How Do You Draw Q Line In Distillation Column

Chemical engineering technique

The McCabe–Thiele method is a chemic engineering science technique for the analysis of binary distillation.^[1] ^[two] ^[3] Information technology uses the fact that the composition at each theoretical tray (or equilibrium stage) is completely determined by the mole fraction of i of the two components and is based on the assumption of constant molar overflow, which requires that:

the tooth heats of vaporization of the feed components are equal;
for every mole of liquid vaporized, a mole of vapor is condensed; and
heat effects such as heats of solution are negligible.

The method was first published by Warren L. McCabe and Ernest Thiele in 1925,^[4] both of whom were working at Massachusetts Institute of Technology (MIT) at the time.

Construction and utilize [edit]

A McCabe–Thiele diagram for the distillation of a binary feed is constructed using the vapor–liquid equilibrium (VLE) information for the lower-humid component of the feed.

Figure one: Typical McCabe–Thiele diagram for distillation of a binary feed

On a planar graph with the horizontal (x) centrality representing the mole fraction of the lower-humid feed component in the liquid phase and the vertical (y) centrality representing the mole fraction of the lower-boiling feed component in the vapor phase, the 45 degree x = y line (see Figure 1) is used as a graphical aid. The equilibrium line (black line in Figure 1), drawn using the VLE data points of the lower boiling component, represents the equilibrium vapor phase compositions for each value of liquid phase composition. Vertical lines from the horizontal axis upwards to the 10 = y line indicate the feed and desired compositions of the elevation distillate product and the corresponding bottoms production (shown in blood-red in Figure 1).

The rectifying section operating line for the section above the feed inlet of the distillation column (shown in greenish in Figure 1) starts at the intersection of the distillate composition line and the x = y line and continues at a downwards gradient (Δy/Δx) of L / (D + 50), where L is the molar flow rate of reflux and D is the molar catamenia rate of the distillate product. For instance, in Figure i, assuming the molar menstruum rate of the reflux 50 is yard moles per hour and the molar catamenia charge per unit of the distillate D is 590 moles per hour, and then the downward slope of the rectifying section operating line is k / (590 + grand) = 0.63, which means that the y-coordinate of whatsoever point on the line decreases 0.63 units for each unit that the 10-coordinate decreases.

Effigy 2: Examples of q-line slopes

The q-line (depicted in blue in Figure 1) starts at the x = y line and intersects the starting point of the rectifying section operating line. The parameter q is the mole fraction of liquid in the feed, and the slope of the q-line is q / (q – 1). For example, if the feed is a saturated liquid it has no vapor, thus q = 1 and the slope of the q-line is space (a vertical line). As another example, if the feed is all saturated vapor, q = 0 and the slope of the q-line is 0 (a horizontal line).^[ii] The typical McCabe-Thiele diagram in Figure 1 uses a q-line representing a partially vaporized feed. Instance q-line slopes are presented in Figure 2.

The stripping section operating line for the section below the feed inlet (shown in purple in Figure 1) starts at the intersection of the red bottoms limerick line and the 10 = y line and continues up to the point where the blueish q-line intersects the green rectifying section operating line.

The number of steps betwixt the operating lines and the equilibrium line represent the number of theoretical plates (or equilibrium stages) required for the distillation. For the binary distillation depicted in Figure 1, the required number of theoretical plates is six.

The use of colored lines is not required. They are employed in Figure one to brand the methodology easier to describe.

Constructing a McCabe–Thiele diagram is non always straightforward. In continuous distillation with a varying reflux ratio, the mole fraction of the lighter component in the meridian part of the distillation column volition subtract every bit the reflux ratio decreases. Each new reflux ratio volition alter the slope of the rectifying department operating line.

When the assumption of constant molar overflow is not valid, the operating lines will not be straight. Using mass and enthalpy balances in addition to vapor-liquid equilibrium information and enthalpy-concentration information, operating lines can be synthetic using the Ponchon–Savarit's method.^[5]

If the mixture can form an azeotrope, its vapor–liquid equilibrium line will cross the ten = y line, preventing farther separation no matter the number of theoretical plates.

References [edit]

^ McCabe, W. 50. & Smith, J. C. (1976). Unit Operations of Chemical Engineering (third ed.). McGraw-Hill. ISBN0-07-044825-6.
^ ^a ^b Perry, Robert H. & Green, Don W. (1984). Perry's Chemical Engineers' Handbook (sixth ed.). McGraw-Hill. ISBN0-07-049479-7.
^ Beychok, Milton (May 1951). "Algebraic Solution of McCabe-Thiele Diagram". Chemical Engineering Progress.
^ W.50. McCabe & E.W. Thiele (June 1925). "Graphical Pattern Of Fractionating Columns". Industrial and Engineering Chemical science. 17: 605–611. doi:x.1021/ie50186a023.
^ Rex, C. Judson (1971). Separation Processes. McGraw-Loma. ISBN0-07-034610-0.

External links [edit]

More detailed information on how to draw a McCabe-Thiele Diagram
Detailed give-and-take of McCabe-Thiele method by Tore Haug-Warberg, Norwegian University of Scientific discipline and Technology, Norway
Interactive McCabe-Thiele Diagram