Article pubs.acs.org/EF
Applicability of an Equilibrium Model To Predict the Conversion of CO2 to CO via the Reduction and Oxidation of a Fixed Bed of Cerium Dioxide Luke J. Venstrom,*,† Robert M. De Smith,‡ Rohini Bala Chandran,‡ Daniel B. Boman,‡ Peter T. Krenzke,‡ and Jane H. Davidson‡ †
Department of Mechanical Engineering, Valparaiso University, 1900 Chapel Drive, Valparaiso, Indiana 46383, United States Department of Mechanical Engineering, University of Minnesota, 111 Church Street Southeast, Minneapolis, Minnesota 55455, United States
‡
ABSTRACT: Production of hydrogen and synthesis gas via solar thermochemical partial redox cycles is one route to renewable fuels and storage of solar energy. The efficiency at which these cycles produce fuel for candidate non-stoichiometric metal oxides and reactor concepts is normally evaluated from thermodynamic models that implicitly assume that the transport processes and reaction kinetics are rapid enough that the gas and solid attain chemical equilibrium. In this paper, we develop an equilibrium model of a fixed-bed reactor and demonstrate its applicability for reduction and oxidation of porous ceria (CeO2) particles with a volume-specific surface area of ∼106 m2 m−3 over a wide range of gas flow rates and reaction temperatures. The model predicts the measured rate of O2 production during reduction for mass-specific flow rates up to 900 mL min−1 gceria−1 and for temperatures from 740 to 1500 °C, and it predicts the measured rate of CO production during oxidation for flow rates up to 50 mL min−1 gceria−1 at 1500 °C. It does not apply for oxidation below 930 °C. We compare the equilibrium model developed for the fixed-bed reactor to the models for the mixed flow and countercurrent flow reactors. In comparison to the mixed flow reactor, the fixed-bed reactor reduces the sweep gas and excess oxidizer required for fuel production, an important step toward increasing efficiency closer to the theoretical limit established by the countercurrent flow reactor.
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stoichiometries of δrd > 0.03 are attained at equilibrium.4 To date, implementation of the reduction reaction in prototype reactors has been accomplished by flowing either nitrogen or argon over porous ceria monoliths,12 ceria felt,13 open cell ceramic foam,14−16 or a bed of porous ceria particles.17,18 Krenzke and Davidson proposed to introduce methane as a reactant into reaction 1 to lower the temperature required for reduction, achieve a larger change in non-stoichiometry, and improve the utilization of solar process heat.19 The commercial viability of solar thermochemical fuel production strongly depends upon the efficiency of the solarto-fuel conversion,20,21 defined as the ratio of the heating value of the fuel to the solar thermal energy required to produce it.
INTRODUCTION The cerium dioxide (ceria, CeO2) thermochemical metal redox cycle is a promising approach to split water and carbon dioxide using concentrated solar radiation because of the favorable thermochemical properties of ceria.1−3 Ceria can be partially reduced at the high temperatures attainable with concentrated solar radiation and retain its cubic fluorite crystal structure up to non-stoichiometries of 0.2.4 1 1 1 CeO2 − δox → CeO2 − δrd + O2 2 Δδ Δδ
(1)
Retention of its crystal structure enables rapid diffusion of oxygen within the ceria, a feature which promotes facile reaction kinetics5,6 and allows for intrinsic separation of gaseous reaction products from the solid. Fuel (hydrogen or syngas) is produced by passing steam, CO2, or a mixture of oxidizing gases over the partially reduced ceria. 1 1 CeO2 − δrd + H 2O → CeO2 − δox + H 2 Δδ Δδ
(2a)
1 1 CeO2 − δrd + CO2 → CeO2 − δox + CO Δδ Δδ
(2b)
ηth =
(3)
The input energy in the denominator includes the direct solar thermal input to the process, Qsolar, and the solar thermal equivalent of the parasitic work, W/ηsolar, required to produce and pump reactant gases and separate product gases. Both the direct solar thermal input and the parasitic work depend upon the flow rate of inert sweep gas and flows of steam or carbon dioxide as a result of the need to heat, produce, and pump the gases. Sensible heating of the gases can be an order of magnitude higher than that of the chemical energy stored in the
The amount of fuel produced is proportional to the change in the non-stoichiometry of the ceria between the reduction and oxidation reactions, Δδ = δrd − δox. To affect reaction 1, a low oxygen partial pressure atmosphere is established by either vacuum pumping7−10 or inert gas sweeping.11 With an oxygen partial pressure of pO2 < 10−2 atm at 1500 °C, non© XXXX American Chemical Society
n fuel HHVfuel Q solar + W /ηsolar
Received: August 15, 2015 Revised: November 9, 2015
A
DOI: 10.1021/acs.energyfuels.5b01865 Energy Fuels XXXX, XXX, XXX−XXX
Article
Energy & Fuels
fixed bed of ceria and, hence, the reaction rates and the utilization of sweep gas and oxidizer.
