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Neutron stars are stellar objects of extreme properties. The dense core enables usto study nuclear matter beyond saturation density. The exact composition of matterat such densities is not yet established, but the thermodynamic states of the matteris theoreticized by the Equation of State (EOS). The EOS cannot be derived analyt-ically and is dependent on constraints from neutron stars and nuclear experiments inlaboratories on earth. Recent advances in astrophysical experiments have probed newconstraints on the EOS by studying properties such as mass, radius and tidal deformabil-ity of neutron stars. Especially the possibility to detect gravitational waves from mergingbinary systems by the LIGO/VIRGO collaboration and the mass-radius measurementsby NICER have contributed a great deal. Constraints from terrestrial experiments havebeen derived by studying matter at supra saturation density in Heavy Ion Collisions andby determining the neutron skin thickness. In this work, an overview of neutron stars,dense matter and the EOS is presented. Further, results of studies aiming to determineand constrain the EOS are reviewed. Even though there is consensus about some neutronstar properties among different research groups, there are still major uncertainties as allresult depend on a relatively small set of observational data. Therefore, the EOS can stillbe considered to be far from precise and the knowledge of the true neutron star matterremains undisclosed.

In the past thirty years, the development of compositional reservoir simulators using various equations of state (EOS) has been addressed in the literature. However, the development of compositional thermal simulators in conjunction with EOS formulation has been ignored, in particular. Therefore in this work, a fully implicit, parallel, compositional EOS-based simulator has been developed. In this model, an equation of state is used for equilibrium calculations among all phases (oil, gas, and aqueous). Also, the physical properties are calculated based on an equation of state, hence obviating the need for using steam tables for calculation of water/steam properties. The governing equations for the model comprise fugacity equations between the three phases, material balance, pore volume constraint and energy equations. The governing partial differential equations are solved using finite difference approximations. In the steam injection process, the solubility of oil in water-rich phase and the solubility of water in oil phase can be high. This model takes into account the solubility of water in oil phase and the solubility of hydrocarbon components in water-rich phase, using three-phase flash calculations. This simulator can be used in various thermal flooding processes (i.e. hot water or steam injections). Since the simulator was implemented for parallel computers, it is capable of solving large-scale thermal flooding problems. The simulator is successfully validated using analytical solutions. Also, simulations are carried out to compare this model with commercial simulators. The use of an EOS for calculation of various properties for each phase automatically satisfies the thermodynamic consistency requirements. On the other hand, using the K-value approach, which is not thermodynamically robust, may lead to results that are thermodynamically inconsistent. This simulator accurately tracks all components and mass transfer between phases using an EOS; hence, it will produce thermodynamically consistent results and project accurate prediction of thermal recovery processes. Electrical heating model, Joule heating and in-situ thermal desorption methods, and hot-chemical flooding model have also been implemented in the simulator. In the electrical heating model, electrical current equation is solved along with other governing equations by considering electrical heat generation. For implementation of the hot-chemical heating model, first the effect of temperature on the phase behavior model and other properties of the chemical flooding model is considered. Next, the material and energy balance and volume constraints equations are solved with a fully implicit method. The models are validated with other solutions and different cases are tested with the implemented models. / text

