(242e) Towards Chemical Equilibrium in Thermochemical Water Splitting

The efficiency of many processes strongly depends on limiting thermodynamic irreversibilities, i.e., how close to equilibrium the system is throughout the process. In thermochemical cycles for water and/or carbon dioxide splitting, operating near equilibrium means that the chemical potential of oxygen in the solid and gas phases must not differ significantly. Here, we show that in co- and counter-current reactors for two-step redox-active metal oxide thermochemical cycles, and in the absence of multiple gas or solid injection points, approaching this ideal reversible path is possible only if the reactions occur at specific, material‑dependent, thermodynamic conditions.

The method presented determines the chemical equilibrium at each infinitesimal point along the reaction and flow path, leading to a variable temperature, thermal reduction and re-oxidation reaction, based on both mass conservation and the Gibbs chemical equilibrium criterion. The mass balance imposes a linear relationship between the extent of reduction (δ) and the O₂/inert gas partial pressure ratio (p*=pO₂/p_inert) in thermal reduction or δ and the H₂ molar fraction (θ=pH₂/(pH₂+pH₂O) in re-oxidation. The Gibbs criterion limits the temperature (T) for which the reaction can take place spontaneously at each infinitesimal point along the flow path. The reaction Gibbs free energy depends on three variables for each reaction: T, pO₂ and δ for thermal reduction, and, T, θ and δfor re-oxidation. Since at equilibrium the reaction Gibbs free energy is zero, knowing any two of the three variables, (T, pO₂, δ) or (T, θ, δ) determines the third. For a co- and counter-current reaction, the mass balance line further constrains (pO₂, δ) for thermal reduction and (θ, δ) for re-oxidation. The equilibrium reaction temperature profile is therefore not arbitrary but follows uniquely from the mass balance and the Gibbs criterion and the boundary conditions.

A common simplification used for thermodynamic system analyses is to assume that each reaction occurs at a single temperature. However, a single-temperature (or isothermal) reacting path leads to the reaction having to always be out of equilibrium at all but one point along the reaction path. Although such an isothermal flow path is theoretically possible, engineering for constant temperature is challenging given expected fast kinetics, as a heat source or heat sink would struggle to supply the energy balance in response. In both cases, the isothermal and the equilibrium path will be compared in this presentation.

The design of the reactor for each reaction depends on four operating variables which fully determines both ends of the mass balance line. Although, the most obvious selection could be the coordinates of both ends at the mass balance line, using these boundary conditions are not the most convenient to specify, since the outlet extent of reduction in both reactions and also the outlet oxygen partial pressure in thermal reduction are more typically reactor outputs. Instead of these four variables, we find it more convenient to set and control: a) the inlet extent of reduction (δ_OX), the inlet oxygen partial pressure (pO_2,in), the maximum reduction temperature (T_TR,max), and the inert sweep ratio (λ=n_inert/2nO₂) for thermal reduction and b) the inlet extent of reduction (δ_TR), the inlet and outlet hydrogen molar fraction (θ_in and θ_out, respectively) and the minimum temperature (T_OX,min) for re-oxidation.

Since the efficiency of two-step thermochemical water and carbon dioxide splitting cycles are critically dependent on the selection of the operating conditions, we have analyzed these conditions in detail. As an example, we choose ceria for the redox active metal oxide, the Zinkevich, et al. [1] model for the ceria thermodynamic properties, and the Coolprop library [2] for the oxygen, hydrogen and water thermodynamic properties.

For thermal reduction, we observe that for a given peak reduction temperature (T_TR,max) and inert sweep ratio (λ), the purity of the inert gas (pO_2,in) has a limited influence on the outlet extent of reduction, the relevance decreasing with decreasing pO_2,in. The reaction is almost complete at the peak temperature, and after that the primary effect is a trade-off between T and pO₂, not substantially furthering the reaction extent. This result suggests a potential process optimization avenue, in terms of resources expended for inert gas purification. Something similar happens with the re-oxidation. For a given minimum re-oxidation temperature and outlet H₂ molar fraction the inlet hydrogen molar fraction has a limited influence. Again, this result suggests a potential process optimization avenue, in terms of resources expended for the H₂/water separation at the gas outlet/ solid inlet of the reactor.

Increasing the inert sweep ratio makes more relevant the purity of the sweep gas in the reduction reaction, further increasing the cycle extent of reduction (Δδ). However, the feasibility of high sweep ratios has limitations. In practical reactors, flows may not be arbitrarily fast and must allow sufficient interaction time for the mass and heat transfer processes to approach equilibrium. Similarly, reducing the outlet H₂ molar fraction makes more relevant the purity of the water stream in the re-oxidation reaction, also increasing Δδ. However, the feasibility of reducing the outlet H₂ fraction also has limitations since the fraction is indicative of the amount of excess steam in the reactor.

In conclusion, the temperature path, i.e., increasing the temperature difference between the peak reduction temperature and the minimum re-oxidation temperature, is the less restrictive approach than the presented before (i.e. reduce the pO_2,in and/or θ_in, and increase λ and/or reduce the θ_out) to high thermochemical water and carbon dioxide splitting efficiencies assuming feasibility of efficient high-temperature heat recovery and high temperature structural materials.

References:

[1] M. Zinkevich, D. Djurovic, and F. Aldinger, “Thermodynamic modelling of the cerium-oxygen system,” Solid State Ionics, vol. 177, no. 11–12, pp. 989–1001, 2006.

[2] I. H. Bell, J. Wronski, S. Quoilin, and V. Lemort, “Pure andPseudo-pure Fluid Thermophysical Property Evaluation and the Open-SourceThermophysical Property Library CoolProp.,” Ind. Eng. Chem. Res., vol. 53, no. 6, pp. 2498–2508, Feb. 2014.

[3] A. de la Calle, I. Ermanoski, and E. B. Stechel, “Towards Chemical Equilibrium in Thermochemical Water Splitting. Part 1: Thermal Reduction,” In preparation.

[4] A. de la Calle, I. Ermanoski, and E. B. Stechel, “Towards Chemical Equilibrium in Thermochemical Water Splitting. Part 2: Re-oxidation,” In preparation.