scholarly journals The Latent Heat of Supercritical Fluids

2019 ◽  
Vol 63 (2) ◽  
pp. 270-275 ◽  
Author(s):  
Daniel Banuti
Keyword(s):  
Latent Heat ◽  
Supercritical Fluids ◽  
Ideal Liquid ◽  
Equilibrium Temperature ◽  
Ideal Gas ◽  
Supercritical State ◽  
Limit States ◽  
Coexistence Line ◽  
Theoretical Evidence ◽  
Low Pressures

The article discusses the notion of a supercritical latent heat during 'pseudoboiling': Experimental, numerical, and theoretical evidence show that the supercritical state space is not homogeneous, but can be divided into liquid-like and gas-like domains, separated by an extension to the coexistence line -- the Widom line. The key concept are two limit states of ideal liquid and ideal gas, characterized by constant heat capacities, and analyze the transition between them. Then, analogous to subcritical vaporization, a supercritical state transition from liquid to gaseous overcomes intermolecular attractive forces, albeit over a finite temperature interval rather than at an equilibrium temperature. This distributed latent heat is in fact approximately invariant with respect to pressure for (0 < p < 3 pcr) and is thus valid at subcritical and supercritical conditions. This view also changes the perspective on subcritical latent heat: while it is an accurate representation of the required energy at very low pressures, the contribution of the distributed latent heat dominates the equilibrium latent heat as the critical pressure is approached.

High Density Thermal Energy Storage With Supercritical Fluids

2012 ◽  
Author(s):  
Gani B. Ganapathi ◽  
Richard Wirz
Keyword(s):  
Molten Salt ◽  
Supercritical Fluids ◽  
Thermal Energy ◽  
High Density ◽  
Salt System ◽  
Supercritical State ◽  
Storage Container ◽  
System Cost ◽  
Molten Salt System ◽  
The Cost

A novel approach to storing thermal energy with supercritical fluids is being investigated, which if successful, promises to transform the way thermal energy is captured and utilized. The use of supercritical fluids allows cost-affordable high-density storage with a combination of latent heat and sensible heat in the two-phase as well as the supercritical state. This technology will enhance penetration of several thermal power generation applications and high temperature water for commercial use if the overall cost of the technology can be demonstrated to be lower than the current state-of-the-art molten salt using sodium nitrate and potassium nitrate eutectic mixtures. An additional attraction is that the volumetric storage density of a supercritical fluid can be higher than a two-tank molten salt system due to the high compressibilities in the supercritical state. This paper looks at different elements for determining the feasibility of this storage concept — thermodynamics of supercritical state with a specific example, naphthalene, fluid and system cost and a representative storage design. A modular storage vessel design based on a shell and heat exchanger concept allows the cost to be minimized as there is no need for a separate pump for transferring fluid from one tank to another as in the molten salt system. Since the heat exchangers are internal to the tank, other advantages such as lower parasitic heat loss, easy fabrication can be achieved. Results from the study indicate that the fluid cost can be reduced by a factor of ten or even twenty depending on the fluid and thermodynamic optimization of loading factor. Results for naphthalene operating between 290 °C and 475 °C, indicate that the fluid cost is approximately $3/kWh compared with $25-$50/kWh for molten salt. When the storage container costs are factored in, the overall system cost is still very attractive. Studies for a 12-hr storage indicate that for operating at temperatures between 290–450 °C, the cost for a molten salt system can vary between $66/kWh to $184/kWh depending on molten salt cost of $2/kg or a more recent quote of $8/kg. In contrast, the cost for a 12-hr supercritical storage system can be as low as $40/kWh. By using less expensive materials than SS 316L, it is possible to reduce the costs even further.

scholarly journals The compressibilities and expansion coefficients of gases at low pressures, and their relation to molecular volume

1939 ◽  
Vol 173 (953) ◽  
pp. 201-211
Keyword(s):  
Low Pressure ◽  
Ideal Gas ◽  
Molecular Volume ◽  
Simple Method ◽  
Gas Laws ◽  
Compressibility Coefficient ◽  
Expansion Coefficients ◽  
Low Pressures ◽  
Limiting Value

