Ultrafiltration of Whole Milk

Ultrafiltration of Whole Milk S. H. Y A N , C, G. H I L L , JR., and C. H. A M U N D S O N 1 Department of Chemical Engineering University of Wisconsin Madison 53706

ABSTRACT

expected because of a 50 to 80% reduction in rennet and starter requirements. There are at least three commercial plants that produce cheese from skim milk coficentrated by ultrafiltration. Studies of the use of ultrafiltration in the dairy industry largely have been concerned with processing of cheese whey and skim milk (12, 15, 16, 23, 29, 30, 34, 3 5 ) a n d use o f t h e skim milk concentrate in cheesemaking (10, 11, 20, 21, 25, 26, 27). Glover (17), however, demonstrated the technical feasibility of concentrating whole milk two-fold by ultrafiltration in the laboratory. Chapman et al. (9) later illustrated the use of the whole milk concentrates in making hard cheese, medium fat soft cheese, and yogurt. The yield of hard cheese prepared from whole milk concentrate was not significantly different from that prepared from normal whole milk. The amount of whey expelled, however, was considerably smaller. Medium-fat soft cheese prepared from whole m i l k concentrate had a 41% increase in yield, and a 50% decrease in making time. Of the 41% increase in yield, 35.8% was due to increased moisture, and 5.2% was due to increased solids-not-fat (SNF). No whey was expelled from the curd. An acceptable yogurt, with 12% total solids, also was made from whole milk concentrate without requiring the usual reinforcement with skim milk powder. Granted the technical feasibility and the potential applicability of the ultrafiltration of whole milk, an understanding of the process behavior via research and experimentation is of primary importance if progress is to be made with this development. This paper presents a study of the effects of process variables, pressure, temperature, feed velocity, and concentration on the permeate flux and various solute rejection coefficients. A process model relating the permeate flux to these process variables also was developed for data correlation and extrapolation, as well as for preliminary plant design and process simulation by computer.

Tubular ultrafiltration membranes were used to concentrate and fraetionate whole milk. Fresh, pasteurized, homogenized whole milk was concentrated to 21.5% total solids and 8.6% protein (40% in dry matter). At all flow rates and temperatures an asymptotic permeate flux was reached at a pressure of about 100 kPa, indicating that whole milk ultrafiltration is limited by concentration- and gelpolarization. The permeate flux increased with fluid velocity to the 1.66 i .16 power. The positive effect of temperature on the permeate flux, particularly at high flow rates, generally followed the Arrhenius form with an average activation energy of 6.8 ± .8 kcal/gmole. The logarithmic decrease of the permeate flux with increasing concentration factor further indicated the importance of concentration polarization in whole milk ultrafiltration. The rejection coefficients for milk proteins, fat, lactose, and ash did not vary with temperature, pressure, or fluid velocity. A four-parameter model adequately described the observed variation of permeate flux with process variables. INTRODUCTION

Interest in the ultrafiltration of milk is due, in part, to the fact that skim milk concentrated by ultrafiltration can be used to prepare certain types of soft cheeses with increased yield and good organoleptic quality (26, 27). Moreover, the problem of whey disposal in traditional cheese making is reduced significantly since little or no whey is produced in this approach. Considerable savings in manufacturing costs are

Received June 21, 1978. 1Department of Food Science. 1979 J Dairy Sci 62:23-40

23

24

YAN ET AL. MATERIALS AND METHODS

used for all liquid transport.

Apparatus

Milk Supply

All experiments in this research involved a pilot ultrafiltration unit containing type HFJ 180 SG tubular membranes from Abcor, Inc. of Cambridge, MA. The Abcor ultrafiltration modules consisted of a membrane cast seamlessly and continuously on the inside of a 2.54 cm i.d. fiber glass tube encased in a clear permeate collection shroud. There were ports at both ends to permit collection of the permeate. Each such tube was 137 cm long, and had about .11 m 2 of membrane area and about .7 liters of hold-up volume. The recommended maximum operating pressure was 340 kPa, and the maximum operating temperature was 60 C. A schematic diagram of the test unit is in Figure 1. The facility included two ultrafiltration modules connected in series by a stainless steel U-bend. Feed was introduced into and withdrawn from the modules through 2.54 cm i.d. stainless steel connectors secured to the membrane unit by stainless steel fittings. The modules were mounted on a movable cart together with a high speed centrifugal pump, feed tank, rotameter, mixer, heating/cooling coil, thermometer, pressure gauges, and gate and ball valves. Except for the stainless steel connectors, tygon tubing and plastic piping were

Fresh, pasteurized, homogenized whole milk from the University of Wisconsin Dairy was used. Concentrated whole milk was obtained by condensing fresh whole milk with a fallingfilm type vacuum evaporator. PROCEDURE Start-Up

The holding tank first was drained and then filled with a sanitizing solution containing 200 ppm chlorine (57 g of Wyandotte Antibac B in 46 liters of water) at 49 C. This sanitizing solution was circulated through the membrane modules for 10 rain at 114 liters/rain and 54 kPa average pressure to sanitize the system and to remove air bubbles that had accumulated since the modules were last used. At the end of the sanitizing period, the pure water permeation rate at 49 C and 100 kPa average pressure was measured. This procedure served as a check on the cleanliness of the membrane and on the long-term flux stability. Deterioration in membrane performance can be measured by periodic checks of this sort. The system then was flushed with 11 to 12 liters of whole milk.

CONCENTRATE

RETURN

IROTAMETER F

-~-,

FEED TANK

v

HEATING

COIL

BALL VALVE

VALVE V-1 CENTRIFUGAL PUMP

FIG. 1. Schematic diagram of the ultrafiltration test facility. Journal of Dairy Science Vol. 62, No. 1, 1979

I

MEMBRANE

MODULES L

VALV E

V-2 PERMEATE

ULTRAFILTRATION OF WHOLE MILK After discharge of this material, the tank was filled with 26 to 40 liters of whole milk for the experiment. Operation

