rafiltration 107 egion in the entry length, so there could be an improvement to the flux by use of higher pressures. They reported that the entrance length may be greater than 1 m, but that most of the benefits to flux which could occur using higher pressures would be over the first 20 cm One much used model considers a number of resistances in series. Therefore, during the transfer of components from the bulk of the solution to the permeate, the main resistances are due to the membrane(rm), the fouling layer(Rt) and the polarisation layer Therefore the flux can be expressed J=△PA(Rm+Rf+Bp) where u is the viscosity of the solvent. The pressure term may be modified to(AP-A7) to account for differences in osmotic pressure, but in most UF applications, the osmotic essure dif This type of model is sometimes known as the 'resistance in series model. In practical terms, the effects of concentration polarisation can easily be seen, as there is a marked reduction in flux, when water is replaced by the solution to be ultrafiltered, using either a dynamic or static start(Fig. 4.5). For a new membrane, flux data is determined usin water, before use, as this provides an indication of the condition of the original membrane and its resistance(Rm), or a membrane after cleaning. Membrane-cleaning protocols are designed to restore the water flux back to its original value. As soon as the water is replaced by the fluid, the flux rate will fall by a factor of 2-10 times, in a very short period of time, usually less than one minute. Thus the equilibrium described is achieved in a relatively short period of time. As concentration proceeds, the flux will further decline, due to a combination of an increase in the viscosity(total solids )and the process of fouling. However, it is not easy to separate the effects of polarisation, fouling and concentration increases. Therefore, experiments to observe the effects of fouling are usually performed at constant composition, by returning the permeate to the feed tank. Also, it is not straightforward to assess the individual contributions of fouling and concentration polarisation to the flux decline during the initial transition from water to product. Some fouling is evident with most systems and is assessed by the decline in flux Time Fig, 4.5. Flux decline due to concentration polarisation and fouling: (1)water flux;(2)moderate flux decline; (3)rapid nux decline
Ultrafiltration 107 region in the entry length, so there could be an improvement to the flux by use of higher pressures. They reported that the entrance length may be greater than 1 m, but that most of the benefits to flux which could occur using higher pressures would be over the first 20 cm. One much used model considers a number of resistances in series. Therefore, during the transfer of components from the bulk of the solution to the permeate, the main resistances are due to the membrane (Rm), the fouling layer (Rf) and the polarisation layer (Rp). Therefore the flux can be expressed as J = AF'/p(R, + Rf + RP) (4.12) where p is the viscosity of the solvent. The pressure term may be modified to (AP - Az), to account for differences in osmotic pressure, but in most UF applications, the osmotic pressure differences (An) are negligible. This type of model is sometimes known as the 'resistance in series model'. In practical terms, the effects of concentration polarisation can easily be seen, as there is a marked reduction in flux, when water is replaced by the solution to be ultrafiltered, using either a dynamic or static start (Fig. 4.5). For a new membrane, flux data is determined using water, before use, as this provides an indication of the condition of the original membrane and its resistance (R,), or a membrane after cleaning. Membrane-cleaning protocols are designed to restore the water flux back to its original value. As soon as the water is replaced by the fluid, the flux rate will fall by a factor of 2-10 times, in a very short period of time, usually less than one minute. Thus the equilibrium described is achieved in a relatively short period of time. As concentration proceeds, the flux will further decline, due to a combination of an increase in the viscosity (total solids) and the process of fouling. However, it is not easy to separate the effects of polarisation, fouling and concentration increases. Therefore, experiments to observe the effects of fouling are usually performed at constant composition, by returning the permeate to the feed tank. Also, it is not straightforward to assess the individual contributions of fouling and concentration polarisation to the flux decline during the initial transition from water to product. Some fouling is evident with most systems and is assessed by the decline in flux 1 3 E 2 3 Time Fig. 4.5. Flux decline due to concentration polarisation and fouling: (1) water flux; (2) moderate flux decline; (3) rapid flux decline
