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Supercritical fluid extraction of coriander seeds: Kinetics modelling and ANN optimization
Accepted Manuscript Title: Supercritical fluid extraction of coriander seeds: Kinetics modelling and ANN optimization Author: Zoran Zekovi´c Oskar Bera Saˇsa Ðurovi´c Branimir Pavli´c PII: DOI: Reference:
S0896-8446(16)30338-2 http://dx.doi.org/doi:10.1016/j.supflu.2017.02.006 SUPFLU 3850
To appear in:
J. of Supercritical Fluids
Received date: Revised date: Accepted date:
27-9-2016 9-2-2017 10-2-2017
Please cite this article as: Z. Zekovi´c, O. Bera, S. Dstrokeurovi´c, B. Pavli´c, Supercritical fluid extraction of coriander seeds: Kinetics modelling and ANN optimization, The Journal of Supercritical Fluids (2017), http://dx.doi.org/10.1016/j.supflu.2017.02.006 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Supercritical fluid extraction of coriander seeds: Kinetics modelling and ANN
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optimization
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Zoran Zeković, Oskar Bera, Saša Đurović, Branimir Pavlić*
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University of Novi Sad, Faculty of Technology, Bulevar Cara Lazara 1, 21000 Novi Sad,
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Serbia
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Corresponding author: Bulevar Cara Lazara 1, 21000 Novi Sad, Serbia; Tel.: +381 63 8743
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420 Fax: +381 21 450 413, E-mail: [email protected]
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Abstract
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The main goal of this research was mathematical modelling and numerical simulation of the
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supercritical fluid extraction (SFE) process of coriander (Coriandrum sativum L.) seeds. SFE
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was performed at different set of process parameters: pressure (100, 150 and 200 bar),
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temperature (40, 55 and 70 ˚C) and CO2 flow rate (0.2, 0.3 and 0.4 kg/h). Both applied
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empirical models, derived from models developed by Brunner and Esquivel et al., adequately
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described SFE process. Second objective was to determine effects of investigated SFE
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parameters on total extraction yield. Furthermore, calculated parameters from the empirical
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models were used for the calculation of initial slope, which was successfully used for
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optimization using artificial neural network (ANN). Optimized SFE conditions for maximized
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initial slope, i.e. initial rate of the solubility-controlled extraction phase, were pressure of 200
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bar, temperature of 40 ˚C and CO2 flow rate of 0.4 kg/h.
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Keywords: Coriandrum sativum L., supercritical fluid extraction (SFE), kinetics, artificial
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neural network (ANN), optimization
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1. Introduction
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Supercritical fluid extraction (SFE) represents a suitable alternative to conventional processes
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such as hydrodistillation, steam distillation and solvent extraction [1]. It has been carried out
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on a commercial scale since 1980s [2], while industrial-scale application of this technique
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comprise diversity of technological processes such as decaffeination of green coffee beans
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and black tea leaves; production of hop extracts; extraction of essential oils, oleoresins, and
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flavouring compounds from herbs and spices; extraction of high-valued bioactive compounds
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from different natural matrices; extraction and fractionation of edible oils; and removal of
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pesticides from plant material [3,4].
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As previously mentioned, SFE process is thoroughly investigated for obtaining the extracts
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from plant matrices [5]. Coriander (Coriandrum sativum L.) is well known by its usage in folk
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medicine, cooking and different industrial branches such as food, pharmaceutical and
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cosmetic [6,7]. Conducted studies showed that the most important constituent of coriander
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seeds are fatty and essential oils, where the main constituent of essential oil is linalool [8].
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Domination of linalool in essential oil of coriander seeds regardless the isolation procedure
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and/or SFE operational conditions [6,9-12] has been confirmed. Besides SFE, other non-
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conventional extraction techniques were applied for extraction of bioactives from coriander
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seeds, such as ultrasound-assisted [13], microwave-assisted [14] and subcritical water
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extraction [15], as well as sequential combination of SFE and ultrasound-assisted extraction
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[11]. Conventional extraction techniques (Soxhlet extraction and hydrodistillation) were also
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applied [10], while obtained results were compared with those obtained with non-
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conventional approaches. Unlike the SFE process, mentioned non-conventional techniques
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were mainly focused on isolation of polar and/or moderately polar compounds, such as
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polyphenolic compounds. This processes were also optimized in order to obtain the highest
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possible yield of those compounds [12-14].
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Artificial Neural Network (ANN) has been broadly and successfully used in a various fields
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to predict variables influence on investigated outputs. Methods based on ANNs mimic the
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natural neural system using computer software and they are quite popular because of several
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advantages such as: non-linearity, adaptively, generalization, model independence, easy to use
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and high accuracy. ANN connection weights are often used to determine the relative
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importance of the various inputs and several equations have been proposed to obtain relative
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importance based on the weights magnitude [16-20]. Due to mentioned properties, ANN
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methods have been successfully employed by some researchers to predict SFE extraction
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kinetics and perform optimization of the process [21-26].
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The main goal of this research was to apply empirical mathematical models which would be
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able to adequately describe SFE process of coriander seeds. Another objective was to
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determine effects of investigated SFE parameters (pressure, temperature and CO2 flow rate)
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on total extraction yield. Furthermore, another aspect was to couple extraction kinetics
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modelling and artificial neural networks, in order to perform optimization of initial slope.
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Innovative approach in this research was usage of adjustable parameters from the applied
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kinetics models for the calculation of the initial slope (k1 Y∞ and Y∞/k2, respectively), which
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was later used as the response variable in ANN optimization instead of total extraction yield.
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2. Materials and methods
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2.1. Plant material
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Coriander (Coriandrum sativum L.) was produced at the Institute of Field and Vegetable
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Crops, Novi Sad, Republic of Serbia (year 2011). The collected plant material (seeds) was air
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dried in solar dryer and stored at room temperature. Dried seeds were grounded in a domestic
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blender and the mean particle size of material was determined using sieve sets (CISA
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Cedaceria Industrial, Barcelona, Spain). Moisture content of plant material was analysed
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using standard procedure, i.e., by drying the coriander seeds at 105 °C until constant weight
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(Laboratory dryer, Sutjeska, Serbia).
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2.2. Chemicals
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Commercial carbon dioxide (Messer, Novi Sad, Serbia), purity >99.98%, was used for
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laboratory supercritical fluid extraction. All other chemicals were of analytical reagent grade.
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2.3. Supercritical fluid extraction
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The supercritical fluid extraction (SFE) processes were carried out on laboratory scale high
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pressure extraction plant (HPEP, NOVA, Swiss, Efferikon, Switzerland) described in detail
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by Pekić et al. [27]. The main plant parts and properties, by manufacturer specification were:
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gas cylinder with CO2, the diaphragm type compressor with pressure range up to 1000 bar,
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extractor with heating jacket for heating medium with internal volume 200 mL, maximum
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operating pressure of 700 bar, separator with heating jacket for heating medium (with internal
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volume 200 mL, maximum operating pressure of 250 bar), pressure control valve,
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temperature regulation system and regulation valves.
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Samples (50.0 g) were placed in an extractor vessel, while rest of the volume was filled with
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glass beads. Extraction process was carried out and extraction yield was measured after 15,
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30, 45, 60, 90, 120, 150, 180 and 240 min of extraction, in order to study the dynamics and
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kinetics of the process. First set of experiments consisted of Box-Behnken experimental
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design with three variables at three levels with three replicates at the central point (15 runs)
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[12]. Pressure (100, 150 and 200 bar), temperature (40, 55 and 70 ˚C) and CO2 flow rate (0.2,
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0.3 and 0.4 kg/h) were independent variables in the process, while all other SFE parameters
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were held constant. Furthermore, experimental design was expanded for 6 more runs, where
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different combinations of independent variables (pressure, temperature and CO2 flow rate)
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were applied in order to provide more detailed information about extraction kinetics and
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influence of SFE parameters on total extraction yield. Expanded Box-Behnken experimental
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design is presented in Table 1. Total extraction yield (Y) was measured after the each
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experimental run and result was expressed as grams of total extractable compounds per 100
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grams of dry plant material (g/100 g), i.e. percentage (%). The separator conditions were 15 bar and 25 °C.
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2.4. Mathematical modelling of SFE process
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Extraction curves for each experimental run (21 runs) were fitted to empirical models
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obtained from two commonly used empirical equations used for modelling of SFE process.
