Short-cut method

To estimate the product of the two variables below, a short cut method is to multiply the low, medium and high values in a matrix (in which numbers have been selected). 

This short-cut method could be repeated to include another variable, and could therefore be an alternative to the previous two methods introduced. This method can always be used as a last resort, but beware that the range of uncertainty narrows each time the process is repeated because the tails of the Input variables are always neglected. This can lead to a false impression of the range of uncertainty in the final result. 

A reahstic estimate of the temperature profile for theoretical plates can probably be obtained by the short-cut method developed on the basis of rigorous computer solutions for about 40 different hypothetical designs (108) which closely resemble those of Figure 27. 

Woods, D. R., Discovering Short Cut Methods of Equipment Sizing and Selection, ASEE Annual Conference Proceedings, 1985. 

Dr. Woods R. and Kodatsky, W. K., Dept, of Chemical Engineering, McMaster University, Hamilton, Ontario, Discovering Short Cut Methods of Equipment Sizing and Selection, presented at 1985 Annual Conference (Computer Aided Engineering) of American Society For Engineering Education, Atlanta, Georgia, June 16-20, 1985, V ol. 1. 

The American Institute of Chemical Engineer s Distillation Tray Efficiency Research [2] program has produced a method more detailed than the short-cut methods, and correspondingly is believed to produce reliable results. This method produces information on tray efficiencies of new systems without experimental data. At present there is not enough experience rvith the method and its results to evaluate its complete range of application. 

Figure 8-46. Yaws short-cut method compared to plate-to-plate calculations. Used by permission, Yaws, C. L. et al. Hydrocarbon Processing, V. 58, No. 2 (1979) p. 99. Gulf Publishing Co., all rights reserved.

Using the graphical short-cut method for component distribution, estimate the recovery of non-key components in distillate and bottoms. 

Pressure losses through the shell side of exchangers are subject to much more uncertainty in evaluation than for tube side. In many instances, they should be considered as approximations or orders of magnitude. This is especially true for units operating under vacuum less than 7 psia. Very little data has been published to test the above-atmospheric pressure correlations at below-atmospheric pressures. The losses due to differences in construction, baffle clearances, tube clearances, etc., create indeterminate values for exact correlation. Also see the short-cut method of reference 279. 

Starczewski, J., Short Cut Method to Exchanger Shell-Side Pressure Drop, Hydro. Proc., V. 50, No. 6, p. 147 (1971). 

Table 7.1 Estimated parameter values with short cut methods for different values of the smoothing parameter (s/N) in IMSL routine CSSMH...

In the dialyzed batch start-up phase and the subsequent continuous operation a substantial increase in viable cell density and monoclonal antibody (MAb) titer was observed compared to a conventional suspension culture. The raw data, profiles of the viable cell density, viability and monoclonal antibody titer during the batch start-up and the continuous operation with a dialysis flow rate of 5 L/d are shown in Figures 17.6 and 17.7. The raw data are also available in tabular form in the corresponding input file for the FORTRAN program on data smoothing for short cut methods provided with the enclosed CD. 

The short-cut methods available can be divided into two classes ... 

MULTICOMPONENT DISTILLATION SHORT-CUT METHODS FOR STAGE AND REFLUX REQUIREMENTS... 

Short-cut methods for non-ideal and azeotropic systems are given by Featherstone (1971) (1973). 

The composition of the feed to a debutaniser is given below. Make a preliminary design for a column to recover 98 per cent of the n-butane overhead and 95 per cent of the isopentane from the column base. The column will operate at 14 bar and the feed will be at its boiling point. Use the short-cut methods and follow the procedure set out below. Use the De Priester charts to determine the relative volatility. The liquid viscosity can be estimated using the data given in Appendix D. 

The short-cut method proposed in Ref. 1 may be used only to obtain a preliminary estimate of the height of catalyst required in the reactor. The reactor should be designed... 