The milk feed was pumped out of a holding tank into the membrane modules by the high speed centrifugal pump. The operating pressure and flow rate were adjusted to the desired values by manipulating valves V1 and V2. Feed temperatures were controlled by circulating w a t e r at the proper temperature through the heating/cooling coil. Uniformity of temperature and composition of the feed were maintained by a mixer mounted on the tank. Experiments were of two basic types. In the first, feed composition was kept constant by continuous recycle of both permeate and concentrate back to the feed tank. The effects of temperature, pressure, and fluid velocity on the permeate flux and solute rejection coefficients were examined systematically at the desired feed concentration. In the second, feed composition was varied by a continuous recycle of only the concentrate. The effects of the concentration factor on the performance characteristics of the system were determined then. During the experiment, the concentrate and permeate were sampled. The initial whole milk sample was collected from the feed tank after the milk had been circulated in the system for about 5 min since the prior circulation of 11 liters of whole milk still would leave a slightly diluted milk in the modules. In all experiments, these data were recorded: (i) permeate rate, (ii) inlet and outlet pressures, (iii) feed temperature, and ( i v ) c o n c e n t r a t e flow rate. Samples of the milk, concentrate, and permeate were analyzed for some or all of: (i) total solids by the gravimetric method of the AOAC (1), (ii) protein and nonprotein nitrogen by the semi-micro Kjeldahl method (7), (iii) milk fat by the Mojonnier method (2), (iv) ash by combustion at 550 C (1), and (v) lactose by difference.

RESULTS A N D DISCUSSION Variation of Permeate Flux with Process Variables

Experience in the ultrafiltration of macro-

25

molecular solutions suggests that the most important process variables are pressure, average fluid velocity, temperature, and degree of concentration. Preliminary trials indicated that permeate flux approached an asymptotic value at pressures above 100 kPa. The experimental program consequently was divided into two phases. Phase I was to test for pressure independence of the permeate flux at different levels of the other variables. Phase II was designed to determine the variation of the permeate flux with temperature, average fluid velocity, and degree of concentration. Tables 1 and 2 show the design matrices for phases I and II, respectively. The phase I design is 22 factorial whereby the pressure variation is determined at two levels each of temperature and average velocity. The phase II design is factorial with 3 velocities, 5 temperatures, and 5 concentration factors, requiring a total of 75 experimental runs. By this factorial approach, it was possible to study the effect of each variable on the permeate flux at a variety of other variables. In particular, a large number of comparisons were from a minimum number of experiments. This approach was particularly useful for identifying suitable functional forms for the dependence of the permeate flux on process variables. This identification is the first step in the model-building described later in this paper. Experiments according to the design matrix in Table 1 were in a random order to ensure independence among observations. A constant feed composition was maintained by a continuous recycle of concentrate and permeate streams back to the feed tank. Figure 2 shows the variation of the flux with transmembrane pressure. Over the ranges of temperature and fluid velocity, the permeate flux approached an asymptotic value at pressures above 100 kPa. Similar conclusions concerning the pressure independence of flux have been reported for ultrafiltration of human

TABLE 1. PHASE I design. Temperature

Velocity

21.1 48.9 21.1 48.9

1.254 m/s 1.254 m/s 3.135 m/s 3.135 m/s

C C C C

Journal of Dairy Science Vol. 62, No. 1, 1979

26

YAN ET AL.

TABLE 2. PHASE II design. Variables

Levels

Velocity, V(m/s) Temperature, T(C) Concentration factor a

1.254, 2.195, 3.135 21.1, 26.7, 32.2, 37.8, 43.3 1.0, 1.14, 1.21, 1.53, 1.86

aThe concentration factor is defined as the ratio of the initial volume of whole milk to the final volume of concentrated whole milk. blood plasma (28) and bovine serum albumin (32). As pointed out by Michaels et al. (28), this flux invariance indicates that gel polarization may occur in the concentration boundary layer. Some experimental evidence for the formation of a protein layer adjacent to the membrane surface during whole milk reverse osmosis has been reported by Glover and Brooker (18). When gel polarization occurs, the overall resistance for permeate transport is governed by the resistances of the concentration boundary layer and the gel layer (R e and Rg in equation 1) J = AP/(R m + R c + Rg)

[11

where J is the permeate flux, Ap the transmembrane pressure drop, R the hydraulic resistance, and subscripts m, c, and g refer to membrane, concentration boundary layer, and gel layer. The permeate flux depends not only on the permeability of the membrane but also on the thickness of the concentration boundary layer and the permeation characteristics of the gel (i.e., its thickness and porosity). An increase in the transmembrane pressure initially produces a transient increase in flux and a higher rate of transport of solutes toward the membrane surface, The impermeability of the membrane and of the gel layer, however, causes the rejected fat and protein molecules to accumulate at the membrane surface. Further increases in pressure will lead only to a thicker and denser gel with increased resistance. Consequently, in terms of equation 1, the effect of increasing the transmembrane pressure, Ap, is nullified by the increase in Rg, leading to an asymptotic flux as indicated in Figure 1. In the regime where the permeate flux is pressure independent, the effects of average fluid velocity, temperature, and degree of Journal of Dairy Science Vol. 62, No. 1, 1979

concentration can be studied by the experimental design matrix in Table 2. The transmembrahe pressure was maintained above 100 kPa. Figure 3 shows a typical variation of the flux with the average fluid velocity over a range of temperatures at a concentration factor of 1.14; this behavior is typical of other concentration factors. For whole milk ultrafiltration, the flux increases more than linearly with the average fluid velocity. The reported asymptotic flux at higher velocity which occurs in the ultrafiltration of cheese whey and skim milk with Havens membranes (15, 16) did not occur in whole milk ultrafiltration with Abcor membranes. The velocities necessary to approach the asymptotic limit would be well beyond the velocity regime investigated. Over the range of temperatures and concentration factors investigated, the membrane transport process is limited by the

,,

~ I,ooo•, 900 ~ ta ~ " ° x ~ z o "~ h ,7 ~ 1"3'

800 700 600

15.6 C

42.9 C, 3. 135m/s

./ 48.9 .C ~ 7 5 9 rn/s

l

500 21.1 C, 3.135m/s

400 300 48.9 C, 1.254m/s 2oo~10oII ~00/ .

21.1 C,I,254m/s

50

I00

PRESSURE,

150

200

kPo

FIG. 2. Variation of flux with pressure for whole milk.

