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Evaluation of process models for fouling control of reverse osmosis of cheese whey
Journal of Membrane Science, 58 (1991) 89-111 Elsevier Science Publishers B.V., Amsterdam
89
Evaluation of process models for fouling control reverse osmosis of cheese whey
of
A.J.B. van Boxtel, Z.E.H. Otten and H.J.L.J. van der Linden NIZO (Netherlands (Received
Institute
April 30,199O;
for Dairy Research),
accepted
PO Box 20,671O BA, Ede, Netherlands
in revised form January
21,199l)
Abstract Long-term
fouling of reverse-osmosis
membranes
processing
dairy products
can be caused by
two phenomena: (1) an increasing thickness of the protein gel layer; (2) deposit formation due to precipitation of calcium phosphate/protein complexes. Mechanistic models describing these two phenomena are evaluated for a tubular reverse-osmosis pilot-plant for concentrating cheese whey during a 20 hour period. The experimental variables were the initial pressure after start-up, flow velocity, concentration ratio and process temperature. The results indicate that the model of a growing gel layer does not fit the process of long-term fouling. However, a precipitation model for calcium phosphate showed good agreement with the experimental results. Finally, experimental results and a modified form of the precipitation model are applied to explore possibilities for controlling fouling by adapting the controlling variables flow velocity, pressure and temperature. Keywords:
fouling; reverse osmosis;
whey; food industry
Introduction
The application of membrane filtration is of growing interest for the process and food industry. Besides a low energy consumption, the possibility of performing product separations under favourable conditions, resulting in better product qualities, is one of the most attractive features of this technology for the food industry. However, long-term fouling of membrane surfaces, resulting in flux decline over hours or days, is one limitation for industrial applications. For design of industrial membrane installations the flux decline must be taken into account by overdimensioning of installations, and special measures must be taken to integrate membrane filtration installations in a production line. Such measures are cyclic operation of parallel membrane filtration units or installation of sufficient buffer capacity. As a consequence investment and operation costs rise. Another limitation for industrial application of membrane processes to foodstuffs is caused by large and uncertain differences in fouling behaviour between succeeding charges of the feed.
0376-7388/91/$03.50
0 1991-
Elsevier
Science
Publishers
B.V.
90
With this background, study of fouling phenomena has always been a very important topic in membrane research. One of the world-wide activities in this field is the development of models describing fouling phenomena. The aim of these studies is to use the insight obtained to make appropriate membrane modifications and to develop product (pre)treatments to reduce fouling. The results of these studies, however, are hardly used for optimal design, optimal process operation, and control of membrane filtration installations. On account of the growing importance of membrane filtration in the foodand particularly the dairy industry, the relevance of fouling models to calculate the optimal process operation and control should be examined. The first step in such application is the selection of an appropriate process model for membrane fouling from the available fouling models. In this investigation, mechanistic models for fouling of reverse osmosis of cheese whey on a semi industrial tubular membrane installation were evaluated. Subjects to be discussed in this paper are: *definition of long-term fouling; @relation between fouling and increasing permeation resistance; *characteristics of membrane fouling for reverse osmosis of cheese whey; two models for fouling: a gel layer model and a precipitation model; *experimental set-up; *evaluation of results; *a qualitative description of possible applications of process conditions in fouling control. l
Definition of long-term fouling For cross-flow membrane filtration installations there is a difference in flux decline characteristics between reverse osmosis (RO) on the one hand and ultrafiltration (UF) and microfiltration (MF) on the other (Fig. 1). In the RO situation, permeate flux at t= 0 is only a little lower than the water flux. Hiddink et al. [l] established, for cheese whey and skim milk, that at t = 0 the permeation resistance was higher than the resistance to permeation of water. This supplementary resistance is caused by, among other thing, concentration polarization phenomena and is a function of the chosen process conditions. After t= 0, flux declines during the next hours or days of the production run. This is due to what we call long-term fouling. For UF and MF, shortly after t=O permeate flux is much lower than the water flux. This is the result of, in comparison to RO, excessive concentration polarization [ 2,3] and blocking of membrane pores and membrane surfaces in the first seconds and minutes after t=O [4,5]. Within a few minutes, flux is
91 permeate flux water flux
IS)
time
Fig. 1. Flux decline characteristics for RO, UF and MF.
between lo%-40% of the water flux. This is what we call short-term fouling. After this initial decline, flux continues to decline due to long-term fouling. Theory
Permeation resistance A common relation between process pressure total permeation resistance (R,,,) is: P-An J=R tot
(P), permeate
flux (J) and
(1)
or P-An
fL,t = __J
(2)
in which An represents the osmotic pressure difference between bulk and permeate. Total permeation resistance (R,,,,) is the sum of individual resistances in series: R,,,, = R, + 4, + R,
(3)
where OR,,, represents the resistance of the membrane to permeation of water. For new membranes this value is weakly time dependent due to membrane compaction. For industrial installations this time dependence is small compared to the resistance increment due to fouling ( Rf ) . Compaction occurs only during a short period of the total life time of the membrane. Therefore the effect of compaction on the optimal operation and control will be neglected.
92
OR, is an additional time-independent resistance which is a result of the chosen process conditions [ 11. This resistance is partly effected by concentration polarization phenomena and by a foul layer which is built up while the industrial installation is being filled with product under the chosen process conditions. Hiddink et al. [l] demonstrate the relationship between these process conditions and R, in graphs. However these results may also be expressed in a mathematical relationship. Statistical analysis of Hiddink’s results indicates that R, is correlated with flow velocity, process pressure and concentration ratio according to the power function: R,=avhPCC~
(4)
.RF is the strongly time-dependent part of the resistance and is characteristic for membrane fouling. In next paragraphs two mechanistic models for this resistance will be discussed. All resistances are temperature dependent as a consequence of the temperature dependency of the dynamic viscosity of the permeate. Rewriting eqn. (1) results in: J=
p-A7T
R,+R,+Rf R,
can be estimated from experiments with (clean) water and R, from the initial permeation resistance just after start-up of an installation. The relation of R, with process conditions and its function of time has to be estimated from long experimental production runs.
Fouling phenomena
for cheese whey
Several authors have derived models for the long-term fouling of membranes. Matthiasson and Sivik [ 61 and Fane and Fell [ 71 survey these models. The literature list includes several other papers discussing the background of fouling models [ 8-141. For the application of process models for optimal operation and control, mechanistic models are to be preferred. These models are more flexible for extrapolation to other process conditions and other membrane installations. For the selection of an appropriate process model, properties of cheese whey should be considered first. Cheese whey contains several components, e.g. fat, lactose, protein and salts (i.a. calcium phosphate). Membrane fouling hardly occurs for decalcified whey [1 ] and because of the ability of protein to cause membrane fouling, it may be stated that protein and calcium phosphate are responsible for membrane fouling during reverse osmosis of cheese whey.
93
Protein In comparison to milk or several other foodstuffs the protein concentration in cheese whey is relatively low. Fresh cheese whey contains approximately 0.6-0.8 weight percent protein. However, the concentration polarization raises the protein concentration near the membrane, and it may reach the gel concentration. If so, the concentration at the membrane surface cannot increase any more. The surplus of material transport in the direction of the membrane results in a growing gel layer which causes an increasing resistance to permeation. Calcium phosphate It is well known that calcium phosphate plays an important role in fouling of membranes [ 151. Schmidt and Both [ 151 mentioned that in milk and whey calcium phosphate is supersaturated. From this supersaturated state first amorphous calcium phosphate is formed which crystallizes subsequently into several crystalline states. However, the precipitation of amorphous and crystallized calcium phosphate is inhibited by the formation of complexes with protein. The solubility and the inhibition of the precipitation both depend on the temperature and pH. Precipitation occurs mainly at temperatures above 40 oC but is also possible at lower temperatures. Fouling of membranes, even at low temperatures, can be reduced by adding acid to whey and milk to give a pH of 5.8-6.0 [ 11. This results in a better solubility of calcium phosphate. Another method is a heat treatment (e.g. 10 min. at 60’ C ) before the feed enters the membrane installation. During this heat treatment calcium phosphate precipitates, with the result that supersaturation of the feed is reduced. Special attention should be paid to the interaction between calcium phosphate and proteins. Both amorphous and crystalline calcium phosphate form complexes within proteins and together with calcium phosphate the protein precipitates. Furthermore, between succeeding charges of cheese whey significant concentration differences of the crystallization and precipitation inhibitors may occur. Consequently the fouling characteristics for succeeding charges of cheese whey varies. Constitution of foul layers Kulozic [ 161 concluded from electron micrographs and chemical analysis that the foul layer consists mainly of proteins and salts, and is 30-50 pm thick. The properties of the layer change with increasing distance from the membrane. Close to the membrane surface the layer is firm and removal of this part is relatively difficult. With increasing distance from the membrane the firmness of the layer decreases and removal becomes easier. The top layer can even be removed by rinsing. Kulozic suggested that calcium is indispensable in the precipitation of protein, as it forms bridges between protein molecules.
