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ATR-FTIR spectroscopy and chemometric techniques for determination of polymer solution viscosity in the presence of SiO2 nanoparticle and salinity
Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 220 (2019) 117049
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ATR-FTIR spectroscopy and chemometric techniques for determination of polymer solution viscosity in the presence of SiO2 nanoparticle and salinity Mahsa Mohammadi, Mohammadreza Khanmohammadi Khorrami ⁎, Hossein Ghasemzadeh Department of Chemistry, Faculty of Science, Imam Khomeini International University, Qazvin, Iran
a r t i c l e
i n f o
Article history: Received 22 December 2018 Received in revised form 17 April 2019 Accepted 17 April 2019 Available online 7 May 2019 Keywords: Chemometrics Viscosity Polyacrylamide ATR-FTIR PLS-R SVM-R
a b s t r a c t An analytical method was proposed for quantitative determination of rheological properties of polyacrylamide (PAM) solution in the presence of SiO2 nanoparticle and NaCl. The viscosity of PAM-SiO2 nanohybrid solution was predicted using attenuated total reflection Fourier-transform infrared (ATR-FTIR) spectroscopy in the wavenumber range of 800–3000 cm−1 and chemometrics methods. Support vector machine regression (SVM-R) as a non-linear multivariate calibration procedure and partial least squares regression (PLS-R) as a linear procedure were applied for calibration. Preprocessing methods such as baseline correction and standard normal variate (SNV) were also utilized. Root mean square error of prediction (RMSEP) in SNV-SVM and SNV-PLS methods were 3.231 and 6.302, respectively. Considering the complexity of the samples, the SVM-R model was found to be reliable. The proposed method is rapid and simple without any sample preparation step for measurement of the viscosity of polymer solutions in chemical enhanced oil recovery (CEOR). © 2019 Elsevier B.V. All rights reserved.
1. Introduction Enhanced oil recovery (EOR) techniques are applied for increasing the amount of crude oil from an oil field. Polymer flooding is one of the most commonly applied methods in the chemical enhanced oil recovery (CEOR) technique [1–5]. The potential of polymers to increase the sweep efficiency of water phase in oil reservoirs has led to the use of polymer solutions in the CEOR techniques. The use of polymer solutions decreases the motility of water and therefore increases the oil recovery [6–10]. Polymers such as polyacrylamide (PAM) and partially hydrolyzed polyacrylamides (HPAM) have been widely used in different EOR applications. However, this type of polymers are sensitive to existence of harsh conditions (e.g., high temperature and inorganic salt), which indicates that the reaction conditions has an important effect on the polymer solutions function in the reservoirs. In sever condition degradation of the polymer can also take place. Additional salt concentration even causes precipitation and thus makes it impossible to control the mobility of the polymer solution [11–14]. At high temperature, the interruption of precipitation is believe to occur [15,16]. To overcome the problems, formation of organic/inorganic ⁎ Corresponding author E-mail address: [email protected] (M.K. Khorrami).
https://doi.org/10.1016/j.saa.2019.04.041 1386-1425/© 2019 Elsevier B.V. All rights reserved.
nanocomposites has been proposed. So, many studies have focused on the use of nanocomposite solutions to improve the performance of polymer flood in EOR. When a nanoparticle is dispersed into a polymer solution, the rheological performance and thermal stability of the solution is significantly affected. Nanofluids production using SiO2 nanoparticles is one of the most general methods for increasing the viscosity of the polymer solutions. If the viscosity of the injected fluid is higher than the viscosity of the oil in the reservoir, desirable mobility control will be obtained and the efficiency of the oil production will increase. Dispersions of nanoparticles in polyacrylamide solution has been studied by many researchers [17–25]. Maghzi and co-workers reported that the viscosity of nanofluid solutions in the presence of salt is affected by the interaction of SiO2 nanoparticles and polyacrylamide [26]. The experiments revealed that PAM solution increases the properties of the nanofluids, including stability, and viscosity [27]. Although viscosity is often measured by rheometer or other devices, these methods are time consuming and expensive. This study focus on the application of analytical technology based on infrared spectroscopy combined with chemometric methods that have been attracted the attention of researchers in many applications. According to our review, there is no report on the application of FT-IR and chemometric to measure the viscosity of polymeric solutions in CEOR. A rapid and low cost method is developed for determination of
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viscosity of polymer solution in the presence of salt and SiO2 nanoparticle based on SVM-R as a non-linear model [28–30] and PLS-R as a linear model [31,32].
