There is a continuing interest in the subject of arene carbonylation, especially in strong acids and environmentally-benign alternatives are sought to HF/BF3 and to AlCl3 as conversion agents. Ionic liquids offer a powerful solvent for useful conversion agents such as aluminum chloride. The ILs permit AlCl3 to be used at lower HCl partial pressures than with other solvents. The superior reactivity demonstrated by acidic, chloroaluminate ILs is probably due to their enhanced solvation power for HCl and CO. Addition of HCl gas increased reactivity of the system by forming Brnsted acids, and toluene carbonylation is a Brnsted demanding reaction. It was found that reaction is stoichiometric in Al species and only intrinsically acidic ILs are active for toluene carbonylation, therefore it was possible to correlate observed conversion with predicted amounts of Lewis + Brnsted acids. Molecular modeling provided information about the different species present in these ILs and predicted 1H NMR, and 27Al NMR spectrum. Predictions suggested that three types of HCl species are present; and these predictions were confirmed using data of 13C-labeled acetone and its 13C-NMR spectra. These data showed that only one of the three types of HCl in the IL were super acidic. Reactivity towards arene formylation can be tuned by adjusting the ligands R and R in the organic cation and by changing the anion. This reactivity tuning can be exploited in a process where high acidity is required for the conversion of substrate but where separation of product from IL is facilitated by low acidity.

Orientadores: Rubens Maciel Filho, Maria Regina Wolf Maciel / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Quimica / Made available in DSpace on 2018-08-15T16:03:08Z (GMT). No. of bitstreams: 1 Junqueira_TassiaLopes_M.pdf: 2287179 bytes, checksum: 791ea76c4ab924d80d0233add3519b5b (MD5) Previous issue date: 2010 / Resumo: No Brasil, o bioetanol é usado para substituir a gasolina, compondo uma porcentagem desta ou sendo usado como combustível alternativo. Esta tendência de substituição dos combustíveis fósseis vem se fortalecendo em âmbito global, sendo necessárias, portanto, alternativas e propostas que viabilizem o aumento da produção de forma economicamente e ambientalmente sustentável. Neste contexto, a otimização energética do processo de separação do bioetanol visa à disponibilização de bagaço de cana-de-açúcar, usado como combustível na geração de vapor de processo, para a produção de bioetanol através do processo de hidrólise. Para tanto, inovações ao processo são essenciais e melhoramento na representação de modelos torna-se necessário para estudos e avaliações. Neste trabalho, simulações da etapa de destilação para a produção de álcool hidratado assim como da etapa de desidratação do bioetanol foram realizadas utilizando o simulador Aspen Plus®. Visando um estudo dentro de um cenário mais realista, a modelagem de estágios de não equilíbrio foi utilizada para prever o comportamento das colunas de destilação envolvidas. Além disso, o uso da correlação de Barros e Wolf para a determinação de eficiência na modelagem de estágios de equilíbrio em colunas de destilação foi avaliado. A comparação entre as modelagens de estágios de equilíbrio e não equilíbrio para as destilações convencional e extrativa indicou que a associação da correlação de eficiência de Barros e Wolf à modelagem de estágios de equilíbrio fornece predições satisfatórias tendo como referência a modelagem de estágios de não-equilíbrio. Para a destilação azeotrópica, o estudo de formação de duas fases líquidas na coluna foi realizado, indicando que os parâmetros de processo, como posição de alimentação, possuem influência significativa. O estudo da fermentação extrativa a vácuo, como configuração alternativa às etapas de fermentação e concentração, revelou seu potencial para redução do consumo de energia na etapa de destilação subseqüente, sendo uma alternativa viável para intensificação de processos / Abstract: In Brazil, bioethanol is used to replace gasoline, being a percentage of this or used as an alternative fuel. This trend of replacing fossil fuels has gained strength globally, necessitating, therefore, alternatives and proposals to enable the increase of production in an economically and environmentally sustainable way. In this context, the energy optimization of the bioethanol separation aims the provision of sugarcane bagasse, used as fuel in process steam generation, for bioethanol production through the hydrolysis process. Consequently, innovations to the process are essential and improvement in the representation