm column used in this paper. It is obvious from these two figures that SCPI-I had a lower pressure drop than the other two SCPI because of the wider gas flow channel. It can be seen that the pressure drop of SCPI could easily be reduced by decreasing the Rcc/cms to account for different CD operating conditions. In Figure 8, at a low gas F-factor, there was an insignificant difference between SCPI-I and KATAPAK-SP 12, which had a lower pressure drop than the other catalytic packings. At high gas F-factor (>1.8), however, the pressure drop for SCPI-I was significantly lower than that for KATAPAK-SP 12. Figure 9 shows the comparison between experimental data in the paper and the results of Behrens.12 It can be seen that the pressure drop of SCPI I−III are comparable to the results of KATAPAK-SP 11−12. The flooding line, a very important parameter for the design of catalytic packed columns, was determined on the basis of the visual observations of the process. Figure 10 shows a comparison of flooding point curves (gas F-factor at flooding point vs liquid sprayed density) between three SCPI catalyst

Figure 7. Pressure drop of SCPI-III at different liquid sprayed density.

above the transition point was caused by interactions between the excess liquid flow and the gas flow in the corrugated metal sheets. The extreme liquid/gas flow rate for avert-overflow baffle at a given height was determined by the value at the transition point. 4.3. Comparison with Other Catalytic Packings. A comparison of the irrigated pressure drop among three SCPI catalyst bundles2 and KATAPAK-SP 1211,12 at about 20 and 30 7450

dx.doi.org/10.1021/ie201686y | Ind. Eng. Chem. Res. 2012, 51, 7447−7452

Industrial & Engineering Chemistry Research

Research Note

pressure drop of the gas for contraction and expansion can be calculated by the Bernoulli equation as follows: gZi +

p p u2 ui 2 + i = gZi + 1 + i + 1 + i + 1 + hf ρ ρ 2 2

(4)

The resistance loss (hf) for contraction and expansion can be calculated as follows: hf = ξ

ui 2 2

(5)

where ui is the superficial gas velocity in the smaller gas channel, and ξ is the coefficient of local resistance loss. The pressure drop due to contraction can be expressed as follows: ⎛ u 2 u 2 u2⎞ ΔPiC = ρg ⎜ξiC i + 1 + i + 1 − i ⎟ 2 2 2 ⎠ ⎝

Figure 10. Comparison of flooding point curves for catalyst bundles,2 Katapak-SP 12,10 and SCPI I−III.

(i = 1, , 3) (6)

and the pressure drop due to expansion likewise: ⎛ u2 u 2 u2⎞ ΔPiE = ρg ⎜ξiE i + i + 1 − i ⎟ 2 2 ⎠ ⎝ 2

bundles3 and KATAPAK-SP 12.11,12 Results show that at the same liquid spray density, the gas F-factor at the flooding point for the SCPI-I bed was higher than the other catalytic packings. Results also indicate that the operational capability of SCPI-I was larger than that of other catalytic packings.

(i = 2, 4) (7)

Equation 6 describes local resistance loss of section Z1 and Z3 of an integrated element of SCPI as shown in Figure 2, and eq 7 describes that of section Z2 and Z4 of an integrated element of SCPI as shown in Figure 2. The pressure drop per unit bed height for SCPI, ΔPsum, is given by the sum of the pressure drop of each segment ΔZi for SCPI (ΔPi), the pressure drop due to contraction loss of gas flow (ΔPiC) and that due to expanding loss of gas flow (ΔPiE). It can be expressed by eq 8.

