How this calculation works
A flash material balance divides one feed into liquid and vapor that coexist under specified equilibrium ratios. The vapor fraction must satisfy every component balance and both phase composition sums, rather than being guessed from one component alone. This page solves the Rachford–Rice equation using K values supplied by the user. It does not calculate those values from temperature, pressure or an equation of state.
sum[z_i(K_i−1)/(1+beta(K_i−1))]=0; x_i=z_i/[1+beta(K_i−1)]; y_i=K_i x_iA worked example
For equal feed fractions with K values two and one half, the symmetric root is vapor fraction one half. The liquid fractions are one third and two thirds, and the vapor fractions reverse those values. Both phase compositions sum to one, and recombining half of each recovers the original equal feed. This checks more than merely obtaining a small numerical root residual.
Good to know
Rachford–Rice endpoint classification is not a complete thermodynamic stability analysis. A supplied set of fixed ratios may need iteration or replacement in a real equilibrium calculation. No energy balance, heat duty or flash equipment sizing is included. The result is a conditional material balance under entered K values, not a prediction of operating conditions or a process recommendation.
Reference: University of Maryland — flash distillation and Rachford Rice (opens in a new tab) ↗
What this calculation answers
A flash material balance divides one feed into liquid and vapor that coexist under specified equilibrium ratios. The vapor fraction must satisfy every component balance and both phase composition sums, rather than being guessed from one component alone.
This page solves the Rachford–Rice equation using K values supplied by the user. It does not calculate those values from temperature, pressure or an equation of state.
The Binary Rayleigh batch distillation residue calculator follows a continuously changing batch pot. A flash split instead uses one supplied set of equilibrium K ratios for the whole feed.
Use the right input conventions
Feed mole fractions must sum to one and each equilibrium ratio K must be positive. K is vapor mole fraction divided by liquid mole fraction for the corresponding component, not a percentage or an equilibrium constant for a chemical reaction.
Use a single internally consistent set of ratios for one stated flash condition. The calculator cannot verify whether those ratios represent an actual mixture or whether they were generated by an appropriate thermodynamic model.
Interpret the result
Endpoint tests distinguish an all-liquid case, an all-vapor case and an interior two-phase root under the entered ratios. For a single phase, the missing phase composition is labeled absent instead of being invented.
If every component with positive feed fraction has K equal to one, the phase split is indeterminate. Both phase compositions can equal feed composition while material balance alone leaves the vapor fraction unspecified.
Work through the example
For equal feed fractions with K values two and one half, the symmetric root is vapor fraction one half. The liquid fractions are one third and two thirds, and the vapor fractions reverse those values.
Both phase compositions sum to one, and recombining half of each recovers the original equal feed. This checks more than merely obtaining a small numerical root residual.
Where the model stops
Rachford–Rice endpoint classification is not a complete thermodynamic stability analysis. A supplied set of fixed ratios may need iteration or replacement in a real equilibrium calculation.
No energy balance, heat duty or flash equipment sizing is included. The result is a conditional material balance under entered K values, not a prediction of operating conditions or a process recommendation.
A few questions, answered
Why not report normalized hypothetical compositions for an absent phase?
Their normalization would invent information unsupported by the single-phase material balance under the supplied ratios.
What changes in the comparison?
Place both K values below one and inspect the all-liquid classification and absent-vapor labels.