Pressure Drop of Structured Packing of Carbon Nanofiber Composite

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Ind. Eng. Chem. Res. 2010, 49, 3944–3951

Pressure Drop of Structured Packing of Carbon Nanofiber Composite Yaojie Cao, Ping Li, Jinghong Zhou, Zhijun Sui, Xinggui Zhou,* and Weikang Yuan State Key Laboratory of Chemical Engineering, East China UniVersity of Science and Technology, 130 Meilong Road, 200237 Shanghai, People’s Republic of China

Carbon nanofibers (CNFs) are grown on graphite fiber felt with a desired shape and dimension to form a structured carbon nanofiber composite. This CNF composite has a bimodal porous structure, containing macropores due to the intertexture of graphite fibers and mesopores due to the intertwist of CNFs. The pressure drop of the composite is derived from the convective flow of fluid through the macropores and is independent of the mesopores. Both viscous and turbulent resistance increases with the CNF’s loading. After being wetted with cyclohexane and dried in the air, the CNF’s layer shrinks and becomes smoother, and the composite has a much smaller viscous and turbulent resistance for the fluid. An extended Ergun equation is developed and is shown to be able to predict very well the pressure drop from the structural parameters that are related to the CNF’s loading, i.e., macropore porosity and expanded diameter of the graphite fibers. 1. Introduction Carbon nanofibers (CNFs) have received extensive interest in catalysis research for their novel chemical and physical properties, such as high external surface area, high resistance to acids and bases, and high mechanical strength. It has been widely reported that CNF-supported catalysts display unusual behaviors compared with traditional supports such as silica, alumina, and active carbon.1-3 But the small dimensions of CNFs inhibit their use as catalyst support directly in the form of powders. When CNFs are used in fixed bed reactors, it will induce a big pressure drop along the bed, while in the fluidized bed, it is difficult to separate CNFs from the fluid. One effective method to overcome the drawback is to synthesize CNFs on a substrate with a macroscopic shape, such as a metallic filter,4 metallic sinter-locked microfibers,5,6 solid carbon foam,7 a cordierite monolith,8 solid particles,9 graphite fiber felt,10 etc. In this research, we grow CNFs on graphite fiber felt to form a CNF/graphite fiber felt composite as a structured catalyst support. This structured catalyst support combines the properties of graphite fiber felt and CNFs and, as a result, has a high porosity (82-93%) and high specific surface area (∼50 m2/g). The hydrodynamics of catalyst support has a strong influence on its catalytic performance. Structured catalysts such as foam, honeycomb, and fibers have received more and more interest because of their high porosity, which induces a lower pressure drop compared with traditional particle bed. Structured fibrous catalysts are reported to have excellent mass/heat transfer characteristics and also low pressure drops11 and have potential applications in both gas and liquid phase reactions such as the oxidation of H2S to sulfur,12 removal of nitrites from water,13 etc. Structured fibrous catalysts can also be used as filtering material, which allows the fibrous catalyst to be used in multifunctional reactors to combine reaction and separation in one process unit.14 The pressure drop through porous media has been widely investigated, and a lot of research has been done to study the flow through particle packings. But the permeability of fibrous porous media was less studied. Kyan et al.15 proposed a correlation for the pressure drop of a fibrous bed. In the correlation, the total pressure drop was composed by three parts, i.e., that due to the viscous flow losses, that due to form drag, * To whom correspondence should be addressed. Tel.: +86-2164253509. Fax: +86-21-64253528. E-mail: [email protected].

and that caused by the deflection of fibers. However, the correlation included four parameters, and the term of deflection energy loss was not well justified. Macdonald et al.16 proposed that the pressure drop through the fibrous bed could be correlated with the Ergun equation, but the Ergun constants deviated from their original values and were not related to the structural characteristics of the fibrous porous media. Some theoretical work on the modeling of a pressure drop through a fibrous bed was also carried out.17,18 Their correlations were obtained through the solutions of the Stokes equation with the assumption that the fibrous bed was composed by regular arrays of parallel rods. These correlations agreed well with the experimental data only when the porosity was larger than 0.8. Moreover, only the pressure drop caused by the viscous effect was taken into account, while the pressure drop due to a turbulent or inertial effect was neglected, which was invalid when the fluid velocity was high. Pavageau et al.19 investigated the pressure drop through layered woven fabrics and found that the value of the permeability coefficient was strongly influenced by the working fluid. Up to now, no satisfactory general pressure drop correlation has been obtained for the fibrous porous media, and the permeability of the CNF/graphite fiber felt has not been reported. In the present study, we report that the pressure drop of CNF/ graphite felt composites can be correlated to the textural properties of the composites by an extended Ergun equation. The changes of different textural properties of the composites can be accounted for by the “expansion” of the graphite fibers in the felt. Moreover, for the first time, we report that the pressure drop of the CNF/graphite fiber felt composite will decrease remarkably after wetting and drying treatment, which changes the porosity of the CNF layer and the degree of the expansion of the graphite fibers in the felt. 2. Pressure Drop through Porous Media The pressure drop of fluid flowing through a porous medium follows the Forchheimer equation: ∆P µ ) u + βFu2 L k

