CHAPTER 2 CONSIDERATIONS FOR INVESTIGATING METAL-SUPPORT
2.2 Batch Reactors: Internal Mass Transfer Effects
Cinnamaldehyde hydrogenation was used as the probe reaction to investigate the differences in performance of catalysts throughout this doctoral work. These hydrogenation tests were first conducted in a three-neck round bottom flask glass reactor using experimental conditions reported by other groups.2 100 mg of the 5 wt% Pd on carbon catalyst was added to the reactor with 40 ml dioxane (99.8% purity, Sigma-Aldrich) and 365 mg decane (internal standard; ≥ 99% purity, Sigma-Aldrich) along with a stir bar. The flask was then connected to a condenser maintained at 4 °C to allow the re-condensation of the dioxane vapors formed upon heating and thereby minimize solvent losses during the reaction. The reactor was placed in an oil bath and stirred at 500 rpm. Initially, the bath temperature was maintained at room temperature using an IKA-RCT magnetic stir plate equipped with a PT1000 thermocouple. Bronkhorst mass flow controllers and a fine frit (10 – 20 µm porosity) were used to control gas flows to the reactor. The reactor was purged with nitrogen gas at 20 ml min-1 for 20 min
at room temperature to remove any oxygen dissolved in the solvent. Following this, the temperature of the oil bath was ramped to 80 °C and simultaneously the gas flow was switched to hydrogen at 20 ml min-1 at ambient pressure for 30 min. 5 g of cinnamaldehyde was dissolved in 10 ml of dioxane and added to the reactor using the third neck, which was fitted with a rubber septum and a syringe needle. This addition of cinnamaldehyde marked the start time of the reaction. The hydrogen flow rate was maintained at 20 ml min-1 under ambient pressure throughout the experiment. 200 µl samples were withdrawn every 15 min, collected in pre-cooled glass vials, and refrigerated immediately to quench the reaction and prevent solvent losses. All catalytic tests were conducted in triplicates.
The reaction samples were diluted 15 times with dioxane and filtered using 0.22 µm nylon filters. 1 µl of this diluted sample was then injected in an Agilent 7890 A gas
chromatograph (GC) equipped with an HP-5 column (30 m X 320 µm X 0.25 µm) and a flame ionization detector (FID). A split ratio of 20:1 at 20 ml min-1, inlet heater temperature of 300 °C, total flow of 24 ml min-1, septum purge flow of 3 ml min-1, and column flow of 1 ml min-1 were used. The initial temperature of the oven was maintained at 40 °C for 1 min and then increased to 180 °C with a ramp rate of 10 °C min-1. The temperature of the FID heater was maintained at 300 °C.
Stacked cup carbon nanotube (SCCNT) catalyst support is represented by a cylindrical geometry as depicted in Figure 1. Component A is hydrogen and B is
cinnamaldehyde. The molar fluxes of the components A and B are represented by NA and NB respectively. The length of the SCCNT is represented by L and its inner radius is represented by R.
The following assumptions were made while conducting the internal mass transfer analysis: i) concentration of component A (CA) and concentration of component B (CB) is constant in the radial direction, ii) reaction only occurs on the catalyst surface, and iii) the system is under steady state.
Figure 1. Representation of the cylindrical stacked cup carbon nanotube of length L and inner radius R.
Based on the kinetic trace of the reaction (Figure 2), which depicts a straight-line plot for the change in cinnamaldehyde concentration with time, the reaction was assumed to be 0th order with respect to cinnamaldehyde. The reaction was considered to be 1st order with respect to hydrogen, based on the common assumption for this reaction as reported in the literature.11
Figure S2. Catalytic trace for palladium catalyst supported on pyrolytically stripped SCCNTs conducted at 80 °C, stirring rate = 500 rpm, hydrogen flow rate = 20 ml min-1, mass of catalyst = 100 mg, and mass of cinnamaldehyde = 5 g.
Mass balance analysis on component A is represented by equation 1:
│ │ 2 0 1
Divide by πRΔz and take limit of Δz tending to 0, to obtain equation 2:
2 0 2
Fick’s law for molar flux of component A is defined in equation 3:
3
where, DA is the effective diffusion coefficient of the reactant A, which is hydrogen. Substituting equation 3 in equation 2, we obtain equation 4:
2 0 4
In order to non-dimensionalize the equation, we define the following parameters:
5
where, CAS is the concentration of the reactant A in the bulk of the solvent.
