Given:

T = 1 minute

TB = 15 minutes

T2 = 4.083 minutes

(1- T1/T2 ) x 100

= SDI

TB

The formula for the SDI is as follows:

SDI = (1 - 1 minute/4.083 minutes) 100/15 minutes = 5.03 silt density index

is known, the concentration of the brine can be calculated for the purpose of estimating scaling concentrations as follows:

Symbols:

Percent Rec. = 100 x the fraction of the feed water that becomes product water

Given:

30 percent of the feed water becomes product

At 30 percent recovery, 70 percent of water contains all the original salt, ∴

1/0.7 x original concentration = final concentration

1

1-Percent Rec. = Concentration factor

100

1

1-30 = 1.429

100

The following equations can be used with membrane manufacturer's water flux constants to calculate a water flux or, by

rearrangement of the equation, a membrane area requirement can be calculated.

Symbols:

Qw = Water flow

Kw = Water flux constant for the membrane

A = Area of membrane

∆P = The pressure drop across the membrane (not including head losses to or from the membrane)

Aπ = The osmotic pressure difference across the membrane

10 pounds per square inch

Usually about:

1,000 milligrams per liter of total dissolved solids

Given:

-7

Kw = 2.53 x 10 gallons/pound-hour

The membrane area, A = 1,000 square feet

The applied pressure, P = 900 pounds/square inch

The osmotic-pressure difference, ∆π = 350 pounds/square inch.

Qw = KwA (∆P - ∆π)

-7

Qw = 2.53 x 10 gallons/pound-hour x 1,000 square feet x 144 square feet x (900 pounds/square inch - 350

pounds/square inch)

Qw = 20 gallons/hour

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