Multi-Unit Flowsheets

Choose the right balance envelope on a flowsheet and name streams consistently across multiple units.

Material & Energy BalancesChemical Engineering Year 1Free preview
⏱️ About 14 min

A flowsheet has a mixer, reactor, and separator with a recycle loop. Where do you draw the balance boundary — and which streams cross it?

💡
The big idea: Multi-unit balances are just single-unit balances applied to a carefully chosen envelope: unit, subsystem, or overall plant.
🎯 By the end, you'll be able to
  • Identify mixers, reactors, and separators on a flowsheet and write their basic balance statements
  • Define fresh feed, recycle, purge, and product streams on a multi-unit flowsheet
  • Choose a balance envelope (unit vs overall) that simplifies the algebra
  • Use consistent stream naming across different envelopes to avoid double-counting
📎 Helpful to know first
  • Material Balances on Multiple Reactions

Balance Envelopes: Unit vs Subsystem vs Overall

On a multi-unit flowsheet, you can draw a material-balance boundary around:

  • A single unit (e.g., the reactor only)
  • A subsystem (e.g., mixer + reactor + separator, excluding only the recycle line)
  • The overall process (everything inside the plant boundary)

The math does not change — only which streams count as in and out. The skill is choosing the boundary that removes internal (unknown) flows from your equations.

Reactor-with-recycle flowsheet: fresh feed and recycle mix before the reactor, reactor effluent goes to a separator, which splits into recycle-back-to-mixer and productMixerReactorSeparatorFresh feedTo reactorReactor effluentProductRecycle back to mixer
Reactor-with-recycle flowsheet used throughout this module.

Stream Types on This Flowsheet

We'll use consistent names based on function:

  • Fresh feed (F): enters the overall process from outside.
  • Recycle (R): leaves a downstream unit and returns upstream (internal loop stream).
  • Product (P): leaves the overall process as desired output.
  • Purge (Pu): a bleed stream taken from the recycle loop to prevent buildup (introduced in Lesson 4).

When you change the balance envelope, a stream can switch categories. For example, the recycle stream is out of the separator unit, but it is internal to an overall-process balance.

\[ \text{Overall envelope:}\quad \sum \dot{n}_{\text{in}} = \sum \dot{n}_{\text{out}} \qquad \text{(steady state, nonreactive)} \]
At steady state with no reaction inside the chosen envelope, total molar flow in equals total molar flow out. Reaction adds generation/consumption terms if the envelope includes a reactor.
⚠️ Don't count internal recycle as both inlet and outlet

A classic pitfall is to write an overall balance and include the recycle stream as both an inlet (to the mixer) and an outlet (from the separator). If the recycle line stays inside your overall boundary, it cancels out — it should not appear in the overall balance.

📝 Worked example: On the flowsheet shown (mixer → reactor → separator with recycle), the separator splits reactor effluent into a product stream and a recycle stream. Given fresh feed F = 100 mol/h entering the mixer and product P = 100 mol/h leaving the separator, the recycle flow is R = 200 mol/h. Compute the flow rates crossing (a) an overall-process envelope that includes all units and the recycle line, and (b) a separator-only envelope.
  1. Overall-process envelope includes mixer + reactor + separator + recycle line (recycle is internal).
  2. Streams crossing the overall boundary: inlet = F; outlet = P (no purge given).
  3. Overall: in = 100 mol/h, out = 100 mol/h (consistent with a steady-state total balance).
  4. Separator-only envelope: inlet = reactor effluent E; outlets = product P and recycle R.
  5. Separator total balance: E = P + R = 100 + 200 = 300 mol/h.
  6. So (a) the overall boundary sees 100 mol/h in and 100 mol/h out; (b) the separator boundary sees 300 mol/h in, split into 100 + 200 mol/h out.
✓ Overall boundary: 100 mol/h in (fresh feed) and 100 mol/h out (product). Separator boundary: E = 300 mol/h in; P = 100 mol/h and R = 200 mol/h out.
✏️ Practice: A splitter takes a stream S = 250 mol/h and sends 40% to a purge line and 60% to recycle. What is the purge flow rate (mol/h)?
mol/h
Solution
  1. Purge = 0.40 × 250 = 100 mol/h
  2. Recycle = 0.60 × 250 = 150 mol/h

Check your understanding

1. If you draw an overall-process balance boundary that encloses a recycle line, the recycle stream should appear in the balance equations as:
Recycle is internal when enclosed by the boundary, so it does not cross the boundary and should not appear in the overall balance.
2. Which envelope is most likely to eliminate the recycle flow variable R from the equations?
The overall boundary makes the recycle internal, removing it from the balance equations.
🔎 Related lessons
Recycle Streams
✅ Key takeaways
  • A multi-unit flowsheet can be analyzed by choosing an appropriate balance envelope
  • Fresh feed and product cross the overall boundary; recycle typically remains internal if enclosed
  • Unit envelopes (e.g., separator-only) expose internal streams like recycle
  • Consistent stream naming prevents double-counting when changing envelopes
➡️ With envelopes and stream naming in place, we can quantify why recycle exists — and how it changes conversion compared with a single pass through the reactor.
Want to test yourself on this? Try the Chemical Aptitude test →