Exploring of the Incompatibility of Marine Residual Fuel: A Case Study Using Machine Learning Methods

Abstract

Providing quality fuel to ships with reduced SOx content is a priority task. Marine residual fuels are one of the main sources of atmospheric pollution during the operation of ships and sea tankers. Hence, the International Maritime Organization (IMO) has established strict regulations for the sulfur content of marine fuels. One of the possible technological solutions allowing for adherence to the sulfur content limits is use of mixed fuels. However, it carries with it risks of ingredient incompatibilities. This article explores a new approach to the study of active sedimentation of residual and mixed fuels. An assessment of the sedimentation process during mixing, storage, and transportation of marine fuels is made based on estimation three-dimensional diagrams developed by the authors. In an effort to find the optimal solution, studies have been carried out to determine the influence of marine residual fuel compositions on sediment formation via machine learning algorithms. Thus, a model which can be used to predict incompatibilities in fuel compositions as well as sedimentation processes is proposed. The model can be used to determine the sediment content of mixed marine residual fuels with the desired sulfur concentration.

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energies
Article
Exploring of the Incompatibility of Marine Residual Fuel: A
Case Study Using Machine Learning Methods
Radel Sultanbekov 1, Ilia Beloglazov 2, * , Shamil Islamov 3and Muk Chen Ong 4


Citation: Sultanbekov, R.;
Beloglazov, I.; Islamov, S.; Ong, M.C.
Exploring of the Incompatibility of
Marine Residual Fuel: A Case Study
Using Machine Learning Methods.
Energies 2021,14, 8422. https://
doi.org/10.3390/en14248422
Academic Editor: Sergei Chernyi
Received: 31 October 2021
Accepted: 9 December 2021
Published: 14 December 2021
Publisher’s Note: MDPI stays neutral
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Copyright: © 2021 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
1Department of Oil and Gas Transport and Storage, Saint Petersburg Mining University,
199106 Saint Petersburg, Russia; Sultanbekov_RR@pers.spmi.ru
2Department of Automation of Technological Processes and Production, Saint Petersburg Mining University,
199106 Saint Petersburg, Russia
3
Department of Petroleum Engineering, Saint Petersburg Mining University, 199106 Saint Petersburg, Russia;
Islamov_ShR@pers.spmi.ru
4Faculty of Science and Technology, University of Stavanger, 4036 Stavanger, Norway; muk.c.ong@uis.no
*Correspondence: Beloglazov_II@pers.spmi.ru
Abstract:
Providing quality fuel to ships with reduced SOx content is a priority task. Marine residual
fuels are one of the main sources of atmospheric pollution during the operation of ships and sea
tankers. Hence, the International Maritime Organization (IMO) has established strict regulations for
the sulfur content of marine fuels. One of the possible technological solutions allowing for adherence
to the sulfur content limits is use of mixed fuels. However, it carries with it risks of ingredient
incompatibilities. This article explores a new approach to the study of active sedimentation of
residual and mixed fuels. An assessment of the sedimentation process during mixing, storage, and
transportation of marine fuels is made based on estimation three-dimensional diagrams developed
by the authors. In an effort to find the optimal solution, studies have been carried out to determine
the influence of marine residual fuel compositions on sediment formation via machine learning
algorithms. Thus, a model which can be used to predict incompatibilities in fuel compositions as well
as sedimentation processes is proposed. The model can be used to determine the sediment content of
mixed marine residual fuels with the desired sulfur concentration.
Keywords:
marine residual fuels; mixing fuels; group composition; sedimentation; machine learning
1. Introduction
Greenhouse gas emissions from ships, especially sulfur oxides (SOx), have serious
impacts on human health, the marine environment, and natural resources. Dozens of
countries, including China and the EU, have already announced their readiness to achieve
carbon neutrality on their territory by 2050–2060, i.e., to reduce to zero the difference
between greenhouse gas emissions and their absorption by taking into account the capabili-
ties of the region’s ecosystem. The EU was one of the first to propose a transition to a carbon
neutral economy by 2050 within the framework of the European Green Deal [
1
]. To achieve
the goal of decarbonization and sustainable development of the fuel and energy complex in
Russia, unprecedented legislative measures have been taken [
2
–
6
] by aiming at tax benefits
for domestic majors, and this stimulates research projects aimed at reducing emissions of
harmful gases [
7
–
10
]. The EU has already launched CO
2
emissions quotas, and the EU
Emissions Trading System has begun to operate. Transboundary carbon regulation for the
EU and the US is becoming a way to preserve EU and US marine fuel markets and a part
of protectionist policies. The Russian economy expects a difficult trade-off between the
recognition of global principles of environmental, social, and governance responsibility
and the realities of a carbon-intensive economy. The most exposed to climate impacts will
be oil and various types of fuel. While maintaining the status quo, BP believes [
11
] that the
peak of world oil consumption was already reached in 2019, although OPEC expects it by
2040 [12], and the International Energy Agency after 2030 [13].
Energies 2021,14, 8422. https://doi.org/10.3390/en14248422 https://www.mdpi.com/journal/energies

