A unified model of the time dependence of flux decline for the long-term ultrafiltration of whey

Journal of Membrane Science 332 (2009) 69–80

Contents lists available at ScienceDirect

Journal of Membrane Science journal homepage: www.elsevier.com/locate/memsci

A unified model of the time dependence of flux decline for the long-term ultrafiltration of whey Kevin W.K. Yee a , Dianne E. Wiley a,∗ , Jie Bao b a b

UNESCO Centre for Membrane Science and Technology, School of Chemical Sciences and Engineering, The University of New South Wales, Sydney, NSW 2052, Australia School of Chemical Sciences and Engineering, The University of New South Wales, Sydney, NSW 2052, Australia

a r t i c l e

i n f o

Article history: Received 9 October 2008 Received in revised form 16 January 2009 Accepted 24 January 2009 Available online 5 February 2009 Keywords: Whey ultrafiltration Long-term fouling Fouling dynamics Dynamic modelling Regression models

a b s t r a c t The performance of industrial membrane processes is affected by the time dependence of permeate flux, which includes both the absolute value and the rate of decrease in permeate flux at a given time. In particular, long-term fouling will affect the performance of industrial membrane processes that operate continuously for long periods of time, such as industrial whey ultrafiltration processes that can operate for up to 14 h every day. Results of whey ultrafiltration experiments conducted on a pilot scale membrane rig were used to establish a unified model for the time dependence of permeate flux during long-term ultrafiltration. Experimental results indicate that the effects of trans-membrane pressure and feed concentration on the rate of decrease in the permeate flux due to long-term fouling are statistically insignificant. The unified model from this paper can be applied in conjunction with the process dynamics models to study the performance of automatic controllers prior to controller design. © 2009 Elsevier B.V. All rights reserved.

1. Introduction Many industrial membrane separation processes need to operate continuously for long periods of time (i.e. hours or days). For example, ultrafiltration (UF) processes used for the industrial production of whey protein concentrates (WPCs) usually operate for up to 14 h every day [1,2]. The performance of the whey UF process can be affected by the decrease in permeate flux due to membrane fouling. There are three stages of membrane fouling for whey UF processes [3–7], namely: protein adsorption and concentration polarization in the first few minutes; protein deposition which is dominant for several hours; and, long-term fouling. Given the length of operation of industrial whey UF processes, long-term fouling is the major mechanism affecting the decrease in permeate flux and the performance of the whey UF process. The performance of the whey UF process is related to the time dependence of permeate flux, which includes not only the absolute value of permeate flux, but also the fouling dynamics (or the rate of decrease in permeate flux) at a given time. While factors affecting the extent of fouling and the value of permeate flux from whey UF processes have been extensively reviewed [8–11], existing work has not paid much attention to factors affecting fouling dynamics. Although experimental results from whey UF processes

∗ Corresponding author. Tel.: +61 2 9385 7661; fax: +61 2 9385 5949. E-mail address: [email protected] (D.E. Wiley). 0376-7388/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.memsci.2009.01.041

[4,12] suggest that the rate of decrease in permeate flux is independent of velocity (see Fig. 1), work on the effects of trans-membrane pressure (TMP) and feed concentration remains limited. Extensive studies have been performed to determine the effects of TMP and feed concentration on fouling dynamics for the membrane separation of feed streams containing protein. Fouling dynamics are often expressed in terms of dynamics models. The fouling dynamics models identified in literature can be classified into empirical, resistance-in-series and mechanistic models as summarized in Table 1. The complexity of the fouling dynamics models in Table 1 increases from the empirical exponential or power-law models to the mechanistic models that take into account the rate of protein aggregation and the subsequent deposition as a function of operating conditions such as cross-flow velocity and feed concentration [14,17,18]. The mechanistic models are also stochastic [14] as they consider the probability of the aggregated protein depositing on the membrane surface for a given set of operating conditions. One of the strengths of the mechanistic models is that the constants in the models can be used to interpret the actual fouling phenomena observed in membrane processes. In particular, the physical significance of the constants in the model from Ho and Zydney [14] is given below and will be referred to later in this paper: • ˛: Membrane area being blocked per unit mass of protein convected to the surface. • Rp0 : Resistance to permeation from the protein molecules before deposition on the membrane surface.

70

Table 1 Fouling dynamics models for the membrane separation of feed streams containing protein. Model type

Model equations JP (t) =

Fouling mechanism

References

(None, from data fitting)

Cheryan [11]

JP (t) = JP (t → ∞) + k exp(−bt)

Gel polarization and protein deposition

Lin et al. [13]

dJP (t) dt

Protein adsorption and deposition

Ho and Zydney [14]

Protein deposition

Fane and Fell [7]

= −kJP (t)(JP (t)A)

2−n

where

n = 0 for cake filtration n = 1 for intermediate blocking n = 1.5 for standard blocking n = 2 for complete pore blocking RF (t) = ˛M(t) dM(t) dt RF (t) Rm

Resistance-in-series

dRF (t) dt dRF (t) dt

Mechanistic

= Kd exp(−kt) =

1 a1 JP (t)+a2

+ a3

Gesan et al. [15]

= A JP (t) − B



 J (t) 

 x(t)

k



= Ka exp

JP (t) =

1 L

0



P

−

cs cb

Gel polarization

2

Mineral precipitation of whey



Jeq (x)dx + (L − x(t))JP (x, t)

qP = qP,0 exp −

˛ Pcb Rm







m t + qP,0 RmR+R × 1 − exp − p

˛Pcb Rm



Protein adsorption and deposition

where Rp = (Rm + Rp0 )

Notes:

• • • • • •

van Boxtel et al. [16]

JP (x, t) is the permeate flux along the channel length (x) at time t. Jeq is the local equilibrium permeate flux. cs is the concentration at which the mineral salts precipitate. A is the total membrane area. M(t) is the mass of protein deposited per unit membrane area. All other parameters in the Table are empirical constants whose values were determined by experiments.

