Reference ID: MET-5D4C | Process Engineering Reference Sheets Calculation Guide
Introduction & Context
Pre-coating with filter aid is a standard unit operation in solid–liquid separation.
A thin, uniform cake of diatomaceous earth, perlite, or cellulose is deposited on the filter medium before the process slurry is introduced.
The pre-coat protects the medium, captures fine solids, and provides a porous matrix that maintains high filtrate flow at modest pressure drop.
Correct mass calculation avoids excessive consumption (cost) or insufficient thickness (break-through).
The sheet below gives the algebraic relations used by plant engineers to size the filter-aid feed system and to verify that operating pressure and cake thickness remain within the valid window for an incompressible-cake model.
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Convert thickness to SI units
\(L = \frac{L_{\text{mm}}}{1000}\)
Mass of dry filter aid
\[m = \rho_{\text{b}} \cdot L \cdot A\]
\(\rho_{\text{b}}\) bulk dry density of the filter-aid (kg m⁻³)
\(L\) pre-coat thickness (m)
\(A\) filter area to be pre-coated (m²)
Add safety factor
\(m_{\text{safety}} = m \cdot F_{\text{s}}\)
Validity regime for incompressible-cake pre-coat model
Parameter
Lower limit
Upper limit
Remark
\(\rho_{\text{b}}\)
250 kg m⁻³
350 kg m⁻³
Outside range → risk of channeling or excessive cake resistance
\(L\)
1 mm
3 mm
Below 1 mm: incomplete medium coverage; above 3 mm: high pressure drop
\(\Delta P\)
—
3 bar
Exceeding 3 bar invalidates the incompressibility assumption
Target 1–2 mm of dry cake thickness per m² of filter area. Start with 500–800 g of filter aid per m², suspend it in 5–10 % w/w slurry, and recirculate for 5–10 min at full design flow. Measure the clarity of the return stream; when it matches the feed clarity, the pre-coat is stable. Adjust the mass upward only if early breakthrough or high differential pressure occurs within the first production cycle.
Select a fine perlite (D50 ≈ 12 µm) or fine diatomite (D50 ≈ 10 µm) to bridge 1–2 µm particles.
If the liquor is viscous (> 50 cP), prefer perlite; its lower density keeps cake resistance low.
Run a 100 mL bench leaf test with two grades; the grade that gives < 20 NTU filtrate in < 2 min is the keeper.
Keep initial differential pressure < 0.3 bar during the pre-coat recirculation step.
Use a 1–2 % body-feed addition once the pre-coat is established; this fills micro-cracks.
Verify that the septum cleanliness specification is < 50 µm absolute; a dirty cloth is the commonest cause of bleed-through.
Re-use is not recommended. Once compressed, the porosity drops 30–50 %, so the re-coated cake shows 2–3× higher resistance and variable clarity. If disposal cost is critical, blend maximum 10 % of dried, sterilised spent aid with fresh aid; beyond this ratio cycle time shortens and product quality drifts.
Worked Example – Pre-coat Quantity for a Diatomaceous-Earth Filter
A small brewery needs to polish 5 m³ of lager before packaging. The plate-and-frame filter has 10 m² of cloth area and must be pre-coated with diatomaceous earth (DE) to protect the cloth and give a bright filtrate. The brewer wants a 2 mm cake thickness at a bulk density of 300 kg m⁻³ and adds a 10 % safety margin to allow for losses while filling the lines.
Knowns
Filter area, A = 10 m²
Desired pre-coat thickness, L = 2 mm = 0.002 m
Bulk density of DE, ρb = 300 kg m⁻³
Safety factor, fs = 1.1
Step-by-step calculation
Calculate the volume of the pre-coat cake:
\[ V = A \cdot L = 10\ \text{m}² \cdot 0.002\ \text{m} = 0.020\ \text{m}³ \]
Determine the dry mass of DE required:
\[ m = \rho_b \cdot V = 300\ \text{kg m}^{-3} \cdot 0.020\ \text{m}³ = 6.000\ \text{kg} \]
Apply the safety factor to cover handling losses:
\[ m_{\text{with safety}} = f_s \cdot m = 1.1 \cdot 6.000\ \text{kg} = 6.600\ \text{kg} \]
Final Answer
Prepare 6.6 kg of diatomaceous earth for the pre-coat. Slurry this mass in filtered beer, recirculate until a uniform 2 mm cake is established on the 10 m² cloth, then proceed with the main filtration.
"Un projet n'est jamais trop grand s'il est bien conçu."— André Citroën
"La difficulté attire l'homme de caractère, car c'est en l'étreignant qu'il se réalise."— Charles de Gaulle
