Transient Diffusion-Reaction Model for CO2 Electrolysis

版本 1.1.0 (632.2 KB) 作者: Robert Haaring
Solves the set of coupled PDEs describing mass conservation across a diffusion layer with an electrochemical reaction occurring at one side.
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This model has two components explained in this order below:
  • MODEL I: Transient-Diffusion Reaction (TDR) Model for a Planar Electrode
  • MODEL II: Transient-Diffusion Reaction Model for a Porous Electrode (pTDR)
The first model is based on efforts presented in the following works and adapted for the current format of interactivity:
  • Gupta et al. J. Appl. Electrochem. 2006, 36, 161–172
  • Resasco et al. ChemElectroChem 2018, 5, 1064–1072
  • Kas et al. ChemElectroChem 2015, 2, 354–358
The second model is an extension of the former and was further inspired by:
  • Raciti et al. Nanotechnology 2018, 19, 044001
  • Burdyny & Smith. Energy Environ. Sci. 2019, 12, 1442–1453
MODEL I: Transient-Diffusion Reaction (TDR) Model for a Planar Electrode
Fig. 1. Model domain with an electrochemical reaction occurring at a planar electrode.
Solving the coupled species' conservation equations across a diffusion boundary layer of length δ_DBL in contact with a planar cathode at which an electrochemical surface reaction takes place (Fig. 1). The pdepe solver is used to this end to model the behaviour of dissolved CO2, HCO3(-), CO3(2-), OH(-), and H(+). The equations that are solved for the five species' concentration profiles (both in time and space) are of the form
with c as concentration, D as diffusion coefficient, and R as source/sink term for the (bi)carbonate equilibrium reactions. The reduction reactions taking place at the cathode surface enter as Neumann boundary conditions at x = 0 and two such reactions are considered. For neutral to alkaline electrolyte the acid components of these chemical reactions may be largely ignored as can be derived from a scaling analysis of the reaction terms. Furthermore, the electrochemical reactions generate OH(-) and therefore serves to raise the pH, further motivating this simplification. This is henceforth referred to as the simplified model, though the option exists to retain the full model equations.
The model file tdr_model.m is supplied with an editor file tdr_model_editor.mlx that allows facile modification of pertinent parameters to study its influence on for example the concentration profiles, pH, and mass transfer limiting current density. The following parameters may be altered:
  • temperature T
  • pressure P
  • molarity c (of CO2-saturated electrolyte)
  • current density j
  • Faradaic efficiency η for CO
  • diffusion boundary layer thickness δ_DBL
The model file runs several subroutines (attached as separate MATLAB files) in order to determine the necessary input data for the model derived from the above input parameters. These files should be located in the same directory as the model and editor files:
  • henry.m CO2 solubiltity as function of temperature and pressure
  • sechenov.m CO2 solubiltity as function of ionic strength
  • viscosity.m viscosity of electrolyte as function of molarity
  • diffusivity.m diffusion coefficients as function of temperature
  • carbonateeq.m equilibrium coefficients as function of temperature and ionic strength for (bi)carbonate equilibria
  • carbonatekin.m rate coefficients as function of temperature and ionic strength for (bi)carbonate equilibria
  • selfionization.m pKw value of water as function of temperature
  • bjerrum.m shows the distribution of CO2, HCO3(-), CO3(2-) as function of pH given equilibrium coefficients
Examples are given of the plots returned by running the model through the editor file or data that may be derived from the results.
Fig. 2. Transient concentration and pH profiles upon imposing -5 mA/cm2 at the cathode (x = 0) for 0.1 M KHCO3.
Fig. 3. Mass transfer limiting current density in 0.1 M KHCO3 as function of diffusion boundary layer (DBL) thickness. The model result is compared with the estimate based on the formula on the right (assuming a linear concentration profile).
MODEL II: Transient-Diffusion Reaction Model for a Porous Electrode (pTDR)
Fig. 4. Model domain with an electrochemical reaction occurring in a porous electrode.
Solving the coupled species' conservation equations across a porous catalyst layer of length δ_CL and diffusion boundary layer of length δ_DBL with an electrochemical reaction taking place in the former (Fig. 4). The pdepe solver is used to this end to model the behaviour of dissolved CO2, HCO3(-), CO3(2-), OH(-), and H(+). The equations that are solved for the five species' concentration profiles (both in time and space) are of similar form as in MODEL I.
The reduction reactions taking place (assumed) homogeneously in the catalyst layer and thus enter as volumetric reaction term in the governing equations. Support is provided for the following reactions, which can be included or excluded by setting their appropriate Faradaic efficiencies.
A no-flux boundary condition is in place for all species at x = 0 with the exception of fixed CO2 concentration (as it is supplied from the gas-diffusion layer side). Support is provided for neutral and alkaline electrolyte (KHCO3 or KOH) and the acid components of the chemical reactions are ignored as reasoned in MODEL I.
The model file ptdr_model.m is supplied with an editor file ptdr_model_editor.mlx that allows facile modification of pertinent parameters to study its influence on for example the concentration profiles, pH, and mass transfer limiting current density, or carbon efficiency. The following parameters may be altered:
  • temperature T
  • pressure P
  • molarity c (of CO2-saturated electrolyte)
  • current density j
  • Faradaic efficiency η for product i
  • catalyst layer porosity ε
  • catalyst layer thickness δ_CL
  • diffusion boundary layer thickness δ_DBL
These model and editor files rely on the same subroutines as MODEL I does, thus they are to be placed in the same directory as these scripts. Example below of the plots returned by running the model through the editor file.
Fig. 5. Transient concentration and pH profiles upon imposing -200 mA/cm2 to the cathode (δ_CL = 1 μm, δ_DBL = 1 μm) for 0.5 M KOH.
In addition, carbon efficiency is also calculated as either the fraction of CO2 consumed in the CL versus that entering the system at x = 0 (η_DBL) or the fraction of CO2 utilized in CO2RR compared to total consumption in the CL (η_CL). Their product is reported as total carbon efficiency. Note that this is distinct from single-pass conversion efficiency of an electrolyzer, of which this model has nothing to say about.
Fig. 6. Visual and formula representation of the two carbon efficiencies and overall carbon efficiency.
Fig. 7. Plot of carbon efficiency as function of DBL thickness for a GDE exposed to 1.0 M KHCO3 with η_CO = 0.9 showing how buffering action by the electrolyte decreases with diffusion length and lowers overall carbon efficiency.

引用格式

Robert Haaring (2024). Transient Diffusion-Reaction Model for CO2 Electrolysis (https://www.mathworks.com/matlabcentral/fileexchange/164046-transient-diffusion-reaction-model-for-co2-electrolysis), MATLAB Central File Exchange. 检索来源 .

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参考作品: polyfitZero

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版本 已发布 发行说明
1.1.0

Additional script and script editor uploaded for simulating a porous (GDE-based) electrode.
1.0.1

Updated notation indexing for rate coefficients.
1.0.0