Systematic Study of Separators in Air-Breathing Flat-Plate Microbial Fuel Cells—Part 2: Numerical Modeling
Abstract
:1. Introduction
2. Results and Discussion
2.1. Parameters Estimation and Model Validation
Parameter | Definition | Value | Unit |
---|---|---|---|
Exchange current density of oxygen reduction in the biofilm | 0.36 | A·m−2 | |
Exchange current density of ethanol oxidation in the biofilm | 0.40 | A·m−2 | |
Mass transfer coefficient of oxygen in the biofiom | 2.7 × 10−6 | m·s−1 | |
Mass transfer coefficient of ethanol in the biofilm | 9.3 × 10−6 | m·s−1 | |
Anodic charge transfer coefficient of ethanol oxidation | 7 × 10−2 | - | |
Anodic charge transfer coefficient of oxygen reduction | 0.24 | - | |
Cathodic charge transfer coefficient of ethanol oxidation | 3 × 10−3 | - | |
Cathodic charge transfer coefficient of oxygen reduction | 0.11 | - |
2.2. Sensitivity Analysis
2.2.1. Performance Sensitivity to Separator Characteristics
Parameter/Value | Change in the Parameter | Change in the Superficial Peak Power Density | ||
---|---|---|---|---|
2 mm | 4 mm | 8 mm | ||
kO = 0.29 × 10−6 m·s−1 | −95% | +49% | +45% | +40% |
+100% | −25% | −19% | −13% | |
+1000% | −70% | −54% | −34% | |
nH+ = 0.59 | −60% | −7% | −7% | −6% |
+60% | +24% | +23% | +23% |
Parameter/Value | Change in the Parameter | Change in the Superficial Peak Power Density | ||
---|---|---|---|---|
2 mm | 4 mm | 8 mm | ||
kO = 9.5 × 10−6 m·s−1 | −95% | +286% | +121% | +48% |
+100% | −10% | −5% | −2% | |
nH+ = 0.78 | −20% | −10% | −9% | −8% |
+20% | +31% | +25% | +20% |
2.2.2. Performance Sensitivity to Electrode Spacing
3. Materials and Methods
3.1. Model Development
- The MFC system is similar to a chemical fuel cell, hence no terms are added to represent the growth and death rate of the microbial communities, the biomass generation, and the biofilm growth on the cathode, and the separator.
- The anode electrode is assumed to be covered by the bacteria. Hence, the ethanol oxidation and oxygen reduction reactions are catalyzed by the biofilm, and do not take place on the naked electrode.
- Transfer of electrons from the bacteria to the electrode is reversible and fast, therefore, considered as a Nernstian electrode process.
- Flow of ions through the biofilm is not limiting the electro-neutrality of the system, and the Ohmic loss is solely due to the distance between the surface of the anode and the separator.
- Complete ethanol oxidation and the oxygen reduction are the sole anodic and cathodic reactions occurring in the MFC. Hence, no by-products (e.g., acetate) are assumed to be generated, to simplify the model.
- Oxygen reduction by the bacteria is assumed to be an electrochemical reaction.
- The electrolyte is assumed to be stagnant, thus no effect of the electrolyte flow on the concentration profile is considered.
- The fuel (ethanol) is well-distributed within the 3D electrode, thus the concentration profile is neglected and no starvation is happening.
- The temperature variation within the anode chamber is negligible, hence the reactions are isothermal.
- The anode is well-buffered and there is no local pH drop within the biofilm. The temperature is also well-controlled at 303 K in both compartments.
- Due to the electro-activity of the 99% of the thickness of the 3D electrode [37], a uniform current and voltage distribution within the 3D electrode is assumed.
