Multiple-effect evaporation: the practical number of effects is limited by which considerations?

Introduction / Context:
Multiple-effect evaporators conserve steam by using vapor from one effect to heat the next at a lower pressure. Adding effects improves steam economy—but only up to a point. Beyond that, diminishing returns and capital costs dominate.

Given Data / Assumptions:

• Total available temperature drop across the train is fixed by heating steam temperature and final effect temperature.
• Each added effect reduces the temperature driving force in every effect.
• Equipment cost, complexity, and control challenges increase with effect count.

Concept / Approach:
As effects are added, the temperature difference per effect shrinks, reducing individual heat-transfer rates (UAΔT). Larger areas (or more effects) are then required for the same duty. Eventually, the gain in steam economy is offset by increased capital and operating costs.

Step-by-Step Solution:
Recognize practical limit: ΔT per effect becomes too small → low heat flux.Recognize economic limit: extra shells, pumps, controls, and area escalate costs.Optimal number occurs where marginal steam savings equal marginal cost.Therefore, both practical and economic limits govern.

Verification / Alternative check:
Pinch analysis and economic optimization often show 3–5 effects as practical for many duties, with exceptions based on utilities pricing and product constraints.

Why Other Options Are Wrong:
(a) alone ignores economics; (b) alone ignores physics; (d) contradicts observed practice.

Common Pitfalls:
Assuming more effects are always better; overlooking fouling, viscosity rise, or boiling-point elevation that further reduce ΔT.

Final Answer:
both (a) & (b)