Dissertations / Theses on the topic 'Real gas equation of state'

This work presents an approach which provides the real-time estimation of the gas concentration in a plume using an unmanned aerial vehicle (UAV) equipped with concentration sensors. The plume is assumed to be generated by a moving aerial or ground source with unknown strength and location, and is modeled by the unsteady advection-diffusion equation with ambient winds and eddy diffusivities. The UAV dynamics is described using the point-mass model of a fixed-wing aircraft resulting in a sixth-order nonlinear dynamical system. The state (gas concentration) estimator takes the form of a Luenberger observer based on the advection-diffusion equation. The UAV in the approach is guided towards the region with the larger state-estimation error via an appropriate choice of a Lyapunov function thus coupling the UAV guidance with the performance of the gas concentration estimator. This coupled controls-CFD guidance scheme provides the desired Cartesian velocities for the UAV and based on these velocities a lower-level controller processes the control signals that are transmitted to the UAV. The finite-volume discretization of the estimator incorporates a second-order total variation diminishing (TVD) scheme for the advection term. For computational efficiency needed in real-time applications, a dynamic grid adaptation for the estimator with local grid-refinement centered at the UAV location is proposed. The approach is tested numerically for several source trajectories using existing specifications for the UAV considered. The estimated plumes are compared with simulated concentration data. The estimator performance is analyzed by the behavior of the RMS error of the concentration and the distance between the sensor and the source.

In this thesis I present two different research topics investigated during the course of my PhD, regarding the analysis of spatial structures in a Bose Einstein condensate. Ultracold atomic gases offer a privileged platform for such kind of experiments, thanks to the fine control that can be achieved on the system’s parameters and to the availability of advanced imaging schemes allowing for a great measurement accuracy. The first topic is about the shape of quantized vortices in an elongated condensate, with the goal of providing a quantitative analysis of the density structure of a quantized vortex filament hosted in a bulk 3D superfluid. We analyzed the shape of the vortex and studied its dynamics during a free expansion, or time of flight (TOF), of the hosting BEC, with the goal of making a quantitative comparison between theory and experiment for the structure of the core of a quantized vortex in three-dimensional (3D) condensates. Simultaneously imaging the sample along orthogonal directions after a long TOF allowed to map the complete 3D shape of the vortex at the end of the free flight, while the full expansion dynamics has been simulated with numerical solutions of the Gross-Pitaevskii equation. The same data analysis procedure has been applied to both the experimental images and to the density profiles computed with the simulations to ensure a faithful comparison. We were able to detail the evolution of the vortex parameters at all times combining a simple analytic scaling-law model valid at early times, experimental data for the width and the depth of the core at long expansion times, and the numerics that were used to bridge between the two. Additionally, we could check the validity of the predictions on the scaling of vortex parameters with the size of the BEC using the experimental data to interpolate between theoretical limiting models. We concluded that quantized vortex filaments can be optically imaged with standard techniques in 3D atomic BECs, at a level of accuracy which indeed is enough to show good quantitative agreement with the predictions of the GP theory for the width, depth, and overall shape of the vortex core. The second topic is a measurement of the equation of state of a single component BEC. The goal of this project is to verify the non-monotonic behaviour of the chemical potential of a homogeneous Bose gas of weakly interacting particles as a function of temperature, where one expects to find a maximum across the critical point of transition to the superfluid phase. This effect is believed to be a general feature of the normal-to-superfluid phase transition: it has been already experimentally demonstrated in unitary Fermi gases, and although the same is predicted to happen also in a gas of weakly interacting bosons, no experimental evidence has been reported so far. The measurement relies on the local density approximation, which allows to extract information about the thermodynamics of a homogeneous system from accurate measurements of the local properties of a trapped one. My work has focused on developing a series of imaging and data analysis techniques to measure the 3D density profile of a harmonically trapped gas, even in regimes of extreme density such as inside a Bose condensate. With a new high-dynamic-range method we were able to image the 3D density distribution of a trapped sample, leading to a low-noise measurement of the density distribution. We confirmed the existence of the non-monotonic behaviour of the chemicial potential across, and set the basis for further measurements of the thermodynamics of the system across the transition.In this thesis I present two different research topics investigated during the course of my PhD, regarding the analysis of spatial structures in a Bose Einstein condensate. Ultracold atomic gases offer a privileged platform for such kind of experiments, thanks to the fine control that can be achieved on the system’s parameters and to the availability of advanced imaging schemes allowing for a great measurement accuracy. The first topic is about the shape of quantized vortices in an elongated condensate, with the goal of providing a quantitative analysis of the density structure of a quantized vortex filament hosted in a bulk 3D superfluid. We analyzed the shape of the vortex and studied its dynamics during a free expansion, or time of flight (TOF), of the hosting BEC, with the goal of making a quantitative comparison between theory and experiment for the structure of the core of a quantized vortex in three-dimensional (3D) condensates. Simultaneously imaging the sample along orthogonal directions after a long TOF allowed to map the complete 3D shape of the vortex at the end of the free flight, while the full expansion dynamics has been simulated with numerical solutions of the Gross-Pitaevskii equation. The same data analysis procedure has been applied to both the experimental images and to the density profiles computed with the simulations to ensure a faithful comparison. We were able to detail the evolution of the vortex parameters at all times combining a simple analytic scaling-law model valid at early times, experimental data for the width and the depth of the core at long expansion times, and the numerics that were used to bridge between the two. Additionally, we could check the validity of the predictions on the scaling of vortex parameters with the size of the BEC using the experimental data to interpolate between theoretical limiting models. We concluded that quantized vortex filaments can be optically imaged with standard techniques in 3D atomic BECs, at a level of accuracy which indeed is enough to show good quantitative agreement with the predictions of the GP theory for the width, depth, and overall shape of the vortex core. The second topic is a measurement of the equation of state of a single component BEC. The goal of this project is to verify the non-monotonic behaviour of the chemical potential of a homogeneous Bose gas of weakly interacting particles as a function of temperature, where one expects to find a maximum across the critical point of transition to the superfluid phase. This effect is believed to be a general feature of the normal-to-superfluid phase transition: it has been already experimentally demonstrated in unitary Fermi gases, and although the same is predicted to happen also in a gas of weakly interacting bosons, no experimental evidence has been reported so far. The measurement relies on the local density approximation, which allows to extract information about the thermodynamics of a homogeneous system from accurate measurements of the local properties of a trapped one. My work has focused on developing a series of imaging and data analysis techniques to measure the 3D density profile of a harmonically trapped gas, even in regimes of extreme density such as inside a Bose condensate. With a new high-dynamic-range method we were able to image the 3D density distribution of a trapped sample, leading to a low-noise measurement of the density distribution. We confirmed the existence of the non-monotonic behaviour of the chemicial potential across, and set the basis for further measurements of the thermodynamics of the system across the transition.