Energies 2021,14, 8422 2 of 16
In January 2020, the International Maritime Organization (IMO) introduced new
requirements for the sulfur content of marine fuels [
14
]. Therefore, the control of COx
and SOx emissions is a major concern in the maritime industry [
15
,
16
]. As a result, the
allowed sulfur content in marine fuels decreased 7 times, from 3.5 to 0.5 wt. For the period
2007–2012, the IMO also estimated the average annual SOx emissions to be 11.3 million
tons of shipping, representing 13% of global SOx emissions [
17
]. In port cities, ship sulfur
oxide emissions are often the main source of pollution [
18
–
20
]. Moreover, SOx emissions
from ships spread to the atmosphere over several hundred kilometers and contribute to the
degradation of air quality on land, even if they are released into the sea [
21
]. Recently, the
IMO has been actively regulating marine pollution rules and introducing emission control
areas [22,23].
Shipowners must be able to ensure that the sulfur content complies with the sulfur
limits based on existing laws. Currently, there are three technologically feasible solutions to
reduce SOx emissions that can be used by ships, namely the use of liquefied natural gas as
a fuel, the installation of gas scrubbers, and marine residual fuels with low sulfur content.
This article discusses the third method—the use of marine fuel with a sulfur content of up
to 0.5 wt. %.
The refineries in Russia are currently unable to fully provide the new type of fuel,
as this requires considerable financial investment and in some cases is not economically
profitable [
24
,
25
]. Therefore, in order to meet the demand for a new type of marine fuel,
bunker companies are actively engaged in mixed fuels operations to obtain the required
quality indicators. Today there is a sharp increase in the share of mixed fuels for ship
installations. As a result, the risks of the manifestation of fuel incompatibility increase,
causing active sedimentation [26].
In this regard, during storage, transportation, and production, this problem becomes
extremely relevant [
27
–
31
]. The maximum permissible content of the total sediment
potential (TSP) in marine fuels is 0.1 wt. % according to ISO 8217. It should be noted
that there are risks of incompatibility even when mixing the same brand of fuels due to
differences in composition [
32
]. The incompatibility of residual fuels is manifested due
to the occurrence of strong intermolecular interactions, which are caused by a change in
the group composition, as well as a change in the concentration ratio of high-molecular
compounds of residual fuels. All these contribute to the formation of associations of
molecules, volumetric colloidal particles of various shapes and structures [33,34].
We carried out studies to determine stability through the xylene equivalent indicator.
It characterizes the resistance of marine fuel to stratification during storage, transportation
and operation, but exact dependences of the influence of the composition have not been
obtained, since the selected indicator of the xylene equivalent does not allow determining
the degree of sedimentation [35].
Also, based on production and experimental data, we carried out studies of the effect
of aromatic hydrocarbons on the precipitation of asphaltenes. We found that an increase
in the proportion of aromatic hydrocarbons reduces sedimentation. However, the effect
of paraffins on the precipitation of asphaltenes has not been considered; therefore, more
detailed studies in this direction are required [
36
,
37
]. We obtained and substantiated
the dependences of the effect of n-paraffins (from 55 to 70 wt. %) at specific values of
asphaltenes (0.5, 1, 1.5, 2, 2.5, 3, 3.5 wt. %) on the basis of experimental studies [38].
In this article, the task is to expand the possibilities of applying the results obtained
using widely tested methods of machine learning [
39
]. All these make it possible to
determine the risks of incompatibility in the considered range (but not at specific values of
asphaltenes and n-paraffins) with a high level of confidence.
A fairly large set of classification/regression algorithms is tested to choose the most
efficient for the problem to be investigated. The tested methods can be divided into
three families: decision trees, k-nearest neighbors (k-NN), multiple linear regression, and
function of two variables. They are briefly described as follows.

Energies 2021,14, 8422 3 of 16
Braidotti et al. [
40
] applied machine learning methods (such as decision trees, k-NN,
and support vector machine) in their study. Based on their research, the best choice was
represented by package decision trees, which showed very good accuracy for methods
of classifying and defining damaged compartments. To solve other problems, they rec-
ommended giving preference to weighted k-NN, which ensured better accuracy of the
prediction scenario.
Codjo et al. [
41
] used various machine learning methods to identify certain features of
the investigated object degradation. Various methods of controlled learning were applied.
A comparison of classifiers and methods showed that logistics regression and decision
tree approaches were robust binary classification tools with an accuracy of 97.917% and
99.884%, respectively, while the k-NN method cannot provide accurate predictions. Due to
the processing of the results by using modern machine learning methods, it is possible to
expand the application of the results obtained.
Zhang et al. [
42
] performed an experiment to simulate the exhaust emissions from
ships. The sulfur content prediction model has made it possible to effectively predict the
sulfur content in marine fuel oil. The paper discusses the use of a deep neural network to
improve the accuracy of predicting the sulfur content in marine residual fuel.
The literature analysis showed that there is a global problem: approximately 15% of
NOx emissions and 4% to 9% of SO2 emissions are caused by shipping [
43
]. About 70%
of exhaust gases are discharged into the maritime atmosphere at a distance of less than
400 km from the land, causing serious air pollution in coastal areas, especially around
ports with a high flow of cargo [
44
–
48
]. Sulfur contained in marine fuel oil leads to the
formation of large amounts of SO
2
as a result of chemical reactions occurring during engine
operation, and the amount of SO
2
emitted is directly related to the sulfur content in the
marine fuel [
49
]. The tightening of requirements for the sulfur content has shown that the
available knowledge is insufficient, and this direction of research is extremely urgent.
Based on the current state of the problem and possible solution methods, it can
be concluded that the use of machine learning tools for predicting and modeling the
composition of marine fuels is relevant. However, to date, there is no specific method
that allows one to accurately determine the characteristics of incompatibility of fuels. In
addition, the accuracy of using various machine learning methods is highly dependent on
the input data.
The lack of exact dependencies on the influence of the composition of residual fuel
oils on sediment formation due to the manifestation of incompatibility allows us to identify
a gap in the studies. Many researchers limit themselves only to general recommendations,
and this problem has not been fully resolved in any way. Understanding and correct use
of machine learning methods will allow you to develop an effective tool and significantly
improve forecast accuracy.
2. Materials and Methods
Several methods of machine learning have been considered for developing a practical
robust tool, which can be used to determine sediment formation based on the results of
experimental studies of the influence of n-paraffins and asphaltenes on the compatibility of
marine residual fuels.
The first method considered is multiple linear regression. This model is one of the
most important and widely used regression techniques. One of its advantages is the ease
of interpretation of the results.
The mathematical model based on graphs—the decision tree—is considered. This
model defines the decision making process in such a way that every possible decision, the
preceding and subsequent events or other decisions, and the consequences of each final
decision are represented. The decision tree is a well-known non-parametric controlled
algorithm based on binary solutions. Decision trees can be used for both classification and
regression (providing a piecewise approximation of the response function). The decision-
making process takes the form of a tree or graph, starting from a zero vertex and then

