← Process Calculations & Thermodynamics

Tie Components, Recycle, Bypass & Purge Calculations

How to use a tie component to solve material balances, and how recycle, bypass and purge streams work — overall versus single-pass conversion, recycle ratio, why a purge is needed to stop inerts building up — with fully worked examples.

📑 Contents (4 sections)

Last reviewed 4 Nov 2026 · 3 min read

1. Tie component

DefinitionTie component

A material that passes from one stream to another unchanged (it is not reacted, and does not enter or leave elsewhere). Its amount fixes the ratio between the two streams.

Worked Example1 — Drying with a tie component

Wet solids with 40% water are dried to 10% water. Per 100 kg of feed, how much water is removed? Dry solid is the tie component: 60 kg in feed = 60 kg in product. Product = 60 ÷ 0.90 = 66.7 kg → water removed = 100 − 66.7 = 33.3 kg.

  • Common tie components: dry solids in drying, N₂ in combustion (inert), dry air in humidification, salt in evaporation.

2. Recycle

A recycle returns part of an outlet stream to an earlier point to use unreacted material or recover heat or solvent.

Term Meaning
Fresh feed Feed from outside
Gross (combined) feed Fresh feed + recycle, entering the unit
Recycle ratio Recycle flow ÷ fresh feed flow (definitions vary — check the question)
Single-pass conversion Reactant converted ÷ reactant entering the reactor
Overall conversion Reactant converted ÷ reactant in the fresh feed
Worked Example2 — Recycle with complete separation

A → B. Fresh feed is 100 mol/h of A; the single-pass conversion is 25%. All unreacted A is separated and recycled. Overall conversion = 100% (no A leaves the process). A reacting = 100 mol/h = 0.25 × (reactor feed F) → F = 400 mol/h. Recycle R = F − fresh = 300 mol/h; recycle ratio = 300/100 = 3.

3. Bypass

Part of the feed skips a unit and joins its outlet — used to control the product composition or temperature.

Worked Example3 — Bypass around an evaporator

100 kg/h of a solution with 20% water. Part of it (x) goes through an evaporator that removes all its water; the rest bypasses and is mixed back. The product must have 5% water. Find x. Solids (80 kg/h) all reach the product. Water in product = 0.2(100 − x). x ≈ 78.9 kg/h through the evaporator; product ≈ 84.2 kg/h.

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