Analytical solutions for non-linear conversion of a porous solid particle in a gas–II. Non-isothermal conversion and numerical verification

In Part I, analytical solutions were given for the non-linear isothermal heterogeneous conversion of a porous solid particle. Account was taken of a reaction rate of general order with respect to the gas reactant, intrinsic reaction surface area and effective pore diffusion, which change with solid conversion and external film transport. In this part, the analytical solutions are extended to non-isothermal conversion. Analytical solutions for the particle overshoot temperature due to heat of reaction are derived from the governing differential equation pertaining to conservation of energy, considering the limiting cases of small and large Thiele moduli. The solutions are used to assess the effect of interaction between chemical reaction rate and particle overshoot temperature on particle conversion. The analytical solutions are shown to compare favourably with numerical simulation results

Analytical solutions for non-linear conversion of a porous solid particle in a gas–I. Isothermal conversion

Analytical description are presented for non-linear heterogeneous conversion of a porous solid particle reacting with a surrounding gas. Account has been taken of a reaction rate of general order with respect to gas concentration, intrinsic reaction surface area and pore diffusion, which change with solid conversion and external film transport. Results include expressions for the concentration distributions of the solid and gaseous reactant, the propagation velocity of the conversion zone inside the particle, the conversion time and the conversion rate. The complete analytical description of the non-linear conversion process is based on a combination of two asymptotic solutions. The asymptotic solutions are derived in closed form from the governing non-linear coupled partial differential equations pertaining to conservation of mass of solid and gaseous reactant, considering the limiting cases of a small and large Thiele modulus, respectively. For a small Thiele modulus, the solutions correspond to conversion dominated by reaction kinetics. For a large Thiele modulus, conversion is strongly influenced by internal and external transport processes and takes place in a narrow zone near the outer surface of the particle: solutions are derived by employing boundary layer theory. In Part II of this paper the analytical solutions are extended to non-isothermal conversion and are compared with results of numerical simulations

Simulation of the Oxygen Reduction Reaction (ORR) Inside the Cathode Catalyst Layer (CCL) of Proton Exchange Membrane Fuel Cells Using the Kinetic Monte Carlo Method

In this paper, a numerical model of the kinetic Monte Carlo (KMC) method has been developed to study the oxygen reduction reaction (ORR) that occurs inside the cathode catalyst layer (CCL). Firstly, a 3-D model of the CCL that consists of Pt and carbon spheres is built using the sphere packing method; secondly, an efficient procedure of the proton-oxygen reaction process is developed and simulated. In the proton-oxygen reaction process, all of the continuous movements of protons and oxygen are considered. The maximum reaction distance is determined to be 8 Å. The input pressures of protons and oxygen are represented by the number of spheres of the species. The value of the current density is calculated based on the amount of reaction during the interval time. Indications are that the results of the present model match reasonably well with the published results. A new way to apply the KMC method in the proton exchange membrane fuel cell (PEMFC) research field is developed in this paper

Substrate Support Ring for More Uniform Layer Thickness

Embodiments of substrate support rings providing more uniform thickness of layers deposited or grown on a substrate are provided herein. In some embodiments, a substrate support ring includes: an inner ring with a centrally located support surface to support a substrate; and an outer ring extending radially outward from the support surface, wherein the outer ring comprises a reaction surface area disposed above and generally parallel to a support plane of the support surface, and wherein the reaction surface extends beyond the support surface by about 24 mm to about 45 mm

Modeling of the oxy-combustion calciner in the post-combustion calcium looping process

The calcium looping process is a fast-developing post-combustion CO2 capture technology in which combustion flue gases are treated in two interconnected fluidized beds. CO2 is absorbed from the flue gases with calcium oxide in the carbonator operating at 650 ºC. The resulting CaCO3 product is regenerated into CaO and CO2 in the calciner producing a pure stream of CO2. In order to produce a suitable gas stream for CO2 compression, oxy-combustion of a fuel, such as coal, is required to keep the temperature of the calciner within the optimal operation range of 880-920°C. Studies have shown that the calcium looping process CO2 capture efficiencies are between 70 % and 97 %. The calciner reactor is a critical component in the calcium looping process. The operation of the calciner determines the purity of gases entering the CO2 compression. The optimal design of the calciner will lower the expenses of the calcium looping process significantly. Achieving full calcination at the lowest possible temperature reduces the cost of oxygen and fuel consumption. In this work, a 1.7 MW pilot plant calciner was studied with two modeling approaches: 3-D calciner model and 1-D process model. The 3-D model solves fundamental balance equations for a fluidized bed reactor operating under steady-state condition by applying the control volume method. In addition to the balance equations, semiempirical models are used to describe chemical reactions, solid entrainment and heat transfer to reduce computation effort. The input values of the 3-D-model were adjusted based on the 1-D-model results, in order to model the behavior of the carbonator reactor realistically. Both models indicated that the calcination is very fast in oxy-fuel conditions when the appropriate temperature conditions are met. The 3-D model was used to study the sulfur capture mechanisms in the oxy-fired calciner. As expected, very high sulfur capture efficiency was achieved. After confirming that the 1-D model with simplified descriptions for the sorbent reactions produces similar results to the more detailed 3-D model, the 1-D model was used to simulate calcium looping process with different recirculation ratios to find an optimal area where the fuel consumption is low and the capture efficiency is sufficiently high. It was confirmed that a large fraction of the solids can be recirculated to both reactors to achieve savings in fuel and oxygen consumption before the capture efficiency is affected in the pilot unit. With low recirculation ratios the temperature difference between the reactors becomes too low for the cyclic carbonation and calcination. As a general observation, the small particle size creates high solid fluxes in the calcium looping process that should be taken into account in the design of the system

