Optimal porosity distribution for minimized ohmic drop across a porous electrode

This paper considers the design of spatially varying porosity profiles in next-generation electrodes based on simultaneous optimization of a porous-electrode model. Model-based optimal design ͑not including the solid-phase intercalation mechanism͒ is applied to a porous positive electrode made of lithium cobalt oxide, which is commonly used in lithium-ion batteries for various applications. For a fixed amount of active material, optimal grading of the porosity across the electrode was found to decrease the ohmic resistance by 15%-33%, which in turn increases the electrode capacity to hold and deliver energy. The optimal porosity grading was predicted to have 40% lower variation in the ohmic resistance to variations in model parameters due to manufacturing imprecision or capacity fade. The results suggest that the potential for the simultaneous model-based design of electrode material properties that employ more detailed physics-based first-principles electrochemical engineering models to determine optimal design values for manufacture and experimental evaluation. © 2010 The Electrochemical Society. ͓DOI: 10.1149/1.3495992͔ All rights reserved. Electrochemical power sources have had significant improvements in design and operating range and are expected to play a vital role in the future in automobiles, power storage, military, and space applications. Lithium-ion chemistry has been identified as a preferred candidate for high-power/high-energy secondary batteries. Applications for batteries range from implantable cardiovascular defibrillators operating at 10 A current to hybrid vehicles requiring pulses of up to 100 A. Today, the design of these systems have been primarily based on ͑i͒ matching the capacity of anode and cathode materials; ͑ii͒ trial-and-error investigation of thickness, porosity, active material, and additive loading; ͑iii͒ manufacturing convenience and cost; ͑iv͒ ideal expected thermal behavior at the system level to handle high currents; and ͑v͒ detailed microscopic models to understand, optimize, and design these systems by changing one or few parameters at a time. Traditionally, macroscopic models have been used to optimize the electrode thickness or spatially uniform porosity in lithium-ion battery design. Many applications of mathematical modeling to design Li-ion batteries are available in the literature. 1-10 An approach to identify the optimal values of system parameters such as electrode thickness has been reported by Newman and co-workers. 2,5-10 Simplified models based on porous-electrode theory can provide analytical expressions to describe the discharge of rechargeable lithium-ion batteries in terms of the relevant system parameters. Newman and co-workers 2,5-8 have utilized continuum electrochemical engineering models for design and optimization as a tool for the identification of system limitations from the experimental data. Equations were developed that describe the time dependence of potential as a function of electrode porosity and thickness, the electrolyte and solid-phase conductivities, specific ampere-hour capacity, separator conductivity and thickness, and current density. Analysis of these equations yields the values of electrode porosity and electrode thickness so as to maximize the capacity for discharge to a given cutoff potential. Simplified models based on porous-electrode theory were used to describe the discharge of rechargeable lithium batteries and derive analytical expressions for the cell potential, specific energy, and average power in terms of the relevant system parameters. The resulting theoretical expressions were used for design and optimization purposes and for the identification of system limitations from experimental data. 5 Studies were performed by comparing the Ragone plots for a range of design parameters. A single curve in a Ragone plot involves hundreds of simulations wherein the applied current is varied over a wide range of magnitude. Ragone plots for different configurations are obtained by changing the design parameters ͑e.g., thickness͒ one at a time and by keeping the other parameters at constant values. This process of generating a Ragone plot is quite tedious, and typically Ragone curves reported in the literature are not smooth due to computational constraints. Batteries are typically designed only to optimize the performance at the very first cycle of operation of the battery, whereas in practice most of the battery's operation occurs under significantly degraded conditions. Further, multivariable optimization is not computationally efficient using most first-principles models described in the literature. A reformulated model Electrochemical Porous-Electrode Model Garcia et al. 14 provided a framework for modeling microstructural effects in electrochemical devices. That model can be extended to treat more complex microstructures and physical phenomena such as particle distributions, multiple electrode phase mixtures, phase transitions, complex particle shapes, and anisotropic solid-state diffusivities. As mentioned earlier, there are several treatments fo

