1. Introduction
Petroleum is an extraordinarily complex mixture consisting of alkane, cycloalkane, aromatic hydrocarbons with different molecular weights, and heteroatom organic compounds containing nitrogen, sulfur, oxygen, and metals [
1,
2]. The exact number of species making up petroleum is still unknown, although some authors suggest that there are millions [
3,
4,
5], while others state that there are thousands [
6,
7]. Alkane hydrocarbons in petroleum were found to range from traces of C
2H
6, dissolved in the liquid petroleum, to C
78H
158 [
1]. Cycloalkanes were reported to have between 1 and 11 cyclic rings with a maximum carbon number of 92 [
8]. Aromatic hydrocarbons were reported to have between 1 and 18 condensed rings [
9]. The content of the elements nitrogen, sulfur, oxygen, and metals in petroleum can vary as follows: 0.05% ≤ N ≤ 3.0%; 0.05% ≤ S ≤ 9%; 0.05% ≤ O ≤ 1.5%; and 0 ppm ≤ metals ≤ 1500 ppm [
10].
All petroleum components can be segregated based on their solubility in four groups: saturates, aromatics, resins, and asphaltenes, called SARA fractions [
11,
12,
13,
14,
15,
16,
17,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29]. The saturate fraction is composed of alkane, cycloalkane hydrocarbons, negligible amounts of nitrogen (0.05%), sulfur (0.1% ≤ S ≤ 0.9%), and oxygen (0.1%) [
17]. The aromatic fraction contains arene hydrocarbons with between one and six fused aromatic rings with attached cycloalkane rings, and alkyl chains with different lengths [
30], and variable amounts of nitrogen (0.05% ≤ N ≤ 0.7%), sulfur (0.4% ≤ S ≤ 6.4%), and oxygen (0.1% ≤ O ≤ 2.9%) [
17]. The resin fraction, also called polar aromatics, is composed predominately of compounds containing between one and six condensed aromatic rings and nitrogen (0.7% ≤ N ≤ 1.2%), sulfur (0.7% ≤ S ≤ 6.1%), oxygen (1.9% ≤ O ≤ 2.7%) [
17], and metals (0 ppm ≤ metals ≤ 980 ppm) [
31]. The asphaltene fraction is composed mostly of aromatic ring structures with numbers of aromatic rings between 1 [
32] and 18 [
9], and the poly-condensed aromatic structures are pericondensed [
12]. The asphaltene contents of nitrogen, sulfur, oxygen, and metals can vary as follows: 0.5% ≤ N ≤ 2.5%; 0.3% ≤ S ≤ 9%; 1% ≤ O ≤ 1.7%; and metals (0 ppm ≤ metals ≤ 1500 ppm) [
31].
Petroleum can be also fractionated into cuts based on the difference of the volatility of its compounds. The variation of amount of different cuts in petroleum can be as follows: gas (C2–C5) (0% ≤ gas ≤ 8.2%); C5–fraction (0% ≤ C5/70 °C ≤ 20.7%); light naphtha (0% ≤ 70 °C/100 °C ≤ 18.9%); medium naphtha (0.2% ≤ 100 °C/150 °C ≤ 31.2%); heavy naphtha (0.8% ≤ 150 °C/190 °C ≤ 16.2%); kerosene (2.2% ≤ 190 °C/235 °C ≤ 16.6%); light diesel (3.4% ≤ 235 °C/280 °C ≤ 21.3%); heavy diesel (6.5% ≤ 280 °C/343 °C ≤ 26.3%); vacuum gas oil (4.8% ≤ 343 °C/565 °C ≤ 50.0%); and vacuum residue (0% ≤ 565 °C+ ≤ 61%). These data have been obtained from our research laboratory library that includes hundreds of crude oil assays from all over the world which pertain to the five main groups: extra light, light, medium, heavy, and extra heavy crude oils.