(1)

where ∆P/L is the pressure drop per unit length of the porous media, µ and F are the viscosity and density of the fluid, k and β are the Darcian and non-Darcian permeability coefficients,

10.1021/ie9020446  2010 American Chemical Society Published on Web 02/25/2010

Ind. Eng. Chem. Res., Vol. 49, No. 8, 2010

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Figure 1. Images of the as-synthesized composite. (a) Macroscopic shape and size of the composite. (b) Original graphite fibers of the felt. (c) SEM image of the graphite fibers covered with CNFs. (d) SEM image of the carbon nanofibers.

and u is the superficial velocity of the fluid. The permeability coefficients k and β are functions of the structural characteristics of the porous media. When the fluid is compressible, the Forchheimer equation is modified to P2i - P2o µ ) ui + βFiu2i 2PiL k

(2)

where Pi and Po are the pressures at the entrance and exit of the bed, respectively, and ui and Fi are the superficial velocity and the density of the fluid at the entrance of the bed. Different correlations of the coefficients k and β with the characteristics of porous media are proposed. The most widely used correlation is the Ergun equation:20 ∆P (1 - ε)2S2 (1 - ε)S 2 )a µu + b Fu L ε3 ε3

(3)

where S is the specific external surface area and ε is the porosity of the porous media. a and b are Eugun constants that depend on the packing properties.21 The Forchheimer equation and Ergun equation have been modified for different porous media, such as fibers,22 parallelepipedal particles,23 foams,24-26 etc. In this study, the Ergun equation is extended to the CNF/graphite fiber felt composite to predict the pressure drop from its structural parameters. 3. Experimental Section Synthesis of CNFs. The graphite felt was tailored into a desired shape and dimension (cylinder, Φ35 mm × 10 mm) and impregnated with an ethanol solution of nickel nitrate to support nickel. The Ni loading calculated from the quantity of nickel nitrate impregnation was about 3 wt %. After impregnation, the wet felt was dried for 12 h in the air at 120 °C and then placed in a vertical quartz tube reactor. The nickel compound was reduced in a mixture of hydrogen and argon with a molar ratio of 1:3 (total flow rate

360 mL/min) at 400 °C for 3 h. Then, the temperature was increased to 640 °C, and the gas was replaced by a mixture of hydrogen and ethane with a molar ratio of 1:1 (total flow rate 180 mL/min) to grow CNFs. The growth time was varied from 3 to 9 h. The CNF loading on the graphite fiber felt was defined as the weight ratio of the CNFs to the graphite fiber felt. Wetting and Drying Treatment of CNFs. After CNFs were synthesized on the felt, the surface of the graphite fibers was coated by a layer of CNFs. This CNF layer was porous and fluffy, and the structure and pressure drop of the composite could be changed when the composite was wetted and dried. In order to test the influence of wetting and drying of CNFs, the composite was immersed in cyclohexane for 3 h and dried in the air at 120 °C for 12 h. Then, the influence of the wetting and drying process on the structure and pressure drop of the composite was examined. Characterization of the Composite. The BET specific surface area of the as-synthesized composite was measured by N2 adsorption-desorption at 77 K on ASAP 2010 (Micromeretics), and the pore size distribution and porosity of the composite was measured by mercury porosimetry on AutoPore IV 9500 (Micromeretics). The morphology of the composite was characterized by scanning electron microscopy (SEM; JSM6360LV). The mechanical strength of the composite was tested using the universal testing machine with which the relation between stress and strain of the composite was obtained. Measurement of the Pressure Drop. The composite, which was wrapped with PTFE tape to avoid bypass of the fluid, was packed in a plexiglass tube with an internal diameter of 35 mm. With air or cyclohexane as a working fluid, the pressure drop of the composite was measured by a manometer at varied flow rates adjusted by a rotameter. 4. Results and Discussion Characterization of the Composite. The morphology of the composite is shown in Figure 1 at different magnifications. The

