Computer minimum stages

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. 

Figure 3.e Calculating minimum reflux and minimum stages by extrapolating the reflux stages curve obtained by computer simulation. Depropanizer In Example 3.4. D = 59.9 lb-mole/h. 

Equation-Based Design Methods Exact design equations have been developed for mixtures with constant relative volatility. Minimum stages can be computed with the Fenske equation, minimum reflux from the Underwood equation, and the total number of stages in each section of the column from either the Smoker equation (Trans. Am. Inst. Chem. Eng., 34, 165 (1938) the derivation of the equation is shown, and its use is illustrated by Smith, op. cit.), or Underwoods method. A detailed treatment of these approaches is given in Doherty and Malone (op. cit., chap. 3). Equation-based methods have also been developed for nonconstant relative volatility mixtures (including nonideal and azeotropic mixtures) by Julka and Doherty [Chem. Eng. Set., 45,1801 (1990) Chem. Eng. Sci., 48,1367 (1993)], and Fidkowski et al. [AIChE /., 37, 1761 (1991)]. Also see Doherty and Malone (op. cit., chap. 4). 

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. 

The purification of value-added pharmaceuticals in the past required multiple chromatographic steps for batch purification processes. The design and optimization of these processes were often cumbersome and the operations were fundamentally complex. Individual batch processes requires optimization between chromatographic efficiency and enantioselectivity, which results in major economic ramifications. An additional problem was the extremely short time for development of the purification process. Commercial constraints demand that the time interval between non-optimized laboratory bench purification and the first process-scale production for clinical trials are kept to a minimum. Therefore, rapid process design and optimization methods based on computer aided simulation of an SMB process will assist at this stage. 

We arbitrarily considered the runaway stage to begin when the computed temperature difference between the and the average temperature of the solution goes through a minimum. For Test 1 (see Figure 5) this occurs when the average temperature was 100°C and was 150°C. 

The output of a Nd YLF laser is focussed by a series of lenses to a spot size of 0.5 pm upon a sample which may be positioned by an x-y-z stepping motor stage and scanned by a computer-controlled high frequency x-y-z piezo stage. Ions are accelerated and transmitted through the central bore of the objective into a time-of-flight (TOF) mass spectrometer. The laser scans an area of 100 x 100 pm with a minimum step size of 0.25 pm. TOF mass spectra of each pixel are evaluated with respect to several ion signals and transformed into two-dimensional ion distribution plots. 

Alternatively, results from a computer simulation can be plotted to determine the optimum feed stage. Simulation runs ere performed at several different feed points, keeping the material balance, reflux ratio, and total number of stages constant. Ksy component concentrations in the product streams are plotted against the feed stage number (Fig. 3.7). The minimum is at the optimum feed stage. 

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