# Optimize Batch Distillation

## Proper design depends upon an understanding of key relationships.

Don’t store hot liquids, e.g., hydrocarbons, or subcool the reflux because this causes internal reflux that requires additional still heat input; install rundown coolers appropriately.

**THERMODYNAMICS**

The Antoine equation can be used to calculate the vapor pressure and concentrations at temperatures other than a solvent’s atmospheric boiling point [3, 4]:

*logp = a – b/(c + t)* (1a)

or for natural log:

ln *p = a _{e} – b_{e}/(c_{e} + T)* (1b)

where p is the vapor pressure of the component, mm Hg; t is temperature, °C; *T* is temperature,* K*; a, b and c are Antoine coefficients (base 10) for each pure solvent [3]; *a _{e}, b_{e}* and

*c*

_{e}are Antoine coefficients (natural) for each pure solvent [per CHEMCAD simulator], where

*lnp = 2.303 log p*.

The coefficients can be converted via:

*a = a _{e}/2.303; b = b_{e}/2.303; and c = c_{e} – 273.*

The Cox equation is an approximation based on Antoine coefficientc being in the 210–250 range. It allows calculation ofa andb from two known points on the vapor-pressure/temperature relationship, and estimation of the relative volatility of an ideal binary mixture throughout the operating temperature range.

*log p = a[b/(t +230)]* (2)

This allows relating the coefficients to relative volatility:

*α = p _{1}/p_{2}*(3)

log *α = log p _{1} – log p_{2}* (4)

log *α = (a _{1} – a_{2}) – (b_{1} – b_{2})/(t+ 230)* (5)

where α is relative volatility based on Raoult’s law, and the subscripts 1 and 2 denote a particular component, with 1 representing the more volatile component (mvc). Note: α increases as the temperature decreases, which is achievable by operating at a reduced pressure.

For ternary mixtures in a simple distillation, a plot of liquid compositions on triangular axes is known as a residue curve. The residue curve indicates the locus of the liquid composition remaining behind in the still bottoms during a simple equilibrium distillation process. The residue curve depends upon the starting liquid composition from which a family of curves can be generated to create a residue curve map (RCM), which is used to determine the viability of a distillation; the RCM provides a great amount of insight into the separation of a mixture [4].

All residue curves originate at low-boiling pure components or azeotropic compositions (low-boiling nodes) and end at high-boiling compositions (high-boiling nodes). An RCM with more than one origin for residue curves has more than one distillation region.

Intermediate-boiling pure components and azeotropes that aren’t nodes are called saddles. In a distillation region (three-sided) with one saddle, all residue curves track back toward the solitary saddle. However, in a region with two non-adjacent saddles (four-sided), some residue curves track toward each saddle.

The RCM and mass balance identify feasible operations because the distillate and bottoms will lie on the same residue curve, which must be in the same distillation region. For heterogeneous azeotropes, overlaying the RCM with the liquid/liquid phase equilibrium (binodal) diagram will show valid operating conditions.

Consider the residue curve for water/benzene/ethanol where there are three binary and one ternary minimum-boiling azeotropes (Figure 2). Only one of the binary azeotropes and the ternary azeotrope are heterogeneous. Each pure component is a high-boiling node in one of the three distillation regions, with the ternary being the low-boiling node in all three regions. Pure ethanol is only obtainable within Region 1. Exploiting the liquid/liquid equilibrium (LLE) allows us to cross the distillation boundaries between Regions 1, 2 and 3 to obtain a benzene-rich stream.

A convenient distillate composition in the two-phase LLE region is the ternary azeotrope, being the low-boiling node in all three regions. The organic layer from the ternary azeotrope is in Region 3 and the aqueous layer is in Region 2 — note that mixing the organic layer with the feed can produce a composition in Region 1.

**MASS AND ENERGY BALANCES**

The primary objective in a batch distillation is to minimize both batch cycle time and heat input by optimizing the number of stages and reflux ratio to achieve the required separation [3, 5]. The process variables are interdependent as determined by the mass and energy balances and the mode of operation.

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