McCabe-Thiele Stages Calculator
Bounded McCabe–Thiele RECTIFYING-ONLY graphical stepping, condenser excluded, feed/stripping/reboiler not modeled and stage cap censoring explicit. Caller independently establishes units, regime, calibration and applicability; this does not establish design-code compliance, authenticity, operational safety, treatment efficacy or a validated forecast.
Description
McCabe-Thiele stepping uses an equilibrium relation and an operating line.
McCabe-Thiele stepping uses an equilibrium relation and an operating line.1
A rectifying-only calculation omits feed and stripping-section changes in a complete column design. Use this tool to calculate mcCabe-Thiele Stages from the supplied measurements and assumptions.
When to use McCabe-Thiele Stages Calculator
Use this tool to calculate mcCabe-Thiele Stages from the supplied measurements and assumptions. Establish the SI units or caller unit basis, load signs, measurement interval, model conditions and independently chosen coefficients or references.
How to use McCabe-Thiele Stages Calculator and understand its results
- Establish the SI units or caller unit basis, load signs, measurement interval, model conditions and independently chosen coefficients or references.
- Enter callerEquilibriumLiquidFractions, callerEquilibriumVaporFractions, distillateFraction, bottomTargetFraction, refluxRatio, maximumRectifyingStages, using the field meanings and rules below, then run the tool.
- Read stageLiquidCompositions, reachedBottom. Interpret the fields using their units, signs and evidence conventions below.
- If input validation fails, correct the reported field and run again. Before applying the result, check reference scope, model assumptions and any missing evidence or placeholder values.
| Input field | Meaning | Value type | Requirement |
|---|---|---|---|
| callerEquilibriumLiquidFractions | Caller equilibrium liquid fractions | list of number | Required |
| callerEquilibriumVaporFractions | Caller equilibrium vapor fractions | list of number | Required |
| distillateFraction | Distillate fraction | number | Required |
| bottomTargetFraction | Bottom target fraction | number | Required |
| refluxRatio | Reflux ratio | number | Required |
| maximumRectifyingStages | Maximum rectifying stages | number | Required |
Enter aligned strictly increasing equilibrium liquid and vapor fractions in [0,1], bottom<distillate fractions covered by liquid data, nonnegative reflux ratio and integer maximum stages 1–128. Start at distillate vapor composition, invert the supplied equilibrium linearly, append liquid composition and stop when it reaches bottom. Otherwise step on the rectifying line and require decreasing vapor composition; pinch or an uncovered vapor query fails. Return sampled stage liquid compositions and whether bottom was reached; no feed or stripping line is added.
x_k=inverseLinearEquilibrium(y_k); y_(k+1)=R/(R+1)×x_k+distillate/(R+1) Use the exact units, boundary rules, ordering and missing-evidence conventions above.
| Output field | Meaning | Value type |
|---|---|---|
| stageLiquidCompositions | Stage Liquid Compositions; follow the units, sign, ordering and evidence convention stated above | list of number |
| reachedBottom | Reached Bottom; follow the units, sign, ordering and evidence convention stated above | boolean |
{
"input": {
"callerEquilibriumLiquidFractions": [
0,
0.5,
1
],
"callerEquilibriumVaporFractions": [
0,
0.75,
1
],
"distillateFraction": 0.75,
"bottomTargetFraction": 0.5,
"refluxRatio": 1,
"maximumRectifyingStages": 10
},
"output": {
"stageLiquidCompositions": [
0.5
],
"reachedBottom": true
}
}Limitations and assumptions
A rectifying-only calculation omits feed and stripping-section changes in a complete column design. Interpretation depends on the units, sampling scope and exact model described above.
All listed fields require explicit values. Unexpected fields, incorrect types, nonfinite numbers and sparse evidence arrays fail validation; the specific bounds and alignment requirements are stated above. Extremely large inputs or outputs can also be rejected. An input error is distinct from a successful result reporting false, no matches or missing evidence.
Alternative or Complementary methods
Use PFR Volume Calculator for this related task: A plug-flow reactor design integral uses inverse reaction rate over conversion.
Use LMTD Correction Factor Calculator when its separate inputs and assumptions fit the question: An LMTD correction factor depends on exchanger arrangement and a matched reference relation.
References
-
McCabe-Thiele Stages Calculator — tool.io
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