Water tools

Osmotic pressure from TDS or an ion analysis

Osmotic pressure sets the floor under RO feed pressure. It depends on how many dissolved particles are in the water, so a full ion analysis beats a TDS figure, and small ions count more than large ones per milligram.

Water described by

Total dissolved solidsmg/L

Temperature°C

Osmotic coefficient φ0.93 to 1.03 for sodium chloride over the desalination range; 1.0 if unknown.

Recovery (for the concentrate)%

Osmotic pressure of the feed

1.70bar

Osmotic pressure of the concentrate

6.79bar

At full rejection the concentrate carries 1/(1 − recovery) times the feed solutes.

Dissolved species

68.4mmol/L

Pressure per 1,000 mg/L

0.85bar

How it works

Van 't Hoff relation with an osmotic coefficient for non-ideality:

π = φ C R T C = \sum_{i} \frac{n_{i} m_{i}}{1000 M_{i}}

(1)

where C is the total molar concentration of dissolved species (each ion counted separately, a salt such as NaCl giving two), R = 0.083145 L·bar/(mol·K), T in kelvin, m_i the mass concentration in mg/L and M_i the molar mass. Effects of several solutes are additive. At full rejection the concentrate carries

π_{c} = \frac{π}{1 - r}

(2)

where

$π$: osmotic pressure, bar
$φ$: osmotic coefficient
$C$: total molar concentration of dissolved species, mol/L
$R$: gas constant, 0.083145 L·bar/mol·K
$T$: absolute temperature, K
$n_{i}$: number of ions solute i dissociates into
$m_{i}$: mass concentration of solute i, mg/L
$M_{i}$: molar mass of solute i, g/mol
$π_{c}$: osmotic pressure of the concentrate, bar
$r$: recovery, fraction

TDS treated as sodium chloride gives about 0.8 bar per 1,000 mg/L at 25 °C. Real seawater sits roughly 10% below the NaCl value at the same TDS because it holds heavier ions. The mole fraction of water is what matters, not solute identity, so on a mass basis the lightest solutes produce the most pressure.

Osmotic pressure from TDS or an ion analysis

How it works

Related reading