A comparative study of thermodynamic models to describe the VLE of the ternary electrolytic mixture H2O–NH3–CO2

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Licianne P. S. Rosa ◽  
Natan Cruz ◽  
Glória M. N. Costa ◽  
Karen V. Pontes
Keyword(s):  
Experimental Data ◽  
Liquid Phase ◽  
Equation Of State ◽  
Activity Coefficient ◽  
Vapor Phase ◽  
Large Scale ◽  
Optimization Problems ◽  
Ideal Gas ◽  
Simultaneous Optimization ◽  
The Ideal

Abstract This study aims to ascertain the influence of the activity coefficient model and equation of state for predicting the vapor–liquid equilibrium (VLE) of the multi-electrolytic system H2O–NH3–CO2. The non-idealities of the liquid phase are described by the eUNIQUAC and eNRTL models. The vapor phase is modeled with the Nakamura equation, which is compared with the ideal gas assumption. The models are validated with experimental data from literature on total pressure and ammonia partial pressure. Results show that the models UNIQUAC and NRTL without dissociation can only reproduce the experimental conditions in the absence of CO2. When the electrolytic term is considered, the eUNIQUAC model is able to reproduce the experimental data with greater accuracy than the eNRTL. The equation of state which describes the vapor phase plays no major role in the accuracy of the VLE prediction in the operational conditions evaluated here. Indeed, the accuracy relies on the activity coefficient, therefore the ideal gas equation can be considered if the non-idealities of the liquid phase are described by a well-tuned model. These findings could be useful for equipment design, flowsheet simulations and large-scale simultaneous optimization problems.

Comparison of Static and Dynamic Powder Compaction: Experiment and Simulation

2015 ◽  
Vol 138 (1) ◽  
Author(s):  
C. A. Braun ◽  
M. Schumaker ◽  
J. Rice ◽  
J. P. Borg
Keyword(s):  
Experimental Data ◽  
Equation Of State ◽  
Large Scale ◽  
Wide Distribution ◽  
Powder Compaction ◽  
Industrial Applications ◽  
Dynamic Compaction ◽  
Experiment And Simulation ◽  
Stress States

In this work, the static and dynamic compaction response of a six-material mixture, containing both brittle and ductile constituents, is compared. Quasi-static and dynamic compaction experiments were conducted on samples and the results compared to simulations. Optical analyses of compacted samples indicate that dynamically compacting samples to near 300 m/s is not sufficient for complete compaction or localized grain melt. Simulations indicate that a wide distribution of temperature and stress states are achieved in the dynamically compacted samples; compaction speeds should be increased to near 800 m/s at which point copper grains achieve melt temperatures on their surfaces. The experimental data is used to fit a bulk P-α equation of state (EOS) that can be used for simulating large-scale dynamic compaction for industrial applications.

Simple Predictions for the Sonic Conditions in a Real Gas

1977 ◽  
Vol 99 (1) ◽  
pp. 217-225 ◽  
Author(s):  
P. A. Thompson ◽  
D. A. Sullivan
Keyword(s):  
Equation Of State ◽  
Closed Form ◽  
Thermodynamic Parameters ◽  
Ideal Gas ◽  
Accurate Prediction ◽  
Bernoulli Equation ◽  
Real Gas ◽  
Similarity Principle ◽  
Isentropic Flow ◽  
The Ideal

The steady isentropic flow of a fluid which satisfies an arbitrary equation of state is treated, with emphasis on the prediction of pressure, density, velocity, and massflow at the sonic state. The isentrope P(v) is described by a limited number of thermodynamic parameters, the most important ones being the soundspeed c and fundamental derivative Γ. Using this description, an application of the Bernoulli equation and appropriate thermodynamic relations yields simple closed-form predictions for the sonic state. These predictions are recognizable as generalizations of well-known ideal gas formulas, but are applicable to fluids very far removed from the ideal gas state, even including liquids. Comparisons in several cases for which precise independent solutions are available suggest that the methods found here are accurate. A derived similarity principle allows the accurate prediction of sonic properties from any single given sonic property.

Pressure Drop Study and Correlation Development for Two-Phase Flow of R134a in Annular Helicoidal Pipe

2004 ◽  
Author(s):  
H. L. Mo ◽  
R. Prattipati ◽  
C. X. Lin
Keyword(s):  
Experimental Data ◽  
Liquid Phase ◽  
Pressure Drop ◽  
Vapor Phase ◽  
Test Section ◽  
Circular Tube ◽  
Phase Flow ◽  
Two Phase ◽  
Annular Section ◽  
Phase Pressure

Pressure drop characteristics of R134a in annular helicoidal pipe was investigated experimentally with R134a flowing in the annular section. The experimental results revealed that when more R134a vapor was condensed, the liquid phase pressure drop increased largely while the vapor phase pressure drop decreased slightly. By comparing with the experimental data obtained from the same test section with R134a flowing in the inner circular tube of the helicoidal pipe, it was observed that the pressure drop for refrigerant in the annular section was always larger. It was also observed that the helicoidal pipe orientation showed little effect on the pressure drop variations. A pressure drop correlation was developed from the experimental data in terms of pressure drop multiplier with respect to Lockhart-Martinelli parameter.

