Binary Distillation McCabe-Thiele Diagram

Calculate total stages, feed point, and generate VLE curves using Constant Volatility, Antoine Eq, K-Values, or Equations of State (PR/SRK).

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1. Project Data

2. Vapor-Liquid Equilibrium (VLE)

Must be > 1.0 for separation.
Relative volatility $\alpha = K_{Light} / K_{Heavy}$

Equation: $\log_{10}(P) = A - \frac{B}{T + C}$
A, B, C must be in P (mmHg), T (°C) — system pressure is unit-converted automatically.

Light Key (More Volatile)
Heavy Key (Less Volatile)
Library parameters are fitted at ~25°C. For distillation at elevated temperatures, results are approximate. Use Experimental Data or EOS for higher accuracy.
$\ln\gamma_1 = x_2^2[\tau_{21}(\frac{G_{21}}{x_1+x_2 G_{21}})^2 + \frac{\tau_{12}G_{12}}{(x_2+x_1 G_{12})^2}]$
$\ln\gamma_1 = -\ln(x_1+\Lambda_{12}x_2) + x_2[\frac{\Lambda_{12}}{x_1+\Lambda_{12}x_2} - \frac{\Lambda_{21}}{x_2+\Lambda_{21}x_1}]$
Light Key (1)
Heavy Key (2)
If no BIP is selected, $k_{12} = 0$ is assumed (ideal mixing). This may underestimate VLE non-ideality for pairs not in the library.
Space or comma-separated X Y pairs, one per line. Must start at (0,0) and end at (1,1).

3. Column Operating Conditions

Partial condenser counts as 1 theoretical stage.
%
Typical: 60–80 % for tray columns. 100 % = theoretical stages only.
Distillation Summary
Note: Because a fractional theoretical stage is typically required at the bottom to reach the exact target composition (xB), the final full stage overshoots the target. This makes the fluid leaving the last theoretical stage richer in the heavy key, resulting in a slightly higher temperature than the actual Reboiler.
x — y — T equilibrium table
x (liquid) y (vapour) T α (local)
Run a calculation first.
Calculation Results
Total Theoretical Stages -
Actual Trays (at Eo) -
Optimal Feed Stage -
Min Stages at Total Reflux (Nmin) -
Minimum Reflux Ratio ($R_{min}$) -
$R / R_{min}$ -
Equation / Status Ready
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Engineering Reference & Technical Basis

1. McCabe-Thiele Method Basics

The method assumes constant molal overflow (CMO). The operating lines relate compositions between passing vapor and liquid streams.

  • Rectifying Line: $y = \frac{R}{R+1}x + \frac{x_D}{R+1}$
  • Feed (q) Line: $y = \frac{q}{q-1}x - \frac{x_F}{q-1}$
  • Stripping Line: Connects $(x_B, x_B)$ to the intersection of the Rectifying and q-lines.
2. VLE Thermodynamics

Vapor-Liquid Equilibrium is calculated using one of several methods to determine $y = f(x)$:

  • Constant Volatility: $y = \frac{\alpha x}{1 + x(\alpha - 1)}$
  • Antoine Eq: Bubble point $T$ found iteratively such that $P_{sys} = x_1 \gamma_1 P^{sat}_1(T) + x_2 \gamma_2 P^{sat}_2(T)$. Supports Ideal, Margules 2-parameter, NRTL ($\ln\gamma_1 = x_2^2[\tau_{21}G_{21}^2/(x_1+x_2G_{21})^2+\tau_{12}G_{12}/(x_2+x_1G_{12})^2]$), and Wilson activity coefficient models.
  • Cubic EOS (PR/SRK): True thermodynamic bubble point flash. Solves for $Z$ and fugacity coefficients $\phi$ using Cardano's method, iterating on $T$ to satisfy $\sum K_i x_i = 1$.
3.Feed Quality ($q$)

Feed Quality ($q$): Represents the thermal condition of the feed. Mathematically, it is the ratio of the increase in liquid molar flow across the feed stage to the molar feed rate.

  • $q > 1$: Subcooled Liquid
  • $q = 1$: Saturated Liquid (Bubble Point)
  • $0 < q < 1$: Two-Phase Mixture (Liquid + Vapor)
  • $q = 0$: Saturated Vapor (Dew Point)
  • $q < 0$: Superheated Vapor
4. Minimum Reflux ($R_{min}$)

Minimum Reflux ($R_{min}$): The lowest reflux ratio at which the desired separation ($x_D$, $x_B$) can be achieved, requiring an infinite number of theoretical stages. It corresponds to the operating line intersecting the VLE curve at a "pinch point" (typically at the $q$-line intersection).

References
  • McCabe, W. L., Smith, J. C., & Harriott, P. (2005). Unit Operations of Chemical Engineering (7th ed.). McGraw-Hill Education.
  • Treybal, R. E. (1980). Mass-Transfer Operations (3rd ed.). McGraw-Hill.
  • Smith, J. M., Van Ness, H. C., & Abbott, M. M. (2005). Introduction to Chemical Engineering Thermodynamics (7th ed.). McGraw-Hill.
  • Peng, D. Y., & Robinson, D. B. (1976). A New Two-Constant Equation of State. Industrial & Engineering Chemistry Fundamentals, 15(1), 59-64.
  • Soave, G. (1972). Modification of the Redlich-Kwong Equation of State with Temperature-Dependent Attraction Parameter. Chemical Engineering Science, 27(6), 1197–1203.
  • Prausnitz, J. M., Lichtenthaler, R. N., & de Azevedo, E. G. (1999). Molecular Thermodynamics of Fluid-Phase Equilibria (3rd ed.). Prentice Hall. [Margules activity coefficient model, Chapter 6.]