Multi-scale modelling of Gibbsite calcination in a fluidized bed reactor

The alumina industry provides the feedstock for aluminium metal production and contributes to around A$6 billion of Australian exports annually. One of the most energy-intensive parts of alumina production, with a strong effect on final product quality, is calcination or thermal decomposition, in which gibbsite powder is converted into alumina. Industrially, gibbsite calcination is conducted in bubbling or circulating fluidized beds. Better modelling of fluid bed calciners is needed to improve process design, control and operations. Multi-scale models, which account for phenomena interacting across different length and time scales, are increasingly being used to describe complex, multidisciplinary, nonlinear, non-equilibrium processes, including fluidized bed reactors. In order to attain more insight into the gibbsite calciner, from a multi-scale viewpoint, this investigation has been conducted in five steps as follows.Firstly, the possibilities for developing a multi-scale model for the fluidized bed calcination of gibbsite are investigated, followed by recommendations on promising directions. The key elements of the multi-scale approach that is considered were: (i) identification of the relevant scales of interest for bubbling and circulating fluidized bed reactors; (ii) characterisation of the dominant phenomena, modelling approaches and available data at each scale; (iii) an integrated communication framework to link the scales of interest, and briefly (iv) experiment design and model validation for multi-scale models. A conceptual model having three scales (particle, volume element / cluster, and vessel) was proposed and the information flows between the scales were outlined. There are several possibilities for the sub-models used at each scale, and these have been noted.Secondly, as a part of the particle scale modelling efforts, a 1-D mathematical model describing the calcination of a single gibbsite particle to alumina has been developed and validated against literature data. A dynamic, spatially-distributed, mass and energy balance model enables the prediction of the evolution of chemical composition and temperature as a function of radial position inside a particle. In the thermal decomposition of gibbsite, water vapour is formed and the internal water vapour pressure plays a significant role in determining the rate of gibbsite dehydration. A thermal decomposition rate equation was developed by closely iimatching experimental data reported previously in the literature. Estimated values of the transformation kinetic parameters are reported.The reaction order with respect to water vapour concentration was negative, meaning that the water vapour that is produced impedes further gibbsite calcination, which is in agreement with previous kinetic studies. Using these kinetic parameters, the gibbsite particle model is solved numerically to predict the evolution of the internal water vapour pressure, temperature and gibbsite concentration. The model prediction is shown to be very sensitive to the values of heat transfer coefficient, effective diffusivity, particle size and external pressure, but relatively less sensitive to the mass transfer coefficient and particle thermal conductivity. The predicted profile of the water vapour pressure inside the particle helps explain some phenomena observed in practice, including particle breakage and formation of a boehmite phase.Thirdly, a new variation on the unreacted shrinking core model has been developed for calcination and similar non-catalytic thermal solid-to-gas decomposition reactions in which there is no gaseous reactant involved and the reaction rate decreases with increasing product gas concentration. The numerical solution of the developed model has been verified against an analytical solution for the isothermal case. The model parameters have been tuned using literature data for the calcination of gibbsite to alumina over a wide range of temperatures. The model results for gibbsite conversion are found to agree well with the published experimental data. Predictions of the non-isothermal unreacted shrinking core model compare well with the more complex, distributed model developed in the previous step.Fourthly, a multi-stage, multi-reaction, shrinking core model is proposed for the simulation of solid-to-gas reactions with self-inhibiting behaviour and in which the build-up of internal pressure caused by the product gas may alter the reaction pathway in a way that favours one pathway over others. This model emphasises the role of the produced gas, not only in mass transfer, but also in the reaction kinetics. It includes parallel and series reactions, allowing for the formation of an intermediate species. The model has been applied to the conversion of gibbsite to alumina, including the formation of intermediate boehmite. Modelling results for gibbsite conversion, boehmite formation and its subsequent consumption, as well as alumina formation, agree well with literature data; the corresponding kinetic parameters are estimated for all reactions. Significantly, the experimentally-observed plateaux in the particle’s temperature history are predicted by the model. The role of heating rate and particle size on boehmite formation is also evaluated using the model, and is in agreement with observation.Fifthly, a simplified version of the multi-scale model proposed in the first step has been developed. Particle scale models are valuable for analysing kinetics, understanding behaviour and some experimental design of gas-solid reactions. However, engineers are always interested in practical, equipment-scale models that can predict the performance of operating units in different scenarios. In this part of the research, some fluid bed reactor phenomena are described along with their modelling methodologies, and then a two-scale model combining one of the particle scale models with a simple reactor scale model is described. The simple reactor model consists of a collection of ideal mixed volumes connected in series. In each volume element, the reaction rate from the particle scale is linked into material and energy balances at the reactor scale. The number of volume elements is variable and thus able to simulate reactor behaviour from an ideal CSTR to a near-ideal PFR, and also for flow regimes in between them. In spite of the simplicity, the solid residence time distribution and gas flow rate variation are accounted for at the reactor scale. Even though a general discussion of fluid bed reactors is presented, gibbsite calcination is again considered for the case study, the same as for the other steps in the project. The developed two-scale model predicts the gas and solid temperature profiles, trends in overall gas flow rate and water vapour pressure, and alumina and gibbsite concentration profiles through the reactor. Sensitivity analyses are conducted into the number of volume elements and the solid throughput rate.Finally, potential research opportunities for multi-scale modelling of fluidized bed reactors are outlined

