Comparison of Packed Beds, Washcoated Monoliths, and Microfibrous

Article pubs.acs.org/IECR

Comparison of Packed Beds, Washcoated Monoliths, and Microfibrous Entrapped Catalysts for Ozone Decomposition at High Volumetric Flow Rates in Pressurized Systems Qiang Gu, Pengfei Zhao, Robert T. Henderson, and Bruce J. Tatarchuk* Center for Microfibrous Materials (CM3), Department of Chemical Engineering, 212 Ross Hall, Auburn University, Auburn, Alabama 36849, United States ABSTRACT: Weight- and volume-sensitive systems such as aircraft require restrictive ducting, which leads to high face velocities (10−40 m/s) in reactive structures. A head-to-head comparison was conducted experimentally among packed beds (estimated data), monoliths, and microfibrous entrapped catalysts (MFECs) during ozone decomposition to investigate the effects of system pressure on the effective reaction rate, gas−solid mass-transfer rate, and heterogeneous contacting efficiency (HCE, the ratio of the logarithmic ozone removal to the pressure drop across the reactor). For the same mass flow rate, higher-pressure systems (2−3 atm) operate at lower face velocities than atmospheric-pressure systems. These higher system pressures result in increased residence times and reaction rates; therefore, HCE is enhanced. In addition, the HCE for the MFEC was more than twice that of the packed bed or monolith at equivalent system pressures because of the higher gas−solid mass-transfer rates and reduced pressure drops of the MFEC.

1. INTRODUCTION High-volumetric-flow catalytic applications such as aircraft ozone removal, automobile catalytic converters, and fuel-cell cathode air filters result in short contact times in reactor structures. High catalytic activity is demanded in these applications to remove contaminants such as ozone, NOx, and SOx.1−6 Moreover, the pressure/volume work done by the reactor in high volumetric flow generates heat (e.g., 5.3 kW at 104 Pa pressure drop and 0.53 m3 air/s), so good reactor heat management is also required. Fixed-bed reactors with low porosity such as monoliths are commercially used in highvolumetric-flow applications.7,8 Other fixed-bed structures such as packed beds are not used because low porosity and small particle sizes lead to high pressure drops across reactors. The performance of monoliths in high-volumetric-flow applications is also limited because of the restrictive ducting systems involved in these applications. The heterogeneous contacting efficiency (HCE, defined as the logarithmic removal of ozone per unit of pressure drop) is used to assess the overall performance of different structures.9−11 To improve HCE, monoliths are required to be simultaneously shorter in length and larger in diameter to reduce the pressure drop and maintain the same conversion rate, which is not practical in weight- and volume-sensitive systems that have restrictive ducting. This is opposed to microfibrous entrapped catalysts (MFECs), which can be pleated to provide larger surface areas; therefore, HCE is improved as a result of the reduced pressure drop and increased residence time and reaction rate for mass-transfer-limited reactions. Another way to change HCE without changing the reactor size of monoliths is to reduce the cell sizes, which enhances the gas−solid mass-transfer rate. However, pressure © 2016 American Chemical Society

drop also increases with smaller cell sizes. Therefore, this method is not preferred in weight- and volume-sensitive systems. Higher system pressures (2−3 atm) are often seen in many high-volumetric-flow applications.7 Higher system pressures affect the pressure drops, mass-transfer rates, and convective heat-transfer properties of reactive structures. In this work, three evaluation criteria, namely, gas−solid mass-transfer coefficient, effective reaction rate, and HCE, are used to conduct a head-to-head comparison among packed-bed, monolith, and MFEC reactors experimentally and theoretically, so that the advantages of higher system pressures in highvelocity flow can be analyzed in comparison with the characteristics of atmospheric-pressure systems. In addition, a convective heat-transfer model is used to study the convective heat-transfer properties of the fibrous medium at different system pressures. Koch et al.12,13 theoretically found enhanced radial and axial thermal conductivities for fixed-bed and fibrous media at increased pressures. This impacts the temperature distribution and, thus, the catalytic performance within the reactor.

