Ideal-gas Isobaric Heat Capacity Research Articles

Thermo-economic performance limit analysis of combined heat and power systems for optimal working fluid selections

In previous works, we have proposed the thermodynamic performance limit analysis methodology for the organic Rankine cycle for analyzing the impact of working fluid properties on system performance. Here the concept is extended to the thermo-economic performance limits, and is applied to a combined heat and power system based on an organic Rankine cycle. Working fluids are characterized with 8 characteristic thermodynamic and transport properties based on a corresponding state model and a residual entropy scaling approach. The 8 fluid characteristic properties along with 3 system operational parameters are optimized using a multi-objective genetic algorithm; a Monte Carlo algorithm is further adopted to avoid sub-optimal convergences. As the result, the performance limits could be well represented by the trade-off (Pareto front) between the maximized thermal efficiency and minimized payback period. The impact of the fluid characteristic properties on both thermodynamic and economic targets is investigated and ultimately guided the choice of working fluids: low molar mass, low thermal conductivity scaling factor, high viscosity scaling factor and high critical pressure are always preferred. "Wet" working fluid is preferred for a high thermal efficiency while "dry" working fluid is favored for a short payback period. Critical temperature has the most profound impact, while ideal gas isobaric heat capacity and acentric factor have negligible impacts. The choice of working fluid, system design (e.g., recuperative effectiveness) and system operational parameters (e.g., evaporation temperature) highly depends on the given hot sources and the preferences to the thermodynamic and economic targets.

Behavior of Isobaric Heat Capacity of trans-1,1,1,4,4,4-Hexafluoro-2-butene in the Gas Phase

The isobaric specific heat capacity cp of trans-1,1,1,4,4,4-hexafluoro-2-butene was carefully measured for temperatures T ranging from (308 to 363) K and at pressures p ranging from (0.2 to 1.0) MPa in the gaseous state. The obtained 33 cp data with a flow calorimeter were tabulated and were shown in the cp–T diagram. It is estimated that the expanded uncertainties (k = 2) of the temperature measurements U(T) and the pressure measurements U(p) are less than 37 mK and 3.6 kPa, respectively. That for cp measurements U (cp) is derived to be less than 36 J·kg–1·K–1. Based on the evaluated data, corresponding isotherms were depicted in the cp–p diagram, and the ideal-gas isobaric heat capacity and saturation in the gas phase of trans-1,1,1,4,4,4-hexafluoro-2-butene were determined.

How to Quickly Evaluate the Thermodynamic Performance and Identify the Optimal Heat Source Temperature for Organic Rankine Cycles?

Abstract Organic Rankine cycle (ORC) is a promising technology to convert low- and medium-temperature energy into power. Identifying the optimal working fluids and heat source temperature are always the focuses in the ORC field. This paper presents a new methodology to evaluate the thermodynamic performance of ORC with different working fluids and identify the optimal heat source temperature. Initially, the parameterization model is developed to characterize the working fluids by thermodynamic property parameters including critical temperature (Tc), critical pressure (pc), acentric factor (ω), and ideal gas isobaric heat capacity (cp0). Subsequently, the simultaneous optimization of thermodynamic property parameters and cycle parameters is conducted to obtain the thermodynamic performance limits of simple and regenerative ORCs at six typical geothermal heat source temperatures. By comparing the thermodynamic performance limits of ORC under different heat source temperatures, the optimal heat source temperature is identified. Then, ten commonly used working fluids are selected as reference working fluids, and the thermodynamic property parameters comparisons between reference and ideal working fluids, which can be characterized by the optimized thermodynamic property parameters, are investigated. Finally, multiple linear regression models are developed to evaluate the thermodynamic performance. The numerical differences of thermodynamic property parameters between the ideal reference and reference working fluids are chosen as initial variables, while the thermal efficiency and volumetric power output are used as thermodynamic performance indicators. The results show that the optimal heat source temperature is 250 °C, which is independent of cycle configuration. The thermodynamic performance of ORCs can be evaluated accurately by the multiple linear regression models. The maximum relative error of the multiple linear regression models is 3.02%. Moreover, Tc is the most dominant thermodynamic property parameter.

