Operating line for absorption

Typical operating lines for absorption or desorption of a slightly soluble gas. 

Figure 10.5.5 shows an equilibrium line along with operating lines for absorption and desorption. The distance between the operating line and the equilibrium line represents the driving force. 

Eq. 12.2-6 is an important result called the operating line of the column. Like the operating line for absorption, it is based on mole balances. It has two important features. First, the reflux ratio Ru which appears in this equation is a major factor in the control of this type of column. Obviously, we can vary R between zero and infinity by changing the amount of condensate we send back into the column. If we send none back, Rj is zero, and we get little separation. If we send all of it back except one tiny drop of distillate, then is infinity and the tiny drop will be the purest product possible with this column. 

Fig. 6. Operating lines for an absorption system line A, high -L /ratio soHd line, medium -L /G ratio line B, -L /G ratio at theoretical minimum...

Four theoretical trays have been stepped off for the key component (butane) on Fig. 14-11, and are seen to give a recovery of 75 percent of the butane. The operating lines for the other components have been drawn with the same slope and placed so as to give approximately the same number of theoretical trays. Figure 14-11 shows that equilibrium is easily achieved in fewer than four theoretical trays and that for the heavier components nearly complete recovery is obtained in four theoretical trays. The diagram also shows that absorption of the light components takes place in the upper part of the tower, and the final recovery of the heavier components takes place in the lower section of the tower. 

Analogous to the minimum reflux ratio in distillation, there exists a minimum L/G ratio in absorption. Figure 6.3 compares the operating line to the equilibrium line for absorption. Because the slope of the operating line is L/G, reducing the liquid mass-separating agent flowrate decreases the slope of the line. Compare lines aA and ab for a separation in which the gas enters with concentration of solute which must be removed to Ya and the liquid... 

A gas containing 2 percent A and 1 percent B is to be scrubbed with a solvent in which A is five times as soluble as B. Show that using two columns in series with separate regeneration of the liquid from each column would permit recovery of A and B in relatively pure form. Use a y-x diagram to show the equilibrium and operating lines for the simultaneous absorption of A and B and estimate the ratio of A and B in the liquid from the first absorber,... 

The McCabe-Thiele analysis for dilute immiscible extraction is very similar to the analysis for dilute absorption and stripping discussed in Chapter 12. It was first developed by Evans (1934) and is reviewed by Robbins (1997). In order to use a McCabe-Thiele type of analysis we must be able to plot a single equilibrium curve, have the energy balances automatically satisfied, and have one operating line for each section. 

To have a straight operating line for the more volatile conponent in distillation we assumed that constant molal overflow (CMO) was valid, which meant that in each section total flows were constant. For absorption, stripping, and extraction we could make the assunption that total flows were constant if the systems were very dilute. For more concentrated systems we assumed that there was one chemical species in each phase that did not transfer into the other phase then the flow of this species (carrier gas, solvent, or diluent) was constant. In general, we have to assume either that total flows are constant or that flows of nontransferred species are constant. 

The solvent ratio v is an important operating variable for absorption, similar to the reflux ratio for rectification. It controls the slope of the balance line for an absorption problem and has to be larger than a minimum solvent ratio is obtained by... 

FIGURE 10.5.5. Operating line and equilibrium line of gas absorption. (Dotted line shows the operating line for gas stripping.)... 

Equation (10.6-2) is the material balance or operating line for the absorption tower... 

The next topics of interest are the operating line for the countercurrent adsorption device and the height of the device or the number of stages needed for the device to achieve a given separation. The device may be of continuous contact type or stagewise contact type. For continuous contact type devices, the approach will follow that in Section 8.1.2.3 employed for gas absorption from a concentrated gas stream. We focus on one particular species i (= A) which is being adsorbed, say, from a gas stream j = g, here the inert (solute-free) gas stream mass flow rate... 

Often if countercurrent adsorption is carried out, it may be of the multistaged type like that in Figure 8.1.43(a), or the Cloethe-Streat type or other configurations. The operating line for such operation may be developed following Section 8.1.2.6 for gas absorption. As shown in Figure 8.1.44(c), for a gas-solid system, for example, a mass balance for species 1 between the top and the nth plate leads for a dilute system to a linear relation between and Wb at the bottom... 

Figure 14-6 illustrates the graphical method for a three-theoretical-plate system. Note that in gas absorption the operating line is above the equihbrium curve, whereas in distillation this does not happen. In gas stripping, the operating line will be below the equihbrium curve. 

Only physical absorption from dilute gases has been considered in this section. For a discussion of absorption from concentrated gases and absorption with chemical reaction, the reader should refer to Volume 2, or to the book by Treybal (1980). If the inlet gas concentration is not too high, the equations for dilute systems can be used by dividing the operating line up into two or three straight sections. 

Figure 5.17. Dual-column ion exchange preconcentration valve. Sa, Sb samples A and B Ca, Cb ion exchange columns A and B Ea, Eb eluant (2 M nitric acid) for columns A and B Wa, Wb waste lines for samples and eluants A and B W waste lines AAS atomic absorption spectrometer. The dimensions of the base plate of the valve are 70 x 45 x 10 mm. See text for details of operation. Source [661]...

The four versus sketches of Fig. 24.2 represent various possible ideal contacting schemes of gas with liquid. Sketch the contacting scheme for straight physical absorption corresponding to the versus operating lines XY shown in Fig. P24.1. 

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