MAE ¼
2. Chemometrics methods
Principal component analysis (PCA) is one of several multivariate methods that creates new reduced dimensions of the data and provides precise mathematical estimations of changes along the object and variable vectors without a priori knowledge. In PCA, the data matrix (X) is decomposed into two matrices: scores and loadings. The scores matrix represents the samples in the PC space, while the loadings matrix represents the new axes of the data set with reduced dimensions. The main use of PCA in infrared (IR) spectroscopy is to differentiate spectra along with outlier detection [33,34]. For finding best latent variable selection, cross-validation has been applied. The first two PCs were selected in this study and captured variance was 99%. The relationship between samples can be explained in the scores plot. Some samples very different from the rest, that can be identified as outlier data. Outliers can be determined with the application of Hotelling's T2 statistic. The Hotelling's T2 statistic measures the variation within the PCA model. In this study, it was used to identify the outlier data in two dimension with the 95% confidence. 2.2. Support vector machine regression SVM-R is a powerful method for regression developed by Cortes and Vapnik [35]. Mapping of data is done by using Kernel function which could be a linear or non-linear function or radial basis function (RBF). Each Kernel function consists of a set of parameters. Optimization of the parameters is important in SVM-R algorithm [36,37]. This problem can be write as a convex optimization: (Eqs. (1), (2))
8 < yi −w:ϕðxi Þ−b≤ε þ ξi Subject to : w:ϕðxi Þ þ b−yi ≤ε þ ξi : ξi ; ξi ≥0
ð1Þ
m X ðαᵢ−αᵢÞ ϕ ðxᵢ; x Þ þ b
ð2Þ
׀yᵢ−yᵢ =Nc
ð5Þ
where, y ᵢ^ is the predicted value of the ith observation in the training set, yᵢ is the measured value of the ith observation in the training set, and Nc is the number of observations. The simplex method with crossvalidation was used to optimize these two modeling parameters. The optimal values of the modeling parameters were selected according to the minimum MAE parameter [38]. 2.3. Partial least squares regression PLS-R is currently the most widely used method for multivariate calibration. PLS estimates regression coefficients in a linear model with a large number of variables that are highly correlated. To construct the calibration model both spectra matrix (X) and the concentration matrix (Y) are decomposed into a sum of significant variables (Eqs. (7), (8)): X ¼ T PT þ EX
ð6Þ
Y ¼ T CT þ EY
ð7Þ
where, T is analogous to scores matrices, whereas P and C are matrices analogous to loadings of the principal component analysis. The linear relationship between the two blocks can be performed using correlating scores for each component with a linear model. The regression vector B is determined by the following (Eq. (9)). −1 B ¼ W PT W CT
ð8Þ
where, W is the matrix of weights in PLS model. The regression vector B considers the contribution of each variable to the PLS model [39–41].
3.1. Materials Hydrophilic SiO2 nanoparticles (purity 99.5%, 15–20 nm size) were supplied from Merck Co. (Germany). PAM with 98% purity in powder form with average molecular weight of 5 × 106 and viscosity of 280 cp was prepared from Sigma-Aldrich (Germany). Deionized (DI) water was used to prepare the fluid samples. Sodium chloride (purity 98%) was used for preparation of brine solution from Merck Co. (Germany). 3.2. Preparation of nanofluid samples
ð3Þ
i¼1
where, αᵢ and αᵢ* indicate the Lagrange multipliers satisfying the subject to 0 ≤ αᵢ, αᵢ ∗ ≤ C, the constant C should be optimized by the analyst and the kernel function ∅(xᵢ, x), maps the input data to feature space [37]. The most commonly used kernel function is the Radial Basis Function (RBF). This function is defined by Eq. (4). 2 k xᵢ; x j ¼ exp −γ xᵢ−x j
! ׀
3. Experimental
where, C is the regularization constant and ξᵢ ∗, ξᵢ are slack variables. The value of epsilon (ε) specifies the number of support vectors. The constrained optimization function of Eq. (2) can be transformed into dual space by application of the Lagrange multiplier method. The solution of this problem lead to the following regression model: f ðxÞ ¼
Nc X I¼1
2.1. Principal component analysis (PCA)
1 m Min : kwk þ C ∑i¼1 ðξi þ ξi Þ 2
function was the mean absolute error (MAE) which is calculated by Eq. (5).
ð4Þ
where, γ parameters should be optimized before the application of the SVM algorithm. For the RBF kernel, γ is a tuning parameter which determines the width of the kernel function, that can be optimized by the analyst. Optimization of modeling parameters in the SVM algorithm is accomplish by minimization of a cost function. The selected cost
SiO2 as a nanoparticle and polyacrylamide (PAM) as a dispersant agent were used as the starting materials for preparation of the nanofluid samples. In the first step, various amount of SiO2 nanoparticles (0.5, 1.0, 1.5, 2.0 wt%) were added to DI water, and the mixture was sonicated in a sonication bath (Ultrasonic Corporation, USA). Then, PAM aqueous solution, 0.1 wt% which is a well-known concentration in CEOR [42], was added and stirred at 600 rpm for 24 h. In the next step NaCl solution (0.5–5 wt%) was added and obtained solution was stirred for 30 min before rheological tests. A dynamic rheometer (MCR300, SN599139) was used to investigate the effect of the SiO2 nanoparticle and salinity on the rheological properties of the polymer solutions. The tests on polymer solutions were performed at 25 °C and shear rates of 200–1000 s−1. The viscosity is measured by injection of fluid within the annulus of a cylinder inside another. One of the cylinders is rotated at a set speed. This determines the shear rate inside the annulus. The liquid tends to drag the other
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optimum factors was found to be two factor (PC1–PC2) for calibration set. The root mean square error of calibration (RMSEC) was also calculated using the appropriate expressions. The root mean square error of cross prediction (RMSEP) and the squared correlation coefficient of regression lines (R2) for calibration model were also calculated. The spectra were processed using the unscrambler software program (version 10.4, Camo ASA Norway) to perform the calibration and validation. The models were compared on the basis of the results of the statistical parameters: squared correlation coefficient (R2), root mean square error of calibration (RMSEC), and root mean square error of prediction (RMSEP). RMSE was calculated according to (Eq. (10)). sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n ^i Þ2 ∑i¼1 ðyi −y RMSE ¼ n
ð9Þ
where, ŷi is predicted value of the ith observation, yi is measured value of the ith observation, and n is the number of samples in train or test. 4. Results and discussion Fig. 1. ATR-FTIR spectra of the polyacrylamide solutions in the range of 800–3000 cm−1.
