Performance prediction of membrane modules incorporating the effects of suction in the mass transfer coefficient under laminar and turbulent flow conditions for non-newtonian fluids

Design equations for spiral wound membrane modules in case of power law fluid are derived for the first time. The case is solved for both laminar and turbulent flow regimes considering orange juice as the model system. The governing equations are solved numerically and the profiles of transmembrane pressure drop, bulk velocity, concentration, permeate flux, membrane surface concentration and permeate concentration along the membrane module are obtained. A detailed parametric study is carried out to observe the effects of operating conditions on the permeate flux and permeate concentration. The present analysis is helpful to design and simulate the performance of the membrane modules adequately. For the model system, it is observed that the axial pressure drop is about 2 to 3% of the inlet transmembrane pressure drop for 1.0 m length of the module. The mass transfer coefficient increases by twofold when the flow regime becomes turbulent. In case of laminar flow, at 7,000-kPa inlet transmembrane pressure drop, the average flux is about 22 L/m²·h and the flux value under turbulent flow condition becomes about 30 L/m²·h at the same pressure drop. For a slightly leaky membrane, at 7,000-kPa pressure drop and 130 kg/m³ of feed soluble sugar concentration, the permeate stream contains about 10 kg/m³ of total sugar. The application of membrane technology is one of the emerging areas in food industry. The major application includes fruit juice clarification and concentration. Therefore, appropriate design of membrane modules is of utmost importance. Most of the fruit juices are non-Newtonian in nature and they obey, in general, power law rheology. The derivation of detailed design equations of a spiral wound module is carried out considering a power law fluid, both under laminar and turbulent flow regimes. The presented method provides a way to design the membrane modules in great detail (i.e., incorporating effects of suction in mass transfer coefficient, developing concentration boundary layer, non-Newtonian fluid, etc.). This will be helpful to design a spiral wound module to meet a target productivity (i.e., permeate flux) and permeate quality (i.e., permeate concentration).