2. MATERIALS AND METHODS 2.1. Atmospheric Testing. The high-volumetric-flow test setup is shown in Figure 1a. This closed-loop setup includes a 40-hp blower (Fan Equipment Company Inc.) to circulate air at Received: Revised: Accepted: Published: 8025

November 9, 2015 June 24, 2016 June 27, 2016 June 27, 2016 DOI: 10.1021/acs.iecr.5b04247 Ind. Eng. Chem. Res. 2016, 55, 8025−8033

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Industrial & Engineering Chemistry Research

Figure 1. High-face-velocity test setup: (a) Schematic of test setup, (b) heat balance of the system.

system-pressure (2−3 atm) testing. This system includes a tubular reactor that is contained in a temperature-controlled oven, with the ozone concentrations (Eco Sensor UV100) and temperatures (Omega J type thermocouples) monitored upstream and downstream of the reactor. The tubular reactor can reach the same temperature and face-velocity range as the atmospheric system. At high flow rates, the pressure drop across the reactor is affected by several factors, including porosity, fiber dimensions, and media compressibility. The most accurate way of acquiring the pressure drop is the medium permeability test. This test was done with IDP10-T differential pressure transmitters upstream and downstream of the reactor. 2.3. Catalyst Materials and Structures. 2.3.1. MFEC. Microfibrous material was prepared using a traditional wet-lay process. Fibers and cellulose were first mixed into a suspension. The cellulose added in this process acts as a temporary binder. The suspension was then transferred into a head box, where catalyst support particles (Al2O3, SiO2, TiO2, etc.) were added and formed preformed sheets. Dried preform sheets were preoxidized at 400 °C to remove the cellulose binder before the sintering process because of the reduction of mechanical strength for the MFEC.14 The sintering process was carried out in a BTU-1000 controlled atmosphere electric furnace (1000 °C for nickel fiber). A nominal 1% Pd/Al2O3 catalyst was prepared by wet impregnation of Al2O3 using an aqueous solution of Pd(NO3)2·2H2O. After impregnation, the catalyst was dried overnight at 383 K, treated under an air flow at 673 K for 4 h, and stored until use. Figure 3 shows SEM images of the microfibrous material (8μm nickel fiber from IntraMicron, Inc.) without (Figure 3a)

high face velocities (10−40 m/s). Ozone concentrations were recorded using two Eco Sensor UV100 sensors upstream and downstream of the reactor. The inlet ozone concentration in any test of this research was 1.5 ppmv. Temperatures were recorded at multiple locations on the loop using Omega J type thermocouples. The pressure drops across the blower and reactor were recorded using IDP10-T differential pressure transmitters. Figure 1b shows the heat balance on the system. The system was constructed as a closed loop because of the difficulty of simulating turbine bleed air temperature using a common blower. The skin friction on the pipe wall increases the system temperature quickly at high face velocities. 2.2. Higher-Pressure (2−3 atm) Tubular Reactor. Figure 2 shows the 1-in.-diameter tubular reactor for higher-

Figure 2. Tubular reactor for testing reactor structures at increased system pressures.

Figure 3. SEM images of MFEC material: (a) 8-μm nickel fiber, (b) 8-μm nickel fiber entrapped with 150−250-μm alumina particles. 8026

DOI: 10.1021/acs.iecr.5b04247 Ind. Eng. Chem. Res. 2016, 55, 8025−8033

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correlations between the Sherwood number and Reynolds number. The Thoenes−Kramers19 correlation