ULTRAFILTRATION OF WHOLE MILK resistance of the fat-protein concentration boundary layer (Rc in equation 1). An increase in the average fluid velocity increases the turbulence as well as the shear rate at the membrane surface, thereby decreasing the thickness of the boundary layer and, thus, its effective resistance to permeate transport. By assuming negligible longitundinal mass transport within the concentration boundary layer, Brian (8) showed, by means of a mass balance, that the steady state ultrafiltration flux, J, is given by J = k ~n [(Cw - Cp)/(CB -- Cp)]

[21

where k (-- D / f ) is the overall mass transfer coefficient between the membrane surface and the bulk solution, D the diffusivity of the macrosolute in the solution, 6 the thickness of the macrosolute concentration boundary layer, C the macrosolute concentration, and subscripts W, B, and P refer to the membrane surface, bulk solution, and permeate. When gelation occurs at the membrane surface and when Cp is negligible compared to C B and the gelation concentration, Cg, J = k ~n [Cg/CB]

[3]

The analogy between convective heat and mass transfer may be used to evaluate the mass transfer coefficient, k, in equation 2 (31). For turbulent flow through tubular membranes, this analogy can be expressed in the form: Sh = kd/D = .023 Re.8 So 33

[4]

where Sh is the Sherwood number, Re (= dV/v) the Reynolds number, Sc (= v/D) the Schmidt number, V the average fluid velocity, v the solution kinematic viscosity, and D the diffusivity. Equation 4 is valid under conditions of turbulent flow with constant wall concentration, small rate of mass transfer, and constant physical properties (3). By combining equations 3 and 4, and regrouping terms, one can write J = [.023 (D "67V'8)/(d "2v .47)] ~n[Cg/CB]

[5] This equation may be written in the following parametric form as characteristic of a particular

>.

N

a

tO

a.-

800 v

700

<> [] A o

600

I.,tJ

I•J

27

/

43.3C 57.8 32.2 26.7 21.1

C C C C

/

500

x" -J

400

Z 0 I4¢

300

nr

h

/

2oo

/

J/ / 1

I00 0

I .5

1 1.0

I 1.5

I 2.0

AVERAGE

/ 2.5

3.0

VELOCITY,

:5,5

4.0

M/S

FIG. 3. Variation of flux with average velocity for whole milk. Concentration factor: 1.14.

module geometry and process fluid J = 01 v ° 2 ~ n

[03/CB]

[61

where 0 1 , 0 2 , and 03 are constants. The validity of equation 6 is indicated by Figure 4 which demonstrates the linear relation between the logarithm of the flux and the logarithm of the average fluid velocity which was observed at each temperature and concentration factor. Although we show only representative plots at a single concentration factor, the slopes of the several plots, i.e., 02 in equation 6, ranged from 1.55 to 1.89 with an average of 1.66 and a standard error of .08. These values are about twice as high as theoretical values for 02 for Newtonian fluids in turbulent flow. Values of 02 exceeding unity have been reported in some cases for the ultrafiltration of colloidal suspensions in turbulent flow (22, 31, 35). The increased dependence of flux or enhanced mass transfer on velocity may be a result of thinning of the gel layer by the increased shear at higher velocities, a factor which is not taken into account in equation 4. Kiviniemi (22) has suggested that such factors as module construction, nature of the feed, and temperature affect Journal of Dairy Science Vol. 62, No. 1, 1979

28

o

Y A N ET A L

800 700

>-

Od !

o

~E 6 0 0

~)

500

43.3C 32.2

Z 0 l-

///

c

//.e

c

400 J X .J

//~

c

£3 i

80(3 o 3. 135 m/s

700

z~ 2. 195 m/s

=E

o

o3 60C n~ tlJ I--

/ / / j

.-I

300

I. 2 5 4 m / s

50(3 i

x

i

3 4001

It.

2OO

Z 0

300-

Ilt

h t, ,~

200

15(3

5nr*

I O0

.o.......~

h

I

0

I

1.0

2.0 AVERAGE

VELOCITY,

3,0

15

4.0

I

I

I

I

I

l

I

20

25

30

35

40

45

50

TEMPERATURE,

M/S

C

FIG. 4. Velocity dependence of flux for whole milk. C o n c e n t r a t i o n factor: 1.14.

FIG. 5. Variation of flux w i t h t e m p e r a t u r e for whole milk. C o n c e n t r a t i o n factor: 1 •53.

the velocity dependence of flux, i.e., 02. Porter (31), however, has suggested that the enhanced mass transfer may result from the so-called "tubular pinch effect." Typical data for the variation of the permeate flux with the temperature are in Figure 5. Flux increases more than linearly with temperature, particularly at high fluid velocities. The reported linear temperature dependence of flux (14, 19) is approximately valid only at low velocities for whole milk ultrafihration. An increase in temperature decreases the fluid viscosity and increases the diffusivity. The net effect of raising the temperature is to increase the mass transfer coefficient k (= D/6). Hence, according to equation 3 the permeate flux increases with increasing temperature. The data in Figure 5 also can be plotted as the logarithm of the flux versus the reciprocal of the absolute temperature (see Fig. 6). The linearity of these plots suggests that the flux-temperature data can be written in Arrhenius form, as

standard error of .4 kcal/gmole. This range of activation energies is typical of activated diffusion processes (14, 31).

70G ,~ 60C c~

NI

50C

o 3. 135 m/s ~ 2,195m/s • m/s

~

40Cm~ 3 0 ( 3 -

,J

x" z 0 c .J la. z

9 ~

IOC-

IX: U.

I-.J i

30!

=

I -I.0

~

I 0

~

[I/T-I/305.2]xlO j cc E x p [ -- ( A E / R )

( 1 / T -- l f F 0 ) ]

~

i 2.0

~

I 3.0

4, * K - I

[7]

The activation energy, AE, varies from 6.0 to 7.6 kcal/gmole, with an average of 6.8 and a J o u r n a l of Dairy Science Vol. 62, No. 1, 1979

I 1.0

FIG. 6. Arrhenius t y p e plot for t e m p e r a t u r e variation of flux for whole milk ultrafiltration. Concentration factor: 1.53.

ULTRAFILTRATION OF WHOLE MILK 900

29

Figure 7 -- with velocity is demonstrated also.

'~ 0 800

04,

Variation of Solute Rejection Coefficients with Process Variables

3. 155 m / s

o

700 II:

The rejection characteristics of a membrane are described by the rejection coefficients of the various solute species:

la,I t- 60c .J

ff

5oc

a = 1 -- (Cp/CB)

-J

[91

400 Z

o

I- 3 0 o 2o~ b.

