Calculation of Petlyuk Columns

The general algorithm of design calculation includes the following steps  

Calculation of minimum flow rate of the entrainer or autoentrainer 

Determination of the average calculated value of the rate of the entrainer or autoentrainer E/D)mtan= 3( / ))niin according to the heuristic rule (Knapp Doherty, 1994) and of a number of other calculated values of E/D in the set interval. 

Calculation of minimum reflux number (L/D)min at ( / )mean (see Section 6.5). 

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Design Calculation of Petlyuk Columns" and of Columns with Side Sections... 

Figure 7.15. Calculation of Petlyuk columns (a) specifications (in brackets), (b) calculation of minimum reflux and reboU ratios and product distribution in two-section columns, and (c) calculation of design variables.

We state below a rigorous method of design calculation of Petlyuk columns and of columns with side sections based on the design calculation of two-section columns described in Section 7.3. 

Design calculation of Petlyuk columns is carried out on the basis of the algorithm of design calculation of two-section columns with optimization by distribution coefficient of pseudoproduct flow rates of the prefractionator, by excess factors of reflux and by distribution of trays among sections in each two-section column. 

For intermediate sections of columns with side products, with side sections, and of Petlyuk columns location of the stationary points of separatrix trajectory bundles (regions Reg jjfj) is the same as for simple columns, product compositions of which coincide with pseudoproduct compositions of these intermediate sections (possible product regions Rego and Reg of simple columns and possible pseudoproduct regions Regn and Reg of intermediate sections coincide). This extends the use of methods of minimum reflux mode calculation worked out for the simple columns to the previously mentioned complex columns and complexes. 

Optimal cross-sections of joining of previous and posterior two-section columns at calculation by method tray by tray of Petlyuk columns and of columns with side strippings are cross-sections of previous columns closest by composition to points S. ... 

The results of the dynamic test for a positive change in the set point of the light component (A) are displayed in Figure 6. For a change in the set point from 0.987 to 0.991, the three systems are shown to be controllable and reach the new value of product composition, although the PUL scheme shows a quicker adjustment. lAE values were also calculated for each response the two best lAE values correspond to the new arrangements 4.20 x 10 for the PUL system, and 6.10 x 10 for the PUV system. The lAE value for the Petlyuk column was 2.35 x 10, which again shows a case in which the dynamic... 

Figure 7 shows the dynamic responses obtained when the set point for the intermediate component was changed from 0.98 to 0.984. One may notice the better response provided by the Petlyuk column in this case, which is faster than the other two systems and without oscillations. When the lAE values were calculated, a remarkable difference in favor of the Petlyuk system was observed 2.87 x 10 for the Petlyuk column, compared to 0.0011 for the PUL system and 0.0017 for the PUV system. The results from this test may seem unexpected, since the new arrangements have been proposed to improve the operation capabilities of the Petlyuk column. The SISO control of the intermediate component, interestingly, seems to conflict with that of the other two components in terms of the preferred choice from dynamic considerations. 

A simulation of a DWC based on the equivalent Petlyuk column has two recycle loops, which requires two recycle blocks (R1 and R2), as shown in Figure 9.6b. The prefractionator column (Pref) has neither reboiler nor condenser, which can be simulated using an absorber column. This column has two recycle streams, which includes a recycled vapor stream to a prefractionator (Vapor pre in) at the bottom, and the recycled liquid stream to the prefractionator (Liquid pre in) at the top. These two streams need the initial estimates to solve the Pref column. A distillation unit for the main column, the material streams. Feed, Vapor pre out. Liquid pre out. Liquid Main out. Vapor Main out. Distillate, Side, and Bottom for Main column are added to the flow sheet. Two recycle blocks need to be added to the flow sheet one recycle block (Rl) for the Liquid Main out and another (R2) for Vapor Main out to initialize the recycle stream. Once the Pref is solved, the main column is simulated with an estimated number of stages and stage locations from the shortcut calculation. 

Connect Streams. Probably the most important (and perhaps the most confusing) issue in setting up a MultiFrac Petlyuk column in Aspen Plus is the definition of where the four interconnecting streams (two liquids and two vapors) leave and enter the two columns. There are four Connect Streams. The flow rates of the two streams entering column C2 (one liquid at the top and one vapor at the bottom of the prefractionator) will be specified. The other two streams are dependent variables and will be calculated in the model. 

The main purpose of design calculation is to determine necessary tray numbers for all sections at fixed values of mode parameters. At design calculation, one takes into consideration the equality of compositions at the tray of output of the side product obtained at the calculation of the second and third columns. Each two-section column entering into a Petlyuk column is calculated with the help of algorithms described before for two-section columns. The algorithm of calculation for splits with a distributed component is used for the first column, the algorithms for the direct and the indirect sphts are used for the second, and the third columns at separation of a three-component mixture, respectively. At separation of multicomponent mixtures, the algorithms for intermediate separation are used. 

Petlyuk, F. B. (1984). Necessary Condition of Exhaustion of Components at Distillation of Azeotropic Mixtures in Simple and Complex Columns. In The Calculation Researches of Separation for R ning and Chemical Industry, 3-22. Moscow Zniiteneftechim (Rus.). 

Theoretic analysis proved that the algorithms employing calculation from the feed cross-section (Petlyuk Danilov, 2001a) can be applied only at n = 4, while algorithms that use calculation from the ends of column can be applied at any n. 

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