and with (Figure 3b) entrapped particles (150−250-μm Al2O3). These small-size catalyst support particles enhance interphase and intrabed mass-transfer rates.14−16 MFECs also have high voidage (>70%) and effective radial thermal conductivity because of the orientation of metal fibers in the bed. This was exploited by Sheng et al.17 during a highly exothermic Fischer−Tropsch synthesis. The prepared MFEC sheets were cut to dimensions of 5 in. × 9 in. and were aligned in a rectangular reactor (5 in. × 5 in. × 9 in.) with a pleat factor of 4 (W structure). The individual pleats were placed in the rectangular reactor in a pair of aluminum U channels with dimensions of 0.5 in. × 0.5 in. × 9 in. Therefore, the effective parts for reaction in the MFEC reactor are four pleats with dimensions of 4 in. × 9 in. 2.3.2. Monoliths. Monoliths were prepared using ceramic honeycombs (synthetic cordierite) from Applied Ceramics of 230 and 400 cells per square inch (CPSI). Higher-CPSI monoliths were not tested in this research even though the mass-transfer properties would benefit from higher CPSI. This is because monoliths of 400 or less CPSI maintain a pressure drop comparable to that of MFECs; higher CPSI values decrease the HCE significantly. The support particles were loaded onto the ceramic substrate by a sol−gel technique:18 urea, 0.3 M HNO3, and boehmite (CATAPAL B from Sasol) were mixed in a 1:2:5 (w/w/w) ratio. The substrate was immersed into the solution for 5 min, and then excess solution was removed . The substrate was then dried at 393 K and calcined at 773 K for 6 h. These steps were repeated until 30 g of support was loaded onto the substrate. The washcoated monolith was then impregnated with Pd catalyst. Each monolith was prepared to have the same amount of pore volume and metal content as the MFECs. However, the particle size in the monoliths and MFECs were different because of the differences in preparation processes. The properties of the monoliths used in the experiments are listed in Table 1.

Sh =

230 CPSI monolith

400 CPSI monolith

wall thickness (0.001 in./μm) channel diameter (mm) void (%) catalyst (vol %) length (cm)

8/203 1.422 72.13 3.484 12.7

6.5/165 1.054 68.89 4.685 12.7

(1)

was used for the packed bed. This semiempirical correlation is valid for packed beds with 40 < Re/(1 − ε) < 400 and 0.25 < ε < 0.5. Figure 4 shows the calculated volumetric mass-transfer coefficients (kmac) at different face velocities. It is noted that the mass-transfer coefficient for each reactor structure was enhanced at higher system pressures and increasing face velocities. This increment is mainly due to the enhancement of the effective diffusivity term. However, the percentage increments in mass-transfer coefficients for the MFEC and packedbed reactors were less than those for the monolith reactors considering the same pressure increment or face-velocity increment. This is due to the smaller particle sizes used in the MFEC and packed bed. The percentage increments in mass-transfer coefficient for the MFEC and packed-bed reactors were almost identical considering the same pressure increment or face-velocity increment, even though the particles were much more dispersed in the MFEC. Voidage effects on the mass-transfer coefficient were minimal in the high-velocity range. The effective diffusivity of ozone in air was calculated using Fuller’s method.20 The mass-transfer coefficient for the packed bed and MFEC were in the same range, because the particle sizes used in these reactors were similar. However, the voidages of these beds were significantly different. The MFEC particles were much more dispersed than the packed-bed particles, making the reactant less likely to interact with the catalyst surface. This accounts for the higher effective reaction rate of the packed bed. In any reactor structure, the turbulent flow conditions of the inlet provide good mixing of the reactant. Even though the fibers in MFEC add additional mixing to the reactant, the fiber contribution to the mass-transfer process in the MFEC reactor was still minimal. 3.1.2. Monolith Reactors. The correlation of Tronconi and Beretta,21 which is valid for the fluid-phase mass-transfer coefficient in a monolith, is given by

Table 1. Properties of the Monoliths property

(1 − ε)1/2 1/2 1/3 Re Sc ε

Sh = 2.967 + 8.827 ×

⎛ 1000 ⎞−0.545 ⎛ −48.2 ⎞ ⎜ ⎟ ⎟ exp⎜ ⎝ Gz ⎠ ⎝ Gz ⎠

(2)

The mass-transfer coefficients for the monolith at different face velocities are shown in Figure 4. Figure 4 also explains why a monolith is not well adapted for use under high-volumetricflow conditions. In high-face-velocity applications, the masstransfer coefficient is the maximum attainable reaction constant for any reactive structure.22 It is noted that the mass-transfer coefficient for a monolith is more than 10 times lower than that for a packed bed or MFEC because of the particle size involved. In addition, previous studies23 found the ozone decomposition reaction to be mass-transfer-limited. This major disadvantage, low gas−solid transfer rate, is the reason why monolith reactors have to be larger, so that more catalyst can be loaded, and more contact time is needed for an acceptable conversion rate. 3.1.3. MFEC Reactor. Dwivedi and Upadhyay22,24 proposed the following correlation for gas−solid mass transfer in a fixed bed

