Concept

Recycle & purge ratio

mass-energy

Overview

A recycle stream returns unconverted reactant from downstream back to the reactor inlet, so feed not consumed in one pass is converted on a later one rather than lost; a purge is a small bleed taken off the recycle loop to stop inert or byproduct species from accumulating without bound. The purge ratio — the fraction of the recycle stream bled off — trades overall conversion against control of those accumulating species.

Body

What recycle does. After the product is separated out, the unreacted reactant is sent back to the reactor inlet instead of leaving the process. This is the mechanism that lifts overall conversion far above the per-pass figure, and it is why a reactor can be designed for a modest single-pass conversion.

The accumulation problem. Anything that enters with the feed but neither reacts nor leaves with the product has no exit from the loop. Inerts (argon and methane carried in with the synthesis gas) and unwanted byproducts therefore build up: every pass adds more, the product separation removes none, and their concentration climbs until they crowd out the reactant’s partial pressure and depress the reaction itself.

The purge fixes it. Bleeding a small fraction of the loop gas gives those species an exit. At steady state, the rate at which an inert enters with the make-up feed equals the rate it leaves in the purge — a balance that an inert tie component solves directly:

inert in (make-up) = purge flow × inert fraction in the loop

so the purge holds the loop’s inert concentration at a steady level set by how hard it is bled. The purge ratio is the purge flow divided by the recycle (or total loop) flow — typically a few percent.

The trade-off. The purge gas is mostly unconverted reactant, so every unit purged to control inerts also carries good reactant out of the loop — lowering overall conversion and often justifying a recovery step on the purge. A wider purge means a lower inert level but more reactant lost; tuning the purge is choosing the inert concentration the loop runs at. The loop flow itself is large — several times the fresh feed — so the recycle drives the size of the recycle compressor and the reactor (see stream).

Limits & typical error

Omitting the purge. A model with recycle but no purge either lets inerts accumulate without bound (an unsteady, never-converging loop) or, if steady state is forced, hides a failed inert balance — there is no exit for a species that has an entrance.
Sizing the purge on inerts while ignoring reactant loss. Setting the purge to hold an inert level, then counting the lost reactant as if it stayed, overstates overall conversion; the purge’s reactant content is a real feed loss.
Solving the loop as a forward pass. A recycle cannot be calculated in one forward sweep — the recycle flow depends on the conversion, which depends on the loop composition the recycle sets; it must be solved as a coupled loop (see mass balance), or it diverges or settles on the wrong flows.
Purge-ratio basis confusion. “Purge ratio” defined against the recycle flow and against the total loop flow give different numbers; an unstated basis makes the figure ambiguous (see basis of calculation).
Wrong feed purity feeds a wrong purge. The inert load is set by feed purity; underestimating the inert entering with the make-up undersizes the purge and lets the steady inert level run higher than modeled, quietly depressing per-pass conversion.

Mini-example

On the ammonia synthesis loop, argon and methane enter with the make-up syngas, are inert in the reaction, and are not removed when ammonia is condensed out — so they have no exit except a purge. A purge of a few percent of the loop gas holds their concentration steady: the argon tie component pins it, since the argon entering with the make-up must equal the argon leaving in the purge. That same purge stream is mostly unconverted H₂ and N₂, so controlling the inerts costs some reactant — trimming overall conversion from near-complete toward ~98% (the running-example figure).

Separately, to show the edge: run the loop with no purge and overall conversion is momentarily highest, but argon and methane climb pass after pass until they dominate the loop gas and starve the reactor of reactant partial pressure — the unbounded accumulation the purge exists to prevent.