FUG Method for Multi-Component Distillation

The presentation gives an overview of the FUG method for multi component distillation in the Process Industries.

1. ) FUG Method of Multi-component Distillation Column Design ( Fenske - Underwood –Gilliland Method

2. Analytical approach is used for multi-component distillation column design as graphical methods do not work in this case. Separation of multicomponent mixture is specified in terms of two key components of the mixture - the light key and the heavy key. The light key will have a specified maximum limit in the bottom product whereas the heavy key will have a specified maximum limit in the overhead product. Normally the keys are adjacent to each other in volatility. The non-key components are called the distributed components.

3. FUG METHOD FUG ( Fenske - Underwood –Gilliland) Method is perhaps the most popular multi-component distillation column design procedure. Most of the commercially available process simulators contain optional shortcut methods as well as more rigorous stage-to-stage algorithms. These shortcut as well as stage-to-stage methods have certain strengths and weakness.

4. FUG Method The separation is specified based on the concentrations of the two key components in the overhead and bottom products. The minimum number of stages is then determined by the Fenske Equation The minimum reflux ratio is determined based on the Underwood method. Based on the selected reflux ratio, the Gilliland correlation is used to estimate the number of equilibrium stages. Concentrations of the distributed components in the overhead and the bottom products are determined by a modified Fenske equation. The method of Kirkbride can then be used to determine tray location.

5. Fenske equation For multicomponent systems, an approximate value of the minimum number of equilibrium stages (at total reflux) may be obtained from Fenske equation (Fenske, 1932). In the Fenske equation below, relative volatility is based on the light key relative to the heavy key. (1) N min = minimum number of equilibrium stages. x LK = mole fraction of light key. x HK = mole fraction of heavy key. D= denotes distillate product B= denotes bottom product. α LK/HK = average value of relative volatility of light key relative to the heavy key.

6. Contd. The average value of relative volatility is calculated from the mean of the relative volatility at the top of the column (α LK/HK ) D and at the bottom of the column (α LK/HK ) B . (α LK/HK ) D is based on the dew point & (α LK/HK ) B is based on bubble point. 2)

7. Bubble Point is the initial boiling point of a mixture and is calculated as 3) Dew Point is the initial point of condensation of a mixture calculated as 4) K i = equilibrium ratio of component i. = vapor pressure of pure component I at the system temperature (force/length 2 ). = Total pressure.

8. Procedure to find dew and bubble point: Assume a temperature. Determine K values. Calculate the sum on the left side of the equation (3). If left side is smaller than unity, increase temperature to assume a new temperature. If left side is higher than 1, then decrease temperature to assume a new one. Continue the process till equation (3) is satisfied. For the determination of Dew point, assume a temperature. If the left side of equation (4) is less than 1, decrease temperature to assume a new one. If left side is higher than 1, increase temperature till equation (4) is satisfied. Proceed till equation (4) is satisfied. After the determination of Dew and Bubble point, vapor liquid composition can be determined graphically.

9. Temperature composition diagram for vapor- liquid

10. Minimum reflux by underwood method: For multicomponent mixtures the Underwood method may be used for estimating minimum reflux ratio (Underwood, 1948). Underwood proposed the equation (5) to calculate minimum reflux ratio. 5) Where, N = Number of components. = average relative volatility based on component i relative to heavy key. = mol fraction of i in the feed. Q = number of mols of saturated liquid produced on the feed tray per mol of feed. θ = unknown parameter to be determined by trial and error.

11. The correct value of θ will be between relative volatility of the two key components. After the value of θ is determined equation (6) may be used to determine minimum reflux ratio. 6) Where, R min = Minimum reflux ratio x Di = Mol. Fraction of component i in distillate (D)

12. Number of equilibrium stages by Gilliland Correlation: Once minimum stages and reflux ratio are known the number of equilibrium stages may be determined as a function of selected values of operating reflux ratio. Several methods have been proposed including the correlation of Gilliland (1942) to determine the no. of equilibrium stages as a function of reflux ratio. The Gilliland correlation was first developed as a plot shown in Fig.1. But later it was a transformed of Eduljee (1975) into eqn. (7). 7) Where, N = No. of equilibrium stages R = Operating reflux ratio N min = Minimum no. of equilibrium stages R min = Minimum reflux ratio

13. The optimum operating reflux ratio may be determined from capital and operating costs at various reflux ratio. Low reflux ratios require a large number of equilibrium stages which translates to high capital cost for equipment. High reflux ratios translate to high energy consumption and operating costs. The optimum operating reflux ratio usually lies between 1.1 and 1.4 times the minimum reflux ratio.

14. Distributed components by Fenske equation: Value for the distributed or non-key components may be determined after the number of minimum stages has been determined. To determine concentrations of distributed components in the distillate and bottoms products, the Fenske equation may be written for any component i as follows: 8) Where, (α i ) n = Average relative velocity of component I relative to heavy key.

15. Location of feed tray: The method of Kirkbride (1944) may be used to determine the ratio of the number of equilibrium stages above and below the feed point: 9) Where, M = No. of equilibrium stages above feed tray B = Bottom product rate

16. Use of Simulator: In Industry, a simulator containing stage to stage calculation algorithms is almost always used to determine the number of equilibrium stages. Such simulators also include thermodynamic databases which also allow determinations of the vapor/liquid equilibria. Such simulators are commercially available. Some Simulators used in Industry: Name Supplier Software description ASPEN PLUS Aspen technology, Inc. In addition to conventional Ten Canal Park, Cambridge distillation this simulators MA02141 addresses adsorption, stripping, extraction, azeotropic distillation, including non-ideal mixtures

17. Name Supplier Software description PRO/II with Simulation Sciences, Inc. 1. PETROFRAC is PROVISION GOIS Valencia, Ave, Brea specifically designed for CA92621 petroleum refinery applications such as preflash towers, crude units, vac. Units, main fractionator, delayed cokers. 2. Provide fine types of robust solutions for distillation, each based on rigorous stage to stage solutions for the MESH equation.