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The first model equation was obtained from the Brunner’s equation [3], which represents a
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specific solution of Fick’s law:
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where Y represents the extraction yield (%), k is the rate constant (min-1), t is the extraction
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time (min) and x0 is the initial content of the solute in the solid phase (g/g), which is usually
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obtained by the Soxhlet extraction with suitable organic solvent. This equation has one
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adjustable parameter (k), while x0 is constant. For mathematical modelling, previous equation
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was modified with addition of one adjustable parameter:
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where Y∞ is the total extraction yield obtained for infinite extraction time and is specific for
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each experimental run, i.e. each set of process parameters.
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Esquivel et al. [28] proposed empirical model with one adjustable parameters, given by the
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following equation:
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where me is the mass of extract (g), F is the mass of solid material (g), t is the extraction time
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(min), x0 is the initial content of the solute in the solid phase (g/g) and b is adjustable
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parameter (min). Again, this equation was modified with addition of one adjustable parameter
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[29,30] and used in following form:
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where Y is the total extraction yield (%), while Y∞ and k2 are the adjustable parameters.
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2.5. Artificial Neural Network (ANN)
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All data analysis was performed using MATLAB software (The Math Works Inc. License
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Number 1108951). The ANN models with one hidden layer were designed using MATLAB
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Neural Network Toolbox. The constructed ANN model had 3 inputs (pressure, temperature
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and CO2 flow rate) and one output (initial slope obtained from the II kinetic model) (Figure
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1). The ANN was also tested on other output parameters obtained from fitting (asymptote and
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rate constant), but without any satisfactory results, therefore, initial slope was chosen as a
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response for the optimization.
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Figure 1. Schematic structure of the ANN architecture used for optimization (5 hidden
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neurons)
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Data necessary for ANN and the kinetic models was obtained from the experimental study.
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From all collected data, 70% has been used for training, 15% was for testing and 15% has
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been considered for validation.
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Tanning procedure, using the Bayesian regularization, was composed from following steps:
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feedforward of the input training pattern, calculation and back propagation of the associated
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error and the adjustment of the calculated weights. Bayesian regularization updates the weight
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and bias values according to Levenberg-Marquardt optimization and it minimizes a
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combination of squared errors and weights and then determines the correct combination. This
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procedure is very useful for further determination of relative importance using the weights
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magnitude.
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In order to determine the relative importance of input variables on initial slope, assessment
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process based on the connection weights partitioning of the obtained networks was used and
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Yoon’s interpretation method was applied.
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Finally, the ANN model was used for optimization with aim to find conditions which will
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result with maximal initial slope (initial rate). The optimization was conducted in MATLAB
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with built in functions fmincon and MultiStart with 15 random starting points in order to find
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global maximum.
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2.6. Statistical analysis
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The accordance between experimentally obtained extraction yields and calculated values
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obtained from fitted model equations by two mathematical models was established by the sum
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of squared errors (SSer) and coefficient of determination (R2).
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3. Results and discussion
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Moisture content and mean particle size of plant material, i.e. coriander seeds, used in all
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experimental runs of supercritical fluid extraction (SFE) were 7.20% and 0.6216 mm,
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respectively. Experimentally observed total extraction yield (Y) obtained at different SFE
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conditions (pressure, temperature and CO2 flow rate) are presented in Table 1. The highest Y
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(7.16%) was observed at pressure of 200 bar, temperature of 55 ˚C and CO2 flow rate of 0.3
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kg/h, while the lowest Y (0.59%) was obtained at following conditions: 100 bar, 70 ˚C and
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0.3 kg/h. SFE of C. sativum was already an objective of various publications. Influence of
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mean particle size on Y [11] and process optimization by response surface methodology
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(RSM) in SFE [12], were already investigated by our research group. According to recent
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publications, the highest Y (0.57%) was achieved using 0.630 mm particle size of the ground
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coriander seeds at 40 ˚C, 150 bar and 21.8 kg/h CO2 flow rate [7].
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Application of mathematical models in SFE provides description of extraction process and
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further exploitation of results. Furthermore, they are commonly used in planning and scaling
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of process from the laboratory to industrial scale. Obtained mathematical models should not
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be limited only to certain equations, but to provide information of plant material and transport
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mechanisms during process. Mathematical modelling of the SFE has been widely investigated
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and applied models could be divided in two main groups: empirical models (based on the
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analogy of heat and mass transfer) and models based on differential mass balance [3,31,32].
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Mathematical modelling of SFE of coriander seeds was already published in scientific
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literature. Catchpole and Gray [33] used model based on differential mass balance, which
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contains intraparticle diffusion coefficient as adjustable parameter. Developed mathematical
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model was able to satisfactorily predict Y as function of extraction time, CO2 flow rate and
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particle diameter. Reverchon and Marrone [34] investigated influence of mean particle size on
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Y and successfully applied model of broken and intact cells to describe SFE of coriander
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seeds. According to Grosso et al. [35], SFE of coriander seeds was controlled by the internal
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diffusion and internal mass transfer coefficient, influenced by pressure, temperature and
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particle size.
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In this work, modified Brunner model (Eq. (2)) and modified Esquivel et al. (Eq. (4)) was
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used for mathematical interpretation of the SFE of coriander seeds. Each model contained two
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adjustable parameters (Y∞ and k1; Y∞ and k2, respectively) and their calculated values, together
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with coefficients of determination (R2) and sum of squared errors (SSer), are presented in
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Table 1. According to statistical parameters, both applied models adequately described SFE
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process, since average SSer and R2 were 0.0651 and 0.9958; 0.0369 and 0.9965 for the first
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and second model, respectively. This indicated that second model showed slightly better fit
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with experimental results. It has been previously mentioned that Y∞ was added as adjustable
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parameter in both model equations and represents asymptotic total extraction yield, which is
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characteristic for the each set of SFE parameters. This provided calculation of the initial slope
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for both applied models (k1 Y∞ and Y∞/k2), which represented measure of the solubility-
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controlled extraction phase. Calculated initial slope was later used as the response variable for
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ANN optimization.
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Table 1. SFE process parameters (pressure, temperature and CO2 flow rate), total extraction
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yield and calculated parameters for the applied mathematical models.
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3.1. Influence of operating SFE parameters
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3.1.1. Influence of pressure
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In order to provide detailed information about influence of each SFE parameter (pressure,
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temperature and CO2 flow rate), six experiments were added to previously performed
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experiments generated by Box-Behnken experimental design. The extraction of coriander
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seeds was performed at 100, 150 and 200 bar at fixed set of temperature and CO2 flow rate
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(55 ˚C, 0.3 kg/h and 40 ˚C, 0.3 kg/h, respectively) and kinetic curves (Y versus t) were
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obtained (Figure 2). It could be observed that Y increased from 1.47 to 7.16% with the
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increase of pressure from 100 to 200 bar at 55 ˚C (Figure 2.a), and 2.69 to 5.95% with the
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increase of pressure from 100 to 200 bar at 40 ˚C (Figure 2.b). Furthermore, it could be noted
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that increment of Y with gradual increase of pressure was more prominent at 55 ˚C, which is
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rather expected since increase in CO2 density is approx. twice higher at 55 ˚C than 40 ˚C
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(Table 1), with the increase of pressure from 100 to 200 bar. Positive effect of pressure is in
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accordance with literature data since it has been reported that Y in SFE of coriander seeds
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increased with increase of pressure from 100 to 150 bar [12] and with increase of pressure
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from 100 to 210 bar [9] at isothermal conditions. According to Fornari et al. [36], pressure has
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been recognized as the most relevant process parameter in SFE from plant matrices. Increase
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of pressure causes increase of CO2 density, which leads to increase of dissolving power of the
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CO2, as well as decrease in extraction selectivity. High pressure is not always recommended,
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particularly if the only aim is extraction of volatile EO compounds [37]. However, in case of
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coriander seeds, which also contain fatty oil [6], both could be extracted simultaneously at
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elevated pressure, i.e. increased density.
