Calculator
Editable inputs
| Constituent | Feed mg/L | Permeate mg/L | Removed solids kg/h dry | Feed load kg/h | Permeate load kg/h | Concentrate load kg/h | Concentrate mg/L | Remove |
|---|---|---|---|---|---|---|---|---|
Calculated outputs
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About this tool
Every concentration step moves water one way and dissolved load another. Enter feed flow, recovery, feed and permeate concentrations and any solids you remove, and the calculator closes the load for each constituent and gives the resulting concentrate quality and wet-cake mass.
Use it one step at a time, from membrane concentration through to final solids removal.
Method and equations
Q_p = Q_f × RQ_c = Q_f × (1 − R)ṁ (kg/h) = C (mg/L) × Q (m³/h) × 0.001ṁ_conc,i = ṁ_feed,i − ṁ_perm,i − ṁ_removed,iC_conc,i = ṁ_conc,i / Q_c / 0.001wet cake = removed dry solids / (1 − moisture)Assumptions
- One process boundary at steady state, with flows in m³/h and loads in kg/h.
- Volumes are treated as additive and concentrations as mg/L of solution, which is a bookkeeping simplification for strong brines.
- Permeate concentrations and removed solids are explicit inputs that you supply.
- Wet-cake moisture is a mass fraction of the wet cake.
Limitations
- The ledger closes arithmetically by construction. Zero closure error means the numbers reconcile, not that the separation is physically achievable.
- The tool does not infer membrane rejection, precipitation or product purity. Enter measured or defensible expected permeate quality.
- Removed-solid entries must be chemically consistent with the constituent ledger (for example, calcium and sulfate removed together as gypsum).
- It is not a membrane-performance, precipitation-equilibrium or crystalliser simulator.
Worked example
A 100 m³/h brine feed is concentrated at 80% water recovery, so permeate is 80 m³/h and concentrate 20 m³/h.
- Sodium: feed load 22,000 × 100 × 0.001 = 2,200 kg/h; permeate load 500 × 80 × 0.001 = 40 kg/h; concentrate load 2,160 kg/h, which is 108,000 mg/L in 20 m³/h.
- Sulfate: 550 kg/h in, 1.6 kg/h to permeate and 50 kg/h removed as solids, leaving 498.4 kg/h or 24,920 mg/L in the concentrate.
- Across all eight constituents: 7,000 kg/h in, 112.8 kg/h to permeate, 80 kg/h removed as dry solids and 6,807.2 kg/h to concentrate. Closure error is 0 kg/h.
- At 30% moisture the 80 kg/h of dry solids becomes 114.29 kg/h of wet cake.
The ledger closes. Whether 20 mg/L sulfate in the permeate and 50 kg/h of sulfate solids are realistic is a separate chemistry and equipment question.
The calculator above opens with these default values. Use Reset to defaults to return to them.
Frequently asked questions
Why is the mass closure error always zero?
Concentrate load is calculated as feed minus permeate minus removed solids, so the ledger reconciles by design. The check is still shown so you can confirm nothing has been dropped, and a negative concentrate load flags inputs that cannot be right.
What does a negative concentrate load mean?
Your permeate load plus removed solids for that constituent exceed what came in with the feed. Recheck the permeate concentration, the solids entry or the recovery.
Why do I have to enter permeate quality myself?
Rejection depends on membrane type, salinity, temperature, flux and fouling. Assuming perfect rejection makes concentrate look cleaner than reality, so the tool asks for measured or defensible values instead of guessing.
Can I use it for a full treatment train?
Use it one step at a time: the concentrate of one step becomes the feed of the next. Reagent addition, batch inventory and product yield need a fuller model.
Related ZLD guide chapters
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Brine Consulting screening tool. Results are not a design guarantee, vendor guarantee, regulatory determination or detailed process design, and do not replace project-specific modelling, pilot testing or professional engineering review.