Machine Learning Applied to Viscosity Prediction: A Case Study
GIL VERA VICTOR DANIEL
Department of Engineering,
University Catholic Luis Amigó,
COLOMBIA
Abstract: - Viscosity emerges as a physical property of primary importance in the modeling of flow within a
porous medium, as well as in the processes of production, transport, and refining of crude oils. The direct
measurement of viscosity is carried out through laboratory tests applied to samples extracted from the bed of a
well, being these samples characterized by their difficult collection and the considerable time lapse required for
their acquisition. Several techniques have been developed to estimate viscosity, among which the empirical
correlation with Nuclear Magnetic Resonance logs stands out. This study presents a methodology for creating a
representative predictive viscosity model, adapted to specific reservoir conditions, using measurements and
well logs using machine learning techniques, in particular, Support Vector Machines (SVM). It is concluded
that SVM trained with a polynomial kernel (R² = 0.947, MSE = 631.21, MAE = 15.16) exhibits superior
performance compared to SVM trained with linear and RBF kernels. These results suggest that SVMs
constitute a robust machine-learning technique for predicting crude viscosity in this context.
Key-Words: - Forecasting, Gravity, Machine Learning, Nuclear Magnetic Resonance, Oil, Permeability,
Porosity, Regression, Saturation, Viscosity.
Received: July 23, 2023. Revised: October 18, 2023. Accepted: November 19, 2023. Published: December 31, 2023.
1 Introduction
Viscosity, as stipulated in literature, [1],
characterizes the fluid's opposition to shear stress or
flow and holds paramount significance in the
computational representation of engineering
procedures spanning the entirety of the petroleum
sector, encompassing fluid processes from
extraction to the refinement stage. Accurately
estimating the propelling forces driving fluid flow
necessitates the accessibility of viscosity data
contingent on pressure, temperature, and density. As
a result, hydraulic computations pertinent to fluid
production and conveyance systems, as well as flow
simulations within porous media, hinge upon the
capability to prognosticate fluid viscosity under
defined procedural circumstances, [2].
The characteristic under consideration assumes
a pivotal role in formulating and advancing
procedures aimed at recuperating, enhancing, and
refining viscous crude oils. Owing to their elevated
viscosity, these oils encounter notable impediments
in spontaneous migration towards the wellbore,
thereby rendering conventional production
techniques insufficient for their extraction, [3]. By
contrast, normal oils have viscosities of around 1
(cP) to 10 (cP), whereas heavy crudes can exceed
the 1 million (cP) limit in normal circumstances.
Since these crudes make up as much as 70% of the
world's petroleum reserves, specific recovery
techniques have been created for the reservoirs that
contain these oils, which makes viscosity mitigation
tactics necessary, [4].
Viscosity measurements are directly obtained by
the study of crude oil samples that are extracted
from the wellbore, [5]. These samples must be of a
significant caliber to provide timely, accurate, and
useful results for effective manufacturing systems.
Fluid characteristics are altered as a result of the
large temperature and pressure changes that the
reservoir fluids undergo during the collection
process. These differences from in situ conditions
are substantial. The samples are forwarded to labs
for analysis once they are collected. Nevertheless,
this procedure may cause a delay in data
availability, which might impair the capacity to
decide on development plans quickly, [6].
Some other approaches to the assessment of
viscosity include petro-physical Nuclear Magnetic
Resonance (NMR) logging. This method is used for
the thorough assessment of characteristics including
saturation, porosity, and permeability as well as the
characterization of various fluids in geological
formations, regardless of lithology, [7]. The
underlying physical process is the induction of a
magnetic field that drives the fluids in the porous
medium's magnetic cores into action. These cores
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interact, especially with hydrogen cores, to collect
energy and then release it again.
Relaxation periods are defined as the rate at
which the magnetic signals connected to this
energy's re-emission diminish exponentially with
time, [8]. Measurements of oil viscosity and this
degradation pattern have been found to correlate
empirically, [9]. The link between temperature and
hydrogen index is dependent on several factors.
Unfortunately, these relationships do not work well
enough to forecast heavy crude viscosities, [10].
Complex and nonlinear engineering problems
have been solved in the scientific literature by using
Machine Learning techniques including Artificial
Neural Networks (ANN), Support Vector Machines
(SVM), and Linear Regression. These methods have
demonstrated impressive effectiveness in the
modeling of issues with many variables,
nonlinearity, and large amounts of data, [11].
In this study, machine learning—more
particularly, Support Vector Machines—is used to
propose a predictive viscosity model based on
Nuclear Magnetic Resonance logs (SVM). A
database composed of 366 logs was employed,
using API gravity, gas-liquid ratio, sampling depth,
temperature, pressure, and X and Y geographic
coordinates as predictor variables. The target
variable was viscosity (cP). The Python
programming language was employed alongside the
application of the Support Vector Machines (SVM)
Machine Learning methodology.
