Development of a continuous reactor for the electro-reduction of carbon dioxide to formate – Part 2: Scale-up

Abstract

This paper reports experimental and modeling work for the laboratory scale-up of continuous “trickle-bed” reactors for the electro-reduction of CO₂ to potassium formate. Two reactors (A and B) were employed, with particulate tin 3D cathodes of superficial areas, respectively, 45 × 10⁻⁴ (2–14 A) and 320 × 10⁻⁴ m² (20–100 A). Experiments in Reactor A using granulated tin cathodes (99.9 wt% Sn) and a feed gas of 100% CO₂ showed slightly better performance than that of the tinned-copper mesh cathodes of our previous communications, while giving substantially improved temporal stability (200 vs. 20 min). The seven-fold scaled-up Reactor B used a feed gas of 100% CO₂ with the aqueous catholyte and anolyte, respectively [0.5 M KHCO₃ + 2 M KCl] and 2 M KOH, at inlet pressure from 350 to 600 kPa(abs) and outlet temperature 295 to 325 K. For a superficial current density of 0.6–3.1 kA m⁻² Reactor B achieved corresponding formate current efficiencies of 91–63%, with the same range of reactor voltage as that in Reactor A (2.7–4.3 V), which reflects the success of the scale-up in this work. Up to 1 M formate was obtained in the catholyte product from a single pass in Reactor B, but when the catholyte feed was spiked with 2–3 M potassium formate there was a large drop in current efficiency due to formate cross-over through the Nafion 117 membrane. An extended reactor (cathode) model that used four fitted kinetic parameters and assumed zero formate cross-over was able to mirror the reactor performance with reasonable fidelity over a wide range of conditions (maximum error in formate CE = ±20%), including formate product concentrations up to 1 M.

Appendix

1.1 Extended reactor (cathode) model [6]

The extended model divides the plug flow tin granule (3D) cathode into N increments of height and calculates the overall performance at steady-state by forward differencing in an Excel spreadsheet. In each height increment the model involves relationships for the stoichiometry, equilibria and kinetics of the electro-chemical reactions, including mass transfer of the CO₂, as detailed in previous communications [3, 5]. In the extended model, changing conditions along the reactor height are handled with extra equations involving the thermo-chemical kinetics, electrolyte conductivity, CO₂ solubility, transport properties, etc., that are used to solve the (steady-state) material and energy balances for the CO₂ partial pressure, CO₂(aq) concentration, formate concentration, pH, temperature and current efficiency profiles up the cathode, such as those shown in Fig. 4.

The extended model does not assume CO₂ equilibrium between gas and liquid but instead calculates the concentration of CO₂(aq) in the bulk catholyte as a dynamic variable that depends on the relative rates of mass transfer, thermo-chemical reaction and electro-chemical reaction of CO₂. The superficial current density is assumed uniformly distributed along the reactor height and the local current density is assumed uniform across the electro-active bed thickness. Formate cross-over from catholyte to anolyte is taken as zero and the reactor is assumed to operate under adiabatic conditions, with no resistance to heat transfer between catholyte and anolyte. The model deals with the intrinsic kinetics of reactions I and II by designating the two rate constants plus two activation energies as adjustable parameters that are fitted to the experimental data as outlined below.

The extended model formulates the reaction kinetics as a function of CO₂(aq) concentration, cathode potential and temperature, i.e. for the reactions:

E ⁰ V (SHE) @ 298 K, pH 14

$$ {\text{CO}}_{{\text{2}}} {\left( {{\text{aq}}} \right)} + {\text{H}}_{{\text{2}}} {\text{O}} + {\text{2e}}^{ - } \to {\text{HCOO}}^{ - } + {\text{OH}}^{ - } \quad - 1.02 $$

(I)

$$ {\text{2H}}_{{\text{2}}} {\text{O}} + {\text{2e}}^{ - } \to {\text{H}}_{{\text{2}}} + {\text{2OH}}^{ - } \quad - 0.83 $$

