Straight operating line

Simplified Design Procedure for Linear Equilibrium and Operating Lines. A straight operating line occurs when the concentrations are low such that and remain essentially constant. (The material balance is obtained from equation 35.) In cases where the... 

The concept of a mass-transfer unit was developed many years ago to represent more rigorously what happens in a differential contactor rather than a stagewise contactor. For a straight operating line and a straight equilibrium line with an intercept of zero, the equation for calculating the number of mass-transfer units based on the overall raffinate phase N r is identical to the Kremser equation except for the denominator when the extraction factor is not equal to 1.0 [Eq. (15-23)]. 

In this case it appears that assuming straight operating lines, even though the molai heats of vaporization are markedly different, results in overestimation of the number of trays needed for the separation. 

Taking straight operating lines in each case, the numbers of trays... 

For an ideal separation at equilibrium and with straight operating lines, and Em are related by ... 

With a straight operating line and a straight equilibrium line (Henry s Law for example), where the entering absorption liquid is pure, i.e., xao = 10, Nqg as shown in Eq. (48), it now becomes... 

Nonparallel, Straight Operating Line, and Equilibrium Curve... 

However, a satisfactory value of V +i can usually be obtained on the first trial by using the flows at the top of the column L and to calculate y i from x in Eq. (18.48) (this corresponds to using a straight operating line based on constant molal overflow). Then is evaluated from and Eq. (18.47) is solved for... 

The slope of a straight operating line is LjV for that section of the column, but the local slope of a curved operating line is not equal to the local value of L/V. Starting with the equation for the rectifying section, Eq. (18.48), the following equations can be obtained by replacing first L and then with — D and L + D ... 

According to basic laws of geometry, the ratio f/Gi +12) is constant if dew point and boiling point lines are parallel straight hnes. Consequently, the eonditions for straight operating lines are ... 

If absorption or stripping can be assumed 1) to be isothermal and 2) to have negligible heat of absorption, then the energy balances will be satisfied. In this case the McCabe-Thiele analysis procedure can be adapted to more concentrated systems where the total flow rates L and V are not constant. We will have the desired straight operating line if we define... 

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. 

With these assumptions the energy balance is automatically satisfied. A straight operating line is easily derived using the mass balance envelope shown in Figure 14-3A. Defining ratios and flow rates... 

---