Complex Distillation Columns

The calculation procedures [the 0 method, Kb method, and constant composition method] developed in Chap. 2 for conventional distillation columns are applied to complex distillation columns in Sec. 3-1. For solving problems involving systems of columns interconnected by recycle streams, a variation of the theta method, called the capital 0 method of convergence is presented in Secs. 3-2 and 3-3. For the case where the terminal flow rates are specified, the capital 0 method is used to pick a set of corrected component-flow rates which satisfy the component-material balances enclosing each column and the specified values of the terminal rates simultaneously. For the case where other specifications are made in lieu of the terminal rates, sets of corrected terminal rates which satisfy the material and energy balances enclosing each column as well as the equilibrium relationships of the terminal streams are found by use of the capital 0 method of convergence as described in Chap. 7. 

A complex distillation column is defined as one which has either more feeds introduced or streams withdrawn or a combination of these than does a conventional distillation column. To demonstrate the application of the 0 method and associated calculational procedures, the complex column shown in Fig. 3-1 

In the application of the aforementioned calculational procedures, the specifications commonly made are as follows the column pressure the number of plates the rate, composition, and thermal condition of each feed as well as the locations of the feed plates and sidestreams. The number of additional specifications that may be made is equal to the total number of streams withdrawn (the distillate, bottoms, and sidestreams). For the column shown in Fig. 3-1, the additional specifications V2 (or Lx), D, Wu and W2 may be made. These in turn fix the dependent variable B. 

In order to make the first trial, temperature and L/V profiles for the column 

The component-material balances are stated in terms of a single set of flow rates, the vapor rates, by use of the equilibrium relationship / I = [Eq. (2-10)]. Except for the plates from which the sidestreams are withdrawn, the equations for the remaining stages of the complex column shown in Fig. 3-1 are formulated in precisely the same manner which was shown in Chap. 2 for conventional columns. 

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If complex distillation columns are being considered, then these also can bring about significant reductions in capital cost. The dividing-wall column shown in Fig. 5.17 not only requires typically 20 to 30 percent less energy than a conventional arrangement but also can be typically 30 percent lower in capital cost than a conventional two-column arrangement. ... 

Table 11.10 Heuristics for separating a mixture of components A, B and C using complex distillation columns. Component A is the most volatile and Component C is the least volatile7.

Table 11.10 presents some heuristics for using complex distillation columns to separate a ternary mixture into its pure component products. On the basis of these heuristics and those for simple columns, suggest two sequences containing complex columns that can be used to separate the mixture described in Table 11.9 into relatively pure products. 

Alatiqi presented (I EC Process Design Dev. 1986, Vol. 25, p. 762) the transfer functions for a 4 X 4 multivariable complex distillation column with sidestream stripper for separating a ternary mixture into three products. There are four controlled variables purities of the three product streams (jCj, x, and Xjij) and a temperature difference AT to rninirnize energy consumptiou There are four manipulated variables reflux R, heat input to the reboiler, heat input to the stripper reboiler Qg, and flow rate of feed to the stripper Lj. The 4x4 matrix of openloop transfer functions relating controlled and manipulated variables is ... 

J. Cerda and A.W. Westerberg. Shortcut methods for complex distillation columns. 1. Minimum reflux. Ind. Eng. Chem. Process Des. Dev., 20 546-557, 1981. 

H. Yeomans and I. Grossmann. Optimal design of complex distillation columns using rigorous tray-by-tray disjunctive programming models. Ind. Eng. Chem. Res., 39(ll) 4326-4335, 2000. 

For process optimization problems, the sparse approach has been further developed in studies by Kumar and Lucia (1987), Lucia and Kumar (1988), and Lucia and Xu (1990). Here they formulated a large-scale approach that incorporates indefinite quasi-Newton updates and can be tailored to specific process optimization problems. In the last study they also develop a sparse quadratic programming approach based on indefinite matrix factorizations due to Bunch and Parlett (1971). Also, a trust region strategy is substituted for the line search step mentioned above. This approach was successfully applied to the optimization of several complex distillation column models with up to 200 variables. 

The reactor system may consist of a number of reactors which can be continuous stirred tank reactors, plug flow reactors, or any representation between the two above extremes, and they may operate isothermally, adiabatically or nonisothermally. The separation system depending on the reactor system effluent may involve only liquid separation, only vapor separation or both liquid and vapor separation schemes. The liquid separation scheme may include flash units, distillation columns or trains of distillation columns, extraction units, or crystallization units. If distillation is employed, then we may have simple sharp columns, nonsharp columns, or even single complex distillation columns and complex column sequences. Also, depending on the reactor effluent characteristics, extractive distillation, azeotropic distillation, or reactive distillation may be employed. The vapor separation scheme may involve absorption columns, adsorption units,... 

In this section we present more complex distillation column processes that go beyond the plain vanilla variety. Industry uses columns with multiple feeds, sidestreams, combinations of columns, and heat integration to improve the efficiency of the separation process. Very significant reductions in energy consumption are possible with these more complex configurations. However, they also present more challenging control problems. We briefly discuss some common control structures for these systems. 

This subsection describes how to generate the feasible combinatorial possibilities of distillation column configurations for separation of mixtures that do not form azeotropes. Components are named A, B, C, D,. . . and they are listed in the order of decreasing volatility (or increasing boiling temperature). We limit our considerations to splits where the most volatile (lightest) component and the least volatile (heaviest) component do not distribute between the top and bottom product. For simplicity we consider only separations where final products are relatively pure components. Systems containing simultaneously simple and complex distillation columns are considered. Simple columns are the conventional columns with one feed stream and two product streams complex columns have multiple feeds and/or multiple product streams. 

