Continuous binary distillation: Which of the following is not a graphical method (i.e., it is an analytical method) for computing the theoretical number of stages?

Introduction / Context:
Determining the theoretical number of stages is fundamental in distillation design. Several classical methods exist: some rely on graphical constructions, while others are analytical or algebraic. Recognising which is which helps in selecting tools and understanding limitations.

Given Data / Assumptions:

• Binary system, constant molal overflow assumptions for the classic graphical methods.
• Steady-state continuous distillation with specified reflux.

Concept / Approach:
The McCabe–Thiele method is a classic graphical approach using equilibrium and operating lines on an x–y diagram. The Ponchon–Savarit method is also graphical, employing enthalpy–composition (H–x) diagrams. In contrast, the Sorel–Lewis method formulates analytical stage-by-stage material balance and equilibrium relations to compute the number of stages without a graphical plot.

Step-by-Step Reasoning:

Verification / Alternative check:
Standard separations textbooks present McCabe–Thiele and Ponchon–Savarit as diagrammatic, whereas Sorel–Lewis is described as an algebraic method predating modern simulations.

Why Other Options Are Wrong:

• McCabe–Thiele and Ponchon–Savarit are graphical by construction.
• “None of these” is invalid since an analytical option exists.
• The Gilliland correlation relates stages and reflux and is a graphical/empirical relation used adjunct to McCabe–Thiele, not a primary stage-count method on its own in this context.

Common Pitfalls:
Applying graphical methods outside their assumptions (e.g., strong non-idealities, significant heat effects) without correction factors or rigorous simulation.

Final Answer:
Sorel–Lewis method