The subsequent sections of the manuscript are
organized as follows: Section 2 delineates the
problem formulation, Section 3 expounds upon the
theoretical framework, Section 4 outlines the
methodology, and Section 5 details the presentation
and discussion of results. The paper culminates with
a conclusion.
2 Problem Formulation
Viscosity, understood as the resistance of a fluid to
shear stress, [12], is used for the modeling of
engineering processes present in all aspects of the
petroleum industry, [13], from production to the
refining of fluids, [14]. Viscosity values at the given
pressure, temperature, and density are required to
estimate the driving forces for the fluid flow, [15].
Therefore, hydraulic calculations for production and
transport systems, as well as the modeling of flow in
porous flow modeling in porous media depend on
the prediction of the fluid viscosity at the process
conditions, [16].
One of the methods to estimate viscosity is the
Nuclear Magnetic Resonance (NMR), [17], which is
used to estimate properties such as porosity,
permeability, saturation, and characterization of the
different fluids present in the geological formation
independent of lithology, [18]. The physical
principle that governs it consists of an induced
magnetic field that stimulates the magnetic nuclei of
the fluids housed in the porous medium, [19], which
absorb and re-emit energy through interaction with
other nuclei of the fluid components, specifically
hydrogen, [20].
In recent years, complex and non-linear
engineering problems have been solved with
Machine Learning techniques such as Artificial
Neural Networks (ANNs), Support Vector Machines
(SVMs), and Linear Regression, as they have shown
satisfactory performance in modeling satisfactory
performance in the modeling of problems with
multiple variables, non-linear and with large
volumes of information, [21]. For this reason, the
objective of the present research is to develop a
methodology to develop a predictive model of
viscosity from petro-physical logs and viscosity
measurements, by implementing the Machine
Learning workflow.
3 Background
-Reservoir Fluids - Petroleum: petroleum
constitutes a sophisticated amalgamation of diverse
constituents, encompassing various natural
hydrocarbon compounds, organic compounds
containing nitrogen, oxygen, and sulfur,
nonhydrocarbons, and trace quantities of metallic
elements such as nickel, iron, and vanadium, [22].
The composition and characteristics of these fluids
exhibit considerable heterogeneity contingent upon
geological formations, including factors such as
density, viscosity, and volatility.
-Presence in the Reservoir: petroleum manifests
itself within the reservoir as either liquid oil or
natural gas. As crude oil pressure diminishes, light
hydrocarbons and nonhydrocarbons separate from
the liquid oil reservoir fluids, transitioning into a
gaseous phase, [23]. Essentially, natural gas
mixtures comprise light alkanes (ranging from
methane to n-butane) and nonhydrocarbons, such as
nitrogen (N2), carbon dioxide (CO2), hydrogen
sulfide (H2S), helium (He), and trace amounts of
water vapor. Moreover, they may contain minimal
quantities of heavier hydrocarbon components, other
gaseous non-hydrocarbons, and inert gases, [24].
-Importance of Physical Properties in Process
Modeling: the physical properties of petroleum
fluids, irrespective of phase, play a pivotal role in
process modeling. Therefore, it is imperative to
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consider diverse classifications of crude oil, [25].
Notably, a primary classification is based on fluid
volatility, which correlates with specific gravity (°
API) and the quantity of dissolved gas (GOR) under
reservoir conditions. In this context, five types of
reservoir fluids are delineated: black oil, volatile oil,
gas condensate, wet gas, and dry gas, [13].
These crude oils can further be categorized based
on their specific gravity (Table 1) or by their density
and viscosity (Table 2).
Table 1. Crude Oil Typology
Type of crude
oil
Density
(Kg/m³)
°API
Light
< 870
> 31.1
Medium
870 - 920
22.3 – 31.1
Heavy
920 - 1000
10.0 – 22.3
Extra-heavy
> 1000
< 10.0
Table 2. Heavy Crude Oil Classification
Type of crude
oil
Viscosity
(cP)
Density
(Kg/m³)
°API
Light
< 100
< 934
> 20
Heavy
100 - 100000
934 - 1000
10-20
Bitumen
>100000
>1000
< 10
Crude oil typologies are also segregated
according to their extraction method. In this
instance, conventional oils denote light and medium
category oils, characterized by relatively low
viscosities, obtained by traditional recovery
methods. In contrast, unconventional crudes
comprise high-viscosity oils, such as heavy, extra-
heavy, and bituminous oils, or light oils hosted in
very low permeability rock formations, [26].
