Feed-Fluid Dynamic Conditions

Feed-side concentration polarization When feed components sorb in the membrane, a local concentration gradient develops in the feed phase adjacent to the membrane upstream face. Owing to this gradient, transport of components from the bulk into the bulk-membrane interface occurs, thus replenishing the components that were absorbed by the membrane. The transport of a solute across the phase adjacent to the membrane can be either convective or diffusive, depending on the solute concentration as well as the fluid dynamic conditions over the membrane surface. 

Industrial-size plate-and-frame modules, for example, consist of a stack of tightly packed membranes over which the feed solution is recirculated (Mulder, 1997). The membranes are separated by spacers and the permeate is withdrawn by a central permeate pipe (Stiirken, 1994). Pressure losses occur on both the feed and the permeate side of the packed membranes and need to be accounted for in the module design. On the feed side, the fluid dynamic conditions over the membrane may be less uniform than on the laboratory scale, resulting in more pronounced concentration polarization. On the permeate side, the packed configuration of the membranes may lead to considerable pressure losses, rendering the instantaneous removal of solutes from the membrane downstream surface more difficult. Both aspects may cause solute fluxes lower than expected (Chapter 3.2) and a possible... 

According to the CPC definition reported in eqn (14.8), CPC was evaluated as a function of several operating conditions, like temperature, feed and permeate pressure, feed composition and fluid-dynamic conditions by means of an elementary steps permeation model (eqn (14.11)) ... 

The model is able to predict the influence of mixing on particle properties and kinetic rates on different scales for a continuously operated reactor and a semibatch reactor with different types of impellers and under a wide range of operational conditions. From laboratory-scale experiments, the precipitation kinetics for nucleation, growth, agglomeration and disruption have to be determined (Zauner and Jones, 2000a). The fluid dynamic parameters, i.e. the local specific energy dissipation around the feed point, can be obtained either from CFD or from FDA measurements. In the compartmental SFM, the population balance is solved and the particle properties of the final product are predicted. As the model contains only physical and no phenomenological parameters, it can be used for scale-up. 

Hydrotreating units in the past were built with one reactor, to meet the 500 ppm S specification however, a second reactor is needed to cope with the actual requirements. Several attempts have been made also to change the operating conditions to improve performance of the units and to achieve the stipulated level of desulfurization. From a co-current fluid-dynamics, the first modification went into countercurrent feeding. In a countercurrent reactor, where hydrogen is fed at one end and the feed in the other, the most difficult to-desulfurize compounds, will react under the higher hydrogen concentration. The countercurrent operation introduces some other problems, such as hot spots and vapor-liquid contact. 

Mass transfer in the feed and strip solutions is limited by the extent of concentration polarization. On the feed side of the membrane, concentration polarization refers to an increase in the concentration of solutes at and near the feed-membrane interface because of evaporation of water into the membrane pores (Fig. 1). The resulting solute concentration gradient between the membrane-feed interface, where the concentration is greatest, and the bulk solution induces diffusive transport of rejected solutes back through the concentration polarization boundary layer into the bulk stream. Bulk solution is simultaneously transported to the membrane wall by convection. When equilibrium has been established under a given set of operating conditions (stream flow rate, temperature, fluid dynamics imposed by membrane module design), the rate of back diffusion is equal to the rate at which the solutes are carried to the membrane surface by convective flow. ... 

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