## Columns with Intermediate Inputs and Outputs of Heat Pinch Method

Columns under consideration are columns of nonadiabatic distillation (that can also be used in simple two-section columns, in complex columns, and in distillation complexes). The application of simple nonadiabatic columns for separation of azeotropic mixtures was examined in Chapter 5, Section 5.7, when separation in adiabatic columns is unfeasible.

Here we examine another application of nonadiabatic columns - to decrease energy consumption in separation. Nonadiabatic columns are widely used for this purpose in petroleum refining (heat output by "pumparounds").

In the mode of minimum reflux adiabatic sections trajectories intersect reversible distillation trajectories in points S2. Therefore, the separation process between product point and point S2 can be carried out in principle, maintaining phase equilibrium between meeting flows of vapor and liquid in the cross-section at the height of the column by means of differential input or output of heat. We call such a separation process, with the same product compositions as at adiabatic distillation, a partially reversible one. A completely reversible process is feasible only for the preferable split that is rarely used in practice. Nonadiabatic distillation used in industry is a process intermediate between adiabatic and partially reversible distillation. Summary input and output of heat at nonadiabatic and adi-abatic distillation are the same, and the energetic gain at nonadiabatic distillation is obtained at the transfer of a part of input or output heat to more moderate temperature level, which uses cheaper heat carriers and/or coolants.

We examine the column with one intermediate input of heat in the bottom section and one intermediate output of heat in the top section. Figure 6.2a shows the change of internal liquid flows along the height of such a nonadiabatic column, depending on the value inverse to absolute temperature (1 /T). Figure 6.2b shows the distillation trajectory of nonadiabatic column:

xD ^ Aft(2) ^ S(2) ^ xf\ xf ^ Aft(3) ^ S® ^ xB RegD QCtn Reg'r Re gsh RegiA RegS RegB '

Liquid flows saltatory increases or decreases in the points of intermediate output or input of heat at the temperature TOl and T^. The minimum possible value of liquid flows at parts from column ends to the points of intermediate input and output of heat is equal to the value of liquid flow at partially reversible process in those cross-sections, where Trev = TOl and Trev = 7^. Calculation of reversible distillation trajectory at parts from column ends to points Sr and Ss determines the function Lrev = f (1/T) for these parts and then determines such optimal values opt TOl and opt T^, at which summary cost of inputs and outputs energy is minimum.

Such an approach was introduced in the work (Terranova & Westerberg, 1989; Dhole & Linnhoff, 1993) and was named "pinch method."

If it is accepted that the price for input heat is proportional to the value (1/T0 -1/Teb) and the price for output heat is proportional to the values (1/TOn -1 /T0), where T0 is the ambient temperature, and amount of input or output heat is proportional to liquid flow, then the cost of energy consumption in the main and intermediate reboilers will turn out to be proportional to the hatched area in the bottom section in Fig. 6.2. In the main and intermediate condensers, it is proportional to the hatched area in the top section. Under the assumptions mentioned, the values opt and opt 7^ will correspond to the minimum of these areas.

Minimum values of the parameters (L/V)r and (V/L)s in the feed cross-section of the column and compositions at trays above and below this cross-section xf -1 and xf at adiabatic and nonadiabatic distillation remain the same. The stationary points Sr and Ss also coincide, but at parts of reversible distillation trajectories between column ends and stationary points Sr and Ss the additional stationary points N"1 and N"1, corresponding to the points of intermediate inputs and output of heat (Fig. 6.2a), appear.

Therefore, the conceptual calculation of infinite column with intermediate input and/or output of heat consists in two stages: (1) calculation of minimum reflux mode for adiabatic column, and (2) determination of opt 70%, opt 00«, opt Tnt, and opt Qrebb ("pinch method").

Figure 6.2 shows the results of such calculation at the example of direct separation of ideal three-component mixtures. However, this approach can also be easily used in the most general case for any kinds of mixtures, including azeotropic ones, at any component numbers and for any splits.

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