Constant molal overflow validity

The HETP of a packed-tower section, valid for either distillation or dilute-gas absorption and stripping svstems in which constant molal overflow can be assumed and in which no chemical reactions occur, is related to the height of one overall gas-phase mass-transfer unit Hqc by the equation... 

L = constant, and V = y , = V = constant. In this case it is possible to dispense with one equation for each stage, namely the enthalpy balance. This is called the constant molal overflow assumption (which was also embodied in (8-5)) and is valid if, over the temperature and pressure operating range of the separator ... 

Because of their relative simplicity, the Underwood minimum reflux equations for Class 2 separations are widely used, but too often without examining the possibility of nonkey distribution. In addition, the assumption is frequently made that (/ )min equals the external reflux ratio. When the assumptions of constant relative volatility and constant molal overflow in the regions between the two pinch-point zones are not valid, values of the minimum reflux ratio computed from the Underwood equations for Class 2 separations can be appreciably in error because of the sensitivity of (12-34) to the value of q as will be shown in Example 12.5. When the Underwood assumptions appear to be valid and a negative minimum reflux ratio is computed, this may be interpreted to mean that a rectifying section is not required to obtain the specified separation. The Underwood equations show that the minimum reflux depends mainly on the feed condition and relative volatility and, to a lesser extent, on the degree of separation between the two key components. A finite minimum reflux ratio exists even for a perfect separation. 

If, for exanple, (frac rec. A in dist) = 1.0, then x bot 0 nd Dx ist A- Once the fractional recovery is assumed, we can find L and V in the rectifying section. Since constant molal overflow is valid. 

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. 

On the other hand, calculation of diffusion in distillation columns tends to be easier if the molar average reference velocity v gf moi is used. In distillation, constant molal overflow is often valid or close to valid fSection 4.2T The resulting equimolar counterdiffusion results in = -Ng, and there is no convection in the reference frame with v,.pf mni = 0. If we choose the reference velocity as the molar average velocity, then Eq. ri5-16ei becomes... 

Unequal Molal Overflow. 1. Ahofoe Feed Plate. The analysis given in the preceding sections was based on constant molal overflow rate, and it is necessary to consider the validity of this assumption. 

If CMO is valid, the total vapor and liquid flow rates will be constant in each section of the column. The total flow rates can change at each feed stage or sidestream withdrawal stage. This behavior is illustrated for a conputer simulation for a saturated liquid feed in Figure 5-2 and is the same behavior we would expect for a binary system. For nonconstant molal overflow, the total flow rates will vary from section to section. This is also shown in Figure 5-2. Although both liquid and vapor flow rates may vary significantly, the ratio L/V will be much more constant. 

---