94
This information suggests the operation of two mechanisms, namely: *the formation of a gel layer, and *formation of a foul layer due to precipitation and crystallization of amorphous calcium phosphate. Concentration
polarization
In Fig. (2) a cross-section of the bulk, membrane and permeate is considered. The mass balance for an arbitrary product component in volume A is given by:
dc
ac
ac
dt+vy.+vy-=
ay
-Llg
(6)
For industrial installations the concentration gradient in the direction of product flow (clC/cly) can be neglected in comparison with dC/dx. With u, = J it follows that:
ac
ac
(7)
dt+Jz=-D$
The boundary
conditions
are:
t=o-
c=c,
x=6--f
C = Cb (6 is thickness
x=0-
JC
m-
of boundary
_-L)g ax
J
T
flow direction
membrane
Fig. 2. Cross-section
of a membrane svstem.
layer) .
95
In this case 100% retention is assumed. This means that no solutes of the bulk will pass the membrane. For positive values of J the product concentration near the membrane will increase until a steady state (dC/dt=O) is reached. Under steady-state conditions the concentration is a function of the distance from the membrane. The solution of eqn. (7 ) under steady-state conditions is: (3) with D/S= Iz (mass transfer coefficient) J=kln%
(9)
or
b
The concentrations of all product components increase in the boundary layer. However, the diffusion coefficients of the components are different because of the variations in molecular dimensions. Consequently, the degree of concentration polarization of protein is higher than that of calcium phosphate (&l>&). The concentration polarization is defined by the ratio between J and k. For reverse osmosis of whey values for J vary between 1.0 x lop6and 5.5 x 10W6 m3/m2-sec. Mean values of lzare approximately 2.0 x low5m/set [ 16-181. This results in values of C, between 1.05 and 1.30 times Cb. Therefore the concentration polarization in RO installations is of less importance in comparison with UF and MF processes, for which the flux (J) may be 5 to 25 times the flux of RO processes. In the steady state transport of material in the direction of the membrane equals back diffusion:
J
c,,= cbk
hl+ b
(11)
Gel layer model This model was proposed by Kimura and Nakao [ 121. Due to polarization the concentration near the membrane surface (C,) can reach the gel concentration (C,,,,) . This means no further increase in concentration will occur and a gel layer will be built up. In the steady state the boundary condition is C= Cg.pr for x= 0. This results in: J=&
ln%
(12)
-
Cg.pr=Cb.preXP
(13)
b.pr
During the time the gel layer is built up the difference between transport in
the direction of the membrane of the gel layer.
e=
JCb+,-- Gprkpr
and back diffusion is proportional
In%,
L(t=O)
to the growth
=o
(14)
b.pr
For a linear relation layer:
between
permeation
resistance
and thickness
of the gel (15)
Rf= EL it follows that
‘% EJCb.pr~.‘%,rk,,rln%,r -=-P G.pr dt P
(16)
This relation contains several parameters which are not exactly known or are totally unknown, e.g. which part of the protein concentration will form the gel layer or the value of t. However, evaluation of the model is possible by using lumped parameters. The equation is reduced to: Mf dt=AJ-B
withA=---
(17)
C.CbJX P
’
B=
t-Cb.prkpr P
lnC,.,r
and R,(t=O)
=O
Cb.pr
Only the values of A and B have to be estimated from experimental data of total permeation resistance (R,,,,) as a function of time. On account of the relationship between mass transfer coefficient (k) and flow velocity (U 1 (the Sherwood relation), B is correlated with u. Precipitation model As mentioned above, because of the supersaturation of calcium phosphate, first amorphous and subsequently crystalline calcium phosphate precipitates. The precipitation is inhibited by the presence of complexes between calcium phosphate and protein. In the bulk of a whey concentrate, there is an equilibrium between the affinity for precipitation and the inhibition. During reverse osmosis the concentration polarization raises the supersaturated state in the boundary layer and precipitation followed by crystallization is continued. Concentration polarization is a function of the applied process conditions (k by flow velocity and J by process pressure) and as a result the precipitation is a function of these process conditions. Okazaki and Kimura [ 131 suggested a model for the precipitation of calcium sulphate at the membrane surface. This model is based on the crystallization kinetics and describes the formation of a smooth foul layer over the membrane
97
surface with a permeation resistance proportional to the thickness of the layer. In that model a second-order reaction kinetic from the crystallization kinetic of calcium sulphate is used. The second order kinetic is also acceptable for the precipitation of calcium phosphate. And similarly this model can also be applied to the deposit formation during reverse osmosis of cheese whey. L(t=0) ~=K,(c,,,,-c,,,,)2,
=o
Combination of eqn. (18) with Cm.cal=Cb,calexp (J/k,,,) (15 ) results in
(18) (10a) and Rf= EL
(19) Like the gel layer model, this model contains several parameters which are not exactly known or are totally unknown. However, it can also be evaluated by using lumped parameters:
(20) where K: = ~KaGxcalal~
and
R,(t=O)
=O
must be estimated from experiThe values of Kg, kcal and the ratio Cs.cal/Cb.cal mental data. kcalshould depend on flow velocity and & is related to the bulk concentration. Borden et al. [ 141 proposed an alternative precipitation model, which differs from that of Okazaki and Kimura by the assumption that crystallization starts at nucleation points. These nucleation points expand by crystallization and will gradually block the membrane surface. Electron micrographs indicate that fouling is not concentrated at nucleation points but spread over the total membrane surface [ 161. Therefore the approach of Borden et al. [ 141 is not considered further. Experimental set-up
Equipment To obtain an appropriate process model for optimal operation and control of industrial installations, experiments were performed on a semi-industrial one-stage recirculation reverse-osmosis pilot plant. This pilot plant consists of four modules containing tubular composite membranes (Stork-Wafilin WFCOOG). In each module, 19 membrane tubes 4 meters long and 14.4 mm in diameter are installed. The total membrane surface is 13.7 m2.
98
Figure 3 shows the flow chart of the pilot plant. In the low-pressure part of the installation the feed is heated up to the specified process temperature. The heat exchanger can optionally be used for a heat treatment of the feed (e.g. 10 min at 60°C). Subsequently the feed is pumped into the membrane installation by the high-pressure pump. Depending on the specified concentration ratio, part of the concentrate runs off the installation as final product, while the majority is recirculated along the membranes. To avoid a rise in temperature due to circulation, the concentrate is kept at the specified temperature with a water cooling system. There are two options for pretreatment of the feed to reduce fouling: *the already mentioned heat treatment in the heat exchanger and temperature holder; *or acidification of the feed in the feed tank to pH 5.8-6.0. The control loops are shown in Fig. 3. These are: *temperature control of heat treatment, specified process temperature and the cooling system. *flow velocity along the membranes. *concentration level. This is realized by a constant ratio between feed capacity and final product flow. aconstant process pressure and/or constant permeate flux. This control offers the possibility for two production phases. The installation is started up below the maximal allowed process pressure. During the first phase the feed capacity is kept constant while process pressure increases due to fouling. The second phase starts as soon as the maximum allowed pressure is reached. Then the process pressure is kept constant while permeated flux decreases due to fouling. Besides these control loops several alarm indicators are installed. To improve reproducibility of experiments, the control, start-up and shut down of the installation are programmed in a process computer system (Siemens Teleperm-M). Experimental data are collected on-line by a personal computer connected to the process computer.
Fig. 3. Pilot-plant
flow sheet with control loops.
99
Experimental procedure All experiments were performed with fresh cheese whey. The pH of the whey was decreased from 6.6 to 5.8 by acidification. Initially the installation was filled with feed and subsequently preconcentration was started by keeping the product valve closed while feed was pumped into the installation. The product valve was opened when the specified concentration was attained and then the continuous production phase started. During the preconcentration phase the process pressure and flow velocity had the same values as during the experiment. The permeate flux was continuously calculated from the difference between the feed capacity and the product capacity. Both were determined by electromagnetic flow measurement devices with an accuracy of + 0.2%. The permeation resistance was calculated according to eqn. (2) in which dn z TS [ 171. After approximately 20 hr the installation was shut down, rinsed with water and cleaned according to the instructions of the membrane manufacturer. After each run the water flux was measured at 25°C and 2.0 MPa as a check on cleaning. Usually a reverse-osmosis installation is operated at the maximally allowed pressure. But, as an alternative procedure, manufacturers of membrane installations recommend starting up the installations at a lower initial pressure while the flux is kept constant until the maximum pressure is attained, after which the pressure is kept at this level with decreasing flux. Both procedures were applied during the experimental runs. In the pilot plant installation the maximal allowed pressure was 4.0 MPa. For all experiments, the protein, lactose, fat and calcium contents of the cheese whey were determined by infra-red analyses. The pH after acidification, density, refractive index and conductivity of feed and refractive index of the final product were also measured. Finally, a regular check was performed to obtain an indication of the contribution of membrane compaction to the time dependency of R,. These checks showed that membrane compaction was negligible.
Experimental programme First, experiments were performed at 30’ C and a concentration ratio of 2.5. The flow velocity (1.5,2.0,2.5 and 3.0 m/set) and initial pressure (2.8,3.4 and 4.0 MPa) were varied. Second, for the initial pressure of 2.8 MPa and process temperature of 30” C, the flow velocity (1.5,2.0,2.5 and 3.0 m/set) and concentration ratio (2.0,2.5, 3.0,3.5 and 4.0) were varied. Third, for an initial pressure of 4.0 MPa. and a concentration ratio of 2.5, temperature (lo,20 and 30°C) and flow velocity (1.5. 2.0,2.5 and 3.0 m/set) were varied.
