In recent years, Integrated Gasification Combined Cycle Technology (IGCC) has become more common in clean coal power operations with carbon capture and sequestration (CCS). Great efforts have been spent on investigating ways to improve the efficiency, reduce costs, and further reduce greenhouse gas emissions. This study focuses on investigating two approaches to achieve these goals. First, replace the subcritical Rankine steam cycle with a supercritical steam cycle. Second, add different amounts of biomass as feedstock to reduce emissions. Finally, implement several types of CCS, including sweet- and sour-shift pre-combustion and post-combustion. Using the software, Thermoflow®, this study shows that utilizing biomass with coal up to 50% (wt.) can improve the efficiency, and reduce emissions: even making the plant carbon-negative when CCS is used. CCS is best administered pre-combustion using sour-shift, and supercritical steam cycles are thermally and economically better than subcritical cycles. Both capital and electricity costs have been presented.

Le CO2 est capté par formation de clathrates hydrates sous l’action d’un promoteur de cristallisation thermodynamique. Les clathrates hydrates sont des composés d’inclusion non stœchiométriques formés de molécules d’eau organisées en réseau de cavités piégeant des molécules de gaz. Ce procédé de captage consiste à piéger de façon sélective le dioxyde de carbone dans les cavités des clathrates hydrates et à le séparer ainsi des autres gaz. Les hydrates mixtes de cyclopentane (CP) + gaz ont été étudiés dans le cadre du projet FUI ACACIA et du projet européen ICAP. Les premières expériences se sont focalisées sur l’étude des équilibres quadri phasiques (gaz CO2/N2, eau liquide, cyclopentane liquide et hydrate). Le cyclopentane est un promoteur thermodynamique qui forme des hydrates mixtes de CO2 + N2 + CP à basse pression et température modérée. La pression d’équilibre des hydrates mixtes est réduite jusqu’à 97% par rapport à la pression d'équilibre initiale des hydrates de gaz. La sélectivité de captage du CO2 dans les hydrates mixtes est augmentée et le volume de gaz stocké est de 40 m3gaz/m3hydrate. Une seconde étude expérimentale, conduite en présence d’une sonde FBRM (Focused Beam Reflectance Measurements) et d’une émulsion stable directe de CP/eau, a montré que la cinétique de cristallisation des hydrates mixtes de CP + CO2 est limitée par la diffusion du gaz à l’interface gaz/liquide. La sonde FBRM permet de détecter parfaitement l’apparition de la nucléation. Le changement de profil de la distribution en longueurs de corde (CLD) est non seulement lié à l’apparition des mécanismes de cristallisation (dont l’agglomération) mais aussi à la disparition des gouttes de CP au profit des hydrates qui cristallisent par un mécanisme à cœur rétrécissant. / CO2 separation and capture by clathrate hydrate crystallization is a non-conventional way of trapping and storing gas molecules from flue gases. Clathrates hydrates are non-stoichiometric ice-like crystalline solids consisting of a combination of water molecules and suitable guest molecules. Mixed hydrates of cyclopentane (CP) + gas have been studied in one national project (FUI ACACIA) and a European program (iCAP). Cyclopentane is an organic additive which forms mixed hydrates of CP + CO2 + N2 at low pressure and moderate temperature. The equilibrium pressure is decreasing up to 97 % (relative to the equilibrium pressure without cyclopentane). CO2 selectivity in hydrates is enhanced and gas storage capacity approaches a roughly constant value of 40 m3gas (STP) /m3hydrate. Crystallization of CP + CO2 mixed hydrates seems limited by gas diffusion through the gas / liquid interface, which gets in the way of the determination of the intrinsic kinetic constants of crystallization. Experimental studies have also been investigated in presence of a Focused Beam Reflectance Measurements (FBRM) probe in stable emulsion of CP in water. FBRM probe can successfully identify hydrate nucleation. The sharp change in the mean chord length and the spread of Chord Length Distribution (CLD) are related to the progressive disappearance of the CP droplets in favor of the CP + CO2 mixed hydrates formation. The change in the mean chord length distribution is not only related to the agglomeration phenomenon of the particles but also to the occurrence of the shrinking core crystallization of the CP droplets.