1+

2+f  R Pcb

(Rm +Rp0 )2

t − Rm

Song and Wang [17,18] Ho and Zydney [14]

K.W.K. Yee et al. / Journal of Membrane Science 332 (2009) 69–80

Empirical

JP (0)q−b P

K.W.K. Yee et al. / Journal of Membrane Science 332 (2009) 69–80

71

the effects of TMP and feed concentration on the time dependence, especially on the fouling dynamics. Whey UF experiments were conducted on a pilot scale rig to obtain the data necessary to estimate the parameters in the proposed unified model. 2. Apparatus and material 2.1. Pilot scale ultrafiltration rig

• f  R : Resistance to permeation from the protein deposits on the membrane surface.

A schematic of the pilot scale cross-flow ultrafiltration rig used in the experiments is shown in Fig. 2. The set-up consists of a stainless steel membrane housing containing one standard spiralwound module with a diameter of 3.8 in. (96 mm) and a length of 38.75 in. (985 mm) (ABCOR® 3838, Koch Membrane Systems). The membrane within the module is made up of semi-permeable polyethersulfone (PES) with a molecular weight cut-off of 10 kDa. The module is designed for the ultrafiltration of food and dairy products and is identical to those found in the industrial whey UF process for WPC production [20]. The pilot scale rig also consists of two centrifugal pumps: a feed pump (Alfa Laval LKH10, Hamilton, New Zealand) which delivers a pressure of up to 3 bar and a recirculation pump (Alfa Laval LKHP10) which provides an extra 1 bar of pressure. When the butterfly valves are open, part of the retentate stream is recycled and mixed with the output stream from the feed pump, and the remainder is the net retentate stream from the membrane module. As practised in industrial membrane processes [11,21,22], recycling part of the retentate stream from the UF process increases the crossflow velocity and shear force of the feed, thus reducing membrane fouling and its effects on permeate flux. The pilot rig operated for 14 h in each experiment. In order to achieve a continuous operation of the rig and to maintain a constant feed concentration throughout the experiment, the permeate and the net retentate streams were returned to the feed tank (capacity of 150 L). The net retentate stream was cooled by a plate heat exchanger before returning to the feed tank. During operation, the temperature and trans-membrane pressure were maintained constant by a distributed control system (ABB Taylor MOD 300 DCS). The temperature of the net retentate stream was automatically controlled by manipulating the cooling water flowrate supplied to the plate heat exchanger. The distributed control system also manipulated the speed of the feed pump to maintain TMP at its specified value. Measurements of the feed flowrate, permeate flowrate and temperature of the feed within the tank were captured by the distributed control system for processing.

Despite differences in their complexities, existing models have focused on processes operating for up to 4 h during which protein adsorption and deposition are the major fouling mechanisms. Mechanisms responsible for long-term fouling, such as the consolidation and densification of the deposits, have been largely ignored. Table 1 also demonstrates a common shortcoming of existing work: that is, each stage of fouling is considered in isolation [19]. In addition, existing studies of fouling dynamics models were based on experimental results obtained at room temperature, whereas industrial whey UF processes are often conducted at 10–15 ◦ C in order to minimize the aggregation and denaturation of protein molecules. Fouling dynamics models valid at the operating temperature of industrial whey UF processes are therefore essential to understand changes in process performance during long-term operation. This paper therefore aims to develop a unified model to describe the time dependence of permeate flux from long-term whey UF processes valid for a temperature range of 10–15 ◦ C, and to evaluate

Fig. 2. A schematic of the pilot scale cross-flow ultrafiltration rig.

Fig. 1. The ratio of permeate flux (JP (t)) to the initial flux (JP (0)) from (a) the ultrafiltration of albumin with cross-flow velocities (u0 ) of 0.5 and 2.0 m s−1 (adapted from Fig. 6 of Meireles et al. [12]) and (b) the ultrafiltration of cheese whey with u0 of 3 and 4 m s −1 (adapted from Fig. 3 of Aimar et al. [4]).

72

K.W.K. Yee et al. / Journal of Membrane Science 332 (2009) 69–80

Table 2 Composition of non-hygroscopic whey powder (according to Murray Goulburn Cooperative Co. Ltd.) Ingredients

w/w%

Protein Lactose Total fat Moisture Sodium Potassium Calcium

12.1 77.1 1.0 3.0 0.63 2.46 0.60

2.2. Feed and cleaning solutions The feed solution used for the experiments was reconstituted non-hygroscopic cheese whey powder supplied by Murray Goulburn Co-operative Co. Limited, Melbourne. The composition of the whey powder provided by the supplier is shown in Table 2. Reconstituted whey powder was used instead of liquid fresh whey because of its commercial availability and its stability during storage. Milli-QTM water was used for preparing all feed and cleaning solutions. Terg-a-zyme (Alconox Inc.), a protease-active powder detergent, was used for cleaning and sanitizing the membrane module before and after each experiment. An aqueous solution of 1% (w/w) of Terg-a-zyme at 50 ◦ C was used for cleaning as recommended by the supplier. 3. Experimental procedures 3.1. Preparation of the new membrane module The new membrane module to be used in the experiments is preserved in glycerol solution. In order to remove the glycerol, the new membrane module was washed with Milli-QTM water at room temperature for 1 h, followed by cleaning with 1% (w/w) Terg-azyme solution at 50 ◦ C for 3 h. The washing and cleaning processes were conducted under a TMP of 50 kPa. The membrane module was then rinsed with Milli-QTM water to remove the Terg-a-zyme solution. 3.2. Fouling experiments Each experiment consisted of four stages, namely (1) preparation of whey solution, (2) fouling, (3) rinsing and cleaning and (4) evaluation of flux recovery. The steps involved in each of the stages are listed below. 3.2.1. Preparation of whey solution In order to prepare whey solution at between 10 and 15 ◦ C for the fouling experiments, the pilot scale rig was first operated with 30 L of Milli-QTM water in the feed tank. Under the TMP of the fouling experiment (e.g. 350 kPa), the permeate and net retentate streams were recycled to the feed tank. The rig was left operating for around 1 h, during which the net retentate stream would be cooled by the plate heat exchanger, reducing the temperature of the water in the feed tank from room temperature to 12–13 ◦ C. By opening the manual divert valve in the net retentate stream, around 15 L of the cooled Milli-QTM water was removed from the rig. Into the Milli-QTM water either 1.8, 2.7 or 3.6 kg of non-hygroscopic whey powder was added to prepare a feed solution of 6%, 9% or 12% (w/w) total solids (based on a total volume of 30 L). In order to minimize protein denaturation, the mixture was gently stirred for around 5–10 min until the whey powder was dissolved and all visible lumps have been removed.

