Article pubs.acs.org/IECR
Analysis of the Membrane Fouling Mechanisms Involved in Clarified Grape Juice Ultrafiltration Using Statistical Tools Beatriz Cancino-Madariaga,*,† Rene Ruby,† Carolina Astudillo Castro,† Jorge Saavedra Torrico,‡ and Mariane Lutz Riquelme§ †
INPROMEM, Research in membrane process, School of Food Engineering, Pontificia Universidad Católica de Valparaíso, Waddington 716, Valparaiso, Chile ‡ Datachem Goup, School of Food Engineering, Pontificia Universidad Católica de Valparaíso, Waddington 716, Valparaíso § Centro de Investigación y Desarrollo de Alimentos Funcionales, CIDAF, Facultad de Farmacia, Universidad de Valparaiso, Gran Bretaña 1093, Valparaíso, Chile ABSTRACT: Statistical tools were used to analyze membrane fouling occurring during ultrafiltration (UF) of clarified grape juice. Experimental flux data were correlated to dead-end and crossflow filtration models. The UF experiments were performed at 30 and 40 °C for an 8-kDa multitubular ceramic membrane and also at 30 °C for a 1-kDa membrane to determine the effect of pore size. ANOVA was used for the statistical analysis of fluxes. The modified Kolmorov-Smirnov and the Shapiro-Wilk tests were used to evaluate the normality of the residuals obtained from each model, thus allowing validation or rejection of initial adjustments given by a simple R-square statistical test. Using the standard error of the estimate and the mean absolute error it was possible to identify the best model for each case. Differences in the permeate flux and fouling mechanisms between both temperatures and pore size were discussed.
1. INTRODUCTION Grape juice is considered a good source of phenolic compounds such as anthocyanins and tannins.1 Phenolics affect organoleptic properties, such as color, flavor, bitterness, astringency, and aroma and contribute to oxidative stability.2 Many health-promoting effects have been attributed to the putatively bioactive phenolic compounds found in grapes; these effects include antimicrobial, anti-inflammatory, antimutagenic, anticarcinogenic, antiallergic, antiplatelet, and vasodilatory actions and neuroprotective effects.3−14 The ability of these compounds to modulate and induce signaling pathways contributes to the reduction of the risk factors for age-related diseases.3−14 For these reasons and because of their antioxidant action, the dietary intake of phenolic compounds is strongly recommended.15,16 Specifically, the consumption of polyphenol-enriched grape juice is a way to enhance the intake of polyphenols in the human diet. Ultrafiltration (UF) is the process most commonly used for the separation of valuable compounds from solutions or juices; it is currently used for the removal of suspended solids during fruit juice clarification and fining. These components are considered haze-inducing and turbidity factors.17 The clarification, fractionation, and concentration of a variety of solutes are among the applications of UF. UF has been successfully used for the concentration of polyphenols in grape musts by membrane retention.18 In this method, the process behavior depends on the targeted particle size and the presence of other particles, such as sugars, polymers, and colloidal matter, that are retained by the membrane.18 Other studies have shown that UF is an attractive alternative for the separation of polyphenols. However, the main process limitation is the decline in permeability that occurs from concentration polarization and membrane fouling. Moreover, the complex effects of © 2012 American Chemical Society
polyphenolic substances on the membrane surface and its behavior have not yet been investigated.19 In juice production, when the UF process is used, it is important to study fouling mechanisms as it is necessary to identify the predominant fouling mechanism19 in order to establish the most appropriate procedure for membrane restoration and the operational strategies for diminishing the membrane fouling. This paper presents an exhaustive statistical analysis of the data from fouling mechanisms that occur on ceramic UF membranes. The analysis is intended to accurately explain the results obtained using the models of pore blocking available in the existing literature. The aim of this work was to identify the membrane fouling mechanisms that occur during the UF of clarified grape juice, as the case of study, using a statistical analysis. Accordingly, experimental tests were conducted in which the effects of temperature and pore size on the UF process were evaluated. 1.1. Models. In general, membrane fouling is affected by three primary factors: the membrane material, the physicochemical characteristics of the solution being filtered, and the imparted operation parameters, such as transmembrane pressure (TMP) and temperature.20,21 The membrane surface chemistry, membrane-solute, and solute−solute interactions are the key factors for the understanding of fouling phenomena.19 Mass transport through the membrane in microfiltration (MF) and UF processes is laminar and governed by diffusion mechanisms.20,21 A few models describe the flux decline that occurs in these processes over time.20 The existing models of Received: Revised: Accepted: Published: 4017
April 22, 2011 December 22, 2011 January 9, 2012 January 9, 2012 dx.doi.org/10.1021/ie201921x | Ind. Eng.Chem. Res. 2012, 51, 4017−4024
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Article
Table 1. Hermia’s Models for Fouling According to Hughes et al.28a
a
J is flux in m3/(m2·s), and t is time in s.