Energies 2021,14, 8422 4 of 16
moving from one vertex to another according to the predictors’ values of the predictors
(the leaves are the predicted answer). A typical decision tree structure is shown in
Figure 1
.
Starting with the route, decisions are made from two possible directions according to the
value of one predictor xj. A similar process is performed in each passed node along with
the tree structure until a decision-by-decision sheet corresponding to the answer class
is reached.
Energies 2021, 14, x FOR PEER REVIEW 4 of 16
regression (providing a piecewise approximation of the response function). The decision-
making process takes the form of a tree or graph, starting from a zero vertex and then
moving from one vertex to another according to the predictors’ values of the predictors
(the leaves are the predicted answer). A typical decision tree structure is shown in Figure
1. Starting with the route, decisions are made from two possible directions according to
the value of one predictor xj. A similar process is performed in each passed node along
with the tree structure until a decision-by-decision sheet corresponding to the answer
class is reached.
Figure 1. Example of a decision tree.
Decision trees are trained using a dataset that provides relationships between pre-
dictors and responses, simulating the relationship between them. In this paper, a single
decision tree method is adopted by using the Gini Diversity Index as a measure of taking
into account the separation criteria [50]. All predictors are tested in each node to select one
that maximizes the benefit of the separation criterion.
The k-NN method is also used to solve the classification problem. It assigns objects
to a class that belongs to most of k of its nearest neighbors in a multidimensional feature
space. The number k is the number of neighboring objects in the feature space that are
compared with the classified object. In other words, if k = 4, then each object is compared
with four neighbors. The method is widely used in Data Mining technologies.
This algorithm can be divided into two simple phases: learning and classification.
During training, the algorithm remembers the observation feature vectors and their class
labels (i.e., examples). Also, the algorithm parameter k is set, which sets the number of
“neighbors” that will be used in the classification. During the classification phase, a new
object is presented for which no class label has been set. The k-nearest preliminary classi-
fied observations are determined for it. Then a class is selected to which most of the k-
nearest neighbor examples belong, and the object being classified belongs to the same
class [51] (Figure 2).
Figure 1. Example of a decision tree.
Decision trees are trained using a dataset that provides relationships between pre-
dictors and responses, simulating the relationship between them. In this paper, a single
decision tree method is adopted by using the Gini Diversity Index as a measure of taking
into account the separation criteria [
50
]. All predictors are tested in each node to select one
that maximizes the benefit of the separation criterion.
The k-NN method is also used to solve the classification problem. It assigns objects
to a class that belongs to most of k of its nearest neighbors in a multidimensional feature
space. The number k is the number of neighboring objects in the feature space that are
compared with the classified object. In other words, if k = 4, then each object is compared
with four neighbors. The method is widely used in Data Mining technologies.
This algorithm can be divided into two simple phases: learning and classification.
During training, the algorithm remembers the observation feature vectors and their class
labels (i.e., examples). Also, the algorithm parameter k is set, which sets the number
of “neighbors” that will be used in the classification. During the classification phase, a
new object is presented for which no class label has been set. The k-nearest preliminary
classified observations are determined for it. Then a class is selected to which most of the
k-nearest neighbor examples belong, and the object being classified belongs to the same
class [51] (Figure 2).
The circle on Figure 2represents the object that needs to be classified into one of the
two classes “triangles” and “squares”. If we choose k = 3, then out of the three nearest
objects, two will turn out to be “triangles” and one “square”.
The Python programming language is used to implement the aforementioned methods.
In addition, to solve the problem, the mathematical method of finding a function of two
variables by approximation in the Matlab program is employed.

