Plot Plan & the Real Cost of a Metre

The 26 metres nobody wanted to pay for

A column sits at one end of the plot. A transfer pump sits diagonally across from it, 60 metres away in a straight line. You are asked to route a DN300 line at 210 °C between them, and the project cost engineer has just circulated a note reminding everyone that carbon steel pipe is $557 a metre installed.

The junior designer draws the straight line: 60 m, $33 k of pipe. The lead redlines it and draws 86 m — up onto the rack, along, across the road at high level, down with a dog-leg into the pump. Twenty-six metres longer. $14.5 k more pipe.

Guess before you read on: which route costs the owner more over the plant's life, and by roughly how much?

The 86 m route is cheaper. On the numbers in this note it is about $21,000 cheaper — and that is before anyone prices the road the short route would have closed.

The misconception, stated plainly

"Shortest pipe is cheapest. Every metre I add costs money, so my job is to minimise length."

It is the most reasonable-sounding wrong idea in piping layout, and it survives because the only number most people ever see is the pipe price per metre. That number is real. It is also the smallest of the three things a metre costs you:

true cost of a metre = pipe & erection
                     + rack steel, shoes, supports & foundations it triggers
                     + the pumping energy to push fluid down it for 20 years

For that DN300 line at 900 m³/h the three terms come out at $557 + $167 + $927 per metre. The fluid is more expensive than the steel. A metre does not cost $557; it costs $1,651.

And yet the shortest route still loses — because there is a fourth term that gets bigger as the route gets shorter.

Symbol key — every symbol on this sheet

• L₀ — straight-line (point-to-point) distance between the two connections · m
• L — actual developed route length, L₀ + whatever you add · m
• x — extra route length added over L₀ (the dog-leg, the loop, the detour) · m
• ℓ — offset leg: the length of the limb of pipe that is free to bend sideways · m
• ℓ_req — offset leg length needed to absorb the growth without overstress · m
• Δ — thermal growth to be absorbed = α·ΔT·L₀ · mm
• α — coefficient of thermal expansion, ≈ 1.2×10⁻⁵ /°C for carbon steel · 1/°C
• ΔT — design temperature minus installed temperature · °C
• D_o / D — pipe outside / inside diameter · mm
• E — Young's modulus, 203 GPa cold · MPa
• S_A — allowable displacement stress range (B31.3 §302.3.5) · MPa
• v — flow velocity · m/s
• f — Darcy friction factor · dimensionless
• ΔP — pressure drop along the route · Pa, bar
• η — combined pump + motor efficiency, ≈ 0.65 · dimensionless
• PV — present value: future money discounted back to today · $
• PVF — present-value factor = (1 − (1+r)⁻ᴺ)/r · years

Why length is not the objective function

The plot plan is settled long before anybody routes a line, and it is settled by things that have nothing to do with pipe length:

• Process flow — gravity flow, thermosyphon returns, reboiler circuits and pump suctions all impose elevation and direction. Sequence equipment along the process, not along the shortest wire.
• Safety spacing — fired heaters away from hydrocarbon inventory, control rooms away from blast sources, escape in two directions from every operating level. Spacing tables (OISD-118, NFPA 30, insurer schedules) are not a cost item; they are a filter that deletes layouts before costing starts.
• Maintenance access — rotor withdrawal behind every pump, tube-bundle pull space in front of every exchanger, davit swing at every column manway, crane standing and laydown for the heaviest lift. These are volumes, not lines. A route that clips one of them is not a cheaper route, it is a deleted route.
• Constructability — can the spool be lifted in, welded, and hydrotested; can the rack be steel-erected before the lines go up; can the line be built at all with the crane you have.

Everything above is a constraint. Cost optimisation happens only among the survivors. This is why "shortest" so rarely wins: shortest is usually not in the feasible set at all.

Open the 3D plot and look at what the short route actually does: ▶ open the interactive: piping layout plot plan 3d — toggle between Route A (44 m, at grade, diagonally across the plot) and Route B (65 m, on the rack). Route A pierces three keep-out volumes: the under-rack grade corridor, the laydown/escape strip, and the road. Route B crosses the road at seven metres, above the 4.5 m headroom envelope, and pierces nothing.

The four costs of a route, and which way each one pulls

1 — Pipe, erection, paint, insulation. Rises with length, roughly as DN^1.15. Real but modest.

2 — Rack steel, shoes, guides, foundations. Rises with length and with weight. Add 20–35 % to the installed pipe cost for the racked portion. The deeper point is that rack width is a finite resource: the corridor you occupy is not available to the next line, and the day it fills, somebody buys a whole new bent. A designer who "saves" pipe by taking a generous slice of rack is spending someone else's money.

