Filter Cake Moisture Explained

Definition

Filter cake moisture is the amount of water held in a discharged filter cake, expressed as a fraction of the cake. It is reported on two distinct bases. Wet-basis (total) moisture divides the water by the total wet cake mass: M_w = (m_wet − m_dry) / m_wet. Dry-basis moisture divides the same water by the dry solids mass: M_d = (m_wet − m_dry) / m_dry. The two are not equal — for the same cake the dry-basis figure is always larger, because its denominator (dry solids) is smaller than the wet cake. Cake percent solids is the complement of the wet-basis moisture (S_w = 1 − M_w), so an 18% wet-basis-moisture cake is an 82% solids cake. Cake moisture is a measured property of a sampled cake (wet mass, then bone-dry mass after oven-drying), not a value these calculations predict.

Why it matters

The single biggest source of error in cake-moisture reporting is failing to say which basis is meant. Eighteen percent wet basis and 18% dry basis describe different cakes — the dry-basis equivalent of 18% wet basis is 21.95%, a meaningful gap in a moisture specification, a transport contract, or a downstream drying or smelting calculation. Mineral-processing practice most often quotes the wet basis (water as a fraction of total wet cake), and the cake percent solids — its complement — is the same information stated the other way; drying and some chemical contexts use the dry basis. Cake moisture also matters commercially and operationally: it sets the mass of water shipped with concentrate (and so transport cost and penalties), the load on any downstream dryer, the handleability of the cake, and, via the filter water balance, how much water the filter actually removed. Because moisture and percent solids are complements on the wet basis, mixing the two up — or mixing the bases — quietly corrupts every number that depends on them. The fix is simple: always state wet basis or dry basis, and keep moisture and percent solids straight as complements.

Formula

Units involved

• •wet cake mass m_wet and dry cake mass m_dry — any consistent mass unit (g, kg, t)
• •moisture (wet and dry basis) and cake % solids — percent
• •water-to-solids ratio — dimensionless (kg water per kg dry solids)
• •the mass ratios are unitless, so the input units need only be consistent

Concept diagram

Worked example

Common mistakes

• •Quoting a moisture without saying wet basis or dry basis — the two differ for the same cake.
• •Treating wet-basis and dry-basis moisture as interchangeable (dry basis is always the larger number).
• •Confusing moisture with percent solids — they are complements only on the wet basis (moisture + solids = 100%).
• •Adding a dry-basis moisture to a percent solids and expecting 100% — only the wet-basis pair sums to 100%.
• •Assuming the "dry" mass is truly bone-dry when the sample was not oven-dried to constant mass.
• •Reading a measured cake moisture as the moisture a filter will achieve on another ore — it is a measurement, not a prediction.

When to use the calculator

Use the filter cake moisture & solids calculator to turn a measured wet cake mass and bone-dry cake mass into the wet-basis moisture, the dry-basis moisture, the cake percent solids, the water-to-solids ratio, and the water held in the cake — with both bases shown side by side so the value cannot be misread. Feed the cake moisture into the filtration mass balance calculator to split the feed into cake and filtrate and get the solids recovery. For predicting the moisture a vacuum or pressure filter will achieve on a given material, use filtration testwork and vendor methods — that is outside this calculator.

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