1. Methodology for Complete McCabe-Thiele Solution
Determine all of the information stated in the problem including:
Configuration of the column
Operating Pressure
Total, partial or no condenser
Total, partial or no reboiler
Location of feed stream(s)
Location of side stream(s)
Location of product stream(s)
Condition of streams (saturated, superheated or subcooled)
Distillate
Bottoms
Feed
Reflux
Boilup
Flow rates and composition of streams
Distillate, xD and D
Bottoms, xB and B
Feed, zF and F
Reflux, L/V or L/D
Boilup, L/V or V/B
Lecture 14

2. Methodology for Complete McCabe-Thiele Solution
Determine equilibrium relationship
Use convenient equilibrium equation – e.g., given relative volatility, α
Curve fit equilibrium data at Pcol – y vs x and/or x vs y (see below)
Setup operating line equations and equilibrium curves in proper format for stepping down or stepping up the column…
Lecture 14

3. Methodology for Complete McCabe-Thiele Solution
Assume CMO when applicable
Determine Top Operating Line
Choose convenient TOL equation or derive
Utilize total and/or component mass balances to determine required variables – e.g., L, V, L/V, L/D – in TOL if not given
Determine Bottom Operating Line
Choose convenient BOL equation or derive
Utilize total and/or component mass balances to determine required variables – e.g., L, V, L/V, V/B – in BOL if not given
Determine Feed Line
Choose convenient feed line equation or derive
Utilize total and/or component mass balances to determine required variables – e.g., F or zF, – for feed if not given
Utilize total and/or component mass balances to determine required variables – e.g., L, V, L, V, LF, VF, – for feed if not given
Use feed-stage relationships to determine q or f at feed conditions
Lecture 14

4. Methodology for Complete McCabe-Thiele Solution
Stepping Up the Column from the Reboiler
Equilibrium Curve
yEq = yEq(xEq) – as normally expressed
Operating Line
xOL = xOL(yOL) – solve operating line for x
Stepping Down the Column from the Condenser
xEq = xEq(yEq) – solve equilibrium relationship for x
yOL = yOL(xOL) – as normally expressed
Lecture 14

5. Methodology for Complete McCabe-Thiele Solution
Determine intersection of operating lines and/or feed line to determine when to switch from the TOL to the BOL by:
Solving simultaneous TOL, BOL, and/or feed line equations using Mathcad’s “Minerr” function or
Solving TOL, BOL, and/or feed line equations algebraically
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6. Intersection of OL’s and Feed Line
Eq. (5-38) Intersection of OL’s
Intersection of TOL and FL
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7. Methodology for Complete McCabe-Thiele Solution
Plot the equilibrium curve, TOL, BOL, and feed line
Check the equations and plot by verifying that the:
TOL intersects y = x at xD
BOL intersects y = x at xB
Feed line intersects y = x at zF
OL’s and feed line all intersect at xI and yI
Lecture 14

8. Methodology for Complete McCabe-Thiele Solution
Implement McCabe-Thiele algorithm and plot stages
Determine total number of equilibrium stages
Determine optimum feed stage
Determine any fractional stages
Answer specific questions, e.g., liquid and/or vapor compositions for a given stage, number of stages above reboiler, condenser, etc.
Keep in mind that a partial condenser and/or partial reboiler are each counted as an equilibrium stage outside the column!
Lecture 14

9. Stage Compositions – Total Condenser
Stage j ∙
Total
Condenser
Equilibrium Curve
Operating Line
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10. Complete McCabe-Thiele Solution Total Condensery
(x5, y5)
xD = y1 = y0 = x0
Equilibrium
Curve
Top
Operating
Line
Bottom
Feed Line
(xB, xB)
(x4, y4)
(x3, y3)
(xI, yI)
(x2, y2)
(x1, y1)
(x1, y2)
(x0, y0)
(x2, y3)
(x3, y4)
(x4, y5)
xB = xN x
Lecture 14

11. Complete McCabe-Thiele Solution Total Condenser
Lecture 14

12. Mathcad McCabe-Thiele Algorithm
Lecture 14

13. Mathcad McCabe-Thiele Algorithm
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14. Stage Compositions – Total Reboiler
Operating Line
Stage N-2
Stage N-1
Stage N ∙
Stage N- n
Stage N-3
Total Reboiler
Equilibrium Curve
Lecture 14

15. Complete McCabe-Thiele Solution Total Reboiler
Equilibrium Curve
Top
Operating
Line
Bottom
Feed Line
(xI, yI)
(xN, yN)
(xN-1, yN-1)
(xN-2, yN-2)
(xN-3, yN-3)
(xN-4, yN-4)
(xN-4, yN-3)
(xN-3, yN-2)
(xN-2, yN-1)
(xN-1, yN)
xB = xN x xD y
(xD, xD)
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16. Fractional Stage at Top of Column
Equilibrium Curve
Operating
Line
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17. Fractional Stage at Bottom of Column
Equilibrium Curve
Operating
Line
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18. Optimal Feed Stage Location
Lecture 14