Inside-out method

The initial version of the inside-out method was developed for rapid calculations of simple and complex distillation, absorption, and... 

Example 7 Calculation of Inside Out Method For the conditions of the simple distillation column shown in Fig, 13-55, obtain a converged solution by the inside-out method, using the SRK eqiiation-of-state for thermodynamic properties (in the outer loop),... 

At this point in the inside-out method, the revised column profiles of temperature and phase compositions are used in the outer loop with the complex SRK thermodynamic models to compute updates of the approximate K and H constants. Then only one inner-loop iteration is required to obtain satisfactory convergence of the energy equations. The K and H constants are again updated in the outer loop. After one inner-loop iteration, the approximate K and H constants are found to be sufficiently close to the SRK values that overall convergence is achieved. Thus, a total of only 3 outer-loop iterations and 4 inner-loop iterations are required. 

To illustrate the efficiency of the inside-out method to converge this example, the results from each of the three outer-loop iterations are summarized in the following tables ... 

From these tables, it is seen that the stage temperatures and total liquid flows are already close to the converged solution after only one outer-loop iteration. However, the composition of the bottoms product, specifically with respect to the lightest component, C, is not close to the converged solution until after two iterations. The inside-out method does not always converge so dramatically, but is usually quite efficient,... 

Baird [Comp. Chem. Engng., 9, 593 (1985)]. Since then, they have been applied successfully to problems involving interlinked distillation (Wayburn and Seader, op. cit.), azeotropic and three-phase distillation [Kovach, 111 and Seider, Comp. Chem. Engng., 11,593(1987)], and reac tive distillation [Chang and Seader, Comp. Chem. Engng., 12, 1243 (1988)], when SC and inside-out methods have failed. Today, many computer-aided distillation-design and simulation packages include continuation techniques to make the codes more robust. 

The calculations were made with the RATEFRAC program and comparisons were made with the compamon RADFRAC program, which utilizes the inside-out method for an eqiiilibniim-based model. 

Quasi-Newton methods like Broyden s and Bennett s do work well when the curves are almost linear across the entire range. To have independent functions nearly linear, they need to be designed so that they are quite simple. The inside-out method (Sec. 4.2,10) is one of the methods that do this. 

The inside-out algorithm has become one of the most popular methods because of its robustness and its ability to solve a wide variety of columns. The inside-out concept was developed by Boston and Sullivan (69) and Boston (70). RuBsell (72) presented an inside-out method that works well for many refinery frectionators. Jelinek (73) presented a simplified Russell method. 

Outlook. The inside-out methods are now the methods of choice for mainstream column simulation. While other methods still have their... 

More than one product purity or recovery specification Not all methods will accept or solve. Replace one purity specification with some other such as reflux rate or a product rate. The methods best suited to solve multiple purity specifications are the inside-out methods (Sec. 4.3.1). 

The inside-out methods (Sec. 4.2,10) can be used for most columns. The Russell method is simple to implement and does work well for a wide variety of refinery and hydrocarbon columns. The Boston method also works well for a wide range of columns and has been shown to work for superfractionators or tall, high-purity columns. Since the outer loops of the two methods are similar, they can be combined with a choice between the two methods, depending on the type of column, as part of the inside loop. 

Aj Term of simple /f-value model in tire inside-out methods, defined by... 

Cj Term of simple vapor enthalpy model in the inside-out methods, de-... 

Fj Term of simple liquid enthalpy model in tbe inside-out methods,... 

Kfy K-value for base component of the K6 method and the simple K-value model of the inside-out methods, stage / Sec. 4.2.10. 

Boston inside-out method. 172-177, 198 Bravo, et al. rfructured packing pressure drop, 447, 499, 500 Bravo Fair et al. mass transfer random packing, 528-530 structured packings, 474, 529, 531, 532 Brown-Martin method, 109 Bryoden method, 161, 162, 175, 176. 179... 

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