3.2.2. Fouling The fouling experiment started as the whey solution was poured back into the feed tank and pumped into the membrane module. Experiments which utilized whey solution of 6%, 9% or 12% (w/w) total solids and operated under TMP of 250 or 350 kPa were conducted. Each fouling experiment lasted for 14 h, during which the temperature of the feed solution was maintained constant by the plate heat exchanger. Measurements of feed flowrate, permeate flowrate and temperature of the feed within the tank were taken every 10 s for the first 10 min of the experiment, and every 3 min thereafter. Experiments with a particular combination of total solids concentration and TMP were conducted at least twice to ensure the consistency of the permeate flowrate measurements. 3.2.3. Rinsing and cleaning After each fouling experiment, the rig was rinsed with tap water to displace the whey solution in the system and to remove the loose layer of deposit within the membrane module. The rinsing water was discarded by opening the manual divert valve of both the permeate and the net retentate streams. This first rinsing process lasted for 1 h before the membrane module was cleaned with Terg-a-zyme solution. The cleaning process first involved heating 20 L of Milli-QTM water in the feed tank to around 50 ◦ C by the plate heat exchanger. A cleaning solution of 1% (w/w) Terg-a-zyme was prepared by dissolving 200 g of Terg-a-zyme powder in the feed tank. This solution was then recirculated in the rig under a TMP of 50 kPa for 1.5 h. The membrane module was then soaked in the Terg-a-zyme solution for 1 h. Recirculation of the cleaning solution then resumed for another hour to remove the protein deposits that were released from the membrane surface during soaking, and to provide further membrane cleaning. After the cleaning process, the rig was rinsed with tap water again to remove any traces of the cleaning solution. This process was continued for 1 h, or until the rinsing water being discarded appeared clear. 3.2.4. Evaluation of flux recovery Impurities in the tap water used in the rinsing process may reduce the permeate flowrate. In addition, the cleaning and rinsing procedures might not have cleaned the membrane module properly. In order to ensure that the permeate flowrate after cleaning and rinsing is restored to approximately the same value before the fouling experiment, flux recovery was determined. After the washing, cleaning and rinsing processes, the permeate flowrate was measured when the pilot scale rig was operating around 25 ◦ C under a TMP of 350 kPa using Milli-QTM water as the feed. If the permeate flowrate was within 90% of the value obtained before the fouling experiment, a flux recovery of at least 90% is achieved and the performance of the membrane module is regarded as having been successfully restored. A flux recovery of at least 90% after cleaning is also essential between fouling experiments to ensure that the experimental results obtained are comparable. If a flux recovery of less than 90% was obtained, the cleaning and rinsing step were repeated.

4. Proposed unified model A unified empirical model is proposed in this paper to describe the time dependence of permeate flowrate throughout the operation of long-term whey UF processes. The proposed model consists of three piecewise functions that reflect the decrease in permeate flowrate due to concentration polarization, protein deposition and long-term fouling, respectively. The general form of the model is

K.W.K. Yee et al. / Journal of Membrane Science 332 (2009) 69–80

given below: qP (t) = qP,f,∞ + kf exp(bf t) or





ln qP (t) − qP,f,∞ = ln kf + bf t

(1)

(2)

where the subscript f represents the various stages of fouling: • When t = 0 − t1 s, f = 1 (stage 1: concentration polarization) • When t = t1 − t2 s, f = 2 (stage 2: protein deposition) • When t = t2 –50,400 s (14 h), f = 3 (stage 3: long-term fouling) Eq. (1) is an exponential decay model, and the rate of decrease in permeate flowrate increases with the magnitudes of b1 , b2 and b3 . The constants bf (where f = 1, 2 and 3) are the rate constants for the decrease in permeate flowrate because differentiating Eq. (2) gives: dqP = bf (qP − qP,f,∞ ) dt

(3)

where qP,f,∞ represents the steady-state permeate flowrate achieved for each stage of fouling. Although experimental results (see Fig. 3) indicate that permeate flowrate decreases linearly with time in the long term, an exponential model was proposed so that the value of b3 can be

73

compared directly with b1 and b2 . In other words, any similarities or differences in the rates of decrease in permeate flowrate throughout the operation of long-term whey UF processes can be easily identified. Since Eq. (2) is a linear equation in t, the values of kf and bf can be determined by regression analysis of the decrease in permeate flowrate (qP ) with time obtained from experiments [23]. However, the value of qP,f,∞ and the time limits for the piecewise functions (denoted by t1 and t2 ) cannot be estimated by regression analysis. Hence, initial estimates of qP,f,∞ , t1 and t2 were required in order to determine the values of kf and bf by regression analysis. The ‘goodness of fit’ of the estimated regression model to the experimental data is expressed in terms of the standard deviation of qP about the estimated model, or the standard error of estimate (denoted by ) ˆ [24]:

 n   (qP,i − q∗P,i,est )2 ˆ =

i=1

(4)

n−2

where n is the number of measurements taken in the experiments and the subscript ‘est’ represents values predicted by the model. By varying the estimates of qP,f,∞ , t1 and t2 , the regression analˆ This ysis can be repeated to determine new values of kf , bf and . procedure was repeated until the value of ˆ converged to a minimum. The final values of bf indicate the rate of decrease in permeate flowrate for the various stages of fouling (i.e. when f = 1, 2 or 3).

5. Results and discussion Fig. 3 shows the permeate flowrates for the pilot scale UF rig during its 14 h of operation when whey solutions with total solids concentrations (TSF %) of 6%, 9% and 12% (w/w) were supplied from the feed tank. The TMP across the membrane module was maintained at 250 or 350 kPa. Since the actual feed flowrate to the membrane module was maintained between 110 and 120 L/min for all the experiments, differences in permeate flowrates as a result of changes in cross-flow velocity are insignificant in these experiments. The operating temperature of the whey UF rig during the experiments is shown in Fig. 4. Except for the increase in temperature immediately after the prepared whey solution was poured back into the feed tank, the operating temperature was able to be maintained within 0.5 ◦ C for each experiment by the distributed control system. The operating temperatures between the experiments also varied by less than 2 ◦ C. Changes in permeate flowrate over time due to changes in temperature are therefore negligible in the experiments. As a result, operating temperature is not included in Eqs. (1) or (2).