(II)

Assuming the intrinsic kinetics of both reactions I and II fit the Tafel form with reaction I under a CO₂ mass transfer constraint, the individual over-potentials are related to the partial real current densities by:

$$ \eta _{1} = E - E_{{{\text{r}},1}} = a_{1} - b_{1} \log {\left( {j_{1} } \right)} + b_{1} \log {\left( {{1 - j_{1} } \mathord{\left/ {\vphantom {{1 - j_{1} } {j_{{1{\text{L}}}} }}} \right. \kern-\nulldelimiterspace} {j_{{1{\text{L}}}} }} \right)} $$

(1)

$$ \eta _{2} = E - E_{{{\text{r}},2}} = a_{2} - b_{2} \log {\left( {j_{2} } \right)} $$

(2)

The Tafel equations 1 and 2 were originally set up with Sn and Cu for the tinned-copper mesh cathode in Reactor A, in which the tin coverage decreased with operating time [3]. Modeling Reactor A and B with a tin granule cathode assumes a fixed tin surface (i.e. tin coverage = 100%) and so does not use the kinetics on copper. The Tafel slopes of both reactions I and II were assumed as 0.118 V/decade at 298 K [15, 16], with a charge transfer coefficient of 0.5, and corrected for temperature by:

$$ b = \frac{{2.303RT}} {{\alpha F}} $$

(3)

in which: α = electro-chemical charge transfer coefficient = 0.5 (assumed).

The Tafel constants and their temperature dependence involve four parameters that were fitted in the model from experimental data. First, the exchange current densities are calculated from:

$$ i_{{{\text{o}},1}} = 2Fk_{1} [{\text{CO}}_{2} ({\text{aq}})]\exp {\left( { - \frac{{E_{{{\text{a}},1}} }} {{RT}}} \right)}\exp {\left( { - \frac{{\alpha _{1} FE_{{{\text{r}},1}} }} {{RT}}} \right)} $$

(4)

$$ i_{{{\text{o}},2}} = 2Fk_{2} \exp {\left( { - \frac{{E_{{{\text{a}},2}} }} {{RT}}} \right)}\exp {\left( { - \frac{{\alpha _{2} FE_{{{\text{r}},2}} }} {{RT}}} \right)} $$

(5)

Then the Tafel constants are obtained as:

$$ a_{1} = {\left( {\frac{{RT}} {{\alpha _{1} F}}} \right)}\ln (i_{{{\text{o}},1}} ) $$

(6)

$$ a_{2} = {\left( {\frac{{RT}} {{\alpha _{2} F}}} \right)}\ln (i_{{{\text{o}},2}} ) $$

(7)

with α_1 = α₂ = 0.5 (assumed).

The electrochemical kinetic parameters k ₁, k ₂, E _a,1 and E _a,2 were fitted in the model from the experimental data—with the constraint that the values of i _o,2 and a ₂ should approximate those found in the literature e.g. respectively about 1 × 10⁻⁷ kA m⁻² and −0.8 V on Sn at 298 K [16, 17]. The activation energies were also kept within the typical range of electrode reactions i.e. about 30 × 10³–100 × 10³ kJ kmol⁻¹ [17].

Figure A1 shows a parity graph of modeled versus measured values of the formate CE for the range of process conditions outlined in Sect. 3 above. The line of best fit, obtained by the method of least squares, has a slope of 1.01, regression coefficient (R ²) of 0.64 and maximum error of about ±20%. These results give some support to the model, while pointing to the need for more work in this area. The corresponding fitted values of the kinetic parameters are given in Table A1 and reflect the relatively slow kinetics and weak effect of temperature for reaction II versus reaction I on a tin cathode.

Fig. A1

Modeled versus measured formate CE for tin granule cathodes in Reactors A & B. Replicate runs excluded

Table A1 Parameter values for best fit of modeled and measured formate CE