Text in English / There are limits on performance of processes and reactions set by material balances and by thermodynamics. The interaction of these theoretical limits and how they influence the behaviour of reactions and equipment is of interest to researchers and designers. This thesis looks at the conversion of biomass to gaseous products under various conditions, including a range of temperatures from ambient to 1500 ⁰C and in the presence or absence of oxygen. The limits of performance of the material balance can be represented as an Attainable Region (AR) in composition or extent space; we call this the MB-AR. The MB-AR represents all possible material balances that can be achieved for a given a set of feeds and set of possible products. The dimension of this space depends on the number of independent material balances. The extreme points of the MB-AR are of particular interest as these define the limiting compositions and the edges of the boundary of the MB-AR represent the limiting material balances. The MB-AR does not depend on temperature. The thermodynamic limits of performance of can be represented as an AR in the space of Gibbs Free Energy (G) and Enthalpy (H); this is called the G-H AR. The G-H AR is always two dimensional, no matter what the dimension of the MB-AR. Extreme points in the G-H AR are also extreme points in the MB-AR are; however not all extreme points in the MB-AR are extreme points in the G-H AR. The extreme points in the MB-AR are transformed by calculating G and H of the points at the condition of interest (reaction temperature and pressure). It is then necessary to find the convex hull in G-H space of this set of transformed points which gives us the boundary of the G-H AR. The extreme points in the G-H AR can be associated with material balances and the extreme point with the minimum G represents the global equilibrium or equivalently the most favoured material balance for the system. The edges of G-H AR are defined by the lines between neighbouring extreme points in the boundary of the G-H AR. These edges represent the limiting material balances in terms of defining the extremes of the G and H of the system. The G-H AR depends on the feed and products through the MB-AR, but also depends on temperature (and pressure). The set of points which are extreme points of both the MB-AR and the G-H AR changes with temperature. Geometrically, the transformed set of extreme points for the MB-AR moves in the GH space as temperature is changed and they move at different rates. Hence when finding the convex hull in the G-H space of the transformed extreme points of the MB-AR, G-H points become either boundary (extreme) points or move into the convex hull at different temperatures. Thus, the material balance which corresponds to the global minimum in G may change with temperature, as do the material balances which are associated with the edges of the G-H AR. Experiments are performed on biomass anaerobically at ambient temperature using microbes as the catalyst, and the products of this process are called biogas. The experiments were performed in a nitrogen plasma system on biomass at higher temperatures (400 ⁰C to 1000 ⁰C) also in the absence of oxygen, and this process would typically be referred to as pyrolysis. Oxygen was added to the plasma system and operated at temperatures between 700 ⁰C and 900 ⁰C, and this would typically be referred to as gasification. Thus, it was able to change the MB-AR by presence or absence of oxygen. By changing operating temperatures, the G-H AR is effectively changed with either the same or different MB-AR’s. The experiments show that in all cases, the product tends towards minimum G. Although this might not be surprising at the higher temperatures, minimizing G is not thought to be the driving force in microbial systems. An important insight from this is that if one were to try and make hydrogen only in a biological system, the system would need to have organisms that make hydrogen only. This is because the material balance that produces hydrogen has a lower change in G than the material balance that make methane. Thus, if there was a consortium of organisms and some of them could make methane, the methane producing organisms would dominate as they have the higher Gibbs Free Energy driving force. If the boundary of the G-H AR around the minimum G is fairly flat, or if many of the extreme points of the MB-AR lie close to the minimum G in the boundary of the G-H AR, then there are many material balances that will give the same G and H. Thus, there are a range of compositions with similar G and H and how one approaches the minimum G will determine the chemical composition of the product. This has important implications for the design, scale up and operation of equipment if a particular product is desired rather process efficiency. The low temperature anaerobic