Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)


Chemical Engineering


Dr. James M. Dickson


The present research investigates, both theoretically and experimentally, transport phenomena in reverse osmosis (RO) membranes.

In order to properly describe and predict RO membrane performance, and to properly design RO units, a good understanding of the fundamentals of the membrane transport is needed; this means that a strong transport model needs to be developed. This research is concerned with the development of such a model. As well, the effects of system pressure, concentration, and temperature on the performance of thin-film composite, aromatic polyamide RO membranes with sodium chloride and some other salts are examined both experimentally and theoretically.

The present research investigates the development of a powerful, novel transport model for reverse osmosis, which does not have the serious shortcomings of the previous models, and an experimental evaluation of this model. As a result, a mechanistic model, called the Modified Surface Force-Pore Flow (MD-SF-PF) model, has been developed. The model assumes that transport through the membrane takes place in very fine pores, and the pores are modeled as perfect cylinders. In this two-dimensional model, a balance of applied and frictional forces acting on the solute in a pore is given as a function of radial and axial positions. The model incorporates a potential field inside the membrane which is responsible for the partitioning effect (at the two sides of the membrane) and, in part, determines the membrane performance. A computer code has been developed, based on the "orthogonal collocation" method of weighted residuals, which has proven to be very efficient and precise to solve the complicated differential equations of the transport models.

Three models have been developed during the present research: i) the Modified Surface Force- Pore Flow (MD-SF-PF) model, briefly described above, which is appropriate for solvent-membrane affinity systems (such as salt-water systems); a temperature-extended version of this model has also been derived; ii) the Extended MD-SF-PF model (a generalized form of the MD-SF-PF model) which can be used to describe or predict any type of RO system, that is, both solvent-membrane affinity systems, such as sodium chloride-water system, and solute-membrane affinity systems, such as toluene-water system; and iii) the Modified Finely Porous Model (MD-FPM) which is a one-dimensional transport model, and can describe simple systems.

Experimental data are used to determine model parameters. Also, experimental data can be compared to model predictions. The following experimental plan was undertaken using aromatic polyamide (FilmTec) FT30 membranes: i) experiments with 2000 ppm aqueous solutions of sodium chloride (brackish water concentration) in the range 350-7000 kPa and 5-60°C (a few experiments at 25°C and 5000, 10000, and 15000 ppm sodium chloride solutions were also performed (Phase I)); ii) experiments with 2000 ppm potassium chloride, lithium chloride, and lithium nitrate at 25°C and 500-4000 kPa (Phase II); and iii) experiments with 35 000 ppm sodium chloride (sea water concentration) at 4000-7000 kPa and 5-60°C (Phase III).

Model parameters were determined from the data of Phase I at 25°C, using a nonlinear optimization routine. The average pore radii for the SW30HR and BW30 types of FT30 membranes were determined at about 1.0 and 1.2 nm, respectively. All the experimental data at other pressures and concentrations are well predicted by the MO-SF-PF model. Somewhat fortuitously, the MO-SF-PF model also predicts well for the other 1-1 electrolytes.

Temperature effects are reasonably predicted by the temperature-extended MD-SF-PF model. The apparent activation energies for pure water permeability for the SW30HR and BW30 membranes are about 25400 and 22500 kJ/kmol at 5-40°C, respectively, and about 18100 and 13 000 kJ/kmol at 40-60°C, respectively. Compaction, which becomes more severe as temperature or pressure is increased, has no effect on predicting the membrane separation or flux ratio (the ratio of total solution flux to pure solvent flux). An empirical model for compaction has also been developed and used to correct the flux ratio to the absolute values of permeation fluxes.

The Extended MD-SF-PF model has been found to well describe the difficult case of strong solute-membrane affinity, in which solute molecules are attracted toward the membrane rather than being rejected. The model implies that once the solute is rapidly sorbed into the membrane the solute molecules creep slowly adjacent to the wall of the membrane pores.

Overall, the family of the MD-SF-PF models has been found to predict RO membrane performance over a wide range of operating conditions. The agreement between the experimental data and model predictions supports, but does not prove, the proposed transport mechanism. In principle, the family of the MD-SF-PF models can be used for different research purposes including membrane development and RO module design.

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