Energies 2021,14, 8422 5 of 16
Energies 2021, 14, x FOR PEER REVIEW 5 of 16
Figure 2. K-NN representation [51].
The circle on Figure 2 represents the object that needs to be classified into one of the
two classes “triangles” and “squares”. If we choose k = 3, then out of the three nearest
objects, two will turn out to be “triangles” and one “square”.
The Python programming language is used to implement the aforementioned meth-
ods. In addition, to solve the problem, the mathematical method of finding a function of
two variables by approximation in the Matlab program is employed.
3. Results
In the present study, marine residual fuels of the following grades are used:
● Sample No.1—Compound oils grade A type 1(KMC).
● Sample No.2—Fuel for TSU-80 marine installations (RMD-80).
● Sample No.3—Fuel for TSU-380 marine installations (RMG-380).
● Sample No.4—Residual oil fuel M-100, low ash (RK-700).
The main physical and chemical indicators of the fuels have been determined, which
are presented in Table 1.
Table 1. Quality indicators of residual fuels [38].
No.
Indicator Name
Unit of Measurement
Regulation of the
Test Method
Result
Sample
No.1
Sample
No.2
Sample
No.3
Sample
No.4
1
Density at 15 °C
kg/m3
ISO 12185
833.5
901.0
956.0
976.0
2
Kinematic viscosity at 50 °C
mm2/s
GOST 33
ISO 3104
12.1
34.5
321.5
680.1
3
Flashpoint PMCC
°C
GOST R EN
ISO 2719
181.0
110.0
98.0
110.0
4
Sulfur mass fraction
%
GOST R 51947
ISO 8754
0.004
0.046
1.276
2.668
5
Pourpoint
°C
ASTM D 6749
26.0
10.0
16.0
20.0
Figure 2. K-NN representation [51].
3. Results
In the present study, marine residual fuels of the following grades are used:
•Sample No.1—Compound oils grade A type 1(KMC).
•Sample No.2—Fuel for TSU-80 marine installations (RMD-80).
•Sample No.3—Fuel for TSU-380 marine installations (RMG-380).
•Sample No.4—Residual oil fuel M-100, low ash (RK-700).
The main physical and chemical indicators of the fuels have been determined, which
are presented in Table 1.
Table 1. Quality indicators of residual fuels [38].
No. Indicator Name Unit of
Measurement
Regulation of the
Test Method
Result
Sample
No.1
Sample
No.2
Sample
No.3
Sample
No.4
1 Density at 15 ◦Ckg/m3ISO 12185 833.5 901.0 956.0 976.0
2Kinematic
viscosity at 50 ◦Cmm2/s GOST 33
ISO 3104 12.1 34.5 321.5 680.1
3 Flashpoint PMCC ◦CGOST R EN
ISO 2719 181.0 110.0 98.0 110.0
4Sulfur mass
fraction %GOST R 51947
ISO 8754 0.004 0.046 1.276 2.668
5 Pourpoint ◦C ASTM D 6749 26.0 10.0 16.0 20.0
6Mass fraction of
water %GOST R 51946
ISO 3733 – – 0.05 0.1
7Total sediment
accelerated (TSA) %GOST R 50837.6
ISO 10307-2 0.01 0.01 0.02 0.03
8Total sediment
potential (TSP) %GOST R 50837.6
ISO 10307-2 0.01 0.01 0.02 0.04

Energies 2021,14, 8422 6 of 16
Using SARA analysis, the group composition of the presented fuels was deter-
mined (Table 2), after which the fuel mixtures were prepared according to the experiment
plan [38,44].
Table 2. Analysis of the hydrocarbon group composition of fuel samples [38].
Fuel
Samples
Asphaltenes,
% wt.
n-Alkanes,
% wt.
Isoalkane,
% wt.
Naphthenes,
% wt.
Alkenes,
% wt.
Aromatic
Hydrocarbons,
% wt.
Resins,
% wt.
No.1 – 71.93 18.35 2.62 5.55 1.55 –
No.2 – 38.68 55.09 4.95 – 1.28 –
No.3 2.53 54.14 22.74 5.43 0.57 14.12 0.47
No.4 7.15 51.15 20.71 4.37 0.41 15.70 0.51
Seven series of laboratory tests have been carried out based on the method proposed
by the authors [
52
] to determine the compatibility and stability of marine residual fuels.
The influence of n-paraffins from 55 to 70 wt. % is determined when the asphaltene content
ranges from 0.5 to 3.5 wt. % with a step of 0.5% and the dependencies shown in Figure 3.
Energies 2021, 14, x FOR PEER REVIEW 6 of 16
6
Mass fraction of water
%
GOST R 51946
ISO 3733
–
–
0.05
0.1
7
Total sediment accelerated
(TSA)
%
GOST R 50837.6
ISO 10307-2
0.01
0.01
0.02
0.03
8
Total sediment potential (TSP)
%
GOST R 50837.6
ISO 10307-2
0.01
0.01
0.02
0.04
Using SARA analysis, the group composition of the presented fuels was determined
(Table 2), after which the fuel mixtures were prepared according to the experiment plan
[38,44].
Table 2. Analysis of the hydrocarbon group composition of fuel samples [38].
Fuel
Samples
Asphaltenes,
% wt.
n-Alkanes,
% wt.
Isoalkane,
% wt.
Naphthenes,
% wt.
Alkenes,
% wt.
Aromatic Hydro-
carbons,
% wt.
Resins,
% wt.
No.1
–
71.93
18.35
2.62
5.55
1.55
–
No.2
–
38.68
55.09
4.95
–
1.28
–
No.3
2.53
54.14
22.74
5.43
0.57
14.12
0.47
No.4
7.15
51.15
20.71
4.37
0.41
15.70
0.51
Seven series of laboratory tests have been carried out based on the method proposed
by the authors [52] to determine the compatibility and stability of marine residual fuels.
The influence of n-paraffins from 55 to 70 wt. % is determined when the asphaltene con-
tent ranges from 0.5 to 3.5 wt. % with a step of 0.5% and the dependencies shown in Figure
3.
Figure 3. Influence of n-paraffins and asphaltenes on the total sediment content.
A total of 112 different fuel mixtures with the required composition are prepared and
laboratory tests are performed to determine the TSP content. Figure 4 shows filters for one
series of tests with an asphaltene content of 0.5 wt. % and n-paraffins from 56 to 70 wt. %,
Figure 3. Influence of n-paraffins and asphaltenes on the total sediment content.
A total of 112 different fuel mixtures with the required composition are prepared and
laboratory tests are performed to determine the TSP content. Figure 4shows filters for one
series of tests with an asphaltene content of 0.5 wt. % and n-paraffins from 56 to 70 wt. %,
as an example [
38
,
52
,
53
]. Even visually, it is possible to determine the incompatibility of
fuel compositions with n-paraffin content of 63 to 70 wt. %, where there is a large amount
of total sediment in the upper filters. Three-dimensional visualization of the obtained
experimental results is shown in Figure 5.

