1.1690 1.1640 1.1593 1.1549 1.1507 1.1467 1.1429 1.139 y>_3_
UNIFAC model is still developing, and there are four versions until now: (1) The original UNIFAC model that can be applied for infinite dilution and finite concentration (thereof called model 1)
The original UNIFAC model [20-26] was widely used before. The activity coefficient is expressed as functions of composition and temperature. The model has a combinatorial contribution to the activity coefficient, i.e. In/' , essentially due to differences in size and shape of the molecules, and a residual contribution, i.e. In/,", essentially due to energetic interactions.
I . Combinatorial part.
L'lx Lrixj j j
Pure component parameters r: and q are, respectively, relative with molecular van der Waals volumes and molecular surface areas. They are calculated as the sum of the group volume and group area parameters, Rk and Qk, r, =5><'X; q, =5>i"& (76)
where v[°, always an integer, is the number of groups of type k in molecule i. Group parameters Rk and Qk are normally obtained from van der Waals group volumes and surface areas, Vk and Ak, given by Bondi ,
k is the group residual activity coefficient, and is the residual activity coefficient of group A: in a reference solution containing only molecules of type i.
lnrA =Qk[\-\nC£dm¥mk)-Y4(emYkjYJd„¥„m)'\ (79)
Xm is the fraction of group m in the mixture.
Parameter anm characterizes the interaction between groups n and m . For each group-group interaction, there are two parameters: anm anm.
Eqs. (79) and (80) also hold for Inr^', except that the group composition variable, 6k, is now the group fraction of group k in pure fluid i. In pure fluid, lnTj = lnl^'1, which means that as ^ —» 1, yf —> 1. yf must be close to unity because as x( —> 1, yf —> 1 and yl -> 1.
(2) The modified UNIFAC model that can be applied for infinite dilution and finite concentration (thereof called model 2)
In the modified UNIFAC(Dortmund) model [28-33], as in the original UNIFAC model, the activity coefficient is also the sum of a combinatorial and a residual part:
The combinatorial part is changed in an empirical way to make it possible to deal with compounds very different in size:
The parameter V: can be calculated by using the relative van der Waals volumes Rk of the different groups.
All other parameters are calculated in the same way as in the original UNIFAC model:
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