Slurry mass balance

A slurry mass balance splits a stream into its parts: from a flow and a density, how much solid and how much liquor it carries, by mass and by volume. It is the everyday accounting of a wet circuit — the step between "there is a pipe with slurry in it" and a closed balance you can design and operate against.

The logic: a chain of links

The logic is a chain, each link the relation from the percent-solids topic. Slurry mass flow is the volumetric flow times the slurry density. Solids mass flow is the slurry mass flow times the solids mass fraction; liquor mass flow is the remainder. Each mass flow becomes a volume flow by dividing by its own density — solids by the solids density, liquor by the liquor density — and the two volume flows sum back to the slurry volume, which is the consistency check that tells you the balance closes. From the volume flows you also recover the percent solids by volume, closing the loop with the previous topic.

This balance is what makes a circuit auditable. Counter-current decantation, thickener duty, wash-water addition, filtration — all of them are slurry mass balances stitched together, each stage taking a stream apart into solids and liquor and recombining them differently. An engineer who can do the single-stream balance cleanly can follow water and solids through a whole washing circuit, which is where soluble losses and reagent carry-over are found. The same balance underlies inventory: the mass of solids held in a tank, the residence time of the solids versus the liquor, the surge in a stream when percent solids shifts.

Closing the balance

The discipline is unit hygiene, the same as everywhere in Module 1 and 2: keep mass flows and volume flows distinct, keep the percent-solids basis explicit, and use the right density for each phase — the liquor density is not 1000 kg/m³ if the liquor is a strong leach solution. A balance that does not close to within a small tolerance is usually telling you a density or a basis is wrong, not that the arithmetic failed.

The habit worth building is to write the closure check every time and treat a non-closing balance as a fault to find, not a rounding error to wave through — the gap is where a misread density or a swapped basis hides, and the check is what surfaces it before it reaches a design.

The calculator below runs the full split from a slurry flow, slurry density, percent solids and the two component densities; the hydromet slurry-calculations guide works the same balance through a series of named scenarios if you want to see it applied across a circuit rather than a single stream.