The determination of molecular and atomic weights by the limiting density and limiting pressure methods has furnished considerable data on the behaviour of gases in the neighbourhood of atmospheric pressure. It is customary in this work to express the deviations from the ideal gas laws in terms of either the compressibility 1 + λ = ( p 0 v 0 )/( p 1 v 1 ) or the compressibility coefficient A , where 1 - A = ( p 1 v 1 )/( p 0 v 0 ), p 0 v 0 is the limiting value of pv at infinitely low pressure, p 1 v 1 the value at 1 atm., and the temperature 0° C. The present paper describes a simple method of expressing compressibilities and related low pressure data for non-polar gases in terms of their effective molecular volume.

Numerical Simulation of Steam Flow Inside the Superheater Section of An Industrial Boiler Using a Real Gas Model

2020 ◽  
Vol 142 (7) ◽  
Author(s):  
Deepak Kumar Kanungo ◽  
Kirti Chandra Sahu
Keyword(s):  
Numerical Simulation ◽  
Reynolds Number ◽  
Supercritical Fluids ◽  
Ideal Gas ◽  
Real Gas ◽  
Absolute Value ◽  
Ideal Gas Law ◽  
Maximum Value ◽  
Industrial Boiler ◽  
The Ideal

Abstract Flow mal-distribution inside manifolds hampers the overall efficiency of processes in industries. In supercritical boilers, improper flow of steam inside the superheater (SH) section is a common cause of thermal accidents. However, carrying out a numerical simulation of supercritical fluids flowing inside manifolds is challenging as the ideal gas law does not describe the behavior of these fluids properly. In the present work, numerical simulation of the flow of supercritical steam inside the superheater section of an industrial boiler has been performed using a real gas model. The proposed real gas model is first validated with experimental data associated with the steam properties. Subsequently, the effect of different inlet and outlet arrangements on the flow mal-distribution of steam in the superheater section of the boiler is investigated numerically using the real gas model. A modified inlet and outlet arrangement of the superheater header is proposed which reduces the maximum value of flow mal-distribution in the header by 19.7% and total pressure drop in the domain by 17%. The effect of the Reynolds number on flow mal-distribution in the header arrangement is found to be negligible. The absolute value of the heat absorption by the superheater tubes increases with an increase in the value of the Reynolds number.

Streamlined Modeling for Reaction Equilibrium

2006 ◽  
Author(s):  
Richard A. Gaggioli
Keyword(s):  
Equilibrium Constant ◽  
Equilibrium Constants ◽  
Equilibrium Temperature ◽  
Ideal Gas ◽  
Property Relations ◽  
Equation Solving ◽  
Volume Energy ◽  
Isothermal Combustion ◽  
Mass Volume ◽  
Reaction Equilibrium

Traditionally, the determination of composition at chemical equilibrium has been carried out using the concept of the "equilibrium constant." Though awkward, the use of equilibrium "constant" is straightforward when the equilibrium temperature and pressure are known. However, even with modern software (such as Stanjan [1]), the usage becomes very burdensome in cases such as: (a) constant volume combustion, with T known, (b) adiabatic combustion, at constant pressure (or volume), when the final temperature and density (or pressure) are unknowns, (c) there are more than one independent reactions, (d) non-isothermal combustion with heat transfer, (e) when ideal-gas or ideal solution assumptions are not acceptable Furthermore, even in the more simple cases, becoming engrossed with the mechanics of applying the equilibrium constant (and other relevant principles), students and practitioners often lose sight of the fundamentals that are being applied. In this paper, via several examples, it is illustrated how to directly employ the fundamental principles - element, mass, volume, energy and entropy balances, along with the property relations - and avoid the use of equilibrium constants. Reaction equilibrium conditions - composition, temperature, pressure, density - are determined in a straightforward, easy manner. The key to this improved and easy approach is the accessibility of equation solving software that includes property relations for gases and liquids. In particular, in the present work, EES [2] is employed.

