Fenskes plate number

Also for calculation purposes, in every theoretical plate the ascending vapour is in thermodynamic equilibrium with the refluxing liquid. Therefore, together with the mass flow and the mole fractions, the calculations in the rectification unit are performed from plate to plate. The minimal theoretical plate number can be graphically and analytically solved by the method of Fenske, using the following assumptions ... 

Calculation of the minimum plate number by the Fenske equation for ideal mixtures and =00... 

For an overview approximation and dimensioning, the relationships of Fenske and Underwood can be used to determine the minimum plate number N j and the minimum reflux ratio (Equations 2.3.2-26 and 2.3.2-27) ... 

By definitioii the Fenske equation for the minimum plate number only applies for plate columns with a plate efficiency of unity. The use of this equation for packed columns leads to considerable errors, especially at high relative volatilities. The minimum plate number of packed columns shoul be calculated with Equation 2.3.2-28 ... 

The approximate location can be determined by the ratio of the total number of theoretical stages above and below the feed plate from the Fenske total reflux relation ... 

Assays. Nitrogen assays to determine 1-amidoethylene unit content were done by Kjeldahl method. Limiting viscosity numbers were determined from 4 or more viscosity measurements made on a Cannon-Fenske capillary viscometer at 30°C. Data was extrapolated to 0 g/dL polymer concentration using the Huggins equation(44) for nonionic polymers and the Fuoss equation(45) for polyelectrolytes. Equipment. Viscosities were measured using Cannon-Fenske capillary viscometers and a Brookfield LV Microvis, cone and plate viscometer with a CP-40, 0.8° cone. Capillary viscometers received 10 mL of a sample for testing while the cone and plate viscometer received 0.50 mL. 

The Underwood and Fenske equations may be used to find the minimum number of plates and the minimum reflux ratio for a binary system. For a multicomponent system nm may be found by using the two key components in place of the binary system and the relative volatility between those components in equation 11.56 enables the minimum reflux ratio Rm to be found. Using the feed and top compositions of component A ... 

Fenske s equation may be used to find the minimum number of plates. 

The number of plates at total reflux. Fenske s method... 

The number of plates required for a desired separation under conditions of total reflux can be found by applying Fenske s equation, equation 11.59, to the two key components. 

The minimum reflux ratio, Rm is calculated using Underwood s method (Example 11.16) as 0.83 and, using Fenske s method, Example 11.17, the number of plates at total reflux is nm = 8. The following data have been taken from Figure 11.42, attributable to Gilliland(30) ... 

This measure was based upon the ratio of the minimum necessary number of plates, A min (averaged over the reboiler composition) in a column to the actual number of plates in the given column, Nj. Christensen and Jorgensen assumed that the mixture has a constant relative volatility a and the column operates at total reflux using constant distillate composition (x o) strategy (section 3.3.2) and evaluated Nmin using the Fenske equation ... 

For single separation duty, Diwekar et al. (1989) considered the multiperiod optimisation problem and for each individual mixture selected the column size (number of plates) and the optimal amounts of each fraction by maximising a profit function, with a predefined conventional reflux policy. For multicomponent mixtures, both single and multiple product options were considered. The authors used a simple model with the assumptions of equimolal overflow, constant relative volatility and negligible column holdup, then applied an extended shortcut method commonly used for continuous distillation and based on the assumption that the batch distillation column can be considered as a continuous column with changing feed (see Type II model in Chapter 4). In other words, the bottom product of one time step forms the feed of the next time step. The pseudo-continuous distillation model thus obtained was then solved using a modified Fenske-Underwood-Gilliland method (see Type II model in Chapter 4) with no plate-to-plate calculations. The... 

In this approach, Fenske s equation [Ind. Eng. Chem., 24, 482 (1932)] is used to calculate which is the number of plates required to make a specified separation at total reflux, i.e., the minimum value of N. Underwood s equations [/. Inst. Pet., 31, 111 (1945) 32,598 (1946) ... 

MINIMUM NUMBER OF PLATES. The Fenske equation (18.41) applies to any two components, i and j, in a conventional plant at infinite reflux ratio. In this case, the equation has the form... 

The minimum number of plates is obtained from the Fenske equation [Eq. 

Distillation The permeate from PDMS PV moduleisfed toaplatecolumn.Operating (L/D)=1.5 x(L/D),nin obtained from Fenske s method. Product composition was fixed at 95 wt% EtOH. Gilliland s equation was used to estimate the number of theoretical plates required and capital cost. An enthalpy balance gave the heat load, reboiler, and condenser capital costs. 

Here m and C are obtained from the least square fittings The number of plates can now be obtained by the following Fenske type equation ... 

The optimum feed plate location can also be estimated. First, use the Fenske equation to estimate where the feed stage would be at total reflux. This can be done by determining the number of stages required to go from the feed concentrations to the distillate concentrations for the keys. 

Having evaluated R i, the corresponding number of plates N can be determined. The calculation is truncated by employing another useful rule of thumb that when R = 2R the number of plates required in the column will be JV = 2N i , where iV is the number of plates required at total reflux. Determination of N begins with Fenske s relationship ... 

Total Reflux Fenske (Ref. 6) developed an algebraic method of calculating the minimum number of theoretical plates by utilizing the relative volatility together with the fact that at total reflux the operating line becomes the y x diagonal. Thus, considering the two... 

Fenske (1932) developed an equation to estimate the number of ideal stages needed under total reflux to go from the bottoms composition Xuh to the top distillation composition Xiu. We will start from the reboiler and then the bottommost plate N. The total reboil mode of operation without any bottoms liquid product means that the following relation is valid for the reboiler ... 

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