Shortcut methods

The GPS A Engineering Data Book provides two methods for performing hand calculations of the hydrate formation. Although these methods are not recommended for acid gas mixture, they will be reviewed here briefly. 

The first of these is based on the gas gravity. A simple chart is provided that plots the temperature-pressure locus with the gas gravity as the third parameter. 

The first reason the chart method is not recommended for acid gases is that the chart is limited to gases with gravities less than 1.0. Typical acid gas mixtures have gravities greater than 1.1 (see table 2.1). The second reason is the chart was developed for sweet gas. It should be used with caution for sour gases and never used for acid gas. 

The second is a K-factor approach. This method is slightly more rigorous but also requires more time to perform the calculations. Using the K-factor charts requires an iterative procedure. This method should not be used for acid gas. Carroll (2004) showed that this method is not very accurate for sour gas mixtures. It predicts the real hydrate temperature to within 1.7 Celsius degrees (3 Fahrenheit degrees) only 40% of the time. It is anticipated that this method would be significantly worse for acid gas. 

In fact, none of the methods designed for rapid estimation of the hydrate formation conditions should be used for acid gas mixtures. If one must do such calculations, without a computer and a rigorous model, then it is probably wise to assume the hydrate formation conditions for the acid gas mixture are the same as 

In Chapters 7 through 11, the performance of multistage separation processes was analyzed qualitatively on the basis of fundamental principles developed in Chapters 3 through 6. The objective was to gain an understanding of the different types of separation processes and columns and the factors that affect their performance. Chapters 5 and 6 employed graphical and semi-quantitative methods to represent a limited set of separation processes, namely binary distillation. Chapters 10 and 11 also used combinations of graphical and analytical methods applied to binary or ternary systems to represent speciflc classes of nonideal separations. 

In spite of the simplifications, these methods are still quite computation-intensive and in most cases must be solved using computer programs. However, due to the much shorter computing time, these methods are useful in situations where computing time is crucial, such as in online, real-time applications. Especially suited for these applications are the modular shortcut methods based on column sections— another topic discussed in this chapter. 

The shortcut solution can often be used as the foundation for progressing toward a rigorous solution of the problem. In many applications the two methods are used in conjunction with each other to attain efficient and reliable simulation strategies. 

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Discussions of shortcut methods have appeared many times in the Hterature (16,36), accompanied by the usual admonition to use such methods only for approximate designs or analyses. For multicomponent systems having significant nonideaUties, the shortcut methods can be grossly in error. 

Unfortunately, there are no satisfactory shortcut methods for doing this. When the utilities cost is relatively small, it may be possible to make an intelhgent guess on the basis of known costs for similar processes in the company. Alternatively, published data for the consumption of utihties per unit of production for various processes may be used. 

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. 

For the McCabe-Thiele type of graphical calculations and shortcut methods, the Bancroft (weight-ratio) concentrations can be used on... 

For the first time through a liqmd-liquid extrac tion problem, the right-triangular graphical method may be preferred because it is completely rigorous for a ternary system and reasonably easy to understand. However, the shortcut methods with the Bancroft coordinates and the Kremser equations become valuable time-savers for repetitive calculations and for data reduction from experimental runs. The calculation of pseudo inlet compositions and the use of the McCabe-Thiele type of stage calculations lend themselves readily to programmable calculator or computer routines with a simple correlation of equilibrium data. 

Assuming that natural gas is used to fire the burner with a known heating value of HVc, calculate the available heat at the operating temperature. A shortcut method usually used for most engineering purposes is ... 

For these parameters, the equations predict a much higher vacuum (24.5 in Hg or 230 percent of the shortcut method) than the gravity-discharge case. Of course, different tank dimensions and pump characteristics coiild give different comparisons between cases. If conditions are such that the pump can completely empty the tank before backflow occurs, the vacuum is Rest calculated from Eq. (26-57). 

More shortcut design methods and rules of thumb have been developed for fractionation than probably any other unit operation. For example the paper reprinted in Appendix 5 on development of shortcut equipment design methods contains 18 references for fractionation shortcut methods out of 37 total. Both the process and mechanical aspects of fractionation design have useful rules of thumb. Many of the mechanical design rules of thumb become included in checklists of do s and don ts. 

Ludwig discusses new work by the A.I.Ch.E. which has produced a method more detailed than the previous shortcut methods. He states that some of the shortcut methods can be off by 15-50% as indicated by the A.I.Ch.E. 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 A.I.Ch.E. values indicate that deviations for the shortcut methods are usually on the safe or low side. 

Early in the life of a project, information has not been developed to allow definitive cost estimates based on material takeoff and vendor quotes for equipment. Therefore, it is necessary to estimate the cost of a facility using shortcut methods. The first step is to develop or check flow-sheets, major equipment sizes, and specification sheets as described in earlier chapters. From the equipment specification sheets, the cost of each piece of equipment is estimated, using techniques discussed later. Once the major equipment cost has been estimated, the total battery limit plant cost can he quickly estimated using factors developed on a similar project. 

October 1891 issue of The Locomotive. We must be careful that our shortcut methods don t become dated ... 

Development of useful shortcut methods by intuitive and evolutionary mental analysis alone must surely be extremely fulfilling. We will see later how other devel-opmentally oriented individuals are able to build upon the original shortcut method ideas to create variations on the theme for specific applications. 

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. 

Considerable work on methods for pre-predicting fractionator tray efficiency continues to the present. Shortcut methods from the past differed rather widely.The... 

Gilliland s work should be an encouragement to us all in developing shortcut methods from rigorous results. The proliferation of computers makes our job relatively easy. 1 feel that when correlations of this type are developed, one shouldn t stop w ith the graph but continue until an equation is fitted to the data. Computers need equations. 

Suppose that the process does not have any process MSAs. How can a lean composite line be developed The following shortcut method can be employed to construct the pinch diagram for external MSAs. A more rigorous method is presented in Chapter Six. 

Sudduth, L. E, Shortcut Methods Help Expander-Plant Performance, Oil and Gas Jour, p. 88, Dec. (1974). 

Start with 1 mol of and let it age for 10 billion years or so. Refer to Table 2.1. What is the maximum number of atoms of " Po that will ever exist Warning This problem is monstrously difficult to solve by brute force methods. A long but straightforward analytical solution is possible. See also Section 2.5.3 for a shortcut method. 

In Chapter 17, where there is a special section with biochemical engineering problems, examples on shortcut methods are presented. 

In this section we shall only present the derivative approach for the solution of the pyrolytic dehydrogenation of benzene to diphenyl and triphenyl regression problem. This problem, which was already presented in Chapter 6, is also used here to illustrate the use of shortcut methods. As discussed earlier, both state variables are measured and the two unknown parameters appear linearly in the governing ODEs which are also given below for ease of the reader. 

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