Multi-stage batch distillation is simulated using animation. 10 kmol of a binary mixture (components A and B, with B being the more volatile component) is placed in a batch still. Use the "initial mole fraction B" slider to set the initial composition of the still. Next, adjust the number of trays in the column with the "equilibrium stages" slider, and adjust the reflux ratio of the column with the "reflux ratio (L/D)" slider. Specify the amount of liquid to be collected using the "amount to collect" slider.
When you click "collect", the outlet valve is opened and liquid evaporates into a collection container. The container is then set aside and an empty container is substituted. This process can be repeated until 1 kmol remains in the still or eight containers have been filled. You may view previously collected distillate by selecting "collected distillate" on the drop-down menu above the plot. Select "reset" to start over. You may hover the mouse over the following to see a tooltip:
Multistage batch distillation can obtain much higher product purity than simple batch distillation. The overall mass balance is:
$$ F = W_{final} + D_{total} $$where \( F \) is the initial molar quantity of the feed mixture, \( W_{final} \) is the molar quantity in the bottoms vessel (the "waste" product), and \( D_{total} \) is the total molar quantity of collected distillate. The component mass balance is:
$$ F \; x_{f} = W_{final} \; x_{W,final} + D_{total} \; x_{D,avg} $$where \( x_{F} \) is the initial mole fraction of component B in the feed, \( x_{D,avg} \) is the average mole fraction of component B within the collected distillate, and \( x_{W,final} \) is the final mole fraction within the bottoms vessel.
Each tray in the column is assumed to be in vapor-liquid equilibrium:
$$ y = f(x) $$The function \( y = f(x) \) represents an equilibrium curve, plotted on an x-y diagram. The composition of each stage lies somewhere upon this curve.
An operating line relates the composition of a stage to the adjacent stage composition. The operating line equation is:
$$ y_{n} = \frac{ R }{ R + 1 } x_{ n + 1 } + \left( 1 - \frac{ R }{ R + 1 } \right) x_{D} $$where \( y_{n} \) is the vapor mole fraction of B at stage \( n \), \( R \) is the reflux ratio, and \( x_{ n + 1 } \) is the liquid mole fraction of B at stage \( n + 1 \). The reflux ratio is:
$$ R = \frac{L}{D} $$where \( L \) is the flow rate of liquid returning from the condenser to the column, and \( D \) is the flow rate of distillate being collected. The Rayleigh equation can be used to solve for the final composition of distillate and bottoms:
$$ \mathrm{ln} \left( \frac{ W_{final} }{ F } \right) = \int_{ x_{F} }^{ x_{ W, final } } \frac{ 1 }{ x_{D} - x_{ W } } \mathrm{d} x_{ W } $$but the relationship between distillate composition and bottoms composition \( f ( x_{ W } ) = x_{ D } \) is complicated with multistage columns, so the mole fractions are obtained numerically.
Reference
[1] P. C. Wankat, "Batch Distillation," Separation Process Engineering: Includes Mass Transfer Analysis, 3rd ed., Upper Saddle River, NJ: Prentice Hall, 2012 pp. 329-347.
This simulation was created in the Department of Chemical and Biological Engineering, at University of Colorado Boulder for LearnChemE.com by Neil Hendren under the direction of Professor John L. Falconer. Address any questions or comments to learncheme@gmail.com. All of our simulations are open source, and are available on our LearnChemE Github repository.