A numerical model is presented to evaluate the dynamic behavior of mas transfer in the shell-and-tube-type membrane modules for metal ion removal from aqueous streams. The analysis that considers the effects of axial-flow velocity on the radial pressure difference across the membrane wall permits the specifications of this operating parameter to avoid expression of impregnated carrier from the membranes adn to prevent membrane wall rupture. The model accounts for effects of boundary layer mass-transfer and kinetic rate resistances at the interfces on membrane flux. The performance of different size membrane modules was estimated for two operating modes of a shell-and-tube-type module: one for the flow of feed solution inside the membrane tube and strip solution flow in the annular region and the other for the flow of strip solution inside the membrane tube and feed solution flow in the annular region of the module. A case system evaluated is copper ion extraction from acidic solutions using 2-hydroxy-5-nonylacetophenone oxime impregnated in α-alumina/silica ceramic membranes. The performance of shell-and-tube-type membrane modules depends on the sizes and operating methods. In these calculations, the operation condition of no-pressure difference across the membrane was imposed on the design. This condition is achieved by adjusting the ratio of the flow velocities of the feed and strip solutions within the inside and annular regions of the modules.
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