A Novel Numerical Approach for Low Mach Number: Application to Supercritical Fluids

2013 ◽  
Author(s):  
Jalil Ouazzani ◽  
Yves Garrabos
Keyword(s):  
Carbon Dioxide ◽  
Equation Of State ◽  
Supercritical Fluid ◽  
Supercritical Fluids ◽  
Energy Equation ◽  
Fluid Flows ◽  
Ideal Gas ◽  
Gas Flows ◽  
Low Mach Number ◽  
Critical Carbon Dioxide

A new numerical algorithm has been developed to compute low Mach number fluids using the cV-formulation of the energy equation. cV is the specific heat at constant volume. It has been applied to both supercritical fluid flows (using a nonlinear equation of state like the van der Waals cubic equation of state) and gas flows (using an ideal gas law). The algorithm is introduced successfully in a finite volume code using the SIMPLE and SIMPLER methods. Its main advantage lies in the decoupling of the energy equation and equation of state from the momentum and continuity equations, leading to decrease significantly the CPU time in the case of supercritical fluids simulations. Moreover it allows for supercritical fluid flow simulations the use of other discretization methods (such as spectral methods and/or finite differences) and any other nonlinear form of the equation of state. The new algorithm is presented after a brief description of the previously existing algorithm to solve supercritical fluid flows. Then three published Benchmark problems for steady and unsteady ideal gas flows are treated, as well as the side heated cavity problem for a near critical carbon dioxide filling. The results are then compared to those obtained from the previous algorithm as well as to those obtained from a spectral code using the new algorithm. This comparative investigation is extended to the Rayleigh-Bénard problem for a near critical carbon dioxide filled square cavity with the use of the Van der Waals and the Peng-Robinson equations of state.

scholarly journals Quasi-equilibrium phase separation in supercritical fluids

2020 ◽  
Author(s):  
Seungtaek Lee ◽  
Juho Lee ◽  
Yeonguk Kim ◽  
Seok Jeong ◽  
Dong Eon Kim ◽  
...  
Keyword(s):  
Phase Transition ◽  
Phase Separation ◽  
Supercritical Fluids ◽  
Cluster Formation ◽  
Formation Rate ◽  
Equilibrium Phase ◽  
Quasi Equilibrium ◽  
Coexistence Line ◽  
Subcritical Fluids ◽  
Phase Fluid

Abstract This study describes the discovery of a phase separation phenomenon in supercritical fluids (SCFs). An SCF is technically a single-phase fluid with two sub-domains separated by the Widom line. A pseudo phase transition occurs between liquid-like (LL) and gas-like (GL) states, similar to the gas-liquid phase transition across the coexistence line in subcritical fluids. By extending the analogy, we demonstrate that LL-GL phase separation is possible by generating submicron size LL argon droplets in a GL argon SCF. The GL fluid is in a quasi-equilibrium clustered state well above the critical temperature, with a significant increase in cluster formation rate traversing the critical pressure. The prolonged phase separation over an hour is consistent with a model of mass transport mediated by clusters. It provides the insight that clustering is an essential factor in transport and non-equilibrium thermodynamic processes in SCFs.

scholarly journals Adsorption Compression Analysis for Supercritical Fluids using Ono-Kondo Model

2012 ◽  
Vol 11 (2) ◽  
pp. 45
Author(s):  
Panita Sumanatrakul ◽  
Chayanoot Sangwichien ◽  
Gregory Aranovich ◽  
Marc D Donohue
Keyword(s):  
Supercritical Fluids ◽  
High Pressures ◽  
The Other ◽  
Kondo Model ◽  
Zeolite 13X ◽  
Adsorbed Phase ◽  
Supercritical Adsorption ◽  
Attractive Region ◽  
Linear Sections ◽  
Low Pressures

In this paper, supercritical data has been evaluated and shown to demonstrate adsorption compression. Ono-Kondo analysis of adsorption isotherms for supercritical systems (including nitrogen, methane, and carbon dioxide on activated carbon Filtrasorb 400 and on zeolite 13X) indicates adsorption compression phenomenon at high pressure end just as in subcritical systems. Experimental isotherms for adsorption of supercritical fluids are plotted in Ono-Kondo coordinates with the Henry’s constant estimated based on results of modeling as well as calorimetric and chromatographic measurements. The linear sections of the results show the range of applicability of the classical Ono-Kondo model with constant energies of interactions. The slopes of these linear sections represent values and signs of these energies: negative slopes indicate repulsive interactions in adsorbed phase due to adsorption compression. Switching interactions from attractive to repulsive with an increase in the pressure for supercritical adsorption suggests that adsorbed phase has two regions. One is an attractive region at low-pressures and the other is a repulsive region at high pressures. It can be indicated that the shape of isotherms in Ono-Kondo coordinates can help to understand adsorbate-adsorbate energies; the slope of the line in Ono-Kondo coordinates gives the sign and magnitude of the energy as a function of adsorbate density.