round cylinder, and the force that it exerts on the cylinders is measured, which can be converted to a shear stress. 3.3. ATR-FTIR spectrometry of the nanofluid About 1 ml of each polymer solution both in the presence and in the absence of SiO2 NP was placed on a zinc-selenide ATR cell. The ATR-FTIR spectra of the samples in the spectral region 800–3000 cm−1, were obtained by accumulating 16 scans at 4 cm−1 resolution using DI water as background spectrum, Fig. 1. The selected wavenumber range was based on two absorption bands in the MIR region. The absorption bands at 920 and 1098 cm−1 are related to the Si-O-H bending and SiO-Si stretching vibrations, respectively. The absorption bands in the range of 1500–1700 cm−1 are related to the C-H, C=O and C-O vibrations [22]. 3.4. Data pretreatment and outlier detection PCA is an accepted method that reduces spectral data into much fewer dimensions using PCs and scores. Before performing PCA, all of the FTIR spectra were baseline corrected and smoothed by omnic software. The standard normal variate (SNV) approach was used in order to remove the multiplicative effect of scattering and elimination baseline shift in the spectra.
4.1. FT-IR spectroscopy FTIR spectroscopy was used to investigate the interaction between SiO2 nanoparticle and PAM. As can be seen from the Fig. 2, the FT-IR spectra of pure SiO2 sample shows two main bands at 800 and 1097 cm−1 correspond to the Si–O–Si bending vibrations and Si–O–Si asymmetric stretching, respectively. The spectrum of PAM/SiO2 nanohybrid sample demonstrates the shifted signals at 850 and 1105 cm−1 while the pure PAM sample lacks these signals. The band at 850 cm−1 refer to a Si–O–H bending vibration indicating the presence of the hydroxyl functional group on silica surfaces as well as the interaction between SiO2 and PAM functioned groups. Hydrogen bond formation between hydroxyl functional groups of SiO2 nanoparticle and the oxygen or nitrogen of PAM enhanced the viscosity of the nanofluids. 4.2. Viscosity measurements 4.2.1. Effect of the SiO2 NPs on the viscosity of PAM/SiO2 nanofluid It is believed that the interaction between SiO2 nanoparticles and polyacrylamide affect the viscosity of the nanofluids. The viscosity of various PAM solutions containing 0.5, 1.0, 1.5, and 2.0 wt% SiO2 nanoparticles were determined. As can be seen from the Fig. 3, the viscosities of the solutions increases with increasing the NP concentration. A rapid
3.5. Multivariate model Multivariate calibrations are useful in spectral data analysis. With the aim of improving the viscosity prediction of nanofluids, a multivariate model (PLS-R and SVM-R using the kernel function RBF) was applied for absorption spectra. However, different spectra were evaluated by performing PLS calibration method. To make calibration models, 59 samples were split into calibration set and prediction set by Kennard Stone algorithm [43]. A set of 47 aqueous standard samples were applied as the calibration samples, whereas 12 other aqueous standard samples were proposed as independent test set. A significant feature of PLS is that it takes into account errors estimates in both the concentration and the spectra matrix. This calibration models was investigated by varying the number of PLS factors in order to optimize the models. To select the optimum number of factors in PLS algorithm, full cross validation method was used. One reason for selection of the optimum number of factors would be the number which yielded the minimum prediction error sum of squares (PRESS). The number of
Fig. 2. FT-IR spectra for PAM, PAM-SiO2 nanohybrid, and SiO2 NP.
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Fig. 3. Viscosities of 0.1 wt% PAM with different amounts of SiO2 NP at 25 °C.
increase in the viscosity was observed beyond a certain nanoparticle concentration that defined as the critical nanoparticle concentration (CNC). For a solution containing 0.1 wt% PAM solution, the CNC values were found to be around 1.5 wt% at 25 °C.