Optimal porosity distribution for minimized ohmic drop across a porous electrode

This paper considers the design of spatially varying porosity profiles in next-generation electrodes based on simultaneous optimization of a porous-electrode model. Model-based optimal design ͑not including the solid-phase intercalation mechanism͒ is applied to a porous positive electrode made of lithium cobalt oxide, which is commonly used in lithium-ion batteries for various applications. For a fixed amount of active material, optimal grading of the porosity across the electrode was found to decrease the ohmic resistance by 15%-33%, which in turn increases the electrode capacity to hold and deliver energy. The optimal porosity grading was predicted to have 40% lower variation in the ohmic resistance to variations in model parameters due to manufacturing imprecision or capacity fade. The results suggest that the potential for the simultaneous model-based design of electrode material properties that employ more detailed physics-based first-principles electrochemical engineering models to determine optimal design values for manufacture and experimental evaluation. © 2010 The Electrochemical Society. ͓DOI: 10.1149/1.3495992͔ All rights reserved. Electrochemical power sources have had significant improvements in design and operating range and are expected to play a vital role in the future in automobiles, power storage, military, and space applications. Lithium-ion chemistry has been identified as a preferred candidate for high-power/high-energy secondary batteries. Applications for batteries range from implantable cardiovascular defibrillators operating at 10 A current to hybrid vehicles requiring pulses of up to 100 A. Today, the design of these systems have been primarily based on ͑i͒ matching the capacity of anode and cathode materials; ͑ii͒ trial-and-error investigation of thickness, porosity, active material, and additive loading; ͑iii͒ manufacturing convenience and cost; ͑iv͒ ideal expected thermal behavior at the system level to handle high currents; and ͑v͒ detailed microscopic models to understand, optimize, and design these systems by changing one or few parameters at a time. Traditionally, macroscopic models have been used to optimize the electrode thickness or spatially uniform porosity in lithium-ion battery design. Many applications of mathematical modeling to design Li-ion batteries are available in the literature. 1-10 An approach to identify the optimal values of system parameters such as electrode thickness has been reported by Newman and co-workers. 2,5-10 Simplified models based on porous-electrode theory can provide analytical expressions to describe the discharge of rechargeable lithium-ion batteries in terms of the relevant system parameters. Newman and co-workers 2,5-8 have utilized continuum electrochemical engineering models for design and optimization as a tool for the identification of system limitations from the experimental data. Equations were developed that describe the time dependence of potential as a function of electrode porosity and thickness, the electrolyte and solid-phase conductivities, specific ampere-hour capacity, separator conductivity and thickness, and current density. Analysis of these equations yields the values of electrode porosity and electrode thickness so as to maximize the capacity for discharge to a given cutoff potential. Simplified models based on porous-electrode theory were used to describe the discharge of rechargeable lithium batteries and derive analytical expressions for the cell potential, specific energy, and average power in terms of the relevant system parameters. The resulting theoretical expressions were used for design and optimization purposes and for the identification of system limitations from experimental data. 5 Studies were performed by comparing the Ragone plots for a range of design parameters. A single curve in a Ragone plot involves hundreds of simulations wherein the applied current is varied over a wide range of magnitude. Ragone plots for different configurations are obtained by changing the design parameters ͑e.g., thickness͒ one at a time and by keeping the other parameters at constant values. This process of generating a Ragone plot is quite tedious, and typically Ragone curves reported in the literature are not smooth due to computational constraints. Batteries are typically designed only to optimize the performance at the very first cycle of operation of the battery, whereas in practice most of the battery's operation occurs under significantly degraded conditions. Further, multivariable optimization is not computationally efficient using most first-principles models described in the literature. A reformulated model Electrochemical Porous-Electrode Model Garcia et al. 14 provided a framework for modeling microstructural effects in electrochemical devices. That model can be extended to treat more complex microstructures and physical phenomena such as particle distributions, multiple electrode phase mixtures, phase transitions, complex particle shapes, and anisotropic solid-state diffusivities. As mentioned earlier, there are several treatments fo

Optimization Studies Of Batch Polymerization For Polystyrene Process

Polymerization is a chemical reaction process of monomer molecules to form a polymer chain. In the polymer industry, batch polymerization reactors are used extensively to manufacture a variety of polymers of numerous grades. Batch process is well suited for low-volume products and for products with numerous grades (as in specialty polymers. However, this process may require higher operation cost because it can achieve high conversion with long batch time. The operation is unsteady-state where the composition and temperature always change with time. Optimum operating conditions are very important for the polymerization process in order to achieve the objective function in the process. In this study, the optimization technique using mathematical models was implemented to obtain those optimum operating conditions. The dynamic optimization problem was solved using an orthogonal collocation method where the differential variables were fully discretized. Collocation method is one of the methods that can be used to solve dynamic optimization. In the case of solving the dynamic optimization problems, collocation formulae can be used to transform the ordinary differential equations into algebraic equations. In this study, the optimization of optimal temperature generations in batch process of polystyrene was investigated theoretically