route to gasifying waste, using microbes as catalysts, has a very simple G-H AR, and the preferred products are CH4 and CO2, known as biogas. These units should be relatively stable to operate as none of the other products have G’s that are as negative as that of the biogas. Although not part of this thesis, small-scale anaerobic digesters were installed in communities and these do run easily and stably with fairly little intervention from the operator which seems to support our conclusion. We however could ask, why then have simple technologies, such an anaerobic digestion, not been widely adopted in Africa? To this end we worked with communities and spoke to people about their knowledge about the technology, their concerns and their possible interest in using new approaches to supply energy for cooking and lighting. We found that people were not aware of the technology but would be very interested in adopting a technology that supplied energy cheaply. To our surprise however, their major concern was around hygiene and safety, in that if the gas was made from “poo” how could the gas be clean and would cooking with it not contaminate the food and make people sick? This in hindsight is a very reasonable concern, although it had never occurred to us that this would be a perception. Engineers will have to work with social scientists and psychologist, amongst others, to address the concerns and needs of communities in order for sustainable technologies to be successfully adopted by communities. In summary, this thesis presents a tool for analysing biomass conversion to gaseous products in general, whether microbial or thermal. This tool gives insight into what is achievable, what the major factors are that affect the favoured product and how this can be manipulated to improve efficiency from an overall material and energy point of view. / Physics / D. Phil. (Physics)

A thesis submitted to the Faculty of Engineering and the Built Environment, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Doctor of Philosophy, 2016 / Solar powered gas micro-turbines present opportunities for off-grid power generation. Due to the intermittent nature of the solar energy supply, existing Solar Gas Turbine (SGT) plants employ hybridisation with fossil fuels to generate dispatchable power. In this work sensible heat and latent heat storage solutions are investigated as a means of increasing the solar share of a SGT cycle, thus reducing the consumption of diesel fuel. The sensible heat storage concept was based on a pressurised packed bed of spherical ceramic particles, using air as the heat transfer fluid. An axisymmetric, two-phase heat transfer model of the system was developed, based on the continuous solid phase approach. The model was successfully validated against experimental data from a packed bed of alumino-silicate particles over the temperature ranges of gas turbine cycles (350-900 °C and 600-900 °C). The validated numerical model was utilised to conduct a parametric design study of a six hour (1.55 MWhth) storage system for a gas micro-turbine. The results show that a high storage efficiency and high utilisation factor can be achieved when combining sensible heat storage in alumina with fossil fuel hybridisation, with somewhat lower values without hybridisation. An analysis of different inventory geometries showed that a packed bed of spherical particles is best suited to pressurised sensible heat storage. The latent heat storage concept was based on a pressurised packed bed of Encapsulated Phase Change Material (EPCM) particles. Sodium sulphate was identified as a suitable phase change material for the gas turbine cycle. The sensible heat storage model was extended to account for intra-particle temperature gradients and phase change within the particles. The intra-particle phase change model was validated against published experimental data for a single EPCM sphere heated and cooled by convection. The full EPCM storage model was further successfully validated against experimental data from a packed bed of macro- encapsulated sodium sulphate particles with alumina shells, up to a temperature of 950 °C. A comparison of the two storage concepts for a 7 m3 bed shows that a packed bed of en- capsulated sodium sulphate particles would have a 36% lower energy storage capacity than a bed of solid alumina particles. This is due to the limited melt fraction in the EPCM bed when a temperature limit is placed on the base. Increasing the packed bed volume to 10.5 m3 would provide a comparable thermal performance to the 7 m3 solid alumina bed, at a 12% lower storage mass. A hybrid three-layer packed bed is proposed to increase the volumetric energy storage density. Modelling shows that this concept could provide a small increase of 5.3% in the amount of energy discharged above 850 °C, compared to the solid alumina particles only.

