Concept

Sizing scalars (by equipment class)

Overview

Sizing scalars are the small reference set that pairs each class of process equipment with the two things needed to scale its cost: the size measure that governs the item’s cost, and the cost-scaling exponent for the six-tenths rule. They’re the lookup table the scaling rule reads from — so a whole plant’s equipment can be costed from a handful of classes, not item by item.

Body

What a scalar records. For each equipment class:

• the size measure S the class is sized and costed on — power for compressors/pumps, area for exchangers, volume for vessels/reactors (the same measure equipment sizing produces); and
• the scaling exponent n for C₂ = C₁·(S₂/S₁)ⁿ.

The six-tenths rule supplies the form; the scalar supplies the n and the S.

Keep the classes few — ~5–6. Group equipment into a handful of classes (e.g. compressors, heat exchangers, pumps, pressure vessels / columns, reactors, and a catch-all). Each carries one representative exponent and size measure. Resolving more is false precision: because cost is only mildly sensitive to the exponent (see Limits), splitting sub-types buys accuracy the rest of the estimate can’t match.

Representative exponents. Class values cluster around the ~0.6 aggregate but spread across roughly 0.4–0.9 — compressors and many vessels toward the high end, pumps and small items toward the low. They come from cost-engineering references (Turton, Towler/Sinnott) and are stable across time and place; the generic 0.6 is the fallback for a class with no better figure. The exponent is the transferable half of a costing anchor — far more portable across years and locations than the reference cost it multiplies.

How it’s used. A sized item’s class fixes both which S to scale on and which n to use; the six-tenths rule returns the scaled cost, which aggregates into capex. A size beyond the class’s largest standard unit moves into numbering up / down.

Limits & typical error

• A class exponent is an average a specific item can depart from — an unusual design or duty scales differently. Sensitivity is mild (a 3× size change moves cost ~15% across the 0.5–0.7 band, per the six-tenths rule), so this rarely dominates, but it grows with the size ratio.
• The exponent only holds over the class’s normal size range — extrapolated far beyond it the cost–size curve bends and the single exponent stops applying, typically at the numbering-up ceiling.
• The size measure must match the one the cost was quoted on — applying an exponent while scaling on a different quantity than the class is defined on silently breaks the scaling (the same basis-matching failure the six-tenths rule warns of).
• Scalars scale size, not a change in kind — they assume like-for-like materials, pressure rating, and configuration; scaling across a metallurgy or pressure-class change folds an unrelated cost step into the size term.
• The paired reference cost ages faster than the exponent — the exponent is stable, but any cost stored alongside it carries a cost year and location; reusing it without escalation imports a dated figure (see reference / comparable process).

Mini-example

Costing the ammonia synthesis loop draws on two class scalars at once. The syngas compressor sits in the centrifugal-compressor class — measure power, n ≈ 0.62 — so its $2.0M / 5 MW reference scales to ~$2.7M at 8 MW (the six-tenths worked case). The ammonia reactor sits in the pressure-vessel / reactor class — measure volume, n ≈ 0.6 — scaling on the vessel volume sizing set from the ~20% per-pass residence time. Two items, two class scalars, each picking the measure and exponent its class is defined on.

Edge case: the same reactor scalar applied across a switch from carbon steel to a high-alloy vessel would fold a metallurgy cost step into what looks like a volume effect — the exponent describes scaling within one material family, not a jump between families.

See also

• Six-tenths rule
• Equipment sizing
• Capex
• Numbering up / down
• Reference / comparable process