For example, when scale-up is desired, a mathematical adjustment to the Darcy law is used. A straight line is desirable; thus, the coefficient of determination (R-square) is used to evaluate whether the data fit well, and the total resistance (RT) is obtained from the experimental data. However, in 1973, Ascombe34 presented four cases of data sets each of which correlated with a straight line and presented exact R-square values; however, only one of the cases showed a real correlation-causation effect . This finding shows that the parameter R-square is insufficient for deciding whether a model is well correlated and that this parameter should not be used for model validation. Although several models have been used to describe the behavior of membrane processes, the lack of fit of these models and their insufficient validation pose a problem. For example, Nehring et al.35 used mathematical modeling to describe the process of batch membrane filtration with ceramic membranes in retrovirus separation. These authors analyzed the different fouling mechanisms using Hermia’s laws for complete blocking, intermediate blocking, standard blocking, and cake blocking. This work also included two other models based on the power law, cake erosion and layer mass limit and obtained the respective K-parameters through multiple running functions and the use of software to solve ordinary differential equations. For the statistical analyses, regression correlation was used. However, no further details about statistical model validation were provided. Nandi et al.26 compared the use of pore-blocking and artificial neural network models to describe the fouling of ceramic membranes by oily wastewater, and Vincent-Vela et al.27 used Hermia’s models to study the fouling mechanisms involved in UF of polyethylene glycol. In both these studies, the coefficient of determination (R-square) and errors calculated with standard deviation were used, but no further statistical analysis was conducted. In other work on dextran UF, again no thorough statistical analysis was presented.36 In another study, Mondal and De37 concluded that it is possible to drive the filtration process by controlling velocity and transmembrane pressure in order to prevent the pore-blocking region instead of cake filtration region. They considered the differences predicted
concentration polarization are very sensitive to mass transport parameters and to the cake hydraulic resistance. These parameters have been calculated for ideal systems but have yet to be determined using empirical methods.22 A variety of models for dead-end filtration that are based on pore-blocking mechanisms have been assessed.23−27 The principal models are presented in Table 1. Most of these models employ Hermia’s equation, which was developed specifically for dead-end conditions.28 These models are based on the Darcy law, which states that the flow through the membrane (J) depends directly on the transmembrane pressure and depends indirectly on the viscosity (μ) and the total membrane resistance (RT).29 In cross-flow operations, the use of Hermia’s equation is appropriate when the amount of material contained in the membrane convective flow is greater than the amount of material removed due to the cross-flow action. In this situation, the cross-flow effect is similar to that of dead-end filtration.28 Thus, fouling models are successful in helping to explain the experimental data obtained in cross-flow studies.29 Models have been developed that consider different blocking mechanisms as successive steps.30 These models explain the blocking as the consequence of a sequence of blocking mechanisms that occur in the membrane over time. Among these models, a mathematical model was developed that considers different thicknesses of the cake formed over the membrane.31 This model was applied in protein batch MF and was able to predict with high goodness of fit, the fouling phenomena produced by the passage of proteins over the membrane.31 Another model considers a smooth transition from pore blocking to cake filtration with time, thus eliminating the need to use different models to describe the entire filtration process.33 Models for flux decline that take the pore morphology into account have also been developed.32 In this work, we focus on the models listed in Table 1. 1.2. Statistical Analysis Applied to Membrane Filtration. Typically, in the description of a membrane process, mathematical modeling is used to describe the membrane behavior, and the coefficient of determination (Rsquare) is used to validate the goodness of fit of the models. 4018
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2. MATERIALS AND METHODS 2.1. Materials. The experiments were conducted using the filtration scheme showed in the Figure 1. The pump impulse
by Hermia’s models and the cross-flow UF steady state in developing new equations. However, the statistical analysis was not an important issue in their study. From these examples, it is evident that model validation is one of the most important and overlooked steps in model building sequences. At present, only the R-square statistic is used for model validation in membrane processes. However, this parameter measures only the fraction of the total variability in the response that is accounted for by the model. The use of a model that does not fit the data well cannot provide sufficient answers to the underlying engineering or scientific questions under investigation. Although many statistical tools for model validation exist, the one used in most process modeling applications is residual analysis.38,39 The residuals obtained from a fitted model represent the differences between the responses