In this thesis I present two different research topics investigated during the course of my PhD, regarding the analysis of spatial structures in a Bose Einstein condensate. Ultracold atomic gases offer a privileged platform for such kind of experiments, thanks to the fine control that can be achieved on the system’s parameters and to the availability of advanced imaging schemes allowing for a great measurement accuracy. The first topic is about the shape of quantized vortices in an elongated condensate, with the goal of providing a quantitative analysis of the density structure of a quantized vortex filament hosted in a bulk 3D superfluid. We analyzed the shape of the vortex and studied its dynamics during a free expansion, or time of flight (TOF), of the hosting BEC, with the goal of making a quantitative comparison between theory and experiment for the structure of the core of a quantized vortex in three-dimensional (3D) condensates. Simultaneously imaging the sample along orthogonal directions after a long TOF allowed to map the complete 3D shape of the vortex at the end of the free flight, while the full expansion dynamics has been simulated with numerical solutions of the Gross-Pitaevskii equation. The same data analysis procedure has been applied to both the experimental images and to the density profiles computed with the simulations to ensure a faithful comparison. We were able to detail the evolution of the vortex parameters at all times combining a simple analytic scaling-law model valid at early times, experimental data for the width and the depth of the core at long expansion times, and the numerics that were used to bridge between the two. Additionally, we could check the validity of the predictions on the scaling of vortex parameters with the size of the BEC using the experimental data to interpolate between theoretical limiting models. We concluded that quantized vortex filaments can be optically imaged with standard techniques in 3D atomic BECs, at a level of accuracy which indeed is enough to show good quantitative agreement with the predictions of the GP theory for the width, depth, and overall shape of the vortex core. The second topic is a measurement of the equation of state of a single component BEC. The goal of this project is to verify the non-monotonic behaviour of the chemical potential of a homogeneous Bose gas of weakly interacting particles as a function of temperature, where one expects to find a maximum across the critical point of transition to the superfluid phase. This effect is believed to be a general feature of the normal-to-superfluid phase transition: it has been already experimentally demonstrated in unitary Fermi gases, and although the same is predicted to happen also in a gas of weakly interacting bosons, no experimental evidence has been reported so far. The measurement relies on the local density approximation, which allows to extract information about the thermodynamics of a homogeneous system from accurate measurements of the local properties of a trapped one. My work has focused on developing a series of imaging and data analysis techniques to measure the 3D density profile of a harmonically trapped gas, even in regimes of extreme density such as inside a Bose condensate. With a new high-dynamic-range method we were able to image the 3D density distribution of a trapped sample, leading to a low-noise measurement of the density distribution. We confirmed the existence of the non-monotonic behaviour of the chemicial potential across, and set the basis for further measurements of the thermodynamics of the system across the transition.In this thesis I present two different research topics investigated during the course of my PhD, regarding the analysis of spatial structures in a Bose Einstein condensate. Ultracold atomic gases offer a privileged platform for such kind of experiments, thanks to the fine control that can be achieved on the system’s parameters and to the availability of advanced imaging schemes allowing for a great measurement accuracy. The first topic is about the shape of quantized vortices in an elongated condensate, with the goal of providing a quantitative analysis of the density structure of a quantized vortex filament hosted in a bulk 3D superfluid. We analyzed the shape of the vortex and studied its dynamics during a free expansion, or time of flight (TOF), of the hosting BEC, with the goal of making a quantitative comparison between theory and experiment for the structure of the core of a quantized vortex in three-dimensional (3D) condensates. Simultaneously imaging the sample along orthogonal directions after a long TOF allowed to map the complete 3D shape of the vortex at the end of the free flight, while the full expansion dynamics has been simulated with numerical solutions of the Gross-Pitaevskii equation. The same data analysis procedure has been applied to both the experimental images and to the density profiles computed with the simulations to ensure a faithful comparison. We were able to detail the evolution of the vortex parameters at all times combining a simple analytic scaling-law model valid at early times, experimental data for the width and the depth of the core at long expansion times, and the numerics that were used to bridge between the two. Additionally, we could check the validity of the predictions on the scaling of vortex parameters with the size of the BEC using the experimental data to interpolate between theoretical limiting models. We concluded that quantized vortex filaments can be optically imaged with standard techniques in 3D atomic BECs, at a level of accuracy which indeed is enough to show good quantitative agreement with the predictions of the GP theory for the width, depth, and overall shape of the vortex core. The second topic is a measurement of the equation of state of a single component BEC. The goal of this project is to verify the non-monotonic behaviour of the chemical potential of a homogeneous Bose gas of weakly interacting particles as a function of temperature, where one expects to find a maximum across the critical point of transition to the superfluid phase. This effect is believed to be a general feature of the normal-to-superfluid phase transition: it has been already experimentally demonstrated in unitary Fermi gases, and although the same is predicted to happen also in a gas of weakly interacting bosons, no experimental evidence has been reported so far. The measurement relies on the local density approximation, which allows to extract information about the thermodynamics of a homogeneous system from accurate measurements of the local properties of a trapped one. My work has focused on developing a series of imaging and data analysis techniques to measure the 3D density profile of a harmonically trapped gas, even in regimes of extreme density such as inside a Bose condensate. With a new high-dynamic-range method we were able to image the 3D density distribution of a trapped sample, leading to a low-noise measurement of the density distribution. We confirmed the existence of the non-monotonic behaviour of the chemicial potential across, and set the basis for further measurements of the thermodynamics of the system across the transition.

