A dredge is paid for what it moves, not for what it pumps. Production monitoring turns two continuous measurements — slurry density and flow velocity — into the numbers a contract is settled on. The arithmetic is simple; the assumptions inside it are where the disputes live.
The three quantities
Start from the measured mixture density ρm (t/m³), with ρw the carrier water density and ρs the solids particle density.
Volume concentration — the fraction of the pipe occupied by solid particles:
Cv = (ρm − ρw) / (ρs − ρw)
Mass concentration — the fraction by weight:
Cw = Cv × ρs / ρm
Dry-solids production — with volumetric flow Q (m³/h):
Pdry = Q × Cv × ρs (t/h)
And where the contract is written in bank volume — cubic metres as they sat in the borrow area before dredging — a further division by (1 − n) is needed, n being in-situ porosity. That conversion is a frequent source of disagreement precisely because n is assumed rather than measured.
A worked example
Sand, ρs = 2.65 t/m³, seawater ρw = 1.025 t/m³. Measured ρm = 1.30 t/m³, flow 7000 m³/h in a DN800 line.
- Cv = (1.30 − 1.025) / (2.65 − 1.025) = 0.169, so 16.9 % by volume
- Cw = 0.169 × 2.65 / 1.30 = 0.345, so 34.5 % by weight
- Pdry = 7000 × 0.169 × 2.65 = 3135 t/h
Where the error actually comes from
Run the sensitivity and the ranking is consistent across projects:
- Density measurement error dominates. Differentiating Cv shows that an error in ρm is amplified by 1/(ρs − ρw) ≈ 0.62 per 0.01 t/m³. At ρm = 1.30 that is roughly a 3.6 % relative error in production for every 0.01 t/m³ of density error. Density accuracy is not a specification detail here; it is the whole ballgame.
- Assumed ρs is a silent bias. Everyone writes 2.65 for sand. Clay, silt, mixed spoil and shell content are not 2.65. An assumed value 3 % high puts a 3 % bias straight into every tonne reported, for the whole job.
- Entrained air. Air lowers mixture density, so production is under-reported during air ingress — the direction that costs the contractor. Cutter-suction dredgers draw air routinely at the start of a cut and when the cutter breaks surface.
- Flow measurement. Usually the smallest of the four, provided the meter is on a full pipe and not fighting a partially filled line.
Choosing the density instrument
Dredge lines are large (DN500–DN1000 is routine), abrasive, and mounted on a vessel that moves. Historically this meant a Cs-137 gauge, with the licensing and transport burden that follows a source across borders. A non-nuclear ultrasonic instrument such as the PS7000 covers the same diameter range, and — because the sensor face sits flush with the bore — presents no obstruction to a stream carrying gravel and shell. See non-nuclear density meters for dredgers for the full comparison.
One practical point that outweighs most specification arguments: install on a vertical rising section where possible. Horizontal runs at the low velocities that occur during a slow cut let coarse material stratify, and a meter reading one part of a stratified pipe is not reading the line average — regardless of how accurate it is.