Ludwig1 discusses a work by the AIChE that has produced a method more detailed than the previous short-cut methods. He states that some of the shortcut methods can be off by 15-50% as indicated by the AIChE work. The spread of the Drickamer and Bradford correlation shown in the Ludwig plot is about 10 points of efficiency or 5 efficiency points around the curve. Ludwig states that comparisons between shortcut and AIChE values indicate that deviations for the shortcut methods are usually on the safe or low side. 

There are few short-cut methods for analyzing simple parallel systems. One useful technique, however, is to use stoichiometric ratios of reactants 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 becomes... 

The short-cut method of determining a character of a set of orbitals by deciding on the number of them unaffected by a symmetry operation is usually straightforward, although complications can arise with some point groups. 

The first two sections of Chapter 5 give a practical introduction to dynamic models and their numerical solution. In addition to some classical methods, an efficient procedure is presented for solving systems of stiff differential equations frequently encountered in chemistry and biology. Sensitivity analysis of dynamic models and their reduction based on quasy-steady-state approximation are discussed. The second central problem of this chapter is estimating parameters in ordinary differential equations. An efficient short-cut method designed specifically for PC s is presented and applied to parameter estimation, numerical deconvolution and input determination. Application examples concern enzyme kinetics and pharmacokinetic compartmental modelling. 

It is planned that the work of API Research Project 6 on the exhaustive examination of one representative crude petroleum will be continued into those portions not yet fully investigated. With firm and reliable data on the components in a given portion of one representative petroleum, short-cut methods may then be developed with confidence for the rapid examination of similar portions of other petroleums. 

Several authors have already developed methodologies for the simulation of hybrid distillation-pervaporation processes. Short-cut methods were developed by Moganti et al. [95] and Stephan et al. [96]. Due to simplifications such as the use of constant relative volatility, one-phase sidestreams, perfect mixing on feed and permeate sides of the membrane, and simple membrane transport models, the results obtained should only be considered qualitative in nature. Verhoef et al. [97] used a quantitative approach for simulation, based on simplified calculations in Aspen Plus/Excel VBA. Hommerich and Rautenbach [98] describe the design and optimization of combined pervaporation-distillation processes, incorporating a user-written routine for pervaporation into the Aspen Plus simulation software. This is an improvement over most approaches with respect to accuracy, although the membrane model itself is still quite... 

Modeling and optimization of MBSE and MBSS of a multicomponent metallic solution in HF contactors is discussed in ref. [77]. A short-cut 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 was suggested by Kertesz and Schlosser [47]. Comparison of performance of the MBSE and MBSS circuit with pertraction through ELM in case of phenol removal presented Reis [78] and for copper removal Gameiro [79]. 

Although there are several books on distillation in general where batch distillation is only briefly introduced, there is only one book currently available in the market that is solely dedicated to Batch Distillation. It addresses some of the issues mentioned above using short-cut methods, simplified models and Maximum Principle based optimisation techniques and therefore is a good book to start with for the undergraduate students and for the practitioners in process engineering whose interests lie in the basics of batch distillation and in the preliminary design of batch distillation columns and operations. 

Tray area. Using an entrainment flooding correlation is the usual method of calculation, but short-cut methods (e.g., Ref. 10) are often adequate. However, to minimize trial and error, the author prefers to perform the preliminary estimate using the flooding correlation which will eventually be used, with some simplifying assumptions. In this example, the Kister and Haas correlation [Eq. (6.12)] will be used for the preliminary determination of tray area. Make the following simplifying assumptions ... 

Short-Cut Methods Based on the Range. For small samples ( from 3 to about 10) the range, R = largest) — (smallest), can be used to obtain rough uncertainty estimates. The range, when multiplied by the appropriate value of K2 from Table 4, gives an approximate but useful estimate of the standard deviation. The factor Tin Table 4 is equivalent to 1X2 yfN, where ris the critical value from the P= 95 percent column in Table 3 for the appropriate degree of freedom. Hence, to get a quick estimate of the 95 percent confidence limits of the mean of a few observations, simply calculate JR. In summary,... 

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