Thesis (MSc)--University of Stellenbosch, 2008. / Bibliography. Also available via the Internet.

Thesis (Ph. D.)--University of Washington, 2005. / Vita. Includes bibliographical references (p. 103-111).

The thermophysical properties of supercritical CO₂ and H₂O-CO₂ mixtures are reviewed and their computation and prediction improved through theory and experiment. A resolution is attempted among inconsistencies between and within data sets, including P-V-T measurements, phase equilibrium experiments and equations of state. Pure carbon dioxide: Equations of state for CO₂ (Kerrick & Jacobs, 1981; Bottinga & Richet, 1981; Holloway, 1977) are based solely on P-V-T data up to 8 kbar and lead to deviations from phase equilibrium data at pressures greater than 10-20 kbar. Mathematical programming analysis has been applied to the fitting of parameters for an equation of state using simultaneously constraints from phase equilibrium and P-V-T data. Phase equilibrium data up to 42 kbar are used to define a feasible region for the adjustable parameters in free energy space. Each half-bracket places an inequality constraint on the fugacity of CO₂ provided the thermophysical properties of the solid phases are known. Except for magnesite thermophysical data from the mineral data base of Berman (1988) were used. A least squares objective function served to optimize parameters to P-V-T data. The enthalpy of formation of magnesite was revised on the basis of recent low pressure phase equilibrium experiments by Philipp (1988) to —1112.505 kj/mole. Piston-cylinder experiments were performed to constrain the equilibrium magnesite ⇌ periclase + CO₂ at high pressure. The equilibrium boundary is located at 12.1(±1) kbar, 1173-1183 °C (±10), and at 21.5(±1) kbar, 1375-1435 °C (±10). A van der Waals type equation of state with five adjustable parameters has been developed for CO₂. The function is smooth and continous above the critical region, behaves well in the high and low pressure limits, and the calculation of ʃ VdP for free energy does not require numerical integration. Computed free energies are consistent with all phase equilibrium data at high pressure, and computed volumes agree reasonably with P-V-T measurements. The proposed equation is: [ Equation omitted ] with B₁ = 28.0647, B₂ = 1.7287.10⁻⁴, B3 = 83653, A₁ = 1.0948.10⁹, A₂ = 3.3 7 47.10⁹, and R = 83.147, in units of Kelvin, bar and cm³/mole. The equation is recommended up to 50 kbar and above 400 K with reasonable extrapolation capabilities. A FORTRAN source code to evaluate the volume and fugacity is provided. Thermophysical properties for the calcium carbonate polymorphs calcite-I, IV, V, and aragonite were derived that are consistent with phase equilibrium experiments. Data required for further improvement include high pressure phase equilibria involving CO₂, constraints on the thermal expansion of magnesite, and P-V-T data to resolve inconsistencies among existing measurements. Water-carbon dioxide mixtures: The two widely used equations of state for H₂O-CO₂ mixtures are those proposed by Kerrick & Jacobs (1981) and by Holloway (1977)-Flowers (1979). Evaluation of existing equations and data is difficult due to inconsistencies among experimental studies. P-V-T-X data by Franck ＆ Todheide (1959) are inconsistent with data by Greenwood (1973) and Gehrig (1980), and cannot be reconciled with measured phase equilibria in H₂O-CO₂ fluid mixtures. Data by Greenwood and Gehrig are in loose agreement but extend only to 600 bar and do not constrain activities at higher pressures. A procedure is developed for using experimental phase equilibrium constraints to put limits on the fugacities of components of the fluid mixture. Inconsistencies among phase equilibrium studies are discussed. It is concluded that the data base available is not yet adequate to derive a reliable equation of state for H₂O-CO₂ mixtures. Future work must include P-V-T-X measurements to 8 kbar and phase equilibrium studies to resolve inconsistencies. These can constrain deviations from ideal mixing in the fluid phase, and constrain specific volumes at high pressures where P-V-T-X data connot be obtained. / Science, Faculty of / Earth, Ocean and Atmospheric Sciences, Department of / Graduate

No / A dynamic system with memory is a system for which knowledge of the equations of motion, together with the state at a given time instant t0 is insufficient to predict the evolution of the state at time instants t>t0. To calculate the response of systems with memory starting from an initial time instant t0, complete knowledge of the history of the system for t<t0 is needed. This is because the state vector does not contain all the information necessary to fully characterize the state of the system, i.e., the state vector of the system is not complete. In this paper, a state space formulation of viscoelastic systems with memory is proposed, which overcomes the concept of memory by enlarging the state vector with a number of internal variables that bear the information about the previous history of the system. The number of these additional internal variables is in some cases finite, in other cases, it would need to be infinite, and an approximated model has to be used with a finite number of internal variables. First a state space representation of the generalized Maxwell model is shown, then a new state space model is presented in which the relaxation function is approximated with Laguerre polynomials. The accuracy of the two models is shown through numerical examples.

Yes / 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.

No description available.

No description available.

