Critical pressure thermophysical properties

An important question for any modeling effort, especially one aimed at a quantitative description of complex transport processes, is the level of accuracy of the model. As will become evident in the discussion of transport models and specific calculations, the values for thermophysical properties and transport coefficients must be known, as well as the dependence of these coefficients on temperature and pressure. Information is lacking for this data base. Critical material properties for semiconductor materials are not known... 

In order to maximize the value of the applied thermodynamics system throughout the enterprise, it must be accessible to all process engineers and chemists who require accurate thermophysical property calculations in their daily work. Web applications, which do not require installation of the calculation engine on the user s computer, facilitate ea.sy access to the system. Web applications can be designed to provide pure component data such as normal boiling point and critical properties. They can also provide access to the most frequently carried out calculations, such as phase equilibrium calculations, tabulation, and plotting of pure component properties as a function of temperature and pressure, and mixture property calculations. 

Values reproduced or converted from a tabulation by Tsykalo and Tabachnikov in V A. Rabinovich (ed.), Thermophysical Properties of Gases and Liquids, Standar-tov, Moscow, 1968 NBS-NSF transl. TT 69-55091,1970. The reader may be reminded that very pure hydrogen peroxide is veiy difficult to obtain owing to its decomposition or instability, c = critical point. The FMC Corp., Philadelphia, PA tech. bull. 67, 1969 (100 pp.) contains an enthalpy-pressure diagram to 3000 psia, 1100 K. 

Values extracted and in some cases rounded off from those cited in Rabinovich (ed.). Thermophysical Properties of Neon, Argon, Krypton and Xenon, Standards Press, Moscow, 1976, This source contains values for the compressed state for pressures up to 1000 bar, etc, m = melting point c = critical point. The notation 2,642,-4 signifies 2,642 x 10 , This book was published in English translation by Hemisphere, New York, 1988 (604 pp,). 

Equations (16.135) with conditions according to Eq. (16.136) are then solved numerically. As an example, we consider a binary mixture consisting of methane (90%) and propane (10%). The mean molecular mass of this mixture is Mg = 18.84 kg kmol . Its thermophysical properties can be determined with the aid of methods for multicomponent mixtures [9-11]. In particular, for mixtures, the critical values of temperature and pressure (referred to as pseudo-... 

For the description of thermophysical properties, estimation methods based on the three parameter corresponding states principle mostly employ the critical temperature (Tc), the critical pressure (Pc), and the acentric factor (co) as characteristic... 

In this book, published experimental data, tables, and equations for four freons are systematized and critically assessed. The freons of the methane series are freon-20, 21, 22, 23. Based on the analysis of the most reliable data, the authors compiled equations from which comprehensive tables of thermophysical properties of the said substances are computed in a temperature interval from normd boiling point to 473 K and in a pressure interval from 0.1 to 20 MPa. The overwhelming majority of these tables are published for the first time. 

Coefficients of the equadon of state and of the equation for transport properties are stored for each substance. Parameters of the critical point and coefficients of equations for calculadon of the ideal-gas functions, the saturated vapor pressure and the melting pressure are kept also. The thermal properties in the single-phase region and on the phase-equilibrium lines can be calculated on the basis of well-known relations with use of these coefficients. The system contains data for 30 reference substances monatomic and diatomic gases, air, water and steam, carbon dioxide, ammonia, paraffin hydrocarbons (up to octane), ethylene (ethene), propylene (propene), benzene and toluene. The system can calculate the thermophysical properties of poorly investigated gases and liquids and of multicomponent mixtures also on the basis of data for reference substances. 

Pioro, I., Mokry, S., Draper, S., 2011. Specifics of thermophysical properties and forced-convective heat transfer at critical and supercritical pressures. Reviews in Chemical Engineering 27 (3—4), 191—214. 

Therefore, the most widely used supercritical fluids as of today and possibly in the future are water, carbon dioxide, helium, and refrigerants. Often, refrigerants, similar to carbon dioxide, are considered as modeling fluids instead of water due to significantly lower critical pressures and temperatures (for example, R-134a Per = 4.0593 MPa Per = 101.06°C), which decreases the complexity and costs of thermal hydraulic experiments. Based on the above mentioned, knowledge of thermophysical properties specifics at critical and supercritical pressures is very important for safe and efficient use of fluids in power and other industries. 

