In this Demonstration, a trayed stripping column is used to remove an impurity from a liquid feed by stripping the impurity into a gas stream. The pink operating line is obtained from a mass balance, and its slope \(L/V\) (the ratio of liquid flow rate to gas flow rate) is shown on the column on the right. The phase equilibrium line, which is obtained from Henry's law, is orange. The top and bottom of the column are labeled on the \(x\)-\(y\) diagram. The number of trays/stages needed to obtain an outlet solute mole ratio of \(x_N\) ppm in the liquid stream is calculated. A stage is a plate that contacts the liquid solvent and the gas to promote mass transfer. When a partial stage is calculated, the number of stages is rounded down to the nearest full stage. Use the sliders to change the pressure and temperature in the column, the gas flow rate \(V\) and the solute mole ratio in the gas feed, \(y_{N+1}\). Check the "\((L/V)_{max}\)" box to show the maximum slope for the operating line; this condition would require an infinite number of stages. Check "show diagram with 5 stages" to set conditions that require five stages and display the mole ratios entering and leaving each stage. Use the "stage" slider to move through each stage and display the solute fluxes in and out of that stage on the \(x\)-\(y\) diagram.

The equilibrium line is calculated using Henry's law: $$y_{eq}=\frac{H}{P}x$$ $$H=H_0 \ e^{-\frac{E}{R}(\frac{1}{T}-\frac{1}{T_0})}$$ where \(H\) is Henry's constant (atm), \(P\) is pressure (atm), \(H_0\) is Henry's constant at \(T_0\) = 298 K (atm), \(R\) is the ideal gas constant (J/(mol K)) and \(T\) is temperature (K).

The operating line is calculated from a mass balance around the stripper: $$x_0 L+y_{N+1} V=x_N L+y_1 V,$$ which rearranges to: $$y_{N+1}=\frac{L}{V}x+(y_1-\frac{L}{V}x_0),$$ where \(L\) is the liquid solvent molar flow rate (Mmol/h), \(V\) is the gas molar flow rate (Mmol/h), \(x_0\) is the mole ratio of the impurity in the inlet liquid solvent stream (ppm), \(y_{N+1}\) is the mole ratio of the impurity in the inlet gas stream (ppm), \(x_N\) is the mole ratio of the impurity in the outlet liquid solvent stream (ppm) and \(y_1\) is the mole ratio of the impurity in the outlet gas stream (ppm).

To count off stages, start at \(x_0\) on the operating line (\(x_0, y_1\)), then draw a horizontal line to the equilibrium line (\(x_1, y_1\)). Then draw a vertical line down to the operating line. Repeat these steps until \(x_N\) is reached.

The outlet liquid mole ratio \(x_N\) is calculated from the mass balance: $$x_N = x_0 + \frac{y_{N+1}-y_1}{L/V}.$$ Reference

[1] P. C. Wankat, Separation Process Engineering: Includes Mass Transfer Analysis, 3rd ed., Upper Saddle River, NJ: Prentice Hall, 2011.

This simulation was created in the Department of Chemical and Biological Engineering, at University of Colorado Boulder for LearnChemE.com by Rachael Baumann and Adam Johnston under the direction of Professor John L. Falconer and was converted to HTML5 by Patrick Doyle and Drew Smith, with additional contributions by Neil Hendren. This simulation was prepared with financial support from the National Science Foundation. Address any questions or comments to learncheme@gmail.com. All of our simulations are open source, and are available on our LearnChemE Github repository.

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