Methodology for Complete McCabe-Thiele Solution

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

2
Methodology for Complete McCabe-Thiele Solution

• Determine equilibrium relationship
• Use convenient equilibrium equation e.g., given
  relative volatility, a
• 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

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

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
• Equilibrium Curve
• xEq xEq(yEq) solve equilibrium relationship
  for x
• Operating Line
• yOL yOL(xOL) as normally expressed

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 Mathcads Minerr function or
• Solving TOL, BOL, and/or feed line equations
  algebraically

6
Intersection of OLs and Feed Line
Eq. (5-38) Intersection of OLs
Intersection of TOL and FL
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
• OLs and feed line all intersect at xI and yI

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!

9
Stage Compositions Total Condenser
10
Complete McCabe-Thiele SolutionTotal Condenser
11
Complete McCabe-Thiele SolutionTotal Condenser
12
Mathcad McCabe-Thiele Algorithm
13
Mathcad McCabe-Thiele Algorithm
14
Stage Compositions Total Reboiler
15
Complete McCabe-Thiele SolutionTotal Reboiler
16
Fractional Stage at Top of Column
17
Fractional Stage at Bottom of Column
18
Optimal Feed Stage Location