4.2.2. Effect of the NaCl salt on the viscosity of PAM/SiO2 nanofluids The influence of the salt concentration on the effective viscosity of PAM, and PAM/SiO2 nanofluids were studied at 25 °C. The viscosity of PAM is affected in the presence of salts. As can be seen from the Fig. 4, the viscosity changes with different concentration of NaCl are nonlinear. A non-monotonic trend was observed for the solutions. The viscosity significantly increases from 0.5 to 1.0 wt%, whereas addition of NaCl more than 1.0 wt% has no significant effect on the viscosity. It is believed that the initial increase in viscosity at low salt concentration is associated with a rise in ion-dipole interactions. With increasing salt concentration, the polarity of the solvent increases resulting in increased viscosity of the nanofluids.
Fig. 5. Score plot of PC1 and PC2 (a) and Hotelling's T2 statistic (b) of the nanofluids solutions.
4.3. Principal components analysis (PCA) Principal components analysis (PCA) is a powerful tool for outlier detection. Because outliers can mask the structure of the other data, the detection and remove of outliers is important. The principal components plot allows us to find outliers in a data set. When outliers are found in a PC plot, one should first identify and eliminate the outlier and then perform the PCA again. Fig. 5a, represents the scores plot of PC1 against PC2 after performing PCA on a data matrix. In PCA plot, two principal components for each sample were selected and 99% of the total variance was explained by these two principal components (PC1, PC2). The relationship between samples can be described in the scores plot. Samples far from the others in the PC1–PC2 plane are considered as outliers. Outliers can also be determined with the application of Hotelling's T2 statistic represents in the Fig. 5b. In this case, all samples in PCA and Hotelling's T2 statistic plots were located within the range indicated that all of them could be used in regression analysis, but one sample (number 20) was located outside the range which was regarded as outlier and eliminated from dataset of analysis. 4.4. Calibration and validation samples Fig. 4. Influence of the NaCl salt concentration on the viscosity of PAM/SiO2 nanofluids at 25 °C and salt concentration range of (0.5–5.0 wt%).
As mentioned, all samples were split into calibration and prediction set by Kennard Stone algorithm. A set of 47 samples were taken as
M. Mohammadi et al. / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 220 (2019) 117049
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a
Viscosity prediction (mpa.s)
70
Viscosity Calibration
Viscosity Prediction
60 50
R2 Cal.
0.969
Slope
0.929
Offset
1.403
RMSEC
5.111
RMSEP
6.302
40 30 20 10 0
0
10
20
30
40
50
60
70
Viscosity reference (mpa.s)
b
70
Viscosity Calibration
Viscosity Prediction
Viscosity prediction (mpa.s)
60 50
R2Cal. Slope
0.984
Offset
3.323
1.104
RMSEC
2.71
RMSEP
3.231
40 30 20 10 0
0
10
20
30
40
50
60
70
Viscosity reference (mpa.s)
Fig. 6. Scatter plot of the predicted viscosity vs reference viscosity using (a) PLS-R, and (b) SVM-R model for calibration and prediction samples (All samples were divided into training and testing subsets by Kennard Stone as a random sample selection algorithm).
calibration and 12 samples were proposed for prediction of viscosity. In order to evaluate the proposed calibration method for viscosity measurement, the viscosity of 60 new samples were analyzed in the range of 6–70 m·pas by FTIR-spectroscopy and chemometrics. The viscosity for calibration samples was carried out in the range of 6.07 to 66.6. As well the average viscosity and standard deviation for calibration samples are 23.83 and 5.3, respectively. The range of viscosity of prediction samples was 6.07 to 21.50. The average viscosity and standard deviation for prediction samples are 11.85 and 4.15, respectively. Fig. 6(a) and (b), show predicted viscosity versus reference viscosity of the samples for calibration and prediction sets. With the aim of improving the analysis for solution rheology, multivariate methods
including PLS and SVM were applied using absorption spectra. After constructing the calibration models by PLS and SVM algorithms, the viscosity of the prediction set samples were predicted by the models. Also R2, RMSEC, and RMSEP statistical parameters for calibration and prediction samples for PLS and SVM models were calculated and presented in Fig. 6(a) and (b) respectively. SVM algorithm showed better modeling of data and prediction ability by higher R2 and lower RMSEC and RMSEP. 5. Conclusion In this study, the viscosity of PAM solution in the presence of SiO2 nanoparticle and NaCl salt was successfully predicted using FT-IR in
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combination with chemometric techniques. This method is expected to provide a rapid quantitative analysis of physicochemical properties of polymer solutions in CEOR due to its simplicity in the sample preparation, non-destructive nature, and sensitivity. The SVM-R and PLS-R models were successfully applied to mid-IR spectra of the polymer solution. Two most important spectral band (850 and 1105 cm−1) were selected for the prediction of viscosity. This study indicated that the SVMR as a non-linear model was more accurate than PLS-R as a linear model for prediction of viscosity in polymer solutions. The RMSEP values for PLS-R and SVM-R were 6.302 and 3.231 respectively. The results of the proposed method are consistent with the results of the reference method in measuring the viscosity of the solution. 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ATR-FTIR spectroscopy and chemometric techniques for determination of polymer solution viscosity in the presence of SiO2 nanoparticle and salinity Mahsa Mohammadi, Mohammadreza Khanmohammadi Khorrami ⁎, Hossein Ghasemzadeh Department of Chemistry, Faculty of Science, Imam Khomeini International University, Qazvin, Iran
a r t i c l e
i n f o
Article history: Received 22 December 2018 Received in revised form 17 April 2019 Accepted 17 April 2019 Available online 7 May 2019 Keywords: Chemometrics Viscosity Polyacrylamide ATR-FTIR PLS-R SVM-R
a b s t r a c t An analytical method was proposed for quantitative determination of rheological properties of polyacrylamide (PAM) solution in the presence of SiO2 nanoparticle and NaCl. The viscosity of PAM-SiO2 nanohybrid solution was predicted using attenuated total reflection Fourier-transform infrared (ATR-FTIR) spectroscopy in the wavenumber range of 800–3000 cm−1 and chemometrics methods. Support vector machine regression (SVM-R) as a non-linear multivariate calibration procedure and partial least squares regression (PLS-R) as a linear procedure were applied for calibration. Preprocessing methods such as baseline correction and standard normal variate (SNV) were also utilized. Root mean square error of prediction (RMSEP) in SNV-SVM and SNV-PLS methods were 3.231 and 6.302, respectively. Considering the complexity of the samples, the SVM-R model was found to be reliable. The proposed method is rapid and simple without any sample preparation step for measurement of the viscosity of polymer solutions in chemical enhanced oil recovery (CEOR). © 2019 Elsevier B.V. All rights reserved.
