Evaluation of the Separation of Liquid–Liquid Dispersions by Flow

Article pubs.acs.org/IECR

Evaluation of the Separation of Liquid−Liquid Dispersions by Flow through Fiber Beds Dragan D. Govedarica,*,† Radmila M. Šećerov Sokolović,† Dunja S. Sokolović,† and Slobodan M. Sokolović‡ †

Faculty of Technology, University of Novi Sad, Bulevar cara Lazara 1, 21000 Novi Sad, Serbia Faculty of Technical Sciences, University of Novi Sad, Trg Dositeja Obradovica 6, 21000 Novi Sad, Serbia

‡

S Supporting Information *

ABSTRACT: The liquid−liquid model dispersions encompassing four mineral oils of different properties were separated using polyurethane fibers. Experiments were carried out over a wide range of oil properties, bed permeabilities, and fluid velocities. The objective was to introduce multivariate analysis as a statistical method for the estimation of the efficiency of separation of liquid− liquid dispersions by flow through fiber beds. The bed coalescence efficiency was followed by monitoring the changes of critical velocity. On the basis of the principal component analysis, reduced dimensionality and a lower number of variables, an improved statistical treatment of the measurement data was performed. An empirical equation was derived describing the critical velocity as a function of the oil viscosity, interfacial tension, dielectric constant, emulsivity, and bed permeability. a set of individual fibers without mutual interactions. Hence, the random line network model brought about a progress in bed coalescence investigations. This geometrical model assumes that the fibrous bed structure consists of a set of layers, and within each layer the fibers are represented by straight lines of random orientations.16 However, this rigorous theoretical approach deviates from the real bed structure. With the variation in the influent droplet size and shape, the analysis may be even more complicated. Each droplet capture mechanism has a certain probability.2,7,11,17−19 Therefore, bed coalescence analysis can be improved by using statistical approaches for the selection of pertinent variables. It should be noted that such an approach is not widespread. Spielman et al.8,20 have developed a semiempirical equation for the estimation of coalesced oil drop diameters using dimensionless analysis. Grilc et al.21,22 have modified this equation and applied regression analysis in order to derive the dependence of the critical velocity on the interfacial tension and bed length. Regression analysis is the most commonly used statistical method for the study of fiber bed coalescence. This statistical method has been used by Šećerov Sokolović et al.23−25 to establish empirical equations for the bed coalescer design. These authors derived several equations for the estimation of the separation efficiency, effluent oil concentration, and critical velocity. The separation efficiency was analyzed in terms of numerous dispersed oil properties, while the effluent oil concentration was estimated as a function of the bed length, permeability, fluid velocity, and the influent oil concentration. Also, they investigated the dependence of the critical velocity on the bed length and bed permeability.

1. INTRODUCTION Fiber bed coalescence is a commonly employed technique for the liquid−liquid separation in the industry. Bed coalescence is performed by passing the liquid−liquid dispersion through a fibrous bed and followed by merging of smaller droplets into larger ones, thereby permitting easy separation by gravity settling. The efficiency of fiber bed coalescence can be evaluated based on graphical plots,1−3 using mathematical models,4−6 or dimensionless groups,7,8 or by a combination of the mentioned approaches.9−11 Each approach tends to investigate phenomena in a specific manner and identify pertinent variables. Although bed coalescers have been used extensively for many years, it appears that there are no reliable mathematical models of such separators yet. The main reasons for the limited success of their mathematical modeling are the existence of numerous factors that influence bed coalescence (properties of the dispersed phase, fiber bed properties, bed geometry, operating conditions, etc.) and the simultaneous occurrence of several coalescence mechanisms. According to the literature, bed coalescence involves the coalescence of the adjacent droplets, coalescence of the droplets on the fibers surface, coalescence of the droplets into the surface of the saturated oil, droplet deformation, redispersion, settling, etc.6,12,13 Thus, bed coalescence incorporates numerous forces acting on a droplet. To develop a mathematical model of the fibrous bed is a demanding task. Moreover, such model should be applied in conjunction with the mechanisms of droplet interception and detachment, droplet−droplet, droplet-fiber, and hydrodynamic interactions, etc.14 If the oil is a multicomponent mixture containing diverse hydrocarbons, heterocompounds (containing S, N, O, metals) and surface active materials, the modeling of the process is even more difficult. These types of emulsions are common in the petroleum industry. The developed coalescence models for droplets on a single fiber7,15 can be imprecise due to the assumption that the bed is © 2012 American Chemical Society