Simulation of Solid Oxide Fuel Cell Anode in Aspen HYSYS—A Study on the Effect of Reforming Activity on Distributed Performance Profiles, Carbon Formation, and Anode Oxidation Risk

A distributed variable model for solid oxide fuel cell (SOFC), with internal fuel reforming on the anode, has been developed in Aspen HYSYS. The proposed model accounts for the complex and interactive mechanisms involved in the SOFC operation through a mathematically viable and numerically fast modeling framework. The internal fuel reforming reaction calculations have been carried out in a plug flow reactor (PFR) module integrated with a spreadsheet module to interactively calculate the electrochemical process details. By interlinking the two modules within Aspen HYSYS flowsheeting environment, the highly nonlinear SOFC distributed profiles have been readily captured using empirical correlations and without the necessity of using an external coding platform, such as MATLAB or FORTRAN. Distributed variables including temperature, current density, and concentration profiles along the cell length, have been discussed for various reforming activity rates. Moreover, parametric estimation of anode oxidation risk and carbon formation potential against fuel reformation intensity have been demonstrated that contributes to the SOFC lifetime evaluation. Incrementally progressive catalyst activity has been proposed as a technically viable approach for attaining smooth profiles within the SOFC anode. The proposed modeling platform paves the way for SOFC system flowsheeting and optimization, particularly where the study of systems with stack distributed variables is of interest

System Level Exergy Assessment of Strategies Deployed for Solid Oxide Fuel Cell Stack Temperature Regulation and Thermal Gradient Reduction

Several operational strategies for solid oxide fuel cell (SOFC) temperature regulation and temperature gradient minimization at cell scale have previously been assessed by the authors (Amiri et al., Ind. Eng. Chem. Res., 2016). The application of such strategies at system scale, however, requires a numerical linkage between the cell and the system performance metrics allowing simultaneous evaluation of the dominant process interactions. The objective of this study is to analytically examine the effectiveness and applicability of the mentioned thermal management methods at system scale. To achieve this, a system level exergy analysis is presented by using a modeling platform in which a detailed four-cell short stack module and the balance-of-plant (BoP) are integrated. Linkage between the system performance metrics and the stack internal temperature gradient is specifically emphasized. For this, the exergy intensive points (unit operations) are identified throughout the plant. Subsequently, the effective strategies that had been employed for the cell level thermal management proposed in our previous work (Amiri et al., Ind. Eng. Chem. Res., 2016) are examined at the system level capturing the effects on the state of BoP exergy intensive components. Moreover, fuel design is proposed and evaluated as a potential thermal management strategy. Combination of a variety of measures including the exergy destruction rates, the electrical and thermal efficiencies, and the stack internal temperature gradient provides a comprehensive set of data contributing to the SOFC system thermal management