THE FORMATION OF LARGE-AMPLITUDE FINGERS IN ATMOSPHERIC VORTICES

2016 ◽  
Vol 57 (4) ◽  
pp. 395-416
Author(s):  
JASON M. COSGROVE ◽  
LAWRENCE K. FORBES
Keyword(s):  
Large Amplitude ◽  
Qualitative Agreement ◽  
Large Scale ◽  
Initial Perturbation ◽  
Ideal Gas ◽  
Fourier Mode ◽  
Ideal Gas Law ◽  
Atmospheric Vortices ◽  
Low Pressure Systems ◽  
The Ideal

Large-scale low-pressure systems in the atmosphere are occasionally observed to possess Kelvin–Helmholtz fingers, and an example is shown in this paper. However, these structures are hundreds of kilometres long, so that they are necessarily affected strongly by nonlinearity. They are evidently unstable and are observed to dissipate after a few days.A model for this phenomenon is presented here, based on the usual $f$-plane equations of meteorology, assuming an atmosphere governed by the ideal gas law. Large-amplitude perturbations are accounted for, by retaining the equations in their nonlinear forms, and these are then solved numerically using a spectral method. Finger formation is modelled as an initial perturbation to the $n$th Fourier mode, and the numerical results show that the fingers grow in time, developing structures that depend on the particular mode. Results are presented and discussed, and are also compared with the predictions of the ${\it\beta}$-plane theory, in which changes of the Coriolis acceleration with latitude are included. An idealized vortex in the northern hemisphere is considered, but the results are at least in qualitative agreement with an observation of such systems in the southern hemisphere.

Extremes in Dependences of Enthalpy and Entropy of Saturated Vapour on Temperature

1997 ◽  
Vol 62 (5) ◽  
pp. 679-695
Author(s):  
Josef P. Novák ◽  
Anatol Malijevský ◽  
Jaroslav Dědek ◽  
Jiří Oldřich
Keyword(s):  
Heat Capacity ◽  
Equation Of State ◽  
Ideal Gas ◽  
Corresponding States ◽  
Saturated Vapour ◽  
Enthalpy And Entropy ◽  
The Ideal

It was proved that the enthalpy of saturated vapour as a function of temperature has a maximum for all substances. The dependence of the entropy of saturated vapour on temperature can be monotonous, has a minimum and a maximum, or has only a maximum. The thermodynamic relations were derived for the existence of the extremes which enable their computation from the knowledge of dependence of the ideal-gas heat capacity on temperature and an equation of state. A method based on the theorem of corresponding states was proposed for estimating the extremes, and its results were compared with literature data. The agreement between the literature and estimated temperatures corresponding to the extremes is very good. The procedure proposed can serve for giving precision to the H-p and T-S diagrams commonly used in applied thermodynamics.

The Ideal Gas in Slow Time

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Christopher Essex ◽  
Bjarne Andresen
Keyword(s):  
Velocity Distribution ◽  
Degrees Of Freedom ◽  
Large Scale ◽  
Heavy Tails ◽  
Local Equilibrium ◽  
Ideal Gas ◽  
Slow Time ◽  
Additional Energy ◽  
Ideal Gas Law ◽  
The Ideal

AbstractWe continue our exploration of thermodynamics at long observational timescales, “slow time,” by including turbulent dynamics leading to a condition of fluctuating local equilibrium. Averaging these fluctuations in wind speed and temperature results in a velocity distribution with heavy tails which, however, are necessarily truncated at some large molecular speed preserving all moments of the velocity distribution including the energy. This leads to an expression for the ideal gas law in slow time which as its core has the superficially familiar term \frac{3}{2}Nk\theta in addition to a term accounting for the large-scale fluctuations, which is also proportional to the particle number N; θ is a new temperature including thermalization of wind. The traditional temperature T no longer exists. Likewise, the additional energy term necessitates a new quantity that parallels entropy in the sense that it captures hidden degrees of freedom. Like entropy, it captures physical properties manifesting indirectly, but on scales larger than the familiar laboratory scales. We call this quantity epitropy.

scholarly journals Una extensión teórica aplicada a los ácidos puros de cadena larga en la fase líquida para analizar su comportamiento en la fase sólida

2021 ◽  
Vol 34 (2) ◽  
Author(s):  
Moilton Franco Junior ◽  
Nattacia Rocha ◽  
Warley Pereira
Keyword(s):  
Experimental Data ◽  
Carbon Dioxide ◽  
Liquid Phase ◽  
Equation Of State ◽  
Bulk Modulus ◽  
Phase Behavior ◽  
Solid Phase ◽  
The One

In this work, Peng-Robinson EOS (equation of state) was chosen to represent liquid phase behavior. Then, regarding the three acids, Lauric, Palmitic and Stearic, bulk modulus coefficients were calculated in three values of pressures (0.1, 1.0 and 2.0 GPa) and a range of temperature of 350-450 K. According to the literature, results for carbon dioxide, bulk modulus in the liquid phase is in the same line for the one in the solid phase considering the temperature dimension. Based on it, in this work, the bulk modulus was estimated at three temperatures for three acids in solid-phase by extrapolating the results in the liquid phase. Despite there are no experimental data available in the literature, these results seem to be consistent with the thermodynamic constraints, and useful discussions were provided.

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