Received: Revised: Accepted: Published: 16085

October 3, 2012 November 14, 2012 November 16, 2012 November 17, 2012 dx.doi.org/10.1021/ie3026967 | Ind. Eng. Chem. Res. 2012, 51, 16085−16091

Industrial & Engineering Chemistry Research

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particular experiment, the value of the critical velocity was determined from the dependence of the effluent oil concentration on the fluid velocity. 2.5. Statistical Analysis. Experimental data were analyzed by regression analysis, PCA, cluster variables analysis, and principal component regression (PCR). In order to conduct linear regression Microsoft Office Excel 2007 and Data Analysis tool were used. Multiple regression analysis, PCA, cluster variables analysis, and PCR were performed using statistical package Statistica 10.

The objective of this work was to introduce multivariate analysis as a statistical method for the estimation of the efficiency of fiber bed coalescence. The investigation encompassed the influences of a wide range of dispersed oil properties and fiber bed permeability on the critical velocity. The goal was to use the principal component analysis (PCA) and reduced dimensionality and number of variables to achieve an improved statistical evaluation of bed coalescence.

2. EXPERIMENTAL SECTION 2.1. Experimental Setup of the Coalescer and Operating Conditions. The experiments were performed on a horizontal laboratory-scale bed coalescer whose design was described in detail in a previous paper.25 The oil-in-water model emulsions, dilute and relatively unstable, were prepared using four different oils. The filter medium was waste polyurethane. The four dispersed oils, containing no additives, were as follows: Vojvodinian crude oil, two vacuum distillation fractions, and blended petroleum product with a high paraffinic content. In an experiment, the following parameters were kept constant: working temperature (20 °C), inlet oil concentration (500 mg/L), bed length (5 cm), and bed permeability. The experiments were carried out in the velocity range of 19−80 m/ h, and the selected velocity was kept constant for 1 h. Each oily water sample was tested on five bed permeabilities, in a broad range of bed permeability (0.18 × 10−9−5.389 × 10−9 m2). The continuous phase was tap water. In order to ensure the inlet mean droplet diameter of about 10 μm, each oily water sample was prepared in two tanks (of 80 L each), by continuous stirring with a stainless steel impeller. Hence, the influent droplet size did not vary significantly. The oil-in-water emulsion was continuously forced through the coalescer with the aid of a dosage pump. Composite samples were taken at the outlet of the coalescer after 45 min at 5-min intervals. The effluent oil concentration was measured by FTIR spectrometry. 2.2. Properties of Dispersed Oils. The main physical and chemical characteristics of the oil samples are given in Table S1 (see the Supporting Information). Viscosity and density were determined according to ISO 3104 and ISO 3675, respectively. The neutralization number was determined by titration (ISO 6619). Mean molecular weight was measured by standard test method ASTM d 2502-67 on the basis of viscosity measurements at 40 and 100 °C. Interfacial tension measurements were done according the du Noüy ring method. Surface tension was measured using a stalagmometer. Emulsivity was estimated using a centrifuge technique26 and the expression E=

VTW − VFW ·100 VTW

3. RESULTS AND DISCUSSION 3.1. Introduction. In the petroleum industry, numerous plants are connected onto the oily wastewater treating facilities, which influences the variation in chemical composition and physical characteristics of dispersed oil in the wastewater. The manner in which the wastewater is handled depends on the nature of dispersed oil. Hence, it is of great importance to adjust the coalescer operating variables and estimate the response to the changing influent oil properties. In this work, the bed coalescence efficiency was followed by monitoring the changes of the critical velocity. In order to evaluate the bed coalescence efficiency, numerous plots are needed. Hence, this approach is often ineffective and time-consuming. In this study, the effects of dispersed oil properties and bed permeability on the critical velocity were followed based on a novel statistical approach using PCA, cluster variables analysis, and PCR. 3.2. Multiple Regression Analysis. The results of the experiments performed in the broad range of dispersed oil properties and bed permeabilities are presented in Table S1 (see Supporting Information). The data in each row of the table are related to a different experiment. Linear regression analysis showed that the critical velocity is dominantly determined by the polyurethane bed permeability (K0), dispersed oil viscosity (μ), neutralization number (Nb), and interfacial tension (σ): Vk = 118.139·K 00.0368μ0.0824 Nb0.0313σ −0.1224

