Pressure Drop and Residence Time Distribution in Carbon-Nanofiber

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Pressure Drop and Residence Time Distribution in Carbon-Nanofiber/ Graphite-Felt Composite for Single Liquid-Phase Flow Yaojie Cao, Ping Li, Jinghong Zhou, Zhijun Sui, and Xinggui Zhou* State Key Laboratory of Chemical Engineering, East China University of Science and Technology, 130 Meilong Road, 200237 Shanghai, People’s Republic of China ABSTRACT: Fibrous carbon nanofiber composite is prepared by growing carbon nanofibers on graphite felt. Pressure drop experiments are carried out with ethanol solution to study the influence of the liquid surface tension on the permeability of the composite, and residence time distribution experiments with cyclohexane and water respectively are performed to study the effect of the fluid wettability on the flow behavior in the composite. Piston dispersion exchange (PDE) model is employed to determine the dynamic liquid holdup, the axial dispersion, and the mass transfer between the dynamic and static liquids. When the fluid is less oleophilic, less space in the CNF layer will be open for the flow, and the fluid will be more likely to slip over the carbon surface. Compared with the flow in spherical particle packing and in monolith, the mass transfer in the composite is high owing to its fibrous structure that splits the fluid into streamlets. The rate of mass transfer in water is lower than that in cyclohexane because water is only trapped in some of the large pores in the CNF layer while cyclohexane suffuses the whole layer.

1. INTRODUCTION Structured catalysts, which have regular structures and are free of randomness at reactor level, have been attracting more and more research interest in catalysis and reactor engineering. Different types of structured catalysts including foams,1 monoliths,2 cloths,3
5 and fibers,6 etc., have been investigated, and advantages over traditional catalyst supports, such as low pressure drop, free from separating problem, short diffusion distance, and easy scale-up have been identified. Fibrous catalytic packing can also be considered as a type of structured catalyst. It has a high porosity and large specific surface area when compared with traditional pellet packing, and therefore has low pressure drop and intensified mass/heat transfer when used for multiphase reactions.7 Recently, CNFs have received extensive academic and industrial interest for their novel chemical and physical properties, such as large external surface area, strong resistance to acids and bases, and high mechanical strength. Applying CNFs as catalyst support has been widely investigated, and the CNF-supported catalysts have been reported to display unusual behaviors compared with traditional catalyst supports such as silica, alumina, and active carbon.8
10 However, the CNFs are in the form of fine powders and are difficult to handle when used in industry. To overcome this problem, the CNFs are grown on graphite fiber felt.11,12 The CNF composite obtained in this way combines the advantages of fiber felt and CNFs to have a high porosity, large geometric specific surface area, and large BET specific surface area. The hydrodynamic properties of a catalyst packing are very important for its catalytic performance. The pressure drop of the CNF composite for single-phase flow (gas or wettable liquid) has been correlated to the structural properties (i.e., the volume fraction of the large pores and the diameter of the expanded fibers) of the composite by an extended Ergun equation.12 The loading of the CNFs has a strong influence on the structural r 2011 American Chemical Society

properties, and further on the pressure drop of the composite. Moreover, the pressure drop of the composite decreases significantly if it undergoes wetting by cyclohexane and then drying in air, owing to the shrinkage of the CNF layer induced by capillary effect. Except for the structural properties, the permeability of porous media can also be influenced by the surface tension of the liquid. When the passage for the flow within the porous media is quite large, such as the millimeter irregular channels formed by the solid particles in fixed beds, the influence of surface tension of the flowing liquid on the permeability can be neglected. As the size of the passage decreases, the influence of surface tension on the permeability of the porous media will be more and more important.13 CNFs are highly hydrophobic and so is the CNF composite. The diameters of the pores in the CNF composite are quite small (20
55 μm), and therefore the permeability of the CNF composite will be affected by the properties of the liquid. The behavior of the liquid flow in the composite is highly dependent on the structural properties of the composite and the physical properties of the fluid. More fluid will be trapped in the CNF layer as static fluid if more CNFs are loaded in the composite and the liquid is more oleophilic. As a result the residence time distribution, the axial dispersion, and the mixing performance of the fluid will be changed accordingly. Up to now, little is known about the influence of the structural properties of the composite and the physical properties of a liquid on the permeability and the flow behavior. Motivated by this, water
ethanol mixtures with different concentrations are used as a working fluid to determine the influence of the liquid surface tension on the permeability of the composite by pressure drop Received: March 2, 2011 Accepted: June 28, 2011 Revised: June 12, 2011 Published: June 28, 2011 9431