The modelling of multi-phase water flow is an important modern-day design tool used by engineers to develop practical systems which are beneficial to society . Multi-phase water flow can be found in many important industrial applications such as large scale conventional and nuclear power systems, heat transfer machinery, chemical process plants, and other important examples. Because of many inherent complexities in physical two-phase flow processes, no generalised system of equations has been formulated that can accurately describe the two-phase flow of water at all flow conditions and system geometries. This has led to the development of many different models for the simulation of two-phase flow at specific conditions. These models vary greatly in complexity. The simplest model that can be used to simulate two-phase flow is termed the homogeneous equilibrium (HEM) two-phase flow model. This model has been found useful in investigations of choking and flashing flows, and as an initial investigative model used before the formulation of more complex models for specific applications. This flow model is fully de ned by three conservation equations, one each for mass, momentum and energy. To close the model, an equation of state (EOS) is required to deliver system pressure values. When solving the HEM, a general practice is to employ an equation of state that is derived from a fundamental expression of the second law of thermodynamics. This methodology has been proven to deliver accurate results for two-phase system simulations. This study focused on an alternative formulation of the equation of state which was previously developed for the time dependent modelling of HEM two-phase flow systems, termed the rate form of the equation of state (RFES). The goal of the study was not to develop a new formulation of the EOS, but rather to implement the RFES in a transient simulation model and to verify that this implementation delivers appropriate results when compared to the conventional implementation methodology. This was done by formulating a transient pipe and reservoir network model with the HEM, and closing the model using both the RFES and a benchmark EOS known to deliver accurate system property values. The results of the transient model simulations were then compared to determine whether the RFES delivered the expected results. It was found that the RFES delivered sufficiently accurate results for a variety of system transients, pressure conditions and numerical integration factors. / MIng (Nuclear Engineering), North-West University, Potchefstroom Campus, 2014

The modelling of multi-phase water flow is an important modern-day design tool used by engineers to develop practical systems which are beneficial to society . Multi-phase water flow can be found in many important industrial applications such as large scale conventional and nuclear power systems, heat transfer machinery, chemical process plants, and other important examples. Because of many inherent complexities in physical two-phase flow processes, no generalised system of equations has been formulated that can accurately describe the two-phase flow of water at all flow conditions and system geometries. This has led to the development of many different models for the simulation of two-phase flow at specific conditions. These models vary greatly in complexity. The simplest model that can be used to simulate two-phase flow is termed the homogeneous equilibrium (HEM) two-phase flow model. This model has been found useful in investigations of choking and flashing flows, and as an initial investigative model used before the formulation of more complex models for specific applications. This flow model is fully de ned by three conservation equations, one each for mass, momentum and energy. To close the model, an equation of state (EOS) is required to deliver system pressure values. When solving the HEM, a general practice is to employ an equation of state that is derived from a fundamental expression of the second law of thermodynamics. This methodology has been proven to deliver accurate results for two-phase system simulations. This study focused on an alternative formulation of the equation of state which was previously developed for the time dependent modelling of HEM two-phase flow systems, termed the rate form of the equation of state (RFES). The goal of the study was not to develop a new formulation of the EOS, but rather to implement the RFES in a transient simulation model and to verify that this implementation delivers appropriate results when compared to the conventional implementation methodology. This was done by formulating a transient pipe and reservoir network model with the HEM, and closing the model using both the RFES and a benchmark EOS known to deliver accurate system property values. The results of the transient model simulations were then compared to determine whether the RFES delivered the expected results. It was found that the RFES delivered sufficiently accurate results for a variety of system transients, pressure conditions and numerical integration factors. / MIng (Nuclear Engineering), North-West University, Potchefstroom Campus, 2014