(2)

The calculated standard error of estimate was 19.34, multiple R-squared was 41.69%, and the adjusted R-squared was 7.19%. The low value of the adjusted R-squared indicates that for the set of the presented fiber bed coalescence experiments, linear regression analysis was not a responsive statistical method. Hence, the multiple regression analysis was applied, and the following equation was obtained: Vk = −2186 + 2.69K 0 + 0.116μ + 2.54ρ − 66.1Nb

(3)

The calculated residual standard error of estimate was 7.83, multiple R-squared was 58.9%, and the adjusted R-squared was 48.0%, indicating an improved fit of the model. It should be noted that the linear and multiple regressions did not provide a possibility to detect general relationships between the data and groups of similar variables. 3.3. Principal Component Analysis. The PCA enables a better understanding of the fundamental data structure and formation of a reduced number of uncorrelated variables. This usually produces avoidance of multicolinearity in the regression. As far as we know, there are no published results in which such a statistical method was used to analyze the bed coalescence operation. The PCA is a multivariate analysis that includes the following steps: selection of the matrix type to analyze raw data, specification of the number of principal components to be

(1)

Dielectric constant was measured using Baur DPA 75. 2.3. Properties of the Bed. The bed was formed of smooth polyurethane fibers obtained by cutting waste blocks used in the furniture industry. The bed permeability was calculated from the measured pressure drop across the bed for tap water, and the data complied with Darcy’s law. The fiber diameter determined by optical microscopy was 50 μm. It was assumed that the bed geometry can be best represented by the permeability without variation in the fiber bed length. 2.4. Critical Velocity (Vk). In our previous investigations,24,27,28 critical velocity was defined as the velocity when the effluent oil concentration reaches 15 mg/L. In each 16086

dx.doi.org/10.1021/ie3026967 | Ind. Eng. Chem. Res. 2012, 51, 16085−16091


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extracted from the raw experimental data, and graphical analysis. In this work, correlation matrix was used, as it is a usual choice when the variables are not measured in the same scale.29 The first step in the PCA was to calculate the eigenvalue and proportion (Table 1). The first principal component (PC1) had Table 1. Eigenvalues and Their Proportions of the Principal Components principal component

PC1

PC2

PC3

PC4

PC5

eigenvalue proportion cumulative

5.958 0.596 0.596

1.596 0.160 0.756

1.300 0.130 0.886

0.858 0.086 0.972

0.287 0.028 1.000

a variance of 5.958, the second (PC2) 1.596, and the third (PC3) 1.300. Further analysis was concerned with the dependence of the eigenvalues on the number of principal components (Figure 1). The obtained diagram was used to Figure 2. Correlation coefficients of the first three PCs with the properties of the dispersed oil and polyurethane bed permeability.

PC1 = −0.026K 0 − 0.288μ − 0.380ρ − 0.375Nb − 0.3M + 0.27σ + 0.387γ − 0.324E − 0.382ε − 0.264Vk (4)

PC 2 = 0.194K 0 + 0.481μ + 0.072ρ + 0.144Nb + 0.148M + 0.563σ + 0.243γ − 0.469E + 0.174ε + 0.237Vk (5)

PC 3 = −0.794K 0 + 0.158μ + 0.142ρ + 0.16Nb Figure 1. Scree plot of ten eigenvalues from the fiber bed coalescence experiments.