Capacity Fade Analysis and Model Based Optimization of Lithium-ion Batteries

Electrochemical power sources have had significant improvements in design, economy, and operating range and are expected to play a vital role in the future in a wide range of applications. The lithium-ion battery is an ideal candidate for a wide variety of applications due to its high energy/power density and operating voltage. Some limitations of existing lithium-ion battery technology include underutilization, stress-induced material damage, capacity fade, and the potential for thermal runaway. This dissertation contributes to the efforts in the modeling, simulation and optimization of lithium-ion batteries and their use in the design of better batteries for the future. While physics-based models have been widely developed and studied for these systems, the rigorous models have not been employed for parameter estimation or dynamic optimization of operating conditions. The first chapter discusses a systems engineering based approach to illustrate different critical issues possible ways to overcome them using modeling, simulation and optimization of lithium-ion batteries. The chapters 2-5, explain some of these ways to facilitate: i) capacity fade analysis of Li-ion batteries using different approaches for modeling capacity fade in lithium-ion batteries,: ii) model based optimal design in Li-ion batteries and: iii) optimum operating conditions: current profile) for lithium-ion batteries based on dynamic optimization techniques. The major outcomes of this thesis will be,: i) comparison of different types of modeling efforts that will help predict and understand capacity fade in lithium-ion batteries that will help design better batteries for the future,: ii) a methodology for the optimal design of next-generation porous electrodes for lithium-ion batteries, with spatially graded porosity distributions with improved energy efficiency and battery lifetime and: iii) optimized operating conditions of batteries for high energy and utilization efficiency, safer operation without thermal runaway and longer life

Optimal control of fed-batch fermentation processes

Optimisation of a fed-batch fermentation process typically uses the calculus of variations or Pontryagin's maximum principle to determine an optimal feed rate profile. This often results in a singular control problem and an open loop control structure. The singular feed rate is the optimal feed rate during the singular control period and is used to control the substrate concentration in the fermenter at an optimal level. This approach is supported by biological knowledge that biochemical reaction rates are controlled by the environmental conditions in the fermenter; in this case, the substrate concentration. Since an accurate neural net-based on-line estimation of the substrate concentration has recently become available and is currently employed in industry, we are therefore able to propose a method which makes use of this estimation. The proposed method divides the optimisation problem into two parts. First, an optimal substrate concentration profile which governs the biochemical reactions in the fermentation process is determined. Then a controller is designed to track the obtained optimal profile. Since the proposed method determines the optimal substrate concentration profile, the singular control problem is therefore avoided because the substrate concentration appears nonlinearly in the system equations. Also, the process is then operated in closed loop control of the substrate concentration. The proposed method is then called "closed loop optimal control". The proposed closed loop optimal control method is then compared with the open loop optimal feed rate profile method. The comparison simulations from both primary and secondary metabolite production processes show that both methods give similar performance in a case of perfect model while the closed loop optimal control provides better performance than the open loop method in a case of plant/model mismatch. The better performance of the closed loop optimal control is due to an ability to compensate for the modelling errors using feedback

Modelamiento, simulación, Optimización dinámica y control de un proceso semibatch de polimerización en emulsión