of models is required for studies and evaluations. In this work, simulations of the distillation step for the production of hydrous bioethanol and the bioethanol dehydration were performed using the simulator Aspen Plus®. In order to study a more realistic scenario, nonequilibrium stage model was used to predict the behavior of the involved distillation columns. Furthermore, the use of Barros and Wolf correlation for the determination of efficiency in equilibrium stage model for distillation columns was evaluated. The comparison between equilibrium and nonequilibrium stage models for conventional and extractive distillation processes indicated that the association between Barros and Wolf efficiency correlation and equilibrium stage model provides satisfactory predictions considering the nonequilibrium stage model as reference. For azeotropic distillation, formation of two liquid phases inside the column was studied, indicating that process parameters, such as feed position, have significant influence. The study of vacuum extractive fermentation, as an alternative configuration to fermentation and concentration steps, showed its potential for reducing energy consumption in the subsequent distillation step, and it seems a viable alternative to process intensification / Mestrado / Desenvolvimento de Processos Químicos / Mestre em Engenharia Química

Cette thèse est consacrée à l’étude des modèles microscopiques pour la dérivation de la conduction de la chaleur. Démontrer rigoureusement une équation diffusive macroscopique à partir d’une description microscopique du système est à aujourd’hui encore un problème ouvert. On étudie un système décrit par l’équation de Schrödinger linéaire discrète (DLS) en dim 1, perturbé par une dynamique stochastique conservative. On peut montrer que le système a une limite hydrodynamique donnée par la solution de l’équation de la chaleur. Quand le système est rattaché aux bords à deux réservoirs de Langevin à deux différents potentiels chimiques, on peut montrer que l’état stationnaire, dans la limite vers l'infinie, satisfait la loi de Fourier. On étudie une chaine des oscillateurs anharmonique immergée en un réservoir de chaleur avec un gradient de température. On exerce une tension, variable dans le temps, à une des deux extrémités de la chaine, et l’autre reste fixe. On montre que sous un changement d’échelle diffusive dans l’espace et dans le temps, la distribution d’étirement de la chaine évolue selon un équation diffusive non-linéaire. On développe des estimations qui reposent sur l’hypocoercitivité entropique. La limite macroscopique peut être utilisée pour modéliser les transformations thermodynamique isothermiques entre états stationnaire de non-équilibre. / The object of research of this thesis is the derivation of heat equation from the underlying microscopic dynamics of the system. Two main models have been studied: a microscopic system described by the discrete Schrödinger equation and an anharmonic chain of oscillators in presence of a gradient of temperature. The first model considered is the one-dimensional discrete linear Schrödinger (DLS) equation perturbed by a conservative stochastic dynamics, that changes the phase of each particles, conserving the total norm (or number of particles). The resulting total dynamics is a degenerate hypoelliptic diffusion with a smooth stationary state. It has been shown that the system has a hydrodynamical limit given by the solution of the heat equation. When it is coupled at the boundaries to two Langevin thermostats at two different chemical potentials, it has been proven that the stationary state, in the limit to infinity, satisfies the Fourier’s law. The second model considered is a chain of anharmonic oscillators immersed in a heat bath with a temperature gradient and a time varying tension applied to one end of the chain while the other side is fixed to a point. We prove that under diffusive space-time rescaling the volume strain distribution of the chain evolves following a non-linear diffusive equation. The stationary states of the dynamics are of non-equilibrium and have a positive entropy production, so the classical relative entropy methods cannot be used. We develop new estimates based on entropic hypocoercivity, that allows to control the distribution of the positions configurations of the chain. The macroscopic limit can be used to model isothermal thermodynamic transformations between non-equilibrium stationary states. CEMRACS project on simulating Rayleigh- Taylor and Richtmyer-Meshkov turbulent mixing zones with a probability density function method at last.