100 Results
The course of permeation resistance Figures 4 (a) and 4 (b) show some typical examples of fouling, expressed by plotting the permeation resistance as a function of time. Figure 4 (a) shows a reduction of the permeation resistance for increasing flow velocities. This demonstrates the possibility of controlling fouling by the flow velocity. Figure 4 (b) illustrates that, after 2-3 hr, the permeation resistance is considerably lower at 10” C and 20” C than at 30°C. This result can partly be explained by the lower fluxes at 10’ C and 20’ C (see eqns. 17 and 20). But the main reason is the temperature dependency of the solubility of calcium phosphate as well as
RtotITPa.s:mi 2.0 a m/s
1.5-
1.5 2 2.5
01
800
1000
1200 time(mlnl
Rtot(TPa.s/m) 2.0_I _
b
-t I 0
I 200
I
I
400
,
I
M)o
I,
,
800
,
,
,
,
1000 1200
Fig. 4. Permeation resistance as a function of time. (a) flow velocity 1.5, 2.0, 2.5, 3.0 m/set Constant pressure P=4.0 MPa, temperature 3O”C, concentration ratio 2.5; (b) process temper. ature lO”C, 2O’C, 30°C. Pressure 4.0 MPa, u=2.0 m/set, concentration ratio 2.5.
101
the precipitation inhibition. This aspect will be discussed in the section “Influence of process temperature”. As a result of the temperature variations, for several experiments at 10°C and 20’ C the total capacity (20 hr ) of the pilot plant was lo-20% higher then for comparable experiments at 30’ C. Remark: Duplicate experiments demonstrated that for feeds with the same specifications a different rate of fouling could occur. Model evaluation
For all the experiments the parameters A, B and Rtot (t= 0) of the gel layer and R,, ( t = 0 ) for the precipitation model were model and &, Ll, CA/G.~~I estimated by non-linear curve-fitting combined with a Runge-Kutta method for solving the differential equations. Both models showed a good agreement with the experimental data. The mean error of the fitted results was about + 0.02 x 101’ Pa-set/m. Figures 5 (a) and 5(b) are a selection of the fitting results including the residuals. Graphical presentations of fitting results and experimental data demonstrated that there was no significant difference between the curve-fitting results of the two models.
a
Rtot(TPa.sim)
Rtot(TPa.sim)
1.5~
0
200
400
600
800
1000 1200 time(mid
0
200
400
600
800
1OW
1200 time(min)
600
800
1000 1200 time(min)
ARtot(TPa.sim)
ARtot(TPa.sim)
0.05$
-o.os‘l 0
200
Fig. 5. Typical
400
600
800
1000 1200 time(min)
0.05l 0
200
400
results of curve-fitting. Precipitation model. (a) constant pressure 4.0 MPa, concentration ratio 2.5, flow velocity 2.5 m/set, 30°C; (b) initial pressure 2.8 MPa, maximally allowed pressure 4.0 MPa attained at 150 min, concentration ratio 2.5, flow velocity 2.5 m/set, 30” C.
102
From the residual graphs it is concluded that there is a systematic variation in the first hours of an experiment. Experiments with increasing process pressure during the first hours showed a stronger deviation. However, the results of curve-fitting did not improve by adding a pressure-dependent parameter or a compaction parameter in the model. Initial permeation
resistance R&t = 0)
For both the gel layer and the precipitation model there was no significant difference between the estimated values of R,,,( t = 0). These values decrease with decreasing pressure, concentration ratio and temperature and with increasing flow velocity. The estimated relation between Rtot (t = 0 ) and the process variables is: R,,,(t=O)=R,+R,
(21)
where R,=0.21~10l~(Pa-set/m) R, = aubPCC,d
(Pa-set/m)
a=1.78X10-g,
b= -1.19,
c=2.96,
d=2.32
R2 of the fit was 0.92, with a standard deviation of the fit +-0.023X 1012 (Pa-
set/m). These values were estimated at 30°C. Resistances at other temperatures follow by multiplication with: ~~/q~~~c. Gel layer model
Values for A and B concerning the concentration ratio of 2.5 and process temperature of 30” C are plotted in Figs. 6 (a) and 6 (b), respectively. Fouling caused by the formation of a gel layer results in a flow-velocitydependent parameter B (according to a Sherwood-like relationship) and a flowvelocity-independent parameter A (see eqn. 17). Despite moderate reproducibility of the experiments, the graphs clearly demonstrate a trend whereby A is velocity dependent and B is not. Precipitation
model
The curve-fitting results of over 30 experiments indicated that the parameare highly correlated. This means that other comters KT kc4 and ~s.cal/Cb.cal binations of these parameters will be satisfactory too. Consequently, the parameter values should be used with care for interpretation of the mechanism. Mathematical analysis indicates that the high correlation is, among other things, a consequence of the moderate flux decline (factor 2 to 5 ) during these experiments. For situations with a larger flux decline more accurate estimation of the parameters is possible. Due to the high correlation, it is difficult to give an exact interpretation of
103 A.1012 lPa.sim2)
,:
04 1
I
I
1.4
I
I
I
I
I
,
I
I
I
I
1.8
2.2
2.6 3.0 3.4 flowvelocity (m/s)
1.8
2.2
2.6 3.0 3.4 flowvelocity (m/s)
B.106 (Pa/m) 30 ,
,i 1
1.4
Fig. 6. Fitted parameters of gel layer model. 3O”C, concentration ratio 2.5, initial pressure 4.0 MPa. (a) parameter A; (b) parameter B.
the values of the parameters. But the following conclusions about trends in parameters could be made: •IZ,,~ depends on flow velocity (see Fig. 7). Most values are between 3.0 x 10W5 m/set and 7.0 x low5 m/set. These values are higher than the mean values for protein established by other authors (approximately 2.0 x 10e5 m/set ) [ 16181. Despite the high correlation among the parameters these values seem reasonable. *for more than 95% of the experiments, Cs.cal/Cb,cal = 1.00 while KL shows no correlation with C,,. This implies that, independent of the level of bulk concentration, the bulk is always just saturated. Although selection is subject of this study instead of the elucidation of fouling mechanisms, a possible explanation for this specific result is given: As mentioned, in the bulk of whey concentrate an equilibrium between the
104
04 1
, , 1.4
1.8
Fig. 7. Precipitation
, , , , , 2.2
2.6
3.0 flow velocitv
model; correlation
3.4 (m/s)
of kcal with u; 3O”C, concentration
ratio 2.5.
precipitation of amorphous and crystalline calcium phosphate and the precipitation inhibitors is settled. Together with concentration polarization of calcium phosphate, concentration polarization of protein occurs. Because of differences in diffusion coefficients, the degree of concentration polarization of these components differ. As a result, the equilibrium between precipitation and its inhibition is disturbed in the boundary layer and further precipitation occurs. The values for Cs.cal/Cb.cal imply that concentration polarization [exp (J/ k) - LOO] is a measure of the driving force for the rate of fouling. Modification of the precipitation model The ratio between the measured values of J and estimated values of kcal ranges between 0.04 and 0.12. Exp (J/h,,,) can be approximated by using a Taylor series: f(x) =f(x,)
+ (x-&l)
f ‘(x0) -
exp
(J/kaI) = few (~0)){I ---x0+J/k4
Choosing x0= 0.0 gives exp (J/k,,,) FZ1+ J/~s,,~.The expression for the precipitation model results in:
$$=K: (J&d2
(22)
Using kcal= aum gives
(23) where Ki =KL/(a2u2”)
105
This modified model is fitted for the experimental data of Rtot as a function of time. The accuracy of this model is comparable to the accuracy of the original precipitation model. Remark: It would be obvious to choose a value 0.04 < 3to< 0.12 in the Taylor series. But such a choice did not improve the quality of fits. To reduce the complexity of calculations and to obtain an easy-to-use expression x0= 0.0 was chosen. The dependency of Ki upon u is clear (see Fig. 8a), and Ki is better correlated with u than /zCal with v in the original precipitation model. This result is realized by the elimination of the correlation between parameters. The power m (eqn. 23) is not equal to 0.80 as was expected from the Sherwood relation but 1.00.
Ka" 1017IPa.s*im3) 40 .
b
0 20
oc
A 10 ‘C
o! 1
: 1
r
1.4
I
1
1.8
: I
I
2.2
I
I
I
:
I
I
2.6 3.0 3.4 flowvelocity (m/s)
Fig. 8. Modified precipitation
model. (a)
Ki as a function of o. 3O”C, concentration ratio 2.5; (b) Kl and u at 30 ’ C (see fig.
values of K:: at 10 ’ C and 20 ’ C. The curve depicts the relation between 8a).