Dans ce manuscrit, nous présentons des mesures haute résolution de chaleur spécifique Cp réalisées sur des anneaux mésoscopiques d'argent à très basses températures. Le but de cette expérience est de mettre en évidence une possible signature thermique due à la présence de courants permanents. Ce phénomène reste encore mal compris malgré de nombreuses expériences. Il existe en effet des contradictions entre les différents modèles théoriques et les résultats expérimentaux. L'approche thermique que nous exposons ici est un angle nouveau qui n'a jamais été exploré. Sous champ magnétique, une oscillation de période égale au quantum de flux Φ0=h/e (ou moitié) de Cp est attendue théoriquement. L'échantillon étudié est composé d'un grand nombre d'anneaux d'argent mésoscopiques déposés sur une membrane en silicium suspendue. Nous avons réalisé, à différentes températures, de multiples balayages en champ de la chaleur spécifique. Un traitement des signaux obtenus a ensuite été réalisé afin de repérer une éventuelle périodicité. Il a révélé la présence sur le signal de phase d'une oscillation de période h/2e n'apparaissant pas sur le module de la chaleur spécifique. Cette signature est maximale à 100mK. La fréquence et l'amplitude obtenues sont en accord avec les prédictions théoriques. La sensibilité atteinte est de ΔC~10^(-14)J/K sur le module (et de Δφ~10^(-2) degrés sur la phase) soit 10^(-21)J/K par anneau. Les résultats présentés ici apportent donc de nouveaux éléments dans l'analyse des courants permanents. / In this thesis, we report very high resolution specific heat measurements of normal metal mesoscopic silver rings at very low temperatures. The objective of this experiment is to measure the possible existence of thermal signatures due to the presence of persistent currents. This phenomenon is still misunderstood despite many measurements. Some contradictions exist between experimental results and the different theories. The thermal approach is a new point of view. Under magnetic field, the Cp variation is expected be periodic with the quantum of flux Φ0=h/e or half of the quantum of flux as it has been theoretically predicted. The studied samples is composed by a large number of silver rings with an electronic phase coherence length of few microns at low temperatures. They were deposited on the suspended membrane of a silicon sensor. We have realized, at different temperatures, a large number of identical scans of the heat capacity variation as a function of the applied field. A signal processing work on this data has then been realized to detect signal periodicities. It showed a difference between the module and the phase of the heat capacity. A peak can be observed on the FFT at a frequency corresponding to h/2e on the phase signal. The peak appears particularly at 100mK with a amplitude which is consistent with previous calculations. A sensitivity of ΔC~10^(-14)J/K on the module (Δφ~10^(-2) degrees on the phase) has been reached whether 10^(-21)J/K per ring. Thus, the presented experiences give new elements in the field of persistent currents.

Cette étude présente une analyse thermomécanique du comportement en fatigue oligocyclique du polyamide 6.6 vierge et renforcé de fibres de verre courtes. Des bilans d'énergie sont réalisés en utilisant, de façon combinée, des techniques d'imagerie quantitative visible et infrarouge. Les champs de température sont obtenus par thermographie et les champs de déformation par corrélation d'images. Sur un cycle de chargement, on montre comment il est possible d'estimer séparément les sources de chaleurs moyennes par cycle, sources associées aux mécanismes dissipatifs et induites par les effets de couplage thermomécanique. On montre ensuite, pour différentes fréquences de chargement, l'évolution du bilan de puissance moyen par cycle sur une zone matérielle correspondant à la partie utile de l'éprouvette. Ce bilan prend en compte le taux de l'énergie de déformation, les chaleurs mises en jeu et les variations d'énergie interne. On observe que la forme du bilan de puissance est très fortement dépendante, pour un rapport de charge donné, à la fréquence de sollicitation, à la teneur en eau, à l'orientation des fibres de verre mais aussi aux niveaux de contrainte appliqués. / This study presents a thermomechanical analysis of fatigue behavior of pure and short glass- fiber reinforced polyamide 6.6. The energy balances are drew up using the combined application of visible and infrared quantitative imaging techniques. Temperature fields are obtained by thermography and strain fields by image correlation. Over one complete cycle, we show how it is possible to separately estimate the heat sources averaged over the cycle, associated with dissipative mechanisms and induced by thermomechanical coupling source effets. Then we show, for different loading rates, the time courses of the energy rate balance for a physical area corresponding to the gage part of the specimen. This balance takes into account the deformation energy rate, the heat sources and the internal energy variations. It is observed that the shape of the energy rate balance is highly dependent, for a given load ratio, to the load rate, the water content, the orientation of the glass fibers and the applied stress levels.

