TM 5-813-8
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.
A-37
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