106
Kl =Kar/vzm
Ka’=K~/a2=4.45X10’8+1.95x1018, m=1.00~0.18
(24)
Major causes of the large variance in these parameters are non measurable differences between charges of feed resulting in a different fouling behaviour. Influence of process temperature Figure 8b demonstrates that most values for Kl are lower at 10’ C and 20’ C that at 30” C (compare experimentally measured points with the fitted line from Fig. 8a). This result is according to the improving solubility of calcium phosphate with decreasing temperature. However, due to the large deviation, no significant correlation between Kl and temperature could be estimated. Discussion of model evaluation Both evaluated models (gel layer and precipitation) agree well with experimental data. The evaluation of the gel layer model indicated that the correlation of parameters with the flow velocity was not conform to the background of the model. From these results it is concluded that fouling is not caused by the formation of a gel layer. The parameters of the precipitation model are highly correlated. For that reason their values cannot be used for exact interpretation of the mechanism. The correlation of mass transfer coefficient (k,,,) with experimental variables is in accordance with the background of the model. Other typical results, the value of Cs,cal/Cb.ca,=1.00, can be understood from the equilibrium between precipitation of amorphous and crystalline calcium phosphate and the suppression of the precipitation by inhibitors. So this model is useful for application. But because of the high correlation among parameters its predictive value is limited. The modified form of the precipitation model has only one parameter which is not affected by any correlation. This parameter is correlated with flow velocity as expected and the tendency of this parameter to lower values for low temperatures is probably the result of a lower precipitation rate of calcium phosphate/protein complexes. The predictive value of this model is quite significant. The mathematical structure of the modified model can be used in calculations. Parameter values for reverse osmosis of whey in a specific installation were estimated in this investigation. These values can be used for a qualitative exploration of optimal operation and control conditions for comparable production situations and installations. For other membrane applications (e.g. spiral wound modules, UF, other products, etc.) typical parameter values have to be estimated first. For higher values of J/k, it is recommended to apply the Taylor series with more terms or to use the original precipitation model.
107
Fouling control
Experimental results and the modified precipitation model indicate that both the initial permeation resistance and the permeation resistance increment, due to fouling, can be controlled by means of the process conditions. The quantitative possibilities for fouling control can be calculated with the model equations. Here a qualitative description is given: (a) The permeation resistance at t = 0 is a function of flow velocity (II), initial process pressure [P( t = 0 ) 1, process temperature ( T) and concentration ratio (C,). In production situations the concentration ratio is normally prescribed, and thus cannot be used in fouling control. Proper choice of u, T and P ( t = 0) results in a low permeation resistance and a high flux value shortly after startup. The total advantage of the choice of P (t = 0)) u and T depends respectively on the driving force for permeation (P-h) and the fouling rate as a function ofvandT (seealsodande). (b ) The process pressure can be applied to compensate fouling in order to keep a constant flux while fouling goes on (eqn. 1) . (c) Process temperature influences the level of permeation resistance by changing the permeate viscosity. Temperature can, like pressure, be applied to compensate for the increased permeation resistance by lowering the permeate viscosity and consequently the actual permeation resistance. (d) Flow velocity is an important variable to reduce the fouling rate (eqn. 23). However, for reverse osmosis of cheese whey it cannot be used for rinsing an existing foul layer. To demonstrate its importance, flux decline simulations for different flow velocities are given in Fig. 9. In these simulations the reduced flux (l/m’.
hl
36
24-
18m/s
12-
3.5 2.5 1.5
60
200
400
600
800 1000 1200 time (mid
Fig. 9. Simulated flux decline for different flow velocities (1.5,2.5 and 3.5 m/set). Concentration ratio 2.5, initial pressure 4.0 MPa, temperature 30°C.
108
initial permeation resistance (eqn. 21) is incorporated. The choice of the optimal flow velocity, to control fouling, should be examined against the background of raising energy costs with increasing flow velocity. (e) Experimental results show a tendency for a lower fouling rate at low process temperatures (see Figs. 4b and 8b). For some experiments the total capacity of the installation was larger at low temperatures.
Conclusions In contrast to the gel layer model, the precipitation model shows a good agreement with the fouling rate of tubular membranes during reverse osmosis of whey. The precipitation model can be modified by using a Taylor series. This results in an easy-to-use model with only moderate loss of accuracy. The reproducibility of curve-fitting is affected by variations in the natural feed which cannot be ascribed to measurable qualities. This results in a larger variance of parameter values. Nevertheless the modified model is useful for exploring possibilities for fouling control. Important conclusions for fouling control are: *flow velocity and temperature can be used to control the fouling rate. Flow velocity should be raised and temperature should be lowered to achieve lower fouling rate. apressure and temperature can be used to compensate for the fouling in order to maintain a constant flux. aat first sight, high temperatures seem to be attractive. But the moderate fouling rate at low temperatures may result in higher performance for long production runs. *for an optimal operation the use of the control variables must be considered with the costs of the fouling rate on the one hand and the costs of these control variables on the other. The model equations can be applied for calculations of optimal process setpoints, characterization of long-term membrane fouling for reverse osmosis and estimation of optimal control policies.
Acknowledgement This investigation was partly supported by the Programme Commission Membrane Technology of the Ministry of Economics (PCM) and Stork-Friesland ( Wafilin ).
109
List of symbols
L
p” R tot R tot (k0)
Rf R,
RP r T t TS V 4 UY x X0
Y
parameter in gel layer model ( Pa-sec/m2) parameter in gel layer model (Pa/m) various constants concentration of solids ( kg/m3 ) concentration of solids in bulk ( kg/m3) gel concentration ( kg/m3) concentration of solids at membrane surface ( kg/m3) concentration ratio between product and feed ( - ) saturation concentration (kg/m”) diffusion coefficient (m”/sec) function denotation first order derivate of function permeate flux ( m3/m2-set) mass transfer coefficient (m/set) constant precipitation rate constant ( m4/kg-see) lumped parameter for precipitation rate (Pa/m) parameter for precipitation rate in the modified model ( Pa-sec2/ m3) thickness of foul layer (m) constant process pressure (Pa) total permeation resistance (Pa-set/m) initial permeation resistance at t= 0 (Pa-set/m) time dependent part of permeation resistance caused by fouling (Pa-set/m) resistance to permeation of water (Pa-set/m) additional permeation resistance as result of chosen process conditions during the preconcentration phase (Pa-set/m) deposition rate of solids (kg/m’-set) temperature ( ’ C ) time (set ) total solids (% ) flow velocity (m/set) flow velocity in the direction perpendicular to the membrane (m/ set ) flow velocity parallel to membrane (m/set) distance perpendicular to the membrane surface (m) constant distance parallel to the membrane surface (m)
110
Subscripts
cal pr
related to calcium phosphate related to protein
Greek symbols 6 thickness of boundary layer (m)
E YI
resistance per unit of foul layer thickness ( Pa-sec/m2) dynamic viscosity (Pa-see) osmotic pressure difference between bulk and permeate (Pa) density (kg/m3)
A7l P
References 1 2
J. Hiddink, R. de Boer and P.F.C. Nooy, Reverse osmosis of dairy liquids, J. Dairy Sci., 63 (1980) 204-214. G.B. van den Berg, Model voorspelt optreden van concentratie-polarisatie I’-Procestech-
3
nologie, 10 (1987) 49-53. G.B. van den Berg and C.A. Smolders,
4
5
6 7 8
9 10 11
12 13
Flux decline in membrane
processes,
Filtration
and
Separation, March/April (1988) 115-121. J.H. Hanemaayer, T. Robbertsen, Th. van den Boomgaard, C. Olieman, P. Both and D.G. Schmidt, Characterization of clean and fouled ultrafiltration membranes, Desalination, 68 (1988) 93-108. J.H. Hanemaayer, T. Robbertsen, Th. van den Boomgaard and J.W. Gunnink, Fouling of ultrafiltration membranes. The role of protein adsorbtion and salt precipitation, J. Membrane Sci., 40 (1989) 199-217. E. Matthiasson and B. Sivik, Concentration-polarization 59-103.
and fouling, Desalination,
35 (1980)
A.G. Fane and C.J.D. Fell, A review of fouling and fouling control in ultrafiltration, Desalination, 62 (1987) 117-136. R.G. Gutman, The design of membrane separation plant, Part 1: Design of reverse osmosis modules, Chem. Engineer, (1977) 510-513, 521; Part 2: Fouling of RO membranes, Chem. Engineer, (1977) 521-523. A. Suki, A.G. Fane and C.J.D. Fell, Flux decline in protein ultrafiltration, 21 (1984) 269-283.
J. Membrane
Sci.,
R.D. Cohen and R.F. Probstein, Colloidal fouling of reverse osmosis membranes, J. Colloid Interface Sci., 114 (1) (1986) 194-207. A.G. Fane, C.J.D. Fell and M.T. Nor, Ultrafiltration/activated sludge system - development of a predictive model, in: A.R. Cooper (Ed.), Ultrafiltration Membranes and Applications, Plenum Press, New York, NY, 1980, pp. 631-658. S. Kimura and S. Nakao, Fouling of cellulose acetate tubular reverse osmosis modules treating the industrial water in Tokyo, Desalination, 17 (1975) 267-288. M. Okazaki and S. Kimura, Scale formation on reverse osmosis membranes, J. Chem. Eng. Jpn., 17 (2) (1984) 145-151.
14
J. Borden, J. Gilron and D. Hasson, Analysis of RO flux decline due to membrane blockage, Desalination, 66 (1987) 257-269.
