Recycle Streams

Understand why recycle is used and how overall conversion differs from single-pass conversion.

Material & Energy BalancesChemical Engineering Year 1Free preview
⏱️ About 16 min

A reactor converts only 25% per pass — but with recycle, the plant can still recover most of the reactant. How do you measure that correctly?

💡
The big idea: Recycle increases utilization of reactants: overall conversion counts what leaves the plant, while single-pass conversion counts what happens in one trip through the reactor.
🎯 By the end, you'll be able to
  • Explain why recycle is used (reactant recovery, improved overall conversion, economics)
  • Define and distinguish single-pass conversion and overall conversion
  • Compute overall and single-pass conversions for a reactor-with-recycle system
  • Relate the recycle flow to reactor conversion and separator recovery via a steady-state loop balance
📎 Helpful to know first

Why Use Recycle?

Recycle is used when a downstream unit can recover valuable material and send it back upstream. Common reasons:

  • Recover unconverted reactant and reduce raw-material waste
  • Improve overall conversion without requiring high per-pass conversion (which may be limited by equilibrium or kinetics)
  • Stabilize operation by increasing total flow through equipment

The trade-off is larger internal flow rates (bigger equipment, higher pumping/compression costs).

\[ X_{\text{sp}} = \frac{\dot{n}_{A,\text{to rxn}} - \dot{n}_{A,\text{from rxn}}}{\dot{n}_{A,\text{to rxn}}} \]
Single-pass (per-pass) conversion: fraction of A consumed in one trip through the reactor.
\[ X_{\text{overall}} = \frac{\dot{n}_{A,\text{fresh}} - \dot{n}_{A,\text{leaving process}}}{\dot{n}_{A,\text{fresh}}} \]
Overall conversion: fraction of fresh-feed A that does not leave the overall process (ultimately consumed or recovered).
⚠️ Overall conversion uses fresh feed, not reactor feed

In a recycle system, the reactor feed includes recycle, so it can be much larger than the fresh feed. If you mistakenly compute 'overall conversion' using the reactor inlet, you will get the wrong answer.

Closing the Loop at Steady State

The recycle flow rate is not a free choice — at steady state it must be consistent with how much unreacted A the separator actually returns. If the separator recovers a fraction f of the unreacted A leaving the reactor (sending the rest to the product stream), then the recycle flow R must satisfy R = f × (unreacted A leaving the reactor), where the reactor's unreacted output itself depends on R through the reactor inlet. Solving this loop balance gives R directly — it is not an independent input you get to pick.

📝 Worked example: A single reactant A is fed to a reactor-with-recycle flowsheet. Fresh feed contains F_A = 100 mol/h of pure A. The reactor's single-pass conversion is X_sp = 0.25. The separator recovers 80% of the unreacted A leaving the reactor back to recycle; the remaining 20% leaves in the product stream. Find the steady-state recycle flow R, the reactor inlet flow, and the overall conversion of A.
  1. Let R = recycle A flow (mol/h). Reactor inlet A = F_A + R = 100 + R.
  2. A consumed in reactor = X_sp × (100 + R) = 0.25(100 + R).
  3. Unreacted A leaving reactor = (1 − 0.25)(100 + R) = 0.75(100 + R).
  4. Steady-state loop balance: recycle = 80% of unreacted A leaving reactor → R = 0.80 × 0.75(100 + R) = 0.60(100 + R).
  5. R = 60 + 0.60R → 0.40R = 60 → R = 150 mol/h.
  6. Reactor inlet = 100 + 150 = 250 mol/h. A consumed = 0.25 × 250 = 62.5 mol/h. Unreacted A leaving reactor = 0.75 × 250 = 187.5 mol/h.
  7. Check recycle: 0.80 × 187.5 = 150 mol/h ✓ (matches R). A to product = 0.20 × 187.5 = 37.5 mol/h.
  8. Overall conversion: X_overall = (100 − 37.5) / 100 = 0.625 = 62.5%.
✓ R = 150 mol/h; reactor inlet = 250 mol/h; overall conversion = 62.5% (compared to 25% single-pass).
✏️ Practice: Fresh feed is F_A = 80 mol/h (pure A) into a reactor-with-recycle system. The recycle flow (already at steady state) is R = 120 mol/h and the reactor's single-pass conversion is X_sp = 0.30. What is the molar flow rate of A consumed in the reactor (mol/h)?
mol/h
Solution
  1. Reactor inlet A = F_A + R = 80 + 120 = 200 mol/h
  2. A consumed = X_sp × (reactor inlet A) = 0.30 × 200 = 60 mol/h

Check your understanding

1. Single-pass conversion is computed using:
Single-pass (per-pass) conversion is based on what enters and leaves the reactor in one pass.
2. Overall conversion is computed using:
Overall conversion compares fresh feed to what leaves the overall process boundary.
🔎 Related lessons
Bypass Streams · soon
✅ Key takeaways
  • Recycle is used to recover unconverted reactants and improve overall utilization
  • Single-pass conversion measures one trip through the reactor; overall conversion measures the entire plant
  • The recycle flow rate is set by a steady-state loop balance, not chosen independently
  • Overall conversion can substantially exceed single-pass conversion when recovery is good
➡️ Recycle sends material back upstream. A bypass does the opposite: it deliberately avoids processing part of a stream so the final blend hits a target property.
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