Planar solid oxide fuel cell modeling and optimization targeting the stack's temperature gradient minimization

Minimization of undesirable temperature gradients in all dimensions of a planar solid oxide fuel cell (SOFC) is central to the thermal management and commercialization of this electrochemical reactor. This article explores the effective operating variables on the temperature gradient in a multilayer SOFC stack and presents a trade-off optimization. Three promising approaches are numerically tested via a model-based sensitivity analysis. The numerically efficient thermo-chemical model that had already been developed by the authors for the cell scale investigations (Tang et al. Chem. Eng. J. 2016, 290, 252-262) is integrated and extended in this work to allow further thermal studies at commercial scales. Initially, the most common approach for the minimization of stack's thermal inhomogeneity, i.e., usage of the excess air, is critically assessed. Subsequently, the adjustment of inlet gas temperatures is introduced as a complementary methodology to reduce the efficiency loss due to application of excess air. As another practical approach, regulation of the oxygen fraction in the cathode coolant stream is examined from both technical and economic viewpoints. Finally, a multiobjective optimization calculation is conducted to find an operating condition in which stack's efficiency and temperature gradient are maximum and minimum, respectively

Evaluation of Fuel Diversity in Solid Oxide Fuel Cell System

Operability of Solid Oxide Fuel Cell (SOFC) on numerous fuels has been widely counted as a leading advantage in literature. In a designed system, however, switching from a fuel to another is not practically a straightforward task as this causes several system performance issues in both dynamic and steady-state modes. In order to demonstrate the system fuel diversity capabilities, these consequences must be well-evaluated by quantifying the characteristic measures for numerous fuel cases and also potential combinations. From this viewpoint, the numerical predictive models play a critical role. This paper aims to investigate the performance of a SOFC system fed by various fuels using a demonstrated system level model. Process configuration and streams results of a real-life SOFC system rig published in literature are used to validate the model. The presented model is capable not only of capturing the system performance measures but also the SOFC internal variable distributions, allowing the multiscale study of fuel switching scenarios. The fuel change impacts on the system are simulated by considering various fuel sources, i.e., natural gas, biogas, and syngas. Moreover, applications of simulated fuel mixtures are assessed. The modelling results show significant concerns about fuel switching in a system in terms of variation of efficiencies, stack internal temperature and current density homogeneity, and environmental issues. Moreover, the results reveal opportunities for multi-fuel design to address the operation and application requirements such as optimisation of the anode off-gas recycling rate and the thermal-to-electrical ratio as well as the system specific greenhouse gases, i.e., g-COx/Wh release

Modelling of gibbsite calcination in a fluidized bed reactor

A steady state, non‐isothermal fluidized bed reactor model for co‐current flow of gas and solids has been developed as a series of Continuous Stirred Tank Reactor (CSTR) compartments. For each CSTR compartment, mass and energy balances were coupled with a particle‐scale gibbsite calcination kinetic model previously developed by the authors. The overall solids residence time distribution is captured by the compartment calcination model. The multi‐scale model was solved numerically through an iterative procedure that alternated between solving particle‐scale and reactor‐scale parts of the model. Gas, water vapour and solids concentrations, as well as particle and gas temperatures and gibbsite conversion profiles, are predicted inside the calcination reactor. The developed model can be used to facilitate improvements in the operation and design of industrial‐scale reactors

Multi-stage shrinking core model for thermal decomposition reactions with a self-inhibiting nature

