Concept
Single-pass (per-pass) conversion is the fraction of reactant consumed in one trip through the reactor; overall conversion is the fraction consumed across the whole process once unreacted feed is recycled back. Recycling the unconverted reactant is precisely what lets a deliberately low per-pass conversion deliver a high overall conversion.
Two conversions, two denominators. Both are “reactant consumed ÷ reactant supplied,” but they count different supplies:
Because the reactor inlet is larger than the fresh feed (it includes the recycle), single-pass conversion is the smaller number; overall conversion is the one that describes how completely the plant uses what it buys.
Why per-pass is kept low on purpose. Reaction equilibrium, kinetics, heat removal, and selectivity all cap the conversion that is economic in a single pass. Forcing per-pass conversion higher — more catalyst, higher pressure, lower throughput — usually costs more than simply recycling the unconverted reactant and converting it on a later pass. So processes are designed around a modest per-pass conversion and a recycle loop, not a single high-conversion pass.
What closes the gap, and what caps it. Recycle raises overall conversion toward 100%, but the purge that keeps inerts from accumulating also bleeds unconverted reactant out of the loop — so overall conversion is held a little below complete by the reactant lost in the purge. Overall conversion is therefore set by the loop and its purge, not by the reactor alone.
Which number sizes what. The reactor and everything inside the loop — the recycle compressor especially — see the loop flow and are sized and parameterized on the per-pass picture; the plant’s feed purchase and product output are set by the overall conversion. Using the right one in the right place is the whole point of keeping them distinct.
The ammonia synthesis loop runs at a per-pass conversion of ~20% (the running-example value), yet converts almost all of the hydrogen and nitrogen it is fed. The reason is recycle: the ~80% that does not react each pass is separated from the product ammonia and returned to the reactor inlet, so the gas circulating through the reactor is roughly 5× the fresh feed, while the fresh feed itself is converted to an overall ~98% once the small purge loss is accounted for (a round figure for a loop with a modest purge; the precise value depends on the purge rate).
The two numbers do different jobs: the recycle compressor and reactor are sized on the ~5×-larger loop flow (the per-pass world), while the plant’s hydrogen and nitrogen purchase is set by the ~98% overall conversion.
Separately, to show the edge: widening the purge to hold inerts down bleeds more unconverted reactant out of the loop, so overall conversion falls below ~98% — the per-pass conversion is unchanged, but the overall number moves with the purge.