Thesis (MEng)--Stellenbosch University, 2015. / ENGLISH ABSTRACT: Long-chain hydrocarbons are of value to numerous lucrative industries. Due to the low volatility and close melting and boiling points of these solutes, traditional fractionation methods lack the required selectivity for separation and cause thermal degradation of the product. This project investigates the feasibility of Supercritical Fluid Extraction (SFE) for processing these systems, with the primary objective of modelling the high-pressure vapour-liquid equilibrium (VLE) properties of hydrocarbon solutes with a light-weight solvent using a semiempirical equation of state (EOS). Pure component vapour pressures and saturated liquid volumes are also investigated. A thorough investigation into the phase behaviour of the n-alkanes, 1-alcohols, carboxylic acids and esters in light weight supercritical solvents CO2, ethane and propane revealed that the solute structure and temperature largely influence the solute solubility and process feasibility. Good selectivity amongst the various solutes was observed for all three solvents, but very high pressures were required for complete miscibility using CO2 (exceeding 30 MPa). The quadrapole moment of CO2 further leads to complexities in phase behaviour such as temperature and density inversions (CO2/alkanes and CO2/alcohols) and 3-phase regions within the operating range. Simple linear trends in pressure vs. carbon number and temperature were observed for all the considered series using ethane and propane and these solvents were thus selected for conducting the modelling for this study. A thorough review of semi-emperical EOS models from literature revealed that the simple cubic equations of state (CEOSs) provide a promising modelling approach for SFE applications due to their simplicity, flexibility and reliability. The simple Peng-Robinson (PR) and Soave-Redlich-Kwong (SRK) EOSs provide good correlation of vapour pressure (%AAD below 5 %) for all the series over a large carbon number range (up to nC20), provided a two parameter alpha function is used. A 3rd parameter in the volume dependence for Patel-Teja (PT) EOS provides considerable improvement over the PR and SRK EOSs for satureate liquid volume correlations of the non-polar solutes (alkanes and esters), but offers virtually no advantage for the more polar alcohols and acids. The CEOSs therefore suffer clear limitations in simultaneous representation of these saturation properties (vapour pressure and liquid molar volume) for the systems of interest. Good correlations of high pressure binary VLE data were obtained using CEOSs available in the Aspen Plus ® simulator (% AAD in P, T and X2 generally below 1 % and ranging from 4 to 12 % for Y2 for all series) provided that two binary interaction parameters (BIPs) are used in the model mixing rules, irrespective of the model used. Aspen Plus ® was further validated as a reliable thermodynamic tool by comparing model fits using the RK-ASPEN model with parameters obtained from the Aspen Plus ® data regression routine and computational methods used in self-developed MATLAB software. Very similar results were obtained for both computational methods, which encourages the use of Aspen Plus ® for process modelling in SFE applications. A statistical sensitivity analysis into the relative effect and interactions between 6 modelling factors in applying the CEOSs revealed that the mixing rules, temperature and solute structure had the largest effect on the correlation of the high pressure VLE, with the pure component limit having negligible effect once BIPs are fitted to data. A significant interaction was, however, observed between the pure component model and the solute structure and temperature, which suggest that accurate correlation of mixture VLE does not solely rely on appropriate mixing rule selection, but also the pure model. Binary interaction parameters (BIPs) in model mixing rules were found to become intercorrelated when more than one are used, greatly impeding the development of generalized correlations. BIPs were also found to be sensitive to the pure component limit (alpha function and pure constants used), the temperature, the combining rules used and possibly the fluid density. These factors should all be taken into account systematically for developing generalized correlations which therefore fell outside the scope of this study. Recommendations were, however, made on how the MATLAB software developed in this study can be used to both expand the size of the statistical analysis already conducted into relevant modelling factors and to develop new generalized correlations for BIPs and new mixing rules. / AFRIKAANSE OPSOMMING: Lang-ketting koolwaterstowwe is van waarde in talle winsgewende industriële toepassings. Vanweë die lae vlugbaarheiden ooreenstemmende kook- en smeltpunte van hierdie molekules, toon tradisionele fraktioneringsmetodes nie die nodige selektiwiteit vir ekstraksie nie en veroorsaak bonop