5.1. Comparison of the proposed unified model with mechanistic models In this section, the suitability of the proposed model (Eqs. (1) or (2)) for describing permeate flowrates during the 14-h operation of the pilot scale UF rig is compared with the mechanistic model from Ho and Zydney [14]. Experimental data obtained from the rig was used to evaluate the values of constants (˛, Rp0 and f  R ) in the mechanistic model: Fig. 3. Permeate flowrate (qP ) from the pilot scale rig using whey solutions with total solids concentrations (TSF %) of 6%, 9% and 12% (w/w) and operating under a TMP of (a) 250 kPa and (b) 350 kPa for 14 h.



 ˛ Pc  b

qP =qP,0 exp −

Rm

Rm t + Rm +Rp



 ˛ Pc  b

1 − exp −

Rm

(5)

74

K.W.K. Yee et al. / Journal of Membrane Science 332 (2009) 69–80

fit of the unified model to the experimental data is demonstrated in Fig. 6(a)–(d), which shows the experimental and the estimated values of permeate flowrate when the pilot scale rig was operated with TSF % of 6% (w/w) under a TMP of 350 kPa. The values of bf obtained in this paper were compared against the estimated values of bf from experimental data reported in the literature. Although the majority of data from the literature is not available in a format that can be used for a direct comparison against the pilot rig data, some data corresponding to the stage in which protein deposition dominates the decrease in permeate flowrate (or stage 2 of the unified model) is available. Only the values of b2 in Table 5 can therefore be quantitatively compared with experimental data from the literature. Fig. 7 shows the ratios of permeate flux (JP (t)) to the initial flux (JP (0)) from the experimental results of protein ultrafiltration in the literature under different feed concentration and TMP [4,25]. The lines of best fit with their corresponding values of b2 are also shown in the figures. The values of b2 estimated from existing experimental data are similar in the order of magnitude (i.e. 10−4 s−1 ) to those from our experimental data in Table 5. 5.2.1. Time dependence of the controlling fouling mechanisms The time at which protein deposition overtakes concentration polarization as the controlling mechanism for the decrease in permeate flux is indicated by the value of t1 , while the time

Fig. 4. Operating temperature of the pilot scale rig using whey solutions with total solids concentrations (TSF %) of 6%, 9% and 12% (w/w) and operating under a TMP of (a) 250 kPa and (b) 350 kPa for 14 h.

where



Rp = (Rm + Rp0 )

1+

2 + f  R Pcb (Rm + Rp0 )2

t − Rm

(6)

The estimated constants shown in Table 3 were determined by minimizing the standard error of estimate () ˆ defined by Eq. (4). Based on the estimated constants, the permeate flowrate predicted by the mechanistic model is shown in Fig. 5. As shown in Fig. 5, the mechanistic model is able to predict the permeate flowrate when the decrease in qP with time is dominated by concentration polarization and protein deposition (or the first 2.70 h of operation). However, predictions on permeate flowrate are not available after 2.70 h of operation. The reason is that when experimental values of qP beyond 2.70 h were included for model estimation, the value of ˆ failed to converge to a minimum and the values of ˛, Rp0 and f  R could not be determined. Due to this limitation of the mechanistic model, the proposed unified model was superior for estimating the time dependence of permeate flowrate during long-term whey UF. 5.2. Estimates of empirical constants in the proposed unified model and their implications The estimated values of the empirical constants in Eq. (1) are shown in Tables 4–6 . In addition to the ˆ values in the tables, the

Fig. 5. The decrease in permeate flowrate obtained by experiment and estimated by the mechanistic model from Ho and Zydney [14], when the pilot plant scale rig was operated with TSF % = 6% (w/w) and a TMP of 350 kPa. (a) shows the initial decrease in permeate flowrate up to 0.15 h, while (b) shows the decrease up to 2.70 h.

K.W.K. Yee et al. / Journal of Membrane Science 332 (2009) 69–80

75

Table 3 Estimated values of constants in the mechanical model from Ho and Zydney [14] based on experimental data from the pilot scale whey UF rig. P (kPa)

TSF % (w/w%)

˛ (m2 kg−1 )

Rp0 × 10−13 (m−1 )

f  R × 10−13 (m−1 )

ˆ

250

6% 9% 12%

65.0 68.2 47.6

1.19 1.43 2.28

1.13 1.18 1.12

0.022 0.023 0.023

350

6% 9% 12%

80.0 65.7 41.6

1.61 2.43 3.16

1.73 1.63 1.25

0.016 0.015 0.020

Table 4 Estimated values of empirical constants for stage 1 of the proposed unified model at various P and TSF % (standard errors of the coefficients estimated by regression analysis are in parenthesis) P (kPa)

TSF % (w/w%)

qP,1,∞ (L/min)

k1 (L/min)

−b1 × 102 (s−1 )

t1 (s)

ˆ (L/min)

250

6% 9% 12%

4.00 3.36 2.39

4.27 (0.08) 4.72 (0.11) 5.59 (0.19)

1.25 (0.02) 1.48 (0.03) 1.54 (0.05)

340 350 340

0.248 0.345 0.588

350

6% 9% 12%

4.58 3.44 2.72

6.83 (0.08) 8.26 (0.12) 8.49 (0.24)

1.51 (0.02) 2.02 (0.06) 2.15 (0.07)

370 290 330

0.260 0.513 0.724

Table 5 Estimated values of empirical constants for stage 2 of the proposed unified model at various P and TSF % (standard errors of the coefficients estimated by regression analysis are in parenthesis) P (kPa)

TSF % (w/w%)

qP,2,∞ (L/min)

k2 (L/min)

−b2 × 104 (s−1 )

t2 (s)

ˆ (L/min)

250

6% 9% 12%

2.97 2.41 1.77

0.960 (0.018) 0.945 (0.015) 0.609 (0.013)

2.45 (0.04) 2.12 (0.03) 1.65 (0.04)

9828 9908 9867

0.117 0.090 0.125

350

6% 9% 12%

3.33 2.51 2.03

1.14 (0.03) 0.839 (0.012) 0.598 (0.016)

2.88 (0.06) 2.50 (0.03) 2.16 (0.06)

9598 9214 9826

0.152 0.092 0.165

Fig. 6. The decrease in permeate flowrate obtained by experiment and estimated by the proposed unified model, when the pilot scale rig was operated with TSF % = 6% (w/w) and a TMP of 350 kPa. (b)–(d) show the magnified portion of stages 1–3 of the decrease in permeate flowrate, respectively.