It is not difficult to observe that, in this example, we have the coupling of a specific reactor for petroleum fractionation together with a complex distillation column. If we intend to show the complexity of the process that will be simulated. 

Shortcut models can also be used to initialize fractionation columns (complex distillation columns with multiple products), as described later. 

To design complex distillation columns, multicomponent methods are used. The true boiling curve is replaced by an approximate stepwise representation as a shown in Figure 12.18. Each step represents a pseudocomponent with a boiling point as indicated and a fraction of the total feed mixture based on the length of the horizontal portion of the step. 

We can regard a simple distillation as equivalent to one step on our diagram. Complex distillation columns carry out the equivalent of many steps on the diagram and their efficiency is defined in terms of the number of these steps—called in technical jargon the number of theoretical plates of the column. The more plates the greater the separation of the components of the solution achieved in the distillation column. 

In the interest of simplicity, the subscript co used to identify the corrected flow rates for conventional and complex distillation columns has been omitted in the above expressions and from those which follow. 

The desired set of 0 s is that set of positive numbers that makes gx = g2 = 0, simultaneously. These 0 s may be found by use of the Newton-Raphson method in a manner analogous to that described in Sec. 3-1 for complex distillation columns. 

The calculational procedure recommended by Nartker et al.12 consists of applying the 6 method of convergence (for conventional and complex distillation columns) one time to each column of the system in succession. The terminal rates so obtained for each column of the system are called the calculated values for the system, and denoted by the subscript ca. To initiate the calculational procedure for the system, the compositions for the minimum number of streams are selected as the independent variables for the system. For example, to initiate the calculational procedure for column 1 of the system shown in Fig. 3-9 the composition of the stream B2 is assumed. One complete column trial is made on column 1. A complete column trial consists of the application of the 6 method for single columns, the calculation of a new set of temperatures by use of the Kb method, and the calculation of a new set of total-flow rates for use of constant-composition method. These temperatures and total-flow rates are stored for use in the next trial calculation for the system. The set of bit s obtained by the... 

For the case of a complex distillation column which has one sidestream withdrawn in addition to the distillate and bottoms, show that the partial derivatives are given by the following expressions. 

Conventional and complex distillation columns 0 method Chaps. 2 and 3... 

The development of this application of the Newton-Raphson method is presented first for an absorber (or stripper)—see Fig. 4-1. Then the method is applied to conventional and complex distillation columns. 

Next, the 2N Newton-Raphson method is applied to reboiled absorbers, conventional distillation columns, and complex distillation columns, and then a procedure which makes use of the calculus of matrices for solving these equations is presented. 

To demonstrate the application of the 2N Newton-Raphson method to reboiled absorbers, Example 4-4 was solved. The statement and solution of this example appears in Table 4-8. The application of the 2N Newton-Raphson method to conventional and complex distillation columns is illustrated by Examples 4-5 and 4-6. Example 4-5 which involves a conventional distillation column, is a restatement of Example 2-7 (see Table 2-2). The... 

ALMOST BAND ALGORITHMS FOR CONVENTIONAL AND COMPLEX DISTILLATION COLUMNS... 

Many separations which would be difficult to achieve by conventional distillation processes may be effected by a distillation process in which a solvent is introduced which reacts chemically with one or more of the components to be separated. Three methods are presented for solving problems of this type. In Sec. 8-1, the 0 method of convergence is applied to conventional and complex distillation columns. In Sec. 8-2, the 2N Newton-Raphson method is applied to absorbers and distillation columns in which one or more chemical reactions occur per stage. The first two methods are recommended for mixtures which do not deviate too widely from ideal solutions. For mixtures which form highly nonideal solutions and one or more chemical reactions occur per stage, a formulation of the Almost Band Algorithm such as the one presented in Sec. 8-3 is recommended. 

The calculational procedures are presented first for conventional distillation columns and then for complex distillation columns. The conventional distillation column is completely determined by fixing the following variables (1) the complete definition of the feed (total flow rate, composition, and thermal condition), (2) the column pressure (or the pressure at one point in the column, say in the accumulator), (3) the type of condenser, (4) ku the number of plates above and including the feed plate, (5) /c2, the total number of plates, and (6) two other specifications which are usually taken to be the reflux ratio and the distillate rate LJD, D or two product specifications such as bjdh bh/d,, XDh xBh > Td, 7, or combinations of these. The subscript / is used to denote the light key and the subscript h is used to denote the heavy key. In all of the optimization problems considered herein, the variables listed in items (1), (2), and (3) are always fixed. For convenience these variables are referred to collectively as the usual specifications. The remaining four variables, ku /c2, and two other specifications such as LJD and D are called additional specifications. ... 

PROCEDURE 1. DETERMINATION OF THE MINIMUM NUMBER OF STAGES REQUIRED TO EFFECT A SPECIFIED SEPARATION AT A GIVEN REFLUX RATIO FOR CONVENTIONAL AND COMPLEX DISTILLATION COLUMNS... 

Procedure 1. Determination of the Minimum Number of Stages Required to Effect a Specified Separation at a Given Reflux Ratio for a Complex Distillation Column... 

Figure 9-2 A complex distillation column with one sidestream.

Procedure 2. Optimum Economic Design of a Complex Distillation Column... 

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