3.2. Parameter Estimation
Separator | kO (×10−6 m·s−1) | kE (×10−6 m·s−1) | RS (×10−4 Ω·m2) | nH+ |
---|---|---|---|---|
Nafion®117 | 0.29 ± 0.02 | 0.49 ± 0.01 | 5.4 ± 0.1 | 0.59 ± 0.01 |
Aquivion® | 0.77 ± 0.05 | 0.98 ± 0.01 | 0.8 ± 0.1 | 0.72 ± 0.01 |
Celgard® | 1.2 ± 0.1 | 0.84 ± 0.01 | 4.4 ± 0.2 | 0.92 ± 0.01 |
Zirfon® | 1.5 ± 0.1 | 0.58 ± 0.01 | 14 ± 0.4 | 0.92 ± 0.01 |
Nylon mesh | 2.2 ± 0.1 | 2.2 ± 0.2 | 1.4 ± 0.1 | 0.89 ± 0.03 |
Glass fiber filter | 0.87 ± 0.06 | 1.0 ± 0.1 | 7.8 ± 0.2 | 0.62 ± 0.02 |
SciMat® | 2.6 ± 0.1 | 1.9 ± 0.1 | 3.1 ± 0.1 | 0.66 ± 0.03 |
J-cloth | 9.5 ± 0.6 | 33 ± 3 | 6.2 ± 0.2 | 0.78 ± 0.02 |
Symbol | Definition | Value | Unit |
---|---|---|---|
R | Universal gas constant | 8.314 | J·mol−1·K−1 |
T | Temperature | 303 | K |
F | Faraday constant | 96485.3 | C·mol−1 |
Number of electrons transferred in ethanol full oxidation | 12 | - | |
Number of electrons transferred in oxygen full reduction | 4 | - | |
Outlet pH | 7 | - | |
Inlet pH | 8.5 | - | |
Exchange current density of oxygen reduction on Pt | 0.015 | A·m−2 | |
Exchange current density of ethanol oxidation on Pt | 0.003 | A·m−2 | |
Mass transfer coefficient of oxygen in the air cathode | 2.7 × 10−5 | m·s−1 | |
Diffusion coefficient of oxygen in the electrolyte | 2 × 10−9 | m2·s−1 | |
Ethanol concentration in the inlet stream | 0.085 | M | |
Standard half-cell potential of ethanol oxidation | 0.084 | V vs. SHE | |
Standard half-cell potential of oxygen reduction | 0.401 | V vs. SHE | |
Partial pressure of oxygen in the air | 0.21 | atm | |
Oxygen concentration at the cathode | 8.3 | mol.m−3 | |
Ionic conductivity of the synthetic wastewater | 0.5 | S·m−1 |
4. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
Abbreviations
Abbreviation | Definition |
MFC | Microbial Fuel Cell |
FPMFC | Flat-Plate Microbial Fuel Cell |
DMFC | Direct Methanol Fuel Cell |
CE | Coulombic Efficiency |
COD | Chemical Oxygen Demand |
SQP | Sequential Quadratic Programming |
SHE | Standard Hydrogen Electrode |
3D | 3 Dimensional |
Symbol | Definition | Unit |
R | Universal Gas Constant | J·mol−1·K−1 |
T | Temperature | K |
F | Faraday Constant | C·mol−1 |
d | Electrode Spacing | m |
Y | Separator thickness | m |
Proton Transport Number of the Separator | - | |
Conductivity of Wastewater | S·m−1 | |
Ionic Resistivity of the Separator | Ω m2 | |
Ionic Conductivity of the Separator | S·m−1 | |
Cell Voltage | V | |
Ohmic Overpotential | V | |
E | Operating Electrode Potential | V vs. SHE |
Cathode Potential | V vs. SHE | |
Anode Potential | V vs. SHE | |
Potential in the Solution Phase | V vs. SHE | |
Standard Half-Cell Potential of the Reaction at 298 K | V vs. SHE | |
Equilibrium Potential of the Reduction Reaction | V vs. SHE | |
Standard half-cell Potential of Ethanol Oxidation at 298 K | V vs. SHE | |
Equilibrium Potential of Ethanol Oxidation at the Anode | V vs. SHE | |
Equilibrium Potential of Ethanol Oxidation at the Cathode | V vs. SHE | |
Standard half-cell Potential of Oxygen Reduction at 298 K | V vs. SHE | |
Equilibrium Potential of Oxygen Reduction at the Anode | V vs. SHE | |
Equilibrium Potential of Oxygen Reduction at the Cathode | V vs. SHE | |
n | Number of Electrons Exchanged in the redox Reaction | - |
Number of Electrons Exchanged in Ethanol Oxidation | - | |
Number of Electrons Exchanged in Oxygen Reduction | - | |
Oxygen Concentration at the anode | M | |
Oxygen Partial Pressure at the Cathode | atm | |
Protons Concentration at the Anode | M | |
Protons Concentration at the Cathode | M | |
Hydroxyls Concentration at the Anode | M | |
