Process Intensification in Photocatalytic Decomposition of Formic Acid over a TiO2 Catalyst by Forced Periodic Modulation of Concentration, Temperature, Flowrate and Light Intensity
Abstract
:1. Introduction
2. Kinetic Model of Formic Acid Decomposition over a Titania Photocatalyst
3. Non-Stationary CSTR Model
4. The NFR Method for Evaluating Forced Periodic Operations
5. Application of the NFR Method for Evaluating Potential Forced Periodic Operations of a Photocatalytic Reactor for Formic Acid Decomposition
5.1. Modulated Inputs and Outputs of Interest and Performance Criteria
5.2. Possible Periodic Operations with One or Two Modulated Inputs
- Case 1: Periodic operation of the volumetric flowrate of the feed stream;
- Case 2: Periodic operation of the feed molar fraction of formic acid;
- Case 3: Periodic operation of the reactor temperature;
- Case 4: Periodic operation of the light intensity.
- Case 5: Modulation of the acid flowrate and the acid molar fraction;
- Case 6: Modulation of the acid molar fraction and temperature;
- Case 7: Modulation of the temperature and the acid flowrate;
- Case 8: Modulation of the acid molar fraction and the light intensity;
- Case 9: Modulation of the temperature and the light intensity;
- Case 10: Modulation of the light intensity and the acid flowrate.
5.3. Frequency Response Functions for Evaluating Periodic Operations
- Sixteen first order FRFs relating each output to each input;
- Sixteen asymmetrical second order FRFs relating each output to each input;
- Twenty-four cross asymmetrical second order FRFs relating each output to each combination of two inputs defined in Case 5 to Case 10.
5.4. Performance Indicators
- For co-sinusoidal modulation of one input (x) with frequency ω and amplitude Ax (Cases 1–4)
- For simultaneous co-sinusoidal modulations of two inputs (x and z) with frequency ω, amplitudes Ax and Az and phase difference φ (Cases 5–10)
6. NFR Analysis for Different Cases
6.1. Selection of the Steady-State Points for Analysis
6.2. Evaluation of Periodic Modulations with a Single Input
6.3. Periodic Modulation of Two Input Parameters
6.4. Multi-Objective Optimisation for Case 5
7. Conclusions
Supplementary Materials
Author Contributions
Funding
Conflicts of Interest
Nomenclature
ABET | Specific surface area | Greek Letters | |
Ax | Amplitude of periodic modulation | Reciprocal absorption length | |
Concentration | Heating rate | ||
Volumetric flowrate | Surface coverage | ||
G | Frequency response function | Density | |
ΔH | Enthalpy | Phase difference | |
I | Intensity of light | Frequency of periodic modulation | |
Kinetic constant | Subscripts | ||
Reaction rate | |||
Mass | A | Formic acid | |
Mass flowrate | C, H | CO2, H2 | |
Molar mass | N | Nitrogen | |
Avogadro number | ads | Adsorption | |
Concentration of catalyst sites | des | Desorption | |
Pressure | in | Inlet | |
Ideal gas constant | max | Maximum | |
Temperature | opt | Optimal phase difference | |
Time | out | Outlet | |
Reactor volume | R | Reactor | |
Input function | 2 | Step 2. Photochemical reaction | |
Output function | tot | Total | |
DC component of the output function | x | First input parameter | |
Molar fraction | z | Second input parameter |
Appendix A
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Parameter | Description | Value | Units |
---|---|---|---|
Regression fit parameter 1 | 1.503 | ||
Regression fit parameter 2 | 1.50 × 10−5 | ||
Enthalpy of adsorption | 3.243 × 104 | ||
Desorption pre-exponential factor 1 | 1.00 × 10−13 | ||
Desorption pre-exponential factor 2 | 2.05 | ||
Recombination rate | 0.24 | ||
Estimation of first desorption energy | 1.131 × 105 | ||
Second desorption energy | 2.092 × 104 | ||
Reaction activation energy | 8.480 × 103 | ||
Reference light intensity | 1.6 |
Parameter | Value | Units |
---|---|---|
Photocatalyst loading | ||
SS1 | SS2 | SS3 | SS4 | SS5 | |
---|---|---|---|---|---|
Inlet molar fraction, - | 0.121 | 0.154 | 0.139 | 0.153 | 0.142 |
4.966 | 4.171 | 4.983 | 4.876 | 5.682 | |
Outlet molar fraction, - | 0.023 | 0.034 | 0.038 | 0.049 | 0.052 |
Surface coverage, - | 99.28 | 99.52 | 99.57 | 99.66 | 99.68 |
5.447 | 4.654 | 5.466 | 5.359 | 6.165 | |
SS conversion, % | 79.383 | 75.172 | 69.919 | 64.944 | 60.049 |
2.156 | 2.301 | 2.475 | 2.667 | 2.885 | |
−2.3473 | −2.6324 | −4.0278 | −5.1532 | −5.5210 | |
−0.0003 | −0.0002 | −0.0003 | −0.0003 | −0.0003 |
Temperature Modulation | SS1 | SS2 | SS3 | SS4 | SS5 |
---|---|---|---|---|---|
Highest conversion at modulation, % | 79.391 | 75.179 | 69.925 | 64.950 | 60.054 |
Relative increase in conversion over steady state, % | +0.010 | +0.010 | +0.010 | +0.010 | +0.010 |
>2.4 × 10−4 | >0 | >0 | >0 | >0 |
Optimisation Parameter | Lower Bound | Upper Bound |
---|---|---|
, - | 0.010 | 0.3189 |
10−9 | 10−6 | |
, - | 0 | 0.7 |
, - | 0 | 1 |
0 | ||
10−6 |
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Ellwood, T.; Živković, L.A.; Denissenko, P.; Abiev, R.S.; Rebrov, E.V.; Petkovska, M. Process Intensification in Photocatalytic Decomposition of Formic Acid over a TiO2 Catalyst by Forced Periodic Modulation of Concentration, Temperature, Flowrate and Light Intensity. Processes 2021, 9, 2046. https://doi.org/10.3390/pr9112046
Ellwood T, Živković LA, Denissenko P, Abiev RS, Rebrov EV, Petkovska M. Process Intensification in Photocatalytic Decomposition of Formic Acid over a TiO2 Catalyst by Forced Periodic Modulation of Concentration, Temperature, Flowrate and Light Intensity. Processes. 2021; 9(11):2046. https://doi.org/10.3390/pr9112046
Chicago/Turabian StyleEllwood, Thomas, Luka A. Živković, Petr Denissenko, Rufat Sh. Abiev, Evgeny V. Rebrov, and Menka Petkovska. 2021. "Process Intensification in Photocatalytic Decomposition of Formic Acid over a TiO2 Catalyst by Forced Periodic Modulation of Concentration, Temperature, Flowrate and Light Intensity" Processes 9, no. 11: 2046. https://doi.org/10.3390/pr9112046
APA StyleEllwood, T., Živković, L. A., Denissenko, P., Abiev, R. S., Rebrov, E. V., & Petkovska, M. (2021). Process Intensification in Photocatalytic Decomposition of Formic Acid over a TiO2 Catalyst by Forced Periodic Modulation of Concentration, Temperature, Flowrate and Light Intensity. Processes, 9(11), 2046. https://doi.org/10.3390/pr9112046