The SARA composition, in addition to providing information on the chemical nature of oil, is used for oil classification and evaluation [
21,
33]. It is also used to assess oil colloidal stability and crude oil compatibility [
34,
35,
36,
37,
38,
39,
40,
41,
42,
43,
44,
45], fouling [
46,
47,
48,
49,
50,
51], flow assurance [
52], oil–water emulsion stability [
53,
54], determination of interactions in crude oils [
55,
56], product stability [
57,
58], and oil reactivity in different conversion processes [
59,
60,
61,
62,
63,
64]. It is also employed to predict petroleum properties like density [
65], viscosity [
66,
67], refractive index [
68,
69,
70], boiling temperature [
71], and others.
The significance of SARA composition for crude oil characterization explains the research interest in prediction of the contents of SARA fractions from easily available petroleum data and the use of computational methods [
72,
73,
74,
75,
76,
77,
78].
Melendez et al. [
72] developed eight chemometrics models to predict SARA composition, measured in accordance with ASTM D 4124 [
79] requirements, of 50 Colombian crude oils, using Fourier transform infrared coupled to attenuated total reflectance (ATR–FTIR). They classified the crude oils into two groups depending on their asphaltene content: (1) 0.17 wt.% ≤ asphaltenes ≤ 3.8 wt.%; (2) 5.5 wt.% ≤ asphaltenes ≤ 17.9 wt.%. For each SARA component, standard errors of prediction (SEP) for group 1 were 1.9, 1.7, 1.3, and 0.4. For group 2, SEP were 2.5, 1.7, 3.7, and 1.4, respectively. The coefficients of determination (R
2) were higher than 0.95. They showed that IR spectroscopy coupled with an ATR cell plus chemometric techniques can provide an alternative way for the quantitative prediction of the SARA composition of petroleum oils whose SARA composition varies in the range 15.0 wt.% ≤ saturates ≤ 66.2 wt.%; 20.3 wt.% ≤ aromatics ≤ 40.2 wt.%; 8.6 wt.% ≤ resins ≤ 39.0 wt.%; 0.17 wt.% ≤ asphaltenes ≤ 17.9 wt.%.
Sanchez-Minero et al. [
73] investigated five crude oils with SARA composition fluctuating in the range 20.0 wt.% ≤ saturates ≤ 51.6 wt.%; 11.4 wt.% ≤ aromatics ≤ 31.4 wt.%; 14.3 wt.% ≤ resins ≤ 36.3 wt.%; 2.8 wt.% ≤ asphaltenes ≤ 32.3 wt.%, predicting their SARA composition from nuclear magnetic resonance (1H NMR and 13C NMR) data with R
2 higher than 0.989. They employed the ASTM D 3279 method [
80] to measure the content of n-heptane insoluble (asphaltenes), and the ASTM D 2007 [
81] method to determine the concentration of saturates, aromatics, and resins in the five studied crude oils whose specific gravity varied in the range 0.8612 ≤ specific gravity ≤ 0.9979.
Mohammadi et al. [
74] measured the SARA composition of 12 crude oil samples from different Iranian oil fields using the ASTM D 4124 method. ATR-FTIR spectroscopy results were used to obtain correlations for prediction of SARA fraction contents by application of a hybrid of genetic algorithm (GA), support vector machine regression (SVM-R), and genetic algorithm–partial least square regression (GA-PLS-R). The crude oil SARA fraction content varied in the range 37.3 wt.% ≤ saturates ≤ 72.4 wt.%; 15.4 wt.% ≤ aromatics ≤ 42.9 wt.%; 7.0 wt.% ≤ resins ≤ 15.0 wt.%; 0.9 wt.% ≤ asphaltenes ≤ 13.1 wt.%. The non-linear GA-SVM-R model demonstrated higher accuracy in SARA fraction content prediction (R
2 ≥ 0.98) than the linear GA-PLS-R (R
2 ≥ 0.94).
