# MCCABE THIELE METHOD

McCabe Thiele software / McCabe Thiele calculator from EQ-COMP can draw temperature concentration diagram (T-x-y plot) and concentration diagram (x-y plot) for any binary mixture of non-polar hydrocarbons at near atmospheric and elevated pressures. The temperature concentration diagram (T-x-y plot) and concentration diagram (x-y plot) can be used in McCabe Thiele method to calculate number of equilibrium stages of a binary distillation column designed to separate the binary mixture.

McCabe Thiele method is a procedure followed in finding number of equilibrium trays of a binary distillation column. A binary distillation column is used to separate a binary hydrocarbon mixture based on the difference in volatilities of the two hydrocarbon compounds forming the hydrocarbon mixture. A temperature-concentration diagram (T-x-y plot) of the hydrocarbon mixture to be separated is initially plotted. A temperature-concentration diagram (T-x-y plot) plots bubble point temperature values and dew point temperature values for varying mole fraction of more volatile component of the hydrocarbon mixture at constant design pressure of the binary distillation column.

FIG 1 : Temperature-concentration diagram (T-x-y plot) for methane-ethane mixture at 10 bars pressure (generated by EQ-COMP)

Based on this temperature-concentration diagram (T-x-y plot), a concentration diagram (x-y plot) is plotted. A concentration diagram (x-y plot) plots dew point concentration of more volatile compound at a given temperature to bubble point concentration of more volatile compound at the same temperature for different temperature values on temperature-concentration diagram (T-x-y plot).

FIG 2 : Concentration diagram (x-y plot) for methane-ethane mixture at 10 bars pressure (generated by EQ-COMP)

The next step is to draw a straight line from the origin of the graph to the point where x and y both equal 1.0, which is the x = y line. This 45 degree line is used simply as a graphical aid for drawing the remaining lines. Then draw the equilibrium line using the VLE data points of the lower boiling component, representing the equilibrium vapour phase compositions for each value of liquid phase composition. Also draw vertical lines from the horizontal axis up to the x = y line for the feed and for the desired compositions of the top distillate product and the corresponding bottoms product.

The next step is to draw the operating line for the rectifying section (the section above the feed inlet) of the binary distillation column. Starting at the intersection of the distillate composition line and the x = y line, draw the rectifying operating line at a downward slope (Δy/Δx) of L / (D + L) where L is the molar flow rate of reflux and D is the molar flow rate of the distillate product.

FIG 3 : Examples of q-line slopes

The next step is to draw the q-line from the x = y line so that it intersects the rectifying 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 infinite which means the line is vertical. As another example, if the feed is all saturated vapor, q = 0 and the slope of the q-line is 0 which means that the line is horizontal. Some example q-line slopes are presented in Figure 3.

Next, draw the operating line for the stripping section of the distillation column (i.e., the section below the feed inlet). Starting at the intersection of the red bottoms composition line and the x = y line, draw the stripping section operating line up to the point where the blue q-line intersects the green operating line of the rectifying section operating line.

Finally, draw the steps between operating lines and the equilibrium line and then count them. Those steps represent the theoretical plates (or equilibrium stages).

This method of finding the number of equilibrium stages is known as McCabe Thiele method and the concentration diagram along with various operating lines and q line is known as McCabe Thiele diagram.

More information regarding use of EQ-COMP software for binary VLE calculation is available at BINARY VLE page. McCabe Thiele software / McCabe Thiele calculator is available for use at VLE CALCULATOR page.