To obtain information about a system of interest a measurement has to be made. In experiments that probe the quantum nature of our world, the system itself is, in general, necessarily affected by the act of measurement. If the system is weakly coupled to its bath and the dynamics are such that information concerning the system is spread throughout the many degrees of freedom of the bath, and the bath is being measured then a stochastic master equation for the conditioned state of the system can be found. This is termed a quantum trajectory equation. Realistic detectors are not perfect. Information is lost in the conversion to a signal that the observer can use. This loss may occur in the detector itself, in the circuit containing the detector (described by a response time and electronic noise) or at the circuit output (electronic output noise). In order to obtain a true quantum trajectory for the experiment, the observer must condition the state of the quantum system on results that are available in the laboratory rather than on the microscopic events considered previously in quantum trajectories. A method for treating this was first proposed by Warszawski, Wiseman and Mabuchi [Phys. Rev. A 65, 023802 (2002)], in which the quantum system is embedded within a supersystem that also contains the state of the detector. They applied their theory to photodetectors of various sorts. Warszawski has also done the preliminary work on applying this theory to detecting the state of a pair of quantum dots using a SET (single-electron transistor) [MSc. Thesis, Griffith University (2001)]. The resulting theory is termed 'realistic' quantum trajectory theory. In this thesis, the approach of Warszawski, et al.is applied to various solidstate readout devices. These include the SET, the QPC (quantum point contact), and the RF-QPC (radio-frequency QPC). Numerically obtained realistic quantum trajectories for the QPC agree with heuristic results. In particular, in certain limits, the realistic quantum trajectories can take on the appearance of ideal quantum trajectories. This thesis also resolves a problem in solid-state continuous quantum measurement theory by deriving a quantum trajectory model for a SET-monitored charge qubit, that guarantees physically meaningful qubit states. The particular limit necessary to achieve this is discussed, and the SET measurement quality is analysed using techniques borrowed from quantum optics. Conditions for which the SET can approach operation at the limit allowed by quantum mechanics are given. This is also done for the QPC, for which the results agree with previous work.<br>Thesis (PhD Doctorate)<br>Doctor of Philosophy (PhD)<br>School of Science<br>Full Text

This thesis deals with the characteristics of natural gas and the problems of transport. Furthermore, this work deals with the most commonly used thermodynamic cycles, both steam and gas and their applications in the energy industry. The main part of this thesis focuses on the calculation of the thermodynamic properties of the gas, determine the minimum temperature gas after expansion in the turbine to prevent the formation of hydrates, design calculation of main dimensions and thermodynamic parameters of the expansion turbine on natural gas. As a final design will be drawn slice computed expansion turbine.

La dimensionnalité d’un système affecte fortement ses propriétés physiques ; les transitions de phasequi s’y déroulent ainsi que le type d’ordre qui y apparaît dépendent de la dimension. Dans les systèmesde basse dimension, la cohérence s’avère plus difficile à établir car les fluctuations thermiques etquantiques y jouent un rôle plus important. Le fluide de Bose à deux dimensions est particulièrementintéressant car, même si un ordre total est exclu, un ordre résiduel à « quasi-longue » portée s’établit àbasse température. Deux ingrédients ont un effet significatif sur l’état du système : (i) la taille finie d’unsystème réel permet de retrouver une occupation macroscopique d’un état à une particule ; (ii) les interactionsentre particules conduisent à l’apparition d’un type non-conventionnel de transition de phasevers un état superfluide.Dans cette thèse, nous présentons une étude expérimentale du gaz de Bose bidimensionnel (2D) utilisantdeux types de paysages énergétiques pour piéger nos atomes. Dans la première partie, nous utilisonsla dépendance spatiale de certaines propriétés locales d’un gaz inhomogène pour caractériser l’étatdu système homogène équivalent. Nous extrayons son équation d’état des profils de densité et noustestons son comportement superfluide en mesurant le chauffage induit par le mouvement d’une perturbationlocale. Dans la deuxième partie, nous observons et caractérisons l’émergence d’une cohérencede phase étendue dans un gaz 2D homogène, en particulier via le passage de trois dimensions à deux(croisement dimensionnel). Nous étudions l’établissement dynamique de la cohérence par un passagerapide du croisement dimensionnel et nous observons des défauts topologiques dans l’état superfluidefinal. Nous comparons nos résultats avec les prédictions du mécanisme de Kibble–Zurek<br>The dimensionality of a system strongly affects its physical properties; the phase transitions that takeplace and the type of order that arises depend on the dimension. In low dimensional systems phasecoherence proves more difficult to achieve as both thermal and quantum fluctuations play a strongerrole. The two-dimensional Bose fluid is of particular interest as even if full order is precluded, a residual"quasi-long" range order arises at low temperatures. Then two ingredients have a significant effecton the state of the system: (i) the finite size of a real system enables one to recover of a macroscopicoccupation of a single-particle state; (ii) the interactions between particles lead to the emergence of anon-conventional type of phase transition toward a superfluid state.In this thesis, we present an experimental study of the two-dimensional (2D) Bose gas using two differentenergy landscapes to trap our atoms. In the first part, we use the spatial dependence of somelocal properties of an inhomogeneous gas to characterize the state of the equivalent homogeneous system.We extract its equation of state with a high accuracy from the gas density profiles and test itssuperfluid behavior by measuring the heating induced by a moving local perturbation. In the secondpart, we observe and characterize the emergence of an extended phase coherence in a 2D homogeneousgas in particular via a 3D-to-2D dimensional crossover. We investigate the dynamical establishment ofthe coherence via a rapid crossing of the dimensional crossover and observe topological defects in thefinal superfluid state. We compare our findings with the predictions for the Kibble–Zurek mechanism

The thermodynamic properties of CO2-mixtures are essential for the design and operation of CO2 Capture and Storage (CCS) systems. A better understanding of the thermodynamic properties of CO2 mixtures could provide a scientific basis to define a proper guideline of CO2 purity and impure components for the CCS processes according to technical, safety and environmental requirements. However the available accurate experimental data cannot cover the whole operation conditions of CCS processes. In order to overcome the shortage of experimental data, theoretical estimation and modelling are used as a supplemental approach.   In this thesis, the available experimental data on the thermodynamic properties of CO2 mixtures were first collected, and their applicability and gaps for theoretical model verification and calibration were also determined according to the required thermodynamic properties and operation conditions of CCS. Then in order to provide recommendations concerning calculation methods for engineering design of CCS, totally eight equations of state (EOS) were evaluated for the calculations about vapour liquid equilibrium (VLE) and density of CO2-mixtures, including N2, O2, SO2, Ar, H2S and CH4.   With the identified equations of state, the preliminary assessment of impurity impacts was further conducted regarding the thermodynamic properties of CO2-mixtures and different processes involved in CCS system. Results show that the increment of the mole fraction of non-condensable gases would make purification, compression and condensation more difficult. Comparatively N2 can be separated more easily from the CO2-mixtures than O2 and Ar. And a lower CO2 recovery rate is expected for the physical separation of CO2/N2 under the same separation conditions. In addition, the evaluations about the acceptable concentration of non-condensable impurities show that the transport conditions in vessels are more sensitive to the non-condensable impurities and it requires very low concentration of non-condensable impurities in order to avoid two-phase problems.   Meanwhile, the performances of evaporative gas turbine integrated with different CO2 capture technologies were investigated from both technical and economical aspects. It is concluded that the evaporative gas turbine (EvGT) cycle with chemical absorption capture has a smaller penalty on electrical efficiency, while a lower CO2 capture ratio than the EvGT cycle with O2/CO2 recycle combustion capture. Therefore, although EvGT + chemical absorption has a higher annual cost, it has a lower cost of electricity because of its higher efficiency. However considering its lower CO2 capture ratio, EvGT + chemical absorption has a higher cost to avoid 1 ton CO2. In addition the efficiency of EvGT + chemical absorption can be increased by optimizing Water/Air ratio, increasing the operating pressure of stripper and adding a flue gas condenser condensing out the excessive water.<br>QC 20100819