Cette thèse de doctorat s’intéresse aux écoulements diphasiques métastables typiques de certains transitoires accidentels qui pourraient intervenir dans les centrales nucléaires. Ces phénomènes sont difficiles à traiter en raison de la complexité topologique de l’écoulement, des transferts entre phases et du couplage fort entre les caractéristiques thermodynamiques et les aspects mathématiques.Les méthodes aujourd’hui en usage dans l’industrie ne décrivent pas complétement la complexité de ces écoulements car elles s’appuient sur des modèles trop simples. En fait ces méthodes ne prennent pas en compte le déséquilibre thermo-chimique entre l’eau liquide et sa vapeur. Par ailleurs, les méthodes hyperboliques proposées récemment dans la littérature pour la simulation des écoulements métastables ne peuvent pas être appliquées dans l’industrie car elles utilisent des lois d’état simples qui ne sont pas adaptées pour les calculs industriels.Le but de cette thèse est de développer une nouvelle approche qui couple les méthodes hyperboliques modernes à des équations d’état précises. Le produit final de ce travail est un nouveau modèle pour l’analyse industrielle des écoulements diphasiques métastables qui associe de nouvelles techniques pour le calcul des transferts interfaciaux et des propriétés de l’eau et de sa vapeur. De plus, cette approche est d’un coût abordable pour les configurations industrielles.Les méthodes développées dans cette thèse ont été systématiquement vérifiées avec des solutions exactes et validées en utilisant des données expérimentales de la littérature. / This Ph.D. thesis deals with the metastable two-phase flows typical of accidental transients that could occur in nuclear power plants. Those phenomena are of difficult treatment due to the topological difficulty of the flow, the interphase transfers and the strong coupling between thermodynamic features and mathematical aspects.The methods today in use in industry do not fully describe the complexity of these flows because based on too simple models. In fact, they do not take into account the thermo-chemical disequilibrium between liquid and vapor water. On the other hand, the hyperbolic methods recently proposed in the literature for the simulation of metastable flows can not be used in the industry because based on simple equations of state that are not adequate for industrial calculations.The purpose of this Ph.D. thesis is to develop a new approach that couples the modern hyperbolic methods to accurate equations of state. The final product of this work is a new model for the industrial analysis of metastable two-phase flows that incorporates novel techniques for the calculation of interfacial transfers and of steam-water properties. Moreover, it is computationally affordable for its use in industrial configurations.The methods developed in this thesis have been sistematically verified against exact solutions and validated using experimental data of the literature.

<p>In this thesis, volumetric, optical and vibrational properties of H₂O were studied at high pressures by combining techniques of Raman spectroscopy, interferometry and optical imaging. Pressures up to 7 GPa were generated in the diamond anvil cell (DAC), entering the stability fields of liquid water and ices VI, VII and VIII. </p><p>A new integrated system for Raman, interferometric and optical-imaging studies has been built up. Utilizing the interferometric patterns formed between closely-spaced diamond anvils, the system allowed the complete monitoring and control of <i>pVT</i>-conditions of studied ices, as well as the determination of their dispersive properties in the visible range using the Airy equation and Cauchy formulation. This setup and technique thus represent a novel tool for the precise determination of equations of state (EOSs) of transparent materials, including fluids and low-Z materials. </p><p>Data-sets on thermal pressure were obtained from heating/cooling experiments carried out on the liquid water and used for checking the mutual consistency between published EOSs. A <i>pVT</i>-EOS for ice VIII and room temperature isotherms for ices VI and VII at 300 K were derived by combined methods of interferometry and imaging. While the agreement with the available EOSs of ices VII and VIII is very good, some inconsistent EOSs of ice VI were identified in the present study.</p><p>The technique of micro-Raman spectroscopy was applied for the monitoring of phase transformations, identification of various ice phases and for studying the response of vibrational symmetry modes to varying conditions. Analysis based on the combination of the <i>pT</i>-dependencies of the vibrational frequencies with the <i>pVT</i>-EOSs showed that, in the studied ices, the implicit volume-driven contributions dominate over the explicit phonon effects in the total temperature-induced changes in vibrational frequencies. The results provide valuable insight on the anharmonic effects and interactions in these molecular solids.</p>

In this thesis, volumetric, optical and vibrational properties of H2O were studied at high pressures by combining techniques of Raman spectroscopy, interferometry and optical imaging. Pressures up to 7 GPa were generated in the diamond anvil cell (DAC), entering the stability fields of liquid water and ices VI, VII and VIII. A new integrated system for Raman, interferometric and optical-imaging studies has been built up. Utilizing the interferometric patterns formed between closely-spaced diamond anvils, the system allowed the complete monitoring and control of pVT-conditions of studied ices, as well as the determination of their dispersive properties in the visible range using the Airy equation and Cauchy formulation. This setup and technique thus represent a novel tool for the precise determination of equations of state (EOSs) of transparent materials, including fluids and low-Z materials. Data-sets on thermal pressure were obtained from heating/cooling experiments carried out on the liquid water and used for checking the mutual consistency between published EOSs. A pVT-EOS for ice VIII and room temperature isotherms for ices VI and VII at 300 K were derived by combined methods of interferometry and imaging. While the agreement with the available EOSs of ices VII and VIII is very good, some inconsistent EOSs of ice VI were identified in the present study. The technique of micro-Raman spectroscopy was applied for the monitoring of phase transformations, identification of various ice phases and for studying the response of vibrational symmetry modes to varying conditions. Analysis based on the combination of the pT-dependencies of the vibrational frequencies with the pVT-EOSs showed that, in the studied ices, the implicit volume-driven contributions dominate over the explicit phonon effects in the total temperature-induced changes in vibrational frequencies. The results provide valuable insight on the anharmonic effects and interactions in these molecular solids.