Full-scale reverse
osmosis (RO) units usually consist of a set
of pressure vessels holding up to six (1 m long) membrane modules
in series. Since process parameters and water composition change substantially
along the filtration channel in full-scale RO units, relevant thermodynamic
parameters such as the ion activities and the osmotic coefficient
change as well. Understanding these changes will lead to more accurate
fouling prediction and to improvement in process and equipment designs.
In this article, a rigorous thermodynamic model for RO concentrates
in a full-scale module is developed and presented, which is capable
of accounting for such changes. The change in concentrate composition
due to permeation of water and ions is predicted locally in the membrane
filtration channel. The local ionic composition is used to calculate
the local activity coefficient and osmotic coefficient along the membrane
channel through the Pitzer model for each modeled anion and cation.
The approach developed was validated against related literature data,
showing that Pitzer coefficient predictions were satisfactory. The
spatial variation model was verified experimentally. It was found
under the modeled conditions of high recovery that individual solute
activity coefficients could be diminished up to 65%, in our case for
sulfate, from their initial value from the membrane inlet to the outlet,
and the water osmotic coefficient increased 3% as concentrate salinity
increased from the membrane inlet to the outlet. Modeled at moderate
recovery, the sulfate still achieved a statistically significant drop
of 34% and an opposing trend of a decrease of 0.5% for the osmotic
coefficient. These variations in internal water chemistry along the
channel can significantly impact predicted recovery, fouling propensity,
and permeate quality. Fouling prediction with our approach was also
assessed through a theoretical fouling index to demonstrate the significance
of ion activity over concentration-based calculations. Additionally,
data from a pilot plant RO filtration channel was used to carry out
a sensitivity analysis to show the capability of the developed model.