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Table 1. Structural Properties of the CNF Composite Used in the Experimenta macropore

fiber diameter

thickness of CNF

porosity

(μm)

layers (μm)

CNF loading (w/w)

a

b

a

b

a

b

0 0.97

0.930 0.650

0.930 0.857

15.8 35.3

15.8 22.5

0 9.8

0 3.4

1.39

0.530

0.769

40.8

28.6

12.5

6.4

1.64

0.454

0.738

45.0

30.9

14.6

7.6

a

a = before wetting and drying treatment; b = after wetting and drying treatment.

measurement. Cyclohexane and water are used as a working fluid respectively to investigate the effect of the liquid wettability on the flow behavior in the composite by residence time distribution (RTD) experiments. RTD measurement is a powerful tool widely used to analyze the flow behavior of fluid in chemical reactors. Significant work has been performed to measure the RTD properties in various structured catalysts such as monoliths,14
16 foams,17,18 and fibers.19 In this paper, the piston dispersion exchange (PDE) model20 is employed to describe the RTD curves to determine the dynamic liquid holdup, the axial dispersion, and the mass transfer between the dynamic and static liquids.

2. EXPERIMENTAL SECTION Synthesis of CNFs. The graphite felt was first tailored into cylinders 10 mm high and 35 mm in diameter. CNFs were then synthesized at 640 °C on the cylinders with nickel as catalyst and ethane as carbon source and in the presence of hydrogen. The synthesis of the CNF composite followed the same procedure described previously.12 Characterization of the Composite. The BET specific surface area of the composite was measured by N2 adsorption
desorption at 77 K with ASAP 2010 (Micromeretics), and the pore size distribution and porosity of the composite were measured by mercury porosimetry with AutoPore IV 9500 (Micromeretics). The morphology (not shown in this paper) of the composite was characterized by scanning electron microscopy (SEM; JSM-6360LV). It was observed that the surface of the graphite fibers was covered uniformly by CNFs. The diameter of the CNFs was 50
100 nm and the BET specific surface area of the composite was 51
59 m2/g. Table 1 summarizes the structural properties of the CNF composite before and after the composite being wetted with cyclohexane and dried in air. The CNF loading is defined as the weight ratio of the CNFs to the original graphite felt. The macropore porosity is the volume fraction of the pores excluding those in the CNF layers. Because the CNFs are grown on the surface of the graphite fibers, the composite remains the same fibrous structure of the graphite felt, but the fiber is expanded by the CNF layers. The expanded fiber diameters listed in Table 1 were determined by pressure drop experiments, as indicated in the previous work.12 Measurement of Pressure Drop. A CNF composite with a CNF loading of 1.39 was used for pressure drop measurement. The column was 20 mm high and 35 mm in diameter. To avoid bypass of the fluid, the composite was wrapped with PTFE,

Figure 1. Viscosity21 and surface tension22 of water
ethanol mixture as functions of ethanol concentration at 24 °C.

which was then installed in a quartz tube 35 mm in diameter. The pressure drop, as indicated by a manometer, was measured at various liquid flow rates. To investigate the effect of surface tension on the permeability of the CNF composite, ethanol solution with different concentration was used as working fluid. Figure 1 shows the changes of the viscosity and surface tension with ethanol concentration. Measurement of Flow Characteristics. Residence time distribution (RTD) experiments were carried out to study the characteristics of the flow in the composite packing with different loadings of the CNFs. The total height of the packing was 40 mm. Cyclohexane was used as the working fluid and o-nitrophenol (2.5 wt % in cyclohexane), which has an absorption peak at 344 nm, was used as a tracer. In each experiment, 0.5 mL of the tracer solution was injected instantaneously into the inlet of the column, and the tracer concentration in the effluent was measured by absorption spectrum with an online fiber optic spectrometer (Avantes). To determine the influence of the shrinkage of the CNF layers, the composite was taken out and then dried in air. It was then reinstalled in the quartz tube for RTD experiments. Water was also used as the working fluid to investigate the flow characteristics in the CNF composite packing. In the RTD experiment with water, the composite employed had a CNF loading of 1.64. Sodium bichromate (6 wt % in water) was used as the tracer, and its concentration in the effluent was measured by absorption spectrum at 350 nm with the same online fiber optic spectrometer. The piston dispersion exchange (PDE) model20 was used to depict the flow behavior in the CNF composite. In this model, the liquid is divided into dynamic liquid and static liquid. The dynamic liquid flows through the porous media as a piston flow with axial dispersion, while the static liquid is stagnant. In addition, there exists mass transfer between the dynamic liquid and static liquid. The mass balance for the dynamic and static liquids constitutes the model equations: ∂Cd 1 ∂2 Cd ∂Cd ¼
NR ðCd
Cs Þ
ϕ Pe ∂z2 ∂θ ∂z ð1
ϕÞ