x 6
Using the parameters defined in equation 5 and 6, equation 4 can be written as:
2 0 7
Rearranging terms to obtain:
2
0 8
We now define the Thiele modulus ( 2), as follows: 2
9
Substituting equation 9 in equation 8, we obtain:
0 10
The solution to the differential equation described above is as follows:
sinh cosh 11
The boundary conditions for this system can be defined as follows: at 0, 0
and at , 1. Using these boundary conditions and the equation 11 can be written as follows:
sech
Effectiveness factor (η) is defined as the ratio of the actual rate of the reaction to the rate of reaction with no diffusion limitations, as represented below:
│
2 2 13
Non-dimensionalizing equation 13 using the parameters defined in equation 5 and 6, and the Thiele modulus as defined in equation 9, we obtain:
2 │ 14
Differentiating equation 12 with respect to x, we obtain:
│ sech
2 sinh 2 15
Substituting equation 15 in equation 14, we obtain the effectiveness factor to be as follows:
2tanh
2 16
To calculate the Thiele modulus using equation 9, the value of ka was calculated by multiplying the kv, the rate constant based on catalyst volume, which was obtained from the catalytic data, with the characteristic length, a, defined as follows:
17
For a tubular catalyst, volume of the inner pore is πR2L and the inner surface area of the pore open on both ends is 2πRL. This results in the characteristic length of R/2. The values for the inner radius of the tube and the length were obtained to be 17.5 nm and 10 µm, respectively, from the literature.12 Therefore, the value of a was 8.75 nm.
kv was obtained to be 1.07 s-1 from the kinetic data and multiplying the kv with a, the value of ka was obtained to be 9.3625 x 10-9 m s-1. The effective diffusion coefficient for
hydrogen was taken to be 8.4 x 10-9 m2 s-1 based on the calculations reported by Toebes et al.13
Substituting these values in equation 9, the Thiele modulus ( 2) was estimated to be 0.013. The effectiveness factor (η) was estimated to be 0.999 using equation 16 and the above obtained value of 2. This combination of the Thiele modulus and effectiveness factor confirms that the reaction is not mass transfer limited in hydrogen under the conditions used in this study.
For studying the internal mass transfer limitations on component B, which is cinnamaldehyde, mass balance was conducted using equation 18:
│ │ 2 0 18
Divide by πRΔz and take limit of Δz tending to 0, to obtain equation 19:
2 0 19
Fick’s law for molar flux of component B is defined in equation 20:
20
where, DB is the effective diffusion coefficient of the reactant B, which is cinnamaldehyde. Substituting equation 20 in equation 19, we obtain equation 21:
2 0 21
Using equation 5 and 12 and using the value of 2 of 0.013 as obtained earlier, CA was obtained to be:
cosh 0.114 22
2 cosh 0.114 0 23
In order to non-dimensionalize the equation, we define the following parameter:
24
where, CBS is the concentration of the reactant B in the bulk of the solvent. Using the parameters defined in equation 6 and 24, equation 23 can be written as:
2 cosh 0.114 0 25
Rearranging terms to obtain:
2
cosh 0.114 0 26
We now define the Thiele modulus ( ′ 2), as follows:
′ 2 27
Substituting equation 27 in equation 26, we obtain:
cosh 0.114 0 28
The solution to the differential equation described above is as follows: cosh 0.114
0.114 29
The boundary conditions for this system can be defined as follows: at 0, 0
and at , 1. Using these boundary conditions and the equation 29 can be written as follows:
1 77.0718 cosh 0.114
To calculate the value of ′ 2, CAS was estimated using the following equation obtained from the literature (Equation 3):14
ln x 5.7347 8.6743T 100 K
31
where, x1 is the mole fraction of hydrogen in dioxane and T is the temperature of the solubility test in K.
Using equation (31), the mole fraction of hydrogen in dioxane at 80 °C was estimated to be 2.77 x 10-4.14 This mole fraction represents a concentration of 6.47 x 10-6 g ml-1 of hydrogen in dioxane. The concentration of cinnamaldehyde at 0% conversion was known based on the amount of reactant added and confirmed using the GC-FID analysis to be 90 mg ml-1. At 10% conversion, the concentration of cinnamaldehyde was 81 mg ml-1. The effective diffusion coefficient for cinnmaldehyde was taken to be 2 x 10-9 m2 s-1 based on the
calculations reported by Toebes et al.13 With the help of these values and equation 27, the Thiele modulus was estimated to be 3.846 x 10-6 and 4.273 x 10-6 at 0 and 10% conversion, respectively.
The effectiveness factor (η’) is defined as the ratio of the actual rate of the reaction to the rate of reaction with no diffusion limitations, as represented below:
′
│
2 2 32
Non-dimensionalizing equation 32 using the parameters defined in equation 6 and 24, and the Thiele modulus as defined in equation 27, we obtain:
′ 2
′ │ 33
│ 0.114 sinh 0.057
0.114 34
Substituting equation 34 in equation 33, we obtain the effectiveness factor to be as follows:
′ 2sinh 0.057
0.114 35
The effectiveness factor was obtained to be 1 for the values of ′ 2 of 3.846 x 10-6 and 4.273 x 10-6 at 0 and 10% conversion, respectively. This combination of the Thiele modulus and effectiveness factor confirms that the reaction is not mass transfer limited in
cinnmaldehyde under the conditions used in this study.