Abstract. In this work, modeling, simulation, dynamic optimization and nonlinear control of an industrial emulsion polymerization process to produce poly-vinyl acetate (PVAc) are proposed. The reaction is modeled as a two-phase system composed of an aqueous phase and a particle phase. A detailed model is used to calculate the weight average molecular weight, the number average molecular weight and the dispersity. The moments of the growing and dead chains are used to represent the state of the polymer and to calculate the molecular weight distribution (MWD). The case study corresponds to an industrial reactor operated at a chemical company in Bogot´a. An industrial scale reactor (11 m3 of capacity) is simulated where a semi-batch emulsion polymerization reaction of vinyl acetate is performed. Dynamic optimization problem is solved directly using a Nonlinear Programming solver. Integration of differential equations is made using Runge-Kutta method. Three different optimization problems are solved from the more simplistic (only one control variable : reactor temperature) to the more complex (three control variables : reactor temperature, initiator flowrate and monomer flowrate) in order to minimize the reaction time. A reduction of 25% of the batch time is achieved with respect to the normal operating conditions applied at the company. The results show that is possible to minimize the reaction time while some polymer desired qualities (conversion, molecular weight and solids content) satisfy the defined constraints. A nonlinear geometric control technique by using input/output linearization is adapted to the reactor temperature control. An extended Kalman filter (EKF) is implemented to estimate unmeasured states and it is tested in different cases including a robustness study where model errors are introduced to verify its good performance. After verification of controller performance, some process changes were proposed in order to improve process productivity and polymer quality. Finally, the optimal temperature profile and optimal feed policies of the monomer and initiator, obtained in a dynamic optimization step, are used to provide the optimal set points for the nonlinear control. The results show that the nonlinear controller designed here is appropriate to follow the optimal temperature trajectories calculated previously.Resumen. En este trabajo se aborda el modelamiento, simulación, optimización dinámica y control de un proceso industrial de polimerización en emulsión para producir poli-acetato de vinilo. La reacción se modela como un sistema bifásico compuesto de una fase acuosa y una fase partícula. El peso molecular promedio en número y en peso, y la dispersidad, se calculan con un modelo detallado. Los momentos de las cadenas vivas y muertas de polímero se utilizan para representar el estado del polímero y calcular la distribución de peso molecular (MWD). El caso de estudio corresponde a un reactor industrial operado en una empresa de productos químicos en Bogotá. Se simuló un reactor de escala industrial (11 m3 de capacidad) en el que se lleva a cabo la reacción en semi-lotes de la polimerización en emulsión de acetato de vinilo. El problema de optimización dinámica se resolvió directamente usando un algoritmo de solución de programación no-lineal. La integración del sistema de ecuaciones diferenciales se realizó a través de un método de Runge-Kutta. Tres diferentes problemas de optimización fueron resueltos partiendo del más sencillo (una sola variable de control : temperatura del reactor) al más complejo (tres variables de control : temperatura del reactor, flujo de iniciador y flujo de monómero) con el fin de minimizar el tiempo de reacción. Una reducción del 25% en el tiempo de reacción, con respecto a las condiciones normales de operación aplicadas en la empresa, fue obtenida. Los resultados muestran que es posible minimizar el tiempo de reacción mientras que algunos parámetros de calidad (conversión, peso molecular y contenido de solidos) satisfacen las restricciones impuestas al problema. Una técnica de control geométrico no-lineal usando linearización entrada/salida fue adaptada para el control de temperatura del reactor. Un filtro de Kalman extendido (EKF) se implementó para estimar los estados no medibles y fue probado en diferentes casos, incluyendo un estudio de robustez en el que se introducen errores en el modelo para verificar el buen desempeño del estimador. Después de verificar el desempeño del controlador, se proponen algunos cambios en el proceso para mejorar la productividad y la calidad del polímero que se obtiene. Finalmente, el perfil ´optimo de temperatura los perfiles óptimosRésumé. Dans ce travail, la modélisation, la simulation, l’optimisation dynamique et la commande nonlinéaire d’un procédé industriel de polymérisation en émulsion produisant du polyacétate de vinyle (PVAc) sont étudiées. La réaction est modélisée comme un système à deux phases constitué d’une phase aqueuse et une phase particulaire. Un modèle détaillé est développé pour calculer la masse molaire moyenne en poids, la masse molaire moyenne en nombre et la dispersité. Les moments de chaînes en croissance et terminées sont utilisés pour représenter l’état du polym`ere et pour calculer la distribution de masse molaire (MWD). L’étude de cas correspond à un réacteur industriel fonctionnant dans une entreprise de produits chimiques à Bogotá. Un réacteur à l’échelle industrielle (11 m3 de capacité) est simulé dans lequel une réaction semi-batch de polymérisation en émulsion de l’acétate de vinyle est effectuée. Le problème d’optimisation dynamique est résolu directement en utilisant un solveur de programmation non linéaire. L’intégration des équations différentielles est faite en utilisant la méthode de Runge-Kutta. Trois problémes d’optimisation différents sont résolus, depuis le plus simpliste (une seule variable d’optimisation : la température du réacteur) au plus complexe (trois variables d’optimisation : la température du réacteur, le débit de l’initiateur et le débit du monomére) en vue de minimiser le temps final de réaction. Une réduction de 25% du temps de traitement par batchs est réalisée par rapport aux conditions normales de fonctionnement appliquées dans l’entreprise. Les résultats montrent qu’il est possible de minimiser la durée de réaction alors que certaines qualités de polyméres souhaitées (conversion, masse molaire et contenu en solides) satisfont les contraintes définies. Une technique de commande non linéaire géométrique à l’aide de la linéarisation entrée/sortie est adaptée à la régulation de la température du réacteur. Un filtre Kalman étendu (EKF) est mis en oeuvre pour estimer les états non mesurés et il est testé dans différents cas, dont une étude de robustesse où des erreurs du modèle sont introduites pour vérifier son bon fonctionnement. Après vérification des performances du régulateur, certains changements d’opération du procédé ont été proposés afin d’améliorer la productivit´e du proc´ed´e et la qualit´e du polym`ere. Enfin, le profil de temp´erature optimale et les politiques d’alimentation optimales de d´ebits du monom`ere et de l’amorceur, obtenues dans l’étape d’optimisation dynamique, ont fourni les consignes optimales pour la commande non linéaire. Les résultats montrent que le régulateur non linéaire concu ici convient pour suivre les trajectoires optimales de température calculées précédemment.Doctorad