Thermodynamic properties of trifluoroethene (R1123): (p, ρ, T) behavior and fundamental equation of state

Abstract The (p, ρ, T) behavior of trifluoroethene (R1123) was investigated with the isochoric method. A total of 87 (p, ρ, T) data were measured along nine isochores (42, 98, 151, 197, 296, 493, 691, 790, and 888 kg · m − 3 ) at temperatures from 300 K to 430 K and pressures up to 6.9 MPa. The uncertainties in temperature are estimated to be within 10 mK below 380 K and 20 mK at higher temperatures, and the uncertainties in pressure are estimated to be within 1 kPa below 380 K and 2 kPa at higher temperatures. The estimated relative uncertainties in the density measurements are 0.15 % or less. A new Helmholtz energy equation of state was formulated based on the (p, ρ, T) data and recently published experimental data for the vapor pressure, liquid and vapor densities including those at saturation, vapor-phase sound speed, and ideal-gas isobaric heat capacity. The equation is applicable at temperatures from the triple-point temperature (195.15 K) to 480 K and pressures up to 20 MPa. Typical uncertainties in calculated properties are 0.1 % for vapor pressures, 0.1 % for liquid densities, and 0.2 % for vapor densities, except in the critical region where larger deviations up to about 1.5 % are sometimes observed in densities. The uncertainties in calculated vapor-phase sound speeds and ideal-gas isobaric heat capacities are 0.03 % and 1 %, respectively. The equation shows reasonable extrapolation behavior at extremely low and high temperatures, and at high pressures.

Approximating the Temperature–Entropy Saturation Curve of ORC Working Fluids From the Ideal Gas Isobaric Heat Capacity

Recently, we proposed an approximate expression for the liquid–vapor saturation curves of pure fluids in a temperature–entropy diagram that requires the use of parameters related to the molar heat capacity along the vapor branch of the saturation curve. In the present work, we establish a connection between these parameters and the ideal-gas isobaric molar heat capacity. The resulting new approximation yields good results for most working fluids in Organic Rankine Cycles, improving the previous approximation for very dry fluids. The ideal-gas isobaric molar heat capacity can be obtained from most Thermophysical Properties databases for a very large number of substances for which the present approximation scheme can be applied.

A corresponding state equation for the prediction of isobaric heat capacity of liquid HFC and HFO refrigerants

This work proposed a corresponding state equation for the prediction of isobaric heat capacity of liquid hydrofluorocarbon (HFC) and hydrofluoroolefin (HFO) refrigerants. The equation was derived from classic corresponding state principle and rigorous data analysis. With known acentric factor, critical point and ideal gas isobaric heat capacity, the equation could provide predictions for isobaric heat capacity of liquid refrigerants at a wide state range with satisfactory accuracy. By means of testing available experimental data, the overall prediction accuracy of the equation was confirmed to be 1.78%, which was much better than other prediction methods.

Improving thermodynamic consistency among vapor pressure, heat of vaporization, and liquid and ideal gas isobaric heat capacities through multi-property optimization

Vapor pressure, heat of vaporization, liquid isobaric heat capacity, and ideal gas isobaric heat capacity can be measured for pure organic compounds between the triple point and critical point. Additionally, heat of vaporization is proportional to the derivative of vapor pressure with respect to temperature through the Clapeyron equation, and the difference of liquid and ideal gas heat capacities are proportional to the derivative of heat of vaporization with respect to temperature. These relationships and experimental data were compared for several compounds to interpolate and extrapolate available data and increase consistency amongst these properties. A methodology for assessing the thermodynamic consistency amongst data sets and optimizing the accepted property values has been developed so that this procedure can be applied to other compounds in the DIPPR 801 database for which there are fewer experimental data available. The process involves critically evaluating available experimental data and the correlations used to fit these temperature-dependent properties. Multi-property optimization includes weighting the various data values based on the accuracy of the data and on the perceived relative importance of the properties in process design. User-defined weighting systems will be established to provide optimization flexibility across these properties for future use of the DIPPR 801 database.