Numerical modelling of subsurface processes, such as geotechnical, geohydrological or geothermal applications requires a realistic description of fluid parameters in order to obtain plausible results. Particularly for gases, the properties of a fluid strongly depend on the primary variables of the simulated systems, which lead to non-linerarities in the governing equations. This thesis describes the development, evaluation and application of a numerical model for non-isothermal flow processes based on thermodynamic principles. Governing and constitutive equations of this model have been implemented into the open-source scientific FEM simulator OpenGeoSys. The model has been verified by several well-known benchmark tests for heat transport as well as for single- and multiphase flow. To describe physical fluid behaviour, highly accurate thermophysical property correlations of various fluids and fluid mixtures have been utilized. These correlations are functions of density and temperature. Thus, the accuracy of those correlations is strongly depending on the precision of the chosen equation of state (EOS), which provides a relation between the system state variables pressure, temperature, and composition. Complex multi-parameter EOSs reach a higher level of accuracy than general cubic equations, but lead to very expansive computing times. Therefore, a sensitivity analysis has been conducted to investigate the effects of EOS uncertainties on numerical simulation results. The comparison shows, that small differences in the density function may lead to significant discrepancies in the simulation results. Applying a compromise between precision and computational effort, a cubic EOS has been chosen for the simulation of the continuous injection of carbon dioxide into a depleted natural gas reservoir. In this simulation, real fluid behaviour has been considered. Interpreting the simulation results allows prognoses of CO2 propagation velocities and its distribution within the reservoir. These results are helpful and necessary for scheduling real injection strategies<br>Für die numerische Modellierung von unterirdischen Prozessen, wie z. B. geotechnische, geohydrologische oder geothermische Anwendungen, ist eine möglichst genaue Beschreibung der Parameter der beteiligten Fluide notwendig, um plausible Ergebnisse zu erhalten. Fluideigenschaften, vor allem die Eigenschaften von Gasen, sind stark abhängig von den jeweiligen Primärvariablen der simulierten Prozesse. Dies führt zu Nicht-linearitäten in den prozessbeschreibenden partiellen Differentialgleichungen. In der vorliegenden Arbeit wird die Entwicklung, die Evaluierung und die Anwendung eines numerischen Modells für nicht-isotherme Strömungsprozesse in porösen Medien beschrieben, das auf thermodynamischen Grundlagen beruht. Strömungs-, Transport- und Materialgleichungen wurden in die open-source-Software-Plattform OpenGeoSys implementiert. Das entwickelte Modell wurde mittels verschiedener, namhafter Benchmark-Tests für Wärmetransport sowie für Ein- und Mehrphasenströmung verifiziert. Um physikalisches Fluidverhalten zu beschreiben, wurden hochgenaue Korrelationsfunktionen für mehrere relevante Fluide und deren Gemische verwendet. Diese Korrelationen sind Funktionen der Dichte und der Temperatur. Daher ist deren Genauigkeit von der Präzision der verwendeten Zustandsgleichungen abhängig, welche die Fluiddichte in Relation zu Druck- und Temperaturbedingungen sowie der Zusammensetzung von Gemischen beschreiben. Komplexe Zustandsgleichungen, die mittels einer Vielzahl von Parametern an Realgasverhalten angepasst wurden, erreichen ein viel höheres Maß an Genauigkeit als die einfacheren, kubischen Gleichungen. Andererseits führt deren Komplexität zu sehr langen Rechenzeiten. Um die Wahl einer geeigneten Zustandsgleichung zu vereinfachen, wurde eine Sensitivitätsanalyse durchgeführt, um die Auswirkungen von Unsicherheiten in der Dichtefunktion auf die numerischen Simulationsergebnisse zu untersuchen. Die Analyse ergibt, dass bereits kleine Unterschiede in der Zustandsgleichung zu erheblichen Abweichungen der Simulationsergebnisse untereinander führen können. Als ein Kompromiss zwischen Einfachheit und Rechenaufwand wurde für die Simulation einer enhanced gas recovery-Anwendung eine kubische Zustandsgleichung gewählt. Die Simulation sieht, unter Berücksichtigung des Realgasverhaltens, die kontinuierliche Injektion von CO2 in ein nahezu erschöpftes Erdgasreservoir vor. Die Interpretation der Ergebnisse erlaubt eine Prognose über die Ausbreitungsgeschwindigkeit des CO2 bzw. über dessen Verteilung im Reservoir. Diese Ergebnisse sind für die Planung von realen Injektionsanwendungen notwendig

