Equilibrium Flash Fraction: Apply the Lever Rule to the Stated Phase Compositions

Define the Phase or Process Boundary

LearnChemE's lever-rule balance relates binary overall composition to the amounts of coexisting phases. With vapor mole fraction of total inventory β, z=(1−β)x+βy. Provided y differs from x, rearrangement gives β=(z−x)/(y−x). All three compositions must use the same component and basis.

Review a Hypothetical Comparison

Assume a fictional equilibrium tie line with x_A=0.15, y_A=0.75 and overall z_A=0.45. Then β=(0.45−0.15)/(0.75−0.15)=0.50. A total inventory of 12 mol would contain 6 mol liquid and 6 mol vapor. The component balance closes as 6×0.15+6×0.75=5.4 mol, equal to 12×0.45. Neither 15% nor 75% is the vapor amount; both are phase compositions.

Keep the Evidence with the Decision

Check that the supplied overall composition lies between the two phase endpoints. Save the tie-line state, total-inventory basis and component balance together. A computed β outside zero to one is a reason to review the data or assumed two-phase state, not to report a negative phase inventory.

This calculation accepts supplied equilibrium endpoints. It does not determine them or close an energy balance. At coincident endpoints the denominator vanishes, so this composition balance alone cannot determine phase amounts.

What vapor fraction closes the overall composition balance when equilibrium liquid and vapor compositions are supplied?

This blank worksheet is for your own project. It contains no H M machine trial result.

Customer Questions

Primary References

These references support the technical principles discussed in this guide. The worked examples and review questions are educational.

• LearnChemE's lever-rule balance
• Reference from hmpharmamachines.com