76

K.W.K. Yee et al. / Journal of Membrane Science 332 (2009) 69–80

piecewise functions in the general form of Eqs. (1) and (2) to estimate the decrease in permeate flowrate during long-term whey UF. The relative values of b1 , b2 and b3 can be used to compare the rate of decrease in permeate flowrate when the different fouling mechanisms are dominant in the whey UF process. According to Table 4, the estimated values of b3 are of the order of 10−5 s−1 , which are one order of magnitude smaller than b2 and three orders of magnitude smaller than b1 . This diminishing rate of decrease is consistent not only with the decreasing gradient of the plot in Fig. 3, but also with results from existing studies [3,12,26]. The difference in the magnitude of b3 compared with those of b1 and b2 implies that once the protein deposit layers are established, their effects on permeate flowrate will remain essentially constant. Scanning electron microscope (SEM) and atomic force microscope (AFM) images of membrane surfaces obtained from the microfiltration of skimmed milk indicated that once the protein deposit layer is established, its surface morphology remains unchanged over time [27]. The surface morphology remains unchanged as the convection of the protein molecules to the membrane surface is balanced by the back diffusion to the bulk phase. The formation of a stagnant deposit layer in equilibrium with the bulk phase is also supported by studies on cross-flow UF from the literature [17,18,28]. The internal structure of the deposit layer will change with time during long-term operation, however. For a colloidal suspension subjected to membrane filtration, particles first form a loose deposit on the membrane surface (or ‘glass phase’) before they realign themselves to form a more orderly arrangement (or ‘solid phase’) [29,30]. Similarly, protein aggregates in the deposit layer can rearrange themselves, resulting in consolidation of the layer [31]. Consolidation increases the volume fraction of protein molecules in the deposit and hence the resistance to permeation, corresponding to the decrease in permeate flowrate in the long term.

Fig. 7. The ratio of permeate flux (JP (t)) to the initial flux (JP (0)) from (a) protein ultrafiltration with feed concentrations of 22% and 30% (adapted from Fig. 4 of Suki et al. [25]) and (b) the ultrafiltration of cheese whey with TMP of 100 and 400 kPa (adapted from Fig. 3 of Aimar et al. [4]).

at which long-term fouling starts to dominate the decrease in permeate flux is determined by the value of t2 . According to Tables 4 and 5, as well as Fig. 6(b)–(d), the values for t1 range from 290 to 370 s (or 4.8 to 6.2 min) and the values for t2 range from around 9214 to 9908 s (or 2.6 to 2.8 h). The decrease in permeate flowrate is therefore controlled by concentration polarization for the first 5–6 min of each experiment, followed by protein deposition until approximately 3 h. Long-term fouling then dominates the decrease in permeate flowrate after approximately 3 h. The time scale at which each mechanism dominates the decrease in permeate flowrate is consistent with values reported in the literature [3–7]. This consistency also supports the use of the three

5.2.2. Effects of TMP and feed concentration on the rate of decrease in permeate flowrate In addition to the insights into the dominance of various fouling mechanisms over the long-term operation of whey UF processes, values of the rate constants bf can provide insights into how TMP and feed concentration affect the rate of decrease in permeate flowrate. When concentration polarization and protein deposition are the dominant mechanisms (i.e. f = 1 and 2), changes in the values of b1 and b2 with TMP and feed concentration can be related to how protein molecules accumulate on the membrane surface and the fundamental structure of the deposit layer. Effects of TMP and feed concentration on the fundamental structure of deposits can be supported by evidence available in the literature. The evidence includes findings from experiments and visual characterization of fouling layers, as well as the estimated constants (Table 3) in the mechanistic model from Ho and Zydney [14] (Eqs. (5) and (6)). The physical significance of the constants in the mechanistic model has already been discussed in Section 1. After the protein deposits have been established (i.e. f = 3), effects of TMP and feed concentration on the consolidation of the

Table 6 Estimated values of empirical constants for stage 3 of the proposed unified model at various P and TSF % (standard errors of the coefficients estimated by regression analysis are in parenthesis) P (kPa)

TSF % (w/w%)

qP,3,∞ (L/min)

k3 (L/min)

−b3 × 105 (s−1 )

ˆ (L/min)

250

6% 9% 12%

2.41 2.00 1.53

0.707 (0.009) 0.595 (0.008) 0.410 (0.008)

1.62 (0.04) 1.65 (0.04) 1.64 (0.06)

0.068 0.074 0.110

350

6% 9% 12%

2.83 2.08 1.67

0.587 (0.009) 0.533 (0.007) 0.467 (0.008)

1.64 (0.05) 1.62 (0.04) 1.63 (0.05)

0.082 0.077 0.096

K.W.K. Yee et al. / Journal of Membrane Science 332 (2009) 69–80

Fig. 8. The estimated values of (a) b2 and (b) b3 (shown as crosses) and their respective 95% confidence intervals (shown as grey bars) for various TMP and feed concentrations.

