Mathematical Modelling for Predicting Rejection of Trace Organic Contaminants by the Nanofiltration Membrane NF270

Journal of Environmental Treatment Techniques

2020, Volume 8, Issue 3, Pages: 900-907

J. Environ. Treat. Tech.

ISSN: 2309-1185

Journal web link: http://www.jett.dormaj.com

Mathematical Modelling for Predicting Rejection of

Trace Organic Contaminants by the Nanofiltration

Membrane NF270

Hai Quang Dang*

Faculty of Environment, the University of Danang, University of Science and Technology, Danang, Vietnam

Received: 21/01/2020

Accepted: 13/04/2020

Published: 20/09/2020

Abstract

This study implemented multiple linear regression model to predict rejection of trace organic contaminants (TrOCs) by the nanofiltration

NF) membrane NF270. Multiple regression analysis by the Statgraphics Centurion software were used to find an optimal mathematical

(

modeling that combines interactions between molecular width, molecular height, molecular length, molecular weight and log D of TrOCs for

predicting rejection. The result shows a relatively good agreement between the predicted rejection and the observed rejection and an

acceptable R-squared correlation coefficient were found (R = 91.42 %) for the best model. In conclusion, a unified general multiple linear

regression equation was able to predict rejections of TrOCs during nanofiltration with the explanatory variables of molecular width, molecular

height, molecular length and molecular weight. Moreover, the present approach is a basis to continue investigation using multiple regression

analysis techniques for understanding rejection of TrOCs by the NF membranes.

Keywords: Trace organic contaminants (TrOCs), Nanofiltration, Multiple linear regression, Mathematical modeling, Rejection

Introduction¹

health. It has been found that the physicochemical properties of

TrOCs, such as molecular size, molecular weight (MW),

hydrophobicity and charge caused by the functional groups, have

significant effects on their rejection by NF membranes [10,11].

According to Kimura et al. [12], the molecular size of the TrOCs

could be considered one of the most important factors influencing

their rejection by the NF membranes. The molecular weight of the

solutes is often used as an indication of size while the molecular

size parameters such as molecular width, molecular length and

molecular height have been confirmed to more appropriate

predicators for describing size exclusion effects on the rejection

of TrOCs by NF membranes [13-16].

The demand for fresh water worldwide is increasing

dramatically caused by continued population growth posing

challenges in the last few decades by growing water stress, both

in terms of water scarcity and quality deterioration. Some of most

important problems in water supply are the necessity of fresh

water production for drinking, domestic, agricultural, landscape

or industrial uses, the requirement of higher performance methods

for wastewater reclamation and reusing applications, as well as

lower maximum levels of contaminants [1]. However, the

potential presence of trace organic contaminants (TrOCs) such as

endocrine disrupting chemicals (EDCs), pharmaceutically active

compounds (PhACs) and disinfection by products (DBPs) in

treated wastewater and other water sources has become a public

concern because of their potential risks on ecological and human

health in recent decades [2-4].

Recognizing these problems, the rejection of TrOCs in water

treatment processes, which are associated with potentially

adverse human health effects, is of increasing interest for

membrane applications. Nanofiltration (NF) has been

demonstrated to be appropriate technologies for removing most

TrOCs [5,6]. An important driving force for the widespread

implementation of NF membranes is their high removal efficiency

for a large number of inorganic salts and TrOCs amongst the

membrane processes [7-9]. This will have special significance

because satisfactory elimination of micropollutants in water

sources is of paramount importance for the protection of public

number of articles have proposed a mechanistic

understanding of the rejection of TrOCs, others have tried to

apply fitting parameter models to model rejection [17-19].

However, there have been few models to predict the rejection of

TrOCs by NF membranes. It would therefore be of interest to have

a statistical model that can use for predicting rejection of TrOCs.

Among modeling approaches, multiple linear regression analysis

is a relatively simple statistical method used to examine the

correlation among variables. The present study is aimed at

developing multiple regression model that can usefully estimate

the rejection of TrOCs by NF membrane based on an integral

approach that considers physicochemical properties of the

compounds.

Corresponding author: Hai Quang Dang, Faculty of Environment, the University of Danang, University of Science and Technology, Danang,

Vietnam. E-mail: dqhai@dut.udn.vn.