15
D.G. Schmidt and P. Both, Studies on the precipitation of calcium phosphate. 1. Experiments in the pH-range 5.3 to 6.8 at 25” C and 50 aC in the absence of additives, Neth. Milk and Dairy J., 41 (1987) 105-120.
surface
111 16
17 18
U. Kulozik, Einfliisse auf die Permeation von Wasser und gel&ten Stoffen sowie auf den Deckschichtabtrag bei der Umkehrosmose, VDI-Verlag, Reihe 3 : Verfahrenstechnik, nr. 120, 1986. J. Hiddink and R. de Boer, Concentration of milk and whey by reverse osmosis, in: P. Linko (Ed.), Food. Proc. Eng., Vol. 1, Appl. Sci. Publ., 1980,561-571. G. Jonsson, Boundary layer phenomena during ultrafiltration of dextran and whey protein solutions, Desalination, 51 (1984) 61-77.
89
Evaluation of process models for fouling control reverse osmosis of cheese whey
of
A.J.B. van Boxtel, Z.E.H. Otten and H.J.L.J. van der Linden NIZO (Netherlands (Received
Institute
April 30,199O;
for Dairy Research),
accepted
PO Box 20,671O BA, Ede, Netherlands
in revised form January
21,199l)
Abstract Long-term
fouling of reverse-osmosis
membranes
processing
dairy products
can be caused by
two phenomena: (1) an increasing thickness of the protein gel layer; (2) deposit formation due to precipitation of calcium phosphate/protein complexes. Mechanistic models describing these two phenomena are evaluated for a tubular reverse-osmosis pilot-plant for concentrating cheese whey during a 20 hour period. The experimental variables were the initial pressure after start-up, flow velocity, concentration ratio and process temperature. The results indicate that the model of a growing gel layer does not fit the process of long-term fouling. However, a precipitation model for calcium phosphate showed good agreement with the experimental results. Finally, experimental results and a modified form of the precipitation model are applied to explore possibilities for controlling fouling by adapting the controlling variables flow velocity, pressure and temperature. Keywords:
fouling; reverse osmosis;
whey; food industry
Introduction
The application of membrane filtration is of growing interest for the process and food industry. Besides a low energy consumption, the possibility of performing product separations under favourable conditions, resulting in better product qualities, is one of the most attractive features of this technology for the food industry. However, long-term fouling of membrane surfaces, resulting in flux decline over hours or days, is one limitation for industrial applications. For design of industrial membrane installations the flux decline must be taken into account by overdimensioning of installations, and special measures must be taken to integrate membrane filtration installations in a production line. Such measures are cyclic operation of parallel membrane filtration units or installation of sufficient buffer capacity. As a consequence investment and operation costs rise. Another limitation for industrial application of membrane processes to foodstuffs is caused by large and uncertain differences in fouling behaviour between succeeding charges of the feed.
0376-7388/91/$03.50
0 1991-
Elsevier
Science
Publishers
B.V.
90
With this background, study of fouling phenomena has always been a very important topic in membrane research. One of the world-wide activities in this field is the development of models describing fouling phenomena. The aim of these studies is to use the insight obtained to make appropriate membrane modifications and to develop product (pre)treatments to reduce fouling. The results of these studies, however, are hardly used for optimal design, optimal process operation, and control of membrane filtration installations. On account of the growing importance of membrane filtration in the foodand particularly the dairy industry, the relevance of fouling models to calculate the optimal process operation and control should be examined. The first step in such application is the selection of an appropriate process model for membrane fouling from the available fouling models. In this investigation, mechanistic models for fouling of reverse osmosis of cheese whey on a semi industrial tubular membrane installation were evaluated. Subjects to be discussed in this paper are: *definition of long-term fouling; @relation between fouling and increasing permeation resistance; *characteristics of membrane fouling for reverse osmosis of cheese whey; two models for fouling: a gel layer model and a precipitation model; *experimental set-up; *evaluation of results; *a qualitative description of possible applications of process conditions in fouling control. l
Definition of long-term fouling For cross-flow membrane filtration installations there is a difference in flux decline characteristics between reverse osmosis (RO) on the one hand and ultrafiltration (UF) and microfiltration (MF) on the other (Fig. 1). In the RO situation, permeate flux at t= 0 is only a little lower than the water flux. Hiddink et al. [l] established, for cheese whey and skim milk, that at t = 0 the permeation resistance was higher than the resistance to permeation of water. This supplementary resistance is caused by, among other thing, concentration polarization phenomena and is a function of the chosen process conditions. After t= 0, flux declines during the next hours or days of the production run. This is due to what we call long-term fouling. For UF and MF, shortly after t=O permeate flux is much lower than the water flux. This is the result of, in comparison to RO, excessive concentration polarization [ 2,3] and blocking of membrane pores and membrane surfaces in the first seconds and minutes after t=O [4,5]. Within a few minutes, flux is
91 permeate flux water flux
IS)
time
Fig. 1. Flux decline characteristics for RO, UF and MF.
between lo%-40% of the water flux. This is what we call short-term fouling. After this initial decline, flux continues to decline due to long-term fouling. Theory
Permeation resistance A common relation between process pressure total permeation resistance (R,,,) is: P-An J=R tot
(P), permeate
flux (J) and
(1)
or P-An
fL,t = __J
(2)
in which An represents the osmotic pressure difference between bulk and permeate. Total permeation resistance (R,,,,) is the sum of individual resistances in series: R,,,, = R, + 4, + R,
(3)
where OR,,, represents the resistance of the membrane to permeation of water. For new membranes this value is weakly time dependent due to membrane compaction. For industrial installations this time dependence is small compared to the resistance increment due to fouling ( Rf ) . Compaction occurs only during a short period of the total life time of the membrane. Therefore the effect of compaction on the optimal operation and control will be neglected.
92
OR, is an additional time-independent resistance which is a result of the chosen process conditions [ 11. This resistance is partly effected by concentration polarization phenomena and by a foul layer which is built up while the industrial installation is being filled with product under the chosen process conditions. Hiddink et al. [l] demonstrate the relationship between these process conditions and R, in graphs. However these results may also be expressed in a mathematical relationship. Statistical analysis of Hiddink’s results indicates that R, is correlated with flow velocity, process pressure and concentration ratio according to the power function: R,=avhPCC~
(4)
.RF is the strongly time-dependent part of the resistance and is characteristic for membrane fouling. In next paragraphs two mechanistic models for this resistance will be discussed. All resistances are temperature dependent as a consequence of the temperature dependency of the dynamic viscosity of the permeate. Rewriting eqn. (1) results in: J=
p-A7T
R,+R,+Rf R,
can be estimated from experiments with (clean) water and R, from the initial permeation resistance just after start-up of an installation. The relation of R, with process conditions and its function of time has to be estimated from long experimental production runs.
Fouling phenomena
for cheese whey
Several authors have derived models for the long-term fouling of membranes. Matthiasson and Sivik [ 61 and Fane and Fell [ 71 survey these models. The literature list includes several other papers discussing the background of fouling models [ 8-141. For the application of process models for optimal operation and control, mechanistic models are to be preferred. These models are more flexible for extrapolation to other process conditions and other membrane installations. For the selection of an appropriate process model, properties of cheese whey should be considered first. Cheese whey contains several components, e.g. fat, lactose, protein and salts (i.a. calcium phosphate). Membrane fouling hardly occurs for decalcified whey [1 ] and because of the ability of protein to cause membrane fouling, it may be stated that protein and calcium phosphate are responsible for membrane fouling during reverse osmosis of cheese whey.
93
Protein In comparison to milk or several other foodstuffs the protein concentration in cheese whey is relatively low. Fresh cheese whey contains approximately 0.6-0.8 weight percent protein. However, the concentration polarization raises the protein concentration near the membrane, and it may reach the gel concentration. If so, the concentration at the membrane surface cannot increase any more. The surplus of material transport in the direction of the membrane results in a growing gel layer which causes an increasing resistance to permeation. Calcium phosphate It is well known that calcium phosphate plays an important role in fouling of membranes [ 151. Schmidt and Both [ 151 mentioned that in milk and whey calcium phosphate is supersaturated. From this supersaturated state first amorphous calcium phosphate is formed which crystallizes subsequently into several crystalline states. However, the precipitation of amorphous and crystallized calcium phosphate is inhibited by the formation of complexes with protein. The solubility and the inhibition of the precipitation both depend on the temperature and pH. Precipitation occurs mainly at temperatures above 40 oC but is also possible at lower temperatures. Fouling of membranes, even at low temperatures, can be reduced by adding acid to whey and milk to give a pH of 5.8-6.0 [ 11. This results in a better solubility of calcium phosphate. Another method is a heat treatment (e.g. 10 min. at 60’ C ) before the feed enters the membrane installation. During this heat treatment calcium phosphate precipitates, with the result that supersaturation of the feed is reduced. Special attention should be paid to the interaction between calcium phosphate and proteins. Both amorphous and crystalline calcium phosphate form complexes within proteins and together with calcium phosphate the protein precipitates. Furthermore, between succeeding charges of cheese whey significant concentration differences of the crystallization and precipitation inhibitors may occur. Consequently the fouling characteristics for succeeding charges of cheese whey varies. Constitution of foul layers Kulozic [ 161 concluded from electron micrographs and chemical analysis that the foul layer consists mainly of proteins and salts, and is 30-50 pm thick. The properties of the layer change with increasing distance from the membrane. Close to the membrane surface the layer is firm and removal of this part is relatively difficult. With increasing distance from the membrane the firmness of the layer decreases and removal becomes easier. The top layer can even be removed by rinsing. Kulozic suggested that calcium is indispensable in the precipitation of protein, as it forms bridges between protein molecules.