observed at each combination of values of the explanatory variables and the corresponding predictions of the responses computed using the regression function.38,39 If the model fits well the data, the residuals approximate the random errors that make the relationship between the explanatory and the response variables a statistical relationship. Formally, the residuals (RES) are the differences between the observed values and the corresponding values that are estimated by a model.38 Hence, the random behavior of residuals suggests that a model has a good goodness of fit. Conversely, if a nonrandom residual structure is evident, the model fits the data poorly.38−40 Normal probability plots are used to check whether it is reasonable to assume that the random errors inherent to the process have been drawn from a normal distribution. If these errors do not follow a normal distribution, incorrect decisions will be made more or less frequently than the stated confidence levels for the indicate differences.36,38 Shapiro and Wilk41 presented a novel and robust statistical procedure to test the normality of a complete sample and cautioned against making the assumption of normality without a test to prove it. Lilliefors42 presented a table for the use of the Kolmogorov− Smirnov statistic when testing whether a set of observations comes from a normal population if the mean and variance are unknown. He described the major advantages of this test, which can be used for small sample sizes, over the chi-square test. This test is often more powerful than the chi-square test for any sample size. At the present time, the most popular omnibus test of normality for general use is the Shapiro−Wilk (SW) test.43−45 Another popular test is the Modified Kolmogorov−Smirnov (K−S) test. It is the best-known and most widely used goodness-of-fit test based on the empirical distribution function (EDF). This test is based on a statistic that measures the deviation of the observed cumulative histogram from a hypothesized cumulative distribution function. The K−S test is valid for all sample sizes and is strictly valid only for continuous distributions.43,46,47 In this investigation, the validation of models taken from the literature, describing the membrane fouling mechanism, was evaluated using the following five statistics: i) the coefficient of determination (R-squared) adjusted for degrees of freedom, ii) the standard error of the estimate and the evaluation of residual normal distribution through, iii) the mean absolute error, iv) the Shapiro-Wilk test, and v) the Modified Kolmogorov− Smirnov test. These statistical tests were used to demonstrate the relative usefulness of each model and to decide which model best applies to the specific case under study.
Figure 1. Membrane system under nonstationary conditions: (1) membrane, (2) pump, (3) manometers, (4) valve.
the feed fluid to the membrane, producing a concentrate flow and a permeate flow. The concentrate goes back directly to the feed tank while the permeate is withdrawing from the system. Two different ultrafiltration multitubular ceramic membranes provided by Tami (France) were used, which are described in Table 2. Three cases were tested, the first one the membrane of Table 2. Commercial Membranes Used membrane material
MWCO
pH range
area (m2)
membrane resistancea (m‑1)
ZrO2−TiO2 ZrO2−TiO2
1 kDa 8 kDa
2−14 2−14
0.0132 0.0132
1.36·1014 1.35·1013
Determined in our work, using deionized water (≤20 μS/cm) at 30 °C. a
8-kDa at 30 °C, the second the same membrane at 40 °C, and the last one the membrane of 1 kDa at 30 °C. A positive displacement pump with a power of 500 W was used (model PA411, Fluid-o-Tech US). The temperature was controlled using a Resun Chiller model C-1500. For all statistical analyses, the commercial software Statgraphics Centurion XVI (StatPoint, USA, 2010) was used. Permeate flux was determined by direct permeate mass registration over time, using an electronic scale (Shimadzu, BX 4200H). Data acquisition was carried out using a computer. The density was calculated using a pycnometer taking temperature into account. 2.2. Grape Juice Description, Pretreatment, and Operating Conditions. A commercial pasteurized and nonclarified grape juice was used in all the experiments. Because raw material used in the juice industry is not processed in a standard manner, the first stage was a microfiltration (MF) step to clarify the juice and prevent quality variations caused by different production lots. For this stage, a commercial ceramic module (PDF Novoflow GmbH, Germany) was used, comprising 5 ceramic discs of 0.2 μm pore size and area of 0.162 m2. The permeate obtained from the MF stage had 18.8 ± 0.25° Brix, a pH of 4.0 ± 0.03, a conductivity of 2.5 ± 0.18 μS/cm, and a turbidity of 27.5 ± 5.6. The clarified juice was frozen at −20 °C prior to use in the subsequent UF process. For all the UF experiments, the transmembrane pressure (TMP) was 7.5 bar. UF experiments were performed at 30 °C for 1-kDa and 8-kDa membranes; however, 40 °C was also tested for the 8-kDa membrane. Sugar analysis was performed using the enzymatic Megazyme K-FRUGL kit (Irland) for determination of glucose and fructose. 4019
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2.3. Fouling Mechanisms Evaluation. In this work, the fouling type was determined using the models described by Hermia reported by Hughes et al.28 (Table 1). The estimation of the K-constant associated with each of the models shown in Table 1 was determined by nonlinear regression of the experimental data (J versus t). The Marquardt method with successive iteration was applied until the sum of the squares’ residuals converged to one value.
