Design Calculation Of An Reverse Osmosis (RO) Module

               Reverse osmosis is the most important technique of desalination of brackish (1000-5000 ppm salt) or sea water (about 35,000 ppm or 3.5% salt). Its potential was identified in the 1950s. But commercial exploitation was not possible until the 1960s. The development of high flux asymmetric cellulose acetate membrane by the phase inversion technique of Lobe and Sourirajan (1963) opened up commercial exploitation of this very important strategy of desalination. Currently, over 12,500 industrial scale desalination plants are operating worldwide with an average production rate of about 23 million cubic meter per day of potable water (less than 200 TDS). The largest sea water desalination plant is in Jeddah, Saudi Arabia, having a capacity of 56,800 cubic meter per day of potable water.

   

Problem Statement And Given Data:

It is required to design an reverse osmosis (RO) module for production of 1500 m³/day potable water containing not more than 250 ppm salt from sea water containing 34 g salt per liter. A proprietory asymmetric cellulose acetate membrane with an inherent salt rejection ability of 98% is to be used. The water permeation coefficient is 0.043 m³/m².day.atm. The recovery of the feed water should be 35% and an operating pressure of 70 atm gauge is suggested. The permeate side is at essentially atmospheric pressure. I spiral wound module of 5 m² effective membrane area each is used, how many modules in parallel are required? What fraction of the input power can be recovered from the retentate if a turbine of 70% efficiency is used for energy recovery? The osmotic pressure of 5% brine (linear in salt concentration) is 39.5 atm.

Solution:

Given: Q_p/Q_fi = 0.35 = ϴ_wo ; rejection, R’ = 0.98 ; salt concentration in the feed, C_fi = 3.4%.

           Retentate concentration, C_fo = C_fi (1- ϴ_wo)^-R = 3.4 x (1-0.35)^-0.98 = 5.186%.

Exit concentration of the mixed permeate water, C_p = 250 ppm = 0.025%; its osmotic pressure = 0.2 atm.

   Osmotic pressure of the feed brine (3.4%) = (39.5/5) x (3.4) = 27.8 atm.

Osmotic pressure of the exit brine (5.186%) = (39.5/5) x (5.186) = 42.08 atm.

Take the average osmotic pressure, ∆π value to calculate the effective pressure driving force (neglect the osmotic pressure of permeate).                                         

                                         (∆π)_av  = (27.8 + 42.08)/2 = 34.94 atm.

                              (∆P - ∆π)_av  = (70 - 34.94) = 35.06 atm.
                               

                                Water flux = (0.043) x (35.06) = 1.51 m³/m².day.

Total membrane area required = 1500/1.51 = 993 m²

    Number of modules = 993/5 = 199, say 200

Calculation of power recovery:

Given Q_fi = Q_fo + Q_P, Q_P = 1500 m³/day.

Now make a salt balance.

(Q_fo + 1500) x (0.034) = (Q_fo) x (0.05186) + (1500) x (0.00025) = Q_fo = 2835 m³/day.

Power efficiency (efficiency, η = 0.7) = (Q_fo x ∆P) x η = (2835 m³/day) (70 atm)(0.7).

= (2835/ (24 x 3600)) x [((70) (1.013) (1x10⁵) N/m²] x (0.7) = 1.692x10⁵ J/s = 163 kW.