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

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

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

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

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 Lecture 14

Intersection of OL’s and Feed Line Eq. (5-38) Intersection of OL’s Intersection of TOL and FL Lecture 14

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

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

Stage Compositions – Total Condenser Stage j ∙ Total Condenser Equilibrium Curve Operating Line Lecture 14

Complete McCabe-Thiele Solution Total Condenser y (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

Complete McCabe-Thiele Solution Total Condenser Lecture 14

Mathcad McCabe-Thiele Algorithm Lecture 14

Mathcad McCabe-Thiele Algorithm Lecture 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

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) Lecture 14

Fractional Stage at Top of Column Equilibrium Curve Operating Line Lecture 14

Fractional Stage at Bottom of Column Equilibrium Curve Operating Line Lecture 14

Optimal Feed Stage Location Lecture 14