data adjustment to the models described by the equations shown in Table 1. Using the K values of Table 3, it was possible to calculate J in the models presented in Table 1 (data not shown). The J-value is typically referred to as ‘J predicted’ or ‘J calculated’. The minimum number of data points needed for regression analysis by the estimation of the Mean Square of Error (or Residual) value is related to the degrees of freedom.48 According to the ANOVA table, the minimum number of degrees of freedom needed to validate the model is 6 to 8. In this work, there were 25 degrees of freedom in each regression analysis. For each regression analysis, an ANOVA analysis was performed to evaluate significances of the model; thus, the number of data points used in this work was sufficient for modeling. Table 4 shows the R-square value adjusted for degrees of freedom, the standard error of the estimate, and the results of the Shapiro-Wilk and Modified Kolmogorov−Smirnov tests. The last two tests were used to check whether the residuals came from a normal distribution. These values were used in the analysis and model validation described in the next section. 3.1. Temperature Effect on Flux and Fouling. The effect of temperature on permeate flux and fouling mechanisms was studied for the 8-kDa UF ceramic membrane with the characteristics shown in Table 2. As expected, increasing the temperature from 30 to 40 °C produced an increase in the permeate flux; this behavior is shown in Figure 2. The two
3. RESULTS AND DISCUSSION Models that have been used to describe the fouling mechanisms that occur during the grape juice UF process were studied. Because a high cross-flow velocity of close to 6 m/s was developed inside the membrane in all the experiments, a pressure-controlled region was expected.20 During the flux measurements, the experimental error was lower than 1.0%. This error was not statistically significant. The sugar concentration of the permeate that accumulated during the experiment conducted at 1-kDa and 30 °C was 194.5 g/L. In the total volume of concentrate, a sugar concentration of 227.9 g/L was measured. These observations provide an indication of the expected osmotic pressure during the concentrate step and how this could affect the model. The fact that the sugar concentration of both the permeate and the concentrate was moderate suggests that there was little effect of osmotic pressure on the behavior of the flux. Table 3 shows the calculated K-values of the fouling constant. These values were calculated using the experimental Table 3. K-Fouling Constant Values for Each Fouling Mechanism Model UF conditions
model
K-value
K-units
8 kDa-40 °C
1 2 3 4 1 2 3 4 1 2 3 4
0.0035 0.6570 484.98 1.29 × 108 0.0030 0.6636 589.20 2.29 × 108 0.0028 0.5265 400.27 1.14 · 108
s−1 (m·s)−0.5 m−1 (m·s)−1 s−1 (m·s)−0.5 m−1 (m·s)−1 s−1 (m·s)−0.5 m−1 (m·s)−1
8 kDa-30 °C
1 kDa-30 °C
Figure 2. Temperature effect on flux for an 8-kDa membrane.
curves were compared using ANOVA, which indicated significant differences between them (p-value ≤.001). The higher flux at 40 °C was probably caused by a decrease in the viscosity of the solution at the higher temperature;49
Table 4. Values of the Statistics Used for the Mechanism Models Evaluation case of study 8 kDa 40 °C
8 kDa 30 °C
1 kDa 30 °C
model
R-squared (adjusted for degrees of freedom)
standard error of the estimate
mean absolute error
modified Kolmogorov−Smirnov, D (p value)
Shapiro-Wilk, W (p value)
1 2 3 4 1 2 3 4 1 2 3 4
0.9874 0.9926 0.9942 0.9937 0.9882 0.9941 0.9964 0.9971 0.9910 0.9963 0.9983 0.9985
0.031 0.022 0.018 0.014 0.029 0.019 0.014 0.012 0.026 0.015 0.010 0.008
0.026 0.018 0.015 0.014 0.022 0.014 0.011 0.008 0.021 0.012 0.007 0.006