1. Introduction Enhanced oil recovery (EOR) techniques are applied for increasing the amount of crude oil from an oil field. Polymer flooding is one of the most commonly applied methods in the chemical enhanced oil recovery (CEOR) technique [1–5]. The potential of polymers to increase the sweep efficiency of water phase in oil reservoirs has led to the use of polymer solutions in the CEOR techniques. The use of polymer solutions decreases the motility of water and therefore increases the oil recovery [6–10]. Polymers such as polyacrylamide (PAM) and partially hydrolyzed polyacrylamides (HPAM) have been widely used in different EOR applications. However, this type of polymers are sensitive to existence of harsh conditions (e.g., high temperature and inorganic salt), which indicates that the reaction conditions has an important effect on the polymer solutions function in the reservoirs. In sever condition degradation of the polymer can also take place. Additional salt concentration even causes precipitation and thus makes it impossible to control the mobility of the polymer solution [11–14]. At high temperature, the interruption of precipitation is believe to occur [15,16]. To overcome the problems, formation of organic/inorganic ⁎ Corresponding author E-mail address: [email protected] (M.K. Khorrami).
https://doi.org/10.1016/j.saa.2019.04.041 1386-1425/© 2019 Elsevier B.V. All rights reserved.
nanocomposites has been proposed. So, many studies have focused on the use of nanocomposite solutions to improve the performance of polymer flood in EOR. When a nanoparticle is dispersed into a polymer solution, the rheological performance and thermal stability of the solution is significantly affected. Nanofluids production using SiO2 nanoparticles is one of the most general methods for increasing the viscosity of the polymer solutions. If the viscosity of the injected fluid is higher than the viscosity of the oil in the reservoir, desirable mobility control will be obtained and the efficiency of the oil production will increase. Dispersions of nanoparticles in polyacrylamide solution has been studied by many researchers [17–25]. Maghzi and co-workers reported that the viscosity of nanofluid solutions in the presence of salt is affected by the interaction of SiO2 nanoparticles and polyacrylamide [26]. The experiments revealed that PAM solution increases the properties of the nanofluids, including stability, and viscosity [27]. Although viscosity is often measured by rheometer or other devices, these methods are time consuming and expensive. This study focus on the application of analytical technology based on infrared spectroscopy combined with chemometric methods that have been attracted the attention of researchers in many applications. According to our review, there is no report on the application of FT-IR and chemometric to measure the viscosity of polymeric solutions in CEOR. A rapid and low cost method is developed for determination of
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viscosity of polymer solution in the presence of salt and SiO2 nanoparticle based on SVM-R as a non-linear model [28–30] and PLS-R as a linear model [31,32].