The size of the monolith reactors used on the high-velocity test system was the same as that of the MFEC reactor. The monolith reactors were fitted into a rectangular housing with dimensions of 5 in. × 5 in. × 9 in. 2.3.3. Packed Bed. Packed-bed reactors were not tested experimentally because of the low porosity of the bed. The maximum face velocity in a packed bed is significantly lower than that in monoliths and MFECs. However, for theoretical calculations, activation energies and pre-exponential factors were determined using the MFEC results. This approach is valid for mass-transfer-limited reactions that are carried out using the same-size particles, as discussed in section 3.2.

3. RESULTS AND DISCUSSION 3.1. Mass-Transfer Correlations. 3.1.1. Packed-Bed Reactor. The mass-transfer coefficients for the packed-bed, monolith, and MFEC reactors were determined by three

Sh = 8027

0.455 0.59 0.33 Re Sc ε

(3) DOI: 10.1021/acs.iecr.5b04247 Ind. Eng. Chem. Res. 2016, 55, 8025−8033

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Figure 4. Volumetric mass-transfer coefficient calculated for packed-bed (150−250-μm Al2O3, 40 vol % loading), monolith (12.5-μm washcoat thickness), and MFEC (20 vol % loading of 150−250-μm Al2O3, 5 vol % loading of 8-μm-diameter nickel fiber) reactors at three system pressures.

1 1 1 = + keff k mac ηk rρc

which is valid for voidages ranging from 0.25 to 0.97 and Reynolds numbers up to 10000. This correlation was chosen for the MFEC reactor because it is the result of correlating large amounts of fixed-bed reactors of different voidages. As shown in Figure 4, small-size particles are needed for high-velocity applications because of the mass-transfer-rate requirements. However, the pressure drop across any reactive structure increases with smaller particles.16 An optimum particle size range is required for applications at velocities in a given range. The packed beds and MFEC in Figure 4 used the same-size particles (150−200 μm). This range was determined by experimental pressure-drop tests for MFEC media of different particle sizes. 3.2. Calculation of Effective Reaction Rates. To determine the appropriate kinetic model, it is important to determine the flow type within the reactor at high face velocity. The intrabed Reynolds number for the MFEC was between 455 and 1818 for face velocities of 10−40 m/s, which indicates weakly turbulent flow.25 Reynolds number analysis for packed beds and monolith also indicate turbulent flow in these reactors. This result has been verified by a numerical analysis,26 in which velocity profile within MFEC is acquired by the Navier−Stokes equation. Plug flow is found to exist in this velocity range within a very thin boundary layer.26 The mass balance for a plug-flow reactor is given by −v

dcA = k macXc(CA − CAS) dx

The effective reaction rate is a measure of catalyst utilization for the reactor, which considers both the surface reaction and the gas−solid mass-transfer rate. The keff term in eq 7 is the only quantity that needs to be determined experimentally. A tubular reactor was used to determine the catalytic performance at three system pressures. 3.2.1. Packed-Bed Reactor. The surface reaction rate, kr, for a packed-bed reactor was calculated by iteratively solving eq 7 with the effectiveness factor equation η=

⎛ φd p ⎞ k rρc Θ=⎜ ⎟ ⎝ 6 ⎠ DDeff

dcA = keff XcCA dx

(8)

(9)

The surface reaction rate term in eq 7 (third term) was determined using the pre-exponential factor and activation energy calculated from the Arrhenius equation for the MFEC in Figure 5. This is because packed beds and MFECs made of particles of the same size have similar mass-transfer coefficients in Figure 4. The mass-transfer coefficient, in this case, is the maximum attainable reaction constant for ozone decomposition. In addition, the low porosity of a packed bed limits the maximum face velocity; experimental determination of the effective reaction rate is not applicable. The mass-transfer rate term in eq 7 (second term) was calculated using the method described in section 3.1. 3.2.2. Monolith Reactors. The same calculation process as described in section 3.1.1 was repeated for the monolith reactors with the effectiveness factor equation