Energies 2021,14, 8422 7 of 16
Energies 2021, 14, x FOR PEER REVIEW 7 of 16
as an example [38,52,53]. Even visually, it is possible to determine the incompatibility of
fuel compositions with n-paraffin content of 63 to 70 wt. %, where there is a large amount
of total sediment in the upper filters. Three-dimensional visualization of the obtained ex-
perimental results is shown in Figure 5.
Asphaltene content 0.5 wt. %
n-Paraffins content
56 wt. %
57 wt. %
58 wt. %
59 wt. %
60 wt. %
61 wt. %
62 wt. %
63 wt. %
64 wt. %
65 wt. %
66 wt. %
67 wt. %
68 wt. %
69 wt. %
70 wt. %
Figure 4. Filters after TSP determination at an asphaltene content of 0.5 wt. %.
A three-dimensional visualization of the present results is presented in Figure 4.
Figure 4. Filters after TSP determination at an asphaltene content of 0.5 wt. %.
A three-dimensional visualization of the present results is presented in Figure 4.
Table 3shows the numerical interpretation of the three-dimensional model due to the
influence of asphaltenes and n-paraffins on sediment formation.

Energies 2021,14, 8422 8 of 16
Energies 2021, 14, x FOR PEER REVIEW 8 of 16
Figure 5. Three-dimensional visualization of the obtained experimental data model on the influence
of n-paraffins and asphaltenes on incompatibility manifestation.
Table 3 shows the numerical interpretation of the three-dimensional model due to
the influence of asphaltenes and n-paraffins on sediment formation.
Table 3. Indicators of the influence of n-paraffins and asphaltenes on sedimentation [38].
n-Paraffins, %
Asphaltenes,%
0.5
1.0
1.5
2.0
2.5
3.0
3.5
55
0.02
0.02
0.02
0.02
0.02
0.02
0.02
56
0.02
0.02
0.02
0.02
0.02
0.02
0.02
57
0.02
0.02
0.02
0.02
0.02
0.02
0.02
58
0.02
0.02
0.02
0.02
0.02
0.02
0.11
59
0.02
0.02
0.02
0.03
0.02
0.05
0.21
60
0.02
0.02
0.02
0.04
0.06
0.12
0.39
61
0.02
0.02
0.04
0.08
0.12
0.33
0.85
62
0.05
0.07
0.09
0.17
0.32
0.65
1.54
63
0.13
0.17
0.22
0.47
0.62
1.28
2.49
64
0.20
0.23
0.35
0.69
1.10
2.22
3.50
65
0.25
0.41
0.62
0.98
1.73
3.08
3.75
66
0.29
0.57
1.01
1.52
2.48
3.19
3.68
67
0.33
0.71
1.19
2.18
2.55
3.25
3.70
68
0.39
0.89
1.59
2.20
2.59
3.22
3.60
69
0.47
1.11
1.56
2.22
2.63
3.22
3.58
70
0.58
1.06
1.54
2.17
2.57
3.17
3.61
Based on the obtained experimental data, it is possible to determine the dependences
of the influence of fuel mixture composition on sedimentation. However, the presented
data only describe dependencies on the specific content of the fuel composition, which is
difficult to apply in practice. Therefore, it is necessary to develop a practical robust tool to
Figure 5.
Three-dimensional visualization of the obtained experimental data model on the influence
of n-paraffins and asphaltenes on incompatibility manifestation.
Table 3. Indicators of the influence of n-paraffins and asphaltenes on sedimentation [38].
n-Paraffins, % Asphaltenes,%
0.5 1.0 1.5 2.0 2.5 3.0 3.5
55 0.02 0.02 0.02 0.02 0.02 0.02 0.02
56 0.02 0.02 0.02 0.02 0.02 0.02 0.02
57 0.02 0.02 0.02 0.02 0.02 0.02 0.02
58 0.02 0.02 0.02 0.02 0.02 0.02 0.11
59 0.02 0.02 0.02 0.03 0.02 0.05 0.21
60 0.02 0.02 0.02 0.04 0.06 0.12 0.39
61 0.02 0.02 0.04 0.08 0.12 0.33 0.85
62 0.05 0.07 0.09 0.17 0.32 0.65 1.54
63 0.13 0.17 0.22 0.47 0.62 1.28 2.49
64 0.20 0.23 0.35 0.69 1.10 2.22 3.50
65 0.25 0.41 0.62 0.98 1.73 3.08 3.75
66 0.29 0.57 1.01 1.52 2.48 3.19 3.68
67 0.33 0.71 1.19 2.18 2.55 3.25 3.70
68 0.39 0.89 1.59 2.20 2.59 3.22 3.60
69 0.47 1.11 1.56 2.22 2.63 3.22 3.58
70 0.58 1.06 1.54 2.17 2.57 3.17 3.61

