Constant filtration flux

Consider first the case of constant filtration flux in cake filtration/microfiltration. Since the volume flux Vs is... 

The apparent reflection coefficient (=(C5g - C pf/C, centration of solute in the permeate) may depend on the filtrate flux, when the real reflection coefficient cr is constant. Explain the possible reason for this. 

As stated in Chapter 9, cross-flow filtration (CFF) provides a higher efficiency than dead-end filtration, as some of particles retained on the membrane surface are swept off by the liquid flowing parallel to the surface. As shown by a solid line in Figure 14.6 [3], filtrate flux decreases with time from the start of filtration due to an accumulation of filtered particles on the membrane surface, as in the case of dead-end filtration. The flux then reaches an almost constant value, where... 

The mechanism of such UF can be explained by the following concentration polarization model (cf. Figure 8.3) [3,4], In the early stages of UF, the thickness of the gel layer increases with time. However, after the steady state has been reached, the solute diffuses back from the gel layer surface to the bulk of solution this occurs due to the difference between the saturated solute concentration at the gel layer surface and the solute concentration in the bulk of solution. A dynamic balance is attained, when the rate of back-diffusion of the solute has become equal to the rate of solute carried by the bulk flow of solution towards the membrane. This rate should be equal to the filtrate flux, and consequently the thickness of the gel layer should become constant. Thus, the following dimensionally consistent equation should hold ... 

Patel et al (1994) employed a combined process of coagulation and MF to avoid a disinfection posttreatment. The coagulation step was used to eliminate phosphorus, arsenic, and viruses, to avoid fouling, decrease particle accumulation on the membrane surface, and improve backflush characteristics. MF pilot plant studies in constant permeate flux mode showed that turbidity, particles, and faecal coliforms could be removed, but TOC removal was unreliable. Crossflow MF showed no difference to dead-end filtration, and both methods were similar to or better than sand filtration. Results with coagulation and MF improved phosphorous and turbidity removal, but the process was not optimised. The treatment lead to a reduction of chlorine demand in the product water. 

Particle shape Shape affects particle packing density and specific surface, which has a marked effect on pressure rise in constant rate filtrations (or filtrate flux decline in constant pressure processes). Needle shaped particles lead to lower pressure losses than equiaxed particles. Platelet shaped particles can be difficult to wash and dewater. 

Fouling propensity is commonly assessed by monitoring permeate flux and transmembrane pressure (TMP). Since membrane processes are generally operated either under constant TMP or constant permeate flux, a decrease in permeate flow rate or an increase of TMP is observed, respectively, once the fouling forms on the membrane. From these two parameters, calculation of hydraulic resistance (m ), membrane permeability (Lm h bar ) or specific cake resistance (mkg ) is also possible and allows further assessment of fouling conditions. The hydraulic resistance of the filtration system can be quantified by correlating TMP and permeate flux during a clean water test. This correlation is described as the Darcy s law ... 

PAN solutiotrs of three different concerrtrations, i.e. 12, 10, and 8 wt%, were electro-sprm arrd carbonized. Carbonization conditions were kept constant as per the previoirs sectiorrs. The thickness of the membranes was carefully controlled by adjusting the electro-spinrring time such that the final thickness of the carbonized membranes was 0.20 0.02 trrm. The PWP of the membranes measured are 3,800, 4,500 and 4,600 L/m h for the 8, 10 arrd 12 wt% PAN membrarres, respectively. The measured filtration fluxes are in agreement with the mean pore size of the membranes, which increases with the polymer concentration. Feed water containing 80 mg/L monochloroacetic acid was then filtered through each membrane arrd its rejection with volume of feed permeated is plotted in Fig. 8.44. 

Let us focus first on cake filtration and microfiltration for the case where the fluid is a liquid. In the configuration of Figure 6.3.21, the techrtique is called deadend filtration. The same configuration is routinely employed in lahoratories with a filter paper on, say, a Buchner funnel and a partial vacuum on the side of the permeate/filtrate a precipitate/ deposit builds up quickly on the filter paper as the slurry is filtered. As time passes, a particle based deposit continues to build up on the filter paper it is called a cake. This cake provides an additional resistance to the flow of the filtrate through the membrane/filter/cloth in deadend filtration. As time passes, deposition of the particles onto/in the cake continues. Therefore the resistance to the flow of the filtrate increases with time. If one wants to maintain a constant eflae of the filtrate flux, the applied pressure difference AP has to increase with time. Alternatively, for a constant applied pressure difference, the flux of the filtrate will decrease with time (Figure 6.3.22). 