08 M.J. Lewis ate with time, usually for a period of 30-120 min, at constant composition. Fouling will be discussed in greater detail later In the absence of fouling, there are two main transport steps: (1)through the boundary (polarisation layer)and (2)through the membrane(Aimar, 1987). The first depends upon the hydrodynamics, on flow rate of solvent to the membrane (permeate flux), fluid composition and transport properties. The second depends upon the applied pressure and the properties of the membrane, namely its average pore size, distribution of pore size and its chemical properties. One of these transport steps is likely to be the rate limiting roce In general terms, the effects of operating parameters are shown in Fig 4.6. It should be noted that results are obtained for a constant composition. As the concentration of the feed increases, the flux will further decline. It can be seen that there is a pressure- dependent region(AB)and a pressure-independent region. However as the flux rate increases, the rejected materials will increase in concentration and concentration polarisation becomes limiting. In this region flux rates can be increased by higher flow rates and operating temperatures. Therefore this resistance approach provides an xplanation for the observed occurrence of pressure-dependent and pressure- independent gimes. At low pressures and low flux rates, the membrane offers resistance. This would suggest that ultrafiltration processes are best operated at pressures corresponding to the initial onset of the gion. Use of high give rise to a decrease in the flux, due to compaction of the membrane or fouling layer o ressures would only be wasteful of energy. There is some evidence that this could als In the pressure-independent region, the following analysis has been performed to model the flux performance, based upon a material balance at the membrane surface This is known as the film theory model(see Fig. 4.7) A dynamic equilibrium is established, where the convective flow of the component to the membrane surface equals the flow of material away from the surface, either in the permeate or back into the bulk of the solution by diffusion, due to the concentration gradient established. This is expressed as Water temperature Pressure Fig. 4.6.(a)Effects of operating pressure and flow rate on flux; (b)flux decline measured against concentration factor
108 M. J. Lewis rate with time, usually for a period of 30-120 min, at constant composition. Fouling will be discussed in greater detail later. In the absence of fouling, there are two main transport steps: (1) through the boundary (polarisation layer) and (2) through the membrane (Aimar, 1987). The first depends upon the hydrodynamics, on flow rate of solvent to the membrane (permeate flux), fluid composition and transport properties. The second depends upon the applied pressure and the properties of the membrane, namely its average pore size, distribution of pore size and its chemical properties. One of these transport steps is likely to be the rate limiting process. In general terms, the effects of operating parameters are shown in Fig 4.6. It should be noted that results are obtained for a constant composition. As the concentration of the feed increases, the flux will further decline. It can be seen that there is a pressuredependent region (AB) and a pressure-independent region. However as the flux rate increases, the rejected materials will increase in concentration and concentration polarisation becomes limiting. In this region flux rates can be increased by higher flow rates and operating temperatures. Therefore this resistance approach provides an explanation for the observed occurrence of pressure-dependent and pressure-independent regimes. At low pressures and low flux rates, the membrane offers the controlling resistance. This would suggest that ultrafiltration processes are best operated at pressures corresponding to the initial onset of the pressure-independent region. Use of higher pressures would only be wasteful of energy. There is some evidence that this could also give rise to a decrease in the flux, due to compaction of the membrane or fouling layer. In the pressure-independent region, the following analysis has been performed to model the flux performance, based upon a material balance at the membrane surface. This is known as the film theory model (see Fig. 4.7). A dynamic equilibrium is established, where the convective flow of the component to the membrane surface equals the flow of material away from the surface, either in the permeate or back into the bulk of the solution by diffusion, due to the concentration gradient established. This is expressed as X x LL LL in viscosity In (conc.) (b) Pressure (4 Fig. 4.6. (a) Effects of operating pressure and flow rate on flux; (b) flux decline measured against concentration factor
Ultrafiltration 109 Fig. 4.7, Concentration polarisation:(a) without a gel layer; b) Jc=d dc/dy+Jcy J(c-Cp)=D dc/dy Integration over the boundary layer of thickness L gives J=D/L In((m-CP)/(cb -Cp) (4.13) where D= diffusion coefficient; L=boundary layer thickness; cm =concentration of component at the membrane surface, Cp=concentration in the permeate and Ch= concentration in the bulk of the feed D/L is replaced by the mass transfer coefficient k (4.14) This is the general equation for any component. For a component which is completely rejected by the membrane(cp =0), this equation becomes This is the more familiar representation of this equation. The term cm/b is known as the membrane polarisation ratio. Several investigators have suggested that the concentra tion at the surface eventually reaches a value at which a gel is formed, i.e.(cm=cp). where cg is the gel concentration. Thereafter no further increase in concentration occurs and the flux remains constant, thus providing a(further)explanation for the existence of a pressure-independent region. The equation also predicts a straight line relationship between the flux and the log of the concentration, which has been found by many investigators. By extrapolating the experimental data to zero flux the gel concentration for various feedstocks and proteins has been estimated. Some values cited by Cheryan (1989)are given in Table 4.5. However, there have been some discrepancies between
II 1: ~I ~1 11