Florez et al. [
75] studied 67 samples of crude oils from different zones of Colombia, availing the standards ASTM D 4124, and ASTM D 2007 to measure their SARA fraction contents. The variation of SARA composition of these 67 crude oils was as follows: 12.4 wt.% ≤ saturates ≤ 41.9 wt.%; 8.3 wt.% ≤ aromatics ≤ 47.2 wt.%; 2.0 wt.% ≤ resins ≤ 37.1 wt.%; 0.4 wt.% ≤ asphaltenes ≤ 17.4 wt.%. The researchers used the Raman spectra of the crude oils and partial least square regression (PLSR) to develop correlations that predicted petroleum SARA fraction contents with R
2 ≥ 0.94.
Pantoja et al. [
76] applied steady-state and time-resolved fluorescence measurements for 21 crude oils whose SARA composition varied in the range 43 wt.% ≤ saturates ≤ 63 wt.%; 27 wt.% ≤ aromatics ≤ 40 wt.%; 7 wt.% ≤ resins ≤ 14 wt.%; 2 wt.% ≤ asphaltenes ≤ 6 wt.%. The SARA composition of studied 21 crude oils was measured by employment of liquid chromatography with a preliminary precipitation of asphaltenes with n-pentane. Using total synchronous fluorescence scan (TSFS) spectral map data, partial least squares (PLS) correlations were developed to predict the crude oil SARA composition with R
2 ≥ 0.88.
Yarranton [
77] proposed an approach to predict the saturate content of crude oil from a simulated distillation (SimDist) assay, the asphaltene content of the oil, and the oil density. The uncertainty of saturate content prediction was reported to compare favorably with the minimum ±3 wt.% uncertainty of the saturate content from a SARA assay. It was pointed out that the proposed method was based on more reliable measurements than the SARA analysis, thereby offering a means for a more standardized determination of saturate content.
Kulkarni et al. [
78] utilized SARA composition data of 216 crude oils from six different literature sources to develop SARA fraction content prediction from petroleum density and viscosity by employing artificial neural network (ANN) techniques. The correlation coefficient R of predicted versus measured SARA fraction contents were reported as follows: saturates (R = 0.844); aromatics (R = 0.54); resins (R = 0.782); asphaltenes (R = 0.745). The literature sources used by Kulkarni et al., however, indicated that the SARA composition was measured by different procedures. For example, Kulkarni et al. [
78] used a set of 44 oil SARA compositions from all 216 SARA data to develop their ANN model from the work of Jokuty et al. [
82]. Those 44 oil SARA compositions were measured in accordance with the ASTM D 2007 requirements. This means that the asphaltenes measured by Jokuty et al. [
82] were C
5-asphaltenes, because according to the ASTM D 2007 standard, asphaltenes are precipitated with n-pentane. Another literature source [
83] referenced by Kulkarni et al. [
78] reported that the asphaltene determination of the studied three crude oils was performed by using either the n-pentane or n-heptane precipitation method. Additionally, another six crude oils whose SARA composition [
84] was also utilized by Kulkarni et al. [
78] to develop their ANN models were analyzed for their asphaltenes by precipitation with petroleum ether that was neither n-pentane nor n-heptane. Understandably, the different procedures applied to measure asphaltenes may result in different reported values for the same oils, which can make the use of such a database unreliable and lead to inaccurate predictions. Therefore, a single-source database should be considered as a preferred way to more appropriately model SARA composition. In addition, distillation data, which have been shown to be influenced by the molecular type composition of the crude oil [
71], may be also deemed meaningful to include in the ANN models.
Yarranton’s [
77] idea of using oil density and simulated distillation to predict oil saturate content can be further developed to predict the contents of the other three groups of petroleum compounds (aromatics, resins, and asphaltenes) using artificial neural networks. To achieve this, we employed the data of 94 petroleum samples taken from [
85], whose SARA composition had been measured following a procedure described therein. Using data from a single source avoided the use of disparate SARA composition data reported in the literature for different SARA analyses [
24]. Artificial neural network models to predict the four SARA fraction contents and non-linear regression models were developed and compared in this research.