(4)

(5)

If keff is the effective reaction rate, then we can also write −v

1 [coth(3Θ) − 1/3Θ] Θ

where

It has been previously determined that ozone decomposition at high face velocity is a mass-transfer-limited reaction.23 The mass-transfer rate is the same as the reaction rate, namely k macXc(CA − CAS) = ηk rρc XcCAS

(7)

(6)

η=

By eliminating the concentration term in the above equations, the effective reaction rate can be expressed as

tanh(Θ) Θ

(10)

where 8028


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utilization by these reactors. For monoliths of different CPSIs, higher-CPSI monoliths offer smaller characteristic lengths, which improves the gas−solid mass-transfer rate; thus, the effective reaction rate is also enhanced for monoliths of higher CPSIs. 3.2.3. MFEC Reactor. It is noted that the effective reaction rate is enhanced for any reactive structure at higher system pressures. This enhancement is mainly due to an improvement in the gas−solid mass-transfer rate (section 3.1.1.). It is also noted that Figures 4 and 6 show almost identical patterns. This is because the surface reaction rate (ηkrρc in eq 7) is much higher than the mass-transfer rate for mass-transfer-limited reactions. Take the monolith reactors at 1 atm as an example. The ηkrρc term is approximately 500 times higher than the mass-transfer rate term, which makes the difference between Figures 4 and 6 negligible. The packed-bed and MFEC reactors have even larger ηkrρc terms because of their slightly higher effectiveness factors. Therefore, their effective reaction curves are also identical to the mass-transfer-coefficient curve. In addition, the effective reaction rate for the packed bed was found to be larger than that for the MFEC. The packed bed had a void fraction of 0.4 compared to 0.7 for the MFEC. The increased void fraction led to a lower face velocity and thus a higher gas−solid mass-transfer rate. 3.3. Heterogeneous Contacting Efficiency. The performances of different reactor structures at different system pressures were compared using a parameter called the heterogeneous contacting efficiency (HCE). The HCE, defined as the ratio of the mass efficiency to the flow efficiency, essentially calculates the logarithmic ozone removal per unit of pressure drop. Combining the mass balance equation for the plug-flow model and the gas−solid mass-transfer equation, the mass efficiency χM is defined as9−11

Figure 5. Arrhenius plot for ozone decomposition using nickel MFEC (1 wt % Pd catalyst on Al2O3 support with 5 vol % 8-μm nickel fiber) and monolith (12.5-μm washcoat thickness, 230 CPSI) reactors at three system pressures.

Θ = tc

k rρc DDeff

(11)

The Arrhenius plots for ozone decomposition using monoliths at 1, 2, and 3 atm are also shown in Figure 5. Table 2 reports the pre-exponential factors and activation Table 2. Pre-Exponential Factors and Apparent Activation Energies for MFEC and Monolith at Various Pressures pressure (atm)

pre-exponential factor (1/s)

1 2 3

2.66 3.91 3.78

1 2 3

5.89 7.33 5.43

MFEC × 108 × 108 × 108 Monolith × 106 × 106 × 106

activation energy (kJ/mol) 23.02 25.12 25.58

χM =

km C L = ln A1 1 + kcac /k rac v CA2

(12)

The flow efficiency χF, also known as the double Euler number, is defined by

15.50 17.15 17.15

χF =

energies for both MFEC and monolith reactors at three system pressures, both of which show no obvious dependence on system pressure. MFECs have larger pre-exponential factors than monoliths because of the smaller characteristic lengths involved in these reactors, which offer higher surface areas. The activation energies involved in these calculations are apparent. They are mixed values of surface-reaction and mass-transfer processes. In this particular case, the effect of mass transfer on the activation energy is much higher than that on the reaction itself. However, the two reactions undergo the same reaction mechanism, as both are gas−solid mass-transfer-limited and occur at the active sites on support particles. Figure 6 shows the effective reaction rates for the three reactor structures at different face velocities. It is clear from Figure 6 that the effective reaction rates for the packed bed and MFEC are more than 10 times higher than those for the monolith. This is because the effective reaction rate is mainly affected by the gas− solid mass-transfer rate, whose value is much larger for the packed bed and MFEC because of the particle sizes in these beds. In addition, packed-bed and MFEC reactors have similar effectiveness factors. The markedly lower effective reaction rates for the monolith reactors imply very low catalyst