900

Journal of Environmental Treatment Techniques

2020, Volume 8, Issue 3, Pages: 900-907

.2 Nanofiltration membrane

The NF270 membrane (Dow-Filmtec, Minneapolis, MN) was

Materials and methods

.1 Background of statistical analysis

selected for this study. According to the manufacturer, it is a thin-

film composite polyamide membrane that is widely used for water

and wastewater treatment application. This is a loose NF

membrane with a relatively high permeability (of approximately

Statistical analysis is useful for exploring and examining the

basic features of the data prior to applying statistical tests and

fitting statistical models. Because the fact that many factors

influence some phenomena, it is necessary to calculate the

interaction among phenomena. In order to attain this, multiple

regression methods can be used. Multiple regression has taken a

very significant place in statistical science. It is a method of

analysis for assessing the strength of the relationship between a

set of explanatory variables known as independent variables, and

a single response or dependent variable. Applying multiple

regression analysis to a set of data results in what are known as

regression coefficients, one for each explanatory variable [20,21].

Regression analysis is a mathematical measure of the average

relationship between two or more variables in terms of the

original units of the data. The concept of regression analysis

involves finding the best relationship between variables.

1 L/bar m h). At pH 4 and above, this membrane is negatively

charged [23]. The flat sheet membrane samples were stored dry

before use.

.3 Trace organic contaminants, analytical chemicals and

reagents

The target TrOCs for this research have been chosen from the

major classes of EDCs, PhACs and DBPs. They have diverse

physicochemical properties such as hydrophobicity, charge,

solubility, and molecular size. A stock solution was prepared at a

concentration of 1 mg/mL in pure methanol. A working solution

of these TrOCs was also prepared in pure methanol. Both these

solutions were stored in a freezer at -18 ºC prior to use.

Chemical solutions and feed waters were prepared with Milli-

Q water. Both the solvents used for solid phase extraction and

analysis of samples including methanol and dichloromethane,

purchased from Sigma-Aldrich (Sydney, Australia). Internal

standard of bisphenol A-d16 and N,O-bis (trimethylsilyl)

In case of researching relationship between two phenomena

and in case of prediction of the value of dependent variable, first

to identify variables and then to find out random sample n size for

the chosen values of dependent variables. Suppose that k

phenomenon is identified as independent variable (predictor), or

, i = 1, 2,…, k, and Y as dependent random variable. The whole

multiple linear model can be presented as one equation for

dependent variable Y

trifluoroacetamide

(BSTFA)

containing

trimethylchlorosilane (TMCS). Pyridine used in the derivatization

process. All reagents and chemicals were purchased from Sigma-

Aldrich (Sydney, Australia).

= β

+ β

+ …+ β

+ ε

(1)

.4 Experimental protocol

A laboratory scale cross flow NF/RO system consisted of a

where Y

of independent variable, β

regression coefficient), and ε

random error which has normal distribution, zero mean and

constant variance. The whole regression model can be estimated

by the sample regression model using least squares fitted

is dependent random variable, x

, x

, …, x

are values

, β

, …, β

are model parameters

stainless steel NF/RO membrane cell with an effective surface

area of 40 cm and channel height of 2 mm, a stainless steel feed

(

is a supporting element, or a

reservoir, and a high pressure pump (Hydra-Cell, Wanner

Engineering Inc., Minneapolis, MN) was used. The temperature

of the feed solution was controlled by a chiller/heater (Neslab

RTE 7, Thermo Scientific Inc., Waltham, MA, USA) equipped

with a stainless steel heat exchanger coil which was submerged

directly into the feed reservoir. A digital flow meter (Optiflow

(prediction) equation (obtained by minimizing Error Sum of

Squares, SSE):

= b

+ b

+ …+ b

(2)

000, Agilent Technologies, Palo Alto, CA) connected to a PC

was utilized to measure permeate flow, and the cross flow was

monitored with a rotameter.

where y

is adjustable or foreseen value of dependent variable Y

, …, x are values of independent variables, and b , b , …,

are estimations of unknown parameters β , β , …, β . Once a

, x

The rejection of TrOCs was performed in a background

electrolyte solution containing 10 mM of NaCl, 1 mM of CaCl

regression model has been constructed, it may be important to

confirm the goodness of fit of the model and the statistical

significance of the estimated parameters. Commonly used

techniques to verify the goodness of fit include the R square,

Adjusted R square, Multiple R, and hypothesis testing. Statistical

significance can be verified by a Fisher distribution (F-test) of the

overall model, followed by tests of the individual parameters

using Student's t-distribution (t-test) [22].