94
This information suggests the operation of two mechanisms, namely: *the formation of a gel layer, and *formation of a foul layer due to precipitation and crystallization of amorphous calcium phosphate. Concentration
polarization
In Fig. (2) a cross-section of the bulk, membrane and permeate is considered. The mass balance for an arbitrary product component in volume A is given by:
dc
ac
ac
dt+vy.+vy-=
ay
-Llg
(6)
For industrial installations the concentration gradient in the direction of product flow (clC/cly) can be neglected in comparison with dC/dx. With u, = J it follows that:
ac
ac
(7)
dt+Jz=-D$
The boundary
conditions
are:
t=o-
c=c,
x=6--f
C = Cb (6 is thickness
x=0-
JC
m-
of boundary
_-L)g ax
J
T
flow direction
membrane
Fig. 2. Cross-section
of a membrane svstem.
layer) .
95
In this case 100% retention is assumed. This means that no solutes of the bulk will pass the membrane. For positive values of J the product concentration near the membrane will increase until a steady state (dC/dt=O) is reached. Under steady-state conditions the concentration is a function of the distance from the membrane. The solution of eqn. (7 ) under steady-state conditions is: (3) with D/S= Iz (mass transfer coefficient) J=kln%
(9)
or
b
The concentrations of all product components increase in the boundary layer. However, the diffusion coefficients of the components are different because of the variations in molecular dimensions. Consequently, the degree of concentration polarization of protein is higher than that of calcium phosphate (&l>&). The concentration polarization is defined by the ratio between J and k. For reverse osmosis of whey values for J vary between 1.0 x lop6and 5.5 x 10W6 m3/m2-sec. Mean values of lzare approximately 2.0 x low5m/set [ 16-181. This results in values of C, between 1.05 and 1.30 times Cb. Therefore the concentration polarization in RO installations is of less importance in comparison with UF and MF processes, for which the flux (J) may be 5 to 25 times the flux of RO processes. In the steady state transport of material in the direction of the membrane equals back diffusion:
J
c,,= cbk
hl+ b
(11)
Gel layer model This model was proposed by Kimura and Nakao [ 121. Due to polarization the concentration near the membrane surface (C,) can reach the gel concentration (C,,,,) . This means no further increase in concentration will occur and a gel layer will be built up. In the steady state the boundary condition is C= Cg.pr for x= 0. This results in: J=&
ln%
(12)
-
Cg.pr=Cb.preXP
(13)
b.pr
During the time the gel layer is built up the difference between transport in
the direction of the membrane of the gel layer.
e=
JCb+,-- Gprkpr
and back diffusion is proportional
In%,
L(t=O)
to the growth
=o
(14)
b.pr
For a linear relation layer:
between
permeation
resistance
and thickness
of the gel (15)
Rf= EL it follows that
‘% EJCb.pr~.‘%,rk,,rln%,r -=-P G.pr dt P
(16)
This relation contains several parameters which are not exactly known or are totally unknown, e.g. which part of the protein concentration will form the gel layer or the value of t. However, evaluation of the model is possible by using lumped parameters. The equation is reduced to: Mf dt=AJ-B
withA=---
(17)
C.CbJX P
’
B=
t-Cb.prkpr P
lnC,.,r
and R,(t=O)
=O
Cb.pr
Only the values of A and B have to be estimated from experimental data of total permeation resistance (R,,,,) as a function of time. On account of the relationship between mass transfer coefficient (k) and flow velocity (U 1 (the Sherwood relation), B is correlated with u. Precipitation model As mentioned above, because of the supersaturation of calcium phosphate, first amorphous and subsequently crystalline calcium phosphate precipitates. The precipitation is inhibited by the presence of complexes between calcium phosphate and protein. In the bulk of a whey concentrate, there is an equilibrium between the affinity for precipitation and the inhibition. During reverse osmosis the concentration polarization raises the supersaturated state in the boundary layer and precipitation followed by crystallization is continued. Concentration polarization is a function of the applied process conditions (k by flow velocity and J by process pressure) and as a result the precipitation is a function of these process conditions. Okazaki and Kimura [ 131 suggested a model for the precipitation of calcium sulphate at the membrane surface. This model is based on the crystallization kinetics and describes the formation of a smooth foul layer over the membrane
97
surface with a permeation resistance proportional to the thickness of the layer. In that model a second-order reaction kinetic from the crystallization kinetic of calcium sulphate is used. The second order kinetic is also acceptable for the precipitation of calcium phosphate. And similarly this model can also be applied to the deposit formation during reverse osmosis of cheese whey. L(t=0) ~=K,(c,,,,-c,,,,)2,
=o
Combination of eqn. (18) with Cm.cal=Cb,calexp (J/k,,,) (15 ) results in
(18) (10a) and Rf= EL
(19) Like the gel layer model, this model contains several parameters which are not exactly known or are totally unknown. However, it can also be evaluated by using lumped parameters:
(20) where K: = ~KaGxcalal~
and
R,(t=O)
=O
must be estimated from experiThe values of Kg, kcal and the ratio Cs.cal/Cb.cal mental data. kcalshould depend on flow velocity and & is related to the bulk concentration. Borden et al. [ 141 proposed an alternative precipitation model, which differs from that of Okazaki and Kimura by the assumption that crystallization starts at nucleation points. These nucleation points expand by crystallization and will gradually block the membrane surface. Electron micrographs indicate that fouling is not concentrated at nucleation points but spread over the total membrane surface [ 161. Therefore the approach of Borden et al. [ 141 is not considered further. Experimental set-up
Equipment To obtain an appropriate process model for optimal operation and control of industrial installations, experiments were performed on a semi-industrial one-stage recirculation reverse-osmosis pilot plant. This pilot plant consists of four modules containing tubular composite membranes (Stork-Wafilin WFCOOG). In each module, 19 membrane tubes 4 meters long and 14.4 mm in diameter are installed. The total membrane surface is 13.7 m2.
98
Figure 3 shows the flow chart of the pilot plant. In the low-pressure part of the installation the feed is heated up to the specified process temperature. The heat exchanger can optionally be used for a heat treatment of the feed (e.g. 10 min at 60°C). Subsequently the feed is pumped into the membrane installation by the high-pressure pump. Depending on the specified concentration ratio, part of the concentrate runs off the installation as final product, while the majority is recirculated along the membranes. To avoid a rise in temperature due to circulation, the concentrate is kept at the specified temperature with a water cooling system. There are two options for pretreatment of the feed to reduce fouling: *the already mentioned heat treatment in the heat exchanger and temperature holder; *or acidification of the feed in the feed tank to pH 5.8-6.0. The control loops are shown in Fig. 3. These are: *temperature control of heat treatment, specified process temperature and the cooling system. *flow velocity along the membranes. *concentration level. This is realized by a constant ratio between feed capacity and final product flow. aconstant process pressure and/or constant permeate flux. This control offers the possibility for two production phases. The installation is started up below the maximal allowed process pressure. During the first phase the feed capacity is kept constant while process pressure increases due to fouling. The second phase starts as soon as the maximum allowed pressure is reached. Then the process pressure is kept constant while permeated flux decreases due to fouling. Besides these control loops several alarm indicators are installed. To improve reproducibility of experiments, the control, start-up and shut down of the installation are programmed in a process computer system (Siemens Teleperm-M). Experimental data are collected on-line by a personal computer connected to the process computer.
Fig. 3. Pilot-plant
flow sheet with control loops.
99
Experimental procedure All experiments were performed with fresh cheese whey. The pH of the whey was decreased from 6.6 to 5.8 by acidification. Initially the installation was filled with feed and subsequently preconcentration was started by keeping the product valve closed while feed was pumped into the installation. The product valve was opened when the specified concentration was attained and then the continuous production phase started. During the preconcentration phase the process pressure and flow velocity had the same values as during the experiment. The permeate flux was continuously calculated from the difference between the feed capacity and the product capacity. Both were determined by electromagnetic flow measurement devices with an accuracy of + 0.2%. The permeation resistance was calculated according to eqn. (2) in which dn z TS [ 171. After approximately 20 hr the installation was shut down, rinsed with water and cleaned according to the instructions of the membrane manufacturer. After each run the water flux was measured at 25°C and 2.0 MPa as a check on cleaning. Usually a reverse-osmosis installation is operated at the maximally allowed pressure. But, as an alternative procedure, manufacturers of membrane installations recommend starting up the installations at a lower initial pressure while the flux is kept constant until the maximum pressure is attained, after which the pressure is kept at this level with decreasing flux. Both procedures were applied during the experimental runs. In the pilot plant installation the maximal allowed pressure was 4.0 MPa. For all experiments, the protein, lactose, fat and calcium contents of the cheese whey were determined by infra-red analyses. The pH after acidification, density, refractive index and conductivity of feed and refractive index of the final product were also measured. Finally, a regular check was performed to obtain an indication of the contribution of membrane compaction to the time dependency of R,. These checks showed that membrane compaction was negligible.
