Modeling of Mass Transfer in Cavity Limited by a Semi Permeable Membrane (Simulation of Spiral Wound Module)

The reverse osmosis process has been applied in large industrial fields (water treatment, food industry, biotechnology, and ect.). Despite, this progress more investigation are required to optimize the reverse osmosis process. The present paper deals the modeling of mass transfer in a cavity limited by a semi-permeable membrane. Mass conservation and momentum balances are developed, dimensionless and control volume method has been applied. The velocity and concentration profiles versus the Reynolds number and Sherwood are studied. The results show that the permeability of the membrane decreases as function of the transversal (radial) component of the velocity. The axial (tangential) component of the velocity presents a good stability along the thickness of the cavity; this phenomenon can be attributed to the zero gradient of the tangential velocity. These preliminary results show that the phenomenon of the concentration polarization affects the mass transfer coefficient in a channel. Current study has considered the cavity without a promoter of the turbulence; whereas, the design of the spacer has an important role on mass transfer coefficient in the reverse osmosis module. Our next interest is the integration of the spacer in the cavity, and the study of the effect of its design on the concentration and velocity profiles and the mass transfer coefficient through the reverse osmosis membrane.