Energies 2021,14, 8422 9 of 16
Based on the obtained experimental data, it is possible to determine the dependences
of the influence of fuel mixture composition on sedimentation. However, the presented
data only describe dependencies on the specific content of the fuel composition, which is
difficult to apply in practice. Therefore, it is necessary to develop a practical robust tool to
determine the sedimentation activity at different values of n-paraffin and asphaltene in the
ranges considered.
The following methods are considered to process the experimental data for the devel-
opment of the numerical tool:
•linear regression,
•decision tree,
•k-NN,
•finding a function of two variables by approximation.
Using a linear regression model, weights for the parameters xand yare found. Based
on this, a linear regression formula is derived that allows combining the results of all
experiments. The linear regression formula for the parameters analyzed parameters:
z= 0.66673469·x+ 0.20424176·y(1)
The determinant coefficient R2of this formula is 0.772.
Using the machine learning model “decision tree”, it is also possible to achieve a
higher coefficient of determination R
2
= 0.910. In the visualization of the decision tree
model, it can be seen how branches and leaves are divided by parameters and values. This
model can be used to predict other results depending on parameters xand y.
By finding the function of the two variables by approximation, a calculation program
has been developed based on the obtained data, which will make it possible to obtain the
result in a convenient format under certain boundary conditions. The pseudo-programming
Procedure 1 is shown below.
Procedure 1. Approximation of two variables
Input: n, m, data
for i = 1 to ndo
for j=1tomdo
Polyfit()the coefficients of the fifth-order polynomial
Linspace()
Polyval() calculating the ordinates of the approximating polynomial
end for
For each k = Ipolynomialcoefficients by xi
Endfor
In order to define the unknown function of two variables Z = f(X,Y), it is necessary to
construct graphs for known values Y from the data presented as a table. Then construct
the most accurate trend line (5th degree polynomial with approximation value above
R2= 0.990)
. The polynomial trend line in the 4th degree gives less accuracy of the ap-
proximation, and in the 6th degree it is identical, as in the 5th degree. To obtain a more
accurate model, the data range of the corresponding n-paraffin content from 57 to
70 wt. %
is considered. The next step is to determine the coefficients of the polynomial and to create
an equation Z = f(X) for each curve. The following is the function Z = f(X,Y) and the
definition of polynomial coefficients for the function of two variables. Thus, introducing
any values of n-paraffins (X) between 55 and 70 and asphaltenes (Y) between 0.5 and
3.5 makes it possible to define TSP values. The results of the calculations are presented
in Figure 6and Table 4.

Energies 2021,14, 8422 10 of 16
Energies 2021, 14, x FOR PEER REVIEW 10 of 16
Figure 6. Three-dimensional model visualization based on finding the function of two variables by
approximation method.
Table 4. Calculated TSP values obtained from finding a function of two variables by approximation
method.
n-Paraffins, %
Asphaltenes,%
0.5
1.0
1.5
2.0
2.5
3.0
3.5
57
0.020
0.022
0.170
0.003
0.022
0.012
0.061
58
0.024
0.019
0.025
0.064
0.107
0.112
0.059
59
0.013
0.015
0.021
0.041
0.040
0.024
0.128
60
0.012
0.016
0.021
0.014
0.013
0.031
0.418
61
0.030
0.031
0.043
0.039
0.066
0.277
0.956
62
0.070
0.069
0.108
0.155
0.320
0.776
1.679
63
0.124
0.136
0.229
0.373
0.732
1.455
2.467
64
0.186
0.239
0.417
0.689
1.246
2.184
3.181
65
0.247
0.378
0.669
1.076
1.783
2.821
3.689
66
0.299
0.550
0.966
1.491
2.256
3.243
3.909
67
0.344
0.730
1.274
1.873
2.592
3.387
3.836
68
0.391
0.904
1.535
2.149
2.743
3.287
3.576
69
0.460
1.032
1.664
2.230
2.710
3.110
3.386
70
0.587
1.063
1.548
2.016
2.557
3.194
3.701
Based on the k-NN method, a program in Python is developed for calculating the
TSP indicator in the fuel mixture from the results of the received experimental data. The
program Procedure 2 is shown as follows.
Figure 6.
Three-dimensional model visualization based on finding the function of two variables by
approximation method.
Table 4. Calculated TSP values obtained from finding a function of two variables by approximation method.
n-Paraffins, % Asphaltenes,%
0.5 1.0 1.5 2.0 2.5 3.0 3.5
57 0.020 0.022 0.170 0.003 0.022 0.012 0.061
58 0.024 0.019 0.025 0.064 0.107 0.112 0.059
59 0.013 0.015 0.021 0.041 0.040 0.024 0.128
60 0.012 0.016 0.021 0.014 0.013 0.031 0.418
61 0.030 0.031 0.043 0.039 0.066 0.277 0.956
62 0.070 0.069 0.108 0.155 0.320 0.776 1.679
63 0.124 0.136 0.229 0.373 0.732 1.455 2.467
64 0.186 0.239 0.417 0.689 1.246 2.184 3.181
65 0.247 0.378 0.669 1.076 1.783 2.821 3.689
66 0.299 0.550 0.966 1.491 2.256 3.243 3.909
67 0.344 0.730 1.274 1.873 2.592 3.387 3.836
68 0.391 0.904 1.535 2.149 2.743 3.287 3.576
69 0.460 1.032 1.664 2.230 2.710 3.110 3.386
70 0.587 1.063 1.548 2.016 2.557 3.194 3.701
Based on the k-NN method, a program in Python is developed for calculating the
TSP indicator in the fuel mixture from the results of the received experimental data. The
program Procedure 2 is shown as follows.

