1. Chloride limited

y < 500 (250 - 50.0)/(500 - 50.0)

y < 222.2 so x 277.8

2. TDS limited

y < 500(500 - 95.5)/(851 - 95.5)

y < 267.7 so x > 232.3

3. Sulfate cannot limit since both waters have sulfates below 250. (The intercept at 4319.4 would require a

removal flow of -3819.4 of second-stage product water x to concentrate the split stream to 250 mg SO4/liter.)

f. Locate Inside Intercepts

1. Since 311.9 < 319.25,

Sulfate limits use of water

z to z < 311.9 with

x > 188.1

2. Since 222.2 < 267.7,

Chloride limits use of water

y to y < 222.2 with

x > 277.8

Step 5:

Identify the coordinates of the corners of the convex polyhedron of acceptable blends.

In this case, the polyhedron is a pentagon with 5 corners.

The coordinates of the corners of acceptability are:

x

y

z

1-

500

0

0

2-

577.8

222.2

0

3-

188.1

0

311.9

4-

182

6.5

311.5

5-

224

224.5

51.5

Step 6:

Use Cost Equation to make each corner and edge a minimum cost solution (use the graph to identify adjacent

corners).

a. All Second-Stage Product (No Blending)

Cx 500 < 188.1 Cx + 311.9 Cz

and Cx 500 < 277.8 Cx + 222.2 Cy

Therefore, don't blend at all if Cx < Cz and Cx < Cy

b. Blend of x and y Waters Only

500Cx > 222.2 Cx + 277.8 Cy and 222.2 Cx + 277.8C y < 224 Cx + 224.5 Cy + 51.5 Cz

or Cx > Cy

and 53.8 Cx < 2.3 Cy + 51.5 Cz

or Cx < 0.0427 Cy + 0.95725 Cz

Therefore, if the cost of water x was greater than the cost of water y, and less than 0.0427 Cy + 0.957 Cz then the

blend of single- and double-pass sea water reverse osmosis products would be more economical than any blend

containing well water.

c. Blend of x and z Water Only

500 Cx > 188.1 Cx + 311.9 Cz and 188.1 Cx + 311.9 Cz < 182 Cx + 6.5 Cy + 311.5 Cz

or Cx > Cz

and 6.1 Cx + .4 C2 < 6.5 Cy

or Cx < 1.066 Cy - 0.066 Cz

Therefore, if the cost of water x was greater than the cost of water z, but less than 1.066 Cy - 0.066 Cz, then the

blend of well water and double-pass sea water reverse osmosis product would be more economical than any blend

containing any single-pass waters.

d. Blend at Point A Figure A-22 containing a small amount of single-pass reverse osmosis water y.

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