deposits can be evaluated from the experimental results obtained from the pilot scale whey UF rig. • Stage 1 (f = 1) The magnitude of b1 increases with an increase in either TMP or feed concentration, indicating that permeate flowrate decreases at a faster rate when TMP or feed concentration is increased. A higher pressure difference across the membrane enhances the convection of the total solids components towards the membrane and promotes the accumulation of protein molecules near the membrane surface, reducing the time required for the boundary layer to be developed. The increased accumulation of protein molecules agrees with increases in the values of Rp0 (the initial resistance to permeation associated with protein molecules before the formation of deposits) with TMP at a given feed concentration. An increase in feed concentration increases the concentration gradient between the bulk stream and the membrane surface. This increase in concentration gradient enhances the flux of protein molecules towards the membrane surface and facilitates the formation of the boundary layer. Experimental studies on the ultrafiltration of macromolecules (such as dextran [32]) indicate that boundary layer concentration increases with feed concentration. Increases in the values of Rp0 with TSF % from Table 3 support the increase in protein concentration at the membrane surface, and hence the initial resistance to permeation. • Stage 2 (f = 2) The confidence intervals for b2 were determined in order to evaluate how the values of b2 change with TMP and feed concentration. Fig. 8(a) shows the 95% confidence intervals for the estimated values of b2 for various TMP and feed concentrations. The confidence

77

coefficient of 95% was chosen because this is the value commonly used for interval estimation of coefficients in regression models [24,33]. From Fig. 8(a), the magnitude of b2 decreases with increasing feed concentration or with decreasing TMP. This is consistent with the decrease in b2 evaluated from experimental results available in the literature with increasing feed concentration (Fig. 7(a)) or with decreasing TMP (Fig. 7(b)). Protein molecules will form aggregates as they deposit on the membrane surface [25]. SEM images obtained for BSA ultrafiltration [34] indicated that aggregates with larger size and protein deposits of higher voidage will be formed when protein concentration in the feed increases. Aggregates with larger size will be less effective in blocking the membrane pores while protein deposit layers of higher voidage will provide smaller resistances to permeation, resulting in a slower decrease in permeate flowrate and hence a smaller value of b2 . The effects of feed concentration on changes in aggregate size and deposit voidage are, respectively supported by the decreasing values of ˛ and f  R in Table 3(with the exception for TSF % = 9% and a TMP of 250 kPa) when TSF % increases. When TMP increases, the protein molecules will be packed closer together as they deposit on the membrane surface, corresponding to an increase in the magnitude of b2 . Evidence supporting the effects of TMP on the deposit layer can be found in existing work on the characterization of the fouling layer based on SEM [35], as well as experimental studies on changes in membrane permeability or resistances under different TMP [36,37]. The increase in resistance to permeation is also demonstrated by increases in the values of f  R in Table 3 when TMP is increased from 250 to 350 kPa. • Stage 3 (f = 3) In contrast to changes in the values of b2 , variation in the values of b3 with TMP and feed concentration is insignificant according to Fig. 8(b). Based on Table 6, the average value of b3 from all the experiments is around −1.63 ± 0.02 × 10−5 s−1 . The statistical insignificance of TMP and feed concentration to the value of b3 is supported by Fig. 3. After around 3 h of operation, the plots in the figure are parallel to each other irrespective of TMP and feed concentration, indicating a constant rate of decrease in permeate flowrate. This independence of the rate of decrease in permeate flowrate to feed concentration and TMP on permeate flowrate was also observed by Kelly and Zydney [38] for the ultrafiltration of BSA. The relative constant value of b3 indicates that consolidation of the protein deposits during long-term whey UF is not affected by feed concentration and TMP. Since the convection of protein molecules towards the membrane surface is balanced by back diffusion after the concentration boundary layer is established, the gel-polarization model in terms of qP of Eq. (7) can be used to analyze the experimental data obtained from the pilot scale rig. qP = kA(ln cG − ln TSF %)

(7)

The permeate flowrates from the pilot scale whey UF rig after t2 , 7 and 14 h are plotted against the logarithm of the feed concentrations (TSF %) in Fig. 9(a). Because of the independence of the rate of decrease in permeate flowrate to TMP, a line of best fit can be drawn through the data points in the plot. According to the gelpolarization model, the values at which the lines of best fit cross the horizontal axis correspond to the values of cG after t2 , 7 and 14 h (Eq. (7)). The values of cG obtained from the plot range from 36 to 38%, which are similar in magnitude to values of 30–35% reported in the literature [11,39]. Results from Fig. 9(a) also indicate a slight increase in cG with time from t2 to 14 h. In other words, the parameter cG is not as static as it is often assumed to be in the literature [11,40,41]. For

78

K.W.K. Yee et al. / Journal of Membrane Science 332 (2009) 69–80

a better illustration of the time dependence of cG , Fig. 9(b) shows the increase in cG with time after t2 (the average t2 from the experiments) up to 14 h. Although the gel layer was not directly observed on the surface of the membrane involved in the whey UF experiments, the increase in gel concentration (cG ) with time can be used to indicate the increase in apparent protein concentration on the membrane surface, and hence the extent of consolidation of the protein boundary layer. As the volume fraction of protein in the boundary layer increases with time during consolidation and/or densification, the apparent protein concentration (and hence the value of cG ) increases. Densification of the boundary layer can be caused by the unfolding of protein molecules by shear stress [42], or entrapment of small whey feed components such as polypeptides, protease or other protein fragments.