∂Cs ¼ NR ðCd
Cs Þ ∂θ

ð1Þ ð2Þ

where Pe is the Peclet number, NR is the number of mass transfer units, and ϕ is the fraction of dynamic liquid. For pulse-input 9432

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Figure 2. Pressure drop of the CNF composite for water
ethanol mixture: (b) water, (O) 10% ethanol, (1) 20% ethanol, (Δ) 30% ethanol, (9) 40% ethanol, (0) 50% ethanol, (() 60% ethanol, ()) 70% ethanol, (2) 80% ethanol, (r) 95% ethanol.

tracer experiments, the initial and boundary conditions are Cd ¼ Cs ¼ 0 at θ ¼ 0

ð3Þ

Cd ¼ δð0Þ at z ¼ 0

ð4Þ

∂Cd ¼ 0 at z ¼ 1 ∂z

ð5Þ

Through the fitting of the PDE model to the RTD curves, the model parameters, i.e., the Peclet number, the fraction of dynamic liquid, and the number of mass transfer units, which indicate the characteristics of the flow, can be estimated. Once the fraction of dynamic liquid is obtained, the static liquid holdup in the CNF composite can be estimated from the following equation: εLt ¼

τQL , εLs ¼ εLt ð1
ϕÞ VR

ð6Þ

where εLt and εLs are the total and static liquid holdup of the composite, respectively, and τ is the average residence time of the fluid obtained from the RTD curves: Z ∞ cðtÞ ð7Þ tf ðtÞdt, f ðtÞ ¼ Z ∞ τ¼ 0 cðtÞdt 0

3. RESULTS AND DISCUSSION Permeability of the CNF Composite. Figure 2 shows the linear dependence of the pressure drop of the CNF composite on the superficial velocity of the ethanol solution. Under the experimental condition, the pressure drop over the composite is caused only by the viscous resistance of the liquid. Figure 3 shows that with the increase of the ethanol concentration, the pressure drop first increases then decreases, and the maximum appears at the ethanol concentration of 40 wt %, which corresponds to the concentration with the highest viscosity. The Darcian permeability coefficient was determined by

ΔP μ ¼ u L k

ð8Þ

which is shown in Figure 3. Generally, k is only related to the structural properties of the porous media, and is independent of

Figure 3. Changes of pressure drop and permeability coefficient with ethanol concentration (liquid superficial velocity: 0.01 m/s).

the physical properties of the flowing fluid. However, a remarkable change of the Darcian permeability coefficient with the ethanol concentration is seen in Figure 3, and there also exists a maximum in the Darcian permeability coefficient at an ethanol concentration of about 60 wt %. This is explained by the hydrophobic surface of the CNF composite and the change of the surface tension of the mixture with ethanol concentration. At a low ethanol concentration, the surface tension of the liquid is high and only the large pores are available for fluid flow. On the other hand, the liquid with a high surface tension will be difficult to wet the fiber surface, and the friction at the liquid
solid interface will therefore be small. This is because of the space for fluid flow and the friction at the interface that result in the existence of the highest permeability for an ethanol solution with certain surface tension. Figure 3 also shows the drying effect of the CNF composite. The pressure drop decreased while the permeability increased remarkably because of the shrinkage of the CNF layer. RTD in the Composite Packing. Figure 4 shows the RTD of cyclohexane flow in the CNF composite that has been subjected to cyclohexane-wetting and air-drying treatment. The CNF loading changes the RTD remarkably because it changes the porosity of the packing. Moreover, the tailing effect is more evident at a higher CNF loading because more fluid is trapped in the CNF layer. In whatever case, the PDE model provides a good fitting of the experiments. Axial Dispersion of the Liquid. To have a clear insight into the effect of CNFs on the axial dispersion of the liquid, the Bodenstein number was calculated with the Peclet number, and the characteristic length of the packing was the diameter of the expanded fibers Bo ¼ Peðdf =LÞ

ð9Þ

In Figure 5 the Bodenstein number is plotted against the Reynolds number that was also calculated with the diameter of the expanded fibers. It is obvious that the Bodenstein number is independent of the Reynolds number. The constant Bodenstein number for small Reynolds numbers was also observed by Westerterp et al.23 who showed that for liquid flow in a packed bed of nonporous spheres, the Bodenstein number was about 0.5 and was independent of the velocity of the liquid when the Reynolds number was lower than 10. The Bodenstein number of the liquid in the CNF composite is much lower than that in the packed bed of spherical particles, which is mainly due to the small diameter of the expanded fibers 9433

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Figure 4. Influence of fluid velocity (a) and CNF loadings (b) on the RTD curves (dots: experiments; curves: PDE model).

