Numerical modeling of transport phenomena in reactive porous structures for solar fuel applications

Abstract

The focus of this work is the development and use of a numerical model to study solar thermochemical fuel production using nonstoichiometric ceria in the form of a reactive porous medium. Volume averaging theorems are applied at the pore-level to obtain a set of governing equations that use effective transport properties to describe the heat and mass transfer processes in the reactive porous medium on the macroscale. Reaction rate expressions are formulated for both the thermal reduction and oxidation steps as an interphase mass flux whose dependence on the partial pressures, solid temperature, and nonstoichiometry is derived from the ionization state of the oxygen vacancies.The porosity and pore-level solid feature size (as represented by a Sauter mean diameter) of a porous monolith are varied from 0.6 to 0.9 and 10 to 1000 μm, respectively, to determine their impact on the rate of oxygen release and the solar-to-chemical energy conversion efficiency during thermal reduction while the macroscale geometry and operating conditions are held fixed. The process is carried out in a batch mode by placing the reactive medium inside a cavity where it is directly irradiated with a concentrated solar flux as a sweep gas passes through its pore network. The best performance is obtained with a non-uniform heating of the solid, which is attributed to the nonlinear temperature dependence of the equilibrium nonstoichiometry. The solar-to-chemical energy conversion efficiency attains its highest value of 10.9 % with a porosity of 0.9 and a Sauter mean diameter of 10 μm. These results imply that high porosities and small feature sizes are preferred, but it is recognized and discussed that these findings are strongly tied to the particular set of operating conditions considered.The mathematical model is also used in conjunction with available experimental data to develop a method for determining a reaction rate expression that characterizes the oxidation of ceria by carbon dioxide. The volume-averaged conservation equations for the porous medium are used to simulate a packed bed of porous particles and the axially-dispersed plug flow model is used to compare numerical predictions of the effluent composition with experimental measurements. Reaction rate expressions are developed and their kinetic parameters are determined by minimizing the difference between the numerical predictions and the experimental measurements as quantified by a root mean square error for a temperature of 1203 K. At this temperature, numerical results obtained using a reaction rate expression based on singly ionized oxygen vacancies provide excellent agreement with the experimental data.