MAE ¼
2. Chemometrics methods
Principal component analysis (PCA) is one of several multivariate methods that creates new reduced dimensions of the data and provides precise mathematical estimations of changes along the object and variable vectors without a priori knowledge. In PCA, the data matrix (X) is decomposed into two matrices: scores and loadings. The scores matrix represents the samples in the PC space, while the loadings matrix represents the new axes of the data set with reduced dimensions. The main use of PCA in infrared (IR) spectroscopy is to differentiate spectra along with outlier detection [33,34]. For finding best latent variable selection, cross-validation has been applied. The first two PCs were selected in this study and captured variance was 99%. The relationship between samples can be explained in the scores plot. Some samples very different from the rest, that can be identified as outlier data. Outliers can be determined with the application of Hotelling's T2 statistic. The Hotelling's T2 statistic measures the variation within the PCA model. In this study, it was used to identify the outlier data in two dimension with the 95% confidence. 2.2. Support vector machine regression SVM-R is a powerful method for regression developed by Cortes and Vapnik [35]. Mapping of data is done by using Kernel function which could be a linear or non-linear function or radial basis function (RBF). Each Kernel function consists of a set of parameters. Optimization of the parameters is important in SVM-R algorithm [36,37]. This problem can be write as a convex optimization: (Eqs. (1), (2))
8 < yi −w:ϕðxi Þ−b≤ε þ ξi Subject to : w:ϕðxi Þ þ b−yi ≤ε þ ξi : ξi ; ξi ≥0
ð1Þ
m X ðαᵢ−αᵢÞ ϕ ðxᵢ; x Þ þ b
ð2Þ
׀yᵢ−yᵢ =Nc
ð5Þ
where, y ᵢ^ is the predicted value of the ith observation in the training set, yᵢ is the measured value of the ith observation in the training set, and Nc is the number of observations. The simplex method with crossvalidation was used to optimize these two modeling parameters. The optimal values of the modeling parameters were selected according to the minimum MAE parameter [38]. 2.3. Partial least squares regression PLS-R is currently the most widely used method for multivariate calibration. PLS estimates regression coefficients in a linear model with a large number of variables that are highly correlated. To construct the calibration model both spectra matrix (X) and the concentration matrix (Y) are decomposed into a sum of significant variables (Eqs. (7), (8)): X ¼ T PT þ EX
ð6Þ
Y ¼ T CT þ EY
ð7Þ
where, T is analogous to scores matrices, whereas P and C are matrices analogous to loadings of the principal component analysis. The linear relationship between the two blocks can be performed using correlating scores for each component with a linear model. The regression vector B is determined by the following (Eq. (9)). −1 B ¼ W PT W CT
ð8Þ
where, W is the matrix of weights in PLS model. The regression vector B considers the contribution of each variable to the PLS model [39–41].
3.1. Materials Hydrophilic SiO2 nanoparticles (purity 99.5%, 15–20 nm size) were supplied from Merck Co. (Germany). PAM with 98% purity in powder form with average molecular weight of 5 × 106 and viscosity of 280 cp was prepared from Sigma-Aldrich (Germany). Deionized (DI) water was used to prepare the fluid samples. Sodium chloride (purity 98%) was used for preparation of brine solution from Merck Co. (Germany). 3.2. Preparation of nanofluid samples
ð3Þ
i¼1
where, αᵢ and αᵢ* indicate the Lagrange multipliers satisfying the subject to 0 ≤ αᵢ, αᵢ ∗ ≤ C, the constant C should be optimized by the analyst and the kernel function ∅(xᵢ, x), maps the input data to feature space [37]. The most commonly used kernel function is the Radial Basis Function (RBF). This function is defined by Eq. (4). 2 k xᵢ; x j ¼ exp −γ xᵢ−x j
! ׀
3. Experimental
where, C is the regularization constant and ξᵢ ∗, ξᵢ are slack variables. The value of epsilon (ε) specifies the number of support vectors. The constrained optimization function of Eq. (2) can be transformed into dual space by application of the Lagrange multiplier method. The solution of this problem lead to the following regression model: f ðxÞ ¼
Nc X I¼1
2.1. Principal component analysis (PCA)
1 m Min : kwk þ C ∑i¼1 ðξi þ ξi Þ 2
function was the mean absolute error (MAE) which is calculated by Eq. (5).
ð4Þ
where, γ parameters should be optimized before the application of the SVM algorithm. For the RBF kernel, γ is a tuning parameter which determines the width of the kernel function, that can be optimized by the analyst. Optimization of modeling parameters in the SVM algorithm is accomplish by minimization of a cost function. The selected cost
SiO2 as a nanoparticle and polyacrylamide (PAM) as a dispersant agent were used as the starting materials for preparation of the nanofluid samples. In the first step, various amount of SiO2 nanoparticles (0.5, 1.0, 1.5, 2.0 wt%) were added to DI water, and the mixture was sonicated in a sonication bath (Ultrasonic Corporation, USA). Then, PAM aqueous solution, 0.1 wt% which is a well-known concentration in CEOR [42], was added and stirred at 600 rpm for 24 h. In the next step NaCl solution (0.5–5 wt%) was added and obtained solution was stirred for 30 min before rheological tests. A dynamic rheometer (MCR300, SN599139) was used to investigate the effect of the SiO2 nanoparticle and salinity on the rheological properties of the polymer solutions. The tests on polymer solutions were performed at 25 °C and shear rates of 200–1000 s−1. The viscosity is measured by injection of fluid within the annulus of a cylinder inside another. One of the cylinders is rotated at a set speed. This determines the shear rate inside the annulus. The liquid tends to drag the other
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optimum factors was found to be two factor (PC1–PC2) for calibration set. The root mean square error of calibration (RMSEC) was also calculated using the appropriate expressions. The root mean square error of cross prediction (RMSEP) and the squared correlation coefficient of regression lines (R2) for calibration model were also calculated. The spectra were processed using the unscrambler software program (version 10.4, Camo ASA Norway) to perform the calibration and validation. The models were compared on the basis of the results of the statistical parameters: squared correlation coefficient (R2), root mean square error of calibration (RMSEC), and root mean square error of prediction (RMSEP). RMSE was calculated according to (Eq. (10)). sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n ^i Þ2 ∑i¼1 ðyi −y RMSE ¼ n
ð9Þ
where, ŷi is predicted value of the ith observation, yi is measured value of the ith observation, and n is the number of samples in train or test. 4. Results and discussion Fig. 1. ATR-FTIR spectra of the polyacrylamide solutions in the range of 800–3000 cm−1.