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Figure 2. Influence of pressure on total extraction yield at a) 55 ˚C, 0.3 kg/h and b) 40 ˚C, 0.3
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kg/h. Symbols – experimental results; lines – fitted values obtained from II model
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3.1.2. Influence of temperature
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Temperature effect on Y was observed at 40, 55 and 70 ˚C at fixed set of pressure and CO2
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flow rate (150, 0.3 kg/h and 200 bar, 0.3 kg/h, respectively) and obtained kinetic curves were
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presented on Figure 3, where it could be seen that Y was highest at 40 ˚C and lowest at 55 ˚C
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at fixed pressure (150 bar) and CO2 flow rate (0.3 kg/h). On the other hand, Y was highest at
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55 ˚C and lowest at 70 ˚C at isobaric conditions (200 bar and 0.3 kg/h). Temperature effect on
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the Y is rather complex, since it affects both solvent and plant material. Density of CO2
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decreases when the temperature is increased, therefore, solubility also decreases. On the other
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hand, temperature affects volatility of the solute, therefore, it is difficult to predict final
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outcome. According to Pourmortazavi and Hajimirsadeghi [37], higher temperature would
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result in lower extraction recovery for non-volatile compounds, while increase of temperature
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causes competition between solubility and volatility of the solute. Therefore, at 150 bar
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(Figure 3.a), the highest yield (5.53%) was observed at 40 ˚C. Further increase of temperature
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to 55 ˚C caused significant decrease recovery of total extract (3.77%) due to decrease of
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solvent density from 780.30 to 651.85 kg/m3. Another increase of temperature to 70 ˚C at
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isobaric conditions caused decrease of CO2 density (515.35 kg/m3), while Y increased
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(4.63%) (Figure 3.a), due to increase of vapour pressure of the solute, so the solubility
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depended on the equilibrium between the solvent density and changes of vapour pressure of
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the diluted compounds [38]. Contrary to this, the highest Y (7.16%) at 200 bar was observed
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at 55 ˚C (Figure 3.b), probably due to increased coextraction of low-volatile compounds at
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elevated temperature and pressure, i.e. CO2 density.
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Figure 3. Influence of temperature on total extraction yield at a) 150, 0.3 kg/h and b) 200 bar,
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0.3 kg/h. Symbols – experimental results; lines – fitted values obtained from II model
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3.1.3. Influence of CO2 flow rate
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Influence of CO2 flow rate (0.2, 0.3 and 0.4 kg/h) was investigated at fixed sets of pressure
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and temperature (150 bar, 55 ˚C and 200 bar, 55 ˚C, respectively), while kinetic curves with
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experimentally observed values and model fitting were presented on Figure 4. It could be
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observed that the highest Y (5.54%) was observed when the highest CO2 flow rate (0.4 kg/h)
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was applied, while there was no significant difference in Y for 0.2 and 0.3 kg/h CO2 flow rate
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at fixed pressure (150 bar) and temperature (55 ˚C) (Figure 4.a). On the contrary, no
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significant difference between 0.3 and 0.4 kg/h applied CO2 flow rate was observed, when
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increased pressure (200 bar) was applied (Figure 4.b). Furthermore, at the same pressure and
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temperature, the lowest Y (4.90%) was observed when the lowest CO2 flow rate (0.2 kg/h)
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was applied (Figure 4.b). The efficiency of the SFE process is improved by a decreasing of
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mass transfer resistance, which could be achieved by reduction of particle size or increase of
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CO2 flow rate [36]. Since application of higher CO2 flow rate promotes an elevation of the
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operational and capital costs, and this fact must be considered from an industrial point of view
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[39], there is rational reason to use 0.3 kg/h CO2 flow rate, when extractions are performed at
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200 bar and 55 ˚C. According to Papamichail et al. [30], very high solvent flow rates actually
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decrease the yield because of the insufficient contact time between the solute and the solvent,
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which is in accordance with results from Figure 4.b. Furthermore, influence of CO2 flow rate
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could be directly connected with extraction time. From industrial point of view, it is important
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to make SFE process economically feasible. Therefore, it is necessary to perform SFE in the
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first part of extraction curve, which is solubility-controlled, rather than performing the process
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in the diffusion controlled period (lower slope of the extraction curve). According to kinetic
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extraction curves from Figures 2-4, process should be stopped approx. in the period of 100-
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160 min of extraction time, when slope of the curve decreases significantly comparing to the
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first period of extraction.
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Figure 4. Influence of CO2 flow rate on total extraction yield at a) 150 bar, 55 ˚C and b) 200
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bar, 55 ˚C. Symbols – experimental results; lines – fitted values obtained from II model
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3.2. ANN optimization
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According to literature, previously applied ANN optimization of SFE processes was
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performed using Y as response variable [21-26]. Since, time consumption must be considered
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as important SFE parameter from economical point of view, it is necessary to achieve
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maximal Y for short extraction time. Therefore, calculation of extraction kinetics parameters
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(asymptote, rate constant and initial slope) was combined with ANN optimization for this
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purpose. Novelty of this approach was usage of calculated initial slope (k1 Y∞ and Y∞/k2,
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respectively) as parameter representing the initial phase of SFE process, i.e. solubility-
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controlled phase. This was applied with purpose to avoid Y, which was obtained at rather
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long extraction time (4 h) for SFE. Since, II applied model showed better fit with
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experimental data (Table 1), initial slope (Y∞/k2) calculated from this model was used as
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response variable. Moreover, other output parameters obtained from fitting (asymptote and
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rate constant) were also tested separately, but without any satisfactory results, therefore,
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initial slope was chosen as a response for the optimization.
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It is known that the results obtained from ANN, including weights values, can vary by
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changing the initial (starting) value of parameters necessary for ANN construction and fitting.
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Also, the different number of hidden neurons can give different ANN model outcomes. In
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order to avoid above mentioned influences on ANN results, the number of neurons in hidden
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layer was varied from 1 to 20 and the training process of each network was repeated 10 times
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with random initial values of weights and biases. The result of this procedure was creation of
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200 ANNs in total. Only the neural networks with coefficient of determination (R2) higher
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than 0.8 were used for further analysis (194 of 200 ANNs). Mean value of R2 was 0.932 for
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all created ANN, while the best fitting was achieved with neural network with 5 hidden
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neurons (R2=0.979, SSer = 0. 25237E-03).
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Influence of hidden neurons number on R2 mean value obtained from 10 repeated trainings
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and regression plot for ANN with best performance are shown in Figure 5 (a and b). It could
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be seen that the R2 value shows rising trend with increasing the number neurons in hidden
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layer and that the mean value was always higher than 0.9. Also, it is important to emphasize
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that the best of all 200 ANNs (ANN with 5 hidden neurons) was used for further optimization
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calculations. In this way “overfitting” with high number of hidden neurons was avoided.
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Figure 5. a) Influence of hidden neurons number on R2 mean value and b) regression plot for
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ANN with best performance (5 hidden neurons)
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Successful creation of ANNs and obtained weight matrices in MATLAB, enabled the
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determination of inputs’ relative importance (RI) and its influence on initial slope using the
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connection weights partitioning methodology. In this paper, the following equation developed
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by Yoon et al. [17] was used:
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where RIij is the relative importance of the ith input variable on the jth output, wik is the
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weight between the ith input and the kth hidden neuron, and wkj is the weight between the kth
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hidden neuron and the jth output. Yoon’s interpretation method can provide the direction of
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the relationship between the input and output variables by avoiding the absolute value of the
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connection weights product sum in numerator (Eq. (5)). Influence of hidden neurons number
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on RI mean value obtained from 10 repeated trainings is shown in Figure 6.a. Mean values of
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all calculated RI values and standard deviations are presented in Figure 6.b. Low variability of
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RI makes the interpretation of the input influence valid and acceptable.
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Influence of SFE parameters on Y has been already discussed in detail. However, ANN
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modelling provided additional acceptable data for influence of SFE parameters on initial
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slope, which is proportional to Y. According to data from Figure 6, it could be observed that
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pressure was the most influential parameter with approx. 50% of relative importance, while
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temperature and CO2 flow rate had relative importance of approx. 18% and 32%, respectively.
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This was in accordance with literature data about ANN modelling of SFE processes [26].
