Applications of the Thiele–Geddes method — In which separation operation is the Thiele–Geddes equation specifically used for rigorous stage-to-stage calculations?

Introduction:
Different mass-transfer operations use different mathematical frameworks. The Thiele–Geddes method is a classic approach used to perform tray-by-tray material balance and equilibrium calculations where multiple components distribute between vapor and liquid phases at each stage. This question asks you to identify the correct operation that relies on this method.

Given Data / Assumptions:

• Multiple components present in both phases.
• Equilibrium relationships (K-values or activity–fugacity models) are known.
• Stagewise (equilibrium-stage) model is appropriate.

Concept / Approach:
The Thiele–Geddes method is a rigorous multicomponent distillation formulation. It sets up a system of difference equations that relate liquid and vapor compositions between adjacent trays subject to equilibrium, mass balance, and flow assumptions (e.g., constant molar overflow), enabling computation of composition profiles and tray requirements. While absorption and extraction also use stagewise models, their canonical design tools differ, and chemical reaction would require additional rate terms beyond the classical Thiele–Geddes formulation.

Step-by-Step Solution:
Recognize a stagewise vapor–liquid contacting operation with many components.Recall that Thiele–Geddes is developed for distillation column calculations.Select “Multicomponent distillation.”

Verification / Alternative check:
Textbook derivations of Thiele–Geddes appear in multicomponent distillation chapters, often paired with Underwood and Fenske methods for minimum trays and minimum reflux.

Why Other Options Are Wrong:

• (a) and (b) use different equilibrium and mass-transfer frameworks.
• (c) Adds reaction coupling, not the original scope of Thiele–Geddes.
• (e) Crystallization uses supersaturation and population balances, not tray-by-tray VLE equations.

Common Pitfalls:
Assuming any stagewise operation uses Thiele–Geddes; it is specifically a multicomponent distillation tool.

Final Answer:
Multicomponent distillation