Distillation Column: Reflux Rate & Relative Volatility

[patouvas]

Dear Colleagues, I write this post in order to clarify some doubts that have been raised after reading Chapter 3 of "Working Guide to Process Equipment" by Norman P. Lieberman.

In this chapter, author talks about importance of choosing an appropriate column pressure also discuss the effects of rising/ lowering column pressure. One of the suggested advantages of lowering column operating pressure is improve fractionation because relative volatility between a light component and a heavier one increases (NOTE: Author defines Relative Volatility as the ratio between the vapor pressure of a light component at a given temperture and the vapor pressure of a heavier component at the same temperature). Author gives as an example the mixture of isobutane/ pentane and indicates their relative volatility is equal to 4.0 at 140ºF and 4.9 at 110ºF; aprox. 20% increase.

Author concludes an increase in relative volatility allows one to make a better split at a given reflux or to make the same split at a lower reflux rate and quantifies this last statement as follows:

DRF = (RVL - RVH) / (RVH - 1)

Where:

* RVH is relative volatility at Column Operating Pressure A.
* RVL is relative volatility at Column Operating Pressure B (Column Operting Pressure A > Column Operting Pressure B).
* DRF is the percent reduction in the reflux rate, when the same degree of fractionation is desired.

I want to share with you the following doubts/ questions about the aforesaid topic.

a) I had never read/heard relative volatility being defined the way Lieberman suggests. Had you ever read something like this before? It seems really different than the "classic definition" of relative volatility:

α = (y_i / x_i ) / ( y_j / x_j )

where:
* α is the relative volatility of the more volatile component "i" to the less volatile component "j".
* y_i is the vapor–liquid equilibrium concentration of component "i" in the vapor phase.
* x_i is the vapor–liquid equilibrium concentration of component "i" in the liquid phase.
* y_j is the vapor–liquid equilibrium concentration of component "j" in the vapor phase.
* x_j is the vapor–liquid equilibrium concentration of component "j" in the liquid phase.

Is there anit way to reconcile both definitions of relative volatility??.

b) How could author obtain the equation to correlate change of relative volatility with pressure with percent reduction in the reflux rate? . Can it be theoretically obtained or is it only a "rule of tumb"??. Does not it seem more logical next equation?

DRF = (RVL - RVH) / (RVH)

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Thanks for reading this post. I hope you could help me. Any additional clarification, please let me know.

Greetings from Madrid, Spain.

 

[Latexman]

a) Using ideal solution conditions, the definition of partial pressure, and Raoult's Law I think you can prove them equivalent.

p_i = y_i * P_T = x_i * p*_i

y_i / x_i = p*_i / P_T



Good luck,
Latexman

To a ChE, the glass is always full - 1/2 air and 1/2 water.

 

[spekuljak]

Hola: 1)la expresión Volat. relat. = (pres. vapor liv./presion vapor pesado) es válida para mezcla binaria e ideales (coefic. de desviación de la idealidad, fases liq. y fase vapor = 1). Se demuestra fácilmente.

2)La expresión de comparación de volat. relativa con la relación de reflujo, se puede ver a partir de la ecuación de Underwood para la determinación del reflujo mínimo, aplicado a 2 componentes. de allí se ve que Rmin. = f(1/volt. relat).

Greetings from Argentina.