termiese degradering van die produk. Hierdie projek ondersoek dus die lewensvatbaarheid van superkritiese ekstraksie vir die prosesering van hierdie sisteme, met primêre fokus op die modellering van die hoë-druk damp-vloeistof ewewig eienskappe van koolwaterstowwe opgelos in ‘n lae-massa oplosmiddel met gebruik van ‘n semi-empiriese toestandsvergelyking. Suiwer-komponent dampdrukke en versadigde vloeistof volumes word ook ondersoek. ‘n Deeglike ondersoek na die fasegedrag van die n-alkane, 1-alkohole, korboksiel-sure asook esters in lae-massa superkritiese oplosmidds CO2, etaan en propaan toon dat die struktuur van die opgeloste stof en die temperatuur ‘n groot invloed het op die oplosbaarheid en proses lewensvatbaarheid. Goeie selektiwiteit tussen die verskillende koolwaterstowwe was waargeneem vir al drie oplosmiddels, alhoewel baie hoë drukke nodig was vir totale vermenging van die fases in CO2 (hoër as 30 MPa). Die quadrupool moment van CO2 veroorsaak verder ongewenste kompleksiteite in fase gedrag soos temperatuuren digtheid inversies (CO2/alkane en CO2/alkohole) en 3-fase-gebiede in die bedryfs-kondisies. Eenvoudige lineêre tendense in druk tenoor die koolstofnommer van die opgeloste stof asook die temperatuur was waargeneem vir al die ondersoekte koolwaterstof reekse in etaan en propaan en hierdie oplosmiddels was dus gekies vir die modellering vir hierdie studie. 'n Deeglike oorsig van semi-empiriese toestandsvergelykings uit die literatuur het getoon dat die eenvoudige kubiese toestandsvergelykings ‘n belowende modelleringsbenadering bied vir superkritiese ekstraksie toepassings vanweë hul eenvoudigeid, buigsaamheid enbetroubaarheid. Die eenvoudige Peng-Robinson (PR) en Soave-Redlich-Kwong (SRK) toestandsvergelykings bied goeie korrelasie van suiwer dampdruk (foute laer as 5 %) vir alle koolwaterstowwe oor ‘n groot koolstofnommer gebied (tot by nC20), met die voorwaarde dat ‘n 2 parameter alpha funksie gebruik word. ‘n 3rde parameter in die volume afhanklikheid van die Patel-Teja (PT) toestandsvergelyking bied ‘n beduidende verbetering in die passing van die versadigde vloeistof volume vir die nie-polêre koolwaterstowwe (n-alkane en die esters), maar bied geen voordeel vir die meer polêre alkohole en karkoksiel sure nie. Die kubiese modelle toon dus duidelike beperkings vir die gelyktydige voorstelling van hierdie versadigingde eienskappe (dampdruk en vloeistof volume) vir die sisteme van belang. Goeie korrelasie van hoë druk binêre damp-vloeistof ewewig data was verkry deur gebruik van die kubiese toestandsvergelykings beskikbaar inAspen Plus ® (fout in P, T en X2 tipies laer as 1 % en van 4 tot 12 % vir Y2 vir alle sisteme), met die voorwaarde dat 2 binêre interaksie parameters gebuik word in die model mengreëls, onafhanklik van die model. Aspen Plus ® was verder bekraktig as ‘n betroubare termodinamiese hulpmiddel deur model passings te vergelyk met die RK-ASPEN model tussen gevalle waar parameters verkry is deur die beskikbare regressie metode in Aspen Plus ® en metodes gebruik in self-ontwikkelde MATLAB sagteware. Eenderse resultate was verkry vir beide berekeningsmetodes, wat die gebruik van Aspen Plus ® vir prosesmodellering in superkritiese ekstrasie toepassings aanmoedig. ‘n Satistiese sensitiwiteits analise op die relatiewe effek en interaksies tussen 6 modelleringsfaktore in die toepassing van die kubiese toestandsvergelykings het gevind dat die mengreëls, temperatuur en die stuktuur van die opgeloste stof die grootste effek op die korrelasie van hoë druk binêre damp-vloeistof ewewig het, met ‘n weglaatbare effek vandie suiwerkomponent limiet waargeneem sodra binêre interaksie parameters gepas is aan data. ‘n Beduidende interaksie was wel waargeneem tussen die suiwerkomponent model en die struktuur van die opgeloste stof asook die temperatuur, wat daarop dui dat akurate korrelasie van mengsel damp-vloeistof ewewig nie slegs afhanklink is van ‘n gepaste keuse van mengreëls nie, maar ook die suiwer-komponent model. Binêre interaksie parameters in die model mengreëls ondergaan inter-korrelasie wanneer meer as een interaksie parameter gebruik word, wat die ontwikkeling van algemeen toepaslike korrelasies grotendeels belemmer. Binêre interaksie parameters was ook bevind om sensitief te wees tot die suiwer component limiet (alpha funksie en suiwer konstantes wat gebruik is), die temperatuur, die kombineringsreëls en moontlik die vloeistof digtheid. Hierdie faktore moet dus almal sistematies in ag geneem word wanneer algemeen toepaslike korrelasies ontwikkel word, wat dus buite die omvang van die huidge studie val. Aanbevelings was wel gemaak vir hoe die MATLAB sagteware ontwikkel vir hierdie studie gebruik kan word om beide die betaande statistiese analise uit te brei, asook nuwe korrelasies vir binêre interaksies parameters en nuwe mengreëls te ontwikkel.

