Page 376 - Water and wastewater engineering

REVERSE OSMOSIS AND NANOFILTRATION 9-15

In mg/L this is

(2 58 10 3 moles/L )(98 000 mg/mole ) 253 mg/LLof pure acid
.
,
Comments:
1. This dose is conservatively high because, as noted in Example 9-1 , the activities were
not considered.

2. Commercial sulfuric acid is not pure. Commercial sulfuric acid is about 77% pure. The
commercial acid dose would be 253 mg/L/0.77 328.57 or about 330 mg/L.

3. Using sulfuric acid can increase the sulfate concentration enough to cause precipitation
of calcium sulfate. If this is a problem, hydrochloric acid is used.

Membrane Element Design. Equations 9-5 and 9 -6 are used to design a membrane element.
The fluxes of water and solute cannot be calculated across the entire membrane because the net
transmembrane pressure declines continuously along the length of the membrane element. This
is a result of headloss in the feed channels and changes in osmotic pressure due to concentra-
tion of salts. Thus, fluxes of both water and solute are dependent on position in the element. To
account for these changes, the design procedure is to numerically integrate Equations 9-5 and 9-6
along the element. Membrane manufacturers provide software to perform these calculations. This
software includes temperature, osmotic pressure, limiting salt solubility, concentration polariza-
tion, mass transfer rates, and permeate water quality. It is specific to the manufacturer’s product.
These programs do not yield final design specifications. They are only tools for developing and
testing various system configurations, and their output should not be regarded as completed de-
signs.

Membrane Array Design. The membrane array design is based on the desired recovery. Mem-
brane arrays are generally one to three stages with multiple elements connected in series in each
stage. Typical permeate recovery rates for a one-, two-, or three-stage arrays with six 1 m long
elements in series in a pressure vessel are as follows (AWWA, 1999; Bergman, 2005):

• One stage: 50%.
• Two stages: 50% but 75%.
• Three stages: 90%.

To achieve 64 percent recovery of a 100 L/s feed water, for example, a 2:1 array could be
used where the first stage has two pressure vessels, each operating at 50 L/s and 40 percent recov-
ery, and the second stage has one pressure vessel operating at 60 L/s and 40 percent recovery. The
permeate flow rate from the first stage would be (50 L/s)(0.40)(2 pressure vessels) 40 L/s. The
concentrate (100 L/s 40 L/s 60 L/s) would flow to the second array. The permeate flow from
the second stage would be (60 L/s)(0.40)(1 pressure vessel) 24 L/s. The total permeate flow
from the system would be 40 L/s 24 L/s 64 L/s. The recovery would be (64 L/s/100 L/s)
(100%) 64%.