Number and sequencing of columns

As was mentioned in Section 11.2, in multicomponent distillations it is not possible to obtain more than one pure component, one sharp separation, in a single column. If a multicomponent feed is to be split into two or more virtually pure products, several columns will be needed. Impure products can be taken off as side streams and the removal of a side stream from a stage where a minor component is concentrated will reduce the concentration of that component in the main product. 

For separation of N components, with one essentially pure component taken overhead, or from the bottom of each column, (N — 1) columns will be needed to obtain complete separation of all components. For example, to separate a mixture of benzene, toluene and xylene two columns are needed (3-1). Benzene is taken overhead from the first column and the bottom product, essentially free of benzene, is fed to the second column. This column separates the toluene and xylene. 

The order in which the components are separated will determine the capital and operating costs. Where there are several components the number of possible sequences can be very large for example, with five components the number is 14, whereas with ten components it is near 5000. When designing systems that require the separation of several components, efficient procedures are needed to determine the optimum sequence of separation see Doherty and Malone (2001), Smith (1995) and Kumar (1982). 

Procedures for the sequencing of columns are also available in the commercial process simulator programs for example, DISTIL in Hyprotech s suite of programs (see Chapter 4, Table 4.1). 

In this section, it is only possible to give some general guide rules. 

Remove the components one at a time as in the benzene-toluene-xylene example. 

Remove any components that are present in large excess early in the sequence. 

---

Distillation. There is a large inventory of boiling liquid, sometimes under pressure, in a distillation column, both in the base and held up in the column. If a sequence of columns is involved, then, as discussed in Chap. 5, the sequence can be chosen to minimize the inventory of hazardous material. If all materials are equally hazardous, then choosing the sequence that tends to minimize the flow rate of nonkey components also will tend to minimize the inventory. Use of the dividing-wall column shown in Fig. 5.17c will reduce considerably the inventory relative to two simple columns. Dividing-wall columns are inherently safer than conventional arrangements because they lower not only the inventory but also the number of items of equipment and hence lower the potential for leaks. 

The sequence of the operation number and selection of the machine, process, or bench are made to manufacture the part. These are required at circle 10 and are shown specifically at (18) and (19). A complete operations sheet will show this column. Even though they are vital in operations planning, their importance is less in detailed estimating once that operation has been selected. 

For azeotropic mixtures, the main difficulty of the solution of the task of synthesis consists not in the multiplicity of feasible sequences of columns and complexes but in the necessity for the determination of feasible splits in each potential column or in the complex. The questions of synthesis of separation flowsheets for azeotropic mixtures were investigated in a great number of works. But these works mainly concern three-component mixtures and splits at infinite reflux. In a small number of works, mixtures with a larger number of components are considered however, in these works, the discussion is limited to the identification of splits at infinite reflux and linear boundaries between distillation regions Reg° . Yet, it is important to identify all feasible splits, not only the spUts feasible in simple columns at infinite reflux and at linear boundaries between distillation regions. It is important, in particular, to identify the spUts feasible in simple columns at finite reflux and curvilinear boundaries between distillation regions and also the splits feasible only in three-section columns of extractive distillation. 

Although batch distillation is covered in a subsequent separate section, it is appropriate to consider the application of RCM and DRD to batch distulation at this time. With a conventional batch-rectification column, a charge of starting material is heated and fractionated, with a vapor product removed continuously. The composition of the vapor prodiic t changes continuously and at times drastically as the lighter component(s) are exhausted from the stiU. Between points of drastic change in the vapor composition, a cut is often made. Successive cuts can be removed until the still is nearly diy. The sequence, number, and limiting composition of each cut is dependent on the form of... 

The table of results is laid out in a column, and a second column is constructed in which in the hrst four rows the results would be added sequentially in pahs, e. g. Xi + X2, xj, + X4, x + jcg etc., and the lower four rows are calculated by subuacting the second value from dre preceding value thus, JC2 — JCi, JC4 — JC3 etc., a thh d column is prepared from these results by canying out the same sequence of operations. The process is continued until there are as many columns as the number of variables. Thus in the present tluee-variable, two level-study the process is repeated tluee times (Table 15.1), and in the general -variable, two-level case it is repeated n times. (The general description of uials of this kind where tlrere are n variables and two levels, is 2 factorial uials ). 

A feature of PC spreadsheets is that the position of rows or columns can be changed at the touch of a key, so the sequence of the rows of activities can be rapidly altered, and the position of the columns varied to preserve the diagonal pattern of crosses. This exercise can be executed a number of times to reduce the scatter of the stars away from the diagonal line and reduce the communicating distances between the activities. This has been carried out, and the result is shown in Table 7.2, where it can be seen that the stars are clustered more closely around the diagonal line. The list now shows the activities arranged in a preferred order of sequence. 

File) (New) A new data file can be generated by defining the number of columns and rows and then filling the table either in a column-by-col-umn or a row-by-row sequence if the option (Leave Empty) is chosen, the file is stored as is. The array size is limited to m < 10, but also by the available memory. 

A closely related problem was considered in the seventeenth century. It is the famous arithmetic triangle developed by Pascal that is shown in Table 4. It is constructed by writing the number one twice as the first line. The first column is then filled with an infinite sequence of the number one. Subsequently, each value in the table is calculated by taking die sum of the number immediately above and the number to the left of the latter. It is then apparent that the second column is given by C(n, 1) = n, the third by C(n, 2) = n n — l)/2, and in general as given by Eq. (5). 

---