Transmembrane pressure concentration

Feed High pressure feed side AP = Transmembrane pressure difference An = Osmotic pressure difference Membrane Concentrate... 

Solution—Diffusion Model. In the solution—diffusion model, it is assumed that (/) the RO membrane has a homogeneous, nonporous surface layer (2) both the solute and solvent dissolve in this layer and then each diffuses across it (J) solute and solvent diffusion is uncoupled and each is the result of the particular material s chemical potential gradient across the membrane and (4) the gradients are the result of concentration and pressure differences across the membrane (26,30). The driving force for water transport is primarily a result of the net transmembrane pressure difference and can be represented by equation 5 ... 

Cross-flow filtration systems utilize high liquid axial velocities to generate shear at the liquid-membrane interface. Shear is necessary to maintain acceptable permeate fluxes, especially with concentrated catalyst slurries. The degree of catalyst deposition on the filter membrane or membrane fouling is a function of the shear stress at the surface and particle convection with the permeate flow.16 Membrane surface fouling also depends on many application-specific variables, such as particle size in the retentate, viscosity of the permeate, axial velocity, and the transmembrane pressure. All of these variables can influence the degree of deposition of particles within the filter membrane, and thus decrease the effective pore size of the membrane. 

The change of flux velocity with transmembrane pressure can be explained by the concentration polarisation phenomenon. The physical processes at the membrane surface during the filtration procedure may be described by theo-... 

Figure 4. The correction for concentration polarization effects. Parent solution was 50 g/L at pH 13.0. Stirrer rates varied from 350 to 510 rpm, transmembrane pressure ranged from 34 to 207 kP0.

Ultrafiltrates obtained using cellophane or polysulphone membranes at 20°C and a transmembrane pressure of c. 100 kPa are satisfactory, but the concentrations of citrate and calcium are slightly low due to sieving effects which are accentuated by high pressures. Dialysis of a small volume of water against at least 50 times its volume of milk (to which a little chloroform or azide has been added as preservative) at 20°C for 48 h is the most satisfactory separation procedure and agrees closely with results obtained... 

If the water flux, /p, through an RO membrane is 8 X 10 cm s under a transmembrane pressure AP = 25 atm at 25 °C, estimate the water flux of a 2.0 wt% NaCl solution under the same transmembrane pressure and temperature. You may assume that a = 1.0 and neglect the effect of the concentration polarization. 

Figure 14.6 Cross-flow filtration flux of baker s yeast suspension. Cell concentration 7%. Transmembrane pressure 0.49 bar. Flow rate 0.5 ms". ...

Daud, W.R.W. 2006. Shortcut design method for reverse osmosis tubular module The effect of varying transmembrane pressure and concentration polarization. Desalination 201 297-305. 

The NF/LPRO pilot plant was supplied by Sepratech (Separation Technoloy, INC, US), and consisted of a feed tank, a pump and planar module, as detailed in Fig. 5. All studies were done using a low conversion rate (5%) and a high tangential flow rate ( 4 ms-1) in order to minimize the polarization concentration effects. The applied transmembrane pressures were in the range of 0-25 bar. The temperature was maintained at 25°C. 

In the Fig. 7, we have reported the flux as function of the transmembrane pressure (AP) for a NaCI solution at a concentration of 10-1molL-1 (6gL 1) which is typical of a synthetic brackish water. The linearity observed suggests that this salty solution follows the Kedem-Katchalscky model (i.e. Spiegler-Ke-dem model, with pressure and osmotic linear gradients). For linear gradients, equation (1) amounts to... 

Fig. 11. F concentrations in the permeate vs. time during the filtration of the Fatick water on NF90, NF270 and BW30 membranes (Feed composition see Table 9 operation conditions Transmembrane pressure 7.5 bars conversion ratio 0.87).

Ultrafiltration (UF) and diafiltration (DF) are very popular methods for conditioning the clarified culture broth for chromatography. As general rule, dilute animal cell culture supernatants are concentrated up to a factor of 20 and even more prior to fractionation. Ultrafiltration is a process in which a solution containing macromolecules is passed across a functional membrane, while macromolecules are retained by the membrane. The process is driven by the pressure drop across the membrane also called transmembrane pressure (PT) expressed as... 

Descriptive model and its division into parts. The first steps in the model construction are related to Fig. 3.7. The pump PA assures simultaneously the suspension transport and the necessary transmembrane pressure. The excessive accumulation of the solid in the retentate is controlled by its permanent removal as a concentrated suspension from the reservoir RZ. The clear liquid (permeate) flow rate and the solid concentration in the exit suspension are permanently measured and these values are transferred to the control and command computer CE. The instantaneous values of the operation pressure and input rate of fresh suspension are established by the computer (this works with software based on the mathematical model of the process) and corrected with the command execution system CSE. 

Successful performance of inorganic membranes depend on three types of variables and their interactions. The first type is related to the characteristics of the feed stream such as the molecular or particulate size and/or chemical nature of the species to be separated and concentration of the feed to be processed, etc. The second type is membrane dependent Those factors are the chemical nature and pore size of the membrane material and how the membrane and its accessory processing components are constructed and assembled. The third type is processing conditions such as pressure, transmembrane pressure difference, temperature, crossflow velocity and the way in which the membrane flux is maintained or restored as discussed earlier in this chapter. 

Alumina and other ceramic membranes of various microfiluaiion pore sizes have been used for the separation of yeast (saccharomyces cerevisiae) from the broth and the clarification of thin stillage [Cheryan, 1994]. A typical flux of 110 L/hr-m can be obtained with a crossflow velocity of 4 m/s and a transmembrane pressure of 1.7 bars. The crossflow velocity is found to markedly affect the membrane flux. Concenuation factors (ratios of final to initial concentrations) of 6 to 10 for both the broth and the stillage can be achieved. Backflushing with a frequency of every 5 minutes and a duration of 5 seconds helps maintain the flux, particularly in the initial operating period. The permeate flux for both types of separation reaches steady state after 30 to 90 minutes. 

As in many other membrane separation applications, the clean water flux is essentially proportional to the transmembrane pressure difference (TMP). When solutes, macromolecules or particulates are to be separated from the solvent (e.g., water), the permeate flux is first a linear function of the TMP and is in the pressure controlled regime. Although similar to the behavior of water flux, the permeate flux is nevertheless lower. Beyond a "threshold pressure," the permeate flux is insensitive to TMP due to concentration and gel polarization near the membrane surface. This behavior is so-called mass transfer controlled. It appears that the larger pore membrane, 50 nm in pore diameter, reaches the threshold pressure sooner than the finer pore membrane, 4 nm in pore diameter. There is a significant advantage of operating the membranes at a higher... 

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