110 M. J. Lewis Table 4.5. Gel concentrations for different Feed Gel concentration cg Skim milk 20-25%0 protein Full cream milk (3.5% fat) 9-11% protein Acid whe 30%o protein Sweet whey 20-28%o protein Gelatin 22-30% protein Defatted soy extract 20-25%o protein Taken from Cheryan(1989) these values and those determined for the proteins by more conventional methods throwing some doubt on the validity of this type of analysis(Aimar, 1987) a further explanation for the discrepancies could be that the rejection of the mponents is not 1.0, making eq. (4.15)not directly applicable evertheless these equations help explain in qualitative terms the observations that in re-independent region, the flux can be increased by increasing the mass transfer coefficient. Because of this, considerable attention has been paid to the determination of this mass transfer coefficient There are various qualitative(empirical)relationships in the literature, which correlate mass transfer coefficient to physical properties, flow channel dimensions and operating parameters. Cheryan (1989)concluded that many of these are not very satisfactory Dimensional analysis has also been frequently used here Sh is the Sherwood number =(kd /D), Re is the Reynolds number=(vdp/u)and Sc is the Schmidt number=(u/pD), where d is the tube diameter and A, a and b are constants. For other flow situations the hydraulic mean diameter can be used, which equals 4(cross-sectional area/wetted perimeter A much used form of the equation for turbulent flow is h=0023Re08sc033 Cheryan(1986)summarises some of the constants for different flow geometries and feed materials, Under turbulent flow conditions, the constant a ranged between 0.5 and 1.1 ith 0.8 being a typical value. The value was 0.3 for laminar flow. Again dimensional analysis predicts that the flux rate can be increased by increasing the Reynolds number and by inducing turbulence. However, it has been noted that high flux rates have been observed at high shear rates under streamline flow conditions. More recently, Colman and Mitchell (1991)have described how pulsed flow and baffles have increased flux rates by a factor of 3, at a Reynolds number of 100. This was stated as giving a mass transfe value equivalent to a steady Reynolds number of 10 000 in unbaffled channels
110 M. J. Lewis Table 4.5. Gel concentrations for different proteins Feed Gel concentration cg Skim milk 20-25% protein Full cream milk (3.5% fat) 9-1 1 % protein Acid whey 30% protein Sweet whey 20-28% protein Gelatin 22-30% protein Egg white 40% protein Defatted soy extract 20-25% protein Taken from Cheryan (1989). these values and those determined for the proteins by more conventional methods, throwing some doubt on the validity of this type of analysis (Aimar, 1987). A further explanation for the discrepancies could be that the rejection of the components is not 1.0, making eq. (4.15) not directly applicable. Nevertheless these equations help explain in qualitative terms the observations that in the pressure-independent region, the flux can be increased by increasing the mass transfer coefficient. Because of this, considerable attention has been paid to the determination of this mass transfer coefficient. There are various qualitative (empirical) relationships in the literature, which correlate mass transfer coefficient to physical properties, flow channel dimensions and operating parameters. Cheryan (1989) concluded that many of these are not very satisfactory. Dimensional analysis has also been frequently used: Sh =A Rea Scb where Sh is the Sherwood number = (kd/D), Re is the Reynolds number = (vdp/p) and Sc is the Schmidt number = (p/pD), where d is the tube diameter and A, a and b are constants. For other flow situations the hydraulic mean diameter can be used, which equals 4 (cross-sectional area/wetted perimeter). A much used form of the equation for turbulent flow is Sh = 0.023 Reo.8 Sc0.33 (4.16) Cheryan (1986) summanses some of the constants for different flow geometries and feed materials. Under turbulent flow conditions, the constant a ranged between 0.5 and 1.1, with 0.8 being a typical value. The value was 0.3 for laminar flow. Again dimensional analysis predicts that the flux rate can be increased by increasing the Reynolds number and by inducing turbulence. However, it has been noted that high flux rates have been observed at high shear rates under streamline flow conditions. More recently, Colman and Mitchell (1991) have described how pulsed flow and baffles have increased flux rates by a factor of 3, at a Reynolds number of 100. This was stated as giving a mass transfer value equivalent to a steady Reynolds number of 10 000 in unbaffled channels
Ultrafiltration 111 Ithough dimensional analysis predicts the importance of turbulence, the value predicted using these models are often lower than those measured in practice. Measure ment often requires an estimate to be made for cm, the concentration at the membrane surface. The reasons for these higher experimental values are attributed to factors other than diffusion, causing the transport of rejected materials back into the bulk of the lution. One such explanation for colloidal partic the tubular pinch effect whereby colloidal molecules were observed to move away from the tube wall Aimar(1987)describes the ultrafiltration of pseudoplastic fluids and reported that in the pressure-independent region, the value of the limiting flux J was found to be given (4.17) which fits in well with conventional mass transfer theory. In short, the information derived from modelling gives qualitative data on the ways of improving mass transfer Some of the drawbacks of modelling for real systems stem from the complexity of