How to Calculate Filtration Performance

Chemical Engineering · Equipment

A quick Büchner or Nutsche trial can tell you a lot about how a slurry will filter at production scale, but only if you turn the raw filtrate-volume-vs-time data into two numbers that actually transfer: specific cake resistance and expected flux.

The Cake Filtration Equation

Where V is filtrate volume, t is time, ΔP is the pressure/vacuum driving force, A is filter area, μ is filtrate viscosity, α is specific cake resistance, c is the mass of dry cake solids per unit volume of filtrate, and R_m is the filter medium resistance. In practice, this is rearranged and the trial data (t/V vs V) is plotted to extract α and R_m from the slope and intercept.

Worked Example

A bench trial at 0.5 bar vacuum through a 20 cm² Büchner filter collects 150 mL of filtrate in 90 seconds, with a slurry concentration giving c = 40 kg/m³. Plotting t/V against V from several timed readings gives a straight line whose slope yields α and whose intercept yields R_m. The regression needs several data points, not just the endpoint, so a single-point trial isn't enough on its own.

Once α is known, expected flux at a given ΔP and cake thickness can be estimated directly from the rearranged equation, and specific cake resistance above roughly 10¹¹–10¹² m/kg is generally considered slow-filtering, prompting a look at flocculation, filter aid, or a different filter type.

In the Plant

Specific cake resistance for compressible cakes (many organic precipitates and biological solids) isn't constant. It increases with ΔP. A trial run at bench-scale vacuum doesn't automatically predict performance at a much higher production-scale pressure differential; ideally, run the trial at a ΔP close to what production will actually use.

Common Mistakes

Using only the total volume and total time (a single point) instead of a proper t/V vs V regression across the run; ignoring filter medium resistance when it's actually a significant fraction of total resistance for a thin cake; and assuming bench-scale flux scales linearly to a production filter of different geometry without accounting for the medium and support structure differences.