On the use of departure function correlations for hydrocarbon isobaric liquid phase heat capacity calculation

Constant pressure heat capacities for pure liquids and mixtures are by default evaluated indirectly, in process simulators and in general purpose calculations, using ideal gas isobaric heat capacity values to which equation of state based departure functions are added. As ideal gas heat capacities are known or can be calculated from theory with small uncertainties and typically comprise 75% of liquid heat capacity values, the large relative deviations present in departure function calculations appear to be tolerated or ignored because deviations between indirectly calculated and measured constant pressure liquid heat capacities are typically less than 15% and large deviations are uncommon. For hydrocarbon and petroleum applications, non-cubic equations of state have a limited range of application and a cubic equation of state departure function calculations possesses a systematic skew with respect to absolute and relative temperature. This provides application windows for stand alone departure function correlations: by Tyagi that requires the input properties (Tc, Pc, ω, M) at high reduced and absolute temperatures; and a difference calculation based on correlations by Dadgostar and Shaw (for hydrocarbon liquids) and Laštovka and Shaw (for ideal gases) which extend the range of fluids for which liquid state heat capacity departure functions can be evaluated to include poorly defined (Tc and M are available) individual hydrocarbons or mixtures or ill-defined (only elemental analysis is available) hydrocarbon mixtures. However, none of these approaches provides consistently low deviations from measurements and consequently, direct calculation of liquid phase heat capacities is recommended for detailed engineering calculations.

Experimental vapor pressures and thermodynamic models of perfluorocarbons PP80 and PP90

Complete thermodynamic models are developed for the perfluorocarbons PP80 (perfluoro-2-methyl-3-ethylpentane, C8F18, CASRN: 354-97-2) and PP90 (perfluoro-2,4-dimethyl-3-ethylpentane, C9F20, CASRN: 50285-18-2). These perfluorocarbons can be used as working fluids in energy conversion applications, like organic Rankine cycle (ORC) power systems operating at medium and high temperatures. Other areas of use of PP80 and PP90 are in the electronic industry for component testing, in the chemical industry as a hazardous reaction suppressant and as tracers in the oil and gas industry. The improved equation of state of Peng–Robinson modified by Stryjek–Vera (iPRSV) is adopted, supplemented with a third order polynomial for the ideal gas isobaric heat capacity as a function of temperature. Vapor–liquid pressures for both fluids were measured in a temperature range spanning 358–508K. The vapor–pressure temperature range for the fitting of the equation of state is extended down to 270K by extrapolation of the Wagner–Ambrose equation that is used for the correlation of the aforementioned measured data. Ideal gas isobaric heat capacities data are estimated with the Joback method. The obtained thermodynamic models are arguably sufficiently accurate for preliminary engineering calculations, for example for the thermodynamic design of ORC power systems.

A Model To Calculate the Theoretical Critical Flow Rate Through Venturi Gas Lift Valves

Summary A model to calculate the theoretical critical flow rate of nitrogen (N2) or natural gas through a Venturi gas lift valve is described herein. This new model considers real-gas effects not only in density calculations but also in other thermodynamic properties that are relevant during gas isentropic evolution. For the properties of N2, the Bennedict, Webb, and Rubin (BWR) equation of state and an accurate correlation for the ideal-gas isobaric heat capacity were used. For natural gas, the Dranchuk and Abou-Kassem equation, which reproduces the well-known Standing and Katz chart, was used, and, for the ideal-gas isobaric heat capacity, it was assumed that the natural gas was a mixture of methane and ethane only, their individual ideal-gas heat capacity being calculated by updated correlations. To validate the use of the proposed equations of state, a comparison of calculated with experimental or reference data on properties of N2 and natural gas (including pure methane and some relevant mixtures) was performed with very good results for N2 and for natural-gas compositions usual in gas lift operations (dry gas with very small amounts of contaminants). For natural gas with moderate amounts of N2 and carbon dioxide (CO2), accurate results were obtained after correction of critical conditions and of ideal heat capacity. The model was also compared with other theoretical models found in the literature, which use compositional approaches for natural gas, with excellent results. Some experimental results obtained with commercial Venturi valves manufactured in Brazil are also presented.

