- Non-Random Two Liquid model
The

**Non-Random Two Liquid**model [*Renon H., Prausnitz J. M., "Local Compositions in Thermodynamic Excess Functions for Liquid Mixtures", AIChE J., 14(1), S.135-144, 1968*] (short**NRTL**equation) is an activity coefficient model that correlates theactivity coefficient s $gamma$ with the composition of a mixture of chemical compounds, expressed bymole fraction s $x$.**Equations**For a binary mixture the following equations [

*Reid R. C., Prausnitz J. M., Poling B. E., The Properties of Gases & Liquids, 4. Edition, McGraw-Hill, 1988*] are used::$ln\; gamma\_1=x^2\_2left\; [\; au\_\{21\}left(frac\{G\_\{21\{x\_1+x\_2\; G\_\{21\; ight)^2\; +frac\{\; au\_\{12\}\; G\_\{12\; \{(x\_2+x\_1\; G\_\{12\})^2\; \}\; ight]$

:$ln\; gamma\_2=x^2\_1left\; [\; au\_\{12\}left(frac\{G\_\{12\{x\_2+x\_1\; G\_\{12\; ight)^2\; +frac\{\; au\_\{21\}\; G\_\{21\; \{(x\_1+x\_2\; G\_\{21\})^2\; \}\; ight]$

with

:$ln\; G\_\{12\}=-alpha\_\{12\}\; au\_\{12\}$

and

:$ln\; G\_\{21\}=-alpha\_\{12\}\; au\_\{21\}$

$au\_\{12\}$ and $au\_\{21\}$ as well as $alpha\_\{12\}$ are fittable parameters. In most cases the parameters $au$

:$au\_\{12\}=frac\{Delta\; g\_\{12\{RT\}$

and

:$au\_\{21\}=frac\{Delta\; g\_\{21\{RT\}$

are scaled with the

gas constant and the temperature and then the parameters $Delta\; g\_\{12\}$ and $Delta\; g\_\{21\}$ are fitted.**Temperature dependent parameters**If activity coefficients are available over a larger temperature range (maybe derived from both vapor-liquid and solid-liquid equilibria) temperature-dependent parameters can be introduced.

Two different approaches are used:

:$au\_\{ij\}=f(T)=a\_\{ij\}+frac\{b\_\{ij\{T\}+c\_\{ij\}\; ln\; T+d\_\{ij\}T$

:$Delta\; g\_\{ij\}=f(T)=a\_\{ij\}+b\_\{ij\}cdot\; T\; +c\_\{ij\}T^\{2\}$

Single terms can be omitted. E. g., the logarithmic term is only used if liquid-liquid equilibria (

miscibility gap) have to be described.**Parameter determination**The NRTL parameters are fitted to activity coefficients that have been derived from experimentally determined phase equilibrium data (vapor-liquid, liquid-liquid, solid-liquid) as well as from heats of mixing. The source of the experimental data are often factual data banks like the

Dortmund Data Bank . Other options are direct experimental work and predicted activity coefficients withUNIFAC and similar models.**Literature**

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