How to Calculate the Osmotic Pressure and Net Driving Pressure for RO membranes: -

1. Calculations for osmotic pressure: -

by using the ideal gas equation

πV ? nRT, π ? nRT/V

where

π ≡ Osmotic pressure (Bar).

R ≡ the ideal gas constant (m3?bar/K?mol).

n ≡ the number of moles (mol).

V≡ volume?(m3).

T ≡ the temperature (K).

-Suppose you have given the following data

no. of mol =1.396 mol for TDS 4200ppm

R=0.083144? m3?bar/K?mol

T= 25 C°

V = 1 m3

.:. π = 1.396 (mol)* 0.0831441 (m3.bar/K.mol) * (273+25)/ m3

.:. π = 34.59 Bar 34.59*14.5 = 500 psi

that mean each 1000ppm need 12psi.

excel sheet have been posted 26/07/2024 includes all calculations.

What is the net driving pressure?

The net driving pressure?is the measure of the actual driving pressure available to force the water through the membrane. As net driving pressure increases, the flux increases also.

Calculations for net driving pressure: -

NDP = π+k(Flux Rate)

Flux Rate(GFD) =?Permeate Flow(G/D)/Total active area of membranes ft2.

where

π ≡ Osmotic pressure (psi).

NDP ≡Net driving pressure Psi.

K≡ the constant flow for the membrane.

1. Calculate K constant for Toray TM820M-400 model

given data from Toray

Test Conditions:- Feed water pressure 800 psi, Membrane Area 400 Ft2 ,Feed water temperature 25°C Product Flow Rate7000 G/D, Feed water concentration 32,000 mg/L as NaCl Recovery rate 8%.

Flux Rate (GFD) = 7000 (G/ D)/400 Ft2 = 17.5 GFD

NDP = π+k(Flux Rate) .:. 800psi= 500psi + 17.5 k .:. k= 17.4

2. Then calculate NDP

the flux rate according the Toray should be between (8-12)GFD

NDP = π+k(Flux Rate)

NDP= 500+17.4*10 .:.NDP= 672psi