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Pressure exhibited positive influence on initial slope, which could be explained with increase
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of CO2 density and further increase in extraction rate (Figure 6.b). Furthermore, CO2 flow rate
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also exhibited significant positive influence on initial slope. This could be explained with the
332
fact that initial phase of extraction depends mainly on solubility and continuous import of
333
fresh solvent would provide faster dissolution of the solute due to high concentration gradient
334
from solid to fluid phase. On the other hand, temperature was the least influential variable
335
affecting initial slope (Figure 6.b). Negative influence of temperature suggested that decrease
336
of CO2 density with increase of temperature would prevail over increase of extraction rate
337
caused by increase of solute’s vapour pressure. It has been previously reported that CO2 flow
338
rate was more influential SFE parameter comparing to temperature [26], which is in
339
accordance with results from this work.
an
us
cr
ip t
330
M
340
Figure 6. a) Influence of hidden neurons number on RI mean value and b) mean values of all
342
calculated RI values and standard deviations
343
Optimization of SFE process regarding initial slope was the second goal of this research. In
344
order to find combinations of process parameters, which will result with the highest value of
345
initial slope/rate, optimization was conducted in MATLAB using ANN model. Constrained
346
optimization was preformed within experimental range. The results are in given in Table 2,
347
together with the experimental conditions when the highest value of initial slope was
348
achieved. It could be seen that ANN optimization predicted following SFE conditions:
349
pressure of 200 bar, temperature of 40 ˚C and CO2 flow rate of 0.4 kg/h, to provide 0.1188 %
350
min-1 initial slope, which was higher that experimentally obtained maximal initial slope
351
(0.1131 % min-1). From Table 2, it could be seen that temperature was the only different
352
variable in optimized and experimentally performed SFE conditions. ANN model predicted
353
temperature of 40 ˚C, which is in accordance with results, since temperature exhibited
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Page 15 of 25
negative influence of initial slope (Figure 6.b). Optimal conditions obtained in this work,
355
using novel approach with initial slope as response, were in accordance with optimal
356
conditions obtained by response surface methodology (RSM) with total extraction yield as
357
response variable [12].
358
Table 2. Optimization of SFE conditions for maximal initial slope and comparison with
359
experimental results
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us
360
4. Conclusions
362
The first goal of this research was to provide empirical model which would be able to
363
adequately describe SFE of coriander seeds. According to results, it could be concluded that
364
both applied models (modified Brunner and Esquıvel et al. models) fitted well with the
365
experimental data. Evaluation of the extraction curves provided data on the influence of SFE
366
parameters (pressure, temperature and CO2 flow rate) on total extraction yield (Y). As
367
expected, pressure effect was more pronounced, causing increase of Y by increasing CO2
368
density. Temperature exhibited complex effect on both CO2 density and vapour pressure of
369
the solute, while CO2 flow caused significant increase of Y only at lower pressure (150 bar).
370
Calculated parameters from the applied models were further used for calculation of initial
371
slope, which was used as response variable for ANN optimization. According to statistical
372
parameters, ANN was successfully used for maximization of initial slope, which has been
373
applied as novel approach for optimization of solubility-controlled extraction period.
374
Furthermore, ANN analysis provided information about relative importance of SFE
375
parameters influence with pressure and CO2 flow rate affecting initial slope positively, while
376
temperature exhibited negative effect.
377
Acknowledgement
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The financial support of the Ministry of Education, Science and Technological development
379
of the Republic of Serbia is gratefully acknowledged (Project No. TR31013).
380
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Page 21 of 25
ip t cr
Table 1. SFE process parameters (pressure, temperature and CO2 flow rate), total extraction yield and calculated parameters for the applied
487
mathematical models. T
CO2
ρ
Y
I model
[bar]
[˚C]
flow
[kg/m3]
[%]
k1
Y∞
[min-1]
[%]
rate [kg/h]
an
P
k1∙ Y∞
SSer
II model R2
[% min-1]
M
Run
us
486
k2
Y∞
Y∞/k2
[min]
[%]
[% min1
SSer
R2
]
150
70
0.2
515.35
2.05a 0.0127
2.08
0.0264
0.0154
0.9966
90.27
2.79
0.0309
0.0024
0.9994
2
200
40
0.3
839.90
5.95a 0.0149
5.91
0.0881
0.2430
0.9932
74.79
7.79
0.1042
0.2507
0.9933
3
100
55
0.4
337.20
1.20a 0.0250
1.17
0.0293
0.0054
0.9964
35.03
1.40
0.0399
0.0009
0.9994
4
150
70
0.4
515.35
3.50a 0.0165
3.44
0.0568
0.0783
0.9939
62.37
4.39
0.0704
0.0103
0.9991
5
200
70
0.3
658.95
5.36a 0.0110
5.62
0.0620
0.0555
0.9982
110.55
7.78
0.0704
0.0083
0.9997
6
150
40
0.2
780.30
4.31a 0.0070
5.26
0.0370
0.0239
0.9989
203.56
8.01
0.0394
0.0315
0.9986
7
200
55
0.2
754.10
4.90a 0.0115
5.16
0.0592
0.0444
0.9982
106.12
7.12
0.0671
0.0529
0.9981
8
150
55
0.3
651.85
3.77a 0.0110
3.91
0.0430
0.1003
0.9932
108.61
5.37
0.0494
0.0390
0.9971
9
150
40
0.4
780.30
5.64a 0.0134
5.72
0.0770
0.0613
0.9981
84.50
7.64
0.0904
0.0180
0.9995
Ac c
ep te
d
1
Page 22 of 25
cr
ip t 489
55
0.3
651.85
4.02a 0.0120
4.08
0.0491
0.1098
0.9936
95.73
5.50
0.0574
0.0288
0.9982
11
100
55
0.2
337.20
0.95a 0.0274
0.95
0.0259
0.0001
0.9999
31.29
1.12
0.0358
0.0066
0.9929
12
200
55
0.4
754.10
7.00a 0.0136
6.98
0.0952
0.2735
0.9946
81.66
9.24
0.1131
0.0505
0.9989
13
100
40
0.3
628.70
2.69a 0.0149
2.59
0.0387
0.1095
0.9849
70.11
3.34
0.0477
0.0375
0.9944
14
150
55
0.3
651.85
4.00a 0.0097
4.37
0.0424
0.0135
0.9992
132.82
6.24
0.0469
0.0109
0.9994
15
100
70
0.3
255.80
0.59a 0.0451
16
200
55
0.3
754.10
7.16
0.0104
17
100
55
0.3
337.20
1.47
0.0136
18
150
40
0.3
780.30
5.53
19
150
55
0.2
651.85
20
150
55
0.4
651.85
21
150
70
a
an
M
0.0282
0.0035
0.9906
14.45
0.69
0.0477
0.0108
0.9711
7.72
0.0807
0.0285
0.9995
120.48
10.86 0.0902
0.0520
0.9991
1.46
0.0199
0.0277
0.9882
79.50
1.92
0.0241
0.0129
0.9939
0.0105
5.92
0.0623
0.0978
0.9969
119.32
8.32
0.0697
0.0980
0.9971
3.89
0.0068
4.83
0.0328
0.0120
0.9993
213.34
7.41
0.0347
0.0204
0.9989
5.54
0.0108
5.84
0.0630
0.0540
0.9983
114.48
8.14
0.0711
0.0198
0.9994
0.0093
5.15
0.0477
0.0102
0.9995
141.04
7.40
0.0525
0.0133
0.9995
ep te
0.63
d
0.3
515.35
us
150
Ac c
488
10
4.63
these results were previously used in another manuscript [12].