Hydroxyls Concentration at the Cathode | M | |
Cathode Overpotential | V | |
Anode Overpotential | V | |
Overpotential of Ethanol Oxidation at the Anode | V | |
Overpotential of Ethanol Oxidation at the Cathode | V | |
Overpotential of Oxygen Reduction at the Anode | V | |
Overpotential of Oxygen Reduction at the Cathode | V | |
j | Local Faradic Current Density | A·m−2 |
J′ | Measured Current Density | A·m−2 |
J | Predicted Current Density | A·m−2 |
Current Density of Ethanol Oxidation at the Cathode | A·m−2 | |
Current Density of Ethanol Oxidation at the Anode | A·m−2 | |
Current Density of Oxygen Reduction at the Cathode | A·m−2 | |
Current Density of Oxygen Reduction at the Anode | A·m−2 | |
Limiting Current Density of Ethanol Oxidation at the Anode | A·m−2 | |
Kinetically Controlled Current Density of Ethanol Oxidation at the Anode | A·m−2 | |
Limiting Current Density of Ethanol Oxidation at the Cathode | A·m−2 | |
Kinetically Controlled Current Density of Ethanol Oxidation at the Cathode | A·m−2 | |
Limiting Current Density of Oxygen Reduction at the Anode | A·m−2 | |
Kinetically Controlled Current Density of Oxygen Reduction at the Anode | A·m−2 | |
Limiting Current Density of Oxygen Reduction at the Cathode | A·m−2 | |
Kinetically Controlled Current Density of Oxygen Reduction at the Cathode | A·m−2 | |
Exchange Current Density | A·m−2 | |
Exchange Current Density of Ethanol Oxidation in the biofilm | A·m−2 | |
Exchange Current Density of Oxygen Reduction in the biofilm | A·m−2 | |
Exchange Current Density of Ethanol Oxidation on Pt | A·m−2 | |
Exchange Current Density of Oxygen Reduction on Pt | A·m−2 | |
Diffusion Coefficient of Oxygen in the Separator | m2·s−1 | |
Diffusion Coefficient of Ethanol in the Separator | m2·s−1 | |
Mass Transfer Coefficient of Oxygen in the Separator | m2·s−1 | |
Mass Transfer Coefficient of Ethanol in the Separator | m2·s−1 | |
Effective Mass Transfer Coefficient of Ethanol at the Anode | m·s−1 | |
Effective Mass Transfer Coefficient of Oxygen at the Cathode | m·s−1 | |
Effective Mass Transfer Coefficient of Ethanol at the Anode | m·s−1 | |
Effective Mass Transfer Coefficient of Oxygen at the Cathode | m·s−1 | |
Mass Transfer Coefficient of Ethanol in the Biofilm | m·s−1 | |
Mass Transfer Coefficient of Oxygen in the Biofilm | m·s−1 | |
Diffusion Coefficient of Oxygen in the Electrolyte | m·s−1 | |
Mass Transfer Coefficient of Oxygen in the Cathode | m·s−1 | |
α | Electron Transfer Coefficient | - |
Anodic Charge Transfer Coefficient of Ethanol Oxidation at the Anode | - | |
Anodic Charge Transfer Coefficient of Ethanol Oxidation at the Cathode | - | |
Cathodic Charge Transfer Coefficient of Ethanol Oxidation at the Anode | - | |
Cathodic Charge Transfer Coefficient of Ethanol Oxidation at the Cathode | - | |
Objective Function | - |
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Kazemi, S.; Barazandegan, M.; Mohseni, M.; Fatih, K. Systematic Study of Separators in Air-Breathing Flat-Plate Microbial Fuel Cells—Part 2: Numerical Modeling. Energies 2016, 9, 79. https://doi.org/10.3390/en9020079
Kazemi S, Barazandegan M, Mohseni M, Fatih K. Systematic Study of Separators in Air-Breathing Flat-Plate Microbial Fuel Cells—Part 2: Numerical Modeling. Energies. 2016; 9(2):79. https://doi.org/10.3390/en9020079
Chicago/Turabian StyleKazemi, Sona, Melissa Barazandegan, Madjid Mohseni, and Khalid Fatih. 2016. "Systematic Study of Separators in Air-Breathing Flat-Plate Microbial Fuel Cells—Part 2: Numerical Modeling" Energies 9, no. 2: 79. https://doi.org/10.3390/en9020079