The response of materials under extreme temperature and pressure conditions is a topic of great significance because of its relevance in astrophysics, geophysics, and inertial confinement fusion. In recent years, environments exceeding several hundred gigapascals in pressure have been produced in the laboratory via laser-based dynamic loading techniques. Shock-loading is of particular interest as the shock provides a fiducial for measuring time-dependent processes in the lattice such as phase transitions. Time-resolved x-ray diffraction is the only technique that offers an insight into these shock-induced processes at the relevant spatial (atomic) and temporal scales. In this study, nanosecond resolution x-ray diffraction techniques were developed and implemented towards the study of shock-induced phase transitions in polycrystalline materials. More specifically, the capability of a focusing x-ray diffraction geometry in high-resolution in situ lattice measurements was demonstrated by probing shock-compressed Cu and amorphous metallic glass samples. In addition, simultaneous lattice and free surface velocity measurements of shock-compressed Mg in the ambient hexagonal close packed (hcp) and shock-induced body centered cubic (bcc) phases between 12 and 45 GPa were performed. These measurements revealed x-ray diffraction signals consistent with a compressed bcc lattice above a shock pressure of 26.2±1.3 GPa, thus capturing for the first time direct lattice evidence of a shock-induced hcp to bcc phase transition in Mg. Our measurement of the hcp-bcc phase boundary in Mg was found to be consistent with the calculated boundary from generalized pseudopotential theory in the pressure and temperature region intersected by the principal shock Hugoniot. Furthermore, the subnanosecond timescale of the phase transition implied by the shock-loading conditions was in agreement with the kinetics of a martensitic transformation. In conclusion, we report on the progress and future work towards time-resolved x-ray diffraction measurements probing solid-liquid phase transitions in high Z polycrystalline materials, specifically Bi. / text

<p>In this thesis, material properties have been examined under extreme conditions in computer-based calculations.</p><p>The research on iron (Fe), nickel (Ni), and ferropericlase (Mg_1-xFe_xO) are not only important for our understanding of the Earth, but also for an improved knowledge of these materials <i>per se</i>.</p><p>An embedded-atom model for Fe demonstrated to reproduce properties such as structure factors, densities and diffusion constants, and was employed to evaluate temperature gradients at Earth core conditions. A similar interaction together with a two-temperature method was applied for the analysis of shock-induced melting of Ni. For Mg_1-xFe_xO, the magnetic transition pressure was shown to increase with iron content. Furthermore, the C₄₄ softening with pressure and iron composition supports the experimentally observed phase transition for Mg_0.8Fe_0.2O at 35 GPa.</p><p>The properties of high density helium (He) is of great interest as the gas is one of the most abundant elements in the solar system. Furthermore, He and neon (Ne) are often used as pressure media in diamond anvil cells. The melting of He showed a possible fcc-bcc-liquid transition starting at T=340 K, P=22 GPa with a Buckingham potential, whereas the bcc phase was not seen with the Aziz form. For Ne, Monte Carlo calculations at ambient pressure showed very accurate results when extrapolating the melting temperatures to an infinite cluster limit. At high pressure, a one-phase <i>ab initio</i> melting curve showed a match with one-phase L-J potential results, which could imply a correspondence between <i>ab initio</i>/classical one-phase/two-phase calculations.</p><p>In the search for hard materials, <i>ab initio</i> calculations for four TiO₂ phases were compared. Just as imposed by experiment, the cotunnite phase was found to be very hard. The anomalous elastic behavior of the superconducting group-<i>V</i> metals V, Nb, Ta was found to be related to shrinking nesting vectors and the electronic topological transition (ETT).</p>