ΔP ρv 2 /2

(13)

Equation 12 can be further simplified by integrating eq 4 with CAS = 0 for gas−solid mass-transfer-limited reactions. Then, the heterogeneous contacting efficiency is defined as χF =

χM χF

CAi CA0 ΔP − 2 ρv

L

ln =

=

k macε v −

ΔP ρv 2

(14)

3.3.1. Packed-Bed Reactor. As in section 3.2, the mass efficiency (χM) in terms of HCE for the packed bed was calculated using the MFEC results with a tubular reactor at different system pressures. The pressure drop (χF) for the packed bed was determined using the Ergun equation because of the difficulty of reaching high face velocity experimentally. Figure 7 shows the HCE values for packed-bed, monolith, and MFEC reactors. The packed-bed reactor has a lower HCE than both the monolith and MFEC reactors. This is due to the low porosity of the bed. A previous study23 on particle size for MFECs and packed beds showed that decreasing the particle size can moderately enhance the mass-transfer properties, which, in turn, enhances the catalytic performance. However, 8029


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Figure 6. Effective reaction rates calculated for first-order mass-transfer-limited reactions in packed-bed (150−250-μm Al2O3, 40 vol % loading), monolith (12.5-μm washcoat thickness), and MFEC (20 vol % loading 150−250-μm Al2O3, 5 vol % loading 8-μm-diameter nickel fiber) reactors at three system pressures.

Figure 7. Heterogeneous contacting efficiencies measured according to eq 14 for packed-bed (150−250-μm Al2O3, 40 vol % loading), monolith (12.5-μm washcoat thickness), and MFEC (20 vol % loading 150−250-μm Al2O3, 5 vol % loading 8-μm-diameter nickel fiber) reactors at three system pressures.

3.3.3. MFEC Reactor. The mass efficiency term in HCE for the MFEC reactor was measured using a tubular reactor at different system pressures. Previous efforts26 have been made to use both experimental and computational fluid dynamics (CFD) techniques to determine the pressure-drop term for MFECs. Because the geometric structure of an MFEC is affected when the system pressure changes, the experimental pressure drop was preferred in this study to avoid erroneous assumptions during simulations. It is shown in Figure 8 that higher pressure drops were observed for higher system pressures. This is due primarily to the increase in air density. Moreover, the higher face velocity compresses the MFEC, which significantly increases the pressure drop as well. The HCE values for the monoliths were approximately 10 times lower than those for the MFEC. These lower values were

pressure drop is increased dramatically by these smaller particles; therefore, HCE is not enhanced. 3.3.2. Monolith Reactors. Both the mass efficiency and pressure drop for the monolith reactors were measured experimentally using a tubular reactor at different system pressures. The monolith reactors have HCEs that are more than 5 times higher than those of the packed-bed reactor in Figure 7, even though the mass-transfer rates of packed beds are several magnitudes higher than monoliths. This is due to the large pressure-drop penalty incurred by the lower voidage of the packed beds in high-velocity applications. The monolith with the higher CPSI also had a higher HCE than its counterpart. This is mainly because the pressure-drop increment from the higher CPSI was not significant compared with the improved gas−solid mass-transfer rate. 8030


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conduction is not well established by the structured cells in monoliths.29 3.4.2. MFEC Reactor. In this model, the thermal conductivities for the radial and axial directions were separately determined using an ensemble-averaging method. The original heat-transfer equation presented by Bird et al.30 can be simplified as in eq 15. When the system pressure increases, the radial and axial thermal conductivities are enhanced. This is a result of the improved thermal diffusivities in the axial and radial directions, respectively given by12,13 ⎛ 1 171 3 aa 2 ⎞ Dx = Df ⎜ + π |7|⎟ −1 3200 kkϕ ⎠ ⎝ 1 − ϕ − ϕm

(16)

⎛ 1 9 3 aa 2 ⎞ Dy = Dz = Df ⎜ + π |7|⎟ −1 6400 kkϕ ⎠ ⎝ 1 − ϕ − ϕm

(17)

The boundary conditions used for solving the equation are

Figure 8. Pressure drops across a pleated MFEC at three system pressures with 8-μm-diameter nickel fibers (5 vol % loading).