+ 0.005M + 0.154σ − 0.01γ − 0.104E + 0.158ε − 0.49Vk

(6)

The criterion for the analysis of the PCs can be the absolute value of the coefficient. The variable significance increases with the increase in the value of the coefficient. In this work, it appeared that the accepted limit was 48% of the absolute value of the highest coefficient (0.794) (Figure 3). This, empirically selected cutoff value of the coefficient enabled us to incorporate

judge the relative magnitude of the eigenvalues. Only the principal components (PCs) with the eigenvalue higher than 1 were kept. This rule is the most common stopping rule in PCA, also known as the Kaiser-Guttman criterion.30 Considering this criterion, it was possible to select three PCs (Figure 1). Table 1 also illustrates how the total variance is shared between the PCs. As can be seen, PC1 accounted for the most of the variance (59.6%). This was a much greater proportion than any of other PCs, whereas PC2 and PC3 accounted for 16.0% and 13.0%, respectively. The last row in the table represents the cumulative proportion. The PC1, PC2, and PC3 accounted for 88.6% of the total variance. This means that it would be possible to use these three PCs to analyze the fiber bed coalescence with the loss of information of 11.4%. Each PC was a linear combination of the original variables obtained with as much as possible variation in the original data. The coefficients were calculated so that the PCs, unlike the original variables, were not correlated with each other. Figure 2 illustrates the calculated coefficients of the PCs. The correlation coefficients are also known as component loadings. The coefficients listed can be used to establish the equations of the PCs. On the basis of these results, the following three equations were derived:

Figure 3. Loading plot representing the interdependence of the PC1 and PC2 coefficients and vectors of variables. 16087



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the pertinent variables into the model and thus reduce the dimensionality, i.e. the description of bed coalescence phenomena by a smaller number of variables. Hence, a coefficient greater than 0.38 in the absolute value is considered as significant. Concerning the accepted limit and eq 3 it can be noted that the dispersed oil density, surface tension, and dielectric constant make the major contribution to the PC1 and minor contribution to the PC2 and PC3. It should be also noted that the coefficients for density and dielectric constant exhibit a negative sign, while the coefficient for surface tension is positive. How can we explain the influence of the variables demonstrated by PC1? The cross-sectional oil phase distribution, droplet capture, and coalescence efficiency as well as the settling velocity are highly influenced by the dispersed oil density.3 The surface tension is the amount of energy required to increase the area of a droplet surface, and it significantly influences the coalescence efficiency and different mechanisms of fiber bed coalescence. The dielectric constant, as a measure of the dispersed oil polarity, determines the frequency and probability of droplet coalescence and interactions between the fiber surface and droplet. Thus, the PC1 may be interpreted as representing the overall influence of these three variables on the separation efficiency of dispersed oil. The PC2 correlates strongly with three original variables: it increases with increasing viscosity and interfacial tension and decreases with the increase in the emulsivity of dispersed oil (eq 4). The dispersed oil viscosity influences the flow of unstable emulsions through the fiber bed and the amount of saturated oil, while the interfacial tension influences the emulsion stability and the efficiency of coalescence of the adjacent droplets in the pore space.31 Emulsivity defines the ability of the dispersed oil to form emulsion. Furthermore, the PC3 correlates most strongly with the bed permeability and the critical velocity (eq 5). Based on the correlation coefficient of −0.794 it can be stated that PC3 is primarily a measure of the bed permeability. The values of PC1, PC2, and PC3 obtained for each bed coalescence experiment can be calculated by substituting the values of K0, μ, ρ, Nb, M, σ, γ, E, ε, and Vk into eqs 1−3. These values are often referred to as the scores of the PCs. Figure 4 illustrates the scores of the first two PCs. Each scatter in this plot represents the score of one fiber bed coalescence experiment. Because each experiment is represented and determined by its position in the coordinate system, the analysis of the fiber bed coalescence is greatly simplified. It can be noticed that the scores were distributed between the four distinctive groups. This could be expected because the experimental program included four dispersed oils of different physicochemical properties. It is shown that the investigated oily waters exhibited remarkably different scores, followed by good arrangement of the I−IV oil groups along this diagram. In this way it was attempted to investigate the occurrence of variations in the physical and chemical characteristics of the dispersed oil. The score distance from the plot origin should depict extreme values of the original data. The scores representing the combination of the extremely high or low values of variables are placed farther away from the plot origin. In this work, the score of the experiment 16 (Table S1, see the Supporting Information) was located the farthest from the plot origin. It indicates that the experiment 16 was distinguished by the extreme values, precisely, the highest values of μ, ε, ρ, K0, Nb,

Figure 4. Score plot of PC2 versus PC1 for 20 oily water samples.

