KEVOS® MAKEOS · Engineering
Reverse Osmosis Concentrate-End Check (Osmotic Coefficient, Concentrate Osmotic Pressure, Least Feed Pressure)
For this salty feed water and recovery, what osmotic pressure must a reverse osmosis unit overcome at the concentrate end, and is my feed pressure high enough to keep water passing the last membrane?
Feed pressure check for a reverse osmosis stage: the molar concentration from the dissolved solids and the salt’s molar mass, the osmotic pressure from the osmotic coefficient, ions per formula unit and absolute temperature, the permeate and concentrate concentrations from the salt rejection and recovery by a solute balance, the net driving pressure at the feed end and at the concentrate end after the element pressure drop and permeate back pressure, and the least feed pressure that keeps the required net driving pressure at the concentrate end.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Feed dissolved solids | g/L | Total dissolved solids of the feed from a water analysis. |
| Molar mass of the dissolved salt | g/mol | Molar mass of the salt the dissolved solids are counted as (sodium chloride for seawater-like water). |
| Ions released per formula unit | Ions each formula unit releases in solution (2 for sodium chloride). | |
| Osmotic coefficient | Osmotic coefficient of the solution, from property data for the salt and concentration. | |
| Feed temperature | °C | Feed water temperature. |
| Membrane stage | ||
| Recovery | % | Permeate flow as a share of feed flow. |
| Salt rejection | % | Share of the salt the membrane holds back. |
| Feed pressure at the membrane inlet | bar g | Gauge pressure at the membrane inlet. |
| Pressure drop along the elements | bar | Pressure lost along the elements from feed to concentrate. |
| Permeate back pressure | bar g | Gauge pressure on the permeate side. |
| Least net driving pressure at the concentrate end | bar | Least net driving pressure the membrane maker wants at the last element. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Feed dissolved solids
- What it is
- The mass of salts dissolved in each litre of feed water, from a water analysis or a calibrated conductivity reading.
- Units and format
- Enter a number in g/L: g/L. The form accepts 0.01 g/L to 300 g/L. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 35 g/L as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Every osmotic pressure rises in proportion to it.
- Get it right
- Seawater is about 35 g/L and brackish waters a few g/L; convert mg/L by dividing by 1000.
What this means: Molar mass of the dissolved salt
- What it is
- The mass of one mole of the salt the dissolved solids are counted as, used to turn grams per litre into moles per cubic metre.
- Units and format
- Enter a number in g/mol: g/mol. The form accepts 1 g/mol to 2000 g/mol. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 58.44 g/mol as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger molar mass means fewer moles per litre and lower osmotic pressures.
- Get it right
- Sodium chloride is 58.44 g/mol; for mixed waters use the analysis to choose a representative salt.
What this means: Ions released per formula unit
- What it is
- The number of separate ions one formula unit of the salt splits into when dissolved; each ion adds to the osmotic pressure.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 10. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Osmotic pressures rise in proportion to it.
- Get it right
- Sodium chloride gives 2, calcium chloride 3 and magnesium sulfate 2.
What this means: Osmotic coefficient
- What it is
- The factor by which the real solution’s osmotic pressure differs from that of an ideal dilute solution of fully separated ions at the same concentration.
- Units and format
- Enter a plain number with no unit. The form accepts 0.1 to 2. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.92 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Every osmotic pressure is directly proportional to it.
- Get it right
- It is below 1 for most salts at moderate strength and varies with concentration; take it from property data for the salt.
What this means: Feed temperature
- What it is
- The temperature of the feed water at the membranes, which sets the absolute temperature in the osmotic pressure.
- Units and format
- Enter a number in °C: degrees Celsius. The form accepts 0 °C to 100 °C. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 25 °C as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Osmotic pressures rise in proportion to the absolute temperature.
- Get it right
- Use the actual feed temperature; membranes also pass more water when warm, which this check does not model.
Membrane stage
What this means: Recovery
- What it is
- The share of the feed flow that leaves as permeate (product water); the rest leaves as concentrate carrying the rejected salt.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 1% to 95%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 45% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Raising it concentrates the reject stream sharply, raising the osmotic pressure at the concentrate end.
- Get it right
- Use the stage or system recovery you are checking: permeate flow divided by feed flow.
What this means: Salt rejection
- What it is
- The share of the dissolved salt that the membrane holds back, so that only the remainder passes into the permeate.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 0% to 100%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 99.5% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Lower rejection puts more salt in the permeate, raising its small osmotic pressure and the driving pressure slightly.