dation of the deposits. Experimental results obtained from the pilot scale rig over 14 h of operation have provided evidence to support the presence of these three stages. Values of the empirical constants in the model are estimated based on experimental results obtained from whey ultrafiltration using a pilot scale membrane rig. By comparing the constants in the models estimated under various operating parameters, such as TMP and feed concentration, their effects on the rate of decrease in permeate flowrate can be determined. When concentration polarization and protein deposition dominate the decrease in permeate flowrate during the first 3 h of whey ultrafiltration, the rate of decrease varies with TMP and feed concentration. The effects of TMP and feed concentrations on the rate of decrease during the first 3 h are supported by other experimental findings, visual characterization of fouling layers and mechanistic fouling models available in the literature. Experimental results from the pilot scale rig suggest that when the consolidation of protein deposits is dominant (i.e. after 3 h), the effects of TMP and feed concentration on the rate of decrease in permeate flowrate are statistically insignificant. An average value of −1.63 ± 0.02 × 10−5 s−1 was obtained to describe the rate of change in permeate flowrate for the whey ultrafiltration process, irrespective of TMP and feed concentration. Another strength of the unified model proposed in this paper lies in the similar form of the equation to describe fouling dynamics under the three stages. In addition to the absolute value of permeate flux, fouling dynamics can affect the dynamic behaviour of whey UF process. Since the constants of the unified model (i.e. bf in Eq. (3)) are generally functions of operating parameters such as TMP, the unified model can be used to determine the achievable performance of automatic controllers prior to controller design. The effects of long-term fouling dynamics on the achievable performance of automatic controllers is significant given the length of operation of industrial membrane processes. Due to the independence of TMP and feed concentration on long-term fouling dynamics, one convenient approach is to represent the process dynamics using a time-variant model: that is, the coefficients of the model are functions of time. When the process dynamics model is expressed as a transfer function, for example, the coefficients of the polynomials in the numerator and denominator are time-variant. Based on this time-variant process dynamics model, changes in achievable control performance at various stages of fouling can be analyzed [2,43]. This approach of incorporating fouling dynamics into the process dynamics model can also be implemented in designing a cluster of controllers to be switched on at different stages of fouling to optimize control performance. In addition to industrial whey UF processes, the methodology for developing the unified model to describe the time dependence of flux decline in this paper can be applied to other membrane processes that operate continuously for long periods of time, such as desalination and wastewater treatment. Although long-term fouling dynamics for other membrane processes may vary with operating parameters, the methodology in this paper can still be applicable. The estimated model can be applied to study the performance of automatic controllers during controller design, after process dynamics models from changes in operating parameters are determined.

6. Conclusions

Acknowledgements

A unified model to describe the time dependence of flux decline over the long-term operation of whey UF processes is proposed in this paper. The proposed model consists of three piecewise exponential decay models that correspond to the three stages of fouling: namely concentration polarization, protein deposition and consoli-

The authors gratefully acknowledge the support of an Australian Research Council Discovery Grant. One of the authors (KWKY) would also like to acknowledge the support of an Australian Postgraduate Award (APA) and a Faculty of Engineering Scholarship from the University of New South Wales.

Fig. 9. A plot of (a) permeate flowrate (qP ) vs. feed concentration (TSF %, in logarithmic scale) at t = t2 , 7 and 14 h and (b) estimated cG vs. time. [Note: In (a), the hollow symbols (♦,  and ) and the filled symbols (, 䊉 and ) represent TMP of 250 and 350 kPa, respectively. Lines of best fit of the data at t = t2 , 7 and 14 h are also included.]

K.W.K. Yee et al. / Journal of Membrane Science 332 (2009) 69–80

Nomenclature A bf c f  R J J k kf M n P q R t t1 , t2 TSF % u0 x

Total membrane area (m2 ) Exponential coefficient for each stage of fouling (Eq. (1)) (s−1 ) Concentration (w/w%) Resistance to permeation from the protein deposits (m−1 ) Flux (m/s) Average flux (m/s) Mass transfer coefficient (Eq. (7)) (m s−1 ) Exponential factor for each stage of fouling (Eq. (1)) (L/min) Mass of protein deposited per unit membrane area (g m−2 ) Number of experimental observations Trans-membrane pressure (TMP) (kPa) Flowrate (L/min) Resistance to permeation (m−1 ) Time (s, min or h) Time limits for the piecewise functions (Eq. (1)) (s) Total solids concentration in the fresh whey feed (w/w%) Cross-flow velocity (m s−1 ) Length of membrane channel (m)

Greek symbols ˛ Membrane area being blocked per unit mass of protein convected to the surface (m2 kg−1 )  Viscosity (Pa s) ˆ Standard error of estimate Subscripts b Bulk phase CP Concentration polarization eq Equilibrium est Model-predicted values f Stages of fouling (f = 1, 2, 3) where f = 1 for concentration polarization; f = 2 for protein deposition; f = 3 for long-term fouling F Fouling G Gel layer ∞ Steady state m Membrane p Protein deposits P Permeate s Mineral salts 0 Initial condition before protein deposition

References [1] K.W.K. Yee, D.E. Wiley, J. Bao, Steady state operability of whey ultrafiltration (UF) system, Desalination 199 (2006) 497–498. [2] K.W.K. Yee, D.E. Wiley, J. Bao, Whey protein concentrates production by continuous ultrafiltration: operability under constant operating conditions, Journal of Membrane Science 290 (2007) 125–137. [3] A. Suki, A.G. Fane, C.J.D. Fell, Flux decline in protein ultrafiltration, Journal of Membrane Science 21 (1984) 269–283. [4] P. Aimar, C. Taddei, J-P. Lafaille, V. Sanchez, Mass transfer limitations during ultrafiltration of cheese whey with inorganic membranes, Journal of Membrane Science 38 (1988) 203–221. [5] A.D. Marshall, P.A. Munro, G. Trägårdh, The effect of protein fouling in microfiltration and ultrafiltration on permeate flux, protein retention and selectivity: a literature review, Desalination 91 (1993) 65–108. [6] A.G. Fane, C.J.D. Fell, A.G. Waters, Ultrafiltration of protein solutions through partially permeable membranes—the effect of adsorption and solution environment, Journal of Membrane Science 16 (1983) 211–224.