Effects of Constitutive Properties on Pressure and Extent of Reaction

2016 ◽  
Vol 230 (10) ◽  
Author(s):  
Elisabetta Arato ◽  
Angelo Morro
Keyword(s):  
Free Energy ◽  
Gibbs Free Energy ◽  
Chemical Potential ◽  
Ideal Gas ◽  
Thermodynamic Relation ◽  
Chemical Potentials ◽  
Theory Of Mixtures ◽  
Low Pressures ◽  
Ideal Gas Model ◽  
The Ideal

AbstractThe paper applies the theory of mixtures to the chemical reaction rate. Concerning the time dependence of pressure, it is shown that pressure increases, is constant or decreases depending on the analogous behaviour of mole numbers. The results are established analytically and then numerically for the ideal gas, the van der Waals and the truncated virial equations. Next, in connection with the ideal gas model, Denbigh assumption is established by starting from the thermodynamic relation between (partial) pressure and Helmholtz free energy. Moreover, it is pointed out that the chemical potential does not exactly equal the partial derivative of the Gibbs free energy with respect to the corresponding mole number. This in turn is shown to imply that the evolution of a reaction is provided by the chemical potentials rather than by the derivative of the Gibbs free energy. Subject to the assumption of ideal gas for the constituents, as a thermodynamic requirement it is shown that if the number of moles increases the reaction is favoured by low pressures, and viceversa, and explicit estimates are established.

scholarly journals Equal Area Laws and Latent Heat ford-Dimensional RN-AdS Black Hole

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Li-Chun Zhang ◽  
Hui-Hua Zhao ◽  
Ren Zhao ◽  
Meng-Sen Ma
Keyword(s):  
Black Hole ◽  
Phase Diagrams ◽  
Latent Heat ◽  
Critical Value ◽  
Phase Coexistence ◽  
Thermodynamic Quantities ◽  
Two Phase ◽  
Equal Area ◽  
The Real ◽  
Coexistence Line

We study the equal area laws ofd-dimensional RN-AdS black hole. We choose two kinds of phase diagrams,P-VandT-S. We employ the equal area laws to find an isobar which is the real two-phase coexistence line. Our calculation is much simpler to derive the critical value of the thermodynamic quantities. According to the thermodynamic quantities, we also study the latent heat of the black hole.

scholarly journals Determination of the applicability limits of the ideal gas model for the calculation of moist air properties

2018 ◽  
Vol 180 ◽  
pp. 02115
Author(s):  
Magda Vestfálová ◽  
Pavel Šafařík
Keyword(s):  
Mixture Theory ◽  
Ideal Gas ◽  
Specific Humidity ◽  
Moist Air ◽  
Relative Deviation ◽  
Low Pressures ◽  
Ideal Gas Model ◽  
Simple Ideal ◽  
The Ideal

The submitted paper deals with the finding of such moist air states in which the components of moist air and hence the humid air itself can be described by the ideal gas model while maintaining a predefined accuracy. Both components of moist air (dry air and water vapor) can be described by a model of ideal gas at sufficiently low pressures and sufficiently high temperatures. In the paper, we are looking for such combinations of pressures and temperatures for both components, where the relative deviation in the density calculation using the ideal gas model does not exceed the desired value. In addition, on the basis of the mixture theory, such moist air conditions (characterized by pressure, temperature and specific humidity) are searched, on which the accuracy of the calculation meets the required conditions. Subsequently, diagrams are constructed that can be used to help identify the interface between a moist air area that can be described by a simple ideal gas model, and areas where it is necessary to use a more accurate model for one of the components.

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