Concept

Equipment sizing

Overview

Equipment sizing turns a process requirement — a stream flow, a heat duty, a reaction volume — into the physical capacity rating of a specific item, the number that then sets its cost. It’s the bridge from the mass-and-energy picture to capital cost: you size an item before you can price it. Sizing comes after the flows and duties are known (from parameterizing each unit operation) and before costing.

Body

The governing measure is class-specific. Each class is sized on the one variable that drives its cost — the S the six-tenths rule scales on and sizing scalars index by class:

• Heat exchangers — area, from A = Q / (U·ΔT).
• Compressors and pumps — power, from volumetric flow and pressure rise / head.
• Vessels and reactors — volume, from throughput and residence time (or, for a reactor, the kinetics that set conversion time).
• Columns — diameter and height, from vapor/liquid loads and number of stages.

Picking the right measure is the substance of sizing — it’s the quantity cost actually tracks.

Size to the design rate, with margin. Equipment must handle the maximum load, so size to the nameplate (design) rate — not the lower operating average — plus a design margin (~10–20%) for fouling, uncertainty, and off-design operation. Sizing to the time-averaged output leaves the plant unable to reach its own rating.

At the maturity anchor. Only the 2–3 cost-dominant items per unit operation are sized carefully; the rest are approximated and swept up in the installation factor. Relations are deterministic and simple — basic arithmetic or single power relations, engineering proxies, not rigorous design. Pressure and temperature enter the size only when the unit op is specifically P/T-intensive (see when pressure / temperature matter); otherwise they’re left out. A size beyond a class’s largest standard unit shifts to numbering up / down rather than one larger item.

Limits & typical error

• Sizing transmits the errors in its inputs — the size is only as good as the mass and energy balance feeding it; an overstated duty prices an oversized exchanger with no internal warning. Sizing doesn’t generate accuracy, it passes it through.
• The wrong measure misses the cost driver — costing an exchanger on flow instead of area scales it on a quantity that doesn’t govern its cost; the six-tenths step that follows is then exact arithmetic on the wrong variable.
• Margin error is two-sided — too little caps output below nameplate (a capacity shortfall, not a price); too much inflates every sized item and thus capex.
• Equipment comes in discrete sizes, with a class maximum — past the largest standard frame, shell, or vessel, continuous sizing returns a unit that can’t be built and must be met by parallel units; the arithmetic gives no warning at the ceiling.
• Omitting P/T where the op is P/T-intensive undersizes cost — for high-pressure or cryogenic service, wall thickness, materials, and compression power are set by P/T; leaving them out understates the item materially (see when pressure / temperature matter).

Mini-example

Sizing the two cost-driving items of the ammonia synthesis loop. The syngas compressor is sized on power, set by the recycle flow and the loop pressure ratio — ~8 MW (the rating carried into the six-tenths example), and because the loop is a high-pressure service (~150–300 bar), that pressure legitimately drives the power here. The reactor is sized on volume, from the loop flow and the residence time for ~20% per-pass conversion (the running-example baseline). Each size measure becomes the S₂ its class exponent scales cost on.

Edge case: a near-ambient feed mixing drum upstream carries no P/T driver, so it’s sized on volume from flow and residence time alone — the same arithmetic shape as the reactor but with P/T correctly left out. The loop’s high pressure earns its place only because that operation is pressure-intensive.

See also

• Six-tenths rule
• Sizing scalars (by equipment class)
• Capex
• Scale: nameplate vs. operating capacity
• Numbering up / down
• When pressure / temperature matter
• Parameterizing a unit operation