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Table 1. Textural Properties of the As-Synthesized Composite CNF loading (w/w)

BET specific surface area of the composite (m2/g)

pore diameter (nm)

pore volume (cm3/g)

0.97 1.36 1.76

51 53 59

13.2 11.7 10.7

0.129 0.124 0.129

original shape and dimension of the graphite felt was retained after the growth of CNFs. The original graphite fibers had a quite smooth surface and therefore a small BET specific surface area (1 m2/g). After the synthesis of CNFs, the macroporous structure of the graphite felt was preserved, and the surface of graphite fibers was covered uniformly by a CNF layer. As indicated in Table 1, this CNF layer provided a large BET specific surface area for the composite. As the CNF loading was increased, the composite had a denser CNF layer and therefore a higher BET specific surface area and a smaller pore size, as also revealed in Table 1. The mechanical strength of the composite with different CNF loadings is shown in Figure 2. The CNFs in the composite bound the junctions of the graphite fibers. Therefore, with a higher CNF loading, the composite had a higher resistance to deformation. The pore size distribution of the composite with different CNF loadings measured by mercury porosimetry is shown in Figure 3. There are two peaks on the pore size distribution curves, the larger one corresponding to the macropores with a relatively large diameter which are derived from the intertexture of the graphite fibers, while the smaller one corresponds to the mesopores derived from the intertwist of the grown CNFs. The diameters of the large and small pores were in the range of 10-100 µm and 10-110 nm, respectively. Figure 3 also shows

Table 2. Porosity and Pore Diameter of the As-Synthesized Composite CNF loading (w/w)

total porosity

macro pore porosity (mercury porosimetry)

macro pore porosity (calculated)

pore diameter (µm)

0.97 1.36 1.76

0.883 0.835 0.820

0.633 0.505 0.402

0.650 0.573 0.410

54.29 36.61 19.42

that most of the volume of the composite was constituted by the macropores, and the volume constituted by the mesopores increased as the CNF loading was increased, which was consistent with the increase of the BET specific surface area of the composite. This bimodal porous structure is advantageous for use as a catalyst support, because the macropores supply the passage for the transport of fluid which decreases the pressure drop along the bed, while the mesopores increase significantly the BET specific surface area of the composite, which is favorable for the dispersion of the catalyst. Increasing the CNF loading would decrease the porosity and pore diameter of the composite, as evidenced in Table 2. Figure 3b illustrates that the mercury cumulative intrusion curve can be divided into four parts. The right-most part is due to the compression of the whole composite, the second part to the filling of mercury into the macropores between graphite fibers, the third part to the compression of the CNF layers, and the last part to the filling of mercury into the mesopores. The porosity used to correlate the pressure drop to the fluid velocity should be determined by the filling of mercury into the macropores, while the contribution of CNF layer compression and the filling of mercury into the mesopores should be excluded because they did not contribute to the bulk flow of the fluid. To determine the macropore volume of the composite, two lines are drawn on the mercury cumulative intrusion curve in Figure 3b, one overlapping the void filling part of the mercury cumulative intrusion curve and the other overlapping the CNF layer compression part. Through the intersection of the two lines at point A, a vertical line is drawn, which intersects the mercury cumulative intrusion curve at point B and gives the specific volume of the macropores in the composite. From the volume of the macropores, the macropore porosity can be calculated by ε ) VB·Fbulk

Figure 2. Relationship between stress and strain of the as-synthesized composite with different CNF loadings.

(4)

where VB is the volume of the macropores and Fbulk is the bulk density of the composite. The porosity of the macropores determined in this way is listed in Table 2. Pressure Drop of the Composite. The pressure drops of the composite with different CNF loadings are shown in Figure 4.

Figure 3. Pore size distribution of the as-synthesized composite with different CNF loadings: (a) log differential intrusion, (b) cumulative intrusion.