Made available in DSpace on 2014-12-17T15:01:27Z (GMT). No. of bitstreams: 1 SidrakJP_DISSERT.pdf: 3365381 bytes, checksum: 55b6f324d82bc4f385aa87921831ed44 (MD5) Previous issue date: 2011-12-20<br>Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior<br>This dissertation aims to assess the representativeness of the manual chilled mirror analyzer (model II Chanscope 13-1200-CN-2) used for the determination of condensed hydrocarbons of natural gas compared to the indirect methods, based on thermodynamic models equation of state. Additionally, it has been implemented in this study a model for calculating the dew point of natural gas. The proposed model is a modification of the equation of state of Peng-Robinson admits that the groups contribution as a strategy to calculate the binary interaction parameters kij (T) temperature dependence. Experimental data of the work of Brown et al. (2007) were used to compare the responses of the dew point of natural gas with thermodynamic models contained in the UniSim process simulator and the methodology implemented in this study. Then two natural gas compositions were studied, the first being a standard gas mixture gravimetrically synthesized and, second, a mixture of processed natural gas. These experimental data were also compared with the results presented by UniSim process simulator and the thermodynamic model implemented. However, data from the manual analysis results indicated significant differences in temperature, these differences were attributed to the formation of dew point of water, as we observed the appearance of moisture on the mirror surface cooling equipment<br>O presente trabalho de disserta??o tem por objetivo avaliar a representatividade do analisador manual de espelho refrigerado (Chanscope II modelo 13-1200-C-N-2) usado para a determina??o do condensado de hidrocarbonetos de g?s natural frente aos m?todos indiretos, fundamentados em modelos termodin?micos de equa??o de estado. Adicionalmente, tem sido implementado neste estudo um modelo para c?lculo do ponto de orvalho de g?s natural. O modelo proposto constitui uma modifica??o na equa??o de estado de Peng-Robinson que admite a contribui??o de grupos como estrat?gia para calcular os par?metros de intera??o bin?ria kij(T) com depend?ncia da temperatura. Dados experimentais do trabalho de Brown et al. (2007) foram utilizados para comparar as respostas de ponto de orvalho do g?s natural com os modelos termodin?micos contidos no simulador de processo UniSim e com a metodologia implementada neste estudo. Em seguida, duas composi??es de g?s natural foram estudadas, sendo a primeira uma mistura padr?o de g?s sintetizada gravimetricamente e, a segunda, uma mistura de g?s natural processado. Tais dados experimentais foram tamb?m comparados com os resultados apresentados pelo simulador de processo UniSim e pelo modelo termodin?mico implementado. No entanto, os dados do analisador manual indicaram diferen?as significativas nos resultados de temperaturas, sendo estas diferen?as atribu?das ? forma??o de ponto de orvalho de ?gua, j? que foi observado o aparecimento de umidade sobre a superf?cie do espelho refrigerado do equipamento

The physics of ultracold quantum gases has been the subject of a long-lasting and intense research activity, which started almost a century ago with purely theoretical studies and had a fluorishing experimental development after the implementation of laser and evaporative cooling techniques that led to the first realization of a Bose Einstein condensate (BEC) over 25 years ago. In recent years, a great interest in ultracold atoms has developed for their use as platforms for quantum technologies, given the high degree of control and tunability offered by ultracold atom systems. These features make ultracold atoms an ideal test bench for simulating and studying experimentally, in a controlled environment, physical phenomena analogous to those occurring in other, more complicated, or even inaccessible systems, which is the idea at the heart of quantum simulation. In the rapidly developing field of quantum technologies, it is highly important to acquire an in-depth understanding of the state of the quantum many-body system that is used, and of the processes needed to reach the desired state. The preparation of the system in a given target state often involves the crossing of second order phase transitions, bringing the system strongly out-of-equilibrium. A better understanding of the out-of-equilibrium processes occurring in the vicinity of the transition, and of the relaxation dynamics towards the final equilibrium condition, is crucial in order to produce well-controlled quantum states in an efficient way. In this thesis I present the results of the research activity that I performed during my PhD at the BEC1 laboratory of the BEC center, working on ultracold gases of 23Na atoms in an elongated harmonic trap. This work had two main goals: the accurate determination of the equilibrium properties of a Bose gas at finite temperature, by the measurement of its equation of state, and the investigation of the out-of-equilibrium dynamics occurring when a Bose Einstein condensate is prepared by cooling a thermal cloud at a finite rate across the BEC phase transition.To study the equilibrium physics of a trapped atomic cloud, it is crucial to be able to observe its density distribution in situ. This requires a high optical resolution to accurately obtain the density profile of the atomic distribution, from which thermodynamic quantities can then be extracted. In particular, in a partially condensed atomic cloud at finite temperature, it is challenging to resolve well also the boundaries of the BEC, where the condensate fraction rapidly drops in a narrow spatial region. This required an upgrade of the experimental apparatus in order to obtain a high enough resolution. I designed, tested and implemented in the experimental setup new imaging systems for all main directions of view. Particular attention was paid for the vertical imaging system, which was designed to image the condensates in trap with a resolution below 2 μm, with about a factor 4 improvement compared to the previous setup. The implementation of the new imaging systems involved a partial rebuilding of the experimental apparatus used for cooling the atoms. This created the occasion for an optimization of the whole system to obtain more stable working conditions. Concurrently I also realized and included in the experiment an optical setup for the use of a Digital Micromirror Device (DMD) to project time-dependent arbitrary light patterns on the atoms, creating optical potentials that can be controlled at will. The use of this device opens up exciting future scenarios where it will be possible to locally modify the trapping potential and to create well-controlled barriers moving through the atomic cloud. Another challenge in imaging the density distribution in situ is determined by the fact that the maximum optical density (OD) of the BEC, in the trap center, exceeds the low OD of the thermal tails by several orders of magnitude. In order to obtain an accurate image of the whole density profile, we developed a minimally destructive, multi-shot imaging technique, based on the partial transfer of a fraction of atoms to an auxiliary state, which is then probed. Taking multiple images at different extraction fractions, we are able to reconstruct the whole density profile of the atomic cloud avoiding saturation and maintaining a good signal to noise ratio. This technique, together with the improvements in the imaging resolution, has allowed us to accurately obtain the optical density profile of the Bose gas in trap, from which the 3D density profile was then calculated applying an inverse Abel transform, taking advantage of the symmetry of the trap. From images of the same cloud after a time-of-flight expansion, we measured the temperature of the gas. From these quantities we could find the pressure as a function of the density and temperature, determining the canonical equation of state of the weakly interacting Bose gas in equilibrium at finite temperature. These measurements also allowed us to clearly observe the non-monotonic temperature behavior of the chemical potential near the critical point for the phase transition, a feature that characterizes also other superfluid systems, but that had never been observed before in weakly interacting Bose gases. The second part of this thesis work is devoted to the study of the dynamical processes that occur during the formation of the BEC order parameter within a thermal cloud. The cooling at finite rate across the Bose-Einstein condensation transition brings the system in a strongly out-of-equilibrium state, which is worth investigating, together with the subsequent relaxation towards an equilibrium state. This is of interest also in view of achieving a better understanding of second order phase transitions in general, since such phenomena are ubiquitous in nature and relevant also in other platforms for quantum technologies. A milestone result in the study of second order phase transitions is given by the Kibble-Zurek mechanism, which provides a simple model capturing important aspects of the evolution of a system that crosses a second-order phase transition at finite rate. It is based on the principle that in an extended system the symmetry breaking associated with a continuous phase transition can take place only locally. This causes the formation of causally disconnected domains of the order parameter, at the boundaries of which topological defects can form, whose number and size scale with the rate at which the transition is crossed, following a universal power law. It was originally developed in the context of cosmology, but was later successfully tested in a variety of systems, including superfluid helium, superconductors, trapped ions and ultracold atoms. The BEC phase transition represents in this context a paradigmatic test-bench, given the high degree of control at which this second-order phase transition can be crossed by means of cooling ramps at different rates. Already early experiments investigated the formation of the BEC order parameter within a thermal cloud, after quasi-instantaneous temperature quenches or very slow evaporative cooling. In the framework of directly testing the Kibble-Zurek mechanism, further experiments were performed, both in 2D and 3D systems, focusing on the emergence of coherence and on the statistics of the spontaneously generated topological defects as a function of the cooling rate. The Kibble-Zurek mechanism, however, does not fully describe the out-of-equilibrium dynamics of the system at the transition, nor the post-quench interaction mechanisms between domains that lead to coarse-graining. Most theoretical models are based on a direct linear variation of a single control parameter, e.g. the temperature, across the transition. In real experiments, the cooling process is controlled by the tuning of other experimental parameters and a global temperature might not even be well defined, in a thermodynamic sense, during the whole process. Moreover, the temperature variation is usually accompanied by the variation of other quantities, such as the number of atoms and the collisional rate, making it difficult to accurately describe the system and predict the post-quench properties. Recent works included effects going beyond the Kibble-Zurek mechanism, such as the inhomogeneity introduced by the trapping potential, the role of atom number losses, and the saturation of the number of defects for high cooling rates. These works motivate further studies, in particular of the dynamics taking place at early times, close to the crossing of the critical point. The aim of the work presented in this thesis is to further investigate the timescales associated to the formation and evolution of the BEC order parameter and its spatial fluctuations, as a function of the rate at which the transition point is crossed. We performed experiments producing BECs by means of cooling protocols that are commonly used in cold-atom laboratories, involving evaporative cooling in a magnetic trap. We explored a wide range of cooling rates across the transition and found a universal scaling for the growth of the BEC order parameter with the cooling rate and a finite delay in its formation. The latter was already observed in earlier works, but for a much more limited range of cooling rates. The evolution of the fluctuations of the order parameter was also investigated, with an analysis of the timescale of their decay during the relaxation of the system, from an initial strongly out-of-equilibrium condition to a final equilibrium state. This thesis is structured as follows: The first chapter presents the theoretical background, starting with a brief introduction to the concept of Bose Einstein condensation and a presentation of different models describing the thermodynamics of an equilibrium Bose gas. The second part of this chapter then deals with the out-of-equilibrium dynamics that is inevitably involved in the crossing of a second-order phase transition such as the one for Bose-Einstein condensation. The Kibble-Zurek mechanism is briefly reviewed and beyond KZ effects are pointed out, motivating a more detailed investigation of the timescales involved in the BEC formation. In the second chapter, I describe the experimental apparatus that we use to cool and confine the atoms. Particular detail is dedicated to the parts that have been upgraded during my PhD, such as the imaging system. In the third chapter I show our experimental results on the measurement of the equation of state of the weakly interacting uniform Bose gas at finite temperature. In the fourth chapter I present our results on the out-of-equilibrium dynamics in the formation of the condensate order parameter and its spatial fluctuations, as a function of different cooling rates.

