Fenske method

The Fenske Method gives a quick estimate for the minimum theoretical stages at total reflux. 

Gilliland (45) used the Fenske method (Sec. 3.2.1) to compute minimum stages, and his own method for computing minimum reflux. However, it was shown (11,48) that the Underwood method (Sec. 3.2.2) for minimum reflux can also be used. 

These methods determine the viscosities of polyols in the range from 10 to 10,000 cP at 25 C and 50 C. Test Method A (Brookfield Viscosity) also applies to more viscous samples soluble in n-butyl acetate. Test Method B is the Cannon Fenske method. 

The Fenske Method gives a quick estimate for the minimum theoretical stages at total reflux. N 1 Xhk)d( hk/Xlk)b] " ln(aLKHK),vG Nomenclature LK = subscript for light key Nm = minimum theoretical stages at total reflux Xhk = mol fraction of heavy key component Xlk = mol fraction of the light key component otLK/HK = relative volatility of component vs the heavy key component... 

First, the minimum number of stages is computed by the Fenske method. Then, the minimum reflux ratio is computed by the Underwood method. Next, the design (operating) reflux ratio is chosen as some multiple of the minimum reflux ratio, e.g., 1.15 x R. (The optimum multiple is in the... 

This special issue celebrating 40 years of computational chemistry seems an appropriate venue to revisit the so-called Fenske-HaU molecular orbital (MO) method. This approximate molecular orbital theory had its origins almost exactly 40 years ago when Richard F. Fenske joined the Department of Chemistry at the University of Wisconsin, Madison. Thus, the method might be more properly called the Fenske method or the Fenske, Radtke, Caulton, DeKock, Hall method as the early development [1] involved many students in addition to one of the authors above (MBH). The name Fenske-HalF was generated not by the first papers on the development of the method, but by the last paper on its theoretical development [2]. The method is still in use today and has... 

Next, the relative volatilities, a, are determined as averages of estimated s obtained from T-value calculations at overhead and bottoms conditions. These conditions include the operating pressure, the estimated overhead and bottoms compositions, and the estimated dew point and bubble point temperatures. With a starting set of relative volatihties, the minimum trays, N , and the overhead and bottoms compositions at total reflux are calculated by the Fenske method (Equations 12.17 and 12.17a) for the specified separation. The new compositions may be used to recalculate more accurately the temperatures, pressures, and relative volatihties. The process is repeated until the a s stabilize. 

The Fenske-Hall method is a modification of crystal held theory. This is done by using a population analysis scheme, then replacing orbital interactions with point charge interactions. This has been designed for the description of inorganic metal-ligand systems. There are both parameterized and unparameterized forms of this method. 

Simple analytical methods are available for determining minimum stages and minimum reflux ratio. Although developed for binary mixtures, they can often be applied to multicomponent mixtures if the two key components are used. These are the components between which the specification separation must be made frequendy the heavy key is the component with a maximum allowable composition in the distillate and the light key is the component with a maximum allowable specification in the bottoms. On this basis, minimum stages may be calculated by means of the Fenske relationship (34) ... 

However, the total number of equilibrium stages N, N/N,n, or the external-reflux ratio can be substituted for one of these three specifications. It should be noted that the feed location is automatically specified as the optimum one this is assumed in the Underwood equations. The assumption of saturated reflux is also inherent in the Fenske and Underwood equations. An important limitation on the Underwood equations is the assumption of constant molar overflow. As discussed by Henley and Seader (op. cit.), this assumption can lead to a prediction of the minimum reflux that is considerably lower than the actual value. No such assumption is inherent in the Fenske equation. An exact calculational technique for minimum reflux is given by Tavana and Hansen [Jnd. E/ig. Chem. Process Des. Dev., 18, 154 (1979)]. A computer program for the FUG method is given by Chang [Hydrocarbon Process., 60(8), 79 (1980)]. The method is best applied to mixtures that form ideal or nearly ideal solutions. 

For preliminary studies of batch rectification of multicomponent mixtures, shortcut methods that assume constant molal overflow and negligible vapor and liquid holdup are useful. The method of Diwekar and Madhaven [Ind. Eng. Chem. Res., 30, 713 (1991)] can be used for constant reflux or constant overhead rate. The method of Sundaram and Evans [Ind. Eng. Chem. Res., 32, 511 (1993)] applies only to the case of constant remix, but is easy to apply. Both methods employ the Fenske-Uuderwood-GiUilaud (FUG) shortcut procedure at successive time steps. Thus, batch rectification is treated as a sequence of continuous, steady-state rectifications. 

The combined Fenske-Underwood-Gillilland method developed by Frank [100] is shown in Figure 8-47. This relates product purity, actual reflux ratio, and relative volatility (average) for the column to the number of equilibrium stages required. Note that this does not consider tray efficiency, as discussed elsewhere. It is perhaps more convenient for designing new columns than reworking existing columns, and should be used only on at acent-key systems. 

A limitation of the Erbar-Maddox, and similar empirical methods, is that they do not give the feed-point location. An estimate can be made by using the Fenske equation to calculate the number of stages in the rectifying and stripping sections separately, but this requires an estimate of the feed-point temperature. An alternative approach is to use the empirical equation given by Kirkbride (1944) ... 

The graphical procedure proposed by Hengstebeck (1946), which is based on the Fenske equation, is a convenient method for estimating the distribution of components between the top and bottom products. 

For binary systems or systems that approach binary, the Fenske-Underwood-Erbar/Maddox Method is recommended. For minimum stages, use the Fenske equation.12... 

The conformational properties of various 1,1 -diheteroferrocenes (7-10) have been the subject of three computational studies using extended Huckel methods.19,46 471,1 -Diphosphaferrocene has also been studied using the Fenske-Hall approach.48 and an MS Xa method.46 Where they overlap, the four treatments are in reasonable qualitative agreement. 

Fenske, R.A., Bimbaum, S.G., Methner, M.M., and Soto, R. (1989) Methods for assessing fieldworker hand exposure to pesticides during peach harvesting, Bull. Environ. Contam. Toxicol, 43 805-815. 

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 measurements were performed in an Ostwald Cannon-Fenske viscometer (No. J-627-25) using the method described by Silberberg and Klein Ci). This involves determining the time of flow as a function of the amount of liquid in the viscometer. Amounts between 7 and 8 g are chosen and the viscometer weighed to determine the exact amount. Buffer replacements were undertaken by dilution. 

C, static method-Hg manometer, measured range 81.0-286.0°C, Myers Fenske 1955)... 

Determine the minimum reflux ratio using Fenske s equation and Colburn s rigorous method for the following three systems ... 

Materials 1,3-Dioxolane (1) and 1,3-dioxepane (5) were prepared and purified conventionally. Compound 1 contained no impurities detectable by GLC, but 5 contained a trace of tetrahydrofuran (THF) which could not be removed even by distillation on a Fenske column with a reflux ratio of 50 1 4-methyl-l,3-dioxolane (4) was prepared by Astle s method [10]. All monomers were dried preliminarily by storage over LiAlH4 in reservoirs attached to a conventional high-vacuum line fitted only with all-metal valves, and then stored with liquid Na-K alloy until used. Methylene dichloride was purified conventionally, distilled on a Normatron 1.5 m column, dried i.vac. over LiAlH4 on a conventional high-vacuum line, and then stored for 24 h over a fresh sodium film immediately before use, in a reservoir attached to the vacuum line. 

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