79

[7] A.G. Fane, C.J.D. Fell, A review of fouling and fouling control in ultrafiltration, Desalination 62 (1987) 117–136. [8] K-P. Kuo, M. Cheryan, Ultrafiltration of acid whey in a spiral-wound unit: effect of operating parameters on membrane fouling, Journal of Food Science 48 (1983) 1113–1118. [9] H.G. Ramachandra Rao, A.S. Grandison, M.J. Lewis, Flux pattern and fouling of membranes during ultrafiltration of some dairy products, Journal of the Science of Food and Agriculture 66 (1994) 563–571. [10] C. Taddei, G. Daufin, P. Aimar, V. Sanchez, Role of some whey components on mass transfer in ultrafiltration, Biotechnology and Bioengineering 34 (1989) 171–179. [11] M. Cheryan, Ultrafiltration and Microfiltration Handbook, Technomic Publishing Company, Inc., 1998. [12] M. Meireles, P. Aimar, V. Sanchez, Albumin denaturation during ultrafiltration: effects of operating conditions and consequences on membrane fouling, Biotechnology and Bioengineering 38 (1991) 528–534. [13] S.-H. Lin, C.-L. Hung, R.-S. Juang, Applicability of the exponential time dependence of flux decline during dead-end ultrafiltration of binary protein solutions, Chemical Engineering Journal 145 (2008) 211–217. [14] C-C. Ho, A.L. Zydney, A combined pore blockage and cake filtration model for protein fouling during microfiltration, Journal of Colloid and Interface Science 232 (2000) 389–399. [15] G. Gésan, G. Daufin, U. Merin, Performance of whey crossflow microfiltration during transient and stationary operating conditions, Journal of Membrane Science 104 (1995) 271–281. [16] A.J.B. van Boxtel, Z.E.H. Otten, H.J.L.J. van der Linden, Evaluation of process models for fouling control of reverse osmosis of cheese whey, Journal of Membrane Science 58 (1991) 89–111. [17] L. Song, Flux decline in crossflow microfiltration and ultrafiltration: mechanisms and modeling of membrane fouling, Journal of Membrane Science 139 (1998) 183–200. [18] L. Wang, L. Song, Flux decline in cross-flow microfiltration and ultrafiltration: experimental verification of fouling dynamics, Journal of Membrane Science 160 (1999) 41–50. [19] D.E. Wiley, The effects of osmotic pressure and solute adsorption on ultrafiltration of ovalbumin. Comments, AIChE Journal 37 (5) (1991) 791–792. [20] D. Wiley, D. Clements, H. Khabbaz, P. Neal, Optimal Operation of Membrane Modules (UNS027)—A Report Prepared for Dairy Australia, Technical Report, UNESCO Centre for Membrane Science and Technology, The University of New South Wales, 2005. [21] R. Rautenbach, R. Albrecht, Membrane Processes, John Wiley & Sons, Chichester, 1989. [22] R. Ghosh, Protein Bioseparation using Ultrafiltration: Theory, Applications and New Developments, Imperial College Press, London, 2003. [23] D.E. Seborg, T.F. Edgar, D.A. Mellichamp, Process Dynamics and Control, 2nd edition, John Wiley & Sons Inc., 2004. [24] D.N. Gujarati, Basic Econometrics, 3rd edition, McGraw-Hill, Inc., 1995. [25] A. Suki, A.G. Fane, C.J.D. Fell, Modeling fouling mechanisms in protein ultrafiltration, Journal of Membrane Science 27 (1986) 181–193. [26] V. Gekas, P. Aimar, J-P. Lafaille, V. Sanchez, A simulation study of the adsorption– concentration polarization interplay in protein ultrafiltration, Chemical Engineering Science 48 (15) (1993) 2753–2765. [27] B.J. James, Y. Jing, X.D. Chen, Membrane fouling during filtration of milk–a microstructural study, Journal of Food Engineering 60 (4) (2003) 431–437. [28] V. Chen, A.G. Fane, S. Madaeni, I.G. Wenten, Particle deposition during membrane filtration of colloids: transition between concentration polarization and cake formation, Journal of Membrane Science 125 (1997) 109–122. [29] P. Bacchin, M. Meireles, P. Aimar, Modelling of filtration: from the polarised layer to deposit formation and compaction, Desalination 145 (2002) 139–146. [30] P. Bacchin, D. Si-Hassen, V. Starov, M.J. Clifton, P. Aimar, A unifying model for concentration polarization, gel-layer formation and particle deposition in cross-flow membrane filtration of colloidal suspensions, Chemical Engineering Science 57 (2002) 77–91. [31] G. Belfort, R.H. Davis, A.L. Zydney, The behavior of suspensions and macromolecular solutions in crossflow microfiltration, Journal of Membrane Science 96 (1–2) (1994) 1–58. [32] R.L. Goldsmith, Macromolecular ultrafiltration with microporous membranes, Industrial and Engineering Chemistry Fundamentals 10 (1) (1971) 113–120. [33] M.C. Phipps, M.P. Quine, A Primer of Statistics, 2nd edition, Prentice Hall of Australia, 1999. [34] K.J. Kim, A.G. Fane, C.J.D. Fell, D.C. Joy, Fouling mechanisms of membranes during protein ultrafiltration, Journal of Membrane Science 68 (1992) 79–91. [35] D.N. Lee, R.L. Merson, Examination of cottage cheese whey proteins by scanning electron microscopy: relationship to membrane fouling during ultrafiltration, Journal of Dairy Science 58 (10) (1975) 1423–1432. [36] W. Senyo Opong, A.L. Zydney, Hydraulic permeability of protein layers deposited during ultrafiltration, Journal of Colloid and Interface Science 142 (1) (1991) 41–60. [37] S.A. Mourouzidis-Mourouzis, A.J. Karabelas, Whey protein fouling of microfiltration ceramic membranes—pressure effects, Journal of Membrane Science 282 (2006) 124–132. [38] S.T. Kelly, A.L. Zydney, Mechanisms for BSA fouling during microfiltration, Journal of Membrane Science 107 (1995) 115–127. [39] M. Cheryan, K.P. Kuo, Hollow fibers and spiral wound modules for ultrafiltration of whey–energy consumption and performance, Journal of Dairy Science 67 (7) (1984) 1406–1413.

80

K.W.K. Yee et al. / Journal of Membrane Science 332 (2009) 69–80

[40] W.F. Blatt, A. Dravid, A.S. Michaels, L. Nelson, Solute polarization and cake formation in membrane ultrafiltration: causes, consequences and control techniques, in: Membrane Science and Technology—Industrial, Biological and Waste Treatment Processes, Plenum Press, New York, London, 1970. [41] M.C. Porter, Concentration polarization with membrane ultrafiltration, Industrial and Engineering Chemistry Product Research and Development 11 (3) (1972) 234–248.

[42] K.J. Kim, V. Chen, A.G. Fane, Some factors determining protein aggregation during ultrafiltration, Biotechnology and Bioengineering 42 (1993) 260– 265. [43] K.W.K. Yee, J. Bao, D.E. Wiley, Effects of long-term membrane fouling on the dynamic operability of an industrial whey ultrafiltration process, in: Proceedings of ICOM 2008, Honolulu, Hawaii, USA, July 12–18, 2008 (available on-line at http://www.icom2008.org/viewpaper.cfm?ID=2009).