IO0 J

f

1.0

t

1.5

I

~)',

2,0

CONCENTRATION

2.5

F

I

3.0 3.5 4.0

FACTOR

FIG. 7. Variation of flux with concentration factor for whole milk. Temperature: 37.8 C.

Typical data for the variation of the permeate flux with the concentration factor are in Figure 7 where the permeate flux is plotted against the logarithm of the concentration factor. The rapid decline in flux with increasing degree of concentration is evident. As the milk is concentrated, the solution viscosity increases, and the diffusivity decreases. The mass transfer coefficient k, therefore, decreases with increasing concentration factor. Consequently, the flux varies with concentration factor as in Figure 7. The linearity of the plots in Figure 7 suggests that, in whole milk ultrafiltration, the permeate flux may be approximated by the logarithmic relationship: J = k £n

[Cg/CB]

= k £n [C.F.max/C.F. ]

[8]

where C.F. is the concentration factor, and C.F.ma x the maximum concentration factor. The intercepts of these plots and of additional plots at other temperatures indicate that whole milk can be concentrated only by a factor of 2.7 to 3.3. The increase in the mass transfer coefficient k - the negative of the slope in

where Cp is the solute concentration in the permeate, and C B the solute concentration in the bulk solution. To study the effect of process variables on solute rejection coefficients, a two level factorial design (Table 3) was employed. By considering variables at only two levels, estimates of the effects and interactions of these variables on the response can be determined by a limited number of experiments. This type of design is particularly useful in the early stage of an investigation where it is not intended to explore the detailed variation of the solute rejection coefficient over the experimental region. Rather, it is major trends and the direction of further experimentation that are determined. Further runs with carefully chosen additional levels of each variable can always be employed if a more detailed variation is sought. Experiments according to the design matrix in Table 3 studied the variations of permeate composition and rejection coefficients with transmembrane pressure drop, temperature, and average velocity. These experiments were done in random order to ensure independence among observations. A constant feed composition was maintained by continuous recycle of permeate and concentrate back to the feed tank. Because of the large hold-up volume in the permeate shroud and the generally low permeate flux, ultrafiltration was continued for a sufficiently long time (in excess of 2 h) after a change in the experimental setting so that the permeate sampled would correspond to the existing experimental condition. The permeate samples were analyzed for total solids, proteinand nonprotein-nitrogen, fat, and ash. Table 4 shows the permeate composition for the eight sets of experimental conditions. Three runs were repeated to estimate experimental error. The permeate compositions were analyzed for the main effect, two-factor, and threeJournal of Dairy Science Vol. 62, No. 1, 1979

30

YAN ET AL.

TABLE 3. A 23 factorial design for studying the effects of process variables on the permeate composition and solute rejection coefficient. Feed: fluid whole milk Temperature

Pressure

Velocity

+

--

--

--

+

--

+

+

--

--

--

+

+

--

+

--

+

+

+

+

+

Levels -

-

+

Pressure

Temperature

Velocity

53.3 kPa 133.3 kPa

15.6 C 48.9 C

1.254 m/s 3.135 m/s

factor interactions of the variables by the Yates's algorithm (6). These are summarized in Table 5. Estimates of the standard error of the main effect and interactions are obtained from the three repeated runs. An examination of the results in Table 5 suggests that the main effects and interactions are of the same magnitude as the noise level, i.e., the standard error. This fact implies that there are negligible effects or interactions of the temperature, pressure, or velocity on the permeate composition or solute rejection coefficient. The independence of the solute rejection coefficient on temperature, pressure, and velocity during whey and skim milk ultrafiltration also has been reported (34, 35). The average permeate composition and solute rejection coefficients (Table 6) agree closely with those reported by Glover (17). Protein rejection coefficients above .9 are common in skim milk and whole milk ultrafiltration (17, 23, 36). This incomplete rejection of protein may be due in part to the distribution of pore sizes in the membrane and in part to the distribution of molecular weights among the milk proteins. The finite rejection of ash or mineral constituents indicates that the rejection of ionic species is not governed by the rejection characteristics of the membrane alone. The gel layer of protein and fat also acts as a series resistance for the transport of microsolutes. Journal of Dairy Science Vol. 62, No. 1, 1979

The binding of calcium and phosphate ions to the casein in milk also can lead to the finite ash rejection. Another possible cause for the relatively high ash rejection may be the polyelectrolyte character of proteins (28). Since milk proteins contain ionizable carboxyl and amine groups, the gel layer may contain a relatively high ionic charge density and, consequently, exclude simple electrolytes such as the mineral constituents in milk. The complete rejection of milk fat is expected because of the size of the fat globules. Some disagreement in lactose rejection coefficient should be noted. Large differences in lactose rejection coefficient also have been reported in skim milk ultrafiltration (23). Kiviniemi (23) suggests that such differences may be due to variability in membrane fouling, microbial breakdown of lactose, and errors in measurement. The effects of increasing concentration on the product composition and rejection coefficient were studied by concentrating milk batchwise at a temperature of 48.9 C, a transmembrane pressure drop of 84.5 kPa, and an average velocity of 5.02 m/s. The variation of product composition with increasing concentration factor is in Figure 8. Figure 8 shows that it is possible to concentrate whole milk to 21.5% total solids, 8.6% protein (40% in dry matter), and 9.6% fat. Starting with 68.1 liters of whole miIk, it is

T A B L E 4. C h e m i c a l c o m p o s i t i o n o f p e r m e a t e .

P

T

V

%

%

%

%

%

%

%

T, S.

Protein

Fat

Lactose b

Ash

TN

NPN

,0662

.0381 .0247 .0227 .0232 ,0218 .0253 .0237 .0221 .0774

23 design at c o n s t a n t feed c o m p o s i t i o n --

_ + +

4-

4-

--

4-

--

+ ÷

÷

-_a --+a + + +a

Whole m i l k

5.50 5.23 5.46 5.38 5.34 5.24 5.38 5.29 11.75

.18 .21 .38 .26 .24 .17 .29 .23 3.47

.00 .00 .00 .00 .00 .00 .00 .00 3.01

4.78 4.56 4.63 4.47 4.61 4.59 4.45 4.61 4.51

.50 .44 .42 .62 .47 .45 .62 .43 .68

.0580 .0835 .0643 .0596 .0511 .0690 .0573 .6213

.45 .48 .43 .45 .41 .45 .68 .70

.0612 .0579 .0601 .0559 .0611 .0534 .6213 .5890

t,4 7~

>

F ;> Z ©

Repeated runs --

+

--

-

c-

4o

4-

+

+

Whole m i l k

g < o

Z O

xo ~q xo

5.32 5.35 5.25 5.21 5.24 5.34 11.75 11.70

a A v e r a g e o f r e p e a t e d runs. b L a c t o s e = %T.S. -- [% p r o t e i n + % fat + % ash + % N P N I .