3 — Pumping power, for the life of the plant. This is the term nobody draws. Friction is Darcy–Weisbach:

ΔP = f · (L_eq/D) · ρ·v²/2                 pressure lost along the route
P_shaft = Q·ΔP / η                         power the motor must supply
PV = P_shaft · 8000 h/yr · tariff · PVF    money, discounted to today
PVF = (1 − (1+r)^−N)/r  = 9.82  at r = 8 %, N = 20 yr

Two consequences follow and both matter: - Every metre of route carries a PV energy tag of its own. At DN300 and 900 m³/h it is $927/m — 1.7× the pipe price. - ΔP goes as 1/D⁵ at constant flow, so the same argument sets the economic diameter. Push the line-size slider in the explorer: total cost bottoms out at DN400, velocity 2.1 m/s. The familiar "1.5–3 m/s for liquid" table is not a rule of nature; it is a cached answer to this optimisation, computed decades ago at somebody else's energy price.

4 — The flexibility penalty. This one gets worse as you get shorter. A dead-straight run between two nozzles has nowhere to put its thermal growth. The guided-cantilever estimate for the offset leg you need is:

Δ      = α · ΔT · L₀                 (mm of axial growth to absorb)
ℓ_req  = √( 3·E·D_o·Δ / S_A )        (metres of leg that can bend it away)

If the route gives you ℓ ≥ ℓ_req, flexibility is free — it is just geometry you were going to buy anyway. If it doesn't, you pay for it in hardware and in risk: an expansion joint, two main anchors sized for the full pressure thrust, guides at spacing, an inspection regime, and a bellows replacement somewhere in the plant's life. Present-valued, that is tens of thousands of dollars on a DN300 hot line — and the first thing it buys you is a nozzle-load check you were going to fail anyway.

S = 6EIΔ/ℓ² · D_o/(2I) = 3·E·D_o·Δ / ℓ²

Putting the four together — the worked example

DN300 (12″) carbon steel, design 210 °C against an installed 30 °C so ΔT = 180 °C, 900 m³/h of water-like fluid, straight-line distance L₀ = 60 m, 20-year life at 8 %.

The arithmetic behind the flexibility column: Δ = 1.2×10⁻⁵ × 180 °C × 60 m = 130 mm of growth. ℓ_req = √(3 × 203000 × 323.9 × 130 / 150) = 13.1 m of offset leg. A dog-leg that goes out and comes back adds about 2ℓ of pipe, so 26 m of extra route buys the 13 m leg — and the penalty falls to zero exactly there. Beyond 26 m you are paying $1,651/m for nothing, which is why the curve turns back up.

Run it yourself and watch the V-shape appear: ▶ open the interactive: piping layout plot plan calc — drag the extra-length slider and watch the red flexibility wedge shrink while the blue and amber bands grow. The minimum is never at zero. Drop ΔT to 20 °C and it collapses from +26 m to about +9 m — flexibility gets cheap, but it never quite stops being worth buying until ΔT reaches zero. Both answers are correct; the point is that you have to know which régime you are in.

Common pitfalls

• Quoting pipe $/m as "the cost of a metre". It is typically a third of it. For a big, hot, high-flow line the pumping PV alone beats the steel.
• Optimising the line after the plot plan is frozen. By then equipment positions, rack elevation and road layout have already decided most of the length. The cheap decisions are the early ones — see the Project discipline's cost-influence curve.
• Treating rack space as free. The marginal cost of your line is not its own steel; it is the bent that has to be added when the corridor fills.
• Adding length "for flexibility" without checking geometry. Extra length in the same direction buys nothing. Only a leg perpendicular to the growth absorbs it — that is the ℓ in the formula, not the L.
• Sizing on the velocity table alone. The table is an economic answer in disguise; at today's tariffs, and for long lines, it often lands a size small.
• Believing the model. Safety spacing, escape routes and maintenance envelopes never appear as a dollar figure. They delete routes. Any cost comparison you run is a lower bound on why the short route loses.

Outcome

• A metre of pipe costs pipe + rack/supports + a lifetime of pumping energy; on a typical DN300 line at 900 m³/h that is $557 + $167 + $927 = $1,651/m, not $557/m.
• The shortest route is rarely the cheapest, because the flexibility penalty increases as length falls: no offset leg means an expansion joint, two anchors, and overloaded nozzles.
• Minimum whole-life cost sits at L₀ + ~2·ℓ_req with ℓ_req = √(3·E·D_o·Δ/S_A) — for the worked case, 26 m longer than the straight line and $21 k cheaper.
• The same ΔP arithmetic sets the economic diameter (DN400, v ≈ 2.1 m/s here); the "1.5–3 m/s" velocity table is a cached result of that optimisation, not an independent rule.
• Plot-plan drivers — process flow, safety spacing, maintenance access, constructability — are constraints that delete routes, not costs to be traded. Cost only decides among survivors.
• Interactive: ▶ open the interactive: piping layout plot plan calc; 3D: ▶ open the interactive: piping layout plot plan 3d.

Open items

• Calibrate the $/m curves against a real project MTO and a current bulk-material tender
• Add a rack-fill term: cost of the additional bent triggered when the corridor saturates
• Extend the flexibility model from one guided cantilever to a two-leg L-bend and a full loop
• Cross-link to the Civil discipline's rack load-path topic — friction on the shoe is the other reason length is not free

Educational teaching material — simplified and illustrative. Not for engineering design use.
© EPiC Circle · provided by PipeAxis