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Multi-Phase Systems
Published in Marc J. Assael, Geoffrey C. Maitland, Thomas Maskow, Urs von Stockar, William A. Wakeham, Stefan Will, Commonly Asked Questions in Thermodynamics, 2022
Marc J. Assael, Geoffrey C. Maitland, Thomas Maskow, Urs von Stockar, William A. Wakeham, Stefan Will
Close to the critical point there is a characteristic opalescence (cloudiness) in the fluid; this arises because the correlation length or mean distance over which the molecules’ order increases by several orders of magnitudes from about 1 nm through the wavelengths of visible light (between about 380 to 780 nm) and these correlated fluctuations scatter the light.
Properties of Pure Substances
Published in Kavati Venkateswarlu, Engineering Thermodynamics, 2020
If the heating of water at different pressures is considered and phase change processes are plotted, T-v diagram as shown in Figure 4.5 is obtained. It can be observed from Figure 4.5 that the shape of the T-v diagram of a pure substance is much similar to that of the p-v diagram except that the constant pressure lines have an upward trend. The specific volume of saturated water decreases as the pressure increases. The saturation line, joining the saturated liquid and saturated vapor, narrows as the pressure increases and it becomes a point when the pressure is 220.06 bar. At this point, both saturated liquid and saturated vapor become identical and is called the critical point. The properties such as pressure, temperature, and specific volume of a substance at the critical point are called critical pressure, critical temperature, and critical specific volume, respectively. For water, these properties are 220.6 bar, 373.95°C, and 0.003106 m3/kg respectively. Table 4.1 shows the critical pressure and critical temperature data of various substances.
Changes of phase: background theory
Published in Michael de Podesta, Understanding the Properties of Matter, 2020
However, for the material present in the liquid phase, the molar volume does not vary so dramatically. In general the volume of liquid held on the co-existence curve increases slightly with temperature. The critical point refers to a point along the co-existence curve at which the volumes of the liquid and gas phases become equal. At this point it becomes impossible to distinguish between the two phases
Theory of supercritical flames with real-fluid equations of state
Published in Combustion Theory and Modelling, 2021
Recognising that higher efficiency and lower emissions of certain pollutants can be achieved at elevated pressures, and that internal combustion engines [1], including gas turbines and rocket engines [2], all operate at elevated pressures, it is of both fundamental and practical interest to investigate the flame response under such conditions. Specifically, an important aspect of high-pressure flame dynamics is the existence of the supercritical state [3], in that when the (local) state of the mixture is near/beyond its critical pressure and temperature, substantial real-fluid effects, which are fundamentally different from the conventional ideal gas or liquid properties, will emerge. For example, phase transition between liquid and gas disappears, with the continuous transition occurring in the phase diagram. Near the critical points, small changes in pressure and temperature could result in large variations in density and other properties.
Critical point calculations by numerical inversion of functions
Published in Chemical Engineering Communications, 2021
C. N. Parajara, G. M. Platt, F. D. Moura Neto, M. Escobar, G. B. Libotte
Critical point calculations have been extensively studied in Chemical Engineering field, since important thermodynamic phenomena and separation operations are dependent on the accurate values for the critical coordinates; for instance, the behavior of oil reservoirs (Peters et al. 1988) and supercritical extraction processes (Raeissi 2004). In this scenario, two methodologies have been largely employed in the last decades: the method of Hicks and Young (1977) and the algorithm of Heidemann and Khalil (1980). The methodology proposed by Heidemann and Khalil is particularly interesting, since the calculation of critical points is represented by a nonlinear algebraic system, to be solved for critical temperature and molar volume in a double-loop structure. Thus, the large quantity of algorithms capable to solve nonlinear sytems can be used (and tested) to solve the problem, such as Newton-type algorithms (Deuflhard 2011) or even stochastic optimization methods (also called metaheuristics; in this case, the nonlinear algebraic system is usually converted into a scalar merit function, to be minimized) (Nichita and Gomez 2010). Both methodologies are extremely useful in most cases (for the Newton-type methods, when the nonlinearity of the problem is not sufficient to demand extremely precise initial estimates). On the other hand, there are some occasions where more robust methods must be employed.
Resource degradation of pharmacy sludge in sub-supercritical system with high degradation rate of 99% and formic acid yield of 32.44%
Published in Environmental Technology, 2023
Yuwei Zhang, Hengxi Zhu, Junjiang Guo, Weizhen Liu, Jiang Qi, Guan Qingqing, Bin Li, Ping Ning
With the change of temperature and pressure, the substance would change between various phases. There is a critical point in the process of phase transition. The supercritical system refers to a state where the temperature and pressure of a substance are above this critical point. The sub-supercritical system refers to the state close to the critical point.