.24 .24

,21 .21 .23 .22 3.47 3.42

.00 .00 .00 .00 .00 .00 3.01 3.03

4.61 4.61 4.58 4.53 4.57 4.65 4,51 4.50

.0238 .0198 .0267 .0227 .0257 .0185 .0774

.0528

© t~ t-

32

V A N ET AL.

possible to achieve such a concentration in about 4 h with an Abcor ultrafiltration unit with .22 m 2 of membrane area. The permeate flux was initially 1409.0 liters/m2-day and declined as the milk was concentrated. The permeate was crystal clear. It contained 6% total solids, 5% lactose, .5% ash, .5% protein, and 0% fat. Figure 8 indicates that the rejection coefficients are not constant but vary with the concentration factor. This conclusion is supported by the results of Table 7 which show the variation of the rejection coefficients' with increasing concentration factors. Fat retention was complete while the lactose retention was negative• The protein retention increased slightly whereas the ash retention almost doubled at the end of the concentration. A large increase in ash rejection coefficient with increasing concentration during skim milk ultrafiltration has been reported (35).

"Ii J~ ~3

q q ~ q q q q q

.-4

>

v

Process Modeling of Whole Milk Ultrafiltration

0

The adaptative model-building strategy of .<

•

•

.

•

•

,.

•

,.

25EXPERIMENTAL RESULTS RESULTS PREDICTED USING AVERAGE REJECTION ~ 3 TOTAL SOLIDS COEFFICIENTS IN TABLE 6 ~ T O T A L SOLIDS

E 20

E

~

m

d

0

",,.,,,-1.,,-

o

~

JO

FAT

..= t~

:Ii

LACTOSE

-o

1.0

~

. . . . . ~ L sH-

1.5

2.0

CONCENTRATION

<

<~>~

Journal Of Dairy Science Vol. 62, N o . 1, 1979

ASH

2.5 FACTOR

FIG. 8. Variation of the milk concentrate composition with increasing concentration factor. Temperature: 4 8 . 9 C. Average velocity: 5.02 m/s. Average pressure: 84.5 kPa.

ULTRAFILTRATION OF WHOLE MILK

33

TABLE 6. Average permeate composition and rejection coefficients (%) of the components in whole milk. Rejection

Composition (%) Components

Milk

Permeate

Total solids Protein Fat Lactose Ash NPN

11.73 3.45 3.02 4.51 .60 .065

5.35 .25 .00 4.50 .49 .025

Box and Hunter (4, 5) facilitates a systematic approach to the development of process models (Fig. 9). This strategy was employed in the elucidation of the functional form of the model J = f(~,_0) which, in the case of whole milk ultrafiltration, provides a mathematical description of the variation of the ultrafiltration permeate flux, J, with the process variables, ~ (the temperature, average velocity, and concentration factor); 0 is the set of constants characteristic of the process. The transmembrane pressure drop is excluded from the process variables since the flux was pressure-invariant when whole milk was ultrafiltered through tubular Abcor membranes at pressures above 100 kPa. (Such a condition was maintained in all subsequent experiments.) The process development data reported earlier suggest that J = 0 x ~ 1 0 2 £n(03/~2) exp [04~3/1.987] [10]

coefficient (%) 54.4 92.8 100.0 .0 29.0 61.5

where ~1 is the average velocity (m/s), ~2 the concentration factor, ~3 the transformed temperature [= (1/T -- 1/305.2) × 10 a, °K-1 ], and 01, 02, 03, and 04 the constants. The validity of this model was tested in the light of the experimental data. Table 8 shows six other four-parameter models based on different forms of the concentration factor dependence as suggested by Kiviniemi (23). These tentative models were useful for comparison of preliminary models and for selection and modification of final models. They are by no means exhaustive or complete. Table 9 shows the final estimates of parameters and the root mean square residuals for these seven models. These parameters were estimated by the nonlinear least square estimation subroutine, NREG (24), utilizing the Marquardt's iterative search method. The magnitudes of the root mean square residuals suggest that except for model 5, none of the semi-empirical models fits the data as well as model 1 (derived from theoretical considerations of the ultrafiltration process). An examination of the functional form of the semiempirical models may help explain the relative

TABLE 7. Variation of solute rejection coefficients a with concentration factor. Concen-

Rejection coefficient (%)

tration factor

Total solids

Protein

Fat

Lactose

Ash

1.0 1.29 1.50 2.20

55.4 58.9 63.3 72.0

90.0 91.6 91.4 94.1

100.0 100.0 100.0 100.0

0.0-0.0-0.0-0.0--

23.3 41.8 46.0 50.5

a

a i = 1 -- (CPi/CBi). Journal of Dairy Science Vol. 62, No. 1, 1979

34

YAN ET AL.

ARE

~

[

DESIGNTO

NADEQUATE t

MODIFY~X~ FIG. 9. Adaptive model-building strategy (4).

inadequacy o f these models. E x c e p t for m o d e l 5, all the empirical models predicted that the p e r m e a t e flux would approach zero only at infinite c o n c e n t r a t i o n factor. This prediction is not consistent with t h e o r y and cannot be achieved in practice. The relatively large r o o t mean square residuals associated with these models, c o n s e q u e n t l y , were n o t unreasonable. On the basis o f this preliminary analysis, models 1 and 5 were chosen as two candidate models to describe the whole milk uhrafiltration process. The a d e q u a c y of models 1 and 5 was checked by examining the distribution of the residuals and the constancy of the parameter estimates. Figures 10 and 11 are plots o f the normalized residuals versus the predicted values for m o d e l 1 and m o d e l 5, respectively. These

normalized residuals appear to be distributed normally about zero in a horizontal band b e t w e e n the values o f + 2, as would be expected for an a d e q u a t e model. There does n o t seem to be any characteristic trend in the distribution o f the residuals that would indicate a n o n c o n s t a n t variance in the observations, an error in the analysis, or an inadequate m o d e l (13). There are, however, several outliers, i.e., normalized residuals outside the range of + 2, as would be e x p e c t e d from a process that is subject to experimental error. The constancy of the parameters with respect to the variables ~ was e x a m i n e d by the analysis of variance m e t h o d ( A N O V A ) (6). The results of such analysis (37) suggest that models 1 and 5 can be m o d i f i e d into the following forms to account for the slight d e p e n d e n c e of some parameters on t h e variables: Model l a : J = 0a~l 0~ £n [(03 + 0s~3)/~2]

" exp (A)

Model 5a: J=(01

+03~2)~102

exp(A)

with A = [(04 + 06~2)~3/1.9871 These models are simple m o d i f i c a t i o n s of models 1 and 5, and are by no means the only possible modifications. These m o d i f i e d forms were tested with the e x p e r i m e n t a l data in some detail.

