On the temperature dependence of the alpha function in the cubic equation of state
On the temperature dependence of the alpha function in the cubic equation of state
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关于三次状态方程中α函数的温度依赖性
DOI：
10.1016/j.ces.2018.08.014
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发表时间：
2018
影响因子：
4.7
通讯作者：
Zhen Yang
中科院分区：
文献类型：
--
作者：
Fufang Yang;Qiang Liu;Yuanyuan Duan;Zhen Yang
三次状态方程（EoS）被广泛应用于模拟化学过程中的流体热力学性质。然而，由于缺乏可区分的参考性质，其唯一与温度相关的参数α函数的超临界外推导致超临界维里系数和热容的非物理预测。从理论角度出发，我们在不指定相互作用势的情况下，利用广义范德华理论，严格推导了α函数的普遍温度依赖行为。为了从EoS结构中分离出α函数的行为，我们研究了低密度实际流体的热力学函数。我们的研究表明，α函数是有限的、正的，并且随着温度的升高而单调减小。我们提出了一组热力学要求，并相应地修正了Redlich-Kwong和Peng-Robinson eos的预测Soave和Twu α函数。我们的研究表明，修正的α函数避免了无限温度下发散的维里系数，以及热容等压线在临界温度以上的非物理颠簸，表明迫切需要对α函数的温度依赖性的热力学要求。焦耳-汤姆逊反演曲线和汽液平衡也进行了研究。
The cubic equation of state (EoS) is widely applied for modeling fluid thermodynamic properties in chemical processes. However, in the absence of a distinguishable reference property, the supercritical extrapolation of its only temperature-dependent parameter, the α function, resulted in nonphysical prediction of supercritical virial coefficients and heat capacities. From a theoretical perspective, we here rigorously derive the universal temperature-dependent behavior of the α function, using the generalized van der Waals theory without specifying the interaction potential. To isolate the behavior of the α function from the EoS structure, we examine the thermodynamic functions of realistic fluids at low densities. Our study reveals that the α function is finite, positive, and monotonically decreases with increasing temperature. We present a set of thermodynamic requirements and accordingly revise the predictive Soave and Twu α functions for the Redlich-Kwong and Peng-Robinson EoSs. Our study shows that the revised α functions avoid the divergent virial coefficients at infinite temperature, and the nonphysical bump on the heat capacity isobars immediately above the critical temperature, demonstrating the imperative need for thermodynamic requirements for the temperature dependence of the α function. Joule-Thomson inversion curve and vapor-liquid equilibria are also investigated.