Figure 5. Dependence of Bodenstein number on Reynolds number. The error bars represent the standard error.

Figure 6. Dependence of dynamic liquid fraction on the liquid velocity. The error bars represent the standard error.

and the high porosity of the composite. Chung and Wen24 correlated the axial dispersion coefficients from literature data and indicated that the Bodenstein number would be small when the porosity of the packed bed was large. The small Bodenstein number for fiber packings was also reported by Van Zee et al.19 The Bodenstein number is strongly dependent on the loading of CNFs. Increasing the CNF loading will increase the thickness of the CNF layers. As a result, the fraction of static liquid holdup, and the mass transfer between the dynamic liquid and the static liquid will be increased, as will be shown below. All this intensifies the axial dispersion, making it stronger than that in packed beds of nonporous particles. The stronger axial dispersion in a porous particle packing was also reported by Iliuta et al.25 Because the Bodenstein number is independent of the velocity of the liquid, the axial dispersion coefficient is proportional to the liquid velocity. Static Liquid Holdup of the CNF Composite. For a packed bed, the static liquid holdup is resulted from the balance between the capillary and gravitational force. Therefore, it depends only on the pore size and distribution and the surface wettability of the porous media, and is independent of the velocity of the fluid, as confirmed by the results shown in Figure 6. For single liquidphase flow, the CNF composite is saturated with the liquid, i.e., the total liquid holdup in the composite is equivalent to the porosity of the composite. Because the static liquid is mainly trapped in the CNF layer, increasing the CNF loading will consequently decrease the fraction of dynamic liquid. Saez and Carbonell26 suggested that the static liquid holdup in a packed bed could be correlated to the modified E€otv€os number

Figure 7. Correlations of static liquid holdup with E€otv€os number.

(E€o) by the following equation: εLs ¼

2 2 1  ¼ FL gde ε , E€ o c þ dE€o σð1
εÞ2

ð10Þ

The relationship between the static liquid holdup and the E€otv€os number for the CNF composite is presented in Figure 7. For solid particles, c and d determined by Saez and Carbonell are 20 and 0.9, respectively, while for the CNF composite, the best fitted values of c and d are 2.74 and 248, respectively. The static liquid holdup of the CNF composite is much higher than that of solid particle packings, which is due to the trapping of the liquid in the CNF layer and at the junctions of the fibers. 9434

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Table 3. Comparison of Model Parameters of Fresh and Treated Composite ϕ

Pe

NR

fresh composite

0.754

33

0.930

wetted and dried composite

0.801

53

0.684

sample

Figure 8. Dependence of mass transfer coefficient on the liquid velocity. The error bars represent the standard error.

Table 2. Comparison of Model Parameters for Water and Cyclohexane fluid

ϕ

Pe

NR

water

0.854

26

0.407

cyclohexane

0.717

23

1.477

Mass Transfer between Dynamic and Static Liquid. By fitting the PDE model to the RTD curves, the number of mass transfer units is determined. From the number of mass transfer units, the mass transfer coefficient between the dynamic and static liquids in the CNF composite is obtained and found to be linearly related to the liquid velocity, as shown in Figure 8. Increasing the CNF loading will increase the liquid velocity in the macropores of the CNF composite, thus intensify the mass transfer. The mass transfer coefficient in CNF composite is much higher than that in a packed bed of solid nonporous spherical particles,27 and is comparable to that in monolith reactors,15,28 although the superficial velocity in our experiments is significantly lower. The high mass transfer coefficient in the CNF composite is attributed to the fibrous-network structure that splits the fluid into streamlets with a size close to the diffusion scale or Kolmogorov scale. The frequent splitting and combination of the fluid further intensifies the mass transfer. Table 2 shows the estimated parameters of the PDE model when water or cyclohexane is used as the fluid. In both cases, the composite has a CNF loading of 0.97 and has been wetted by cyclohexane and dried in air. Under the investigated range of the liquid flow rate, the parameters are almost constant. Owing to the strong hydrophobicity of the CNFs, the CNF layer can be completely suffused by cyclohexane but only partially filled by water. This explains why the axial dispersion is low when water is used as the fluid because the axial dispersion in the CNF composite is mainly caused by the static liquid in the CNF layer. However, the number of mass transfer units in water is much smaller than that in cyclohexane. Because the mass flow rate of the dynamic liquid in the composite is similar for water and cyclohexane, the small mass transfer unit is mainly contributed by the small interfacial area between the dynamic and static liquids. As can be seen from the SEM of the expanded fiber,12 the CNF layer has very irregular pore sizes. Because of the hydrophobicity of the CNFs, only the pores in the CNF layer with a capillary pressure smaller than the static pressure of the fluid will trap static liquid, while water will just slip over the mouth of the smaller

