Enter the feed, distillate, and bottoms compositions into the calculator to determine the minimum number of theoretical plates required for a distillation process using the Fenske Equation.
Fenske Equation Formula
The Fenske Equation is used to estimate the minimum number of theoretical plates (stages) required in a distillation column to separate a mixture into its components. The formula is given by:
N = log((xD * (1 - xB)) / (xB * (1 - xD))) / log(xF / xB)
Variables:
- N is the number of theoretical plates (stages)
- xD is the distillate composition (mole fraction)
- xF is the feed composition (mole fraction)
- xB is the bottoms composition (mole fraction)
To calculate the number of theoretical plates using the Fenske Equation, input the mole fraction of the feed, distillate, and bottoms compositions. Ensure that the distillate composition is greater than the feed composition, which in turn should be greater than the bottoms composition.
What is the Fenske Equation?
The Fenske Equation is a fundamental equation in the field of distillation that provides an estimate of the minimum number of theoretical plates required to achieve a given separation. It assumes constant relative volatility, ideal solutions, and total reflux in the distillation process. The equation is particularly useful during the design phase of a distillation column and helps in understanding the efficiency of the separation process.
How to Calculate the Number of Theoretical Plates?
The following steps outline how to calculate the number of theoretical plates using the Fenske Equation.
- First, determine the distillate composition (xD) as a mole fraction.
- Next, determine the feed composition (xF) as a mole fraction.
- Then, determine the bottoms composition (xB) as a mole fraction.
- Use the Fenske Equation: N = log((xD * (1 – xB)) / (xB * (1 – xD))) / log(xF / xB).
- Finally, calculate the number of theoretical plates (N).
- After inserting the variables and calculating the result, check your answer with the calculator above.
Example Problem:
Use the following variables as an example problem to test your knowledge.
Feed composition (xF) = 0.30 (mole fraction)
Distillate composition (xD) = 0.95 (mole fraction)
Bottoms composition (xB) = 0.05 (mole fraction)