Considerable jump and slip phenomena are observed at the non-equilibrium phase interface in microflows. Hence, accurate modelling of the liquid-vapour interface transport mechanisms that matches the observations is required, e.g. in applications such as micro/nanotechnology and micro fuel cells. In the sharp interface model, the classical Navier-Stokes-Fourier (NSF) equations can be used in the liquid and vapour phases, while the interface resistivities describe the jump and slip phenomena at the interface. However, resistivities are challenging to find from the measurements, and most of the classical kinetic theories consider them as constants. One possible approach is to determine them from a model that resolves the phase interface. In order to resolve the interface and the transport processes at and in front of the interface in high resolutions, there are two ways in general, microscopic or macroscopic. The microscopic studies are based either on molecular dynamics (MD) or kinetic models, such as the Enskog-Vlasov (EV) equation. The EV equation modifies the Boltzmann equation by considering dense gas effects, such as the interaction forces between the particles and their finite size. It can be solved by the Direct Simulation Monte Carlo (DSMC) method, which considers sample particles that stand in for thousands to hundred thousands of particles and determine most likely collisions based on interaction probabilities, but it is time-consuming and costly. Here, a closed set of 26-moment equations is numerically solved to resolve the liquid-vapour interface macroscopically while considering the dense gas and phase change effects. The 26-moment set of equations is derived by Struchtrup & Frezzotti as an approximation of the EV equation using Grad's moment method. The macroscopic moment equations resolve the phase interface in a high resolution competitive to the microscopic studies. The resolved interface visualizes the interface structure and the changes of the system variables between the two phases at the interface. The 26-moment equations are solved for a one-dimensional steady-state system for non-equilibrium evaporation/condensation process. Then, solutions are used to find the jump and slip conditions at the interface, which leads to determining the interface resistivities at different interface temperatures and non-equilibrium strengths from the Linear Irreversible Thermodynamics (LIT). The interface resistivities show their dependence on the temperature of the liquid at the interface as well as the strength of the non-equilibrium process. As a result, in further studies, similar systems can be modelled using the sharp interface method with the appropriate jump conditions at the phase interface that can be found from the determined EV interface resistivities. / Graduate

We study the thermodynamic properties induced by non-reciprocal interactions between stochastic degrees of freedom in time- and space-continuous systems. We show that, under fairly general conditions, non-reciprocal coupling alone implies a steady energy flow through the system, i.e., non-equilibrium. Projecting out the non-reciprocally coupled degrees of freedom renders non-Markovian, one-variable Langevin descriptions with complex types of memory, for which we find a generalized second law involving information flow.We demonstrate that non-reciprocal linear interactions can be used to engineer non-monotonic memory, which is typical for, e.g., time-delayed feedback control, and is automatically accompanied with a nonzero information flow through the system. Furthermore, already a single non-reciprocally coupled degree of freedom can extract energy from a single heat bath (at isothermal conditions), and can thus be viewed as a minimal version of a time-continuous, autonomous ‘Maxwell demon’.We also show that for appropriate parameter settings, the non-reciprocal system has characteristic features of active matter, such as a positive energy input on the level of the fluctuating trajectories without global particle transport.

