102 M.J. Lewis Thus Vc=(V-dv)(c-dc)+c(l-r)dv (Note: d vdc is assumed to be negligible.) Integration between the final and initial conditions gives In(VFVc)=l/R In(cc/cF) If In(Va/Vc) is plotted against In(cc/ce), the gradient is 1/R vE/vc=f=(cc/cF) (4.5) From eqs.(4.2)and(4.3), it can be shown that Substitution into eq (4.5)gives VE/Vc =(f 1/R Therefore =(y/R. This simplifies to Y=fR-I. Therefore the yield r=f <s However, this equation applies only if the rejection remains constant. Nevertheless,it extremely useful, as it gives an insight into the features of the separation process, Let us consider the two extreme values of rejection IfR= l, then yield 1; all the material is recovered in the concentrate i.e. it is not possible to remove all of a component from a feed by ultrafiltration alone Diafiltration may be more useful in helping to achieve this objective(see Section 4.4). However, for most components being concentrated, the rejection values are close to 1.0, typically 0.9-1.0, whereas for those being removed the values would be between 0 Table 4.3 shows a range of yield values for some different concentration factors. One interesting point is that losses can be quite high, even though the rejection value appears good; e.g. for R=0.95 and a concentration factor of 20, the yield is 0.86. Therefore 14%0
102 M. J. Lewis Thus cp=c(l -R) Eliminating cp gives VC= (V-dV) (c-dc)+c(l-R)dV - Vdc = cR dV (Note: dVdc is assumed to be negligible.) dV cc dc 1 - -- I v -IcF -zi Integration between the final and initial conditions gives: In (vF/vC)=l/R In (cC/cF) (4.4) vF/Vc = f = (cC/cF)l'R If In (VF/Vc) is plotted against In (cc/cF), the gradient is 1/R. (4.5) From eqs. (4.2) and (4.3), it can be shown that CC/CF = yf Substitution into eq. (4.5) gives vF/vC =(fY)'lR Therefore f = (fY)'IR. This simplifies to Y = f '-'. Therefore the yield y= fR-1 (4.6) However, this equation applies only if the rejection remains constant. Nevertheless, it is extremely useful, as it gives an insight into the features of the separation process. Let us consider the two extreme values of rejection: If R = 1, then yield = 1; all the material is recovered in the concentrate. If R = 0, then yield = l/J in this case the yield is determined by the concentration factor. As the concentration factor is finite (typically 2-20), the yield can never be zero; i.e. it is not possible to remove all of a component from a feed by ultrafiltration alone. Diafiltration may be more useful in helping to achieve this objective (see Section 4.4). However, for most components being concentrated, the rejection values are close to 1.0, typically 0.9-1.0, whereas for those being removed the values would be between 0 and 0.1, Table 4.3 shows a range of yield values for some different concentration factors. One interesting point is that losses can be quite high, even though the rejection value appears good; e.g. for R = 0.95 and a concentration factor of 20, the yield is 0.86. Therefore 14%
Ultrafiltration 103 Table 4.3. Yield values for different concentration factors and rejections Concentration factor Re ection 0 0.1 0.2 0.5 090951.00 0.500.540.570.710930.971.0 0200.240.28 45 850921.0 0.100.1 0.160.32 0.050.0 0.090.22 861.0 0.020.030.040.140.680.821.0 of the component is lost in the permeate. Yield values are also sometimes quoted as percentage However, this equation gives the maximum yield, which would be for a batch process The yield is likely to be lower for a continuous single or multistage process, simply because steady state is achieved at higher levels of concentration. For such a process th ield is given by ∫-R(f-1) The concentration of a component in the final resulting concentrate(cc)can be calculated from the following equation Cc=cFF However, there is some evidence that rejection does not remain constant During a batch ultrafiltration experiment the rejection of most components rises, as has been observed on many occasions(see Fig 4.3) 4.2.3 Average rejectic situations where the rejection does change significantly, an alternative evaluation procedure is to measure the yield for the process, and then to work backwards to calculate the rejection value, which would have given rise to that yield. This rejection value is termed the average rejection value(Rav C CC ce f If this expression for yield is equated with that from eq (4.6)
Ultrafiltration 103 Table 4.3. Yield values for different concentration factors and rejections Concentration factor Rejection 0 0.1 0.2 0.5 0.9 0.95 1.00 2 0.50 0.54 0.57 0.71 0.93 0.97 1.0 5 0.20 0.24 0.28 0.45 0.85 0.92 1.0 10 0.10 0.13 0.16 0.32 0.79 0.89 1.0 20 0.05 0.07 0.09 0.22 0.74 0.86 1.0 50 0.02 0.03 0.04 0.14 0.68 0.82 1.0 of the component is lost in the permeate. Yield values are also sometimes quoted as percentages. However, this equation gives the maximum yield, which would be for a batch process. The yield is likely to be lower for a continuous single or multistage process, simply because steady state is achieved at higher levels of concentration. For such a process the yield is given by 1 Y= f - R(f -1) The concentration of a component in the final resulting concentrate (CC) can be calculated from the following equation: CC = CF Yf (4.7) cc=cF fR (4.8) or However, there is some evidence that rejection does not remain constant. During a batch ultrafiltration experiment the rejection of most components rises, as has been observed on many occasions (see Fig. 4.3). 4.2.3 Average rejection In situations where the rejection does change significantly, an alternative evaluation procedure is to measure the yield for the process, and then to work backwards to calculate the rejection value, which would have given rise to that yield. This rejection value is termed the average rejection value (Rav) (4.9) 1 y - vccc - cc VFCF CF f If this expression for yield is equated with that from eq. (4.6):