Yes<br>Three equations of state with a group contribution model for binary interaction parameters were employed to calculate the vapor-liquid equilibria of synthetic and real natural gas mixtures with heavy fractions. In order to estimate the binary interaction parameters, critical temperatures, critical pressures and acentric factors of binary constituents of the mixture are required. The binary interaction parameter model also accounts for temperature. To perform phase equilibrium calculations, the heavy fractions were first discretized into 12 Single Carbon Numbers (SCN) using generalized molecular weights. Then, using the generalized molecular weights and specific gravities, the SCN were characterized. Afterwards, phase equilibrium calculations were performed employing a set of (nc + 1) equations where nc stands for the number of known components plus 12 SCN. The equations were solved iteratively using Newton's method. Predictions indicate that the use of binary interaction parameters for highly sour natural gas mixtures is quite important and must not be avoided. For sweet natural gas mixtures, the use of binary interaction parameters is less remarkable, however.

Multiple hydrocarbon phases are observed during miscible gas floods. The possible phases that result from a gas flood include a vapor phase, an oleic phase, a solvent-rich phase, a solid phase, and an aqueous phase. The solid phase primarily consists of aggregated asphaltene particles. Asphaltenes can block pore throats or change the formation wettability, and thereby reduce the hydrocarbon mobility. The dissolution of injected gas into the aqueous phase can also affect the gas flooding recovery because it reduces the amount of gas available to contact oil. This is more important in CO₂ flooding as the solubility of CO₂ in brine is much higher than hydrocarbons. In this research, we developed efficient and fast multi-phase equilibrium calculation algorithms to model phase behavior of asphaltenes and the aqueous phase in the compositional simulation of gas floods. The PC-SAFT equation of state is implemented in the UTCOMP simulator to model asphaltene precipitation. The additional computational time of PC-SAFT is substantially decreased by improving the root finding algorithm and calculating the derivatives analytically. A deposition and wettability alteration model is then integrated with the thermodynamic model to simulate dynamics of precipitated asphaltenes. Asphaltene deposition is shown to occur with pressure depletion around the production well and/or with gas injection in the reservoir domain that is swept by injected gas. It is observed that the profile of the damaged area by asphaltene deposition depends on the reservoir fluid. A general strategy is proposed to model the phase behavior of CO₂/hydrocarbon/water systems where four equilibrium phases exist. The developed four-phase reduced flash algorithm is used to investigate the effect of introducing water on the phase behavior of CO₂/hydrocarbon mixtures. The results show changes in the phase splits and saturation pressures by adding water to these CO₂/hydrocarbon systems. We used a reduced flash approach to reduce the additional computational time of the four-phase flash calculations,. The results show a significant speed-up in flash calculations using the reduced method. The computational advantage of the reduced method increases rapidly with the number of phases and components. We also decreased the computational time of the equilibrium calculations in UTCOMP by changing the sequential steps in the flash calculation where it checks the previous time-step results as the initial guess for the current time-step. The improved algorithm can skip a large number of flash calculation and stability analyses without loss of accuracy.<br>text

