Columns at Total Reflux

The concept of total reflux was discussed in Chapters 3 and 6. The conditions of total reflux may be approached either by operating the column at flnite feed and product rates with a very large reflux rate or by cutting off the feed and products and maintaining internal boilup and reflux by adding and removing heat at the reboiler and condenser. 

By using a simplified model of binary distillation with two stages, it was shown in Chapter 3 that maximum separation is achieved at total reflux. Also, the Y X diagram was applied in Chapter 6 to verify that for a given number of stages, maximum separation of a binary mixture is obtained at total reflux. A corollary to this statement is that for a specified separation, the required number of stages is least at total reflux. The performance of multi-component columns at total reflux is discussed next. 

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Equations (13-31) and (13-32) are rigorous relationships between the splits obtained for components i and r in a column at total reflux. However, the correct value of Ot must always be estimated, and this is where the approximation enters. It is usually estimated from... 

The program starts up the column at total reflux (R very high). After steady state is reached on all plates, vary the reflux ratio interactively and attempt to carry out the distillation in minimum time, while attempting to... 

If the number of stages is known, equation 11.57 can be used to estimate the split of components between the top and bottom of the column at total reflux. It can be written in a more convenient form for calculating the split of components ... 

Consider first total reflux conditions, corresponding with the minimum number of theoretical stages. The bottom of a distillation column at total reflux is illustrated in Figure 9.13. 

The distillation lines in the distillation line map were in this case developed by carrying out a balance around the bottom of the column, as indicated in Figure 9.13. Equally well, the distillation line could have been developed by drawing an envelope around the top of the column at total reflux, and the calculation developed down the column in the direction of increasing temperature. 

Equations 12.17 and 12.18 for packed columns at total reflux could also have been developed by considering a mass balance around the bottom of the column. The same result would have been obtained. 

If good VLE data are available, run the Oldershaw column at total reflux and calculate efficiency, Obtain overall Oldershaw column efficiency and assume it is the same as the commercial column point efficiency. Use a mixing model to calculate the overall column efficiency for the commercial column, A conservative alternative is to assume that overall commercial column efficiency is the same as overall Oldershaw column efficiency,... 

Run column at total reflux to stabilize concentration distill off the low-boilers cut 6 h... 

Figure 6.2. Schematic of the wetted wall column at total reflux.

Equations (13-31) and (13-32) are exact relationships between the splits obtained for components i and r in a column at total reflux. 

Other Operating Methods and Optimization A useful control method for difficult industrial or laboratory distillations is cycling operation. The most common form of cycling control is to operate the column at total reflux until steady state is established, take off the complete distillate for a short time, and then return to total reflux. An alternative scheme is to interrupt vapor flow to the column periodically by the use of a solenoid-operated butterfly valve in the vapor line from the pot. In both cases, the equations necessary to describe the system are complex, as shown by Schrodt et al. [Chem. Eng. Sci, 22, 759 (1967)]. The most reliable method for establishing the cycle relationships is by experimental trial on an operating column. Several investigators have also proposed that batch distillation be programmed to attain time optimization by proper variation of the reflux ratio. A comprehensive discussion was first presented by Coward [Chem. Eng. Sci, 22, 503 (1967)] and reviewed and updated by Kim and Diwekar [Rev. Chem. Eng., 17, 111 (2001)]. 

This constraint follows from the definition of a distillation curve. Each point along a distillation curve represents both the vapor and the liquid compositions just above (or below) any tray, including those at the ends of the column where products would normally be withdrawn. This constraint, together with the material balance constraint, completely defines the reachable products for a column at total reflux. 

Figure 14.17. Composition profiles in the distillation of acetone-methanol-water system in a bubble cap column at total reflux. Data of Vogelpohl (1979). Calculations by Krishnamurthy and Taylor (1985b).

This equation applies throughout the column at total reflux. Equation 12.2 is written for tray j + 1,... 

Operation of a column at total reflux is important in two ways it is a convenient startup condition that enables a column to be lined out at steady state before feed is processed, and in experimental work it is a simple and yet effective means for obtaining mass transfer information. The number of stages at total reflux is also important in design calculations in that it represents a lower limit to the required stages and it also represents a parameter used in short cut estimates of stage requirements (to be discussed in Section 5.3-7). 

If a set of bifdis corresponding to a given D are known for a column at total reflux and a system for which the a, s are constant, then the 9 method of conver-... 

Figure 2-6 A graphical representation of 0 is obtained by considering two arbitrarily specified values for a base component b in a column at total reflux.

Total reflux of type 1 may be approached in a continuous distillation column by approaching total reflux conditions in both the rectifying and stripping sections. The designer approaches this type of operation of a continuous distillation column as the reflux ratio is increased indefinitely at a fixed feed rate and nonzero product rates. In the limit, this type of operation is recognized as total reflux of type 1, continuous distillation columns at total reflux. The necessary conditions for an equivalence to exist between columns at the operation conditions of total reflux of types 1 and 2 are presented in Sec. 10-2. Total reflux of types 1 and 2 are of significant interest because columns at these types of operation produce the best possible separations. 

In the analysis of continuous distillation columns at total reflux, three different calculational procedures are presented namely, the 6 method of convergence and two formulations of the Newton-Raphson method, one analogous to the 2N Newton-Raphson method and the other to the Almost Band Algorithm. The formulation of each of these methods for continuous distillation columns at total reflux is presented below. 

Fewer equations are required to describe distillation columns at total reflux than are required to describe columns operating at finite reflux ratios. The condition that Ljt 4 J + x = 1 (in the limit as -> oo) eliminates the necessity for the determination of the total flow rates, and consequently the energy balance for each stage may be omitted from the set of equations to be solved. This type of total reflux appears to have been first proposed by Robinson and Gilliland.13... 

Figure 10-1 An [N(c + l) + c] Almost Band Formulation of the Newton-Raphson method for a distillation column at total reflux.

CONTINUOUS AND BATCH DISTILLATION COLUMNS AT TOTAL REFLUX IN BOTH SECTIONS,... 

The equations required to describe distillation columns at total reflux in both sections are formulated in a manner analogous to that shown in Sec. 10-1 for the 0 method and the two Newton-Raphson methods. For purposes of illustration, the equations for the 0 method are developed below. 

EXAMPLES To demonstrate the effect of the holdup specifications on the steady state solution of a batch distillation column at total reflux (a column operating at total reflux of type 2 D — 0, B = 0, F = 0), Examples 10-2 and 10-3 are presented in Table 10-6. The temperature profiles given in Table 10-7 were found by solving Examples 10-2 and 10-3 by use of the calcula-tional procedure described above.. 

Table 10-6 Statement of Examples 10-2 and 10-3 effect of holdup on distillation columns at total reflux, type 1 (D = 0, B = 0, F = 0)...

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