Plate Fenskes

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) ... 

Fenske and Long (F2) have described a small, laboratory extractor of 20 countercurrent stages of unique design. The mixers are agitated by rapidly reciprocating perforated plates, reminiscent of the early Van Dijck design (VI), and produce an action similar in many ways... 

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... 

The filtrates from two such runs are combined and distilled through a Whitmore-Fenske column of 10-15 theoretical plates at a 5 1 reflux ratio. The yield of fer/.-butylamine is 55-60 g. (75-82%) the product boils at 44-44.5°, and its refractive index is n 1.3770 (Note 8). 

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) ... 

The viscosity of the solutions was measured using the Cannon-Fenske viscometer. The foam tests were done by the conventional cylinder shake test In which a fixed amount of the solution Is shaken vigorously for a minute and the foam height Is monitored with time. The surface pressure measurements were carried out using a conventional Langmuir trough set-up, again with a platinum plate sensor. See text for further details. 

The reaction mixture consists of unchanged heptaldehyde, heptaldehyde enol acetate, heptaldehyde diacetate, and a small amount of polymerized material. The proportion of free heptaldehyde and heptaldehyde diacetate depends upon the time of heating, longer periods of heating favoring the formation of the diacetate. An eflBcient fractionating column, preferably of the Whitmore-Fenske type, should be used in order to obtain the enol acetate free of the heptaldehyde and heptaldehyde diacctatc impurities. The checkers used a Whitmore-Fenske type column of about six theoretical plates. 

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 ... 

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. 

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

---