Figs. A3.5—A3.12 show variations in the basic thermophysical properties of water at three subcritical pressures [all (a) figures] (1) 7 MPa—usual operating pressure of boiling water reactors (BWRs) and many Ranldne steam turbine cycles in pressurized water reactor (PWR), BWR, and RBMK NPPs (2) 11 MPa—usual inlet pressure for CANDU reactors and (3) 15 MPa—usual pressure for PWRs and the critical (Per = 22.064 MPa) and four supercritical pressures (P = 25, 30, 35, and 40 MPa) [all (b) figures]. The range of critical and supercritical pressures covers current range... 

It should be noted that thermophysical properties of 121 pure fluids, including water, carbon dioxide, helium, refrigerants, etc. 5 pseudo-pure fluids (such as air) and mixtures with up to 20 components at different pressures and temperatures, including critical and supercritical regions, can be calculated using the NIST REFPROP software (2010), Version 9.1. 

Analysis of profiles shown in Figs. A3.5—A3.12 for subcritical water [figures (a)] and critical/supercritical water [figures (b)] shows similar trends. However, for subait-ical water, there are two different values of any thermophysical property on the saturation line one for liquid and one for vapor (steam). However, for example, at pressure of 7 MPa, values of specific heat of water (5.4025 kJ/kg K) and steam (5.3566 kJ/kg K) can be very close (see Fig. A3.9(a)). Also, it can be clearly seen that pressure has almost negligible effect of liquid properties. Just closer to the saturation line, some small differences can be seen in property profiles at various pressures. 

Supercritical fluids are used intensively in various industries. Therefore, understanding specifics of thermophysical properties and their behavior at critical and supercritical pressures is an important task. Supercritical fluids are considered as single-phase substances in spite of significant variations of all thermophysical properties within critical or pseudocritical regions. Some of these variations in thermophysical properties are similar to those at subcritical pressures during crossing of the saturation line. 

The majority of empirical correlations were proposed in the 1960s—1970s (Pioro and Duffey, 2007), when experimental techniques were not at the same level (ie, advanced level) as they are today. Also, thermophysical properties of water have been updated since that time (eg, a peak in thermal conductivity in critical and pseudocritical points within a range of pressures from 22.1 to 25 MPa for water (see Appendix A3) was not officially recognized until the 1990s). 

Eq. [A4.4] is applicable for subcritical and supercritical pressures. However, adjustment of this expression to conditions of supercritical pressures, with singlephase dense gas and significant variations in thermophysical properties near the critical and pseudocritical points, was the major task for the researchers and scientists. In general, two major approaches to solve this problem were taken an analytical approach (including numerical approach) and an experimental (empirical) approach. 

Technical Appendices, which provides readers with additional information and data on current nuclear power reactors and NPPs thermophysical properties of reactor coolants, thermophysical properties of fluids at suhcritical and critical/supercritical pressures, heat transfer and pressure drop in forced convection to fluids at supercritical pressures, world experience in nuclear steam reheat, etc. 

On a different note, after some 50 years of intensive research on high-pressure shock compression, there are still many outstanding problems that cannot be solved. For example, it is not possible to predict ab initio the time scales of the shock-transition process or the thermophysical and mechanical properties of condensed media under shock compression. For the most part, these properties must presently be evaluated experimentally for incorporation into semiempirical theories. To realize the potential of truly predictive capabilities, it will be necessary to develop first-principles theories that have robust predictive capability. This will require critical examination of the fundamental postulates and assumptions used to interpret shock-compression processes. For example, it is usually assumed that a steady state is achieved immediately after the shock-transition process. However, due to the fact that... 

Thermophysical and transport properties are presented for water. The results include physical constants, critical values, vapor pressure, density of liquid, enthalpy of vaporization, surface tension, heat capacity, viscosity, and thermal conductivity. Both gas and liquid are covered. The coefficients for property values as a function of temperature are provided in an easy to use tabular format. 

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