Developing A Model Approximation Method and Parameter Estimates for Solid State Reaction Kinetics

The James S. Markiewicz Solar Energy Research Facility was built to research solar chemistry and currently being used to research the change in metal oxides such as iron or magnesium oxide that act as a medium for the production of hydrogen from water. This is significant because hydrogen can be used in vehicles equipped with appropriate fuel cells and due the decreased cost of producing hydrogen with this method. The shrinking core model which governs this process has proved difficult to solve due to the high number of unknown constants and its non-linearity. We detail in this work the implementation of less common heuristics, mainly Particle Swarm Optimization. This technique was used because of its wide unbiased search for the possible constants. The development and method we are using to solve these unknown constants will be shown

Developing A Model Approximation Method and Parameter Estimates for Solid State Reaction Kinetics

The James S. Markiewicz Solar Energy Research Facility was built to research solar chemistry and currently being used to research the change in metal oxides such as iron or magnesium oxide that act as a medium for the production of hydrogen from water. This is significant because hydrogen can be used in vehicles equipped with appropriate fuel cells and due the decreased cost of producing hydrogen with this method. The shrinking core model which governs this process has proved difficult to solve due to the high number of unknown constants and its non-linearity. We detail in this work the implementation of less common heuristics, mainly Particle Swarm Optimization. This technique was used because of its wide unbiased search for the possible constants. The development and method we are using to solve these unknown constants will be shown

Efficient Solar Thermal Electricity Unlocked: Sodium Heat Pipes in the Solar Furnace

Heat pipes were evaluated as an approach to distribute concentrated solar process heat in a solar receiver application. The ability of a plain 304 stainless steel (304SS) plate to absorb and distribute concentrated solar thermal irradiation was compared to a thermally enhanced board, outfitted with constant conductance sodium heat pies (CCHP TEB). Temperatures on the 304SS and CCHP TEB were measured using thermocouples and corroborated using an infrared camera. The 304SS plate was found to have a temperature range from 423℃ from minimum to peak, compared to a temperature range of 185℃ for the CCHP TEB. The result confirmed the enhanced capacity of the board enhanced by sodium heat pipes to convey heat across the entire plate relative to the plain plate, which had drastic hot and cold spots. Further, the power input of the solar furnace was calculated using a calorimeter and measured heat fluxes. The required solar power to reach a maximum temperature of 719℃ was 0.93 kW for the 304SS, while 1.57 kW was required for the CCHP TEB to reach a comparable maximum temperature. The broader impacts of this technology are two-fold. First, it can enable higher thermal efficiency in solar-electric power plants by facilitating higher solar receiver temperatures. Second, improved efficiency reduces both the land area and cost required to support the U.S. and greater global electricity demand

The kinetics of the heterogeneous oxidation of zinc vapor by carbon dioxide

The heterogeneous oxidation of Zn(g) is a promising reaction pathway for the conversion of CO2 into CO in the two-step Zn/ZnO solar thermochemical cycle as it eliminates the solid-state diffusion limitation that plagues the oxidation of Zn(l,s). The rate of the heterogeneous oxidation of Zn(g) is measured gravimetrically in a quartz tubular flow reactor operated at atmospheric pressure for temperatures between 800 and 1150 K, Zn(g) concentrations up to 36 mol%, and CO2 concentrations up to 45 mol%. The surface kinetics are extracted from the global reaction rate using a numerical reacting flow model that accounts for the transport of reacting species in the gas phase. The oxidation of Zn(g) by CO2 is rapid, on the order of 10−8–10−5 mol cm−2 s−1, and the rate is proportional to the product of the Zn(g) and CO2 partial pressures at the reaction surface. The activation energy for the Arrhenius reaction rate parameter is 44±3 kJ mol−1 and the pre-exponential factor is (92±6)×10−3 mol cm−2 s−1 atm−2. As a result of the rapid rate of oxidation of Zn(g), less than 1 s is required to convert more than 85% of Zn to ZnO

A parameter estimation method for stiff ordinary differential equations using particle swarm optimisation

We propose a two-step method for fitting stiff ordinary differential equation (ODE) models to experimental data. The first step avoids integrating stiff ODEs during the unbounded search for initial estimates of model parameters. To avoid integration, a polynomial approximation of experimental data is generated, differentiated and compared directly to the ODE model, obtaining crude but physically plausible estimates for model parameters. Particle swarm optimisation (PSO) is used for the parameter search to overlook combinations of model parameters leading to undefined solutions of the stiff ODE. After initial estimates are determined, the second step numerically solves the ODE. This refines model parameter values through a bounded search. We demonstrate this method by fitting the model parameters (activation energies and pre-exponential factors) of the Arrhenius-based temperature-dependent kinetic coefficients in the shrinking core solid-state chemical kinetics model for the reduction of Cobalt (II, III) Oxide (Co3 role= presentation style= display: inline; line-height: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; font-family: Helvetica Neue , Helvetica, Arial, sans-serif; position: relative; \u3e33O4 role= presentation style= display: inline; line-height: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; font-family: Helvetica Neue , Helvetica, Arial, sans-serif; position: relative; \u3e44) particles to Cobalt (II) Oxide (CoO)

