Columns design calculations

X. Post-analysis Methods Column Design Calculations 166... 

A horizontal concentration gradient will develop in the liquid due to mass transfer into and from the liquid as the liquid flows across the tray. Thus, the composition of the vapor above the froth will change as we traverse the tray even if the composition of the vapor just below the tray is uniform. The point efficiency defined in the preceding section models the mass transfer processes at a particular point on the tray but does not take into account the fact that the liquid may have a significant concentration change as it crosses the tray. Thus, the point efficiency must be related to the tray efficiency before it can be used in column design calculations. 

A similar efficiency can be defined for the liquid phase ml however, the vapor-phase efficiency is used more widely in column design calculations. 

At intermediate splits and spUts with distributed component calculation, tray by tray calculation should be carried out from the ends of the column. Design calculation of necessary trays number in each section is carried out for the set of values of the summary concentrations of the impurity components at the... 

ATM = Minimum column cross-sectional area, tV. Further detailed design calculations may result in a change in tower diameter. 

A more quantitative and lengthy method, but still very useful for checking of the type required here is the Smith-Brinkley method (Reference 5). It uses two sets of separation factors for the top and bottom parts of the column for a fractionator or reboiled absorber and one overall separation factor for a simple absorber. The method is tailor-made for analysis of a column design or a field installed column. The Smith-Brinkley method starts with the column parameters and calculates the resulting product compositions unlike other methods that require knowing the compositions to determine the required reflux. 

Equation (16) was first developed by Purnell [3] in 1959 and is extremely important. It can be used to calculate the efficiency required to separate a given pair of solutes from the capacity factor of the first eluted peak and their separation ratio. It is particularly important in the theory and practice of column design. In the particular derivation given here, the resolution is referenced to (Ra) the capacity ratio of the first... 

Atwood and Goldstein [16] examined the effect of pressure on solute diffusivity and an example of some of their results is shown in Figure 7. It is seen that the diffusivity of the solutes appears to fall linearly with inlet pressure up to 40 MPa and the slopes of all the curves appear to be closely similar. This might mean that, in column design, diffusivities measured or calculated at atmospheric pressure might be used after they have been appropriately corrected for pressure using correction factors obtained from results such as those reported by Atwood and Goldstein [16]. It is also seen that the... 

Column design involves the application of a number of specific equations (most of which have been previously derived and/or discussed) to determine the column parameters and operating conditions that will provide the analytical specifications necessary to achieve a specific separation. The characteristics of the separation will be defined by the reduced chromatogram of the particular sample of interest. First, it is necessary to calculate the efficiency required to separate the critical pair of the reduced chromatogram of the sample. This requires a knowledge of the capacity ratio of the first eluted peak of the critical pair and their separation ratio. Employing the Purnell equation (chapter 6, equation (16)). 

Equation (13) is the first important equation for open tubular column design. It is seen that the optimum radius, with which the column will operate at the optimum velocity for the given inlet pressure, increases rapidly as an inverse function of the separation ratio (cc-1) and inversely as the square root of the inlet pressure. Again it must be remembered that, when calculating (ropt)5 the dimensions of the applied pressure (P) must be appropriate for the dimensions in which the viscosity (r)) is measured. 

In a packed column the HETP depends on the particle diameter and is not related to the column radius. As a result, an expression for the optimum particle diameter is independently derived, and then the column radius determined from the extracolumn dispersion. This is not true for the open tubular column, as the HETP is determined by the column radius. It follows that a converse procedure must be employed. Firstly the optimum column radius is determined and then the maximum extra-column dispersion that the column can tolerate calculated. Thus, with open tubular columns, the chromatographic system, in particular the detector dispersion and the maximum sample volume, is dictated by the column design which, in turn, is governed by the nature of the separation. 

A tower separates a weak ammonia solution. Design trays using perforated plates without downcomers for the following conditions as determined from the column performance calculations. 

There is no need to calculate the reflux flow to the distillation column that will be determined by the column design. 

In an operating column the effective reflux ratio will be increased by vapour condensed within the column due to heat leakage through the walls. With a well-lagged column the heat loss will be small and no allowance is normally made for this increased flow in design calculations. If a column is poorly insulated, changes in the internal reflux due to sudden changes in the external conditions, such as a sudden rain storm, can have a noticeable effect on the column operation and control. 

The precise location of the feed point will affect the number of stages required for a specified separation and the subsequent operation of the column. As a general rule, the feed should enter the column at the point that gives the best match between the feed composition (vapour and liquid if two phases) and the vapour and liquid streams in the column. In practice, it is wise to provide two or three feed-point nozzles located round the predicted feed point to allow for uncertainties in the design calculations and data, and possible changes in the feed composition after start-up. 

Continuous binary distillation is illustrated by the simulation example CON-STILL. Here the dynamic simulation example is seen as a valuable adjunct to steady state design calculations, since with MADONNA the most important column design parameters (total column plate number, feed plate location and reflux ratio) come under the direct control of the simulator as facilitated by the use of sliders. Provided that sufficient simulation time is allowed for the column conditions to reach steady state, the resultant steady state profiles of composition versus plate number are easily obtained. In this way, the effects of changes in reflux ratio or choice of the optimum plate location on the resultant steady state profiles become almost immediately apparent. 

Norman, W. S. Trans. Inst. Chem. Eng. 23 (1945) 66. The dehydration of ethanol by azeotropic distillation. Ibid. 89. Design calculations for azeotropic dehydration columns. 

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