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Figure 4. Pressure drop of the as-synthesized composite with different CNF loadings: (a) air, (b) cyclohexane. Table 3. Permeability Coefficients of the Composite CNF loading (w/w) 0 1.59 1.76

-1

2

value of β (m )

value of k (m ) air

cyclohexane -10

1.99 × 10 3.86 × 10-12 2.03 × 10-12

-10

1.75 × 10 3.94 × 10-12 1.60 × 10-12

air 2.11 × 104 3.53 × 106 7.02 × 106

Either air or cyclohexane was used as a working fluid. The CNF loading of the composite had a strong influence on the pressure drop, which was mainly due to the decrease of porosity of the composite at an increased CNF loading. Since the velocity of cyclohexane was quite small, the pressure drop of the composite was linearly related with the superficial velocity of cyclohexane. As a result the quadratic term of the superficial velocity in the Forchheimer equation was neglected. The pressure drop of the composite for cyclohexane was correlated by ∆P 1 ) µu L k

(5)

For air, eq 2 was reformed as (P2i - P2o)/(2PiL) Fiu2i

)

1 µ +β k Fiui

(6)

Therefore, the permeability coefficients k and β for air were obtained by plotting [(Pi2 - Po2)/(2PiL)]/(Fiui2) against µ/(Fiui). Table 3 shows the values of the permeability coefficients of the composite for air and cyclohexane. The value of k was slightly lower for cyclohexane than for air. This difference was mainly due to the possible presence of stagnant zones around the fiber junctions that did not contribute to the bulk flow of

cyclohexane. As indicated by Kyan et al.,15 the fraction of effective porosity decreases as the total porosity decreases when liquid is flowing through the fibrous bed, which can explain why the composite with a CNF loading of 1.76 had a relatively larger difference between the values of k for air and cyclohexane. Moreover, Cunningham et al.27 suggested that the air retained in the fibrous porous media and the air dissolved in the liquid could also induce an increase of the resistance for the liquid flowing through the composite. However, this difference was not remarkable, and the composite was considered to have the same permeability for air and cyclohexane. In the following sections, the experimental data obtained with air as the fluid were used to calculate the Darcian and non-Darcian permeability coefficients k and β of the composite. The permeability coefficients k and β for the composite with different CNF loadings are shown in Figure 5 and are correlated to the CNF loading, y, with empirical equations. As the CNF loading was increased from 0 to 1.76, the Darcian permeability coefficient k decreased from 1.99 × 10-10 to 2.03 × 10-12 m2 while non-Darcian permeability coefficient β increased from 2.11 × 104 to 7.02 × 106 m-1. This indicated that both viscous and turbulent resistance increased significantly owing to the decrease in the porosity of the composite. Pressure Drop Model. As already shown in Figure 1, after the CNFs were grown on the graphite felt, the surface of the graphite fibers was covered uniformly by a layer of CNFs, but the fibrous structure of the graphite felt was preserved. Because the pores in the CNF layer were so small that the fluid in the CNF layer was stagnant, it was assumed that the effect of the grown CNFs on the structure of the graphite felt was just to “expand” the graphite fibers and only the macropores constituted by the “expanded fibers” were available for the convective flow. The void fraction of the packing for convective flow was the

Figure 5. Relationship between the CNF loading and the permeability coefficients for air: (a) k, (b) β.

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Figure 6. Relationship between the structural parameters and the CNF loading: (a) porosity, (b) fiber diameter.

macropore porosity, which was related to the diameter of the expanded fibers by

( )

1 - ε0 df0 ) 1-ε df

2

(7)

where ε0 and df0 are the porosity and fiber diameter, respectively, of the original felt and ε and df are the macropore porosity and the expanded fiber diameter of the composite. The specific external surface area of the composite was calculated from the diameter of the expanded fibers, i.e. S)

4 df

(8) Figure 7. Relationship between Ergun constant b and the CNF loading.

