Write a balance for each component
Use flows measured over the same period and the component concentration in all three streams. Repeat for TSS, salts or the analyte of interest. In transient operation add tank accumulation and any purge or wash losses.
Hydraulic recovery is Qp/Qf. It differs from solute rejection, which depends on feed and permeate concentrations.
- Qf: feed; Qp: permeate; Qc: concentrate.
- Check that flows and samples describe the same operating state.
- Record internal recirculation separately: it is not a fourth net outlet.
Illustrative solids concentration example
Assume 10 m³/h feed with 20 kg/m³ retainable solids, permeate free of that component, and approximately constant density. The feed carries 200 kg/h. At a target concentrate of 40 kg/m³, the balance gives 5 m³/h concentrate and 5 m³/h permeate. This does not guarantee that a membrane can reach that concentration or production.
If permeate instead carries 2 kg/m³ of the component, 5 m³/h permeate would carry 10 kg/h away and concentrate would contain 190/5 = 38 kg/m³. Actual composition must be recalculated rather than assumed.
| Stream | Flow (m³/h) | Solids (kg/m³) | Load (kg/h) |
|---|---|---|---|
| Feed | 10 | 20 | 200 |
| Idealised permeate | 5 | 0 | 0 |
| Idealised concentrate | 5 | 40 | 200 |
What to check in a pilot
Measure net production after washes, maximum pumpable concentration, permeate quality and cycle stability. Close water and material balances with their uncertainty. If mass is missing, investigate settling, sampling, fouling and instruments before scaling a plant.
For reporting, convert each concentration-flow product into one load unit before summing it. At 1 m³/h, 1 mg/L corresponds to 1 g/h, or 0.001 kg/h. Always identify whether a percentage is mass fraction, volume fraction or analytical concentration.
Common questions
Does a balance determine membrane area?
No. Area needs a sustainable flux measured for the feed and intended cleaning regime.