Shortcut methods rating

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. 

Finally, there is an interesting article" that shows how to use Taylor s series to generate shortcut methods from established theory. Examples are given for developing a criterion for replacing log mean temperature differences with average differences and for estimating the effect of temperature on reaction rate. 

Modeling of H F contactors is in most papers based on a simple diffusion resistance in series approach. In many systems with reactive extractants (carriers) it could be of importance to take into account the kinetics of extraction and stripping reactions that can influence the overall transport rate, as discussed in refs. [30,46], A simple shortcut method for the design and simulation of two-phase HF contactors in MBSE and MBSS with the concentration dependent overall mass-transfer and distribution coefficients taking into account also reaction kinetics in L/L interfaces has been suggested [47]. 

Table 13-6 shows subsequent calculations using the Underwood minimum reflux equations. The a and Xo values in Table 13-6 are those from the Fenske total reflux calculation. As noted earlier, the % values should be those at minimum reflux. This inconsistency may reduce the accuracy of the Underwood method but to be useful, a shortcut method must be fast, and it has not been shown that a more rigorous estimation of x values results in an overall improvement in accuracy. The calculated firnin is 0.9426. The actual reflux assumed is obtained from the specified maximum top vapor rate of 0.022 kg- mol/s [ 175 lb-(mol/h)] and the calculated D of 49.2 (from the Fenske equation). 

The shortcut method proposed in Reference 1 may be used only to obtain a preliminary estimate of the height of catalyst required in the reactor. The reactor should be designed from first principles using the rate equation, below, taken from Reference 1 ... 

This fractionation problem (rating sheet courtesy of Koch-Glitsch Inc.) illustrates both the shortcut methods for a new column and also those for an existing column. 

The shortcut methods can also be used for approximate analysis of the performance of an existing column. Here, the number of trays, N, is fixed, and the objective is to determine the reflux ratio required to meet a specifled separation. The Fenske and Underwood methods (Equations 12.17, 12.29, and 12.30) are used to calculate the minimum trays and minimum reflux ratio, and R. The operating reflux ratio corresponding to the given number of trays is then read from the Gilliland chart (Figure 12.4). The internal vapor and liquid rates are calculated from the reflux ratio and product rates. A check must be made to determine if the existing column can handle the calculated vapor and liquid traffic. 

As in other shortcut methods, the liquid and vapor molar flow rates are assumed constant in the column section ... 

The first step is to assume a set of temperatures Tj and vapor flows Vj. The temperatures can be obtained by linear interpolation between the condenser and reboiler temperatures, determined by dew point and bubble point calculations of products estimated by shortcut methods or on the basis of past experience with similar columns. The vapor rates are estimated from the specified distillate and reflux rates. Constant vapor rates are assumed above and below the feed. The... 

To begin the calculations the column variables must be first initialized to some estimated values. Simple methods can be used for this purpose, based on the column specifications and possibly supplemented by shortcut methods. The column temperature profile may be assumed linear, interpolated between estimated condenser and reboiler temperatures. The values for Lj and Vj may be based on estimated reflux ratio and product rates, assisted by the assumption of constant internal flows within each column section. The compositions Xj- and T, may be assumed uniform throughout the column, set equal to the compositions of the liquid and vapor obtained by flashing the combined feeds at average column temperature and pressure. The other variables to be initialized are Rf,Rj, and Sj, which are calculated from their defining equations. The values for Qj may either be fixed at given values (zero on most stages) or estimated. 

If the distillation were to be started at twice the minimum reflux ratio, determine the required number of stages. If the initial charge is 100 kmol and the distillate rate is 10 kmol/h, calculate the reflux rate, the amounts of distillate and residue, and the residue composition as a function of time. Irrespective of tray hydraulics and reboiler and condenser capacity constraints, when should the distillation be stopped Assume negligible tray holdups and use shortcut methods. 

Utilizing this shortcut method, catalyst concentration and reaction temperature are the critical parameters that impact the selectivity through the enantioselectiv-ity factor. The effect of these two parameters on the yield and ee performance of the HKR is graphically illustrated in Fig. 24. The data clearly indicate that operating at the highest catalyst concentration and the lowest reaction temperature maximizes the difference in the rates of reaction for the two enantiomers, and thereby... 

Continuously operated chromatographic processes such as simulated moving beds (SMB) are well established for the purification of hydrocarbons, fine chemicals, and pharmaceuticals. They have proven ability to improve the process performance in terms of productivity, eluent consumption, and product concentration, especially for larger production rates. These advantages, however, are achieved with higher process complexity with respect to operation and layout. A purely empirical optimization is rather difficult and, therefore, the breakthrough for practical applications is linked to the availability of validated SMB models and shortcut methods based on the TMD model as described in Chapter 6. 

There are few shortcut methods for analyzing simple parallel systems. One useful technique is to use stoichiometric ratios of reactants in the experimental work so that the ratio of the time derivatives of the extents of reaction simplifies where possible. For higher-order irreversible simple parallel reactions represented by equations (5.2.41) and (5.2.42), the degenerate form of the ratio of reaction rates then becomes... 

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