The fit of a multiple regression model can be judged with

calculation of the multiple correlation coefficient, Multiple R,

defined as the correlation between the observed values of the

response variable and the values predicted by the model. The

and 1 mM of NaH PO (pH 7) and conducted over 24 hours. Prior

to each experiment, the NF270 membrane samples were gently

washed with copious Milli-Q water to remove any preservatives.

They were then compacted using Milli-Q water at 1,000 kPa for

at least one hour until a stable permeate flux had been obtained.

The background electrolyte solution was then added to the feed

reservoir, and made up to the total feed volume of 10 litres.

During the experiment, the feed reservoir temperature and cross

flow velocity were kept constant at 20 ± 0.1 °C and 42 cm/s,

respectively. The permeate flux was set to the manufacturer’s

quoted nominal membrane flux of 42 L/m h throughout the

experiment. Both permeate and retentate were recirculated to the

feed reservoir. A mixture of 25 target TrOCs was then added to

the feed reservoir to obtain a concentration of 25 μg/L of each.

The feed solution pH was kept constant during the experiments

by periodically adding a small amount of 1 M of NaOH or 1 M

HCl. Approximately 100 mL of feed and permeate samples were

taken at specific times. Samples were stored in clean glass bottles,

squared value of R (R ) gives the proportion of the variability of

the response variable accounted for by the explanatory variables.

Adjusted R square used to compare models with different sets of

independent variables in terms of predictive capabilities. Analysis

of variance (ANOVA) will provide an F-test of the null

hypothesis that each of b

words that R is zero [21].

1 k

, b , b2,… b , is equal to zero, or in other

901

Journal of Environmental Treatment Techniques

2020, Volume 8, Issue 3, Pages: 900-907

wrapped in aluminium foil, stored in the fridge for subsequent

extraction and GC/MS analysis. The effective rejection was

defined as R (%):

than 0.99. The detection limits and quantification limits for

analytes were estimated with the signal to noise (s/n) ratio higher

than 3 and higher than 10, respectively.

A Metrohm model 744 pH Meter was calibrated before

beginning of an experiment and utilized to measure the feed

solution pH for the duration of the experiment.

R 100 (1

)

(3)

Results and discussion

where C

respectively.

and C

were the feed and the permeate concentrations,

3.1 Properties of trace organic contaminants and their rejection

efficiency

The major physicochemical properties of the target TrOCs

and their rejection efficiency are shown in Table 1. The standard

deviation of data obtained from two independent experiments.

The compounds selected for this investigation exhibited

considerably difference in their physicochemical properties.

These compounds have low molecular weight, ranging between

138.12 and 361.82 g/mol for salicylic acid and bezafibrate,

respectively. However, they are markedly different in their

.5 Analytical methods

The Oasis HLB SPE cartridges (6 mL, 200 mg, Waters,

Milford, MA, USA) for extraction of the TrOCs in feed and

permeate samples were used in this investigation. The feed and

permeate samples of 100 mL were allowed to reach room

temperature and adjusted by 4 M sulphuric acid to pH range

between 2 and 3. Before the samples were extracted, the SPE

cartridges were conditioned sequentially by

dissociation constants (pK ), molecular dimension (width, height

dichloromethane and methanol (1:1, v/v), 7 mL methanol, and

about 2 x 7 mL reagent water on a vacuum manifold at a flow rate

of 2 mL/min. Subsequently, the samples were passed through the

cartridges with a flow rate of 2 mL/min. The loaded cartridges

were washed with 6 x 7 mL of Milli-Q water and dried under

vacuum for 30 minutes along with a stream of nitrogen. The SPE

columns containing the TrOCs were eluted with 7 mL methanol

followed by 7 mL dichloromethane and methanol (1:1, v/v) at a

flow rate of 1 - 5 mL/min. The elution volume was then

evaporated to dryness under a gentle stream of nitrogen in a water

bath at 40 °C. An amount of 200 µL methanol solution containing

and length) and hydrophobicity properties. Most TrOCs are weak

acids and will dissociate into an ionic form at pH above the pK_a.

The molecular widths, heights and lengths of these TrOCs are

from 0.354 to 0.435, 0.505 to 1.313 and 0.615 to 1.179 nm,

respectively. The difference in molecular weight and dimension

can play a major role in the rejection of TrOCs.

On the other hand, it is striking to note that the intrinsic

hydrophobicity of TrOCs was an important factor in determining

their rejection by a NF process [27,28]. The logarithm of the

effective octanol-water distribution coefficient, log D, is a good

parameter which can be used to evaluate the hydrophobicity of

TrOCs at any pH value [29,30]. According to Wells [31] and

Alturki et al. [32], organic compounds with log D equal to 3 or

higher are generally referred to as hydrophobic. By contrast,

organic compounds with log D below 3 are referred to as

hydrophilic.