Energies 2021,14, 8422 11 of 16
Procedure 2. k-NN method
Input: import pandas as pd
from sklearn.neighbors import KNeighborsRegressor
from sklearn.preprocessing import StandardScaler
from sklearn.metrics import r2_score
df = pd.read_csv(‘data.csv’, sep = ‘;’)
X = df[[‘x’, ‘y’]]
z = df[‘z’]
scaler = StandardScaler()Normalized by StandardScaler
X_sc = scaler.fit_transform(X)
model_knn = KNeighborsRegressor(n_neighbors = 4)
model_knn.fit(X_sc, z)
z_pred = model_knn.predict(X_sc)
r2_score(z, z_pred)
x_new, y_newinput new variables
new = scaler.transform([[x_new, y_new]])
model_knn.predict(new)
array([0.02])
df[‘z_pred’] = z_pred
df.to_csv(‘z_pred.csv’, sep = ‘;’, decimal = ‘,’)
To increase the numerical precision, normalization is performed and four neighbors
are taken, i.e., k = 4. With an increase in the coefficient k, the accuracy of calculations will
decrease due to the insufficient data set. The essence of the method is the classification
of objects that belong to a larger number of nearest neighbors in a multidimensional
feature space compared to the object being classified. This method is used in Data Mining
technologies. Mathematically, this method is based on measuring the minimum distance
from the center of the group to each observation (2), for which the length of the vector
is determined:
ai=q(ax−bx)2−ay−by2(2)
By calculating the length of each vector, when entering the values xand y, the value z
is determined by interpolation, based on known data from «neighbors». This model has a
high confidence level in the approximation R2= 0.985.
For a visual comparison with the experimental data, Figure 7shows the three-
dimensional model, and Table 5presents the results of the calculations that are performed
in the developed program.
Table 5. Calculated TSP values from the k-NN model.
n-Paraffins, % Asphaltenes, %
0.5 1.0 1.5 2.0 2.5 3.0 3.5
55 0.020 0.020 0.020 0.020 0.020 0.020 0.020
56 0.020 0.020 0.020 0.020 0.020 0.020 0.042
57 0.020 0.020 0.020 0.020 0.020 0.020 0.042
58 0.020 0.020 0.020 0.020 0.020 0.027 0.090
59 0.020 0.020 0.025 0.042 0.055 0.130 0.390
60 0.027 0.032 0.042 0.080 0.130 0.292 0.747
61 0.027 0.032 0.042 0.080 0.130 0.292 0.747
62 0.055 0.070 0.092 0.190 0.280 0.617 1.317
63 0.157 0.220 0.320 0.577 0.942 1.830 2.820
64 0.217 0.345 0.550 0.915 1.482 2.457 3.355
65 0.217 0.345 0.550 0.915 1.482 2.457 3.355

Energies 2021,14, 8422 12 of 16
Table 5. Cont.
n-Paraffins, % Asphaltenes, %
0.5 1.0 1.5 2.0 2.5 3.0 3.5
66 0.267 0.480 0.792 1.322 1.957 2.940 3.655
67 0.370 0.815 1.337 1.985 2.577 3.240 3.640
68 0.442 0.937 1.470 2.130 2.595 3.237 3.622
69 0.442 0.937 1.470 2.130 2.595 3.237 3.622
70 0.625 0.905 1.697 2.242 2.757 3.320 3.490
Energies 2021, 14, x FOR PEER REVIEW 12 of 16
Figure 7. Three-dimensional visualization based on k-NN.
Table 5. Calculated TSP values from the k-NN model.
n-Paraffins, %
Asphaltenes, %
0.5
1.0
1.5
2.0
2.5
3.0
3.5
55
0.020
0.020
0.020
0.020
0.020
0.020
0.020
56
0.020
0.020
0.020
0.020
0.020
0.020
0.042
57
0.020
0.020
0.020
0.020
0.020
0.020
0.042
58
0.020
0.020
0.020
0.020
0.020
0.027
0.090
59
0.020
0.020
0.025
0.042
0.055
0.130
0.390
60
0.027
0.032
0.042
0.080
0.130
0.292
0.747
61
0.027
0.032
0.042
0.080
0.130
0.292
0.747
62
0.055
0.070
0.092
0.190
0.280
0.617
1.317
63
0.157
0.220
0.320
0.577
0.942
1.830
2.820
64
0.217
0.345
0.550
0.915
1.482
2.457
3.355
65
0.217
0.345
0.550
0.915
1.482
2.457
3.355
66
0.267
0.480
0.792
1.322
1.957
2.940
3.655
67
0.370
0.815
1.337
1.985
2.577
3.240
3.640
68
0.442
0.937
1.470
2.130
2.595
3.237
3.622
69
0.442
0.937
1.470
2.130
2.595
3.237
3.622
70
0.625
0.905
1.697
2.242
2.757
3.320
3.490
4. Discussion
This article considers four methods for processing experimental data and obtaining
a robust tool applicable in practice: linear regression, decision tree, k-NN, and finding the
function of two variables as the approximation. Linear regression showed a low
Figure 7. Three-dimensional visualization based on k-NN.
4. Discussion
This article considers four methods for processing experimental data and obtaining a
robust tool applicable in practice: linear regression, decision tree, k-NN, and finding the
function of two variables as the approximation. Linear regression showed a low confidence
result (R
2
= 0.772), and the decision tree method (R
2
= 0.910) is not reliable enough to
address this issue. Presumably, a larger sample of data is required to construct a more
accurate model based on this method.
The relatively accurate predictions are obtained from the methods to find the function
of two variables by approximation (R
2
= 0.90) and k-NN (R
2
= 0.985). It can be noted that
the performed calculations of the TSP values by the k-NN method have the greatest error
at the boundary maximum values, since neighbors are represented only by groups from
opposite sides relative to the data border in the area of maximum values.
On the contrary, in calculations based on a function of two variables, the largest error is
observed at a low concentration of n-paraffins and simultaneously at the highest asphaltene
values. The trend line is represented by a polynomial function of the 5th degree. Therefore,
the beginning of the dependence has a wave form. The amplitude of polynomial function