TABLE 8. Tentative models, a 1.

J =01~102 Qn (03/~2) ex p [04~3/1.987] "

2.

j =01~102 ~0~ exp [04 ~3 /1.987]

3.

J =0t~102 0s ~- exp [04~s/1.987]

4.

J = 0 1 ~ 02 exp [03~ 2] • exp [04~3/1.987]

5.

J =(01 + 0 ~ 2 ) ~ 1 0 2 exp [04~z/1.987]

6.

J =(01 +03/~z) ~10: exp [0a~3/1.987]

7.

J = [1/(01 + 03~2)]~102 exp [04 ~3 /1.987]

aWhere J = ultrafihration permeate flux, liters/meter 2-day, ~1 = the average velocity, m/s, ~2 = the concentration factor, and ~3 = (1/T -- 1/305.2) X 104 , °K -a . Journal of Dairy Science Vol. 62, No. 1, 1979

ULTRAFILTRATION OF WHOLE MILK

35

TABLE 9. Final parameter estimates and the root mean square residuals. Root mean square residual

Final parameter estimates Models

0x

1 2 3 4 5 6 7

02

72.8096 83.5487 202.807 202.816 133.8748 -12.3127 -.002325

03

1.6502 1.6510 1.6504 1.6503 1.6496 1.6509 1.6512

04

3.1084 -1.1757 .4070 -.8978 -52.7383 96.0583 .01434

12.258 18.271 13.180 13.180 10.656 17.159 19.180

-.6725

-.6730 ~.6726 .6726 -.6723 -.6729 -.6731

eventually may arrive at a m o d e l that can provide a reduced u n c e r t a i n t y in terms of data correlation and interpolation, the increase in the n u m b e r of parameters, the empirical nature of the model, and the high correlation a m o n g some of the estimates of parameters would reduce the overall reliability of the m o d e l in extrapolation outside the experimental region. In addition, for the purpose of preliminary design and cost estimation, an e x t r e m e l y precise m o d e l is not needed due to uncertainties associated with o t h e r processes in the entire plant. F r o m this p o i n t of view, the simpler models 1 and 5 are as good as models l a and 5a. Little differentiation has been m a d e concerning the relative adequacies of models 1 and 5. A l t h o u g h the smaller r o o t mean square residuals of m o d e l 5 suggests that it fits the

Table 10 shows the least square estimates o f parameters and the r o o t m e a n square residuals associated with these models. The m o d i f i e d forms are only slightly better than the initial models as indicated by the slight decreases in the m a g n i t u d e o f the r o o t m e a n square residuals. These improvements, however, occur at the expense of increasing the n u m b e r of parameters in the models. E x a m i n a t i o n of the normalized correlation matrices in Table 11 shows that, in b o t h models l a and 5a, 06 is correlated highly with 04. These added parameters are, therefore, very unstable and in some instances are not significantly different f r o m zero. Further m o d e l modifications are possible, but t h e y may not be practical f r o m the standpoint o f the expenditures in time and m o n e y necessary for the detailed analysis. Even though one

4 ,J

O3

z •

I-•

C~

0

lad N -J;-..I

0 Z

oo

-.',.t-

Joo

.;:._

.."1 •

.

zoo

."

PREDICTED

VALUE

°O

ooo o

•

r:

..

I

400

300

,

,I

500

"

I

1

I

600

700

800

° e

-3--

FIG. 10. Plot of normalized residuals versus predicted values of flux: model 1. Journal of Dairy Science Vol. 62, No. 1, 1979

36

YAN ET AL.

TABLE 10. Parameter estimates and root mean square residuals of two modified models. Root Final parameter estimates Model

0~

la 5a

02

73.4386 134.5698

03

1.6499 1.6495

3.1049 -53.2853

04

0s

06

mean square residual

-.4086 -.6057

.3056

-.3219 -.05547

11.919 10.607

Model (la) J = 0 x ~ 02 ~n l(Oa + Os~ ~)/~2 ] " exp [(04 + 06~;2)~a/1.987]. Model (Sa) J = (01 + 03 ~)~102 exp [(04 + 06 ~2)~3/1-987].

data with less uncertainty, the higher correlation b e t w e e n the estimates of parameters associated with m o d e l 5 implies t h e y are m o r e interd e p e n d e n t (Table 12). In addition, the semi-empirical nature of the m o d e l m a y limit its usefulness for e x t r a p o l a t i o n outside the experimental region of the process variables. Model 1, however, has a stronger theoretical basis and is expected to give m o r e reliable predictions outside the region o f experimentation. Within the range of e x p e r i m e n t a t i o n , m o d e l 5 is still adequate for use. However, over an e x t e n d e d range o f the process variables, m o d e l 1 is r e c o m m e n d e d . The goodness of fit of m o d e l 1 is indicated by several predicted value plots (Fig. 12).

and fractionating whole milk by ultrafiltration is demonstrated. Whole milk concentrates containing 21.5% total solids and 8.6% protein (40% in dry matter) were obtained by the use of A b c o r tubular membranes. The permeates were crystal clear, and contained no milk fat and little protein. A l t h o u g h milk fat lowered the permeate flux below that achieved with skim milk, it did not cause severe m e m b r a n e fouling that w o u l d exclude its applicability to whole milk ultrafiltration. Variation of permeate flux and solute rejection coefficients with process variables suggests that whole milk ultrafiltration is limited by c o n c e n t r a t i o n - and gel-polarization. The effect of the process variables on the p e r m e a t e flux can be described by a fourparameter m o d e l which was developed by the adaptive model-building strategy of Box and

CONCLUSIONS

The

technical

feasibility of c o n c e n t r a t i n g

4 ..J

'~

2

o:

I

Or) ILl

a ILl N

o

, ~.._" • •

~

•o

PREDICTED

• °°

•

=to

• . °.riO0" h. %5,• •

eo

.~0I 0 " •

• 300

•

~ 400

•

I" 500

i 600"

.J

~

-2

0 Z

3 -4

FIG. 11. Plot of normalized residuals versus predicted values of flux: model 5. Journal of Dairy Science Vol. 62, No. I, 1979

VALUE I 700

1 800

TABLE 11. Normalizing elements and correlation matrices (models l a and 5a). Parameters

0~

02

03

0s

04

06

Model la: J = 01 ~102 ~n[(O 3 + 0s~3)/~2 ] exp [(04 + 0 6 ~ ) ~ 3 / 1 . 9 8 7 ] 02 0z 03

t-

04 06

1.000 -.735 -.642 -.174 .358 -.304

1.000 .000 -.000 -.000 -.000

1.000 .452 -.449 .337

1.000 .179 -.459

1.000 -.938

1.000

~q

Normalizing elements

1.787 X l f f ~

1.738 X l f f I

4.833 X 10-3

4.498 X 1 ~ 3

5.559 X 1 ~ 3

5.493 × 10-3

Z ©

05

Parameters

O1

03

02

04

06

© b-1

Model 5a: J = (01 + 03~2)~102 exp [(04 + 0

<

Z 0

-q x~

01 03 02 04 06

1.000 -.953 -.892 .208 -.192

Normalizing elements

2.695 X

06~2)~3/1.987] F

10 -l

1.000 .734 -.328 .319

1.000 .000 .000

1.000 -.981

1.000

1.297 X 10-~

1.737 × l f f 3

5.015 X 10 -3

4.102 X 10 -3

38

o ~, :E

,.=,

VAN ET AL.

800

\ \

700

\

I--

.J

600

x" _J h

500

IO00L,,~ L, r,,[r,,H,r,IHIHH,H[,I,,I,,,, ,. , 8

80C

o:::-::,':: ?:73

~a-

70C

~

x

~t

50C 400

4oo

Z 0

3o0

n.-

E

zoo

3

135

~ ~1:3

: 2 195

6oc

=' ..1 EL

Iir

.04\ 6oo

-

p-

Z

: 0.0

300 IO0

200

V- 9op 80p

h

E

I00

I00

0 3

CONCENTRATION

2

I

4

3

CONCENTRATION

FACTOR (¢2 }

"~

7op

\

"J 601,- o~p =3.135

~, 4o[-oe, =,z~4

4

FACTOR E2)

301,,,, h , , , h , l , ~ , , l l h m H H,h i , , h , -2.0 -LO 0 ~0

0

[~/T-~/~O~.Z] ,~0%°W'%)

~000 9OO 8130 7OO 6OO

1000 ,,, , j , , , , T r m , , I r , , ' l r , , F , , I r [ , r , r j , , I . 900 ~;t= 1.53 8OO 700 600 o

500

5O0 400

¢~J IE

400

"~

300

O41

300

"J

1,000 900

....

I ....

I

~ ' ' 'I

I~''L

....

~o,.53

80c

/

70C 600 o

500

i

40C

300 W

3

200

200

J

20C

=xz --

--

n. i-

I00 90

--

100 __///~/

100 90 8C 70

8o 70

I-n,..

60

~, E

60 5¢ ~_

All2, = o ~3

=

~,

4c ~-

D ~5

=

5o ao

'" ~ i = t.254

30 ~,Jl, ,H,,,,I,, ,,I,H,h,I,h,HJ,H, --2.0 --I.0 0 I0 2.0

3C

[,/v-,/3os.z], fo". ~-'%)

r i [!lrrl

• ~'3 = - I

150

0~3 =-

.5904

0

6013

I r ,llJlJEtll 2 3 4

AVG. V E L O C I T Y ,

50~//

o ~3 =

.6013

1.237

M/S

({I)

I

2

AVG. V E L O C I T Y ,

3

4

5

M/S (~1)

F I G . 12. F i t t e d c u r v e s f o r m o d e l 1.

Hunter (4, 5). Whole milk uhrafihration can best be carried out with (i) high feed flow rates, (ii) relatively low pressures, e.g., 100 kPa for Abcor membranes, and (iii) relatively high temperatures. Uhrafiltration at low pressure will result in a looser fat-protein cake which is removed more readily by the high shear rate at the J o u r n a l o f D a i r y S c i e n c e V o l . 6 2 , N o . 1, 1979

membrane surface. The highest temperature compatible with membrane and protein stability should be used. For whole milk ultrafiltration, temperatures between 50 and 55 C are desirable since processing in this temperature range can increase the permeation rate, inhibit bacterial growth, reduce the residence time of the concentrate, and be compatible with

U L T R A F I L T R A T I O N OF WHOLE MILK

39

TABLE 12. Normalizing elements and correlation matrices (models 1 and 5). Parameters

0~

02

0a

04

1.000 .000

1.000

4.084 X 10 -3

9.846 ×

Model 1: J = 01 ~102 •n (03/(~) exp [04~s/1.9871 01

1.000

02

-.769

1.000

0s 04

-.612 .091

.000 .000

Normalizing elements

1.692 × 10-1

Parameters

01

1.738 × 10-3

03

1 0 -4

02

04

-.091

1.000 .000

1.000

1.224 × 10 -1

1.737 × 10 -3

9.844 X 10-4

Model 5: J = (01 + 0s~2)~102 exp [04~3/1.987] 01 0s 02 04

1.000 -.958 -.908 .107

Normalizing elements

2.635 × 10 -1

protein and membrane

i .000

-.770

stability.

ACKNOWLEDGMENTS The authors acknowledge the financial support of the Wisconsin Alumni Research Foundation, the Exxon Research Foundation, and the Schuhe Scholarship. W e t h a n k A b c o r , Inc. f o r m a k i n g a v a i l a b l e the pilot uhrafiltration unit.