It can be observed that rejection efficiency of TrOCs varied

considerably depending on the different physicochemical

characteristics of the compounds, ranging from 49.27 to 98.30 %.

In general, larger MW and molecular dimension compounds

showed higher rejections than small MW and molecular

dimension compounds on size exclusion grounds. Because of the

large MW and molecular dimension, TrOCs do not significantly

penetrate into the membrane pores, resulting in their adsorption

occurring mainly at the membrane surface. Consequently, the

diffusion of these compounds across the membrane is very

limited, leading to the high rejection efficiencies observed. These

results are consistent with the observations of Yangali-Quintanilla

µg bisphenol A-d16 was utilized to dissolve the extracted

residues, and was transferred into 1.5 mL vials before further

evaporation to dryness under a gentle nitrogen stream. Finally, the

derivatization of the dried residues in the vials was performed by

adding 100 µL of BSTFA (N,O-bis (trimethylsilyl)

trifluoroacetamide) (1 % TMCS (trimethylchlorosilane)) and 100

µL of pyridine (dried with KOH solid). The conditions of the

derivatization reaction were 30 min at 60 - 70 °C. The derivatives

were allowed to cool to room temperature before analysis by GC-

MS [24].

Shimadzu GCMS-QP5000 system consisting of

Shimadzu AOC 20i autosampler and a Phenomenex Zebron ZB-

(5 % diphenyl - 95 % dimethylpolysiloxane) capillary column

30 m × 0.25 mm ID, df = 0.25 µm) was used to determine the

(

concentrations of the organic compounds. Helium was used as the

carrier gas at a constant flow rate of 1.3 mL/min. The GC oven

temperature program was conducted as follows: 100 °C for 1 min,

first ramp 10 °C/min to 175 °C, 3 min at 175 °C, second ramp 30

and coworkers [33,34], who also demonstrated

a strong

°C to 210 °C, third ramp 2 °C/min to 228 °C, fourth ramp 30 °C

correlation between molecular weight, width, length and the

rejection for hydrophilic compounds (such as acetaminophen,

phenacetine, caffeine, metronidazole, phenazone and

sulfamethoxazole) by NF200 and NF90 membranes, and that

rejection of these compounds may be attributed to the domination

of the size exclusion effect. Agenson et al. [13] demonstrated that

size exclusion effect represented by molecular weight and

molecular width of solutes played a major influence on the

rejection efficiency in membrane separation. Additionally, Van

der Bruggen and Vandecasteele [35] suggested that the rejection

of neutral TrOCs can be predicted using the molecular weight of

the compound, a higher rejection for the compounds with larger

molecular weight was obtained.

to 260 °C, fifth ramp 3 °C/min to 290 °C, 3 min at 290 °C. The

injector port and the temperature of the GCMS interface were set

at 280 °C. A sample volume of 1 µL was injected in splitless

mode.

The MS was obtained by electron impact ionisation in full

scan mode from 50 to 600 of m/z, and later on in selected ion

monitoring (SIM) mode for qualitative determinations. The most

abundant ions of each organic compound were selected from its

spectrum for quantitation, in accordance with previous studies

[25,26]. A series of standard TrOCs at 1, 10, 50, 100, 500, and

000 ng/mL and a bisphenol A-d16 internal standard were

prepared for the instrument calibration. The calibration curves

obtained for each compound had correlation coefficients greater

902

Journal of Environmental Treatment Techniques

2020, Volume 8, Issue 3, Pages: 900-907

Table 1: Physicochemical properties and rejection efficiency of the selected trace organic contaminants

Trace organic compounds Log Kow^a

Molecular Molecular Molecular Molecular Log D at pH

Rejection ±

STDEV (%)

Width (nm) Height (nm)

Length weight (MW)

(nm)

(g/mol)