Discharge precipitate's impact in Li-air battery: Comparison of experiment and model predictions

This paper presents a fundamental study on the precipitate formation/morphology and impact of discharge precipitates in Li-air batteries and compares the voltage loss with two Li-air battery models, namely a film-resistor model and surface coverage model. Toray carbon cloth is selected as cathode, which serves as large-porosity electrodes with an approximately planar reaction surface. Imaging analysis shows film formation of precipitates is observed in all the experiments. In addition, toroidal and aggregate morphologies are present under lower currents as well. Specially, toroidal or partially toroidal deposit is observed for 0.06 A/cm2. Aggregates, which consist of small particles with grain boundaries, are shown for 0.03 A/cm2. We found that the film-resistor model is unable to predict the discharge voltage behaviors under the two lower currents due to the presence of the deposit morphologies other than the film formation. The coverage model's prediction shows acceptable agreement with the experimental data because the model accounts for impacts of various morphologies of precipitates

Analysis of Air Cathode Perfomance for Lithium-Air Batteries

Lithium-air (Li-air) batteries have a theoretical specific energy comparable to gasolines. The air cathode plays a critical role in battery operation, where oxygen reacts with Li ions and electrons; and discharge products are stored in the pore structure. In major non-aqueous electrolytes, discharge products are insoluble and extremely low in electric conductivity, causing electrode passiviation and raising transport polarization. As discharging proceeds, insoluble materials are deposited at the reaction site and accumulate, increasing voltage loss and eventually shutting down operation. In this work, we present analysis of air cathode performance, taking into account both electrode passivation and transport resistance raised by insoluble products. Both effects are theoretically evaluated and compared. Validation is carried out against experimental data under low currents. The effects of electrode pore structure, such as porosity and tortuosity, on both the influence of insoluble precipitates and discharge capability are investigated. © 2013, The Electrochemical Society, Inc. All rights reserved

Analysis and multi-dimensional modeling of lithium-air batteries

This study contributes to: 1) a multi-dimensional model framework of lithium-air (Li-air) battery, 2) incorporation of mechanisms of insoluble precipitates' impacts, and 3) analysis and discussion on oxygen supply channel for Li-air battery. The model consists of a set of partial differential equations of species and charge conservation, in conjunction with the electrochemical reaction kinetics, and takes into account the two major mechanisms of voltage loss caused by insoluble discharge products: namely, electrode passivation and increased oxygen transport resistance. Two-dimensional (2-D) simulation indicates that the pore space in the cathode electrode is not fully utilized for Li compounds storage, particularly under high discharging current. For selected battery designs, considerable variation of quantities is observed only in the thickness direction. Through analysis, we evaluate the oxygen concentration drop along an oxygen supply channel and relate it to the Damköhler (Da) number, and further explore potential cases that yield oxygen starvation

Investigation on the Removal of Carbon Dioxide Exhausted from Industrial Units in a Lab-Scale Fluidized Bed Reactor

In this study, CO2 removal efficiency from flue gas was investigated in a fluidized bed reactor under semi-dry conditions. A lab-scale fluidized bed reactor, filled with inert glass beads, was used to investigate the effect of operating parameters on the CO2 removal efficiency using calcium hydroxide slurry as the absorbent. The Taguchi design method was used to design the experiments. The maximum inlet concentration of CO2 was 3 vol%. The most important factors were the reaction surface area, inlet gas velocity, inlet CO2 concentration, absorbent solution flow rate, inlet gas temperature and calcium hydroxide slurry concentration. The experimental results indicated that the CO2 removal efficiency increased when increasing the effective surface area of the reaction. Moreover, the removal efficiency increased by decreasing the input gas flow rate and inlet CO2 concentration. By performing experiments under optimum conditions, the maximum obtained CO2 removal efficiency was 79%. Copyright © 2020 by Authors, Published by BCREC Group. This is an open access article under the CC BY-SA License (https://creativecommons.org/licenses/by-sa/4.0).