Calculating Silo Inventory From Radar Level When Bulk Density Varies

A radar level meter measures the distance to one area of the material surface; it does not weigh the silo. Converting that reading to tonnes requires a vessel model, an estimate of the three-dimensional material surface and a defensible bulk-density value. Each element has its own uncertainty, so the result should be treated as an inventory estimate unless it is reconciled against an independent mass reference.

Separate the measurement chain

Start with the antenna reference plane, empty distance and usable measuring range. Convert radar distance to level only after confirming the datum used by the vessel drawing. Then convert level to occupied volume using validated geometry. Apply bulk density only at the final stage. Keeping the raw distance, calculated level, volume and mass as separate tags makes errors traceable.

Do not hide all corrections inside one PLC multiplier. A constant percentage-to-tonnage factor is valid only when cross-sectional area and density are effectively constant. Conical hoppers, transition sections and irregular roofs need piecewise equations or a calibrated lookup table.

Model the pile rather than assuming a flat surface

Solids form peaks during filling and valleys or rat holes during discharge. An off-centre inlet can move the representative surface away from the radar beam. Record inlet and outlet positions, angle of repose and typical operating sequence, then decide whether one measurement point can support the required inventory decision.

For higher-value inventory, use multiple measurement points or a scanning method and define how their readings form an average surface. For refill scheduling, a single stable point may be adequate. The design should match the business consequence of the stated error.

Use density by material and operating state

Bulk density can change with product grade, moisture, particle size, aeration, compaction and storage time. Density from a supplier data sheet may describe a laboratory condition rather than the material delivered to the silo. Create controlled density values by material code and retain the sampling method and date.

Pneumatically conveyed powder may settle after filling, increasing apparent tonnes without any change in radar level. If settling is important, use time-dependent factors only when supported by site records. Never tune the radar calibration merely to make one delivery balance.

Reconcile with independent mass evidence

Compare opening inventory plus receipts minus consumption with the radar-derived closing estimate over matching timestamps. Suitable references include weighbridge tickets, load cells, belt scales and batch records. Account for material in transfer lines and transactions posted late.

Review repeated bias by product and operating state. A level error tends to follow distance or echo conditions; a density error follows material properties; a geometry error varies with the occupied section. This separation points to the correct correction rather than an arbitrary offset.

State uncertainty and alarm duties

Report a practical range or rounded estimate instead of displaying unsupported decimal precision. Document expected error at low, middle and high inventory because pile geometry often makes it non-uniform. Inventory estimation must not replace independently designed high-level protection where overfill consequences are significant.

Commission across filling, settling and discharge. Save echo curves, surface observations, density samples, calculation versions and reconciliation results so future changes can be distinguished from instrument faults.

Worked example

A silo model indicates 80 cubic metres of material at the measured level. Recent controlled samples range from 0.72 to 0.78 tonnes per cubic metre, giving 57.6 to 62.4 tonnes before pile-shape uncertainty. Reporting exactly 60.0 tonnes would conceal the dominant uncertainty.

The plant displays an operational estimate of about 60 tonnes with an agreed tolerance band, retains the raw level, and reconciles weekly against weighed receipts and feeder totals. The high-level trip remains a separate tested function.

Engineering checklist

Confirm the radar and drawing use the same datum.
Validate every vessel section and lookup table.
Record pile geometry and the representative measurement point.
Maintain density values by material and condition.
Reconcile against independent mass records.
Keep inventory estimation separate from overfill protection.

Frequently asked questions

Can one radar provide legal-for-trade silo weight?

No. Radar provides level; legal-for-trade mass requires an approved weighing system and procedure.

How often should density be updated?

Update it when material grade, supplier, moisture, conveying or compaction changes, and verify the interval from reconciliation data.

Why can tonnes change while level stays constant?

Settling or moisture can change bulk density and pile shape without a comparable change at the radar point.

Need a project-specific review? Send the vessel drawing, material data, operating conditions and acceptance criteria through our contact page.