TM 5-813-8
c. Two-Way Blends
for Chloride
500y + 50x 250(500)
x = 500 - y
∴500y + 50(500) - 50y 250(500
or y 500(250 - 50)/(500 - 50)
for Total Dissolved Solids
851y + 95.5x 500(500)
x = 500 - y
∴851y + 95.5(500) - 95.5y 500(500)
or y 500(500 - 95.5)/(851 - 95.5)
For sulfate, neither water y nor x are limited.
for Sulfate
400z + 1.2x 250(500)
x = 500 - z
∴400z + 1.2(500) - 1.2z 250(500)
or z 500(250 - 1.2)/400 - 1.2)
for Total Dissolved Solids
792z + 95.5x 500(500)
x = 500 - z
∴792z + 95.5(500) - 95.5z 500(500)
or z 500(500 - 95.5)/(729 - 95.5)
For Chlorides, neither water x nor z are limited.
d. Cost
Cxx + Cyy + Czz = C
Step 2: Project constraints onto water balance equation to eliminate one variable (preferably the most expensive water).
a. Chloride 50x + 500y + 30z 125,000
- 50x - 50y - 50z = - 25,000
450y - 20z 100,000
b. Sulfate 1.2x + 30y + 400z 125,000
-1.2x - 1.2y - 1.2z = - 600
28.8y + 398.8z 124,400
95.5x + 851y + 729z 250,000
c. Total Dissolved Solids
-95.5x - 95.5y - 95.5z = - 47,750
755.5y + 633.5z 202,250
Step 3: Graph resulting constraint questions, two dimensions at a time in the M dimensional space required (i.e., for
blending 10 waters, all combinations of 9 things taken two at a time; for this example of 3 waters all combinations
of 2 things taken two at a time). See figure A-22.
Step 4: Solve all constraints simultaneously to identify corners and edges. The most economical blend will almost always
occur at a corner, but it is possible that an entire range of blend values along a constraint edge will be equally
economical.
a. Chloride - Sulfate Pair
=
SO4 = 28.8y + 398.8z 124,400
-
(398.8/20)Cl = 8973.0y-398.8z 1,994,000
9001.8y 118,400
A-34
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