Seawater is to be desalinated by reverse osmosis using the scheme indicated in t

Question

Seawater is to be desalinated by reverse osmosis using the scheme indicated in the Figure. Using the data given in the

4. Seawater is to be desalinated by reverse osmosis using the scheme indicated in the Figure. 1000 kg/hr Sea Water Using the data given in the figure, determine a) Convert ppm to mass fraction. b) the rate of waste brine removal c) rate of desalinated water production. d) the fraction of the brine recycled. | Reverse Brine Waste (B) 5.25 % Salt 40% 1000 kg/hrOsmosis Osmosis 3.1% Salt SCell D Desalinised Water 500 ppm Salt

Explanation / Answer

a) 500 ppm =0.05%=0.05/100 =0.0005 mass fraction

b) Recycle (R) and Waste (W ) will have same composition. Hence salt in Recylce= 5.25%

Feed =1000 kg/hr and contains salt at 3.1% salt entering = 1000*3.1/100= 31 kg/hr

salt in Recycle = R*5.25/100 =R*0.0525

Total salt enterinf = 31+R*0.0525 (1)

It is given that water at inlet contains 4.1% salt. Hence salt at inlet= (1000+R)*4/100 (2)

Eq.1 and Eq.2 are equal 31+R*0.0525=(1000+R)*4/100

31+R*0.0525= 40+0.04R

R*(0.0525-0.04)= 9

R=720 kg/hr

Writing overall balance of the plant F= B+D

1000= B+ D , D= 1000-B (3)

Salt balance gives 1000*3.1/100 = B*5.25/100 + D*0.0005 (4)

from Eq.3, 31= B* 5.25/100+(1000-B)*0.0005

31= B*5.25/100 +1000*0.0005 -B*0.0005

31= 0.5 +B(0.0525-0.0005)

30.5= B*(0.052)

B= 30.5/0.052= 586.5 Kg/hr D= 1000-586.5= 413.5 Kg/hr, Rate of brine waste removal = 586.5 kg/hr

Rate of desalinated water production= 413.5 kg/hr

Treated Outlet of RO plant contains B = 413.5 kg/hr and R= 720 kg/hr

Fraction of brine recycled= (720/{720+413.5)}=0.635

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