Energies 2021,14, 8422 13 of 16
increases with increasing TSP values, so the graph of the function may cross the x-axis. In
order to avoid the occurrence of negative values, the obtained data are taken modulo.
The present results show that it is possible to calculate the incompatibility manifesta-
tion in the mixing of marine residual fuels in practice. Because of the obtained dependences
of the influence of n-paraffins and asphaltenes on the manifestation of incompatibility, it
is possible to reduce the risks in advance when constructing the logistic supply chain of
fuels to marine fuel terminals and tank farms. The present results can be used to create a
numerical model for predicting the sediment content in compounded marine fuels with
the required sulfur content.
The change in the symmetrical position of the three-dimensional surface shown in
Figures 4–6indicates a change in the dependence between asphaltene and n-paraffin
content as well as the corresponding sedimentation. Thus, the asymmetry of the three-
dimensional diagrams is the incompatibility degree of residual marine fuels, showing the
influence of the presented factors on precipitation [54–59].
5. Conclusions
In this study, experiments are performed to determine the physical and chemical
characteristics of the fuels. Measurements of the influence of n-paraffins and asphaltenes
on the total sediment content have been carried out. By analysis of the experimental
results, the main correlations between the composition of the fuel mixture composition
and sedimentation are obtained. Various machine learning methods are used in processing
the data. In this way, a robust tool has been developed to determine the possibility of
incompatibility occurrence in the mixing of various types of marine residual fuels.
The absence of requirements in the international standard ISO 8217 for the content of
asphaltenes in marine residual fuels preserves the risks of incompatibility. In this regard,
active sediment formation can cause not only environmental problems, but technical
problems as well. During the operation of marine engines, a high sediment content can
lead to a breakdown of the entire fuel system and clogging of filters, which is a substantial
threat to normal operation and personnel safety, especially if a breakdown occurs during
navigation far from berths and ports and/or in bad weather conditions. It is proposed to
regulate this parameter. This will allow shipowners and buyers to assess in advance the
risks of incompatibilities and thus maintain fuel quality.
In future studies, it is possible to carry out experiments to determine the sulfur
content of the exhaust gases as well as in the sediment itself, depending on the calculated
incompatibility parameters, to create a model to predict SO
2
concentration in the exhaust
gases of ships. In addition, the deep neural network will be enhanced in order to improve
the accuracy of its predictions and calculations
6. Patents
Method of determining compatibility and stability of fuel mixture components. Avail-
able online: https://new.fips.ru/ofpstorage/Doc/IZPM/RUNWC1/000/000/002/733/7
48/%D0%98%D0%97-02733748-00001/document.pdf (accessed on 23 September 2021).
Program for calculating kinematic viscosity, density, sulfur, and water content for
a mixture of crude oil and petroleum products. Available online: https://new.fips.ru/
ofpstorage/Doc/PrEVM/RUNWPR/000/002/020/613/357/2020613357-00001/document.
pdf (accessed on 23 September 2021).
Author Contributions:
Conceptualization, R.S., I.B. and S.I.; methodology, I.B.; software, R.S. and
I.B.; validation, S.I.; formal analysis, I.B.; investigation, R.S., I.B., S.I. and M.C.O.; resources, R.S.
and I.B.; data curation, R.S. and I.B.; writing—original draft preparation, R.S., I.B. and S.I.; writing—
review and editing, R.S., I.B., S.I. and M.C.O.; visualization, S.I. and M.C.O.; supervision, R.S.; project
administration, R.S. All authors have read and agreed to the published version of the manuscript.
Funding:
The research was performed at the expense of the subsidy for the state assignment in the
field of scientific activity for 2021: FSRW-2020-0014.

Energies 2021,14, 8422 14 of 16
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement: Not applicable.
Acknowledgments:
The authors thank Saint Petersburg Mining University for enabling the labora-
tory experiments. The investigations were carried out using the equipment of the Scientific Center
“Issues of Processing Mineral and Technogenic Resources” and Educational Research Center for
Digital Technology of the Saint Petersburg Mining University.
Conflicts of Interest: The authors declare no conflict of interest.
Abbreviations
GOST Russian government standard
ISO International organization for standardization
IMO International Maritime Organization
k-NN k-nearest neighbors
SARA Saturate, aromatic, resin, and asphaltene
TSA Total sediment accelerated
TSP Total sediment potential
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