fuel.11 Gas separation is also energy-intensive, particularly for the production of sweep gas.7,8,11 Assuming a solar-to-work conversion efficiency of ηsolar = 40%, 30 and 15 kJ of solar thermal energy (W/ηsolar) are required per mole of N2 to provide sweep gas with purities of 1 and 10 000 ppm oxygen via cryogenic and pressure swing adsorption separations,22 respectively. These values represent 5−10% of the higher heating value of hydrogen, 286 kJ mol−1, and carbon monoxide, 283 kJ mol−1, even in the optimistic case when 1 mol of N2 is required to produce 1 mol of fuel. Consequently, solar reactors must implement gas-phase heat recuperation23−25 and reduce the flow rates of sweep gas and oxidizer to the minimums predicted when the gases remain equilibrated with the ceria to reach commercially viable efficiencies of 20%.20 Prior studies project efficiencies under the assumption that equilibrium is attained between the ceria and process gases. These analyses apply different assumptions regarding the flow configuration and, consequently, provide different results regarding the requirements for sweep and oxidizing gases. The flow configurations considered in the analyses are the countercurrent model,8,11,24 which assumes that the ceria and gas flow in opposite directions, the mixed flow model,11 which assumes parallel flow of ceria and gas, and the fixed bed model,7 which assumes a continuous flow of gas through stationary ceria. As applied in prior work, the countercurrent model predicts unrealistically low flows of sweep gas and oxidizer.11 The mixed flow model is a fitting description of a continuously stirred tank reactor with a large enough tank volume to approach equilibrium. Unlike the countercurrent and mixed flow models, the fixed-bed model applies to a batch process in which the ceria non-stoichiometry and the equilibrium gas mixture change in time. Most demonstrations of the ceria redox cycle in solar reactors to date employ such a batch process,12−18 yet the conditions under which the fixed-bed equilibrium model is appropriate have not been determined. In the present study, we examine conditions for which the equilibrium assumption is valid for the flow of sweep gas and oxidizer in a fixed bed of ceria and compare the fixed-bed equilibrium model to the mixed flow and countercurrent models. In the fixed-bed equilibrium model, gases attain chemical equilibrium with ceria as they flow through the bed and concentration gradients between the ceria surface and the bulk gas phase are neglected. Oxygen and fuel are produced as fast as the products can be swept away from the ceria surface. The application of equilibrium to predict reaction rates requires that the intrinsic kinetics of reduction and oxidation are rapid enough that they do not limit either O2 release or fuel production, which prior data26 suggest is true at 1500 °C for mass-specific flow rates from 50 to 300 mL min−1 gceria−1. This requirement may not be met at the oxidation temperatures used in prototype solar reactors.12,14,27,28 To address the question of when an equilibrium model is appropriate in a fixed bed, we compare predictions of an equilibrium model to rates of O2 and CO production measured in packed beds of porous ceria particles over a range of N2 and CO2 flow rates and temperatures. Isothermal oxidation was investigated at temperatures between 800 and 1500 °C. Isothermal reduction was investigated at 1500 °C. Reduction was also investigated during heating of the ceria from 750 to 1500 °C. The comparison of the model to the data illustrates the range of temperatures and flow rates for which the equilibrium approach predicts the reaction conversion in the
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FIXED-BED EQUILIBRIUM MODEL Under the equilibrium assumption, process gases remain in local quasi-equilibrium with ceria during its transient reduction and oxidation.29 The partial pressure of oxygen in the gas, pO2, and the ceria non-stoichiometry, δ, are related at equilibrium by the state equation ⎛ pO ⎞ ΔhOo2(δ) − T ΔsOo2(δ) = RT ln⎜⎜ 2 ⎟⎟ ⎝ pref ⎠
(4)
where pref = 1 atm. The partial molar enthalpy, ΔhoO2, and entropy, ΔSoO2, of oxygen in ceria measured by Panlener et al. are employed in the present study.4 Regardless of the reactor type to which it is applied, the equilibrium model enforces eq 4 locally throughout the reacting volume at all times. In the present study, we apply the equilibrium model to predict the rates of oxygen and fuel production in a fixed-bed reactor in which spatial gradients of ceria non-stoichiometry, oxygen concentration, and total pressure are small (