The macropore porosity and specific external surface area of the expanded fibers were then used as structural parameters in the Ergun model: ∆P µ (1 - ε)2S2 (1 - ε)S 2 ) u + βFu2 ) a µu + b Fu (9) 3 L k ε ε3 with ε3 k) a(1 - ε)2S2

(10)

b(1 - ε)S ε3

(11)

β)

The first term of the Ergun equation was the viscous resistance of the fluid which was independent of the surface roughness of macropores. As a result, Ergun constant a should be independent of the CNF loading. The second term of the Ergun equation was the turbulent resistance of the fluid. Several characteristics of the CNF layer might contribute to the turbulent resistance of the flow in the macropores, which included at least the surface roughness and the rigidness of the CNF layer. The rough and elastic surface of the CNFs on the graphite fibers would deflect the turbulent fluid, cause fluid pulsation and energy dissipation, and thus increase the pressure drop. Therefore, Ergun constant b would change with the amount of CNFs grown on the graphite fibers. The macropore porosity and expanded fiber diameter were calculated from eq 10; while Ergun constant a was obtained from the original felt with eq 10 and the experimentally determined Dacian permeability for bald graphite felt (with a porosity and a fiber diameter of 0.930 and 15.8 µm, respectively). The Ergun constant a for the bald graphite felt was calculated as 12.8, which was also valid for the composite. With

Table 4. Correlation between structural parameters of the composite and the loading of CNFs as-synthesized composite

wetted and dried composite

ε ) 0.948 - 0.301y ε ) 0.941 - 0.124y df ) 1.74 × 10-5 + 1.68 × 10-5y df ) 1.58 × 10-5 + 9.19 × 10-6y 2.3740y b ) 1.0673 + 0.0377e2.9292y b ) 0.8713 + 0.1347e

the Dacian permeability of the composite, one could calculate the macropore porosity and the diameter of the expanded fibers, which were found to be linearly related with the CNF loading, as shown in Figure 6. The calculated macropore porosities of the composites were found in good agreement with that determined by mercury porosimetry, as compared in Table 2. With the non-Darcian permeability coefficient β, the calculated porosity of the composite, and the diameter of the expanded fibers, Ergun constant b was obtained from eq 11. As shown in Figure 7, Ergun constant b was strongly related to the CNF loading. As the loading of CNFs was increased, the elasticity of the CNF layer and the roughness of the surface increased, and consequently the turbulent resistance increased. A similar phenomenon was also found in other porous media, such as that reported by Richardson et al.24 for ceramic foams and Macdonald et al.16 for particle packings. An empirical equation was used to correlate Ergun constant b to the CNF loading, as shown in Figure 7. Finally, the extended Ergun equation for the composite had the following form: ∆P (1 - ε)2 (1 - ε) 2 ) 204.8 3 2 µu + 4b 3 Fu L ε df ε df

(12)

The dependences of ε, df, and b on the CNF loading are summarized in the first column of Table 4.


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Figure 8. Comparison between the experiments and the extended Ergun equation for as-synthesized composite: (a) air, (b) cyclohexane.

Figure 9. Influence of wetting and drying of CNFs on permeability coefficients k and β.

Figure 10. Changes in the morphology of the CNFs layer: (a) before drying, (b) after drying.

With eq 12 and the correlations listed in Table 4, the pressure drop through the composite was calculated and was found to agree very well with the experimental data, as shown in Figure 8. Without altering the constants, the extended Ergun equation was also used to predict the pressure drop for cyclohexane. Figure 8b shows that the prediction was very good except for high CNF loading. This was because the permeabilities for air and cyclohexane were more different when the CNF loading was high. Better prediction of the pressure drop for cyclohexane by the extended Ergun equation would be achieved if the macropore porosity and the expanded fiber diameter were slightly adjusted. Effect of Wetting and Drying Treatment of CNFs with Cyclohexane. The pressure drop measurement for air and cyclohexane was highly reproducible. But when the assynthesized composite was wetted with cyclohexane and then dried in the air at 120 °C, the pressure drop would decrease remarkably, as shown in Figure 9. The Darcian permeability

coefficient increased while the non-Darcian permeability coefficient decreased remarkably after the composite underwent wetting and drying treatment, indicating that both the viscous and turbulent resistance of the fluid were decreased. Figure 10 shows the CNF layer of the composite before and after the wetting and drying treatment. Due to the effect of capillary force, the CNF layer shrank and the composite had larger macropore porosity for convective flow. In addition, the fluffy CNF became denser and smoother and therefore caused less fluid pulsation and energy dissipation. As a result, the composite had a much smaller viscous and turbulent resistance for the fluid. The shrinkage was not reversible, and repeated wetting and drying did not make a further difference, which was because the CNFs were compact and intertwisted. Figure 11 shows the change of the macropore porosity of the composite and the diameter of the expanded fibers after the composite was wetted and dried. In fact, the pressure drop measurements on the as-synthesized and the wetted and dried composite were highly reproducible