5. MODELING STUDIES 5.1. Model Building. The pressure drop model for SCPI reflects the geometric structure of the internal, which consists of catalyst containers and corrugated metal sheets. To establish a pressure drop model, an ideal flow pattern of gas and liquid in the SCPI is assumed, as shown in Figure 2. The model is based on the following assumptions: (1) gas flows only through the corrugated metal sheets; (2) liquid flows equally and evenly through the corrugated metal sheets and the catalyst containers. Upon entering the column, the gas flows only into the corrugated metal sheets, so: A1u1 = A 2 u 2 = A3u3 = A4 u4 (1)

4

∑i = 1 ΔPi + ∑i = 1,3 ΔPiC + ∑i = 2,4 ΔPi E ΔPsum = 4 ΔZ ∑i = 1 ΔZi

(8)

5.2. Model Verification. Figure 11 shows a comparison of the pressure drop below the flooding point between

where A1, A2, A3, A4 and u1, u2, u3, u4 are the sectional area of gas channel and superficial gas velocity in section Z1, Z2, Z3, Z4, respectively. The interaction of gas and liquid in the corrugated metal sheets causes a substantial pressure drop. The basis for the model developed here to predict the pressure drop of SCPI is the Leva correlation equation13 for the prediction of the pressure drop of the corrugated sheet packing. ΔP = k × 10 βL(ug ρg )α (2) ΔZ where α, β, and k are coefficients, which are obtained by Zhang.14 So the pressure drop ΔPi of each section ΔZi for SCPI can be calculated by −3

−3

ΔPi = 9.48 × 104.46 × 10 L(ui ρg )1.72 + 3.8 × 10 L ΔZi (i = 1, 2, 3, 4)

Figure 11. Comparison of experimental pressure drop and calculated values.

(3)

where L is the liquid spray density, ui is the superficial gas velocity in section Zi of SCPI, ρg is the density of gas, and ΔZi is the height of section i. According to the above assumption, the gas undergoes twice the amount of contraction and twice the amount of expansion when it passes through an integrated element of SCPI. The

experimental data and calculated values. The maximum deviation between calculated and experimental results was 12%, and the mean deviation was 5.41%. The reason for the deviation was that abnormal column operation occurred when gas and liquid flow were close to the flooding point. The second reason was that the precision and accuracy of the 7451

dx.doi.org/10.1021/ie201686y | Ind. Eng. Chem. Res. 2012, 51, 7447−7452

Industrial & Engineering Chemistry Research

Research Note

Ai = sectional area of gas channel in section Zi (i = 1,2,3,4), m2 ui = superficial gas velocity in section Zi (i = 1,2,3,4), m/s ΔP/ΔZ = pressure drop per unit packed height, Pa/m L = liquid sprayed density, m3/(m2h) ug = superficial velocity of gas, m/s ΔP = pressure drop, Pa g = acceleration due to gravity, 9.81 m/s2 hf = resistance loss, m2/s2 ΔPiC = pressure drop due to contraction, Pa ΔPiE = pressure drop due to expansion, Pa

experimental data were not sufficient. Since the pressure drop is an inevitable fluctuant in the experiment, we estimate the experimental error to be about 3% according to the range of fluctuation. The model fits the experimental data very well (R2 > 0.99) suggesting that the assumed ideal flow pattern of gas and liquid in the SCPI was reasonable and the application of this model could be extended to the design and scale up of CD columns.

6. CONCLUSIONS Information on the influence of fluid dynamics on the interaction between chemical reaction and distillation separation is important for the design and scale-up of catalytic distillation columns. In the present work, detailed experimental studies on the pressure drop of three lab-scale SCPI were carried out in a 600 mm diameter column. Results show that SCPI had a lower pressure drop and higher operational capability than conventional column internals for heterogeneous catalytic distillation. SCPI was more flexible for various ratios of the reaction zone to the separation zone, which is preferable for different catalytic distillation process requirements. On the basis of the analysis of the gas/liquid flow pattern in SCPI, a reasonable model for predicting the pressure drop of SCPI was developed. The model involved the effects of geometric specifications of the SCPI bed on its pressure drop behavior. The irrigated pressure drop calculated by the model in this work agrees well with experimental data. Details of the other studies about SCPI are presently being developed. The application of these findings to the simulation of reactive distillation processes needs to be further studied.

