Thermodynamic critical point

Fluids both above and below their thermodynamic critical point in condensing two-phase flow can be handled under this case as well. 

The single-component fluid is far from its thermodynamic critical point (T, < 0.9Tct or PI < 0.5Pcr). Note the or if the relieving temperature, for example, is equal to the critical temperature but the relieving pressure is below 50% of the critical pressure, then the condition is verified. 

The single-component fluid is far from its thermodynamic critical point (Tj < 0.9TcrorP1 < 0.5PCT). 

In general, any substance that is above the temperature and pressure of its thermodynamic critical point is called a supercritical fluid. A critical point represents a limit of both equilibrium and stability conditions, and is formally delincd as a point where the first, second, and third derivatives of the energy basis function for a system equal zero (or, more precisely, where 9P/9V r = d P/dV T = 0 for a pure compound). In practical terms, a critical point is identifled as a point where two or more coexisting fluid phases become indistinguishable. For a pure compound, the critical point occurs at the limit of vapor-Uquid equilibrium where the densities of the two phases approach each other (Figures la and lb). Above this critical point, no phase transformation is possible and the substance is considered neither a Uquid nor a gas, but a homogeneous, supercritical fluid. The particular conditions (such as pressure and temperature) at which the critical point of a substance is achieved are unique for every substance and are referred to as its critical constants (Table 1). 

A supercritical fluid (SCF) is any substance at a temperature and pressure above its thermodynamic critical point. Such a fluid can diffuse through soHds such as a gas and dissolve materials such as a liquid. Carbon dioxide and water are the most commonly used SCFs. 

An exothermic mixture usually leads to mixing in all proportions. This is the case for water and ethanol. If the mixing is endothermic, the number of coexisting phases and their composition depend on temperature. Increasing the temperature usually results in an increase in the mutual solubility of the two compounds, eventually leading to complete miscibility above a critical temperature, the upper consolute temperature (UCT). Note that some abnormal systems can also have a lower consolute temperature (LCT). Both UCT and LCT are thermodynamic critical points. At a critical point, the compositions of the two phases in equilibrium become identical. 

SFC is the application of a supercritical fluid, any substance at a temperature and pressure above its thermodynamic critical point (Figure 9.2) with both gas- and liquid-like abilities to diffuse through solids, and dissolve materials, respectively, as the mobile phase in the chromatographic process. The most widely used mobile phase for SFC is carbon dioxide because of its low critical pressure (73 atm), low critical temperature (31°C), inertness, low toxicity, and high purity at low cost [12,13], Historically there were two approaches in developing modern SFC the use of either the packed and microbore columns designed for HPLC application or the open-tubular capillary GC type columns [13,14], The conventional packed HPLC... 

Supercritical solvents, compounds at a temperature and pressure above their thermodynamic critical points, are interesting reaction media because their properties,... 

It may be pointed out that the statements of this section are applicable to any fluid exhibiting a thermodynamic critical point and the corresponding two-phase behavior below this point,... 

As noted by [7], in many high-pressure spray applications, the drop phase approaches the thermodynamic critical point where Oh increases rapidly. At elevated Oh, the observed breakup modes remain the same, but experiments have shown an increase in the transitional We and breakup times. 

A supercritical fluid is defined as one that is above its thermodynamic critical point, as identified by the critical pressure (p ) and critical temperature (Tc). Supercritical fluid behavior can be peculiar because of the variation of theimophysical properties such as density and specific heat near and at the critical point. Supercritical fluids have some properties similar to liquids (e.g., density), and some properties that are comparable to those of gases (e.g., viscosity). Thus, they cannot be considered either a liquid or a gas. 

Supercritical fluid, especially supercritical water (SCW), that is above the thermodynamic critical point of water (374"C, 22.1 MPa), has attracted increasing attention in various applications, such as in supercritical water oxidation (SC WO), in supercritical water gasification (SCWG), and for the continuous synthesis of nanoparticles. The environment of reactors presents a big challenge for structural materials used in the components. Many kinds of materials including stainless steel, alloys, and ceramics have been studied for using in SCW atmosphere. However, the details of the corrosion mechanism of each ceramic in an SCW environment were not fully clarified. 

Internal gravitational waves near thermodynamic critical point 239... 

Internal Gravitational Waves Near Thermodynamic Critical Point... 

The created experimental setups allowed to investigate for the first time the dynamics of internal gravitational waves near thermodynamical critical point. 

The SCWR is composed of a high-temperature, high-pressure, water-cooled reactor, which operates above the thermodynamic critical point of water (22.1 MPa, 374° C) to achieve a high thermal efficiency. Since the coolant does not change phase in the SCWR, the balance-of-plant is considerably simplified and directly coupled to the energy conversion equipment. 

The supercritical-water-cooled reactor (SCWR) ( Fig. 58.21) system features two fuel cycle options the first is an open cycle with a thermal neutron spectrum reactor the second is a closed cycle with a fast-neutron spectmm reactor and full actinide recycle. Both options use a high-temperature, high-pressure, water-cooled reactor that operates above the thermodynamic critical point of water (22.1 MPa, 374°C) to achieve a thermal efficiency approaching 44%. The fuel cycle for the thermal option is a once-through uranium cycle. The fast-spectrum option uses central fuel cycle facilities based on advanced aqueous processing for actinide recycle. The fast-spectrum option depends upon the materials R D success to support a fast-spectrum reactor. 

To use extremum principles, which can identify states of equilibrium, we find points at which derivatives are zero. In mathematics, a critical point is w here a first derivative equals zero. It could be a maximum, a minimum, or a saddle point. In statistical thermodynamics, critical point has a different meaning, but in this chapter critical point is used only in its mathematical sense. 

Nearby the thermodynamic critical temperature (T, = 1.05), the real gas factor drops off, at first very strongly, reaches a minimum at a reduced pressure of somewhat over 1, and then increases again. The further away the temperature of the gas is from the thermodynamic critical point, the less strongly pronounced the minimum is. 

The real behavior of a gas essentially depends on how far away the actual pressure and temperature are from the thermodynamic critical point and not on the absolute values of pressure or temperature of the gas. The assumption that a gas behaves ideally (Z = 1) may lead to significant errors in the sizing of safety valves. Basically, the required cross-sectional area of the valve seat is rather underestimated if a too small real gas factor is assumed. 

In practice, often an ideal behavior of gases is assumed at moderate pressures when sizing a safety valve for gas service. Real gas behavior is only assumed at a very high pressure, for example, at a pressure of more than 100 bar. In general, the real gas behavior is rather determined from the proximity of the thermodynamic critical point. With the reduced thermodynamic pressure and the reduced thermodynamic temperature, the deviation from ideal behavior can be described much better than with the absolute values of pressure and temperature. If the reduced pressure and the reduced temperatures at the entrance of the nozzle exceed p/pc > 0.5 or T/Tc > 0.9, the deviations from the ideal behavior are usually no longer tolerable. 

Applying the REAL nozzle flow model, care must be taken for averaging the parameter. Close to the thermodynamic critical point, it might be necessary to stepwise average the parameter or to solve the equation numerically. 

Harden, D.G., 1963. Transient Behavior of a Natural-circulation Loop Operating Near the Thermodynamic Critical Point. Argonne National Laboratory Report, ANL-6710. 

---