TM 5-813-8
182 Cx + 6.5 Cy + 311.5 Cz < 224 Cx + 224.5 Cy + 51.5 Cz and 182 Cx + 6.5 Cy + 311.5 Cz
< 188.1 CX + 311.9 Cz
or
260 Cz < 42 CX + 218 Cy
and 0.4 Cz > 6.5 Cy - 6.1 Cx
or
16.25 Cy - 15.25 Cx < Cz c 0.1615 Cx + 0.838 Cy
Therefore, if the cost of well water is less than 0.1615 Cx + 0.838 Cy and greater than 16.25 Cy - 15.25 Cx, then
the use of 6.5 gallons/minute of first-stage reverse osmosis product water in a blend to reduce the amount of
second-stage product needed, to dilute well water, from 188.1 gallons/minute to 182 gallons/minute will be
economical.
e. Blending at Point B Figure A-22
using 224 gallons/minute of water x
224.5 gallons/minute of water y
and 51.5 gallons/minute of water x
224 Cx + 224.5 Cy + 51.5 C, < 182 Cx + 6.5 Cy + 311.5 Cz, and 224 Cx + 224.5 Cy + 51.5 Cz
< 277.8 Cx + 222.2 Cy
or
42 CX + 218 Cy < 260 Cz
and 51.5 Cz < 53.8 Cx - 23 Cy
or
0.1615 Cx + 0.838 Cy < Cz
and Cz < 1.0447 Cx - 0.0447 Cy
Therefore, if the cost of well water is greater than 0.1615 Cx + 0.838 Cy and less than 1.0447 Cx - 0.0447 Cy, then
the use of a blend of 51.5 gallons/minute of product-staged double-pass reverse osmosis water, with 224.5
gallons/minute of first-pass reverse osmosis product water and 224 gallons/minute of well water, would be the
most economical blend.
Step 7: Make Reasonable Assumptions and Worst Case Scenarios
a. The cost of second-stage reverse osmosis product water must be greater than the cost of first-stage reverse
osmosis product water, because second-stage water is made from first-stage water.
b. The maximum recovery available with most triple-reject-staged reverse osmosis membrane module assemblies is
85%.
c. The second-stage low-pressure desalination of first-stage product water is almost always less expensive than the
initial first-stage desalination of sea water.
d. The expansion of a drain field collection or a well field system is almost always cheaper than the desalination of
even brackish water.
Step 8: Put Assumptions and Scenarios into Mathematical Form
a. Using 2 from step 7
Cx > Cy
b. Using a and b from step 7
CX > 1/.85 Cy = 1.176 Cy
c. Using c and a from step 7
Cx < 2 Cy usually
d. Using d from step 7
C2 < Cy usually
e. Using a and d above
Cx > Cy > Cz usually
f. Using c and d above
1/2 Cx < Cy > Cy usually
g. Using b and d above
.85 Cx > Cy > Cz usually
A-38
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