490
Page 23 of 25
491
Table 2. Optimization of SFE conditions for maximal initial slope and comparison with
492
experimental results Temperature
CO2 flow
Initial slope
[°C]
rate [kg/h]
[% min-1] 0.1188
200
40
0.4
Experimental
200
55
0.4
us
493 494
498 499 500
Application of empirical mathematical models for SFE process, Evaluation of SFE parameters effects (pressure, temperature and CO2 flow rate), Artificial neural network modelling with initial slope as response Influence analysis using relative importance and ANN ANN optimization of the solubility-controlled extraction phase
501
Ac
504
ce pt
502 503
an
497
M
496
Highlights of the Manuscript
ed
495
0.1131
cr
ANN model
ip t
Pressure [bar]
Page 24 of 25
ip t cr us an M ed Ac
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505 506
Page 25 of 25
S0896-8446(16)30338-2 http://dx.doi.org/doi:10.1016/j.supflu.2017.02.006 SUPFLU 3850
To appear in:
J. of Supercritical Fluids
Received date: Revised date: Accepted date:
27-9-2016 9-2-2017 10-2-2017
Please cite this article as: Z. Zekovi´c, O. Bera, S. Dstrokeurovi´c, B. Pavli´c, Supercritical fluid extraction of coriander seeds: Kinetics modelling and ANN optimization, The Journal of Supercritical Fluids (2017), http://dx.doi.org/10.1016/j.supflu.2017.02.006 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Supercritical fluid extraction of coriander seeds: Kinetics modelling and ANN
2
optimization
3
Zoran Zeković, Oskar Bera, Saša Đurović, Branimir Pavlić*
4
University of Novi Sad, Faculty of Technology, Bulevar Cara Lazara 1, 21000 Novi Sad,
5
Serbia
ip t
1
Corresponding author: Bulevar Cara Lazara 1, 21000 Novi Sad, Serbia; Tel.: +381 63 8743
7
420 Fax: +381 21 450 413, E-mail: [email protected]
8
Abstract
9
The main goal of this research was mathematical modelling and numerical simulation of the
10
supercritical fluid extraction (SFE) process of coriander (Coriandrum sativum L.) seeds. SFE
11
was performed at different set of process parameters: pressure (100, 150 and 200 bar),
12
temperature (40, 55 and 70 ˚C) and CO2 flow rate (0.2, 0.3 and 0.4 kg/h). Both applied
13
empirical models, derived from models developed by Brunner and Esquivel et al., adequately
14
described SFE process. Second objective was to determine effects of investigated SFE
15
parameters on total extraction yield. Furthermore, calculated parameters from the empirical
16
models were used for the calculation of initial slope, which was successfully used for
17
optimization using artificial neural network (ANN). Optimized SFE conditions for maximized
18
initial slope, i.e. initial rate of the solubility-controlled extraction phase, were pressure of 200
19
bar, temperature of 40 ˚C and CO2 flow rate of 0.4 kg/h.
20
Keywords: Coriandrum sativum L., supercritical fluid extraction (SFE), kinetics, artificial
21
neural network (ANN), optimization
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Page 1 of 25
1. Introduction
24
Supercritical fluid extraction (SFE) represents a suitable alternative to conventional processes
25
such as hydrodistillation, steam distillation and solvent extraction [1]. It has been carried out
26
on a commercial scale since 1980s [2], while industrial-scale application of this technique
27
comprise diversity of technological processes such as decaffeination of green coffee beans
28
and black tea leaves; production of hop extracts; extraction of essential oils, oleoresins, and
29
flavouring compounds from herbs and spices; extraction of high-valued bioactive compounds
30
from different natural matrices; extraction and fractionation of edible oils; and removal of
31
pesticides from plant material [3,4].
32
As previously mentioned, SFE process is thoroughly investigated for obtaining the extracts
33
from plant matrices [5]. Coriander (Coriandrum sativum L.) is well known by its usage in folk
34
medicine, cooking and different industrial branches such as food, pharmaceutical and
35
cosmetic [6,7]. Conducted studies showed that the most important constituent of coriander
36
seeds are fatty and essential oils, where the main constituent of essential oil is linalool [8].
37
Domination of linalool in essential oil of coriander seeds regardless the isolation procedure
38
and/or SFE operational conditions [6,9-12] has been confirmed. Besides SFE, other non-
39
conventional extraction techniques were applied for extraction of bioactives from coriander
40
seeds, such as ultrasound-assisted [13], microwave-assisted [14] and subcritical water
41
extraction [15], as well as sequential combination of SFE and ultrasound-assisted extraction
42
[11]. Conventional extraction techniques (Soxhlet extraction and hydrodistillation) were also
43
applied [10], while obtained results were compared with those obtained with non-
44
conventional approaches. Unlike the SFE process, mentioned non-conventional techniques
45
were mainly focused on isolation of polar and/or moderately polar compounds, such as
46
polyphenolic compounds. This processes were also optimized in order to obtain the highest
47
possible yield of those compounds [12-14].
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Page 2 of 25
Artificial Neural Network (ANN) has been broadly and successfully used in a various fields
49
to predict variables influence on investigated outputs. Methods based on ANNs mimic the
50
natural neural system using computer software and they are quite popular because of several
51
advantages such as: non-linearity, adaptively, generalization, model independence, easy to use
52
and high accuracy. ANN connection weights are often used to determine the relative
53
importance of the various inputs and several equations have been proposed to obtain relative
54
importance based on the weights magnitude [16-20]. Due to mentioned properties, ANN
55
methods have been successfully employed by some researchers to predict SFE extraction
56
kinetics and perform optimization of the process [21-26].
57
The main goal of this research was to apply empirical mathematical models which would be
58
able to adequately describe SFE process of coriander seeds. Another objective was to
59
determine effects of investigated SFE parameters (pressure, temperature and CO2 flow rate)
60
on total extraction yield. Furthermore, another aspect was to couple extraction kinetics
61
modelling and artificial neural networks, in order to perform optimization of initial slope.
62
Innovative approach in this research was usage of adjustable parameters from the applied
63
kinetics models for the calculation of the initial slope (k1 Y∞ and Y∞/k2, respectively), which
64
was later used as the response variable in ANN optimization instead of total extraction yield.
65
2. Materials and methods
66
2.1. Plant material
67
Coriander (Coriandrum sativum L.) was produced at the Institute of Field and Vegetable
68
Crops, Novi Sad, Republic of Serbia (year 2011). The collected plant material (seeds) was air
69
dried in solar dryer and stored at room temperature. Dried seeds were grounded in a domestic
70
blender and the mean particle size of material was determined using sieve sets (CISA
71
Cedaceria Industrial, Barcelona, Spain). Moisture content of plant material was analysed
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using standard procedure, i.e., by drying the coriander seeds at 105 °C until constant weight
73
(Laboratory dryer, Sutjeska, Serbia).
74
2.2. Chemicals
75
Commercial carbon dioxide (Messer, Novi Sad, Serbia), purity >99.98%, was used for
76
laboratory supercritical fluid extraction. All other chemicals were of analytical reagent grade.
77
2.3. Supercritical fluid extraction
78
The supercritical fluid extraction (SFE) processes were carried out on laboratory scale high
79
pressure extraction plant (HPEP, NOVA, Swiss, Efferikon, Switzerland) described in detail
80
by Pekić et al. [27]. The main plant parts and properties, by manufacturer specification were:
81
gas cylinder with CO2, the diaphragm type compressor with pressure range up to 1000 bar,
82
extractor with heating jacket for heating medium with internal volume 200 mL, maximum
83
operating pressure of 700 bar, separator with heating jacket for heating medium (with internal
84
volume 200 mL, maximum operating pressure of 250 bar), pressure control valve,
85
temperature regulation system and regulation valves.
86
Samples (50.0 g) were placed in an extractor vessel, while rest of the volume was filled with
87
glass beads. Extraction process was carried out and extraction yield was measured after 15,
88
30, 45, 60, 90, 120, 150, 180 and 240 min of extraction, in order to study the dynamics and
89
kinetics of the process. First set of experiments consisted of Box-Behnken experimental
90
design with three variables at three levels with three replicates at the central point (15 runs)
91
[12]. Pressure (100, 150 and 200 bar), temperature (40, 55 and 70 ˚C) and CO2 flow rate (0.2,
92
0.3 and 0.4 kg/h) were independent variables in the process, while all other SFE parameters
93
were held constant. Furthermore, experimental design was expanded for 6 more runs, where
94
different combinations of independent variables (pressure, temperature and CO2 flow rate)
95
were applied in order to provide more detailed information about extraction kinetics and
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96
influence of SFE parameters on total extraction yield. Expanded Box-Behnken experimental
97
design is presented in Table 1. Total extraction yield (Y) was measured after the each
98
experimental run and result was expressed as grams of total extractable compounds per 100
99
grams of dry plant material (g/100 g), i.e. percentage (%). The separator conditions were 15 bar and 25 °C.
101
2.4. Mathematical modelling of SFE process
102
Extraction curves for each experimental run (21 runs) were fitted to empirical models
103
obtained from two commonly used empirical equations used for modelling of SFE process.
