Recycle and Purge Calculations

Recycle-and-purge problems distinguish two conversions: overall (based on fresh feed) and single-pass (based on reactor inlet). A purge stream is added to bleed accumulating inerts and is sized so inert generation equals inert removal at steady state.

Key formulas & points

Skim these first — then read the full notes below.

  • Recycle increases single-pass conversion but not necessarily overall
  • Purge controls buildup of inerts in closed loops
  • Bypass stream skips a unit without mixing — separate balance needed

Topic details

Introduction

This topic extends the material balance to loops. The recommended sequence is to balance the overall process across an envelope that cuts only fresh feed and net product, which hides the recycle, and then to balance the reactor and separator individually to find recycle and purge flows. Bhatt & Vora stress that at steady state nothing accumulates, so inert entering with fresh feed must leave in the purge.

Key relations & formulas

Formulas (Indian textbook notation)

  • OverallconversionXo=(FinFout,unreacted)FinOverall conversion X_{o} = \frac{(F_{in} - F_{out},unreacted)}{F_{in}}

Formulas (Indian textbook notation)

  • SinglepassconversionXsp=r(Ffresh+Frecycle)perpassbasisSingle-pass conversion X_{sp} = \frac{r}{(F_{fresh} + F_{recycle})} per pass basis
PurgerateP=Fin×(1xp)xpPurge rate P = F_{in} \times \frac{(1 - x_{p})}{x_{p}}
(for bleed of inerts)

Notation and sign conventions

Relation 1 —
OverallconversionXo=Overall conversion X_{o} =

Formulas (Indian textbook notation)

  • OverallconversionXo=(FinFout,unreacted)FinOverall conversion X_{o} = \frac{(F_{in} - F_{out},unreacted)}{F_{in}}
Write this relation with symbols exactly as in Stoichiometry — Bhatt & Vora before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Relation 2 —
SinglepassconversionXsp=r/Single-pass conversion X_{sp} = r /

Formulas (Indian textbook notation)

  • SinglepassconversionXsp=r(Ffresh+Frecycle)perpassbasisSingle-pass conversion X_{sp} = \frac{r}{(F_{fresh} + F_{recycle})} per pass basis
Write this relation with symbols exactly as in Stoichiometry — Bhatt & Vora before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Relation 3 —
PurgerateP=Fin×Purge rate P = F_{in} \times
PurgerateP=Fin×(1xp)xpPurge rate P = F_{in} \times \frac{(1 - x_{p})}{x_{p}}
(for bleed of inerts)
Write this relation with symbols exactly as in Stoichiometry — Bhatt & Vora before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.

Concept in depth

Recycle raises single-pass throughput while keeping reagent usage high, but overall conversion is still governed by what ultimately leaves as unreacted feed. The purge exists because any inert or by-product that has no other exit would otherwise build up without limit inside the loop; setting inert in equal to inert out fixes the purge flow. A bypass is the opposite of recycle — part of the feed skips the unit and remixes downstream, so it needs its own splitter and mixer balances rather than a loop balance.

Assumptions and validity limits

State assumptions explicitly before using any relation for recycle and purge calculations — steady state, uniform properties, linear elastic material, ideal gas, incompressible flow, etc., as applicable.
Wrong assumptions invalidate the entire solution even when the formula is correct. In Process Calculations viva and GATE descriptive questions, listing valid assumptions often earns separate marks.

Step-by-step problem approach

1. Read the question and list given data with SI units (common in Process Calculations papers).
2. Draw a neat labelled diagram where applicable — examiners in Indian universities award diagram marks even when arithmetic slips.
3. Identify which relation from this topic applies to recycle and purge calculations.
4. Use equation 1:
OverallconversionXo=Overall conversion X_{o} =
.
5. Use equation 2:
SinglepassconversionXsp=r/Single-pass conversion X_{sp} = r /
.
6. Substitute values, compute, and verify units and sign (direction).
7. State conclusion in one line — e.g. safe/unsafe, stable/unstable, feasible/infeasible.

Applications & exam relevance

Recycle and Purge Calculations appears in every chemical process design. In Indian chemical curricula this topic is tested because it connects theory to material and energy balances.
GATE and semester exams often combine recycle and purge calculations with earlier units — revise prerequisites before attempting mixed problems.
Industry interview panels sometimes ask: "Where did you use recycle and purge calculations?" — answer with a lab, mini-project, or plant visit example if possible.

Common mistakes in exams

A very common error is confusing single-pass with overall conversion, and quoting reactor conversion as if it were the plant conversion. Students also forget that the purge and recycle have identical composition (they split from the same stream) and neglect the inert balance that actually sizes the purge.

Quick revision checklist

Before attempting recycle and purge calculations problems, confirm you can:
1. Recycle increases single-pass conversion but not necessarily overall
2. Purge controls buildup of inerts in closed loops
3. Bypass stream skips a unit without mixing — separate balance needed
Revise the solved examples in Stoichiometry — Bhatt & Vora and one previous-year GATE or university paper for this unit.

Worked examples

Try the problem first — open the solution when you are ready to check.

Purge to control inerts

Problem

Fresh feed to a loop contains 2 mol% inert. To hold the recycle inert at 20 mol%, what fraction of the recycle-plus-purge stream must be purged if 100 mol/h fresh feed enters?

Solution

Inert in = 0.02 × 100 = 2 mol/h must leave in the purge. Purge inert fraction equals recycle inert fraction ≈ 0.20, so purge flow = 2/0.20 = 10 mol/h. Setting inert in = inert out is the key balance.

Conceptual check — Recycle and Purge Calculations

Problem

In a Process Calculations semester or GATE paper you are asked: "State the main assumption, the governing relation, and one practical consequence of recycle and purge calculations." What should a complete answer include?

Exams & GATE

Draw recycle loop explicitly; solve outer then inner balances.

📖 Standard books (India)

  • StoichiometryBhatt & Vora

    Read: Syllabus unit

    Process calculations for chemical engineering