Figure 6.3.22(a) shows that, for constant AP, the filtration flux decreases. Substitution of expression (6.3.138c) for Sc t) in expression (6.3.136d) yields... 

Let us now focus on the right-hand side of equations (7.2.130) or (7.2.123). At z = 0, the particle boundary layer starts forming (Figure 7.2.6(a)). The filtration flux value or the permeation velocity magnimde v o is constant for a certain length of the membrane. Therefore, on integration we obtain... 

Table 4 summarizes the efficiency of membrane filtration as preliminary treatment in the hybrid process to obtain regenerated water for industrial reuse. Working with the adequate cleaning cycle to avoid fouling and to keep a constant flux (10 1 min ) important reduction in suspended solids (90%) and turbidity (60%) of the wastewaters is achieved but there is no significant reduction of other chemical or physical parameters, e.g., conductivity, alkalinity or TDS, or inactivation of E. coli. 

In order to develop a continuous flux maintenance procedure, the present study examined the transmembrane flux values from the cross-flow filtration module with a filtration media area of 0.0198 m2 (0.213 ft2), a slurry density of approximately 0.69 g/cm3 at 200°C, 17 kg of simulated FT wax with a catalyst loading of 0.26 wt%, and a TMP between 0.68 and 1.72 bar (10-25 psig). The filtration process was run in a recycle mode, whereas clean permeate was added back to the slurry mixture, thus allowing the catalyst concentration to remain approximately constant over the course of the run (given minor adjustments for about 5 ml permeate and slurry samples collected throughout the test). 

Problems encountered with filtration ate that membrane fouhng can occur, which causes a decline in flux with time under constant operating conditions. Furthermore, concentration polarization, the effect that the increased concentration of components on the membrane surface reduces the flux due to the additional hydrodynamic resistance, is observed. This effect can be minimized in cross-flow filtration, by applying high flux rates across the membrane surface (Wang et al, 1979 Lee, 1989). 

Polymer-Assisted Ultrafiltration of Boric Acid. The Quickstand (AGT, Needham, MA) filtration apparatus is pictured schematically in Figure 3. The hollow fiber membrane module contained approximately 30 fibers with 0.5 mm internal diameter and had a nominal molecular weight cut-off of 10,000 and a surface area of 0.015 m2. A pinch clamp in the retentate recycle line was used to supply back pressure to the system. In a typical run, the transmembrane pressure was maintained at 25 psig and the retentate and permeate flow rates were 25 ml/min and 3 ml/min, respectively. Permeate flux remained constant throughout the experiments. 

Then, water is added continuously while the filtration continues at nearly constant flux. This latter filtration stage, when water is added to maintain a constant flux, is referred to as diafiltration. Proper choice of the diafiltration starting time can minimize the required membrane area, which is often the major part of the capital cost in an ultrafiltration process. 

In the filtration-type methods (the first three techniques listed above), components accumulate as a steady-state (polarization) layer at a barrier or membrane [4] this occurs in much the same way as in field-flow fractionation or equilibrium sedimentation. However, there are several complications. First, fresh solute is constantly brought into the layer by the flow of liquid toward and through the filter. This steady influx of solute components can be described by a finite flux density term J0. Second, components can be removed from the outer reaches of the layer by stirring. Third, the membrane or barrier may be leaky and thus allow the transmission of a portion of the solute, profoundly affecting the attempted separation. In fact, one reason for our interest in layer structure is that leakiness depends on the magnitude of the solute buildup at the membrane surface. As solute concentration at the surface increases, more solute partitions into the membrane and is carried on through by flow. 

FIGURE 8.3 TMP and flux profiles for (a) constant pressure and (b) constant flux filtration. 

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