The prevention of further climate as well as the exhaustion of natural resources in our planet are two of the biggest challenges faced by humankind. To achieve this objectives, emissions and fossil fuel consumption must be reduced. At the same time humankind puts great effort in the understanding of our universe, space ights are an important mean to achieve such knowledge and for those better performance and reliability of rocket engines are required. Increasing the operating pressure and temperature of power systems such as diesel engines, gas turbines, rocket engines, and others, is a known way of increasing ef ciency and performance. Over the past years, this increase has become an important trend in the design of new power units. In order to study the high pressure and high temperature operating condition of the variety of internal combustion engines, a cryogenic nitrogen jet injected into supercritical chamber conditions was simulated numerically. The Favre averaged Navier-Stokes equations were employed together with a k 􀀀 " turbulence model. To determine the density value different approaches were employed, one making use of Amagat’s law based on mixture fraction, and another employing the Soave-Redlich-Kwong or the Peng-Robinson real uid equations of state, and also integrating the favre averaged energy equation. To determine the uid properties also different approaches were tested. The obtained results have shown an acceptable agreement with experiments, mainly in terms of the jet spreading rate as well as for radial density distribution. For the axial density distribution was found a more dif cult agreement for the length of the potential core. Results also suggest the a strong in uence of the turbulent characteristics over the ow of study.<br>O presente trabalho tem como o objectivo o estudo e modelação de jactos de azoto criogénico numa gama de condições transcriticas e supercriticas. A injecção de combustível em condições de alta pressão e temperatura apresenta-se como o principal objecto de aplicação da presente investigação. Este tipo de injecção é típica não só em motores foguetes mas também em modernos motores diesel assim como em turbinas de gás, em ambos os casos pressões e temperaturas de combustão têm aumentado com o objectivo de aumentar e ciência e performance reduzindo ao mesmo tempo e emissão de poluentes. Uma aproximação numérica de densidade variável, originalmente desenvolvida para a modela ção de jactos gasosos, turbulentos e incompressíveis foi utilizada para a modelação deste tipo de escoamentos. Os resultados demonstraram o potencial desta aproximação. No entanto, a mesma não previa os efeitos resultantes da transmissão de calor nos uidos nem o comportamento de gases reais. Para colmatar estas de ciências foi incluída a equação da energia assim como equações de estado de gás real. Para a determinação das propriedades dos uidos foram empregues e testadas diferentes metodologias. Os resultados obtidos mostram uma boa concordância no seu geral com os dados experimentais divergindo apenas no comprimento do cone potencial. Uma conclusão importante dos resultados é a da importância que a turbulência tem neste tipo de escoamento quando comparada com as propriedades moleculares.<br>Fundação para a Ciência e Tecnologia

by D. Obradovic, L. Valavani.<br>Includes bibliographical references (p. 15).<br>Supported by AFOSR/Eglin AFB. FO 8635-87-K-0031 Supported by the Boeing Company. Supported by the NASA Ames and Langley Research Centers. NASA/NAG 2-297

No<br>Using fugacity coefficient of a cubic equation of state, Henry’s law constant of a solute in a solvent isincorporated into binary interaction parameter of the classical attractive parameter mixing rule. Thedeveloped equation is a function of temperature. The binary interaction parameter is evaluated by purecomponent critical properties and acentric factors of the solute and the solvent and the Henry’s lawconstant of the solute in the solvent. The developed model accurately describes the solubility of gasesincluding methane, ethane, nitrogen, carbon dioxide and hydrogen sulphide in heavy n-alkanes from lowto high pressure for wide range of temperature. The solubility of methane and carbon dioxide in wateris also predicted adequately.

Numerical simulation has been used, as common practice, to estimate the CO2 storage capacity of depleted reservoirs. However, this method is time consuming, expensive and requires detailed input data. This investigation proposes an analytical method to estimate the ultimate CO2 storage in depleted oil and gas reservoirs by implementing a volume constrained thermodynamic equation of state (EOS) using the reservoir?s average pressure and fluid composition. This method was implemented in an algorithm which allows fast and accurate estimations of final storage, which can be used to select target storage reservoirs, and design the injection scheme and surface facilities. Impurities such as nitrogen and carbon monoxide, usually contained in power plant flue gases, are considered in the injection stream and can be handled correctly in the proposed algorithm by using their thermodynamic properties into the EOS. Results from analytical method presented excellent agreement with those from reservoir simulation. Ultimate CO2 storage capacity was predicted with an average difference of 1.3%, molar basis, between analytical and numerical methods; average oil, gas, and water saturations were also matched. Additionally, the analytical algorithm performed several orders of magnitude faster than numerical simulation, with an average of 5 seconds per run.

In industrial fuel gas preparation, there are several compositional properties that must be controlled within specified limits. This allows client plants to use the fuel gas mixture safely without having to adjust and control the composition themselves. The variables to be controlled are the Higher Heating Value (HHV), Wobbe Index (WI), Flame Speed Index (FSI), and Pressure (P). These variables are controlled by adjusting the volumetric flow rates of several inlet gas streams of which some are makeup streams (always available) and some are wild streams that vary in composition and availability (by-products of plants). The inlet streams need to be adjusted in the correct ratios to keep all the controlled variables (CVs) within limits while minimising the cost of the gas blend. Furthermore, the controller needs to compensate for fluctuations in inlet stream compositions and total fuel gas demand (the total discharge from the header). This dissertation describes the modelling and model validation of an industrial fuel gas header as well as a simulation study of three different Model Predictive Control (MPC) strategies for controlling the system while minimising the overall operating cost.<br>Dissertation (MEng)--University of Pretoria, 2011.<br>Electrical, Electronic and Computer Engineering<br>unrestricted

A novel technique for measuring gas temperature and spectral particle emissivity in high-temperature gas-particle streams is presented. The main application of this optical sensor is to improve the process control of batch unit operations, such as steelmaking furnaces. The spectral emission profile of CO and CO2 and the continuous particle emission in the 3.5 to 5 μm wavelength region was recorded and analyzed in real time with a low-resolution passive sensor. The sensor consisted of light collecting optics, a dispersion element (grating spectrometer) and a 64-pixel pyroelectric array. Wavelength and radiance calibrations were performed. The temperature of the gas-particle medium (Tg+p) followed from the least-squares minimization of the difference between the measured radiance in the 4.56-4.7 μm region –which saturates due to the large CO2 concentrations and path lengths in industrial furnaces– and the corresponding blackbody radiance. Particle emissivity (εp) was calculated at 3.95 μm from an asymptotic approximation of the Radiative Transfer Equation that yields the emerging radiance from a semi-infinite particle cloud. The major source of error in the magnitude of Tg+p and εp could come from particle scattering. Through the method of embedded invariance an expression was developed to estimate the lowering effect of particle size and volume fraction on the saturation of the 4.56-4.7 μm CO2 emission region. An iterative procedure for correcting the values of the gas-particle temperature and particle emissivity was applied to the datasets from the two industrial tests. Results from the measurement campaigns with the infrared sensor prototype at two full-scale furnaces are presented. A proof-of-concept test at a coal-fired boiler for electricity production was followed by more extensive measurements at a Basic Oxygen Furnace (BOF) for steelmaking. The second test provided temperature and particle emissivity profiles for eight heats, which highlighted the simplicity of the technique in obtaining in-situ measurements for modeling studies. Through the analysis of the particle emissivity profile in the BOF and the definition of a new variable –the minimum carbon time– a novel end-point strategy to stop the injection of high-purity oxygen during low-carbon heats in BOF converters was proposed.