High-pressure solution behavior such as density and phase behavior is a critical fundamental property for the design and optimization of various chemical processes, such as distillation and extraction in the production and purification of oils, polymers, and other natural materials. In this PhD study, solution behavior data are experimentally determined and equation of state (EoS) modeled for n-hexadecane, n-octadecane, n-eicosane, methylcyclohexane, ethylcyclohexane, cis-1,2-dimethylcyclohexane, cis-1,4-dimethylcyclohexane, trans-1,4-dimethylcyclohexane, o-xylene, m-xylene, p-xylene, and 2-methylnaphthalene at temperatures to 525 K and pressures to 275 MPa. A variable-volume view cell coupled with a linear variable differential transformer is used for the high-pressure determination. The reported density data are less than 0.4% of available literature data, which is within the estimated accumulated experimental uncertainty, 0.75%. Special attention is paid to the effect of architectural differences on the resultant high-pressure solution behavior. The reported data of low molecular weight hydrocarbons are modeled with Peng-Robinson (PR) equation of state (EoS), high-temperature high-pressure volume-translated cubic (HTHP VT-cubic) EoS, and perturbed-chain statistical fluid theory (PC-SAFT) EoS. The three pure-component parameters in PC-SAFT EoS can be either obtained from literature or from a group contribution (GC) method. Generally, PR EoS gives the worst predictions and HTHP VT-cubic EoS provides modest improvements over the PR EoS, but both of the equations underpredict the densities at high pressures. On the other hand, PC-SAFT EoS, with parameters from the literature or from a GC method, gives the improved density predictions with respect to PR EoS and HTHP VT-cubic EoS, although an overprediction of densities is found at high pressures. Model calculations also highlight the capability of these equations to account for the different densities observed for the hydrocarbon isomers. However, none of the EoS investigated in this study can fully account for the effect of isomeric structural differences on the high-pressure densities. For a better prediction of densities at high pressures, a new set of PC-SAFT pure-component parameters are obtained from a fit of the experimental density data obtained in this study and the mean absolution percent deviation is within 0.4%. The experimental technique and PC-SAFT EoS modeling method are extended to a star polymer-propane mixture. Star polymers with a fixed number of arms have a globular structure that does not promote chain entanglements. Star polymers can be synthesized with a large number of functional groups that can be readily modified to adjust their physical properties for specific applications in the areas of catalysis, coatings, lubrication, and drug delivery. In this study, a star polymer with a divinylbenzene core and statistically random methacrylate copolymer arms is synthesized with reversible addition-fragmentation-transfer method and fractionated with supercritical carbon dioxide and propane to obtain fractions with low molecular weight polydispersity. The phase behavior and density behavior are experimentally determined in supercritical propane for fractionated star polymers and the corresponding linear copolymer arms at temperatures to 423 K and pressures to 210 MPa. Experimental data are presented on the impact of the molecular weight, the backbone composition of the lauryl and methylmethacrylate repeat units in the copolymer arms, and the DVB core on the polymer-propane solution behavior. The star polymer is significantly more soluble due to its unique structure compared with the solubility of the linear copolymer arms in propane. The resultant phase behavior for the two homopolymers and the copolymers in propane are modeled using the PC-SAFT and copolymer PC-SAFT EoS, which give reasonable predictions for both phase behavior and density behavior. Model calculations are not presented for the phase behavior of the star polymers in propane since the PC-SAFT approach is not applicable for star polymer structures.

We present Chandra/ACIS-S subarray observations of the quiescent neutron star (NS) low-mass X-ray binaries X7 and X5 in the globular cluster 47 Tuc. The large reduction in photon pile-up compared to previous deep exposures enables a substantial improvement in the spectroscopic determination of the NS radius and mass of these NSs. Modeling the thermal emission from the NS surface with a non-magnetized hydrogen atmosphere and accounting for numerous sources of uncertainties, we obtain for the NS in X7 a radius of R = 11.1(-0.7)(+0.8) km for an assumed stellar mass of M = 1.4 M-circle dot (68% confidence level). We argue, based on astrophysical grounds, that the presence of a He atmosphere is unlikely for this source. Due to the excision of data affected by eclipses and variable absorption, the quiescent low-mass X-ray binary X5 provides less stringent constraints, leading to a radius of R = 9.6(-1.1)(+0.9) km, assuming a hydrogen atmosphere and a mass of M. =. 1.4 Me. When combined with all existing spectroscopic radius measurements from other quiescent low-mass X-ray binaries and Type I X-ray bursts, these measurements strongly favor radii in the 9.9-11.2 km range for a similar to 1.5 M-circle dot NS and point to a dense matter equation of state that is somewhat softer than the nucleonic ones that are consistent with laboratory experiments at low densities.