M, and Vk. In view of this, a maximum of the critical velocity (78.74 m/h) was found in this experiment. On the other hand, the minimum of the critical velocity was 32.08 m/h (experiment 7). The experiment 7 corresponds to the lowest ρ, Nb, E, and ε and the highest γ, and its score was located further away from the plot origin. Also, the scores of the experiments 7, 8, and 9 were located close to each other in the score plot. It can be assumed that similar operating conditions corresponding to the experiments 7, 8, and 9 resulted in the scores with similar position. Moreover, the score plot showed the grouping of the experiments 13, 14, and 15, exhibiting an extremely high value of E and low values of σ and γ, and a large score distance from the plot origin. The 3D plot (Figure 5) depicts even better the position of the fiber bed coalescence experiments and the oil groups.

Figure 5. 3D score plot representing the interdependence of the PC1, PC2, and PC3 for 20 oily water samples. 16088



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The fiber bed coalescence loading plot of coefficients (Figure 3) displays 75.6% of the total variation of the analyzed data of the 20 experiments. Each variable is represented by a vector running from the origin. The bed coalescence efficiency was analyzed by referring to the vector angle and length. Based on the vector angle in relation to the Vk, two groups of variables were found: (1) a negative correlation (obtuse angle) with γ and E and (2) a positive correlation (acute angle) with all other variables (ρ, Nb, ε, M, μ, K0, and σ). Furthermore, it should be noted that a similar orientation of the γ and σ vectors was observed. It is clear that the length of the K0 vector is considerably shorter (Figure 3). It is related to both PC1 and PC2, and it implies that this variable tends to be independent of the variables with longer vectors.32,33 Therefore, this variable may be considered to belong to the third group. Based on the 2D plots of the PC coefficients against one another it is possible to test where the result for a certain observation lies. The main disadvantage of the analysis based on 2D plots is the difficulty in detecting the influence of the remaining PCs. Because of that, the results were subsequently analyzed using the 3D scatter plot representing the interdependence of the PC1, PC2, and PC3 coefficients (Figure 6). This 3D plot enabled more precise grouping of the

groups with similar variables. In this work, use was made of the correlation method for distance measure, and the average linkage method to define the distance between two clusters. The prediction on which variables can be combined was based on the dendrogram. The dendrogram resulting from the application of the cluster variables method is illustrated in Figure 7. The variables ρ, Nb, and ε formed a cluster within the

Figure 7. Dendrogram of the bed coalescence variables by cluster variables analysis.

highest similarity exhibited (99.5%). The similarity of the Nb and ε stems from the fact that these two variables are a measure of the polarity of dispersed oil. It can be assumed that the contribution of the oil density to the coalescence efficiency is similar to that of Nb and ε. The variables μ and M form the second cluster, while the third cluster grouped γ and σ. As can be seen from the interdependence of the first and the second cluster, a high similarity (75%) can be observed for the two groups. The variables Vk and E tend to form a cluster with the variables from the first (ρ, Nb, and ε) and second (μ and M) cluster. The dendrogram illustrates that the fiber bed coalescence variables can be classified with the results very similar to those of the PCA. 3.5. Principal Component Regression. The PCR of the data was carried out in order to obtain an equation for predicting Vk. From each group (cluster) previously identified by PCA and cluster variables method, a variable (K0, μ, σ, E, or ε) was selected corresponding to the highest values of the calculated coefficients. The aim of PCR was to reduce the number of variables by using the PCs previously selected by PCA (scores of PC1, PC2, and PC3) rather than the original variables. The regression equation of Vk on the scores of PC1, PC2, and PC3 was found to be