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Figure 11. Influence of wetting and drying of CNFs on the structural parameters of the composite: (a) porosity, (b) fiber diameter.

superficial velocity of the fluid. The dependences of macropore porosity, fiber diameter, and Ergun constant b on CNF loading are also summarized in Table 4. With the extended Ergun equation, the pressure drops over the composites after wetting and drying treatment were calculated for both air and cyclohexane, and the results are compared with the experiments and shown in Figure 13. Again the prediction was excellent, except for cyclohexane when the CNF loading was high, which was mainly due to the enlarged difference between the permeabilities for air and cyclohexane. 5. Conclusion Figure 12. Change of Ergun constant b after drying and wetting treatment of the composite.

over months, indicating the structural stability of the composite material in flowing fluids. After wetting and drying, the macropore porosity of the composite was increased while the diameter of the expanded fibers was decreased, and the changes in the porosity and the fiber diameter were more remarkable when the composite had a higher CNF loading. Figure 12 shows that, after the composite had been treated by wetting and drying, the Ergun constant b was slightly decreased. This is reasonable because the CNF layer was less elastic and the surface of the CNF layer was smoother. Therefore, less energy was dissipated by the movement of the CNFs under turbulent flow conditions. Following the same procedures for the as-synthesized composite mentioned above, eq 12 was also utilized to correlate the pressure drop of the wetted and dried composite to the

A porous structured catalyst support was synthesized by growing CNFs on graphite fiber felt. This composite combined the structural properties of graphite fiber felt and CNFs and had a bimodal pore structure containing macropores due to the intertexture of graphite fibers and mesopores due to the intertwist of CNFs. The pressure drop of the composite was derived from the convective flow of the fluid through the macropores, while the fluid in the mesopores was stagnant and had no influence on the pressure drop. The CNF loading strongly affected the pressure drop of the composite because the CNFs had expanded the diameter of the fibers and increased the roughness of the composite. After being wetted with cyclohexane and dried in the air, shrinkage in the CNF layer occurred. As a result the diameter of the expanded fibers decreased and the surface of the CNF layer became smoother, which resulted in a much smaller viscous and turbulent resistance for the fluid. An extended Ergun equation was developed to correlate the pressure drop of the composite to the superficial velocity of the fluid. The macropore porosity and expanded fiber diameter were used

Figure 13. Comparison between the experimental data and the prediction of the extended Ergun equation for wetted and dried composite: (a) air, (b) cyclohexane.


as the structural parameters in the equation. The Ergun constant a was 12.8 and was unchanged for the composite with different CNF loadings, while Ergun constant b depended on the CNF loading and decreased slightly after the wetting and drying treatment due to the decreased roughness and looseness of the CNF layer. Calculated results from the extended Ergun equation agreed quite well with experimental data, indicating that this equation could be used to predict the pressure drop from the structural parameters of the composite with different CNF loadings. Acknowledgment We are grateful to the financial support by the NSFC (20776041, 20736011), the “111” Project (No. B08021), the opening project of Skloche (SKL-ChE-08C07) and the international cooperation project of MOST (2007DFC61690). Notation a, b ) Ergun constants df ) fiber diameter of the composite (m) df0 ) fiber diameter of the graphite felt (m) k ) Darcian permeability coefficient (m2) L ) bed length (m) ∆P ) pressure drop (Pa) Pi ) pressure at bed entrance (Pa) Po ) pressure at bed exit (Pa) S ) external surface area per volume of solid (m-1) u ) superficial velocity (m/s) ui ) superficial velocity in the bed entrance (m/s) VB ) volume of the macropores of the composite (cm3/g) y ) CNFs loading (w/w) ()(weight of CNFs)/(weight of the graphite felt)) Greek letters β ) non-Darcian permeability coefficient (m-1) ε ) macropore porosity of the composite ε0 ) porosity of the graphite felt µ ) viscosity of the fluid (Pa · s) F ) density of the fluid (kg/m3) Fbulk ) bulk density of the composite (g/cm3) Fi ) density of the fluid at bed entrance (kg/m3)

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ReceiVed for reView December 23, 2009 ReVised manuscript receiVed February 11, 2010 Accepted February 16, 2010 IE9020446

Pressure Drop of Structured Packing of Carbon Nanofiber Composite

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