Multiple-effect evaporation: approximate steam economy. In an n-effect system, the kilograms of water evaporated per kilogram of live steam are roughly how many times those of a single effect?

Introduction / Context:
Multiple-effect evaporators reuse vapor energy sequentially to reduce live steam consumption. A key performance metric is steam economy, defined as kilograms of water evaporated per kilogram of live steam supplied. This question asks for the rule-of-thumb relationship between steam economy and the number of effects n.

Given Data / Assumptions:

• An n-effect forward or backward feed evaporator train.
• Reasonable condensate and heat losses; negligible heat leaks for a rule-of-thumb estimate.
• Comparable heat transfer areas and operating strategy across effects.

Concept / Approach:
In a single effect, approximately 1 kg of steam evaporates roughly 1 kg of water (ignoring sensible heating and losses). In an n-effect train, the vapor from one effect serves as the heating medium for the next at a lower pressure. Ideally, this cascaded reuse boosts the evaporation accomplished per kg of steam by about n-fold, minus real-world penalties such as boiling point elevation, sensible preheating needs, and heat losses.

Step-by-Step Solution:
Define steam economy E_single ≈ 1 kg/kg for single effect.For n effects, reuse of latent heat ≈ n times → E_n ≈ n * E_single.Adjust for non-idealities: E_n is slightly less than n in practice, but the rule of thumb remains “about n.”Match to options: “n times” best represents the approximate relationship.

Verification / Alternative check:
Industrial data often show steam economies of 2.2–2.8 for triple-effect and ~4–5 for quintuple-effect systems, consistent with the “about n” guideline accounting for losses.

Why Other Options Are Wrong:
1/n times: contradicts the fundamental benefit of multiple effects.0.5 n times or 1.5 n times: arbitrary modifiers with no general basis; actual penalties are system-specific.

Common Pitfalls:
Confusing steam economy (per kg steam) with overall capacity or evaporation per unit area; ignoring boiling point elevation and feed preheating energy.

Final Answer:
n times