T (z = 0) = T0

mainly caused by the lower mass-transfer term in the monolith reactors because the pressure drop across the monolith reactors was only slightly higher than that for the MFEC. The effect of particle size on pressure drop was the same for MFEC reactor as for the packed-bed reactor. In addition, the particle size variation in the MFEC was relatively narrow (50− 300 μm). Therefore, HCE for the MFEC reactor was relatively stable in a certain velocity range. However, when the system pressure changes, the HCE value is expected to change, given that the catalytic performance and pressure drop are significantly affected by the system pressures. As the massefficiency term is enhanced at higher system pressures, HCE does show an increase in Figure 8, even though the pressuredrop term was more than doubled. This result implies the importance of system pressure in enhancing the overall performance of reactive structures at high face velocities, because the gas−solid mass-transfer enhancement surpasses the pressure-drop penalty. In addition, the system can run at onehalf the face velocity required at atmospheric pressure to maintain the same mass flow rate. As a result, the HCE will be further enhanced at the reduced face velocities. 3.4. Convective Heat-Transfer Model. 3.4.1. PackedBed and Monolith Reactors. The temperature distribution profile for any reactive structure that operates at high velocity can be calculated by numerically solving the equation

∂T ∂z

z=z

∂T ∂r

r=0

=0

=0

T (r = r ) = Tw

(18)

In this specific application, the pressure/volume work by air compression through the fibrous medium is the main heat source. The heat of reaction from ozone decomposition is negligible because of the low ozone concentration. Equation 19 shows the Nusselt number calculation that was used to compare the heat convection under different system pressures for the MFEC Nu =

1 hL = 2πL /D K

∫0

L/D

∫0

2π

⎛ ∂T ⎞ ⎜− ⎟ dθ dz ⎝ ∂r ⎠

(19)

Nusselt numbers were calculated with the temperature distribution profile from previous modeling using eq 15. The results from the modeling showed that the axial temperature difference between leading edge and trailing edge of the MFEC was insignificant, as the majority of fibers were not aligned in this direction and the thickness of the MFEC bed was relatively small (∼4 mm). The radial temperature distribution was mostly uniform along the radial direction, with a large temperature gradient near the reactor wall (Figure 9). Compared with that of the packed-bed reactor, the temperature difference between the centerline and the near-wall region was at least 100 times smaller for the MFEC reactor than the packed-bed reactor running at even lower face velocity.27 The majority of catalyst particles remained in a small temperature range for the MFEC reactor because of the uniform temperature distribution, whereas only a small portion of the catalyst was at the desired temperature for the packed bed.27 The good heat-transfer properties of the metal-fiber bed provided better catalytic performance and catalyst lifetime by reducing unwanted reactions. A larger temperature gradient was found at the wall in the higher-pressure system because of the increased radial and axial thermal conductivities at higher pressures. Overall, the heat convection at higher system pressures was enhanced. Figure 10

⎛ ∂T ΔP ∂ 2T ∂ 2T ∂T ⎞⎟ k r ∂T + vz + krr 2 + krz = + vz ρc p⎜ ⎝ ∂t l ∂z ⎠ r ∂r ∂z 2 ∂r (15)

with adjusted axial and radial thermal conductivities. Sheng et al. experimentally and theoretically studied the temperature distribution in packed beds during highly exothermic reactions.27 The radial temperature distribution was found to exhibit a large gradient between the centerline and the near-wall region because of the poor effective thermal conductivity of packed beds. Tsinoglou et al.28 studied the radial temperature distributions of monoliths for automotive catalytic converters. A large temperature gradient was also observed in these monolith reactors. Metal monoliths are used in many exothermic applications to help with the heat-transfer performance of the reactor. However, the issue of temperature gradients still exists because the network structure for heat 8031


