A new corresponding-states model for estimating the vaporization heat of working fluids used in Organic Rankine Cycle
Introduction
Nowadays, with the ever rapid development of science and technology, the conventional primary energy consumption in the world has risen to an unprecedented level, and in the same process a large quantity of CO2 has been released into the atmosphere [[1], [2], [3]]. In addition, in quite a lot processes such as chemical reactions in industrial and fuel combustion in power plants, a massive amount of low grade waste heat is emitted from steam boiler, gas turbine, internal combustion engine (ICE) and so on, leading to a low energy efficiency. Thus, the waste heat release is threatening the world as it is also a contributing factor to the global warming at the present time [4].
In this case, in order to tackle the energy and environmental problems, clean and effective ways for energy utilization and conversion have to be explored [5]. The recovery of the low grade waste heat has become an essential option, and it could be carried out in numerous ways. A lot of thermodynamic cycles such as the Organic Rankine Cycle (ORC) [6,7], Supercritical Rankine cycle [8,9], Kalina Cycle [10,11], Goswami Cycle [12] and Trilateral Flash Cycle [13] have been adopted to study the recovery of the low grade heat sources. The principle of ORC is the same as the steam rankine cycle, while it uses organic working fluids as the circulating working medium instead of water. And ORC has been the new focus of numerous researchers because of its system is not complicated and needs less maintenance. Many investigators have performed studies on the thermodynamic analysis and performance optimization of ORC from theoretical and experimental perspectives [[14], [15], [16], [17]].
The performance of ORC systems, in particular the efficiency that is closely related to the critical temperature, the vaporization heat, the thermal conductivity and viscosity, strongly depends on the thermodynamic properties of working fluids [18,19]. The vaporization heat, sometimes referred to as the enthalpy of vaporization Δh, is a very important thermophysical property of working fluids in distillation, evaporation, drying, etc [20,21]. Moreover, the vaporization heat sometimes could be used in the estimation of other thermophysical properties of working fluids. The vaporization heat can be obtained through the method of calorimetry directly, or by calculating the difference between the enthalpy of the saturated vapor and that of the saturated liquid indirectly [22]. Majer and Svoboda have collected the experimental values of the vaporization heat about 600 organic compounds since 1932, but most of them are obtained at a given temperature such as normal boiling point [23]. In the case of the insufficient experimental data of vaporization heat, theoretical methods can be used for their estimation. In the past decades, estimation of the vaporization heat has been the topic of many studies [[20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], [34], [35], [36], [37]]. For example, Cachadina and Mulero (2007, 2008) have done some research on comparing several presented models of estimating the vaporization heat [28,30]. Cerlani et al. (2009) presented a new model for estimating the vaporization heat of fatty compounds found in edible oil and biofuels industries [31]. Mulero et al. (2010) used a general expression to accurately correlate the liquid density, the vaporization heat, the surface tension, and the isobaric heat capacity of a saturated liquid versus temperature along the whole coexistence curve [32]. Additionally, they studied the accuracy of eighteen correlations of the vaporization heat by using data retrieved from both the DIPPR and the NIST databases for forty-eight substances, and they found that the choice of the database does not influence the choice of the best overall model [33]. Srinivasan et al. (2012) analyzed correlations for the maxima of products of some liquid-vapor saturation properties [34]. Parhizgar et al. (2013) presented a new model for prediction of vaporization heat of petroleum fractions as well as pure hydrocarbons by utilizing genetic programming [35]. Baghban (2016) utilize the adaptive neuro-fuzzy inference system to predict the vaporization heat of petroleum fractions and pure hydrocarbons [36]. Alibakhshi (2017) introduced a novel theoretical approach to study the temperature dependence of the vaporization heat exploiting the statistical and classical thermodynamics of evaporation [37]. Indeed, most of these theoretical methods are proposed based on group contribution method, molecular aggregation method, residual function method, the corresponding states principle, etc. It is essential to know the chemical groups in the molecule as well as its chemical structure when it is calculated by means of group contribution method [24,26,31]. For some general equations based on the corresponding states principle [21,27,28,30,38], only certain properties of fluids, such as the critical temperature and the acentric factor, are required. These correlations do not require the calculation of specific coefficients for each fluid, but rather fixed coefficients valid for a broad range of fluids. In spite of their simplicity, corresponding states principle equations are able to produce very accurate estimations of thermophysical properties of fluids based on a small amount of experimental information. Generally, the previous corresponding states models can be used for calculating vaporization heat of most fluids with acceptable accuracy. While for organic working fluids, they are not suitable enough because of their lower precision or complex form. So it is necessary to propose a special equation for organic working fluids to satisfy the requirement of their worldwide application. The aim of this paper is to obtain a correlation to estimate the vaporization heat of organic working fluids with high accuracy and convenient form.
Section snippets
New correlation for the vaporization heat
Van der Waals, who detected that the reduced version of his equation of state is the same for all fluids, initially constructed the corresponding states principle. Although the establishment of the corresponding states principle originally had only an empirical basis, its theoretical solidity has strongly confirmed by the subsequent investigations in kinetic theory and statistical mechanics.
At present, there are several estimation equations of vaporization heat based on corresponding states
Classification of organic working fluids
As presented above, it is concluded that the new vaporization heat equation is simpler than Morgan equation and more accurate than Pitzer equation. Nevertheless, for some fluids such as R41, R32 and R245fa, the absolute deviations are a little high. Thus, the following attempt has been made to optimize the new equation.
By further analysis of the above calculated results and the property of working fluids, it is detected that the constant a is related not only to the acentric factor, but also to
Conclusion
In this paper, based on the corresponding states principle, an accurate new correlation in simple format was proposed to estimate the vaporization heat of working fluids in Organic Rankine Cycle. A further majorization has been proceeded, while 36 organic working fluids of different kinds are classified into the polar and the non-polar according to the molecular structure and chemical bonds. The vaporization heat of these working fluids has been estimated, and the average absolute deviations
Acknowledgement
We acknowledge the support of the National Natural Science Foundation of China (Grant No. 51606032) and Jilin science and technology innovation and development plan of China (20166015).
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