Q line

Condition of Feed (q Fine). The q line, which marks the transition from rectifying to stripping operating lines, is determined by mass and enthalpy balances around the feed plate. These balances are detailed in distillation texts (15). 

The q line, therefore, depends on the enthalpy condition of the feed. Types of q lines are shown in Figure 9 and are hsted below. 

Feed enthalpy condition Slope of q line q Line coord... 

Similaily, the entice equilibiium curve is calculated and is plotted in Figure 10. The feed is at the boiFng point so the q line is drawn vertically with an infinite slope. 

Calculate reflux ratios. The minimum internal reflux ratio is a line from the intercept of the q line with the equiUbtium curve to the yP point on... 

Minimum Reilux with Pinch Zone. There are some distillations where the minimum reflux does not occur at the intersection of the upper and lower operating lines and the q line. These cases arise when the equiUbrium is skewed from positive activity coefficients and when the operating line intersects the equiUbrium line in a 2one of constant composition, a pinch 2one, which is not at the line intersection. Figure 14 illustrates such a case. An example of such a pinch 2one in an ethanol—water column is available (37). 

FIG. 13-31 Typical intersection of the two operating lines at the q line for a feed stage. The q line shown is for a partially flashed feed. 

FIG. 13-32 AU five cases of q lines (1) superheated-vapor feed, (2) saturated-vapor feed, (3) partially vaporized feed, (4) saturated-liquid feed, and (5) siih-cooled-liqiiid feed. Slope of q line = q/(q — 1). 

FIG. 13-33 Typical construction for a sidestream showing the intersection of the two operating lines with the q line and with the x — q diagonal, (a) Liquid sidestream near the top of the column, (h) Vapor sidestream near the bottom of the column. 

This point phis the point of intersection of the two operating lines on the sidestream q line (vertical at Xs = 0.746) permits the location of the middle operating line. (The slope of the middle operating line conld... 

The thermal condition of the feed is designated as q, and is approximately the amount of heat required to vaporize one mole of feed at the feed tray conditions, divided by the latent heat of vaporization of the feed. One point on the q line is on the 45° line at Xp. 

Bubble point liquid feed, q = 1.0 (q-line vertical)... 

One point is on the 45° line at Xr, and the slope is Ls/Vs, where S refers to the stripping section. Another point is the intersection of the rectifying section operating line with the q line. And still another point is on the Y axis at the location below the origin of -(B/Vs)(Xb). 

Identify mislocated feed points where the feed, for binary mixtures, is not where the q-line intersects the equilibrium curve. This is not necessarily the case for multicomponent feed, however. 

The q-line starts on the x-axis at Xp. The value of q is the same as for conventional McCabe-Thiele. The slope of the q-line in the Ryan graph is the McCabe-Thiele slope minus 1. Therefore for bubble point feed the q-line is vertical for the conventional McCabe-Thiele and Ryan. For dew point feed the slope is 0 for the conventional McCabe-Thiele and -1 for Ryan. 

This graphical representation is easier to use for nonideal systems than the calculation method. This is another limiting condition for column operation, i.e., below this ratio the specified separation cannot be made even with infinite plates. This minimum reflux ratio can be determined graphically from Figure 8-23, as the line with smallest slope from xp intersecting the equilibrium line at the same point as the q line for mixture following Raoul t s Law. 

Read from graph at intersection of q line for 1.5 and minimum reflux operating line. 

This represents feed as all vapor (not superheated). Slope of q line ... 

NOTE PLACE POINT WHERE CONTROL BIT RUN IS LOCATED USING SHIP CURVE, FIT Q-LINE BELOW POINT MOVE SHIP CURVE UP TO POINT. EFFECT OF A CHANGE IN HYDRAULICS CAN THEN BE TRACED. POINTS OF COMPLETE BIT CLEANING ARE ON THE "MAXIMUM HYDRAULICS" CURVE. 

The point of intersection of the two operating lines is dependent on the phase condition of the feed. The line on which the intersection occurs is called the q line (see Volume 2). The q line is found as follows ... 

Draw in the bottom operating line from Xb on the diagonal to the point of intersection of the top operating line and the q line. 

For this problem the condition of minimum reflux occurs where the top operating line just touches the equilibrium curve at the point where the q line cuts the curve. 

This equation is known as the q-line. On the x-y plot, it is a straight line with slope q/(q—1) and intersects the diagonal line at x p. It is plotted in Figure 9.8 for various values of q. 

---