In this thesis extensions to the formalism of endoreversible thermodynamics for multi-extensity fluxes and chemical reactions are introduced. These extensions make it possible to model a great variety of systems which could not be investigated with standard endoreversible thermodynamics. Multi-extensity fluxes are important when studying processes with matter fluxes or processes in which volume and entropy are exchanged between subsystems. For including reversible as well as irreversible chemical reaction processes a new type of subsystems is introduced - the so called reactor. It is similar to endoreversible engines, because the fluxes connected to it are balanced. The difference appears in the balance equations for particle numbers, which contain production or destruction terms, and in the possible entropy production in the reactor. Both extensions are then applied to an endoreversible fuel cell model. The chemical reactions in the anode and cathode of the fuel cell are included with the newly introduced subsystem -- the reactor. For the transport of the reactants and products as well as the proton transport through the electrolyte membrane, the multi-extensity fluxes are used. This fuel cell model is then used to calculate power output, efficiency and cell voltage of a fuel cell with irreversibilities in the proton and electron transport. It directly connects the pressure and temperature dependencies of the cell voltage with the dissipation due to membrane resistance. Additionally, beside the listed performance measures it is possible to quantify and localize the entropy production and dissipated heat with only this one model. / In dieser Arbeit erweitere ich den Formalismus der endoreversiblen Thermodynamik, um Flüsse mit mehr als einer extensiven Größe sowie chemische Reaktionsprozesse modellieren zu können. Mit Hilfe dieser Erweiterungen eröffnen sich zahlreiche neue Anwendungsmöglichkeiten für endoreversible Modelle. Flüsse mit mehreren extensiven Größen sind für die Betrachtung von Masseströmen ebenso nötig wie für Prozesse, bei denen sowohl Volumen als auch Entropie zwischen zwei Teilsystem ausgetauscht werden. Für sowohl reversibel wie auch irreversibel geführte chemische Reaktionsprozesse wird ein neues Teilsystem - der "Reaktor" - vorgestellt, welches sich ähnlich wie endoreversible Maschinen durch Bilanzgleichungen auszeichnet. Der Unterschied zu den Maschinen besteht in den Produktions- bzw. Vernichtungstermen in den Teilchenzahlbilanzen sowie der möglichen Entropieproduktion innerhalb des Reaktors. Beide Erweiterungen finden dann in einem endoreversiblen Modell einer Brennstoffzelle Anwendung. Dabei werden Flüsse mehrerer gekoppelter Extensitäten für den Zustrom von Wasserstoff und Sauerstoff sowie für den Protonentransport durch die Elektrolytmembran benötigt. Chemische Reaktionen treten in der Anode und Kathode der Brennstoffzelle auf. Diese werden mit dem neu eingeführten Teilsystem, dem Reaktor, eingebunden. Mit Hilfe des Modells werden dann Wirkungsgrad, Zellspannung und Leistung einer Brennstoffzelle unter Berücksichtigung der Partialdrücke der Substanzen, der Temperatur sowie der Dissipation beim Protonentransport berechnet. Dabei zeigt sich, dass experimentelle Daten für die Zellspannung sowohl qualitativ als auch näherungsweise quantitativ durch das Modell abgebildet werden können. Der Vorteil des endoreversiblen Modells liegt dabei in der Möglichkeit, mit nur einem Modell neben den genannten Kenngrößen auch die abgegebene Wärme sowie die Entropieproduktion zu quantifizieren und den einzelnen Teilprozessen zuzuordnen.