En cas d’accident grave dans un réacteur nucléaire à eau sous pression, l’alliage absorbant Ag-Cd-In est susceptible d’interagir à haute température avec leurs tubes guides en zircaloy. L’étude thermodynamique du liquide et des équilibres impliquant cette phase dans les systèmes Ag-Zr et Ag-Cd-In est une étape pour une estimation des relâchements de produits de fission. Le système Ag-Zr est difficile à étudier en raison de la réactivité du zirconium, à l’état liquide et avec l’oxygène, et de la difficulté à atteindre l’équilibre et enfin car les stabilités des phases intermédiaires AgZr et AgZr2 sont faibles. Après la mise en place de protocoles expérimentaux, les réactions invariantes du système sont établies en couplant l’analyse thermique différentielle avec des caractérisations par MEB. Un diagramme de phases Ag-Zr est proposé. Des mesures de calorimétrie de dissolution en bain aluminium sont effectuées à 723°C dans le but de déterminer l’enthalpie de formation de AgZr et AgZr2. Les résultats montrent la difficulté de dissoudre le zirconium dans l’aluminium liquide. Un modèle est développé pour quantifier la cinétique de dissolution. L’enthalpie de formation de AgZr est déterminée par calorimétrie de dissolution en bain acide à 25°C. L’extension dans le diagramme Ag-In-Cd du domaine de stabilité de la phase liquide est précisée en combinant une méthode isotherme de recuit et trempe d’échantillons biphasés solide/liquide avec la calorimétrie différentielle à balayage . La cohérence de ces nouveaux résultats entre eux et avec les données de la littérature est testée par le biais d’une optimisation thermodynamique suivant la méthode CALPHAD. / During a severe accident in a Pressurized Water Reactor, the Ag-In-Cd absorbing alloy is likely to interact at a high temperature with their guide tubes or with the fuel rod cladding, both in Zry. The thermodynamic study of liquid phase and its equilibria in the Ag-Zr and Ag-Cd-In systems is a necessary step for an estimate of the fission product release and of the corium progression. The aim is to bring an experimental contribution to this thermodynamic study. The Ag-Zr system is difficult to study experimentally for various reasons. Zirconium, especially when liquid, is reactive with oxygen. Equilibria often prove difficult to reach. Last, the stabilities of AgZr and AgZr2 are low. After the establishment of experimental protocols, the invariant transformations of the system were established by coupling differential thermal analysis with characterization by metallography and scanning electron microscopy. A Ag-Zr phase diagram is proposed. Solution calorimetry measurements in an Al bath were performed at 723°C to determine the enthalpy of formation of AgZr and AgZr2. Results show the difficulty of dissolving solid zirconium in aluminum. A model was developed to quantify the dissolution kinetics. The formation enthalpy of AgZr was determined by solution calorimetry in an acid bath at 25°C. In the Ag-In-Cd system, the extension of the liquid phase stability domain is specified by combining an isothermal method of annealing and quenching of biphasic solid / liquid samples with differential scanning calorimetry. The consistency of the new results between them and compared to the literature has been tested by means of a thermodynamic optimization following the CALPHAD method.

Sintetizou-se uma nova diimida naftálica difosfônica, a N, N-bis(2-fosfonetil)naftaleno diimida (DPN), pela reação do dianidrido 1,4,5,5-naftálico com o ácido 2-aminoetil-fosfônico. Essa molécula foi caracterizada por H-RMN, micro-análise, titulação potenciométrica e análise de fosfato. Através de estudos fotofísicos e fotoquímicos do DPN em solução verificou-se que essas moléculas encontravam-se na forma monomérica em água e na forma de agregados em solventes orgânicos. Verificou-se que o rendimento quântico de fluorescência Φf dessa molécula é dependente do pH do meio, uma vez que ocorre diminuição do Φf com aumento do pH. Por estudos com fotólise de relâmpago e por experimentos de lente térmica resolvida no tempo, verificou-se que a diminuição do Φf com aumento do pH. Por estudos com fotólise de relâmpago e por experimentos de lente térmica resolvida no tempo, verificou-se que a diminuição Φf é causada principalmente por um aumento no cruzamento intersistema, de singleto a tripleto. Multicamadas à base de zircônio (Mallouk et al. 1987) do DPN foram obtidas substratos como vidro, silício e ouro. O crescimento de filmes em vidro foi acompanhado por espectroscopia de absorção e em filmes sobre o silício por elipsometria. Sobre a superfície de ouro, foram estudadas as propriedades de oxido-redução do filme por voltametria cíclica. Por estudos fotofisicos desses filmes depositados em vidro, verificou-se que os mesmos eram fotoativos, formando produtos fotoquímicos por processos radicalares. Por outro lado, quando se preparou micro-cristais, pricipitando-se o radical do DPN com o zircônio em solução, observou-se por espectroscopia de ressonância de spin eletrônico (EPR) que estas estruturas micro-cristalinas estabilizavam o radical do DPN em presença de ar por vários dias. / The new diimide N, N\' -bis-(2-phosphoethyl)-1,4,5,8-naphtalenediimide (DPN) was synthesized by reaction of 2-aminoethylphosphonic acid with the compound 1,4,5,8-naphatalene tetracarboxylic dianhydride. This molecule was characterized by 1H-RMN, elemental analysis, potentiometric titration and phosphorus analysis. By photophysical and photochemical studies of DPN in solution, it was verified that DPN is in monomeric form in aqueous solution and DPN is in an aggregated state in organic solvents. When the fluorescence spectra in aqueous media show a sharp decrease in the fluorescence quantum yield (Φf) with the increase in pH. By laser flash photolysis and thermal lensing, it was verified that this reduction of Φf with the increase pH can be attributed to an increment in the intersystem crossing processes when the pH increased. The zirconium phosphonate thin films formed from 1,4,5,8-naphtalene diimides were assembled on quartz, borosilicate glass (BK7), silicon or gold. The film growth was followed by absorption spectroscopy on quartz and BK7 and by ellipsometry on silicon substrate. Toe oxidation and reduction properties of the films were studied by cyclic voltammetry of films deposited on gold. Photophysical and photochemical data revealed that the films were photosensitive, giving rise to products derived by radicalar reactions. On the other hand, when the DPN radical was precipitated with Zr4+ in solution, micro-crystals were obtained which stabilized the radical in the presence of air for several days.