104 M.J. Lewis 04 叶2456}。。 Concentration factor Fig. 4. 3. Change in rejection during UF:(a)glucosinolates; ( b)total solids; (c)protein f= Rlogf=log(cc/cF R= log(cc/cF)/logf This expression for the rejection is effectively an average rejection(Ray) for the process Therefore Rav =log(cc/cF (4.11) Estimation of average rejection is based upon knowing the initial and final concentrations and the concentration factor It is interesting to note that, in this case, the membrane rejection can be determined without sampling the permeate herefore the average rejection is defined as the rejection value which would provide the same yield which was actually found in the process, even though the instantaneou rejection may have been changing throughout 4.2.4 Practical rejection data Although some of the proposed models predict how rejection will be influenced by operating conditions and pH, there is often little agreement between theory and practice
0.4 0.2 0 - - IIIIIIIII
Ultrafiltration 105 for most food systems. Therefore it is very important to measure rejection data under the prevailing operating conditions Lewis(1982) has compiled rejection data for different systems. It was not al ways clear some confusion between the terms rejection and yield in some of the earlier repord R whether rejection data for proteins was based upon crude protein or true protein. U filtration could be useful for removing non-protein nitrogen. There also appeared Table 4. 1 shows some rejection data for some dairy products, reported by the Interna tional Dairy Federation (1979) Figure 4.3 shows rejection data taken during the batch ultrafiltration process during concentration of rapeseed meal, for crude protein, total solids and glucosinolates. For all components, there is an increase in rejection as concentration proceeds, with the increase being most marked between concentration factors of 1 and 2. Many investigators have reported similar increases in rejection as concentration proceeds Table 4.4 shows some data for the average rejection data for proteins and glucosinolate, extracted at different pH values, determined by the method above, Yield alues are also presented. In such complex systems the performance is also strongly affected by pH(see Sections 4.3.2 and 4.5.2) Table 4.4. Average rejection(Ray) and yield values for glucosinolates and crude protein during batch ultra filtration processes at different pH values Glucosinolate Crude protein 2.5 0.5000.45) 0.970.95) 0.39(0.38) 0.93(0.89) 7.0 0.28(0.31) 081(0.74) 9.0 0.36(0.36) 0.95(0.92) 11.0 0.44(041) 0.85(0.92) Yield values in brackets Glucosinolates are expressed as isothiocyanates Therefore on values are very important as they influence the nature of the separation obtained, as well as the yield (or loss)of components. These aspects assume greater importance as the value of the product increases. Changes in rejection during process could also be indicative of some important changes taking place at the surface of the membrane. The effects of pressure and temperature on rejection, as predicted by some f the models, are discussed in Chapter 3. Some practical problems associated with UF of proteins, such as adsorption and pH effects, are described by Sirkar and Prasad(1987) 4.3 PERFORMANCE OF ULTRAFILTRATION SYSTEMS Permeate flux In UF process applications, the two most important parameters are the membrane
Ultrafiltration 105 for most food systems. Therefore it is very important to measure rejection data under the prevailing operating conditions. Lewis (1982) has compiled rejection data for different systems. It was not always clear whether rejection data for proteins was based upon crude protein or true protein. Ultrafiltration could be useful for removing non-protein nitrogen. There also appeared to be some confusion between the terms rejection and yield in some of the earlier reports. Table 4.1 shows some rejection data for some dairy products, reported by the International Dairy Federation (1979). Figure 4.3 shows rejection data taken during the batch ultrafiltration process during concentration of rapeseed meal, for crude protein, total solids and glucosinolates. For all components, there is an increase in rejection as concentration proceeds, with the increase being most marked between concentration factors of 1 and 2. Many investigators have reported similar increases in rejection as concentration proceeds. Table 4.4 shows some data for the average rejection data for proteins and glucosinolate, extracted at different pH values, determined by the method above. Yield values are also presented. In such complex systems the performance is also strongly affected by pH (see Sections 4.3.2 and 4.5.2). Table 4.4. Average rejection (Rav) and yield values for glucosinolates and crude protein during batch ultrafiltration processes at different pH values. PH Glucosinolate Crude protein 2.5 0.50 (0.45) 0.97 (0.95) 3.5 0.39 (0.38) 0.93 (0.89) 7.0 0.28 (0.31) 0.81 (0.74) 9.0 0.36 (0.36) 0.95 (0.92) 11.0 0.44 (0.41) 0.85 (0.92) Yield values in brackets. Glucosinolates are expressed as isothiocyanates. Therefore, rejection values are very impofiant as they influence the nature of the separation obtained, as well as the yield (or loss) of components. These aspects assume greater importance as the value of the product increases. Changes in rejection during a process could also be indicative of some important changes taking place at the surface of the membrane. The effects of pressure and temperature on rejection, as predicted by some of the models, are discussed in Chapter 3. Some practical problems associated with UF of proteins, such as adsorption and pH effects, are described by Sirkar and Prasad (1987). 4.3 PEKFORMANCE OF ULTRAFILTRATION SYSTEMS Permeate flux In UF process applications, the two most important parameters are the membrane