round cylinder, and the force that it exerts on the cylinders is measured, which can be converted to a shear stress. 3.3. ATR-FTIR spectrometry of the nanofluid About 1 ml of each polymer solution both in the presence and in the absence of SiO2 NP was placed on a zinc-selenide ATR cell. The ATR-FTIR spectra of the samples in the spectral region 800–3000 cm−1, were obtained by accumulating 16 scans at 4 cm−1 resolution using DI water as background spectrum, Fig. 1. The selected wavenumber range was based on two absorption bands in the MIR region. The absorption bands at 920 and 1098 cm−1 are related to the Si-O-H bending and SiO-Si stretching vibrations, respectively. The absorption bands in the range of 1500–1700 cm−1 are related to the C-H, C=O and C-O vibrations [22]. 3.4. Data pretreatment and outlier detection PCA is an accepted method that reduces spectral data into much fewer dimensions using PCs and scores. Before performing PCA, all of the FTIR spectra were baseline corrected and smoothed by omnic software. The standard normal variate (SNV) approach was used in order to remove the multiplicative effect of scattering and elimination baseline shift in the spectra.
4.1. FT-IR spectroscopy FTIR spectroscopy was used to investigate the interaction between SiO2 nanoparticle and PAM. As can be seen from the Fig. 2, the FT-IR spectra of pure SiO2 sample shows two main bands at 800 and 1097 cm−1 correspond to the Si–O–Si bending vibrations and Si–O–Si asymmetric stretching, respectively. The spectrum of PAM/SiO2 nanohybrid sample demonstrates the shifted signals at 850 and 1105 cm−1 while the pure PAM sample lacks these signals. The band at 850 cm−1 refer to a Si–O–H bending vibration indicating the presence of the hydroxyl functional group on silica surfaces as well as the interaction between SiO2 and PAM functioned groups. Hydrogen bond formation between hydroxyl functional groups of SiO2 nanoparticle and the oxygen or nitrogen of PAM enhanced the viscosity of the nanofluids. 4.2. Viscosity measurements 4.2.1. Effect of the SiO2 NPs on the viscosity of PAM/SiO2 nanofluid It is believed that the interaction between SiO2 nanoparticles and polyacrylamide affect the viscosity of the nanofluids. The viscosity of various PAM solutions containing 0.5, 1.0, 1.5, and 2.0 wt% SiO2 nanoparticles were determined. As can be seen from the Fig. 3, the viscosities of the solutions increases with increasing the NP concentration. A rapid
3.5. Multivariate model Multivariate calibrations are useful in spectral data analysis. With the aim of improving the viscosity prediction of nanofluids, a multivariate model (PLS-R and SVM-R using the kernel function RBF) was applied for absorption spectra. However, different spectra were evaluated by performing PLS calibration method. To make calibration models, 59 samples were split into calibration set and prediction set by Kennard Stone algorithm [43]. A set of 47 aqueous standard samples were applied as the calibration samples, whereas 12 other aqueous standard samples were proposed as independent test set. A significant feature of PLS is that it takes into account errors estimates in both the concentration and the spectra matrix. This calibration models was investigated by varying the number of PLS factors in order to optimize the models. To select the optimum number of factors in PLS algorithm, full cross validation method was used. One reason for selection of the optimum number of factors would be the number which yielded the minimum prediction error sum of squares (PRESS). The number of
Fig. 2. FT-IR spectra for PAM, PAM-SiO2 nanohybrid, and SiO2 NP.
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Fig. 3. Viscosities of 0.1 wt% PAM with different amounts of SiO2 NP at 25 °C.
increase in the viscosity was observed beyond a certain nanoparticle concentration that defined as the critical nanoparticle concentration (CNC). For a solution containing 0.1 wt% PAM solution, the CNC values were found to be around 1.5 wt% at 25 °C.
4.2.2. Effect of the NaCl salt on the viscosity of PAM/SiO2 nanofluids The influence of the salt concentration on the effective viscosity of PAM, and PAM/SiO2 nanofluids were studied at 25 °C. The viscosity of PAM is affected in the presence of salts. As can be seen from the Fig. 4, the viscosity changes with different concentration of NaCl are nonlinear. A non-monotonic trend was observed for the solutions. The viscosity significantly increases from 0.5 to 1.0 wt%, whereas addition of NaCl more than 1.0 wt% has no significant effect on the viscosity. It is believed that the initial increase in viscosity at low salt concentration is associated with a rise in ion-dipole interactions. With increasing salt concentration, the polarity of the solvent increases resulting in increased viscosity of the nanofluids.
Fig. 5. Score plot of PC1 and PC2 (a) and Hotelling's T2 statistic (b) of the nanofluids solutions.