The past decade has witnessed dramatic changes in the oil and gas industry with the drilling and production extending into progressively deeper waters and higher operating pressures, therefore making it essential to gain a better understanding of the behaviour of gas hydrate at high pressure conditions. New experimental 3-phase H−LW−V (Hydrate−Liquid Water−Vapour) equilibrium data for nitrogen and H−LW−V (Hydrate−Liquid Water−Vapour) and H−LW−LHC (Hydrate−Liquid Water−Liquid Hydrocarbon) data for ethane and propane simple clathrate hydrates were generated by a reliable fixed-volume, isochoric, step-heating technique. The accuracy and reliability of the experimental measurements are demonstrated by comparing measurements with reliable literature data from different researchers. Additional experimental data up to high pressure (200 MPa when available) for CH4, C2H6, C3H8, i-C4H10, N2, Ar, Kr, Xe, H2S, O2, CO and CO2 clathrates have been gathered from literature. The Valderrama modification of the Patel-Teja (VPT) equation of state combined with non-density-dependent (NDD) mixing rules is used to model the fluid phases with previously reported binary interaction parameters. The hydrate-forming conditions are modelled by the solid solution theory of van der Waals and Platteeuw. Langmuir constants have been calculated by both Kihara potential as well as direct techniques. Model predictions are validated against independent experimental data and a good agreement between predictions and experimental data is observed, supporting the reliability of the developed model.

Numerical modelling of subsurface processes, such as geotechnical, geohydrological or geothermal applications requires a realistic description of fluid parameters in order to obtain plausible results. Particularly for gases, the properties of a fluid strongly depend on the primary variables of the simulated systems, which lead to non-linerarities in the governing equations. This thesis describes the development, evaluation and application of a numerical model for non-isothermal flow processes based on thermodynamic principles. Governing and constitutive equations of this model have been implemented into the open-source scientific FEM simulator OpenGeoSys. The model has been verified by several well-known benchmark tests for heat transport as well as for single- and multiphase flow. To describe physical fluid behaviour, highly accurate thermophysical property correlations of various fluids and fluid mixtures have been utilized. These correlations are functions of density and temperature. Thus, the accuracy of those correlations is strongly depending on the precision of the chosen equation of state (EOS), which provides a relation between the system state variables pressure, temperature, and composition. Complex multi-parameter EOSs reach a higher level of accuracy than general cubic equations, but lead to very expansive computing times. Therefore, a sensitivity analysis has been conducted to investigate the effects of EOS uncertainties on numerical simulation results. The comparison shows, that small differences in the density function may lead to significant discrepancies in the simulation results. Applying a compromise between precision and computational effort, a cubic EOS has been chosen for the simulation of the continuous injection of carbon dioxide into a depleted natural gas reservoir. In this simulation, real fluid behaviour has been considered. Interpreting the simulation results allows prognoses of CO2 propagation velocities and its distribution within the reservoir. These results are helpful and necessary for scheduling real injection strategies.<br>Für die numerische Modellierung von unterirdischen Prozessen, wie z. B. geotechnische, geohydrologische oder geothermische Anwendungen, ist eine möglichst genaue Beschreibung der Parameter der beteiligten Fluide notwendig, um plausible Ergebnisse zu erhalten. Fluideigenschaften, vor allem die Eigenschaften von Gasen, sind stark abhängig von den jeweiligen Primärvariablen der simulierten Prozesse. Dies führt zu Nicht-linearitäten in den prozessbeschreibenden partiellen Differentialgleichungen. In der vorliegenden Arbeit wird die Entwicklung, die Evaluierung und die Anwendung eines numerischen Modells für nicht-isotherme Strömungsprozesse in porösen Medien beschrieben, das auf thermodynamischen Grundlagen beruht. Strömungs-, Transport- und Materialgleichungen wurden in die open-source-Software-Plattform OpenGeoSys implementiert. Das entwickelte Modell wurde mittels verschiedener, namhafter Benchmark-Tests für Wärmetransport sowie für Ein- und Mehrphasenströmung verifiziert. Um physikalisches Fluidverhalten zu beschreiben, wurden hochgenaue Korrelationsfunktionen für mehrere relevante Fluide und deren Gemische verwendet. Diese Korrelationen sind Funktionen der Dichte und der Temperatur. Daher ist deren Genauigkeit von der Präzision der verwendeten Zustandsgleichungen abhängig, welche die Fluiddichte in Relation zu Druck- und Temperaturbedingungen sowie der Zusammensetzung von Gemischen beschreiben. Komplexe Zustandsgleichungen, die mittels einer Vielzahl von Parametern an Realgasverhalten angepasst wurden, erreichen ein viel höheres Maß an Genauigkeit als die einfacheren, kubischen Gleichungen. Andererseits führt deren Komplexität zu sehr langen Rechenzeiten. Um die Wahl einer geeigneten Zustandsgleichung zu vereinfachen, wurde eine Sensitivitätsanalyse durchgeführt, um die Auswirkungen von Unsicherheiten in der Dichtefunktion auf die numerischen Simulationsergebnisse zu untersuchen. Die Analyse ergibt, dass bereits kleine Unterschiede in der Zustandsgleichung zu erheblichen Abweichungen der Simulationsergebnisse untereinander führen können. Als ein Kompromiss zwischen Einfachheit und Rechenaufwand wurde für die Simulation einer enhanced gas recovery-Anwendung eine kubische Zustandsgleichung gewählt. Die Simulation sieht, unter Berücksichtigung des Realgasverhaltens, die kontinuierliche Injektion von CO2 in ein nahezu erschöpftes Erdgasreservoir vor. Die Interpretation der Ergebnisse erlaubt eine Prognose über die Ausbreitungsgeschwindigkeit des CO2 bzw. über dessen Verteilung im Reservoir. Diese Ergebnisse sind für die Planung von realen Injektionsanwendungen notwendig