In dieser Arbeit wird eine Methode zur Leistungsoptimierung der Kolbenpfade von Stirling-Motoren entwickelt, die auf der Theorie der optimalen Steuerung beruht. Für die effiziente praktische Umsetzbarkeit ist dabei ein geringer numerischer Aufwand des eingesetzten thermodynamischen Modells entscheidend. In detaillierten Modellen von Stirling-Motoren resultiert ein Großteil des numerischen Aufwandes aus der Beschreibung des Regenerators, einem gasdurchströmten Kurzzeit-Wärmespeicher. Im ersten Teil der Arbeit wird der Fokus deshalb auf die Entwicklung eines effizienten Regeneratormodells gelegt. Hierbei wird ein neuartiger Ansatz gewählt, der sich aus der Perspektive der Endoreversiblen Thermodynamik ergibt: Der Regenerator wird als endoreversibles Teilsystem betrachtet, welches an zwei Kontaktpunkten durch irreversible Interaktionen mit den benachbarten Teilsystemen Gasteilchen, Entropie und Energie austauscht. Innere Irreversibilitäten des Regenerators werden als Entropiequellterme in die Modellierung einbezogen. Im zweiten Teil der Arbeit wird dann ein iterativer Optimierungsalgorithmus erarbeitet, der die Leistung von Stirling-Motoren unter periodischen Randbedingungen für eine vorgegebene Periodendauer maximieren kann. Der Algorithmus startet mit vorgegeben initialen Kolbenpfaden, die im Laufe der Iterationen graduell verschoben und so den optimalen Pfaden angenähert werden. Um diese graduelle Verschiebung zu bestimmen, muss in jedem Iterationsschritt neben dem Differentialgleichungssystem, das die Thermodynamik des Stirling-Motors beschreibt, ein konjugiertes Differentialgleichungssystem gelöst werden. Der erarbeitete Algorithmus nutzt dabei die Existenz eines Grenzzyklus des konjugierten Differentialgleichungssystems unter Zeitumkehr zu dessen Lösung für periodische Randbedingungen aus. Unter Verwendung des endoreversiblen Regeneratormodells wird mit diesem iterativen Optimierungsalgorithmus die Theorie der optimalen Steuerung erstmals für die Kolbenpfadoptimierung eines beispielhaften Stirling-Motors in α-Konfiguration eingesetzt. / In this thesis a method for power optimization of the piston paths of Stirling engines is developed, which is based on Optimal Control Theory. For the efficient practical feasibility of this task, low numerical effort of the utilized thermodynamic model is crucial. In detailed models of Stirling engines, a large part of the numerical effort results from the description of the regenerator, which is a short-time heat storage. Therefore, in the first part of this thesis the focus is on the development of an efficient regenerator model. Here, a novel ansatz is chosen which arises from the perspective of Endoreversible Thermodynamics: The regenerator is described as an endoreversible subsystem that has two contact points, at which it exchanges particles, entropy, and energy with the adjacent subsystems through irreversible interactions. Internal irreversibilities of the regenerator are included in the model as entropy source terms. In the second part of the thesis an iterative optimization algorithm is worked out, which can maximize the power output of Stirling engines under periodic boundary conditions for given cycle time. The algorithm starts with predefined initial piston paths, which are gradually shifted over the course of the iterations and thus approach the optimal paths. To determine this gradual shift, in every iteration not only the system of differential equations describing the thermodynamics of the Stirling engine needs to be solved, but also a conjugate system of differential equations. The algorithm here exploits the existence of a limit cycle of the conjugate system under time reversal to solve it for periodic boundary conditions. By means of the endoreversible regenerator model, with this iterative optimization algorithm Optimal Control Theory is applied for the first time to optimize the piston paths of an exemplary Stirling engine in α-configuration.