SARA prediction models typically employ regression and metaheuristic methods [
72,
73,
74,
75,
76,
77,
78]. However, no comparison between the two techniques has been provided so far. That was the reason for us to employ linear and non-linear regression along with an ANN as a metaheuristic method to model petroleum SARA composition, combining their capability to accurately predict SARA composition using the same method of measurement. The aim of this study is to discuss the results of SARA oil composition modeling obtained using an ANN with linear and non-linear regression.
2. Materials and Methods
The set of data for SARA composition, density, sulfur content, flash point, and high-temperature simulated distillation (HTSD) of the 94 petroleum samples used for SARA fraction content modeling is presented in
Table S1, while
Table 1 indicates the range of variation in these properties. The data were taken from [
85], which contains 100 oil SARA compositions, and the bulk properties of flash point, pour point, viscosity, and surface tension. Unfortunately, not all the petroleum samples had been analyzed for all these properties. The biggest selection from this data set of 100 petroleum fluids was that including SARA composition, density, sulfur content, and flash point. This selection consisted of 94 data points, which are shown in
Table S1. The petroleum data set is shown in
Table S1; the reported mass balance of SARA composition was between 99 and 102 wt.%, with prevailing data of 100 wt.%.
Three data mining (DM) or knowledge discovery in databases (KDD) techniques were employed in this study. The first one aimed at understanding the analyzed petroleum SARA data and the relations between the oil characteristics shown in
Table 1. It was an intercriteria analysis (ICrA), built on intuitionistic fuzzy sets and index matrices. Two parameters μ and υ were calculated in the process of ICrA evaluation of oil SARA data by using specialized software freely available as open source from
https://intercriteria.net/software/ (accessed on 20 May 2024), and described in detail in [
86,
87,
88,
89]. ICrA avoids the term “correlation” between investigated variables and instead applies the terms “positive consonance”, “negative consonance”, and “dissonance”. For μ = 0.75–1.00 and υ = 0–0.25, a region of statistically meaningful positive consonance is obtained, whereas at μ = 0–0.25 and υ = 0.75–1.00, an area of statistically meaningful negative consonance is derived. All other cases are deemed to be dissonance. A comprehensive description of ICrA application in oil refining is given in [
90]. ICrA is preferred as a method to search for the presence of statistically meaningful relations which are both linear and non-linear. In contrast, conventional correlation analysis registers the presence only of linear relations.
The second and third DM techniques used in this work aimed at predicting oil SARA composition are the regression and ANN approaches. Two types of models were used for regression analysis: linear and non-linear (i.e., linear combination of powered independent variables). The optimal parameters of regression coefficients were identified by means of the non-linear least squares method (LSM). In both cases, as an optimization tool, the differential evolution (DE) algorithm was used to search for the best parameter values in compact subsets in the parameter space. The DE algorithm does not require differentiability or even continuity of the optimized function. Moreover, it is very applicable to construct some necessary bounds in the parameter space. All calculations were realized by the use of CAS Maple 2024, Global Optimization Tool (method = diffevol) and verified by a simple Python script, based on a differential evolution package from scipy.optimize library.
