Diameter calculation, columns

Formulation of the mathematical model here adopts the usual assumptions of equimolar overflow, constant relative volatility, total condenser, and partial reboiler. Binary variables denote the existence of trays in the column, and their sum is the number of trays N. Continuous variables represent the liquid flow rates Li and compositions xj, vapor flow rates Vi and compositions yi, the reflux Ri and vapor boilup VBi, and the column diameter Di. The equations governing the model include material and component balances around each tray, thermodynamic relations between vapor and liquid phase compositions, and the column diameter calculation based on vapor flow rate. Additional logical constraints ensure that reflux and vapor boilup enter only on one tray and that the trays are arranged sequentially (so trays cannot be skipped). Also included are the product specifications. Under the assumptions made in this example, neither the temperature nor the pressure is an explicit variable, although they could easily be included if energy balances are required. A minimum and maximum number of trays can also be imposed on the problem. 

The column diameter calculations will target a pressure drop of 0.2 kPa/m... 

Figure 6.7 gives flowsheet conditions and equipment sizes. Based on a feed flowrate of 2000 kmol/h and a feed composition of 6 mol% THF, the column diameters calculated by Aspen s Tray Sizing lae 1.36 and 1.43 m. The total number of stages in each column is set at 17 since the separations are fairly easy. Feed tray locations are shown in the figure. The economizers are sized using minimum approach temperatures of 10-15°C and overall... 

Use U.S. customary units only in this equation. In sizing the column diameter, it is ususlly assumed that the continuous phase velocity will set at 40 percent of this value, and therefore the column diameter is calculated by ... 

Calculation of column diameter (for packed columns, this is usually based on flooding conditions, and, for plate columns, on the optimum gas velocity or the liquid-handling capacity of the plate)... 

Methods for quick sizing trayed fractionation and absorption column diameter have been reduced here to equations to facilitate programming for calculators or computers. Three methods are discussed and it is not a bad idea to compare results with all three. 

The diameter of the column is selected from the volume of sample that is to be processed. As a rule of thumb the maximum productivity is obtained at a sample volume of 2-6% of the bed volume in preparative gel filtration on a 50-/rm chromatographic medium (Hagel et al., 1989). Thus, the required column diameter is calculated from the bed volume needed to cope with the sample volume and the column length needed to give the resolution desired. 

Such effects principally cannot be observed in multi band detectors such as a UV diode array detector or a Fourier transform infrared (FTIR) detector because all wavelengths are measured under the same geometry. For all other types of detectors, in principle, it is not possible to totally remove these effects of the laminar flow. Experiments and theoretical calculations show (8) that these disturbances can only be diminished by lowering the concentration gradient per volume unit in the effluent, which means that larger column diameters are essential for multiple detection or that narrow-bore columns are unsuitable for detector combinations. Disregarding these limitations can lead to serious misinterpretations of GPC results of multiple detector measurements. Such effects are a justification for thick columns of 8-10 mm diameter. 

To determine the column (with trays) diameter, an approach [130] is to (1) assume 0 hours (2) solve for V, Ib/hr vapor up the column at selected, calculated, or assumed temperature and pressure (3) calculate column diameter using an assumed reasonable vapor velocity for the type of column internals (see section in this volume on Mechanical Designs for Tray Performance ). 

Calculate column diameter using Uflood reduced by 15-25%, or increase the calculated column area by about 25% and convert to a working diameter. 

As an alternate consideration, assume various pressure drops/foot of packing (same) and determine effect on calculated column diameter. Use the same input information as original stated conditions, then ... 

Calculate the column net inside diameter from the area values. Round to the nearest practical commercial column diameter such as 12 in., 15 in., 18 in., 24 in., 30 in., 36 in., and in increments of 6 in. Then recalculate the actual resulting vapor velocity. 

To calculate the column diameter an estimate of the net area An is required. As a first trial take the downcomer area as 12 per cent of the total, and assume that the hole-active area is 10 per cent. 

The extra-column dispersion governs the dimensions of the column that we use. In the calculation above, the dispersion is increased by about 8% by the extra-column effects. If we want the dispersion to be increased by no more than this, then should not be any smaller than the value calculated above. This in turn limits the retention volume, and thus the volume of the column itself. The minimum column volume we can use will depend on the amount of extracolumn dispersion and on what we consider to be an acceptable increase in peak width that is produced by extra-column effects. In practice, this acceptable increase is taken as 10%, based on an unretained solute, and if we take 50 (i as a typical figure for extracolumn dispersion then the minimum column diameter works out at about 4.5 mm for a column 25 cm long. 

The linear superficial flow velocity in the packing voids v is calculated from volumetric flow rate Lin, voidage fraction of the adsorbant bed e and column diameter d as... 

This equation relates the hold-up to the flowrates of the phases and column diameter through the characteristic velocity, u0. It therefore gives a method of calculating the holdup for a given set of flowrates if u0 is known. Conversely, equation 13.33 may be used to calculate uq from experimental hold-up measurements made at different flowrates. Thus, if hold-up data are plotted with L d + (J/( 1 — j))L c as the ordinate against j( 1 — j) as the abscissa, a linear plot is obtained which passes through the origin and which has a slope equal to fir, Wl. 

The method of calculation introduced in this chapter not only allows an exact determination of the column diameter for nonpulsed sieve tray columns, but also allows a good estimation of the diameters of pulsed and stirred extractors. For the latter, however, more exact specific equations exist for the flooding point, see for example [1,4]. 

Employing equation (24), the minimum column diameter was calculated for a column 10 cm long packed with particles of different diameters. The standard deviation of the extra column dispersion was assumed to be 5, 10 and 15 microlitres respectively, values that embrace those that would be... 

The organic vapor diffuses through the porous membrane into the air stream at a calculable rate. A wide range of contaminant concentrations can be obtained by varying the column diameter, length, flow rate, or temperature. 

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