Infinite reflux conditions

The definition of the separation factor, Equation 7, when combined with infinite reflux condition. Equation 11, gives... 

There are two limits at which we can examine the behavior of a distillation column. The first is at total reflux (i.e., with an infinite reflux ratio, which is often called infinite reflux conditions). The other extreme is to operate at minimum reflux. In this section we shall limit our discussion to the total reflux case in later sections we shall look at operating columns at finite reflux (ratio) conditions. Intuitively, we tend to expect that a column will give its maximum separation when run at infinite reflux. While this is true for ideally behaving species, it does not have to be true when separating nonideally behaving species. Thus, we need to look carefully at running colunons all the way from minimum to total reflux conditions. 

Fig. 52. All compositions that can be reached for both finite and infinite reflux conditions from the distillate D and bottoms B compositions by stepping away from them using a tray-by-tray...

The term transformed is used to indicate the shift in the nodes from infinite reflux conditions, where the nodes all lie on the vertices of the MET (i.e., at the pure components) to their current positions in the CPM. 

This section has thus presented a quick synthesis and analysis method for two simplified infinite reflux cases. Just like simple columns, it can be generally stated that if a design is considered feasible at infinite reflux conditions, then a feasible design can be found at finite reflux too. This fact is particularly useful for nonideal systems. An illustration of a more complex infinite Petlyuk column example is given in the following example for the azeotropic acetone/benzene/chloroform system. 

It is interesting to note that Equation 9.14 is mathematically similar to the residue curve equation for distillation processes (refer to Equation 2.8). As one may recall from preceding chapters, this simplification of the MDPE under total reflux conditions is comparable to the simplification of the distillation-based DPE under infinite reflux conditions. 

As the reflux ratio is decreased from infinity for the total reflux condition, more theoretical steps or trays are required to complete a given separation, until the limiting condition of Figure 8-23 is reached where the operating line touches the equilibrium line and the number of steps to go from the rectifying to stripping sections becomes infinite. 

Note that the last condition implies infinite reflux and infinite number of stages. The assessment of feasibility of a design for zeotropic mixtures is fully correct, the only problem left being the sizing. 

Minimum reflux conditions correspond to a situation of minimum L/V, maximum product, and infinite stages. In the McCabe-Thiele constructions minimum reflux was determined either by feed conditions or an equilibrium line pinch condition as in Fig. 8.15. 

The plate equivalent is the minimum number of plates required at infinite reflux ratio to attain the same enrichment (xB- -Xg) as in a countercurrent distillation with a finite reflux ratio. All distillation conditions except the reflux ratio remain the same. Thus, in the McCabe-Thiele diagram the separating stages are drawn between the diagonal and the equilibrium curve v = oo). 

The smaller the refluxes become, the larger the differences between L and V become and simultaneously the greater the departure from RCM conditions become. As shown in Section 3.6.1, the other extreme reflux condition, infinite reflux, results in the residue curve equation and at these conditions the TT and the MET will coincide with each other exactly. 

The second inhnite reflux condition in the Petlyuk column is where CSj and CSe operate at infinite reflux, but we do not specify that CS2-5 operate under these conditions, that is, the vapor and liquid flowrates in 82-5 are finite values and are not equal to each other. Since the overall reflux is infinite, there is still no effect from feed addition or product removal on the column. Therefore, the CS breakdown for this structure is equivalent to the one shown in Figure 7.2. We can again apply the mass balance around the thermally coupled junction at the top of the column as in Equation 7.4. In this case, we again have the condition that Va = La and x = y , but in this case Vb 7 Lb, Vc Lc- Under these conditions, we find that Equation 7.4 reduces to... 

Recall that for all our previous designs we had to satisfy the condition for all products to be connected by a set of profiles for the design to be classified as feasible. The finite reflux Petlyuk is no different, but as alluded to in the infinite reflux case, the thermal coupling in two sections means this composition matching constraint is a little more complicated. Thus, let us consider where we need to search for profile intersections in the column by systematically highlighting areas of interest. 

As the first step of conceptual process design, the distillation column is considered at infinite reflux ratio, J = with an infinite number of stages, N = oo. Under these perfect separation conditions, the distillation column will yield a bottom product that contains pure A2 x = 0. Then the distillate mole fraction only depends on the size of the reactor (Da), the recycling ratio (gj), and the chemical equilibrium concentration Combining (5.6) and (5.7) yields... 

We need to discuss some of the limiting conditions in distillation systems. The minimum number of trays for a specified separation corresponds to total reflux operation. If the column is mn under total reflux conditions, the distillate flow rate is zero. Therefore, the reflux ratio is infinite, and the slope of the operating lines is unity. This is the 45° line. Thus, the minimum number of trays can be determined by simply stepping up between the 45° line and the VLB curve (see Fig. 2.8). 

The minimum number of trays corresponds to total reflux operation (an infinite reflux ratio). The Fenske equation relates the compositions at the two end of a column to the number of stages in the column under this limiting condition. 

As in distillation, a given separation with defined feed, top, and bottom products may be achieved in different ways a reduction in the number of theoretical stages may be compensated for by increased reflux and vice versa. In any section of the column there is, however, a minimum reflux, defined by Eq. (12.23), below which the required separation cannot be achieved. At this minimum reflux condition, an infinite number of stages would be required. This condition corresponds to the intersection or tangency of equilibrium and... 

Rule of connectedness condition satisfied to product points at R = oo and N = oo. The stable node of the top product boundary element of distillation region at infinite reflux Reg and the unstable node Njj of the bottom product boundary element of distillation region at infinite reflux Reg should coincide (N = iVjj), or should be connected with each other by the bond (N — Nj ) or chain of bonds in direction to the bottom product. 

The minimum reflux condition represents the opposite of total reflux, and thus an infinite number of ideal separation stages. 

The minimal number of theoretical separation stages which is required for the crude argon column to accomplish the O2—Ar separation, is estimated with the Fenske formula. This formula holds for infinite reflux, L/ V 1. This condition is almost fulfilled since typically only 1 part out of 30 parts of ascending vapour is withdrawn as crude argon from the top of the crude argon column, whereas 29 parts of liquid remain as reflux. 

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