104
The first model equation was obtained from the Brunner’s equation [3], which represents a
105
specific solution of Fick’s law:
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M
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where Y represents the extraction yield (%), k is the rate constant (min-1), t is the extraction
108
time (min) and x0 is the initial content of the solute in the solid phase (g/g), which is usually
109
obtained by the Soxhlet extraction with suitable organic solvent. This equation has one
110
adjustable parameter (k), while x0 is constant. For mathematical modelling, previous equation
111
was modified with addition of one adjustable parameter:
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113
where Y∞ is the total extraction yield obtained for infinite extraction time and is specific for
114
each experimental run, i.e. each set of process parameters.
115
Esquivel et al. [28] proposed empirical model with one adjustable parameters, given by the
116
following equation:
117
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where me is the mass of extract (g), F is the mass of solid material (g), t is the extraction time
119
(min), x0 is the initial content of the solute in the solid phase (g/g) and b is adjustable
120
parameter (min). Again, this equation was modified with addition of one adjustable parameter
121
[29,30] and used in following form:
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118
122
where Y is the total extraction yield (%), while Y∞ and k2 are the adjustable parameters.
124
2.5. Artificial Neural Network (ANN)
125
All data analysis was performed using MATLAB software (The Math Works Inc. License
126
Number 1108951). The ANN models with one hidden layer were designed using MATLAB
127
Neural Network Toolbox. The constructed ANN model had 3 inputs (pressure, temperature
128
and CO2 flow rate) and one output (initial slope obtained from the II kinetic model) (Figure
129
1). The ANN was also tested on other output parameters obtained from fitting (asymptote and
130
rate constant), but without any satisfactory results, therefore, initial slope was chosen as a
131
response for the optimization.
134
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Figure 1. Schematic structure of the ANN architecture used for optimization (5 hidden
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neurons)
135
Data necessary for ANN and the kinetic models was obtained from the experimental study.
136
From all collected data, 70% has been used for training, 15% was for testing and 15% has
137
been considered for validation.
138
Tanning procedure, using the Bayesian regularization, was composed from following steps:
139
feedforward of the input training pattern, calculation and back propagation of the associated
Page 6 of 25
error and the adjustment of the calculated weights. Bayesian regularization updates the weight
141
and bias values according to Levenberg-Marquardt optimization and it minimizes a
142
combination of squared errors and weights and then determines the correct combination. This
143
procedure is very useful for further determination of relative importance using the weights
144
magnitude.
145
In order to determine the relative importance of input variables on initial slope, assessment
146
process based on the connection weights partitioning of the obtained networks was used and
147
Yoon’s interpretation method was applied.
148
Finally, the ANN model was used for optimization with aim to find conditions which will
149
result with maximal initial slope (initial rate). The optimization was conducted in MATLAB
150
with built in functions fmincon and MultiStart with 15 random starting points in order to find
151
global maximum.
152
2.6. Statistical analysis
153
The accordance between experimentally obtained extraction yields and calculated values
154
obtained from fitted model equations by two mathematical models was established by the sum
155
of squared errors (SSer) and coefficient of determination (R2).
156
3. Results and discussion
157
Moisture content and mean particle size of plant material, i.e. coriander seeds, used in all
158
experimental runs of supercritical fluid extraction (SFE) were 7.20% and 0.6216 mm,
159
respectively. Experimentally observed total extraction yield (Y) obtained at different SFE
160
conditions (pressure, temperature and CO2 flow rate) are presented in Table 1. The highest Y
161
(7.16%) was observed at pressure of 200 bar, temperature of 55 ˚C and CO2 flow rate of 0.3
162
kg/h, while the lowest Y (0.59%) was obtained at following conditions: 100 bar, 70 ˚C and
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0.3 kg/h. SFE of C. sativum was already an objective of various publications. Influence of
164
mean particle size on Y [11] and process optimization by response surface methodology
165
(RSM) in SFE [12], were already investigated by our research group. According to recent
166
publications, the highest Y (0.57%) was achieved using 0.630 mm particle size of the ground
167
coriander seeds at 40 ˚C, 150 bar and 21.8 kg/h CO2 flow rate [7].
168
Application of mathematical models in SFE provides description of extraction process and
169
further exploitation of results. Furthermore, they are commonly used in planning and scaling
170
of process from the laboratory to industrial scale. Obtained mathematical models should not
171
be limited only to certain equations, but to provide information of plant material and transport
172
mechanisms during process. Mathematical modelling of the SFE has been widely investigated
173
and applied models could be divided in two main groups: empirical models (based on the
174
analogy of heat and mass transfer) and models based on differential mass balance [3,31,32].
175
Mathematical modelling of SFE of coriander seeds was already published in scientific
176
literature. Catchpole and Gray [33] used model based on differential mass balance, which
177
contains intraparticle diffusion coefficient as adjustable parameter. Developed mathematical
178
model was able to satisfactorily predict Y as function of extraction time, CO2 flow rate and
179
particle diameter. Reverchon and Marrone [34] investigated influence of mean particle size on
180
Y and successfully applied model of broken and intact cells to describe SFE of coriander
181
seeds. According to Grosso et al. [35], SFE of coriander seeds was controlled by the internal
182
diffusion and internal mass transfer coefficient, influenced by pressure, temperature and
183
particle size.
184
In this work, modified Brunner model (Eq. (2)) and modified Esquivel et al. (Eq. (4)) was
185
used for mathematical interpretation of the SFE of coriander seeds. Each model contained two
186
adjustable parameters (Y∞ and k1; Y∞ and k2, respectively) and their calculated values, together
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with coefficients of determination (R2) and sum of squared errors (SSer), are presented in
188
Table 1. According to statistical parameters, both applied models adequately described SFE
189
process, since average SSer and R2 were 0.0651 and 0.9958; 0.0369 and 0.9965 for the first
190
and second model, respectively. This indicated that second model showed slightly better fit
191
with experimental results. It has been previously mentioned that Y∞ was added as adjustable
192
parameter in both model equations and represents asymptotic total extraction yield, which is
193
characteristic for the each set of SFE parameters. This provided calculation of the initial slope
194
for both applied models (k1 Y∞ and Y∞/k2), which represented measure of the solubility-
195
controlled extraction phase. Calculated initial slope was later used as the response variable for
196
ANN optimization.
197
Table 1. SFE process parameters (pressure, temperature and CO2 flow rate), total extraction
198
yield and calculated parameters for the applied mathematical models.
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ed
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3.1. Influence of operating SFE parameters
201
3.1.1. Influence of pressure
202
In order to provide detailed information about influence of each SFE parameter (pressure,
203
temperature and CO2 flow rate), six experiments were added to previously performed
204
experiments generated by Box-Behnken experimental design. The extraction of coriander
205
seeds was performed at 100, 150 and 200 bar at fixed set of temperature and CO2 flow rate
206
(55 ˚C, 0.3 kg/h and 40 ˚C, 0.3 kg/h, respectively) and kinetic curves (Y versus t) were
207
obtained (Figure 2). It could be observed that Y increased from 1.47 to 7.16% with the
208
increase of pressure from 100 to 200 bar at 55 ˚C (Figure 2.a), and 2.69 to 5.95% with the
209
increase of pressure from 100 to 200 bar at 40 ˚C (Figure 2.b). Furthermore, it could be noted
210
that increment of Y with gradual increase of pressure was more prominent at 55 ˚C, which is
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rather expected since increase in CO2 density is approx. twice higher at 55 ˚C than 40 ˚C
212
(Table 1), with the increase of pressure from 100 to 200 bar. Positive effect of pressure is in
213
accordance with literature data since it has been reported that Y in SFE of coriander seeds
214
increased with increase of pressure from 100 to 150 bar [12] and with increase of pressure
215
from 100 to 210 bar [9] at isothermal conditions. According to Fornari et al. [36], pressure has
216
been recognized as the most relevant process parameter in SFE from plant matrices. Increase
217
of pressure causes increase of CO2 density, which leads to increase of dissolving power of the
218
CO2, as well as decrease in extraction selectivity. High pressure is not always recommended,
219
particularly if the only aim is extraction of volatile EO compounds [37]. However, in case of
220
coriander seeds, which also contain fatty oil [6], both could be extracted simultaneously at
221
elevated pressure, i.e. increased density.
