Question

Water is to be desalinized by reverse osmosis using a thin film composite membrane. determine the required membrane area, rejection rate, and the concentration of the concentrate stream.

Given:

Feed flowrate = 20,000 m³/day, Influent TDS = 2,000 g/m³ , Permeate TDS = 400 g/m³? , Net operating pressure = 2,800 kPa ,

k_W, Flux coefficient = 1.0 x 10^-6 m/s-bar , k_i, mass transfer rate coefficient = 6.0 x 10^-8 m/s , recovery = 89%

Answer 1

(1) Concentration of the concentrate stream

Recovery = 89%

Feed flow rate = 20,000 m3/day

Feed TDS = 2,000 g/m3

Permeate TDS = 400 g/m3

Permeate flow rate = 0.89*20,000

= 17,800 m3/day

Reject flowrate = 20,000 - 17,800

= 2,200 m3/day

A simple mass balance gives,

(20,000*2000) = (17,800*400) + (2,200*x)

x = 14,945 g/m3

(2) Rejection rate

Rejection rate = 1 - Cp/Cf

= 1 - (400/2,000)

= 0.8

= 80%

(3) Area = Permeate flowrate/(flux*pressure)

First we need to obtain unit consistency.

(i) Permeate flowrate = 17,800/(24*36) = 20.6 m3/s

(ii) Net operating pressure = 2800000/100000 = 28 Pa

Area = 20.6/(1.0x10-6 * 28)

= 735,780 m2