138.12

206.28

250.33

296.15

236.27

266.34

150.22

206.32

220.35

289.54

228.29

270.37

272.38

288.38

296.40

314.42

194.19

218.25

290.32

253.28

277.40

361.82

249.09

268.26

270.24

Salicylic acid

Ibuprofen

Gemfibrozil

Diclofenac

Carbamazepine

Pentachlorophenol

2.011

3.502

4.302

4.548

1.895

5.115

3.397

5.180

6.142

5.343

3.641

3.624

4.146

2.527

4.106

5.111

-0.628

0.829

0.594

0.659

4.410

2.504

3.125

2.860

3.114

3.01

4.41

4.75

4.18

13.94

4.68

10.13

10.15

7.80

10.29

10.25

10.27

10.25

10.24

10.26

0.52

12.26

7.04

5.81

9.18

3.29

12.13

6.99

6.51

0.354

0.340

0.356

0.354

0.412

0.426

0.420

0.412

0.435

0.420

0.412

0.354

0.577

0.561

0.670

0.767

0.676

0.640

0.505

0.595

0.519

0.602

0.570

0.693

0.842

0.676

0.740

0.766

0.595

0.933

1.313

0.668

0.760

0.706

0.615

0.900

0.972

0.829

0.818

0.659

0.735

0.822

1.179

0.926

0.876

0.697

0.751

0.788

0.947

0.750

0.734

1.047

1.032

0.871

0.773

0.902

1.015

1.033

-1.130

0.940

2.070

1.770

1.890

2.850

3.400

5.180

6.140

5.280

3.640

3.620

4.150

2.530

4.110

5.110

-7.110

0.830

0.310

-0.560

4.410

-1.210

3.120

2.550

2.500

49.27 ± 3.21

80.61 ± 2.13

93.08 ± 2.45

98.03 ± 1.05

81.32 ± 2.88

92.74 ± 3.96

51.28 ± 5.99

80.77 ± 2.73

88.95 ± 2.76

92.28 ± 1.49

78.61 ± 4.68

82.40 ± 4.83

84.38 ± 1.10

95.72 ± 0.40

95.36 ± 1.94

98.30 ± 1.03

89.52 ± 3.75

92.07 ± 1.86

93.64 ± 3.27

88.15 ± 1.75

91.05 ± 0.84

98.23 ± 0.05

81.02 ± 5.36

85.88 ± 5.27

87.15 ± 5.52

(pH-pKa)

-tert-butylphenol

-tert-octylphenol

-n-nonylphenol

Triclosan

Bisphenol A

Estrone

7β-estradiol

Estriol

7α-ethinylestradiol

7β-estradiol acetate

Caffeine

Primidone

Trimethoprim

Sulfamethoxazole

Amitriptyline

Bezafibrate

Linuron

Formononetin

Genistein

Scifinder Scholar, calculated using Molecular Modeling Pro Plus software, calculated by the equation: log D(pH) = Log Kow – Log (1+10

It is however noteworthy that there was no correlation

statistics included R-squared = 91.42 percent, R-squared

between rejection and log D of these TrOCs. These observations

can be attributed to the fact that in addition to the effect of the log

D, there are a number of other factors which may influence TrOCs

rejection such as MW, molecular dimension, charge, and so on.

Correlation between the physicochemical properties and the

rejection for the TrOCs will be discussed in detail in the following

section.

(adjusted for d.f.) = 86.27 percent and Standard error of Est. =

4.56.

The output shows the results of fitting a multiple linear

regression model to describe the relationship between Y and

independent variables. The equation of the fitted model is as

follows:

Y = -1886.76 + 5020.79X1 + 2267.82X2 + 2092.90X3 +

0.267792X4 - 0.837608X5 - 5891.10X1X2 - 5464.52X1X3 -

2505.03X2X3 + 6448.92X1X2X3

.2 Multiple linear regression model for trace organic

contaminants rejection

Physicochemical properties of the TrOCs and their rejection

efficiency were used as indicators in the model development.

Database using for multiple regression analysis are presented in

the Table 2. Statistical analysis of multiple regression by

Statgraphics Centurion software was used to construct the best

optimal mathematical modeling for trace organic contaminants

rejection by the NF270 membrane. The whole multiple regression

model can be presented as one equation for dependent variable Y:

In determining whether the model can be simplified, the

highest P-value on the independent variables is 0.1038, belonging

to X5 (Table 3). Since the P-value is greater or equal to 0.05, that

term is not statistically significant at the 95.0 % or higher

confidence level. Consequently, it should consider removing X5

from the model. Whereas, the regression coefficients (include X1,

X2, X3, X4, X1X2, X1X3, X2X3, and X1X2X3) contribute

significantly to the model (exist in multiple regression equation)

due to their P-values are less than 0.05. Since the P-value in the

ANOVA table is less than 0.05, there is a statistically significant

relationship between the variables at the 95.0 % confidence level.

The R-squared statistic indicates that the model as fitted