Using artificial neural networks leverages the natural connectivity of individual neurons to create an architecture for predicting the hydrocarbon group composition of oil. The neural network constructed in this work was such that the outputs of each layer were connected to the inputs of the next layer. In this case, the neural network had no feedback loops, making it a feedforward neural network. Its structure was as follows: at the entrance where the input part of the training sequence was fed, the first hidden layer had 123 neurons. Next, the second layer had 42 neurons, the third contained 16 neurons, the fourth contained 10 neurons, the fifth had 8 neurons, and the sixth layer contained only 1 neuron. The neural network used in this study was feed-forward (no feedback from any of the layers to any of the inputs of the neural network). To make it easier to train and in order not to occupy too much computer memory, larger numbers of neurons were used in the first layers, and the number of neurons gradually reduced. In our case, the output neural layer had only one neuron (as the number of parameters to be predicted). In neural network training, the data are divided into three parts: training, validation, and testing. The training set is employed to train the model, the validation set assists in model selection and hyperparameter tuning, and the test set evaluates the ANN implementation on data not included in the training or validation data. The moment the error computed on the validation data starts to increase, it is considered best to stop training the neural network. At this point, the neural network training data are reported. In determining the architecture of the ANN to strike a balance between the accuracy of the neural network, its training speed, and the amount of memory which is used for it, it is also important to note that a larger number of neurons in the neural network introduces additional systematic error into its training. When determining the structure of the neural network, we were guided by the complexity of the process. The application of a simpler neural network structure like, for example, 100-50-25-12-6, resulted in a higher mean squared error at the network’s output, due to the complexity of the process. By increasing the number of neurons in the critical first layer, we sought the best result. However, further increasing the number of neurons led to an accumulation of the error that accompanied each neuron. In this way, we experimentally found the balance in the numbers of neurons in each layer that resulted in the lowest mean squared error. At the input of the neural network, the following data were provided: density at 15 °C, g/cm
3; flash point, °C; sulphur, wt.%; and the yield of components boiling up to 180 °C, 200 °C, 250 °C, 300 °C, 400 °C, 500 °C. At the output of the neural network, we sequentially provided the following: saturates, wt.%; aromatics, wt.%; resins, wt.%; asphaltenes, wt.%. In this way, we trained the neural network to predict the four SARA fraction contents. The ANN SARA composition modeling was accomplished using Matlab 2020 software. The training, validation, and test sets of the data used by the ANN were divided as follows: 68% for training; 21% for testing; and 11% for validation. These data sets for the four fractions separated into training, validation, and testing are presented in
Tables S2–S5. A random splitting algorithm was employed for the data allocation.
The regression models were developed by using 89% of the data for training and 11% for validation.
The following statistical parameters, presented as Equations (1)–(5), were availed to evaluate the accuracy of the SARA prediction models:
4. Conclusions
Three data mining techniques: intercriteria analysis, regression, and artificial neural networks were employed to study a data base of 94 petroleum fluids containing information on SARA composition, density, sulfur content, flash point, and simulated distillation characteristics. The density, sulfur content, and simulated distillation characteristics were found to have statistically meaningful relations to the saturate, resin, and aphaltene fraction contents. The aromatic fraction content, unlike the other SARA fractions, did not show statistically meaningful relations to the same petroleum properties. This is in line with the lower accuracy of prediction of aromatics attained with both ANN and regression models. The ANN models were superior over the regression models in the process of data fitting. However, with the testing data, it was found that the ANN models best predicted the resins and asphaltenes content, while the saturates and aromatics were best predicted by the non-linear regression model. The ANN model forecasted the content of resins and asphaltenes within the reproducibility of the SARA composition measurement. Aromatics that were characterized with a very low reproducibility of measurement were predicted within these limits by the regression models. Despite the best prediction of saturate content by the non-linear regression model, its accuracy was lower than the uncertainty of its measurement. It was found that the petroleum properties of density, sulfur content, yield of fraction boiling up to 500 °C, and flash point affected the accuracy of SARA fraction content prediction for the studied 94 oils.
When testing the models with an additional 66 petroleum fluids, the prognosis of saturate, aromatic, and resin fraction contents worsened, while that for asphaltenes content estimated via linear regression from density and sulfur content maintained an acceptable fair dispersion from the measured value for all data examined in this work. Supplementary research where extra petroleum properties are included as independent input variables in the SARA composition models, possibly with separation of the data by a selected criterion, is needed to improve the accuracy of prediction.