osmotic-pressure-calculation

This calculator is under construction

This calculator determines the osmotic pressure of a solution containing dissolved solids. The osmotic pressure is based on theoretical calculations and gives you an indication about the operational pressure of a reverse osmosis system. The osmotic pressure can be calculated with the following formula:

(1)

where:

	number of ions produced during dissociation of solute
	osmotic coefficient, unit less
	concentration of all solutes, moles/L
	universal gas constant, 0.083145 L·bar/moles·K
	absolute temperature, K

The factor i is also called the dissociation factor or the van't Hoff factor.

When you have a water analysis you often have the TDS in mg/L. The TDS does not give an indication about how the different solids are partitioned, it means that you cannot know the molar concentrations of the different solids dissolved in water. However, when you are making calculations for seawater the calculator spreads the TDS over Sodium (Na⁺) and Chloride (Cl^-). This is possible because the concentration of these two elements is much higher than the concentrations for other elements in seawater.

The theoretical formula (1) used above is adapted to operational conditions by membrane manufacturers. Formula (2) is used by Dow / Filmtec to calculate the osmotic pressure:

(2)

where:

:sum of molality concentration of all constituents in a solution (moles of solute/kg of solvent)

The molality is calculated with the following formula:

The obtained osmotic pressure with formula (2) is in psi (pounds per square inch). This calculator converts automatically the pressure to bar with the following conversion factor: 1 psi = 6.8948·10^-2 bar.

If you do not have a water analysis you can use the values given in the right column in the input table. The values an indication about the standard seawater composition and brackish water. Click on the SW or BW button to put the values in the input fields of the table.

Table 1: Input table

Element	Concentration	unit	example
Ammonium (NH4⁺)			0.05	-
Potassium (K⁺)			3.3	390
Sodium (Na⁺)			36	10900
Magnesium (Mg²⁺)			6	1310
Calcium (Ca²⁺)			84	410
Strontium (Sr²⁺)			0.7	13
Barium (Ba²⁺)			0.07	0.05
Carbonate (CO₃^2-)			-	-
bicarbonate (HCO₃^-)			265	152
Nitrate (NO₃^-)			4.3	0.6
Chloride (Cl^-)			45	19700
Fluoride (F^-)			0.14	1.4
Sulfate (SO₄^2-)			24	2740
Silica (SiO₂)			9	5
Boron (B)			-	5

TDS

Temperature

Table 2: Output table

TDS
Total molality (mol/kg)
Total molar mass (g/mol)
Osmotic pressure (bar)
Indication about operational pressure

If you want to eliminate one of the chemical elements given in table 1 Lenntech can look to your water analysis and propose you a reverse osmosis installation if it is suited for your application.
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The indication about the operational pressure is given by multiplying the theoretical osmotic pressure by 2. As you can see in the formula the osmotic pressure depends on the temperature. So if you are in an environment with changing water temperatures calculate the osmotic pressure for different temperatures.

Warning: This calculator is accurate for the following parameters:

20000 mg/L <	TDS for SW	< 43000 mg/L
100 mg/L <	TDS for BW	< 15000 mg/L
10° C <	Temperature	< 35° C

The calculations are made using 1 membrane with a production of 0,2 m³/h or (200 L/h).
The membrane used for seawater is the SW 30-4040 from Dow/Filmtec.
The membrane used for brackish water is the BW 30-4040 for Dow/Filmtec.

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Warning: Lenntech BV cannot be held responsible for errors in the calculation, the program itself or the explanation. For questions or remarks please contact us.