Figure 6. 3D loading plot representing the interdependence of the PC1, PC2, and PC3 coefficients and vectors of variables.

pertinent variables. The vectors running from the origin, as defined previously (Figure 3), indicated the second group of variables (ρ, Nb, ε, M, μ, K0, and σ), but the 3D analysis of PCs revealed that this group of vector variables had a remarkably different orientation. Hence, the K0, M, and μ vectors were separated from this group. Since the vector K0 is seen in Figure 6 as the longest vector, it demonstrates that the efficiency of the fiber bed coalescence is dominantly influenced by the bed permeability. The effect of permeability can be explained by the domination of the different coalescence mechanisms at the different values of the bed permeability. 3.4. Cluster Variables. In order to confirm the classification of the variables into groups, a cluster variables method was applied. The cluster variables approach is a hierarchical method that includes separation and formation of

Vk = 30.2 − 0.0835PC1 + 0.160PC 2 + 2.69PC 3

(7)

The calculated residual standard error of estimate was 7.62, multiple R-squared was 58.6%, and the adjusted R-squared was 50.9%. The regression assumptions were checked using the residual plot (Figure 8). The PCR showed that the regular residuals were normally distributed. With the exception of the experiments 5, 10, and 16, the remaining points appeared to lie approximately on a straight line. The dependence of the calculated Vk values on the experimental ones shows a relatively good correlation (Figure 9). If we compare the results of the PCR with the multiple regression analysis, it is obvious that the PCR analysis of the 16089



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ensure the desired critical velocity and effluent oil concentration.

■

ASSOCIATED CONTENT

S Supporting Information *

The results of bed coalescence experiments performed in the broad range of dispersed oil properties and bed permeabilities. Table S1: Physical and chemical characteristics of dispersed oil samples, bed permeability, and the critical velocity selected for the PCA of the bed coalescence. This material is available free of charge via the Internet at http://pubs.acs.org.

■

Figure 8. Normal probability plot of the residuals of the principal component regression.

AUTHOR INFORMATION

Corresponding Author

*Phone: +381214853747. Fax: +38121450413. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■ ■

ACKNOWLEDGMENTS The work was supported by the Ministry of Education and Science of the Republic of Serbia, Grant number 172022.

■

Figure 9. Relationship between the calculated and experimental values of the critical velocity.

fiber bed coalescence provided the possibility to reduce the dimensionality by lowering the number of highly correlated PCs, while the variability in the data was retained. Furthermore, we developed the following regression equation:

■

Vk = 30.2 + 2.69K 0 + 0.0736μ − 0.0506σ + 0.1568E + 0.000203ε

(8)

Equation 8 gives the possibility of predicting the values of the critical velocity for a given set of variables, and it may be useful for the estimation of the coalescence efficiency.

■

NOMENCLATURE K0 = bed permeability, m2 Vk = critical velocity for the effluent oil concentration of 15 mg/L, m/h Nb = neutralization number of dispersed oil, mg KOH/L M = mean molecular weight of dispersed oil, kg/kmol E = dispersed oil emulsivity, %vol VTW = total water volume, mL VFW = free water volume, mL GREEK LETTERS μ = dispersed oil viscosity, mPas ρ = dispersed oil density, kg/m3 γ = surface tension, mN/m σ = interfacial tension, mN/m ε = dielectric constant of dispersed oil ABBREVIATIONS PCA = principal component analysis PC = principal component PCR = principal component regression REFERENCES

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4. CONCLUSIONS A novel statistical approach based on the PCA, cluster variables method and PCR, allows one to develop the fiber bed coalescence model and detect the critical velocity with reduced dimensionality. The proposed method enabled more precise grouping of the pertinent variables with avoidance of multicolinearity in regression. An empirical equation was derived to describe the critical velocity as a function of the bed permeability, oil viscosity, interfacial tension, emulsivity, and dielectric constant. The PCA confirmed that the change of polyurethane bed permeability essentially influences the critical velocity. The proposed statistical approach greatly simplifies the analysis of fiber bed coalescence, and it may serve to determine the optimal coalescer design and the working parameters that 16090



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