A-5. Sample of multiple component water blend optimization. A base on a volcanic island in the Pacific is to be
expanded. While inadequate disinfection has often been blamed for the maladies of newcomers, the analysis requested
before pumping and drilling tests are continued indicate a hard, high total dissolved solids, sulfate-rich fresh water lens on
the island. For these reasons you have been assigned to direct a study to evaluate the various desalination options. You
have good reason to believe that both water quantity and brine disposal will prevent the simple desalination of island well
water to supply the projected 500 gallons per minute of potable water. A product-staged or double-pass reverse osmosis
sea water desalination facility will apparently be required.
= The flow rate of fully treated relatively pure second-stage reverse osmosis product water used in
y = The flow rate of the first-stage reverse osmosis product water used to blend.
z = The flow rate of island well water used to blend.
Cx = The unit cost of second-stage reverse osmosis water (water x).
Cy = The unit cost of first-stage reverse osmosis product water (water y).
Cz = The unit cost of island well water (water z).
C = The unit cost of final blended water.
Given: The high quality two-pass water (water x) contains:
50.0 mg Cl /liter
1.2 mg SO4 /liter
and 95.5 mg TDS/liter
The single-pass water (water y) contains:
500 mg Cl /liter
30 mg SO4 /liter
85 mg TDS/liter
The well water presently being used (water z) contains:
30 mg Cl /liter
400 mg SO4 /liter
729 mg TDS/liter
The final blend must meet TB MED 576 standards or
Cl 250 mg Cl /liter
SO4 250 mg SO4 /liter
TDS 500 mg TDS/liter
Σ Flowi Concentrationi Flow Total = Final Concentration
1=n Flowi Costi/Gallon Flow Total = Final Unit Water Cost = C
Step 1: List Equations
a. Water Balance
x + y + z = 500
b. Blend Concentration Constraints
50x + 500y + 30z 500(250)
1.2x + 30y + 400z 500(250)
Total Dissolved Solids
95.5 + 851y + 729z 500(500)