4.3. Principal components analysis (PCA) Principal components analysis (PCA) is a powerful tool for outlier detection. Because outliers can mask the structure of the other data, the detection and remove of outliers is important. The principal components plot allows us to find outliers in a data set. When outliers are found in a PC plot, one should first identify and eliminate the outlier and then perform the PCA again. Fig. 5a, represents the scores plot of PC1 against PC2 after performing PCA on a data matrix. In PCA plot, two principal components for each sample were selected and 99% of the total variance was explained by these two principal components (PC1, PC2). The relationship between samples can be described in the scores plot. Samples far from the others in the PC1–PC2 plane are considered as outliers. Outliers can also be determined with the application of Hotelling's T2 statistic represents in the Fig. 5b. In this case, all samples in PCA and Hotelling's T2 statistic plots were located within the range indicated that all of them could be used in regression analysis, but one sample (number 20) was located outside the range which was regarded as outlier and eliminated from dataset of analysis. 4.4. Calibration and validation samples Fig. 4. Influence of the NaCl salt concentration on the viscosity of PAM/SiO2 nanofluids at 25 °C and salt concentration range of (0.5–5.0 wt%).
As mentioned, all samples were split into calibration and prediction set by Kennard Stone algorithm. A set of 47 samples were taken as
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a
Viscosity prediction (mpa.s)
70
Viscosity Calibration
Viscosity Prediction
60 50
R2 Cal.
0.969
Slope
0.929
Offset
1.403
RMSEC
5.111
RMSEP
6.302
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Viscosity reference (mpa.s)
b
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R2Cal. Slope
0.984
Offset
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RMSEC
2.71
RMSEP
3.231
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Fig. 6. Scatter plot of the predicted viscosity vs reference viscosity using (a) PLS-R, and (b) SVM-R model for calibration and prediction samples (All samples were divided into training and testing subsets by Kennard Stone as a random sample selection algorithm).
calibration and 12 samples were proposed for prediction of viscosity. In order to evaluate the proposed calibration method for viscosity measurement, the viscosity of 60 new samples were analyzed in the range of 6–70 m·pas by FTIR-spectroscopy and chemometrics. The viscosity for calibration samples was carried out in the range of 6.07 to 66.6. As well the average viscosity and standard deviation for calibration samples are 23.83 and 5.3, respectively. The range of viscosity of prediction samples was 6.07 to 21.50. The average viscosity and standard deviation for prediction samples are 11.85 and 4.15, respectively. Fig. 6(a) and (b), show predicted viscosity versus reference viscosity of the samples for calibration and prediction sets. With the aim of improving the analysis for solution rheology, multivariate methods
including PLS and SVM were applied using absorption spectra. After constructing the calibration models by PLS and SVM algorithms, the viscosity of the prediction set samples were predicted by the models. Also R2, RMSEC, and RMSEP statistical parameters for calibration and prediction samples for PLS and SVM models were calculated and presented in Fig. 6(a) and (b) respectively. SVM algorithm showed better modeling of data and prediction ability by higher R2 and lower RMSEC and RMSEP. 5. Conclusion In this study, the viscosity of PAM solution in the presence of SiO2 nanoparticle and NaCl salt was successfully predicted using FT-IR in
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combination with chemometric techniques. This method is expected to provide a rapid quantitative analysis of physicochemical properties of polymer solutions in CEOR due to its simplicity in the sample preparation, non-destructive nature, and sensitivity. The SVM-R and PLS-R models were successfully applied to mid-IR spectra of the polymer solution. Two most important spectral band (850 and 1105 cm−1) were selected for the prediction of viscosity. This study indicated that the SVMR as a non-linear model was more accurate than PLS-R as a linear model for prediction of viscosity in polymer solutions. The RMSEP values for PLS-R and SVM-R were 6.302 and 3.231 respectively. The results of the proposed method are consistent with the results of the reference method in measuring the viscosity of the solution. Acknowledgement The second author of this paper gratefully acknowledges the support from department of Food Science and Agricultural Chemistry, Macdonald Campus, McGill University and special thanks Dr. Ashraf Ismail for providing research facilities. References [1] D.A.Z. Wever, F. Picchioni, A.A. Broekhuis, Polymers for enhanced oil recovery: a paradigm for structure-property relationship in aqueous solution, Prog. Polym. Sci. 36 (2011) 1558–1628, https://doi.org/10.1016/j.progpolymsci.2011.05.006. [2] D. Levitt, G.A. Pope, Selection and screening of polymers for enhanced-oil recovery, SPE Symp. Improv. Oil Recover. (2008) 19–23, https://doi.org/10.2118/113845-MS. [3] P. Raffa, A.A. Broekhuis, F. Picchioni, Polymeric surfactants for enhanced oil recovery: a review, J. Pet. Sci. Eng. 145 (2016) 723–733, https://doi.org/10.1016/j.petrol. 2016.07.007. [4] G. Cheraghian, S.S. Khalili Nezhad, M. Kamari, M. Hemmati, M. Masihi, S. 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