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Goal-seek and Solver subroutines make the hunt for three unknown constants in the NRTL equation set easy
(ProQuest: ... denotes formulae omitted.)
You can't sensibly design a distillation column without an accurate vapor-liquid equilibrium (VLE) curve. The Dechema Series of VLE data [2] provides a compilation for a wide variety of mixtures, along with corresponding regressed parameters for several of the liquid activity-coefficient equations. However, it is necessary for engineers to occasionally perform their own regression of VLE data.
This need arises when the data can be found in literature but without regressed parameters or when VLE data are developed in a laboratory. Reference [2] describes laboratory methods for generating VLE data, and criteria for deciding if distillation is the appropriate process for a separation.
The spreadsheet program described below makes regression of binary VLE data a fast operation. A relatively simple Microsoft Excel macro is outlined in Figure 1. It can shorten this solution process to several minutes, instead of several hours.
A brief review
One form of equilibrium equation (Equation [1]) uses a distribution coefficient that relates compositions of liquid and vapor phases.
... (1)
When the components form an ideal solution, K¿ is a function of temperature, pressure and composition. KL can be defined in terms of vapor pressure and system pressure by combining Equation (1) with Raoult's Law and Dalton's Law of Partial Pressures, as per Equation (2).
... (2)
Vapor-pressure values can be found in the literature. A good correlation is the Antoine equation (Equation [3]).
... (3)
When there is interaction of the components within the solution, it is not ideal, so one must include a correction factor or a liquid-phase activity coefficient, y, in the equilibrium equation (Equation [4]).
... (4)
The activity coefficient depends on temperature, pressure, and concentration of all constituents of the liquid. It corrects for non-idealities only in the liquid phase, and so should be used to model systems where the vapor phase is ideal (systems with low to moderate pressures).
Several equations have been developed for use in calculating the liquidphase activity coefficient. These equations incorporate several parameters that can be adjusted to fit experimental VLE data. Some of the more common equations are those for the NRTL (non-random two-liquid) [3], Wilson,...