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Figure 2. Influence of pressure on total extraction yield at a) 55 ˚C, 0.3 kg/h and b) 40 ˚C, 0.3
224
kg/h. Symbols – experimental results; lines – fitted values obtained from II model
225
3.1.2. Influence of temperature
226
Temperature effect on Y was observed at 40, 55 and 70 ˚C at fixed set of pressure and CO2
227
flow rate (150, 0.3 kg/h and 200 bar, 0.3 kg/h, respectively) and obtained kinetic curves were
228
presented on Figure 3, where it could be seen that Y was highest at 40 ˚C and lowest at 55 ˚C
229
at fixed pressure (150 bar) and CO2 flow rate (0.3 kg/h). On the other hand, Y was highest at
230
55 ˚C and lowest at 70 ˚C at isobaric conditions (200 bar and 0.3 kg/h). Temperature effect on
231
the Y is rather complex, since it affects both solvent and plant material. Density of CO2
232
decreases when the temperature is increased, therefore, solubility also decreases. On the other
233
hand, temperature affects volatility of the solute, therefore, it is difficult to predict final
234
outcome. According to Pourmortazavi and Hajimirsadeghi [37], higher temperature would
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result in lower extraction recovery for non-volatile compounds, while increase of temperature
236
causes competition between solubility and volatility of the solute. Therefore, at 150 bar
237
(Figure 3.a), the highest yield (5.53%) was observed at 40 ˚C. Further increase of temperature
238
to 55 ˚C caused significant decrease recovery of total extract (3.77%) due to decrease of
239
solvent density from 780.30 to 651.85 kg/m3. Another increase of temperature to 70 ˚C at
240
isobaric conditions caused decrease of CO2 density (515.35 kg/m3), while Y increased
241
(4.63%) (Figure 3.a), due to increase of vapour pressure of the solute, so the solubility
242
depended on the equilibrium between the solvent density and changes of vapour pressure of
243
the diluted compounds [38]. Contrary to this, the highest Y (7.16%) at 200 bar was observed
244
at 55 ˚C (Figure 3.b), probably due to increased coextraction of low-volatile compounds at
245
elevated temperature and pressure, i.e. CO2 density.
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Figure 3. Influence of temperature on total extraction yield at a) 150, 0.3 kg/h and b) 200 bar,
248
0.3 kg/h. Symbols – experimental results; lines – fitted values obtained from II model
249
3.1.3. Influence of CO2 flow rate
250
Influence of CO2 flow rate (0.2, 0.3 and 0.4 kg/h) was investigated at fixed sets of pressure
251
and temperature (150 bar, 55 ˚C and 200 bar, 55 ˚C, respectively), while kinetic curves with
252
experimentally observed values and model fitting were presented on Figure 4. It could be
253
observed that the highest Y (5.54%) was observed when the highest CO2 flow rate (0.4 kg/h)
254
was applied, while there was no significant difference in Y for 0.2 and 0.3 kg/h CO2 flow rate
255
at fixed pressure (150 bar) and temperature (55 ˚C) (Figure 4.a). On the contrary, no
256
significant difference between 0.3 and 0.4 kg/h applied CO2 flow rate was observed, when
257
increased pressure (200 bar) was applied (Figure 4.b). Furthermore, at the same pressure and
258
temperature, the lowest Y (4.90%) was observed when the lowest CO2 flow rate (0.2 kg/h)
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Page 11 of 25
was applied (Figure 4.b). The efficiency of the SFE process is improved by a decreasing of
260
mass transfer resistance, which could be achieved by reduction of particle size or increase of
261
CO2 flow rate [36]. Since application of higher CO2 flow rate promotes an elevation of the
262
operational and capital costs, and this fact must be considered from an industrial point of view
263
[39], there is rational reason to use 0.3 kg/h CO2 flow rate, when extractions are performed at
264
200 bar and 55 ˚C. According to Papamichail et al. [30], very high solvent flow rates actually
265
decrease the yield because of the insufficient contact time between the solute and the solvent,
266
which is in accordance with results from Figure 4.b. Furthermore, influence of CO2 flow rate
267
could be directly connected with extraction time. From industrial point of view, it is important
268
to make SFE process economically feasible. Therefore, it is necessary to perform SFE in the
269
first part of extraction curve, which is solubility-controlled, rather than performing the process
270
in the diffusion controlled period (lower slope of the extraction curve). According to kinetic
271
extraction curves from Figures 2-4, process should be stopped approx. in the period of 100-
272
160 min of extraction time, when slope of the curve decreases significantly comparing to the
273
first period of extraction.
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Figure 4. Influence of CO2 flow rate on total extraction yield at a) 150 bar, 55 ˚C and b) 200
276
bar, 55 ˚C. Symbols – experimental results; lines – fitted values obtained from II model
277
3.2. ANN optimization
278
According to literature, previously applied ANN optimization of SFE processes was
279
performed using Y as response variable [21-26]. Since, time consumption must be considered
280
as important SFE parameter from economical point of view, it is necessary to achieve
281
maximal Y for short extraction time. Therefore, calculation of extraction kinetics parameters
282
(asymptote, rate constant and initial slope) was combined with ANN optimization for this
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purpose. Novelty of this approach was usage of calculated initial slope (k1 Y∞ and Y∞/k2,
284
respectively) as parameter representing the initial phase of SFE process, i.e. solubility-
285
controlled phase. This was applied with purpose to avoid Y, which was obtained at rather
286
long extraction time (4 h) for SFE. Since, II applied model showed better fit with
287
experimental data (Table 1), initial slope (Y∞/k2) calculated from this model was used as
288
response variable. Moreover, other output parameters obtained from fitting (asymptote and
289
rate constant) were also tested separately, but without any satisfactory results, therefore,
290
initial slope was chosen as a response for the optimization.
291
It is known that the results obtained from ANN, including weights values, can vary by
292
changing the initial (starting) value of parameters necessary for ANN construction and fitting.
293
Also, the different number of hidden neurons can give different ANN model outcomes. In
294
order to avoid above mentioned influences on ANN results, the number of neurons in hidden
295
layer was varied from 1 to 20 and the training process of each network was repeated 10 times
296
with random initial values of weights and biases. The result of this procedure was creation of
297
200 ANNs in total. Only the neural networks with coefficient of determination (R2) higher
298
than 0.8 were used for further analysis (194 of 200 ANNs). Mean value of R2 was 0.932 for
299
all created ANN, while the best fitting was achieved with neural network with 5 hidden
300
neurons (R2=0.979, SSer = 0. 25237E-03).
301
Influence of hidden neurons number on R2 mean value obtained from 10 repeated trainings
302
and regression plot for ANN with best performance are shown in Figure 5 (a and b). It could
303
be seen that the R2 value shows rising trend with increasing the number neurons in hidden
304
layer and that the mean value was always higher than 0.9. Also, it is important to emphasize
305
that the best of all 200 ANNs (ANN with 5 hidden neurons) was used for further optimization
306
calculations. In this way “overfitting” with high number of hidden neurons was avoided.
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Figure 5. a) Influence of hidden neurons number on R2 mean value and b) regression plot for
309
ANN with best performance (5 hidden neurons)
310
Successful creation of ANNs and obtained weight matrices in MATLAB, enabled the
311
determination of inputs’ relative importance (RI) and its influence on initial slope using the
312
connection weights partitioning methodology. In this paper, the following equation developed
313
by Yoon et al. [17] was used:
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an
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where RIij is the relative importance of the ith input variable on the jth output, wik is the
316
weight between the ith input and the kth hidden neuron, and wkj is the weight between the kth
317
hidden neuron and the jth output. Yoon’s interpretation method can provide the direction of
318
the relationship between the input and output variables by avoiding the absolute value of the
319
connection weights product sum in numerator (Eq. (5)). Influence of hidden neurons number
320
on RI mean value obtained from 10 repeated trainings is shown in Figure 6.a. Mean values of
321
all calculated RI values and standard deviations are presented in Figure 6.b. Low variability of
322
RI makes the interpretation of the input influence valid and acceptable.
323
Influence of SFE parameters on Y has been already discussed in detail. However, ANN
324
modelling provided additional acceptable data for influence of SFE parameters on initial
325
slope, which is proportional to Y. According to data from Figure 6, it could be observed that
326
pressure was the most influential parameter with approx. 50% of relative importance, while
327
temperature and CO2 flow rate had relative importance of approx. 18% and 32%, respectively.
328
This was in accordance with literature data about ANN modelling of SFE processes [26].
