Multicomponent Distillation using the Fenske-Underwood-Gilliland Method.pdf
- 1. Multicomponent Distillation using the Fenske-Underwood- Gilliland Method
- 2. Outline of FUG Method • Two key components need to be specified as the light key (LK) and Heavy key (HK). These may approximately represent separation based on these key components • Non-key components are assumed to fully separate into either distillate or bottoms product along with the light and heavy key respectively.
- 3. Outline of FUG Method • Components listed in order of decreasing volatility.
- 4. Fenske Equation for finding minimum number of theoretical stages (NTmin) • i- LK and j – HK • Simpler version of Fenske equation, assuming a geometric mean for relative volatility: • di and bi are desired flow rate of LK in distillate and bottoms product. dj and bj are HK flow rates in distillate and bottoms product. • While yi,N and xi,1 can be obtained by material balance, K values may be required to find xi,N and yi,1.
- 5. Distribution of non-key components • Once Nmin is known, all other non-key component flowrates can be calculated. • For example, taking the HK as the reference component “r”, any non- key component “i” can be found by: • in the above equation gives: • Note: relative volatilities between each non-key and and the reference component needs to be known.
- 6. Underwood equation for minimum reflux ratio (Rmin) • As previously mentioned, determining Rmin is essential for obtaining R. R = 1.2Rmin to 1.5Rmin • A material balance may be conducted over the rectifying section as shown. • With: as per phase equilibrium • Combining the above equations and writing in term of relative volatility:
- 7. Underwood equation for minimum reflux ratio (Rmin) • Assuming some liquid feed and that all products exist in all product streams at least to some minimal extent (ie. Class 1 separation): • All non-key components must satisfy the condition below for the above equation to be valid: • More complex (Class 2) calculations apply if such conditions are not met.
- 8. Gilliland Correlation for actual number of theoretical stages (NT) • Once Rmin is obtained, R may be calculated. • NT may be found using the Gilliland correlation graphically or algebraicly where Valid for:
- 9. Gilliland Correlation for actual number of theoretical stages (NT) • Linear scaled graphs of the Gilliland correlation is also available, as well as a more accurate version taking into account feed state
- 10. Kirkbride Equation for feed stage location • Feed stage is obtained indirectly by first calculating the number of stages the rectifying and stripping section should have. • A ratio of number of rectifier stages to stripping stages may be calculated and applied to the total number of theoretical stages • NT = NR + NS = NS + NS