Due to failure of the continuum hypothesis for higher Knudsen numbers, rarefied gases and microflows of gases are particularly difficult to model. Macroscopic transport equations compete with particle methods, such as the direct simulation Monte Carlo method (DSMC) to find accurate solutions in the rarefied gas regime. Due to growing interest in micro flow applications, such as micro fuel cells, it is important to model and understand evaporation in this flow regime. To gain a better understanding of evaporation physics, a non-steady simulation for slow evaporation in a microscopic system, based on the Navier-Stokes-Fourier equations, is conducted. The one-dimensional problem consists of a liquid and vapor layer (both pure water) with respective heights of 0.1mm and a corresponding Knudsen number of Kn=0.01, where vapor is pumped out. The simulation allows for calculation of the evaporation rate within both the transient process and in steady state. The main contribution of this work is the derivation of new evaporation boundary conditions for the R13 equations, which are macroscopic transport equations with proven applicability in the transition regime. The approach for deriving the boundary conditions is based on an entropy balance, which is integrated around the liquid-vapor interface. The new equations utilize Onsager relations, linear relations between thermodynamic fluxes and forces, with constant coefficients that need to be determined. For this, the boundary conditions are fitted to DSMC data and compared to other R13 boundary conditions from kinetic theory and Navier-Stokes-Fourier solutions for two steady-state, one-dimensional problems. Overall, the suggested fittings of the new phenomenological boundary conditions show better agreement to DSMC than the alternative kinetic theory evaporation boundary conditions for R13. Furthermore, the new evaporation boundary conditions for R13 are implemented in a code for the numerical solution of complex, two-dimensional geometries and compared to Navier-Stokes-Fourier (NSF) solutions. Different flow patterns between R13 and NSF for higher Knudsen numbers are observed which suggest continuation of this work. / Graduate

In dieser Arbeit verwende ich den Formalismus der endoreversiblen Thermodynamik um ein hydraulisches Rekuperationssystem für Nutzfahrzeuge zu modellieren und zu untersuchen. Dafür führe ich verlustbehaftete Übergänge extensiver Größen zwischen Teilsystemen eines Systems ein. Diese können einerseits der Modellierung von Leckagen und Reibungsverlusten, welche als Partikel- oder Drehmomentverluste dargestellt würden, dienen. Andererseits ermöglichen sie die Modellierung einer endoreversiblen Maschine, welche – durch Definition eines solchen verlustbehafteten, internen Überganges – ein gegebenes Wirkungsgradkennfeld und daraus resultierende Entropieproduktion inne hat. Diese wird infolge zur Modellierung der Hydraulikeinheit des Rekuperationssystems verwendet. Desweiteren basiert die Beschreibung des Rekuperationssystems auf der Modellierung der Hydraulikflüssigkeit als Van-der-Waals-Fluid, sodass Druckverluste im endoreversiblen Sinne konsistent berücksichtigt werden können. Von gegebenen Materialparamtern werden die dafür notwendigen Van-der-Waals-Parameter hergeleitet. Weitere Aspekte sind Wärmeverluste an die Umgebung sowie Wärmeübergänge zwischen Teilsystemen. Auf Grundlage realer Fahrdaten der Nutzfahrzeuge werden verschiedene dynamische und thermodynamische Effekte im Rekuperationssystem analysiert. Ihr Einfluss auf die resultierenden energetischen Einsparungen beim Abbremsen und Beschleunigen wird durch Variation zugehöriger Parameter aufgezeigt. Zuletzt wird mit einem vereinfachten Modell ohne Druck- und Wärmeverluste, aber unter Einbeziehung des Verbrennungsmotors des Fahrzeuges, eine Optimierung der Steuerung des hydraulischen Rekuperationssystems mit Hinblick auf minimalen Kraftstoffverbrauch durchgeführt. Hier zeigt sich eine erhebliche Verbesserung durch die Leistungsaufteilung zwischen Verbrennungsmotor und Rekuperationssystem nach deren Betriebsbereichen mit maximalem Wirkungsgrad. / In this work I use the formalism of endoreversible thermodynamics to model and investigate a hydraulic recuperation system for commercial vehicles. For that, I introduce lossy transfers of extensive quantities between subsystems of an endoreversible system. On the one hand, these allow modeling of leakages and friction losses, which can be represented as particle or torque losses. On the other hand, they can be used as internal extensity transfers in endoreversible engines which, as a result, have a given efficiency or efficiency map and among other things give an expression for their entropy production. Such an engine is used to model the hydraulic unit of the recuperation system. Furthermore, the description of the recuperation system is based on the modeling of the hydraulic fluid as a van der Waals fluid, so that pressure losses can be taken into account in a consistent endoreversible fashion. From given material parameters the necessary van der Waals parameters are derived. Other aspects of the modeling include heat losses to the environment and heat transfers between subsystems. On the basis of real driving data, various dynamic and thermodynamic effects within the recuperation system are observed and their influence as well as the influence of selected parameters on the resulting energy savings for both acceleration and deceleration are shown. Finally, using a simplified model neglecting pressure and heat losses, but including the internal combustion engine of the vehicle, an optimization of the control strategy for the hydraulic recuperation system with regard to minimum fuel consumption is performed. Here, a significant improvement due to a power distribution between combustion engine and recuperation system according to their high efficiency operating ranges can be achieved.

