KEVOS® MAKEOS · Hydraulics
Reverse Osmosis Pressure Check (van ’t Hoff Osmotic Pressure, Concentrate End, Net Driving Pressure)
Is the feed pressure of this reverse osmosis unit enough to keep water passing through the membrane at the concentrate end, where the dissolved solids, and so the osmotic pressure, are highest?
Thermodynamic pressure check of a reverse osmosis stage: the osmotic pressure of the feed, the concentrate and the permeate by the van ’t Hoff equation with your dissociation factor and osmotic coefficient, the concentrate strength from a solute mass balance at the recovery and salt passage you enter, the net driving pressure at the feed end and at the concentrate end, and the least feed pressure, against the net driving pressure you require at the concentrate end.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Dissolved solids in the feed | g/L | Mass of dissolved solids per litre of feed water, from a water analysis. |
| Molar mass of the dissolved solute | g/mol | Molar mass of the dissolved solute (for a mixed water, an average formula weight from the analysis). |
| Dissolved particles per formula unit (van ’t Hoff factor) | Number of particles each dissolved formula unit separates into (2 for sodium chloride; 1 for a non-electrolyte). | |
| Osmotic coefficient | Osmotic coefficient of the solution: 1 for an ideal dilute solution, below 1 for most salt solutions, from solution data. | |
| Water temperature | °C | Temperature of the feed water. |
| Recovery (permeate as a share of feed) | % | Permeate flow as a share of the feed flow. |
| Salt passage (permeate strength as a share of feed) | % | Strength of the permeate as a share of the feed strength, from the membrane maker’s data or measurement. |
| Pressures | ||
| Feed pressure (gauge) | bar | Gauge pressure at the inlet of the pressure vessel. |
| Pressure drop from feed to concentrate | bar | Pressure lost along the feed channels from the inlet to the concentrate outlet. |
| Permeate back pressure (gauge) | bar | Gauge pressure on the permeate side, from any height or back pressure in the permeate line. |
| Least net driving pressure at the concentrate end | bar | The smallest net driving pressure you accept at the concentrate end, from the membrane maker’s design guidance or your own practice. |
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: Dissolved solids in the feed
- What it is
- The mass of dissolved solids in each litre of feed water to the reverse osmosis unit, from a laboratory analysis or a conductivity reading converted to dissolved solids.
- Units and format
- Enter a number in g/L: g/L. The form accepts 0.000001 g/L to 400 g/L. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3 g/L as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- All osmotic pressures rise in proportion, so the net driving pressure falls.
- Get it right
- Use the dissolved solids, not suspended solids or hardness alone; seasonal changes can raise it.
What this means: Molar mass of the dissolved solute
- What it is
- The mass of one mole of the dissolved solute, which turns the mass concentration into a molar concentration for the van ’t Hoff equation.
- Units and format
- Enter a number in g/mol: g/mol. The form accepts 1 g/mol to 100000 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 for the same mass and lower osmotic pressures.
- Get it right
- For a mixed water, use an average formula weight weighted by the analysis, not the molar mass of one salt.
What this means: Dissolved particles per formula unit (van ’t Ho…
- What it is
- The number of separate particles each formula unit of the solute forms when it dissolves, since osmotic pressure counts particles: 2 for sodium chloride, 3 for calcium chloride, 1 for sugar.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 10. 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
- All osmotic pressures rise in proportion to it.
- Get it right
- Use the ideal count here and put the non-ideal correction in the osmotic coefficient, not both in one number.
What this means: Osmotic coefficient
- What it is
- The ratio of the real osmotic pressure of the solution to the ideal van ’t Hoff value, which corrects for the interaction between dissolved ions.
- 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 1 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- All osmotic pressures rise in proportion to it.
- Get it right
- Take it from solution data for the concentrate strength, where the check is made; 1 is the ideal dilute case.
What this means: Water temperature
- What it is
- The temperature of the feed water, which enters the van ’t Hoff equation as an absolute temperature.
- 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
- A warmer feed raises the osmotic pressures slightly, in proportion to the absolute temperature.
- Get it right
- Use the actual water temperature; membrane permeability changes with temperature far more than the osmotic pressure does.
What this means: Recovery (permeate as a share of feed)
- What it is
- The share of the feed flow that passes through the membrane as permeate; the rest leaves as concentrate carrying the rejected solids.
- 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 99%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 75% 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 as 1 ÷ (1 − r), raising its osmotic pressure and the feed pressure needed.
- Get it right
- Use the stage or system recovery you plan to run, and check the scaling limits of the water at that recovery.
What this means: Salt passage (permeate strength as a share of f…
- What it is
- The strength of the permeate as a share of the feed strength, the part of the dissolved solids that passes through the membrane.
- 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 2% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More passage puts more solute in the permeate, slightly lowering the concentrate strength and raising the permeate’s osmotic pressure.