real feeds. Most are multicomponent, with many compounds which are totally or partially rejected, with interactions between components. Their rheological behaviour is complex and there are difficulties of measuring the physical properties of the solutions under conditions found within the membranes and a lack of accurate diffusion data for macro molecules There is a further suggestion that osmotic effects are likely to be more important than initially thought for ultrafiltration, because the osmotic pressure difference over the membrane depends upon the concentration at the membrane surface and not on that in the bulk solution. However, those components which contribute most to the osmotic pressure ave a low rejection and therefore show little accumulation at the membrane surface When the membrane system is operating at very low transmembrane pressures, say about I atmosphere, the osmotic pressure difference may be significant 4.3.2 Fouling In most practical applications, fouling of the membrane takes place and this is a major operating problem in ultrafiltration. Fouling material collects on the surface of the mem- brane(and perhaps internally) and gives rise to a steady decline in the permeate flux(see Fig. 4.5). This could be particularly important for continuous processes operating at teady state, where a long-term decline in the flux would be extremely detrimental to the process. It could also give rise to a reduced life for the membrane, due to more stringent cleaning regimes being needed to remove the fouling Fouling is almost impossible to avoid. Removal of colloidal and particulate matter is of paramount importance prior to processing and should al ways be carried out. However, both Fane and Fell (1987)and McGregor(1986) have described situations where fouling as apparent, even with purewater Mc Gregor also reported that prolonged exposure to 200 ppm of sodium hypochlorite caused considerable flux decline. When more comple aterials are involved, such as proteins, interactions can occur between the proteins and the membrane material; for example proteins may bind to the membrane by hydrophobic effects, charge transfer such as hydrogen bonding and electrostatic interactions, or through combinations of these Conditions that minimise the amount of binding to the
Ultrafiltration 11 1 Although dimensional analysis predicts the importance of turbulence, the values predicted using these models are often lower than those measured in practice. Measurement often requires an estimate to be made for c,, the concentration at the membrane surface. The reasons for these higher experimental values are attributed to factors other than diffusion, causing the transport of rejected materials back into the bulk of the solution. One such explanation for colloidal particles is the ‘tubular pinch effect’, whereby colloidal molecules were observed to move away from the tube wall. Aimar (1987) describes the ultrafiltration of pseudoplastic fluids and reported that in the pressure-independent region, the value of the limiting flux JL was found to be given JL = Auacb (4.17) which fits in well with conventional mass transfer theory. In short, the information derived from modelling gives qualitative data on the ways of improving mass transfer. Some of the drawbacks of modelling for real systems stem from the complexity of real feeds. Most are multicomponent, with many compounds which are totally or partially rejected, with interactions between components. Their rheological behaviour is complex, and there are difficulties of measuring the physical properties of the solutions under conditions found within the membranes and a lack of accurate diffusion data for macromolecules. There is a further suggestion that osmotic effects are likely to be more important than initially thought for ultrafiltration, because the osmotic pressure difference over the membrane depends upon the concentration at the membrane surface and not on that in the bulk solution. However, those components which contribute most to the osmotic pressure have a low rejection and therefore show little accumulation at the membrane surface. When the membrane system is operating at very low transmembrane pressures, say about 1 atmosphere, the osmotic pressure difference may be significant. 4.3.2 Fouling In most practical applications, fouling of the membrane takes place and this is a major operating problem in ultrafiltration. Fouling material collects on the surface of the membrane (and perhaps internally) and gives rise to a steady decline in the permeate flux (see Fig. 4.5). This could be particularly important for continuous processes operating at steady state, where a long-term decline in the flux would be extremely detrimental to the process. It could also give rise to a reduced life for the membrane, due to more stringent cleaning regimes being needed to remove the fouling. Fouling is almost impossible to avoid. Removal of colloidal and particulate matter is of paramount importance prior to processing and should always be carried out. However, both Fane and Fell (1987) and McGregor (1986) have described situations where fouling was apparent, even with ‘pure’ water. McGregor also reported that prolonged exposure to 200 ppm of sodium hypochlorite caused considerable flux decline. When more complex materials are involved, such as proteins, interactions can occur between the proteins and the membrane material; for example proteins may bind to the membrane by hydrophobic effects, charge transfer such as hydrogen bonding and electrostatic interactions, or through combinations of these. Conditions that minimise the amount of binding to the by