In this thesis extensions to the formalism of endoreversible thermodynamics for multi-extensity fluxes and chemical reactions are introduced. These extensions make it possible to model a great variety of systems which could not be investigated with standard endoreversible thermodynamics. Multi-extensity fluxes are important when studying processes with matter fluxes or processes in which volume and entropy are exchanged between subsystems. For including reversible as well as irreversible chemical reaction processes a new type of subsystems is introduced - the so called reactor. It is similar to endoreversible engines, because the fluxes connected to it are balanced. The difference appears in the balance equations for particle numbers, which contain production or destruction terms, and in the possible entropy production in the reactor. Both extensions are then applied to an endoreversible fuel cell model. The chemical reactions in the anode and cathode of the fuel cell are included with the newly introduced subsystem -- the reactor. For the transport of the reactants and products as well as the proton transport through the electrolyte membrane, the multi-extensity fluxes are used. This fuel cell model is then used to calculate power output, efficiency and cell voltage of a fuel cell with irreversibilities in the proton and electron transport. It directly connects the pressure and temperature dependencies of the cell voltage with the dissipation due to membrane resistance. Additionally, beside the listed performance measures it is possible to quantify and localize the entropy production and dissipated heat with only this one model. / In dieser Arbeit erweitere ich den Formalismus der endoreversiblen Thermodynamik, um Flüsse mit mehr als einer extensiven Größe sowie chemische Reaktionsprozesse modellieren zu können. Mit Hilfe dieser Erweiterungen eröffnen sich zahlreiche neue Anwendungsmöglichkeiten für endoreversible Modelle. Flüsse mit mehreren extensiven Größen sind für die Betrachtung von Masseströmen ebenso nötig wie für Prozesse, bei denen sowohl Volumen als auch Entropie zwischen zwei Teilsystem ausgetauscht werden. Für sowohl reversibel wie auch irreversibel geführte chemische Reaktionsprozesse wird ein neues Teilsystem - der "Reaktor" - vorgestellt, welches sich ähnlich wie endoreversible Maschinen durch Bilanzgleichungen auszeichnet. Der Unterschied zu den Maschinen besteht in den Produktions- bzw. Vernichtungstermen in den Teilchenzahlbilanzen sowie der möglichen Entropieproduktion innerhalb des Reaktors. Beide Erweiterungen finden dann in einem endoreversiblen Modell einer Brennstoffzelle Anwendung. Dabei werden Flüsse mehrerer gekoppelter Extensitäten für den Zustrom von Wasserstoff und Sauerstoff sowie für den Protonentransport durch die Elektrolytmembran benötigt. Chemische Reaktionen treten in der Anode und Kathode der Brennstoffzelle auf. Diese werden mit dem neu eingeführten Teilsystem, dem Reaktor, eingebunden. Mit Hilfe des Modells werden dann Wirkungsgrad, Zellspannung und Leistung einer Brennstoffzelle unter Berücksichtigung der Partialdrücke der Substanzen, der Temperatur sowie der Dissipation beim Protonentransport berechnet. Dabei zeigt sich, dass experimentelle Daten für die Zellspannung sowohl qualitativ als auch näherungsweise quantitativ durch das Modell abgebildet werden können. Der Vorteil des endoreversiblen Modells liegt dabei in der Möglichkeit, mit nur einem Modell neben den genannten Kenngrößen auch die abgegebene Wärme sowie die Entropieproduktion zu quantifizieren und den einzelnen Teilprozessen zuzuordnen.