Experimental programme First, experiments were performed at 30’ C and a concentration ratio of 2.5. The flow velocity (1.5,2.0,2.5 and 3.0 m/set) and initial pressure (2.8,3.4 and 4.0 MPa) were varied. Second, for the initial pressure of 2.8 MPa and process temperature of 30” C, the flow velocity (1.5,2.0,2.5 and 3.0 m/set) and concentration ratio (2.0,2.5, 3.0,3.5 and 4.0) were varied. Third, for an initial pressure of 4.0 MPa. and a concentration ratio of 2.5, temperature (lo,20 and 30°C) and flow velocity (1.5. 2.0,2.5 and 3.0 m/set) were varied.
100 Results
The course of permeation resistance Figures 4 (a) and 4 (b) show some typical examples of fouling, expressed by plotting the permeation resistance as a function of time. Figure 4 (a) shows a reduction of the permeation resistance for increasing flow velocities. This demonstrates the possibility of controlling fouling by the flow velocity. Figure 4 (b) illustrates that, after 2-3 hr, the permeation resistance is considerably lower at 10” C and 20” C than at 30°C. This result can partly be explained by the lower fluxes at 10’ C and 20’ C (see eqns. 17 and 20). But the main reason is the temperature dependency of the solubility of calcium phosphate as well as
RtotITPa.s:mi 2.0 a m/s
1.5-
1.5 2 2.5
01
800
1000
1200 time(mlnl
Rtot(TPa.s/m) 2.0_I _
b
-t I 0
I 200
I
I
400
,
I
M)o
I,
,
800
,
,
,
,
1000 1200
Fig. 4. Permeation resistance as a function of time. (a) flow velocity 1.5, 2.0, 2.5, 3.0 m/set Constant pressure P=4.0 MPa, temperature 3O”C, concentration ratio 2.5; (b) process temper. ature lO”C, 2O’C, 30°C. Pressure 4.0 MPa, u=2.0 m/set, concentration ratio 2.5.
101
the precipitation inhibition. This aspect will be discussed in the section “Influence of process temperature”. As a result of the temperature variations, for several experiments at 10°C and 20’ C the total capacity (20 hr ) of the pilot plant was lo-20% higher then for comparable experiments at 30’ C. Remark: Duplicate experiments demonstrated that for feeds with the same specifications a different rate of fouling could occur. Model evaluation
For all the experiments the parameters A, B and Rtot (t= 0) of the gel layer and R,, ( t = 0 ) for the precipitation model were model and &, Ll, CA/G.~~I estimated by non-linear curve-fitting combined with a Runge-Kutta method for solving the differential equations. Both models showed a good agreement with the experimental data. The mean error of the fitted results was about + 0.02 x 101’ Pa-set/m. Figures 5 (a) and 5(b) are a selection of the fitting results including the residuals. Graphical presentations of fitting results and experimental data demonstrated that there was no significant difference between the curve-fitting results of the two models.
a
Rtot(TPa.sim)
Rtot(TPa.sim)
1.5~
0
200
400
600
800
1000 1200 time(mid
0
200
400
600
800
1OW
1200 time(min)
600
800
1000 1200 time(min)
ARtot(TPa.sim)
ARtot(TPa.sim)
0.05$
-o.os‘l 0
200
Fig. 5. Typical
400
600
800
1000 1200 time(min)
0.05l 0
200
400
results of curve-fitting. Precipitation model. (a) constant pressure 4.0 MPa, concentration ratio 2.5, flow velocity 2.5 m/set, 30°C; (b) initial pressure 2.8 MPa, maximally allowed pressure 4.0 MPa attained at 150 min, concentration ratio 2.5, flow velocity 2.5 m/set, 30” C.
102
From the residual graphs it is concluded that there is a systematic variation in the first hours of an experiment. Experiments with increasing process pressure during the first hours showed a stronger deviation. However, the results of curve-fitting did not improve by adding a pressure-dependent parameter or a compaction parameter in the model. Initial permeation
resistance R&t = 0)
For both the gel layer and the precipitation model there was no significant difference between the estimated values of R,,,( t = 0). These values decrease with decreasing pressure, concentration ratio and temperature and with increasing flow velocity. The estimated relation between Rtot (t = 0 ) and the process variables is: R,,,(t=O)=R,+R,
(21)
where R,=0.21~10l~(Pa-set/m) R, = aubPCC,d
(Pa-set/m)
a=1.78X10-g,
b= -1.19,
c=2.96,
d=2.32
R2 of the fit was 0.92, with a standard deviation of the fit +-0.023X 1012 (Pa-
set/m). These values were estimated at 30°C. Resistances at other temperatures follow by multiplication with: ~~/q~~~c. Gel layer model
Values for A and B concerning the concentration ratio of 2.5 and process temperature of 30” C are plotted in Figs. 6 (a) and 6 (b), respectively. Fouling caused by the formation of a gel layer results in a flow-velocitydependent parameter B (according to a Sherwood-like relationship) and a flowvelocity-independent parameter A (see eqn. 17). Despite moderate reproducibility of the experiments, the graphs clearly demonstrate a trend whereby A is velocity dependent and B is not. Precipitation
model
The curve-fitting results of over 30 experiments indicated that the parameare highly correlated. This means that other comters KT kc4 and ~s.cal/Cb.cal binations of these parameters will be satisfactory too. Consequently, the parameter values should be used with care for interpretation of the mechanism. Mathematical analysis indicates that the high correlation is, among other things, a consequence of the moderate flux decline (factor 2 to 5 ) during these experiments. For situations with a larger flux decline more accurate estimation of the parameters is possible. Due to the high correlation, it is difficult to give an exact interpretation of
103 A.1012 lPa.sim2)
,:
04 1
I
I
1.4
I
I
I
I
I
,
I
I
I
I
1.8
2.2
2.6 3.0 3.4 flowvelocity (m/s)
1.8
2.2
2.6 3.0 3.4 flowvelocity (m/s)
B.106 (Pa/m) 30 ,
,i 1
1.4
Fig. 6. Fitted parameters of gel layer model. 3O”C, concentration ratio 2.5, initial pressure 4.0 MPa. (a) parameter A; (b) parameter B.
the values of the parameters. But the following conclusions about trends in parameters could be made: •IZ,,~ depends on flow velocity (see Fig. 7). Most values are between 3.0 x 10W5 m/set and 7.0 x low5 m/set. These values are higher than the mean values for protein established by other authors (approximately 2.0 x 10e5 m/set ) [ 16181. Despite the high correlation among the parameters these values seem reasonable. *for more than 95% of the experiments, Cs.cal/Cb,cal = 1.00 while KL shows no correlation with C,,. This implies that, independent of the level of bulk concentration, the bulk is always just saturated. Although selection is subject of this study instead of the elucidation of fouling mechanisms, a possible explanation for this specific result is given: As mentioned, in the bulk of whey concentrate an equilibrium between the
104
04 1
, , 1.4
1.8
Fig. 7. Precipitation
, , , , , 2.2
2.6
3.0 flow velocitv
model; correlation
3.4 (m/s)
of kcal with u; 3O”C, concentration
ratio 2.5.
precipitation of amorphous and crystalline calcium phosphate and the precipitation inhibitors is settled. Together with concentration polarization of calcium phosphate, concentration polarization of protein occurs. Because of differences in diffusion coefficients, the degree of concentration polarization of these components differ. As a result, the equilibrium between precipitation and its inhibition is disturbed in the boundary layer and further precipitation occurs. The values for Cs.cal/Cb.cal imply that concentration polarization [exp (J/ k) - LOO] is a measure of the driving force for the rate of fouling. Modification of the precipitation model The ratio between the measured values of J and estimated values of kcal ranges between 0.04 and 0.12. Exp (J/h,,,) can be approximated by using a Taylor series: f(x) =f(x,)
+ (x-&l)
f ‘(x0) -
exp
(J/kaI) = few (~0)){I ---x0+J/k4
Choosing x0= 0.0 gives exp (J/k,,,) FZ1+ J/~s,,~.The expression for the precipitation model results in:
$$=K: (J&d2
(22)
Using kcal= aum gives
(23) where Ki =KL/(a2u2”)
105
This modified model is fitted for the experimental data of Rtot as a function of time. The accuracy of this model is comparable to the accuracy of the original precipitation model. Remark: It would be obvious to choose a value 0.04 < 3to< 0.12 in the Taylor series. But such a choice did not improve the quality of fits. To reduce the complexity of calculations and to obtain an easy-to-use expression x0= 0.0 was chosen. The dependency of Ki upon u is clear (see Fig. 8a), and Ki is better correlated with u than /zCal with v in the original precipitation model. This result is realized by the elimination of the correlation between parameters. The power m (eqn. 23) is not equal to 0.80 as was expected from the Sherwood relation but 1.00.
Ka" 1017IPa.s*im3) 40 .
b
0 20
oc
A 10 ‘C
o! 1
: 1
r
1.4
I
1
1.8
: I
I
2.2
I
I
I
:
I
I
2.6 3.0 3.4 flowvelocity (m/s)
Fig. 8. Modified precipitation
model. (a)
Ki as a function of o. 3O”C, concentration ratio 2.5; (b) Kl and u at 30 ’ C (see fig.
values of K:: at 10 ’ C and 20 ’ C. The curve depicts the relation between 8a).