Speed of sound predictive modeling in a three-parameter corresponding states format: Application to pure and mixed haloalkanes

A three-parameter corresponding states model is proposed for the prediction of speed of sound surfaces of pure fluids and mixtures belonging to a homogeneous family of fluids as the halogenated alkanes. A preliminary conformality study is developed confirming the high potentiality of the corresponding states methods when applied within a property-dependent framework. A procedure that separately models the ideal-gas part and the residual contribution of the speed of sound surface is assumed. The ideal term is obtained for each target fluid from an individual equation for the ideal-gas isobaric heat capacity, whereas the residual term is represented with a three-parameter corresponding states technique introducing a fluid- and property-specific scaling parameter. A high effectiveness in the modeling of the whole speed of sound surface is obtained. The predictive character of the proposed model is evidenced by the few required inputs for a target fluid, i.e., a single speed of sound value at saturated liquid conditions for the assigned reduced temperature and its ideal-gas heat capacity function. The model format is directly extended to mixture simply by introducing enhanced mixing rules. The model has been successfully validated at both vapor and liquid conditions for 1978 experimental points of eight haloalkane fluids, obtaining the overall average absolute deviation (AAD) of 1.10%, and for mixtures in predictive mode for 927 experimental points, with the AAD of 0.62%. The correlative mode for mixtures has been applied to 600 points in the liquid region with an AAD of 0.67%, which is slightly better than the performance of the corresponding dedicated equations of state. The satisfactory results obtained assure the effectiveness of the proposed procedure.

Modelling enthalpy and entropy of pure and mixed refrigerants with an innovative corresponding states method

In this work an original improvement of the Corresponding States technique is developed and a new model, based on a three parameters CS format, is proposed to predict the enthalpy and the entropy of the new generation halogenated alkanes fluids together with some alkanes. Limiting the analysis of the selected fluids to a specific thermodynamic property behaviour, an appropriate conformality approach can be deduced, which allows to set up a predictive model of high accuracy level on a wide range of the enthalpy and entropy surfaces. The fundamentals of the model are innovative scaling parameters deduced from the enthalpy of vaporization and from two dedicated equations, belonging to the selected family of fluids. This allows to set up innovative models following a CS format. Through the introduction of advanced mixing rules, the models can be simply extended to calculate the corresponding properties for mixtures. The proposed models allow also the calculation of VLE for systems of rather regular behaviour. The required inputs for a pure target fluid are an ideal gas isobaric heat capacity correlation, a single value of saturated liquid density and of vaporization enthalpy; if the last one is lacking, a single value of vapor pressure can be alternatively supplied. For non azeotropic mixtures the enthalpy and entropy models are predictive, whereas in case of azeotropy VLE calculations are possibly only applying regressed interaction coefficients. Due to the lack of accurate experimental enthalpy data and to the particular nature of the entropy function, the validation of the models is proposed against fundamental dedicated EoS available, both for pure and mixtures, for a significant number of the studied family of fluids. The predictive character of the proposed approach as well as the high performances reached, make these models particularly suitable for the new families of fluids regarding advanced technological applications.

Thermodynamic Property Models for Moist Air and Combustion Gases

A new model for the prediction of caloric properties of moist air and combustion gases has been developed. The model very accurately predicts ideal gas caloric properties of undissociated gas mixtures at temperatures from 200 K to 3300 K. In addition, a simple model has been developed to account for caloric effects of dissociation at temperatures up to 2000 K. As a part of the project, scientific equations for the ideal gas isobaric heat capacity of the individual combustion gas components have been established. Based on this reference, an assessment and comparison of the new model with the most common technical models have been carried out. Results of the simplified dissociation model are compared to the results of complex chemical equilibrium programs. To mark out the limits of the ideal gas hypothesis, some sample calculations are given, which compare results of the new ideal gas model to results from sophisticated real gas models.