Membranes pressure drop/reverse osmosis

First multi-leaf spiral wound membrane module developed by Don Bray and others at Gulf General Atomic, under US Patent no. 3,417,870, "Reverse Osmosis Purification Apparatus," December, 1968. A multi-leaf spiral configuration improves the flow characteristics of the RO module by minimizing the pressure drop encountered by permeate as it spirals into the central collection tube. 

Ilias and Govind [1993] also used the CFD approach to solve coupled transport equations of momentum and species describing the dynamics of a tubular ultraflltration or reverse osmosis unit. An implicit finite-difference method was used as the solution scheme. Local variations of solute concentration, u ansmembranc flux and axial pressure drop can be obtained from the simulation which, when compared to published experimental data, shows that the common practice of using a constant membrane permeability (usually obtained from the data of pure water flux) can grossly overestimate... 

For small applied pressures the solvent flux through the membrane is proportional to the applied pressure. Flowever, as the pressure is increased further, the flux begins to drop below that which would result from a linear flux-pressure behavior (Fig. 5.6.1). For macromolecular solutes this nonlinear behavior may be ascribed to concentration polarization, that is, the buildup of rejected solute at the membrane surface. This buildup increases the local osmotic pressure and leads to a lower effective driving pressure and, hence, lower flux, as was shown for reverse osmosis. For macromolecular solutes the... 

Membrane separations involve the selective solubility in a thin polymeric membrane of a component in a mixture and/or the selective diffusion of that component through the membrane. In reverse osmosis (3) applications, which entail recovery of a solvent from dissolved solutes such as in desalination of brackish or polluted water, pressures sufficient to overcome both osmotic pressure and pressure drop through the membrane must be applied. In permeation (4), osmotic pressure effects are negligible and the upstream side of the membrane can be a gas or liquid mixture. Sometimes a phase transition is involved as in the process for dehydration of isopropanol shown in Fig. 1.8. In addition, polymeric liquid surfactant and immobilized-solvent membranes have been used. 

The method of reverse osmosis [7] is based on filtration of solutions under pressure through semi-permeable membranes, which let the solvent pass through while preventing (either totally or partially) the passage of molecules or ions of dissolved substances. The phenomenon of osmosis forms the physical core of this method. Osmosis is a spontaneous transition of the solvent through a semi-permeable membrane into the solution (Fig. 6.4, a) at a pressure drop AP lower than a certain value n. The pressure n at which the equilibrium is estabUshed, is known as osmotic pressure (Fig. 6.4, b). If the pressure drop exceeds n, i.e. pressure p > p" - -K is applied on the solution side, then the transfer of solvent will reverse its direction. Therefore, this process is known as reverse osmosis (Fig. 6.4,... 

Since the solute is rejected by the membrane, it accumulates and starts to build up at the surface of the membrane. As pressure drop is increased and/or concentration of the solute is increased, concentration polarization occurs, which is much more severe than in reverse osmosis. This is shown in Fig. 13.11-la, where cj is the concentration of the solute in the bulk solution, kg solute/m, and is the concentration of the solute at the surface of the membrane. 

Reverse osmosis uses a membrane to separate a virtually pure solvent from a solution while simultaneously conceiuiating the solutes in the solution. The motive force for the separation is the pressure drop across die membrane, which must be con derably greater than the osmotic pressure of the solvent in the concentrated uent to generate an accqxaMe flux through the membrane. The fiiel equivalent is related to the puiiqiing work required by the erqiresskm... 

Eq. VUI - 12 shows that as the pressure increases the water flux (J, ) also increases and consequently the retention coefficient R increases. Although the equations given here show how the flux and rejection in reverse osmosis are related to each other for a given membrane, they must be considered simply illustrative. They show very clearly and in a (mathematically) simple way how important membrane parameters are related to each other, but they cannot be used to calculate the simation in a process or system under practical conditions. The feed solution becomes more concentrated in going from the inlet stream (Cf) to the outlet stream (c ). and if it is assumed that the retention coefficient R of the membrane remains constant (independent of feed concentration) the permeate concentration will also increase and varies from (1 - R) Cf to (1 - R) c, . Equations will now be derived for cross-flow reverse osmosis that relate the permeate concentration (Cp) and retentate concentration (c ) to volume reduction and rejection [1]. In this derivation it is assumed that the process conditions remain constant (no pressure drop, no change in osmotic pressure and that the rejection coefficient R is independent of feed concentration). 

The reverse osmosis process, also known as hyperfiltration , is based on the passage of solvent molecules through a dense membrane from a concentrated solution to a dilute one. As this process is opposed by osmotic pressure, the pressure drop across the membrane must be higher to overcome it. Figure 11.8 shows how simple the process is in principle. The solution is pumped over a membrane held on a permeable support and it is split into the solvent (permeate) and concentrate streams. 

On the basis of the above observation, Schultz and Asunmaa developed the following transport mechanism. They made an assumption that the low-density and the noncrystalUnc region of the polymer that fills the space between the circular cells is incorporated into the unit cell as its part. Those spaces (between the unit cells) were therefore assumed to be vacant. In reverse osmosis operation these vacant spaces are filled only with water, and this water is assumed to be more ordered than the ordinary water under strong influence from the polymeric material. This water flows by the viscous flow mechanism through channels that arc formed by connecting the vacant spaces. Suppose r is the effective radius of this pore (m), np is the number of the pore in a unit area (1/m ), p is the pressure drop across the membrane (Pa), 17 is the water viscosity (Pa s), L is the effective layer thickness (m), and r is the tortuosity factor (-), the volumetric... 

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