■

Greek Symbols

■

REFERENCES

(1) Harmsen, G. J. Reactive distillation: The front-runner of industrial process intensification A full review of commercial applications, research, scale-up, design and operation. Chem. Eng. Process. 2007, 46, 774. (2) Breijer, A. A. J.; Nijenhuis, J.; Ommen, R. Prevention of flooding in a countercurrent trickle-bed reactor using additional void space. Chem. Eng. J. 2008, 138, 333. (3) Xu, X.; Zhao, Z.; Tian, S. Study on catalytic distillation processes, Part III: Prediction of pressure drop and holdup in catalyst bed. Trans. Inst. Chem. Eng. 1997, 75 (A), 625. (4) Moritz, P.; Hasse, H. Fluid dynamics in reactive distillation packing Katapak-S. Chem. Eng. Sci. 1999, 54, 1367. (5) Han, M.; Lin, H.; Wang, L.; Jin, Y. Characteristics of reactive distillation column with a novel internal. Chem. Eng. Sci. 2002, 57, 1551. (6) Miller, C.; Kaibel, G. Packings for fixed bed reactors and reactive distillation. Chem. Eng. Sci. 2004, 59, 5373. (7) Gao, X.; Li, X.; Li, H. Review for catalyst loading technology in catalytic distillation column. Chem. Ind. Eng. Prog. 2010, 29 (3), 419. (8) Mohammad, M. A.; Safekordi, A. A.; Zarrinpashne, S. A study on the capacity of reactive distillation bale packing: experimental measurements, evaluation of the existing models, and preparation of a new model. Ind. Eng. Chem. Res. 2000, 39, 3051. (9) Li, X. G.; Gao, X.; Li, Y. H.; Li, H.; Guang, C. Catalyst container and catalyst packing internal. CN Pat. No. 101219400, 2008. (10) Bird, R.; Stewart, W.; Lightfoot, E. Transport Phenomena, 2nd ed.; Wiley: New York, 2007. (11) Ratheesh, S.; Kannan, A. Holdup and pressure drop studies in structured packings with catalysts. Chem. Eng. J. 2004, 104, 45. (12) Behrens, M. Hydrodynamics and mass transfer performance of modular catalytic structured packing. Ph.D. Thesis, Delft University of Technology, Delft, The Netherlands, 2006. (13) Leva, M. Pressure drop through packed tubes−Part I. A general correlation. Chem. Eng. Progress 1947, 43, 549. (14) Zhang, R. The study of reactive distillation process used in FCC light gasoline etherification on seepage catalysts packing internal. MS. Thesis, Tianjin University, Tianjin, China, 2010.

AUTHOR INFORMATION

Corresponding Author

*Tel.: +86-022-27404701. Fax: +86-022-27404705. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The authors are grateful for the financial support from the National Basic Research Program of China (No. 2009CB219905), Program for Changjiang Scholars and Innovative Research Team in University (No. IRT0936), National Natural Science Foundation of China (No. 21176172), The Municipal Natural Science Foundation of Tianjin (No.11JCYBJC05400) and National Key Technology R&D Program (No.2011BAE03B07).

■

α = constant, dimensionless β = constant, dimensionless k = constant, dimensionless ρg = density of gas, kg/m3 ξ = coefficient of local resistance loss, dimensionless ξiC = coefficient of local resistance loss due to contraction, dimensionless ξiE = coefficient of local resistance loss due to expansion, dimensionless

NOMENCLATURE

Symbols

Rcc/cms = width ratio of catalyst container to corrugated metal sheets, dimensionless a = specific surface area, m2/m3 FCC = volume fraction of the catalysts in the column, m3/m3 FCMS = volume fraction of the corrugated metal sheets in the column, m3/m3 hA = height of avert-overflow baffle of catalysts container, m hC = height of catalysts bed of catalysts container, m Z1 = height of corrugated metal sheets of Z1 section, m Z3 = height of corrugated metal sheets of Z3 section, m 7452

dx.doi.org/10.1021/ie201686y | Ind. Eng. Chem. Res. 2012, 51, 7447−7452