In recent years, high strength concrete (HSC) is becoming an attractive alternative to traditional normal strength concrete (NSC), and is used in a wide range of applications. With the increased use of HSC, concern has developed regarding the behavior of such concrete in fire. Until now, the fire performance of HSC is not fully understood and more research is needed. Full-scale fire testing is time consuming and expensive, and the real fire scenario is different from the standard fire. Performance-based assessment methods, including numerical analysis and simplified method, are being accepted in an increasing number of countries. In this dissertation, the fire testing results both of HSC and NSC are presented, performance-based numerical models are developed to study the fire performance of reinforced concrete (RC) members, and simplified calculation methods are proposed to estimate the load capacity of fire-damaged RC columns/beams. A detailed and comprehensive literature review is presented that provides background information on the high temperature behavior of concrete materials and RC members, as well as information on fire performance assessment procedures and objectives. The fire testing results of seven batches of HSC and NSC are presented and discussed. The test results indicated that the post-fire re-curing results in substantial strength and durability recovery, and its extent depends upon the types of concrete, temperature level, and re-curing age. The fire tests also showed that violent explosive reduced the risk of HSC explosive spalling. The surface crack widths were also reduced during the re-curing process, and in most cases, they were found within the maximum limits specified by the American Concrete Institute (ACI) building code. / Numerical models are developed herein to investigate the behavior in fire of RC columns and beams. The models have been validated against fire test data available in literature, and used to conduct parametric studies, which focused on the size effect on fire resistance of RC columns, and the effect of concrete cover thickness on fire endurance of RC beams. Simplified calculation methods have been developed to predict the load capacity of fire damaged RC columns/beams. This method is validated by five case studies, including thirty-five RC columns tested by other investigators. The predicted results are compared with the experimental results, and the good agreement indicates the adequacy of the simplified method for practical engineering applications. / by Lixian Liu. / Thesis (Ph.D.)--Florida Atlantic University, 2009. / Includes bibliography. / Electronic reproduction. Boca Raton, Fla., 2009. Mode of access: World Wide Web.

Tougher legal demands on pollutions require a better developed understanding of the processes that take place in the cylinder. The thesis contributes with a cylinder model that uses the same set of equations for intake, compression,expansion/combustion and exhaust. The cylinder model describes the states temperature, pressure and the mass fraction of air.The model is able to simulate the gas exchange with compressible flows over the valves, it handles VVT, CRB and blowby. The combustion is modeled with asingle Vibe function that describes the heat release and the consumption of air.The model is general enough to be able to simulate both SI and CI engines. The calibrations that are needed are the discharge coefficient CD values for intake and exhaust valves, blowby, and heat release/transfer parameters. Furthermore, the engine geometry parameters have to be provided to be able to calculate the instanteneous cylinder volume. The model has shown good agreement for cylinder pressure curves with and without combustion and can handle phasingof the valve lifts. That shows that the model can handle the important casesin combustion engines. It is easy to replace sub models in the cylinder model e.g. single Vibe with double Vibe. In the model, in the cylinder is calculated and the average instantenous torque for the entire engine is calculated from thestates in one cylinder. These two calculations have shown good agreement withthe stationary measurments done in an engine test cell. The model is able to use fixed step lengths for even processor loads, the size of the step lengths are resonable for real time implementation on an ECU.