106 M.J. Lewis ejection(see also Chapter 3)and the flow rate of permeate or permeate flux, hereafter abbreviated to'flux'. The flux will probably be measured in gallons/ min or litres/ hour, but it is usually presented in terms of volume per unit time per unit area(I m h -) Expressed this way it allows a ready comparison of the performance of different mem brane configurations with different surface areas. Flux values may be as low as 5 or as high as 450 I m-h. The flux is one of the major factors influencing the viability of many processe UF processes have been subject to a number of modelling processes, in an attempt to predict flux rates and rejection values from the physical properties of the solution, the membrane characteristics and the hydrodynamics of the flow situation, in order to opti mise the performance of the process 4.3.1 Transport phenomena and concentration polarisation Ultrafiltration is usually regarded as a sieving process and in this sense the mechanisms are simpler than for RO. However, it is important to remember that for pressure-driven membrane processes, the separation takes place not in the bulk of solution, but in a very small region close to the membrane, known as the boundary layer, as well as over the membrane itself. This gives rise to the phenomenon of concentration polarisation over the boundary layer.(Note that in streamline flow the whole of the fluid will behave as a oundary layer) Concentration polarisation occurs whenever a component is rejected by the membrane As a result there is an increase in the concentration of that component at the membrane surface, and a concentration gradient over the boundary layer. This increase in concentra tion offers a very significant additional resistance, and for macromolecules may also give se to the formation of a gelled or fouling layer on the surface of the membrane(see Fig 3.4). It is interesting to note that the boundary layer does not establish itself immediately at the point where the fluid first contacts the membrane. Rather it takes some distance fo it to be fully established. This distance taken for it to be fully established has been defined as the entry length, and the process of establishment is illustrated for a tubular membrane in Fig. 4.4. Howell et al.( 1990)have analysed flux conditions over the entry length and have concluded that the flux and wall concentrations change quite consider ably over the developing boundary layer, although changes were less marked for a fouled membrane. There would also be less likelihood of operating in the pressure-independent Membrane d Retentate Boundary layer Membrane Permeate Fig. 4.4. Development of the concentration polarisation or boundary layer
106 M. J. Lewis rejection (see also Chapter 3) and the flow rate of permeate or permeate flux, hereafter abbreviated to 'flux'. The flux will probably be measured in gallons/min or litres/hour, but it is usually presented in terms of volume per unit time per unit area (1 m-2 h-l). Expressed this way it allows a ready comparison of the performance of different membrane configurations with different surface areas. Flux values may be as low as 5 or as high as 450 1 m-* h-'. The flux is one of the major factors influencing the viability of many processes. UF processes have been subject to a number of modelling processes, in an attempt to predict flux rates and rejection values from the physical properties of the solution, the membrane characteristics and the hydrodynamics of the flow situation, in order to optimise the performance of the process. 4.3.1 Transport phenomena and concentration polarisation Ultrafiltration is usually regarded as a sieving process and in this sense the mechanisms are simpler than for RO. However, it is important to remember that for pressure-driven membrane processes, the separation takes place not in the bulk of solution, but in a very small region close to the membrane, known as the boundary layer, as well as over the membrane itself. This gives rise to the phenomenon of concentration polarisation over the boundary layer. (Note that in streamline flow the whole of the fluid will behave as a boundary layer.) Concentration polarisation occurs whenever a component is rejected by the membrane. As a result, there is an increase in the concentration of that component at the membrane surface, and a concentration gradient over the boundary layer. This increase in concentration offers a very significant additional resistance, and for macromolecules may also give rise to the formation of a gelled or fouling layer on the surface of the membrane (see Fig. 3.4). It is interesting to note that the boundary layer does not establish itself immediately at the point where the fluid first contacts the membrane. Rather it takes some distance for it to be fully established. This distance taken for it to be fully established has been defined as the entry length, and the process of establishment is illustrated for a tubular membrane in Fig. 4.4. Howell et al. (1990) have analysed flux conditions over the entry length and have concluded that the flux and wall concentrations change quite considerably over the developing boundary layer, although changes were less marked for a fouled membrane. There would also be less likelihood of operating in the pressure-independent Permeate Membrane Feed inlet --+- Retentate Boundary layer Membrane Permeate Fig. 4 4. Development of the concentration polansation or boundary layer