106
Kl =Kar/vzm
Ka’=K~/a2=4.45X10’8+1.95x1018, m=1.00~0.18
(24)
Major causes of the large variance in these parameters are non measurable differences between charges of feed resulting in a different fouling behaviour. Influence of process temperature Figure 8b demonstrates that most values for Kl are lower at 10’ C and 20’ C that at 30” C (compare experimentally measured points with the fitted line from Fig. 8a). This result is according to the improving solubility of calcium phosphate with decreasing temperature. However, due to the large deviation, no significant correlation between Kl and temperature could be estimated. Discussion of model evaluation Both evaluated models (gel layer and precipitation) agree well with experimental data. The evaluation of the gel layer model indicated that the correlation of parameters with the flow velocity was not conform to the background of the model. From these results it is concluded that fouling is not caused by the formation of a gel layer. The parameters of the precipitation model are highly correlated. For that reason their values cannot be used for exact interpretation of the mechanism. The correlation of mass transfer coefficient (k,,,) with experimental variables is in accordance with the background of the model. Other typical results, the value of Cs,cal/Cb.ca,=1.00, can be understood from the equilibrium between precipitation of amorphous and crystalline calcium phosphate and the suppression of the precipitation by inhibitors. So this model is useful for application. But because of the high correlation among parameters its predictive value is limited. The modified form of the precipitation model has only one parameter which is not affected by any correlation. This parameter is correlated with flow velocity as expected and the tendency of this parameter to lower values for low temperatures is probably the result of a lower precipitation rate of calcium phosphate/protein complexes. The predictive value of this model is quite significant. The mathematical structure of the modified model can be used in calculations. Parameter values for reverse osmosis of whey in a specific installation were estimated in this investigation. These values can be used for a qualitative exploration of optimal operation and control conditions for comparable production situations and installations. For other membrane applications (e.g. spiral wound modules, UF, other products, etc.) typical parameter values have to be estimated first. For higher values of J/k, it is recommended to apply the Taylor series with more terms or to use the original precipitation model.
107
Fouling control
Experimental results and the modified precipitation model indicate that both the initial permeation resistance and the permeation resistance increment, due to fouling, can be controlled by means of the process conditions. The quantitative possibilities for fouling control can be calculated with the model equations. Here a qualitative description is given: (a) The permeation resistance at t = 0 is a function of flow velocity (II), initial process pressure [P( t = 0 ) 1, process temperature ( T) and concentration ratio (C,). In production situations the concentration ratio is normally prescribed, and thus cannot be used in fouling control. Proper choice of u, T and P ( t = 0) results in a low permeation resistance and a high flux value shortly after startup. The total advantage of the choice of P (t = 0)) u and T depends respectively on the driving force for permeation (P-h) and the fouling rate as a function ofvandT (seealsodande). (b ) The process pressure can be applied to compensate fouling in order to keep a constant flux while fouling goes on (eqn. 1) . (c) Process temperature influences the level of permeation resistance by changing the permeate viscosity. Temperature can, like pressure, be applied to compensate for the increased permeation resistance by lowering the permeate viscosity and consequently the actual permeation resistance. (d) Flow velocity is an important variable to reduce the fouling rate (eqn. 23). However, for reverse osmosis of cheese whey it cannot be used for rinsing an existing foul layer. To demonstrate its importance, flux decline simulations for different flow velocities are given in Fig. 9. In these simulations the reduced flux (l/m’.
hl
36
24-
18m/s
12-
3.5 2.5 1.5
60
200
400
600
800 1000 1200 time (mid
Fig. 9. Simulated flux decline for different flow velocities (1.5,2.5 and 3.5 m/set). Concentration ratio 2.5, initial pressure 4.0 MPa, temperature 30°C.
108
initial permeation resistance (eqn. 21) is incorporated. The choice of the optimal flow velocity, to control fouling, should be examined against the background of raising energy costs with increasing flow velocity. (e) Experimental results show a tendency for a lower fouling rate at low process temperatures (see Figs. 4b and 8b). For some experiments the total capacity of the installation was larger at low temperatures.
Conclusions In contrast to the gel layer model, the precipitation model shows a good agreement with the fouling rate of tubular membranes during reverse osmosis of whey. The precipitation model can be modified by using a Taylor series. This results in an easy-to-use model with only moderate loss of accuracy. The reproducibility of curve-fitting is affected by variations in the natural feed which cannot be ascribed to measurable qualities. This results in a larger variance of parameter values. Nevertheless the modified model is useful for exploring possibilities for fouling control. Important conclusions for fouling control are: *flow velocity and temperature can be used to control the fouling rate. Flow velocity should be raised and temperature should be lowered to achieve lower fouling rate. apressure and temperature can be used to compensate for the fouling in order to maintain a constant flux. aat first sight, high temperatures seem to be attractive. But the moderate fouling rate at low temperatures may result in higher performance for long production runs. *for an optimal operation the use of the control variables must be considered with the costs of the fouling rate on the one hand and the costs of these control variables on the other. The model equations can be applied for calculations of optimal process setpoints, characterization of long-term membrane fouling for reverse osmosis and estimation of optimal control policies.
Acknowledgement This investigation was partly supported by the Programme Commission Membrane Technology of the Ministry of Economics (PCM) and Stork-Friesland ( Wafilin ).
109
List of symbols
L
p” R tot R tot (k0)
Rf R,
RP r T t TS V 4 UY x X0
Y
parameter in gel layer model ( Pa-sec/m2) parameter in gel layer model (Pa/m) various constants concentration of solids ( kg/m3 ) concentration of solids in bulk ( kg/m3) gel concentration ( kg/m3) concentration of solids at membrane surface ( kg/m3) concentration ratio between product and feed ( - ) saturation concentration (kg/m”) diffusion coefficient (m”/sec) function denotation first order derivate of function permeate flux ( m3/m2-set) mass transfer coefficient (m/set) constant precipitation rate constant ( m4/kg-see) lumped parameter for precipitation rate (Pa/m) parameter for precipitation rate in the modified model ( Pa-sec2/ m3) thickness of foul layer (m) constant process pressure (Pa) total permeation resistance (Pa-set/m) initial permeation resistance at t= 0 (Pa-set/m) time dependent part of permeation resistance caused by fouling (Pa-set/m) resistance to permeation of water (Pa-set/m) additional permeation resistance as result of chosen process conditions during the preconcentration phase (Pa-set/m) deposition rate of solids (kg/m’-set) temperature ( ’ C ) time (set ) total solids (% ) flow velocity (m/set) flow velocity in the direction perpendicular to the membrane (m/ set ) flow velocity parallel to membrane (m/set) distance perpendicular to the membrane surface (m) constant distance parallel to the membrane surface (m)
110
Subscripts
cal pr
related to calcium phosphate related to protein
Greek symbols 6 thickness of boundary layer (m)
E YI
resistance per unit of foul layer thickness ( Pa-sec/m2) dynamic viscosity (Pa-see) osmotic pressure difference between bulk and permeate (Pa) density (kg/m3)
A7l P
References 1 2
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3
nologie, 10 (1987) 49-53. G.B. van den Berg and C.A. Smolders,
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5
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A.G. Fane and C.J.D. Fell, A review of fouling and fouling control in ultrafiltration, Desalination, 62 (1987) 117-136. R.G. Gutman, The design of membrane separation plant, Part 1: Design of reverse osmosis modules, Chem. Engineer, (1977) 510-513, 521; Part 2: Fouling of RO membranes, Chem. Engineer, (1977) 521-523. A. Suki, A.G. Fane and C.J.D. Fell, Flux decline in protein ultrafiltration, 21 (1984) 269-283.
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R.D. Cohen and R.F. Probstein, Colloidal fouling of reverse osmosis membranes, J. Colloid Interface Sci., 114 (1) (1986) 194-207. A.G. Fane, C.J.D. Fell and M.T. Nor, Ultrafiltration/activated sludge system - development of a predictive model, in: A.R. Cooper (Ed.), Ultrafiltration Membranes and Applications, Plenum Press, New York, NY, 1980, pp. 631-658. S. Kimura and S. Nakao, Fouling of cellulose acetate tubular reverse osmosis modules treating the industrial water in Tokyo, Desalination, 17 (1975) 267-288. M. Okazaki and S. Kimura, Scale formation on reverse osmosis membranes, J. Chem. Eng. Jpn., 17 (2) (1984) 145-151.
14
J. Borden, J. Gilron and D. Hasson, Analysis of RO flux decline due to membrane blockage, Desalination, 66 (1987) 257-269.
15
D.G. Schmidt and P. Both, Studies on the precipitation of calcium phosphate. 1. Experiments in the pH-range 5.3 to 6.8 at 25” C and 50 aC in the absence of additives, Neth. Milk and Dairy J., 41 (1987) 105-120.
surface
111 16
17 18
U. Kulozik, Einfliisse auf die Permeation von Wasser und gel&ten Stoffen sowie auf den Deckschichtabtrag bei der Umkehrosmose, VDI-Verlag, Reihe 3 : Verfahrenstechnik, nr. 120, 1986. J. Hiddink and R. de Boer, Concentration of milk and whey by reverse osmosis, in: P. Linko (Ed.), Food. Proc. Eng., Vol. 1, Appl. Sci. Publ., 1980,561-571. G. Jonsson, Boundary layer phenomena during ultrafiltration of dextran and whey protein solutions, Desalination, 51 (1984) 61-77.