A Review of the Alpha Functions of Cubic Equations of State for Different Research Systems

  • Wenying Zhao
  • Li Xia
  • Xiaoyan Sun
  • Shuguang XiangEmail author


Alpha functions affect the predictive accuracy of cubic equations of state for the thermodynamic properties. The alpha functions usually aimed at predicting the specific compounds. This article reviewed various alpha functions for the prediction of five kinds of compounds—non-polar and weakly polar compounds, polar compounds, heavy hydrocarbons, reservoir fluids and natural gases, and water. Most alpha functions in polynomial and exponential forms can predict the thermodynamic properties of non-polar and weakly polar compounds. The alpha functions for the polar compounds usually have more coefficients or terms of variables in forms. Some alpha functions for heavy hydrocarbons are similar in forms to that for the simple fluid, some are generalized with the re-defined acentric factor, and the others are modified by introducing the triple temperature and normal boiling temperature into the functions. For the complex reservoir fluids and natural gases, the alpha functions are set as the characteristic constants of pseudo-components—pseudo-three phase temperature, pseudo-normal boiling temperature, pseudo-critical temperature, and pseudo-molecular weights—as the variables. The alpha functions for water are modified by adding more terms of reduced temperature into the functions to improve the predictive accuracy of vapor pressure. According to the properties of each kind of compounds, the universal alpha functions should be proposed for the simple fluid, and the specific alpha functions should be dedicatedly explored for the complex fluid and water.


Alpha functions Cubic equations of state Non-polar and polar compounds Reservoir fluids Research progress 





Equation of state




Liquid–liquid equilibrium












Statistical associate fluid theory






Translated Peng–Robinson


Universal functional-group activity coefficients


Van der Waals


Translated VDW EOS


Vapor–liquid equilibrium


Volume-translated Peng–Robinson

A, B, L, M, N, X, Y, a, b, c, d, f, k, l, m, n, p, q, x

Parameters of alpha functions


Van der Waals attractive parameter/specific parameter


A function of temperature and pressure


Concentration of brine




A function of Tb and Tc or a function of characteristic energy


Triple phase temperature


Reduced temperature of water

Greek Symbols


Alpha function


A function of Tbr and Tr


A function of ω and Tr


Acentric factor


Re-defined acentric factor


Parameter of alpha function


Parameter of alpha function



Normal boiling point property


Critical property


Triple property


Reduced by critical parameter



Reference fluid property (ω = 0)


Reference fluid property (ω = 1)



This research was supported by the National Natural Science Foundation of China (No. 21476119) and Major Science and Technology Innovation Projects of Shandong Province (No. 2018CXGC1102).


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Authors and Affiliations

  1. 1.Institute of Process System EngineeringQingdao University of Science & TechnologyQingdaoPeople’s Republic of China
  2. 2.College of Chemistry and Chemical EngineeringQilu Normal UniversityJinanPeople’s Republic of China

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