Mass Transfer-I
Distillation
Lecture 6
Dr. Hemant Kumar
Department of Chemical Engineering
DDU Nadiad
10/9/2020 Mass transfer-I Dr Hemant Kumar 1
Number of Ideal Plates; McCabe-Thiele Method
1. The McCabe–Thiele method is considered to be the simplest
method for the analysis of binary distillation
2. This method is used to calculate number of idea trays
required needed to accomplish a definite concentration
difference in either the rectifying or the stripping section
3. This method is based on the assumption of constant molar
overflow which results from
– nearly equal molar heats of vaporization
– Heat loss from the column is negligible. If there will be
heat loss or gain there will be accompanying
condensation or vaporization within the column and the
flow rates will vary along the column and as a result
violating the assumption.
Number of Ideal Plates; McCabe-Thiele Method
• Rectifying section operating line eqn
(13)
• Stripping section operating line eqn
• (10)
• Reflux ratio
Number of Ideal Plates; McCabe-Thiele Method
(a) Top Plate (b) Total condenser (c) Partial condenser
Number of Ideal Plates; McCabe-Thiele Method
X1
First tray in the column : For total condenser (abc triangle)
and for partial condenser (a’b’c’ triangle)
Additional tray for partial condenser : (aba’triangle)
Number of Ideal Plates; McCabe-Thiele Method
• In the preceding treatment it is assumed that the condenser
removes latent heat only and that the condensate is liquid
at its bubble point
• Then the reflux L is equal to LC the reflux from the condenser,
and V =V1
• If the reflux is cooled below the bubble point, a portion of the
vapor coming to plate 1 must condense to heat the reflux; so
V1 < V and L > LC
• The additional amount ∆L that is condensed inside the
column is found from the equation
Number of Ideal Plates; McCabe-Thiele Method
• (15)
• The actual reflux ratio in the column is then:
• (15) (15) (16)
Number of Ideal Plates; McCabe-Thiele Method
• Temperature T1 is not usually known, but it normally almost
equals Tbc the bubble-point temperature of the condensate
• Thus Tbc is commonly used in place of T1 in Eqs. (15) and (16)
BOTTOM PLATE AND REBOILER:
• The action at the bottom of the column is analogous to that
at the top. Thus, Eq (11), written for constant molal overflow,
becomes, with L and V used to denote flow rates in this
section
• (17)
• If Xm is set equal to XB in Eq. (17), Ym+1 is also equal to XB , so
the operating line for the stripping section crosses the
diagonal at point (XB, XB)
Number of Ideal Plates; McCabe-Thiele Method
• The vapor leaving the reboiler is in equilibrium with the liquid
leaving as bottom product.
• Then xB and yr are coordinates of a point on the equilibrium
curve, and the reboiler acts as an ideal plate
FEED PLATE:
Consider the section of the
column at the tray where the feed
is introduced:
Overall MB:
Enthalpy balance
Feed Plate
Overall MB:
(18)
Enthalpy balance:
(19)
• The vapors and liquids inside the tower are all saturated, and
the molal enthalpies of all saturated vapors at this section
are essentially identical since the temperature and
composition changes over one tray are small
• The same is true of the molal enthalpies of the saturated
liquids, so that HG f = HG f+1 and HL f-1 = HL f
• Equation (19) then becomes
Feed Plate
• Equation (19) then becomes
• (20)
• Combining this with Eq. (18) gives
• (21)
• The quantity q is defined as the heat required to convert 1
mol of feed from its condition HF to a saturated vapor, divided
by the molal latent heat HG - HL
• The feed may be introduced under any of a variety of
thermal conditions for each of which the value of q will be
different
Feed Plate
• Combining Eqs. (18) and (21)
• (22)
• Rewriting the rectifying section and stripping section eqns
without subscripts (instead of V we are using G for vapor
flow rate, w for lower section product and D for distillate)
• (23 & 24)
• Subtracting enqs (23 & 24)
• (25)
• Further, by an overall material balance,
(26)
Substituting this and Eqs. (21) and (22) in (25) gives
Feed Plate
q z
y=− + F (27)
1− q 1− q
• This is the straight line eqn for feed plate with a slope
-q/(1-q)
• Where ZF is the feed composition. Since y=zF , when x=zF it
passes through the point x = y = ZF on the 45° diagonal
• The value of slopes are summarized as
Feed Plate
CONSTRUCTION OF OPERATING LINES
1. Draw a square on a graph paper and mark x and y axis from
0 to 1.
2. Draw a diagonal line
3. Plot the equilibrium curve with the help of data provided (x
and y) or from relation y=f(x) or if you know α then us eqn
y= αx/[1+(α-1)x]
4. locate the feed line according to a slope of q/q-1
5. Calculate the y-axis intercept xD/(RD + 1) of the rectifying
line and plot that line through the intercept and the point
(xD, xD)
6. Draw the stripping line through point (xB, xB) and the
intersection of the rectifying line with the feed line
Feed plate location
Thanks
Practice example 18.2 Mccabe smith vth edition