Among the variety of thermal decomposition reactions, some display self-inhibiting behaviour, where the produced gas negatively influences the reaction progress. Further, a build-up of internal pressure caused by the product gas may alter the reaction pathway over the reaction duration in a way that favours a particular pathway over others. Two well-known cases of this kind of reaction are the thermal decomposition of limestone and gibbsite, in which carbon dioxide and water vapour are the produced gases, respectively. A multi-stage, multi-reaction, shrinking core model is proposed for this type of reaction. The model emphasises the role of the produced gas, not only in the mass transfer rate, but also in the reaction kinetics. It also includes parallel and series reaction pathways, which allows for the presence of an intermediate species. The model has been applied to the conversion of gibbsite to alumina, and it includes the formation of boehmite as an intermediate product. The model results are in good agreement with experimental data for gibbsite calcination reported in the literature. Gibbsite conversion, boehmite formation and subsequent consumption, as well as alumina formation, are successfully simulated. Further, the corresponding kinetic parameters are estimated for all reactions of interest

Planar SOFC system modelling and simulation including a 3D stack module

A solid oxide fuel cell (SOFC) system consists of a fuel cell stack with its auxiliary components. Modelling an entire SOFC system can be simplified by employing standard process flowsheeting software. However, no in-built SOFC module exists within any of the commercial flowsheet simulators. In Amiri et al. (Comput. Chem. Eng., 2015, 78:10-23), a rigorous SOFC module was developed to fill this gap. That work outlined a multi-scale approach to SOFC modelling and presented analyses at compartment, channel and cell scales. The current work extends the approach to stack and system scales. Two case studies were conducted on a simulated multilayer, planar SOFC stack with its balance of plant (BoP) components. Firstly, the effect of flow maldistribution in the stack manifold on the SOFC's internal variables was examined. Secondly, the interaction between the stack and the BoP was investigated through the effect of recycling depleted fuel. The results showed that anode gas recycling could be used for managing the gradients within the stack, while also improving fuel utilisation and water management

SOFC Stack and System Modeling, Fault Diagnosis and Control

This report is an account of research and development activities undertaken by the Centre for Process Systems Computations, Department of Chemical Engineering at Curtin University, Western Australia in the area of solid oxide fuel cells. The focus of work of the group included 1) effect of cell macrostructure and microstructure on electrochemical performance with a view to optimise both macro- and micro-structure 2) electrochemistry modeling for simulating electrochemical performance 3) internal reforming aspects impacting performance at cell/stack and system levels 4) system level modeling investigating cell internal profiles (temperature, gas composition), homogeneity improvement, thermal management, anode recycle, fuel diversity, oxygen quality, and 5) monitoring for diagnostics, optimisation and control. The report summarizes work done over a period of 15 years and highlights areas of research gaps and future directions for research in the path to mass-scale commercialisation of the solid oxide fuel cell technolog

Mathematical model of a proton-exchange membrane (PEM) fuel cell

This work presents a mathematical modelling of a proton-exchange membrane fuel cell (PEMFC) system integrated with a resistive variable load. The model was implemented using MATLAB Simulink software, and it was used to calculate the fuel cell electric current and voltage at various steady-state conditions. The electric current was determined by the intersection of its polarisation curve and applied as an input value for the simulation of the PEM fuel cell performance. The model was validated using a Horizon H-500xp model fuel cell stack system, with the following main components: a 500 W PEM fuel cell, a 12 V at 12 A battery for the start-up, a super-capacitor bank to supply peak loads and a 48 V DC-DC boost converter. The generated power was dissipated by a variable resistive load. The results from the model shows a qualitative agreement with test bench results, with similar trends for stack current and voltage in response to load and hydrogen flow rate variation. The discrepancies ranged from 2% to 6%, depending on the load resistance applied. A controlled current source was utilised to simulate the variation of fan power consumption with stack temperature, ranging from 36.5 W at 23°C to 52 W at 65°C. Both model and experiments showed an overall PEMFC system maximum efficiency of about 48%