- Get it right
- Take the membrane maker’s nominal or measured rejection; it falls as membranes age.
What this means: Feed pressure at the membrane inlet
- What it is
- The gauge pressure of the feed water entering the first membrane element, delivered by the high-pressure pump.
- Units and format
- Enter a number in bar g: bar g. The form accepts 0 bar g to 150 bar g. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 60 bar g as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Every bar added raises the net driving pressure at both ends by a bar.
- Get it right
- Read it at the membrane inlet, after any pressure loss through the pump discharge piping.
What this means: Pressure drop along the elements
- What it is
- The pressure lost by the feed-concentrate stream as it flows along the membrane elements from the inlet to the concentrate outlet.
- Units and format
- Enter a number in bar: bar (1 bar = 100 kPa). The form accepts 0 bar to 20 bar. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.5 bar as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Lowers the driving pressure at the concentrate end bar for bar.
- Get it right
- Use the measured feed-to-concentrate pressure difference; it rises as the elements foul.
What this means: Permeate back pressure
- What it is
- The gauge pressure on the permeate side of the membranes, set by permeate piping, tanks and any downstream use.
- Units and format
- Enter a number in bar g: bar g. The form accepts 0 bar g to 20 bar g. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.5 bar g as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Lowers the driving pressure at both ends bar for bar.
- Get it right
- Include the static head of a raised permeate tank and any back-pressure valve.
What this means: Least net driving pressure at the concentrate e…
- What it is
- The smallest net pressure across the last membrane element that keeps it producing enough water, as asked for by the membrane maker or your design.
- Units and format
- Enter a number in bar: bar (1 bar = 100 kPa). The form accepts 0 bar to 50 bar. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3 bar as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Moves the pass line and the least feed pressure; the calculated driving pressures do not change.
- Get it right
- Take it from the membrane maker’s design guide for the element type.
Method and formulas
- Molar concentration c = TDS ÷ M; osmotic pressure Π = φ ν c R T, the dilute-solution form of the osmotic pressure relation with the osmotic coefficient φ (Guggenheim §5.10, §5.16, §5.28).
- Permeate c_p = (1 − rejection) c_f; concentrate c_c = (c_f − r c_p) ÷ (1 − r) for recovery r, by a salt balance.
- Net driving pressure at the concentrate end = p_f − Δp_elements − p_permeate − (Π_c − Π_p); least feed pressure = required NDP + Δp_elements + p_permeate + Π_c − Π_p.
- Example: 35 g/L of sodium chloride at 25 °C has 27.318 bar of osmotic pressure; at 45 % recovery the concentrate reaches 49.557 bar, leaving 8.5797 bar of driving pressure from 60 bar g; 54.42 bar g is the least feed pressure.
Limitations
- One osmotic coefficient for all streams; it changes with concentration, so use a value for the concentrate where it matters.
- Salt at the membrane surface is more concentrated than the bulk (concentration polarisation), so the real osmotic pressure there is higher.
- Mixed waters are treated as one salt; this is a screening check, and the membrane maker’s design program governs the final design.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check whether a high-pressure pump can reach the recovery you want
- See how much osmotic pressure rises as recovery increases
- Estimate the least feed pressure for a new feed water
Who it is for
- Water treatment engineers
- Process engineers
- Plant operators
What you get
- Feed, concentrate and permeate osmotic pressures
- Net driving pressure at both ends
- Least feed pressure
Interpreting the result
- The concentrate end sets the pressure: osmotic pressure there rises as 1 ÷ (1 − recovery), so the last few percent of recovery cost the most pressure.
- A negative driving pressure at the concentrate end means the last elements make no water.
Before relying on the result
- Compare the least feed pressure with the membrane maker’s projection for the same water analysis and temperature.
References
- E. A. Guggenheim, Thermodynamics: An Advanced Treatment for Chemists and Physicists, 5th revised edition (North-Holland, 1967), §5.10 (osmotic coefficient), §5.16 (osmotic pressure), §5.28 (volume concentrations), §7.06–7.08 (electrolyte solutions). Method reference; no text, tables or examples are reproduced.
Learn the Concepts Behind This Tool
These KEVOS® Library readings explain the method this tool uses, with worked examples.
Method explained here · KEVOS® original book
Osmotic pressure: the pressure to beat
In Reverse Osmosis by the Numbers
What it covers: Why salty water pulls fresh water through a membrane, the van 't Hoff osmotic pressure with an osmotic coefficient, and how to calculate it from an ion analysis rather than one figure.
KEVOS® tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.