REFERENCES 1 AOAC. 1975. Official m e t h o d s of analysis, 12th ed. Association of Official Agricultural Chemists, Washington, DC. 2 Atherton, H. V., and J. A. Newlander. 1977. Chemistry and testing of dairy products, 4th ed. AVI Publishing Co., Westport, CT. 3 Bird, R. B., W. E. Stewart, and E. N. Lightfoot. 1960. Transport phenomena. John Wiley and Sons, Inc., New York. 4 Box, G. E. P., and W. G. Hunter. 1962. A useful m e t h o d for model building. Technometrics 4: 301. 5 Box, G. E. P., and W. G. Hunter. 1965a. The experimental s t u d y of physical mechanisms. Technometrics 7 : 23. 6 Box, G. E. P., W. G. Hunter, and J. S. Hunter. 1976. Statistics for experimenters. Mimeographed notes. Department of Statistics, University of Wisconsin, Madison.

7 Bradstreet, R. 1965. The Kjeldahl m e t h o d of organic nitrogen. Academic Press, New York. 8 Brian, P. L. T. 1966. Mass transfer in reverse osmosis. Page 161 in Desalination by reverse osmosis. U. Merten, ed. M.I.T. Press, Cambridge. 9 Chapman, H. R., V. E. Bines, F. A. Glover, and P. J. Skudder. 1974. Use of milk concentrated b y u h r a f i h r a t i o n for making hard cheese, soft cheese, and yoghurt. J. Dairy Technol. Soc. 27:151. 10 Covacevich, H. R., and F. V. Kosikowski. 1974. Utilization of uhrafiltration for cream cheese manufacture. J. Dairy Sci. 57:488. 11 Covacevich, H. R., and F. V. Kosikowski. 1975. Mozzarella, cottage, and cheddar cheese from u h r a f i h e r e d retentates concentrated to m a x i m a . J. Dairy Sci. 58:793. 12 Covacevich, H. R., and F. V. Kosikowski. 1977. Skim milk concentration for cheesemaking b y alternative u h r a f i h r a t i o n procedures. J. Food Sci. 42:1359. 13 Draper, N. R., and H. Smith. 1966. Applied regression analysis. John Wiley and Sons, New York. 14 Fenton-May, R. I. 1971. The use o f reverse osmosis and u h r a f i h r a t i o n in the food industry. Ph.D. dissertation. Department of Chemical Engineering, University of Wisconsin, Madison. 15 Fenton-May, R. I., C. G. Hill, Jr., and C. H. A m u n d s o n . 1971. Use of ultrafiltration/reverse osmosis systems for the concentration and fractionation of whey. J. Food Sci. 36:14. 16 Fenton-May, R, I., C. G. Hill, Jr., C. H. A m u n d s o n , M. H. Lopez, and P. D. Auclair. 1972. Concentration and fractionation of skim milk by reverse Journal of Dairy Science Vol. 62, No. 1, 1979

40

YANETAL.

osmosis and ultrafiltration. J. Dairy Sci. 55 : 1561. 17 Glover, F. A. 1971. Concentration of milk by ultrafiltration and reverse osmosis. J. Dairy Res. 38:373. 18 Glover, F. A., and B. E. Brooker. 1974. The structure o f the deposit formed in the m e m b r a n e during the concentration of milk by reverse osmosis. J. Dairy Res. 41:89. 19 Hernandez, J. 1977. Processing of sweet w h e y in an ultrafiltration unit of the plate and frame design. M.S. thesis. Department o f Food Science, University of Wisconsin, Madison. 20 Jepsen, S. 1977. Membrane filtration in t h e m a n u facture of cultured milk products. Amer. Dairy Rev. Jan. p. 29. 21 Jepsen, S. 1977. Ultrafiltration for Danish blue cheese. Dairy and ice cream field. 160(4):78. 22 Kiviniemi, D. L. 1974. C o n t i n u o u s process ultrafiltration. Kemia-Kemi, 2:70. 23 Kiviniemi, D. L. 1977. Processing of sweet w h e y and skim milk by ultrafiltration. Valio Laboratory Publications, No. 2. 24 MACC. 1972. Nonlinear regression routines reference manual. Madison Academic C o m p u t i n g Cen_ter, University of Wisconsin, Madison. 25 Mathews, M. E., S. E. So, C. H. A m u n d s o n , and C. G. Hill, Jr. 1976. Cottage cheese from ultrafiltered skim milk. J. Food Sci. 41:619. 26 Maubois, J. L., and G. Mocquot. 1971. Preparation de fromage a partir de "pr6-fromage liquide" o h t e n u par ultrafiltration du lair. Le Lait 508:495. 27 Maubois, J. L., and G. Mocquot. 1976. Application o f m e m b r a n e ultrafiltration to preparation of various types of cheese. J. Dairy Sci. 58:1001. 28 Michaels, A. S., L. Nelson, and M. C. Porter. 1971.

Journal of Dairy Science Vol. 62, No. 1, 1979

29

30

31

32

33 34

35

36

37

Ultrafiltration. Page 197 in Membrane processes in industry and biomedicine. M. Bier, ed. Plenum Press, New York. Peri, C., C. Pompei, and F. Rossi. 1973. Process optimization in skim milk protein recovery and purification by ultrafiltration. J. Food Sci. 38:135. Pompei, C., P. Resimini, and C. Peri. 1973. Skim milk protein recovery and purification by ultrafiltration: Influence of temperature on permeation rate and retention. J. Food Sci. 38:867. Porter, M. C. 1972. Concentration polarization with m e m b r a n e ultrafiltration. Ind. Eng. Chem. Res. and Develop. 11:234. Porter, M. C., and L. Nelson. 1972. Ultrafiltration in t h e chemical, food processing, pharmaceutical, and medical industries. Page 227 in Recent develo p m e n t s in separation science. Vol. 2. N. N. Li, ed. CRC Press, Cleveland, OH. Reesen, L., and P. S. Nielsen. 1975. utilization of the permeate. DDMM Information No. 1. Setti, D., and C. Peri. 1976a. Whey and skimmilk ultrafiltration. 1. Parameters affecting permeation rate in sweet w h e y ultrafiltration. Milchwissenschaft 31:135. Setti, D., and C. Peri. 1976b. Whey and skimmilk ultrafiltration. 2. Parameters affecting permeation rate in skimmilk ultrafiltration. Milchwissenscbaft 31:466. T h o m p s o n , S. J., and J. M. deMan. 1975. Concentration and fractionation of milk by ultrafiltration. J. Canadian Inst. Food Sci. and Technol. 8:113. Van, S. H. 1978. Ultrafiltration of milk: Some studies o f process behavior and process modeling. M.S. thesis. Department of Chemical Engineering, University of Wisconsin, Madison.