Cutting 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). 

Plant engineering is such a broad subject incorporating a multitude of disciplines and a wide variety of solutions to virtually every problem or situation, unlike some subjects that have clear-cut methods. 

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... 

Johnston TF (1998) Beam propagation (M2) measurement made as easy as it gets the four-cuts method. Appl Opt 37 4840 1850... 

The MINLP-problems were implemented in GAMS [7, 8] and solved by the outer approximation/equality relaxation/augmented penalty-method [9] as implemented in DICOPT. The algorithm generates a series of NLP and MILP subproblems, which were solved by the generalized reduced gradient method [10] as implemented in CONOPT and the integrality relaxation based branch and cut method as... 

Thermal cutting or fuel cutting for end preparation is acceptable if the surface is reasonably smooth, true, and free of slag. The thermal cutting shall be followed by mechanical preparation to achieve the final weld joint end detail. Discoloration (oxidation) remaining from the cutting method shall be removed. 

It should be emphasized that the phosphorus oxydichlorofluoride method for preparing esters of phosphorofluoridic acid cannot compare in speed with the hydrogen phosphite method already described (p. 46). Furthermore, it is not very suitable for very large-scale work. On the other hand, once the apparatus is set up and a supply of POCl2F is obtained, one has a simple, clear-cut, method for producing a large variety of phosphorus compounds, not only esters but amino compounds (p. 87) and mixed compounds (p. 90). In other words, the method is extremely valuable for exploratory purposes and where an unequivocal synthesis is required. 

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