329
Pressure exhibited positive influence on initial slope, which could be explained with increase
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Page 14 of 25
of CO2 density and further increase in extraction rate (Figure 6.b). Furthermore, CO2 flow rate
331
also exhibited significant positive influence on initial slope. This could be explained with the
332
fact that initial phase of extraction depends mainly on solubility and continuous import of
333
fresh solvent would provide faster dissolution of the solute due to high concentration gradient
334
from solid to fluid phase. On the other hand, temperature was the least influential variable
335
affecting initial slope (Figure 6.b). Negative influence of temperature suggested that decrease
336
of CO2 density with increase of temperature would prevail over increase of extraction rate
337
caused by increase of solute’s vapour pressure. It has been previously reported that CO2 flow
338
rate was more influential SFE parameter comparing to temperature [26], which is in
339
accordance with results from this work.
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Figure 6. a) Influence of hidden neurons number on RI mean value and b) mean values of all
342
calculated RI values and standard deviations
343
Optimization of SFE process regarding initial slope was the second goal of this research. In
344
order to find combinations of process parameters, which will result with the highest value of
345
initial slope/rate, optimization was conducted in MATLAB using ANN model. Constrained
346
optimization was preformed within experimental range. The results are in given in Table 2,
347
together with the experimental conditions when the highest value of initial slope was
348
achieved. It could be seen that ANN optimization predicted following SFE conditions:
349
pressure of 200 bar, temperature of 40 ˚C and CO2 flow rate of 0.4 kg/h, to provide 0.1188 %
350
min-1 initial slope, which was higher that experimentally obtained maximal initial slope
351
(0.1131 % min-1). From Table 2, it could be seen that temperature was the only different
352
variable in optimized and experimentally performed SFE conditions. ANN model predicted
353
temperature of 40 ˚C, which is in accordance with results, since temperature exhibited
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Page 15 of 25
negative influence of initial slope (Figure 6.b). Optimal conditions obtained in this work,
355
using novel approach with initial slope as response, were in accordance with optimal
356
conditions obtained by response surface methodology (RSM) with total extraction yield as
357
response variable [12].
358
Table 2. Optimization of SFE conditions for maximal initial slope and comparison with
359
experimental results
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4. Conclusions
362
The first goal of this research was to provide empirical model which would be able to
363
adequately describe SFE of coriander seeds. According to results, it could be concluded that
364
both applied models (modified Brunner and Esquıvel et al. models) fitted well with the
365
experimental data. Evaluation of the extraction curves provided data on the influence of SFE
366
parameters (pressure, temperature and CO2 flow rate) on total extraction yield (Y). As
367
expected, pressure effect was more pronounced, causing increase of Y by increasing CO2
368
density. Temperature exhibited complex effect on both CO2 density and vapour pressure of
369
the solute, while CO2 flow caused significant increase of Y only at lower pressure (150 bar).
370
Calculated parameters from the applied models were further used for calculation of initial
371
slope, which was used as response variable for ANN optimization. According to statistical
372
parameters, ANN was successfully used for maximization of initial slope, which has been
373
applied as novel approach for optimization of solubility-controlled extraction period.
374
Furthermore, ANN analysis provided information about relative importance of SFE
375
parameters influence with pressure and CO2 flow rate affecting initial slope positively, while
376
temperature exhibited negative effect.
377
Acknowledgement
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The financial support of the Ministry of Education, Science and Technological development
379
of the Republic of Serbia is gratefully acknowledged (Project No. TR31013).
380
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Page 21 of 25
ip t cr
Table 1. SFE process parameters (pressure, temperature and CO2 flow rate), total extraction yield and calculated parameters for the applied
487
mathematical models. T
CO2
ρ
Y
I model
[bar]
[˚C]
flow
[kg/m3]
[%]
k1
Y∞
[min-1]
[%]
rate [kg/h]
an
P
k1∙ Y∞
SSer
II model R2
[% min-1]
M
Run
us
486
k2
Y∞
Y∞/k2
[min]
[%]
[% min1
SSer
R2
]
150
70
0.2
515.35
2.05a 0.0127
2.08
0.0264
0.0154
0.9966
90.27
2.79
0.0309
0.0024
0.9994
2
200
40
0.3
839.90
5.95a 0.0149
5.91
0.0881
0.2430
0.9932
74.79
7.79
0.1042
0.2507
0.9933
3
100
55
0.4
337.20
1.20a 0.0250
1.17
0.0293
0.0054
0.9964
35.03
1.40
0.0399
0.0009
0.9994
4
150
70
0.4
515.35
3.50a 0.0165
3.44
0.0568
0.0783
0.9939
62.37
4.39
0.0704
0.0103
0.9991
5
200
70
0.3
658.95
5.36a 0.0110
5.62
0.0620
0.0555
0.9982
110.55
7.78
0.0704
0.0083
0.9997
6
150
40
0.2
780.30
4.31a 0.0070
5.26
0.0370
0.0239
0.9989
203.56
8.01
0.0394
0.0315
0.9986
7
200
55
0.2
754.10
4.90a 0.0115
5.16
0.0592
0.0444
0.9982
106.12
7.12
0.0671
0.0529
0.9981
8
150
55
0.3
651.85
3.77a 0.0110
3.91
0.0430
0.1003
0.9932
108.61
5.37
0.0494
0.0390
0.9971
9
150
40
0.4
780.30
5.64a 0.0134
5.72
0.0770
0.0613
0.9981
84.50
7.64
0.0904
0.0180
0.9995
Ac c
ep te
d
1
Page 22 of 25
cr
ip t 489
55
0.3
651.85
4.02a 0.0120
4.08
0.0491
0.1098
0.9936
95.73
5.50
0.0574
0.0288
0.9982
11
100
55
0.2
337.20
0.95a 0.0274
0.95
0.0259
0.0001
0.9999
31.29
1.12
0.0358
0.0066
0.9929
12
200
55
0.4
754.10
7.00a 0.0136
6.98
0.0952
0.2735
0.9946
81.66
9.24
0.1131
0.0505
0.9989
13
100
40
0.3
628.70
2.69a 0.0149
2.59
0.0387
0.1095
0.9849
70.11
3.34
0.0477
0.0375
0.9944
14
150
55
0.3
651.85
4.00a 0.0097
4.37
0.0424
0.0135
0.9992
132.82
6.24
0.0469
0.0109
0.9994
15
100
70
0.3
255.80
0.59a 0.0451
16
200
55
0.3
754.10
7.16
0.0104
17
100
55
0.3
337.20
1.47
0.0136
18
150
40
0.3
780.30
5.53
19
150
55
0.2
651.85
20
150
55
0.4
651.85
21
150
70
a
an
M
0.0282
0.0035
0.9906
14.45
0.69
0.0477
0.0108
0.9711
7.72
0.0807
0.0285
0.9995
120.48
10.86 0.0902
0.0520
0.9991
1.46
0.0199
0.0277
0.9882
79.50
1.92
0.0241
0.0129
0.9939
0.0105
5.92
0.0623
0.0978
0.9969
119.32
8.32
0.0697
0.0980
0.9971
3.89
0.0068
4.83
0.0328
0.0120
0.9993
213.34
7.41
0.0347
0.0204
0.9989
5.54
0.0108
5.84
0.0630
0.0540
0.9983
114.48
8.14
0.0711
0.0198
0.9994
0.0093
5.15
0.0477
0.0102
0.9995
141.04
7.40
0.0525
0.0133
0.9995
ep te
0.63
d
0.3
515.35
us
150
Ac c
488
10
4.63
these results were previously used in another manuscript [12].
490
Page 23 of 25
491
Table 2. Optimization of SFE conditions for maximal initial slope and comparison with
492
experimental results Temperature
CO2 flow
Initial slope
[°C]
rate [kg/h]
[% min-1] 0.1188
200
40
0.4
Experimental
200
55
0.4
us
493 494
498 499 500
Application of empirical mathematical models for SFE process, Evaluation of SFE parameters effects (pressure, temperature and CO2 flow rate), Artificial neural network modelling with initial slope as response Influence analysis using relative importance and ANN ANN optimization of the solubility-controlled extraction phase
501
Ac
504
ce pt
502 503
an
497
M
496
Highlights of the Manuscript
ed
495
0.1131
cr
ANN model
ip t
Pressure [bar]
Page 24 of 25
ip t cr us an M ed Ac
ce pt
505 506
Page 25 of 25