Recycle ratio in process flows:\nWhich expression correctly defines the recycle ratio used in chemical process calculations?

Introduction / Context:
Recycle streams are common in reactors and separation systems to improve conversion, recover unreacted materials, and stabilize operation. The recycle ratio is a key dimensionless metric indicating how much material is being recirculated relative to the fresh input.

Given Data / Assumptions:

• Definitions follow standard process design texts.
• Streams are clearly labeled: fresh feed, recycle, and gross (combined) feed.

Concept / Approach:
The recycle ratio quantifies the intensity of recirculation: it is most usefully defined relative to the fresh feed, since fresh feed sets the scale of new material entering the process. This helps analyze residence time, conversion, and equipment sizing impacts.

Step-by-Step Solution:

Verification / Alternative check:
Process simulators and standard textbooks adopt RR = R / F_fresh. Other ratios can be defined for specific analyses but are not the conventional “recycle ratio.”

Why Other Options Are Wrong:

• Gross/Fresh or Recycle/Gross are auxiliary ratios; they do not define the conventional recycle ratio.
• “None of these” is incorrect because a standard definition exists.
• Fresh/Recycle is the inverse and not the commonly reported metric.

Common Pitfalls:
Confusing gross feed with fresh feed, or using inconsistent bases when comparing cases. Always report which convention you use.

Final Answer:
Recycle stream / Fresh feed stream