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involved in these applications. To improve HCE, both reactors are required to be simultaneously shorter in length and larger in diameter to reduce pressure drop and maintain the same conversion rate, which is not practical in weight- and volumesensitive systems that have restrictive ducting. On the other hand, microfibrous entrapped catalysts (MFECs) can be pleated to provide larger surface areas; therefore, HCE is improved because of both the reduced pressure drop and the increased residence time in the reaction zone. In addition, the axial and radial temperature profiles at different pressures were calculated by numerically solving the heat-transfer equation with adjusted thermal conductivities. The MFEC reactor exhibited a more evenly distributed temperature profile than the packed-bed and monolith reactors, giving the MFEC better catalytic performance by reducing temperature variations. The Nusselt number also indicated that convective heat transfer was enhanced at higher system pressures.

■

Figure 9. Radial temperature distributions within an MFEC at three face velocities.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: +1-334-844-2023. Fax: +1334-844-2063. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work was supported by U.S. Army Tank-Automotive Research, Development and Engineering Center (TARDEC), Contract W56HZV-05-C-0686. The authors thank Mr. Ronald Putt and Troy Barron for technical assistance.

■

NOMENCLATURE a = external surface area per unit volume of catalyst (1/m) aa = fiber radius (m) C = reactant concentration (mol/m3) D = effective thermal diffusivity (m2/s) DD = molecular diffusivity (m2/s) Gz = Graetz number h = convective heat-transfer coefficient i = index in the axial direction j = index in the radial direction k = mass-transfer coefficient (m/s) kk = scalar permeability ofan isotropic bed kr = thermal conductivity [W/(m K)] L = bed thickness (m) M = index at the wall m = ratio of the heat capacity in the fluid to the heat capacity in the fiber Nu = Nusselt number 7 = Peclet number ΔP = pressure drop (Pa) r = radius (m) Re = Reynolds number Sc = Schmidt number Sh = Sherwood number T = temperature (K) t = time (s) tc = monolith wall thickness (m) v = face velocity (m/s) X = volume fraction of the catalyst support x = position along the reactor length (m)

Figure 10. Nusselt numbers calculated for a nickel-fiber MFEC (5 vol % loading) at three system pressures.

compares the Nusselt number at three system pressures for the MFEC reactor. The preceding discussions are generic and not specific to any type of heat source existing in the reactor. The additional benefit to heat-transfer properties for fiber beds provides more opportunities for them to be used in highly exothermic reactions.

4. CONCLUSIONS The effects of system pressure on reactive structure performance in high-velocity applications were evaluated and compared with respect to several factors, including effective reaction rate, gas−solid mass-transfer rate, and HCE. The gas−solid mass-transfer rates for all reactor structures were enhanced by increased system pressure. The major contributor to this enhancement is the increased gas diffusivity. Because many reactions, including ozone decomposition, are mass-transfer-limited at high volumetric flow rates, both packed-bed and MFEC reactors were found to have effective reaction rates that were more than 10 times higher than those of monolith reactor because of the smaller particles used. At identical mass flow rates per unit cross-sectional area of the reactors, HCE was enhanced at higher system pressures. This enhancement is a combination of enhanced mass transfer and reduced pressure drop. However, the performance of monoliths and packed beds in high-volumetric-flow applications is limited because of the restrictive ducting system 8032


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z = axial direction (m) Greek Letters

ε = voidage η = internal effectiveness factor Θ = Thiele modulus ρ = density (kg/m3) φ = sphericity of particles ϕ = volume fraction of the fiber χ = heterogeneous contacting efficiency Subscripts

0 = inlet A = reactant A AS = surface reactant c = catalyst eff = effective f = tracer M = mass m = gas phase r = surface w = wall x = x direction y = y direction z = z direction

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Comparison of Packed Beds, Washcoated Monoliths, and Microfibrous

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