PARAMETER ESTIMATION AND MODELING OF SPIRAL-WOUND

Reverse Osmosis is a process used to de-mineralize water, to clean brackish water or to desalt seawater. The process consists in recovering water from a saline solution pressurized by pumping it into a closed vessel to a point grater than the osmotic pressure of the solution. Thus, the solution is pressed against a membrane so that it is separated from the solutes (the dissolved material). The portion of water that passes through the membrane reducing strongly the solute concentration is called permeate. The remaining water (brine) is discharged with a high salt concentration. Reverse osmosis is a pressure driven membrane separation process, used for removing low molecular weight solutes, such as inorganic salts or small organic molecules, from a solvent. It relies on the use of a semi permeable membrane, which allows solvent molecules to pass through it, impeding the pass of solutes. When two solutions of different concentrations are separated by such a membrane, the solvent from the lower concentration solution will move through the membrane into the concentrated one, in a process called osmosis. The osmotic flow is attributed to the tendency to equalize the both size’s solute concentrations. However, if the liquid on one side of the membrane is pure solvent, the two concentrations can never be equal. In this case, the process of osmosis continues until the chemical potentials of both solutions are equal. This happens when the pressure exerted by the concentrated solution against the membrane is high enough to prevent any further solvent flow. The hydrodynamic pressure difference between the two solutions found at chemical potential equilibrium is called the osmotic pressure difference. In a reverse osmosis process, a pressure must be applied to the concentrated solution in order to overcome the osmotic pressure and to force the solvent to cross the membrane against the concentration gradient.
The purpose of the present work is to develop a model for the spiral-wound module using a three-parameter non-linear membrane transport model by Spiegler and Kedem (SK). The pressure variations in both feed and permeate streams and the variations of concentration and the mass transfer coefficient along the length of feed and permeate channels are taken into account in the model. The value of nF in the pressure drop equation is taken from the literature. The proposed model is then used to simulate results for various operating conditions, and the significance of the third parameter, the reflection coefficient, introduced into the SK model, is further investigated. A parameter estimation program is also developed for determining membrane parameters along with the mass transfer coefficient parameters for the spiral-wound module. The data available in the literature on spiral-wound modules are further analyzed, and a correlation for the mass transfer coefficient is proposed for the Roga spiral-wound module.