Heterogeneous oxidation of zinc vapor by steam and mixtures of steam and carbon dioxide

The kinetics of the heterogeneous oxidation of zinc vapor by water vapor were measured in a tube flow reactor for temperatures from 800 to 1100 K, zinc vapor partial pressures up to 0.39 atm, and water vapor partial pressures up to 1.0 atm. The results extend the prior data for oxidation of zinc by water vapor from zinc partial pressures on the order of 0.01 atm to higher values appropriate for fuel production via the Zn/ZnO thermochemical cycle. (cont.

Heliostat Attitude Control Strategy in the Solar Energy Research Facility of Valparaiso University

In this paper, a continuous tracking strategy for the heliostat in the James S. Markiewicz Concentrated Solar Energy Research Facility at Valparaiso University is developed. A model of the nonlinear dynamics of the heliostat motion is developed and the open-loop control strategy is presented. Asymptotic stability of the heliostat control using the Lyapunov and LaSalle\u27s theorems were proven. Simulations using the nonlinear dynamic model are presented and interpreted to identify the feedback gain that maximizes the time response of the heliostat without introducing oscillations in its motion. Finally, the control strategy is put to the test during summer-time operation. Data are presented that show that the tracking strategy has an RMS tracking error of 0.058 mrad, where the error is defined as the difference between the desired and actual heliostat positions. Images of the the aperture of a high-temperature solar receiver over 8 hours of testing are also presented to qualitatively demonstrate the success of the tracking strategy

Solar Reduction of Cobalt Oxide Particles: Rotary Kiln Reactor Model and Experimental Results

A solar rotary kiln reactor was analyzed numerically to determine how efficiently it utilizes concentrated solar energy to reduce Co3O4 to CoO as a function of reactor operational parameters, including the rotation rate, the feed rate of Co3O4, and the solar power. The solar thermal efficiency, defined as the fraction of solar energy used to drive the reduction reaction, is calculated using an axisymmetric, finite-volume model of the rotary kiln reactor. The model iteratively solves the nonlinear, coupled energy and species equations accounting for conduction heat transfer, volumetric and surface radiation heat transfer, and cobalt oxide reduction kinetics within cloud of cobalt oxide particles that moves through the reactor in a plug flow. Radiation is simulated using Monte Carlo Ray Tracing, and the reduction kinetics follow the shrinking core model. For a cloud of 15 micrometer-diameter particles with a volume fraction of 10-5, we show an optimum solar thermal efficiency of 27% with a Co3O4 feed rate of 3.6 kilograms per hour and 3.5 kilowatts of solar power. At this optimum operating point, we show the temperature and conversion fields within the reactor. Furthermore, the results of a preliminary experiment are shown and provide experimental evidence of the promise of the solar rotary kiln reactor: 18% of the Co3O4 was reduced to CoO

Model of the solar-driven reduction of cobalt oxide in a particle suspension reactor

We develop a model to investigate the impact of volume fraction and extent of mixing on the thermal efficiency with which a cavity-based particle suspension solar reactor reduces Co3O4 into CoO and O2. Thermal efficiency is defined as the fraction of solar energy used to drive the endothermic reduction. In the model, particles move continuously through the reactor in either mixed or plug flow—mixing conditions that give rise to isothermal and nonisothermal suspensions, respectively—and reduce at a rate governed by shrinking core kinetics, the parameters of which are determined using thermogravimetric data. Radiation is simulated using the Monte Carlo Ray Tracing technique. The model is applied to a reactor heated by 4 kW of point-focused solar radiation with a mean concentration ratio of 1400 suns containing monodisperse suspensions of 40 μm diameter particles with volume fractions between 1×10⁻⁵ and 1×10⁻². Thermal efficiency is insensitive to mixing for the two conditions considered. The maximum thermal efficiency obtained for mixed flow with an isothermal suspension is 34.1% at 102 g min⁻¹ and a volume fraction of 2×10⁻⁴. At the same volume fraction, the maximum thermal efficiency for nonisothermal plug flow is 33.2% at 94 g min⁻¹. Thermal efficiency is more sensitive to the volume fraction, but only below a threshold value of 2×10⁻⁴. Thus, from the perspective of coupling heat transfer to the chemical reaction, design and operational efforts of particle suspension reactors for the reduction of cobalt oxide should focus on generating suspensions of at least this threshold value rather than on mixing the particles within the suspension