- Get it right
- Take it from the membrane maker’s rejection figure for your water: 99 % rejection is 1 % salt passage.
Pressures
What this means: Feed pressure (gauge)
- What it is
- The gauge pressure of the feed water at the inlet of the pressure vessel, delivered by the high-pressure pump.
- Units and format
- Enter a number in bar: bar (1 bar = 100 kPa). The form accepts 0.000001 bar to 200 bar. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 15 bar as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The net driving pressure rises one for one with it at both ends.
- Get it right
- Read it at the vessel inlet, not at the pump outlet, if there is a valve or long pipe between them.
What this means: Pressure drop from feed to concentrate
- What it is
- The pressure lost by the feed flowing along the membrane channels from the vessel inlet to the concentrate outlet.
- Units and format
- Enter a number in bar: bar (1 bar = 100 kPa). The form accepts 0 bar to 100 bar. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2 bar as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger drop lowers the net driving pressure at the concentrate end one for one.
- Get it right
- Measure feed minus concentrate pressure; a rising difference over time points to fouling.
What this means: Permeate back pressure (gauge)
- What it is
- The gauge pressure on the permeate side of the membrane, from the height the permeate is lifted or any back pressure in its line.
- Units and format
- Enter a number in bar: bar (1 bar = 100 kPa). The form accepts 0 bar to 100 bar. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.5 bar as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The net driving pressure falls one for one with it.
- Get it right
- Never let permeate pressure exceed feed pressure; the membrane maker limits back pressure.
What this means: Least net driving pressure at the concentrate e…
- What it is
- The smallest net driving pressure you accept at the concentrate end of the stage, below which the last membranes produce little water, used as the pass or fail limit.
- Units and format
- Enter a number in bar: bar (1 bar = 100 kPa). The form accepts 0 bar to 100 bar. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1 bar as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Only moves the pass or fail line and the least feed pressure; the osmotic pressures do not change.
- Get it right
- Take it from the membrane maker’s design guidance or your operating experience; no value is built in.
Method and formulas
- van ’t Hoff osmotic pressure Π = φ i c R T, with c the molar concentration of the solute.
- Solute mass balance with permeate strength c_p = salt passage × c_f: concentrate c_c = (c_f − r c_p) ÷ (1 − r).
- Net driving pressure = applied pressure − permeate pressure − (Π on the feed side − Π of the permeate); at the concentrate end the applied pressure is the feed pressure less the pressure drop.
- Example: 3 g/L of a 58.44 g/mol salt splitting in two, ideal, at 25 °C: Π = 2.5451 bar in the feed; at 75 % recovery the concentrate is 11.82 g/L with Π = 10.028 bar, leaving 2.5231 bar of net driving pressure at the concentrate end from a 15 bar feed; the least feed pressure is 13.477 bar.
Limitations
- The osmotic coefficient is taken as constant from feed to concentrate; it changes with concentration, so enter the value for the concentrate strength for a closer tail check.
- No concentration polarisation at the membrane surface, which raises the osmotic pressure there.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check that a reverse osmosis pump can reach the recovery wanted
- Find the least feed pressure for a feed water and recovery
- See why raising recovery needs more pressure
Who it is for
- Water treatment engineers
- Utilities and process engineers
- Maintenance technicians
What you get
- Concentrate and permeate strength
- Osmotic pressures of feed, concentrate and permeate
- Net driving pressure at each end and the least feed pressure
Interpreting the result
- The concentrate end sets the limit: as recovery rises the concentrate strength, and its osmotic pressure, rise as 1 ÷ (1 − r).
- This is the thermodynamic minimum; the membrane’s permeability then decides how much flow each bar of driving pressure gives.
Before relying on the result
- Run the membrane maker’s projection software for the actual water analysis before buying a pump or membranes.
- Measure feed, concentrate and permeate conductivity and pressures at commissioning.
References
- Linder, B., Thermodynamics and Introductory Statistical Mechanics (Wiley-Interscience, 2004), section 10.4.4, printed pp. 112–113: osmotic pressure and the van ’t Hoff equation Π = R T c_B for dilute solutions. Method reference; no source text, tables or examples are reproduced.
- IUPAC Compendium of Chemical Terminology (Gold Book), entry ‘osmotic coefficient’: the correction for non-ideal solutions.
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
Recovery and the concentrate
In Reverse Osmosis by the Numbers
What it covers: Water and salt mass balances for a reverse osmosis stage: recovery, salt passage, concentrate strength, the log-mean concentration factor and how recovery sets the feed pressure.
Useful alongside · Library collection
Clean water as an engineered system: barriers, gravity and supply security, and lessons for operations
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What it covers: Urban water supply saved more lives than almost any other engineering. How treatment, sewerage, storage and desalination developed, and what they teach about barriers and monitoring.
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.