pores in the CNF layer. From the volumetric mass transfer coefficients for cyclohexane and water, which are calculated from the number of mass transfer units, it is estimated that less than 36% of the pores in the CNF layer will trap water. Table 3 shows the parameters of the PDE model for the CNF composite before and after wetting and drying treatment when cyclohexane is used as working fluid. After the treatment, the CNF layer shrinks significantly owing to the capillary effect and hence traps much less static liquid. Therefore, the axial dispersion is diminished. In addition, because the velocity of the dynamic liquid decreases, the mass transfer coefficient and the number of mass transfer units are lowered.

4. CONCLUSION The hydrodynamic properties of CNF composite for single liquid-phase flow are investigated. The permeability of the CNF composite for liquid depends on the surface tension of the flowing liquid owing to the strong hydrophobicity of the CNFs and the small dimensions of the passages in the composite. When the fluid is less oleophilic, less space in the CNF composite will be open for the flow, while the fluid will be more likely to slip over the carbon surface. The CNF composite shows the highest permeability when the ethanol concentration of the water
ethanol mixture is 60 wt %. The flow characteristics of the liquid in the CNF composite for single liquid-phase flow are determined by RTD experiments and the PDE model. Increasing the loading of CNFs will increase the thickness of CNF layers and hence increase the static liquid holdup, the axial dispersion, and the mass transfer between the dynamic and static liquids. When the CNF layer is shrunk by wetting and drying treatment, the flow behaves the same as with a lower loading of CNFs. The static liquid holdup of the composite is much higher than that of packed bed of solid particles owing to the strong capillary effect of the composite and the existence of CNF layers. The static liquid holdup is very sensitive to the loading of CNFs, and can be described as a function of the modified E€otv€os number. Compared with the flow in spherical particle packing and in monolith, the mass transfer in the composite is higher owing to its fibrous structure that splits the fluid into streamlets. The fibrous-network structure splits the fluid into streamlets with a size close to the diffusion scale or Kolmogorov scale, and the frequent splitting and combination of the fluid in the composite further intensifies the mass transfer. The rate of mass transfer in water is lower than that in cyclohexane because water is only trapped in some of the large pores in the CNF layer, which reduces the interfacial area between the dynamic and static liquids. ’ AUTHOR INFORMATION Corresponding Author

*Tel.: +86-21-64253509. Fax: +86-21-64253528. E-mail: xgzhou@ ecust.edu.cn. 9435

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’ ACKNOWLEDGMENT We are grateful for the financial support by the NSFC (20776041, 20736011), and the 111 Project (B08021). ’ NOTATION Bo = Bodenstein number (= uddf/Dax) c, d = coefficients in eq 10 Cd = concentration of tracer in dynamic phase Cs = concentration of tracer in static phase Dax = axial dispersion coefficient (m2/s) de = equivalent diameter of fibers (= 3df/2) (m) df = diameter of expanded fibers (m) E€o* = modified E€otv€os number (= Fgde2ε2/(σ (1
ε)2)) f(t) = residence time distribution function (s
1) g = gravitational acceleration constant (m/s2) k = Darcian permeability coefficient (m2) L = length of the fixed bed (m) NR = number of mass transfer units (= kLaL/(ϕud)) ΔP = pressure drop (Pa) Pe = Peclet number (= udL/Dax) QL = liquid flow rate (m3/s) Re = Reynolds number (= Fudf/(μ(1
ε))) u = superficial velocity of the fluid (m/s) ud = velocity of liquid in dynamic zone (m/s) VR = volume of packed bed (m3) z = distance down the fixed bed (dimensionless) Greek letters

δ = Dirac function ε = porosity of the CNF composite εLs = static liquid holdup εLt = total liquid holdup θ = dimensionless time μ = viscosity of liquid (kg/(m 3 s)) F = density of liquid (kg/m3) σ = surface tension (N/m) τ = average residence time (s) ϕ = dynamic liquid fraction

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