The hydrocarbon sampling procedure plays a
crucial role in reservoir development decision-
making. Two main approaches for acquiring such
samples stand out: downhole sampling and surface
sampling. The former involves the introduction of
sampling tools through a production test string
(DST), wireline, or tubing to the productive region.
In situations where the well has not been cased or
the hole remains open, sampling can be carried out
using the modular formation dynamics tester
(MDT), [27].
Cased hole sampling incorporates the Cased
Hole Dynamics Tester (CHDT), which seals a pack
against the borehole or casing wall and then presses
a probe against the formation. When pumping is
initiated, the fluid contained in the rock is drawn out
through the probe's intake port. This type of
sampling allows, in general, the preservation of the
sample in conditions as close as possible to those of
the reservoir, [28].
On the other hand, surface sampling is most
often carried out at the separator under stable flow
conditions. It involves the collection of gas and
liquid samples and can be performed throughout the
productive life of the well, [29].
After sample collection, samples are subjected
to a series of laboratory tests for fluid
characterization. Standardized analyses in this
context include composition, density, gas-oil ratio,
saturation pressure, asphaltene stability, and
viscosity, [30]. Viscosity is the resistance of a fluid
to shear stress. In Newton's viscosity law, it is
defined in terms of the velocity gradient () and the
shear stress (xy) as follows:
(1)
The generation of momentum transfer is
attributable to shear stress, and viscosity is defined
as the proportionality constant between the driving
force and the subsequent velocity gradient, [31].
Crude viscosity is evaluated using various
laboratory devices, such as rheometers and
viscometers designed to operate at high pressures. In
addition, the use of other instruments such as
hydrometers, pressure pumps, and temperature
baths, among others, is necessary, [32].
4 Methodology
The dataset consisted of 7 attributes and 366 logs. It
contains, geographic coordinates and depth data,
physicochemical characteristics of the crude oil, and
viscosity tests with its corresponding pressure and
temperature. The dataset used is available in, [33].
Table 3 presents the complete description of the
same.
The CRISP-DM methodology was used to build
the model. Figure 1 shows all the phases that
comprise it, each of them is described below:
- Stage 1 Business Understanding: In this phase,
a comprehensive understanding of the business
objectives is pursued. Critical factors related to the
desired results are identified, the project objectives
are established, and a plan is drawn up that defines
the steps to be followed, the tools and techniques
required, and the success criteria that will determine
the achievement or failure of the proposed
objectives, [34]. Likewise, success criteria are
defined, which will determine the achievement or
failure of the proposed objectives, [35].
- Stage 2 Data Understanding: Data collection,
identification of quality problems in the data, and
obtaining the first relevant knowledge are carried
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out. During this phase, subsets of data of interest for
the formulation of new hypotheses may be
identified, [36].
- Stage 3 Data Preparation: The raw data are
cleaned and converted before the processing and
analysis stage. The final objective of this phase is to
obtain the final data on which the models will be
applied; the universe of data to work with is
established and debugged, [37].
- Stage 4 Modeling: With the data normalized
and cleaned, we proceed to the construction of the
models with the optimal parameters (cross-
validation), [38].
- Stage 5 Evaluation: The performance of the
models built from the performance metrics is
evaluated and the optimal one is selected, [39].
- Stage 6 Implementation: The optimal model
identified in the previous phase is implemented,
either through a graphical user interface or directly
from software (Python, R, Matlab, etc.), [40].
Table 3. Description
Variable
Description
API Gravity
(V1)
Crude oil density indicator at standard
conditions. Samples within the range of
9.9 to 13.8 °API have been
incorporated, covering crudes from
extra-heavy to heavy category.
Gas Oil
Ratio
(V2)
The ratio of the volume of gas released
by the fluid to the volume of oil at
standard conditions (scf/bbl). The data
set contains information from tests on
dead crude and live samples in the
range of 5.3 to 24.8 scf/bbl.
Sampling
Deth
TVDES
(V3)
Vertical depth to sea level of the well in
feet (ft). Samples were obtained in the
depth range of -5329 to -6462 ft.
Viscosity
Test
Temperature
(V4)
Temperature in (°F) at which the
viscosity measurement was performed.
Tests were performed from 140 to 350
ºF.
Viscosity
Test
Pressure
(V5)
Pressure (psi) at which the viscosity
measurement was made. The evaluation
range is 15 to 4015 psi.
Geographic
coordenate
X
(V6)
X east-west geographic coordinate of
the location of the well where the crude
oil sample was obtained.
Geographic
coordenate
Y
(V7)
Geographic Y north-south coordinates
of the location of the well where the oil
sample was obtained.
Viscosity
(V8)
Dynamic viscosity (cP) is measured at
constant temperature and variable
pressure.
Note: All variables are continuous numerical.
Fig. 1: CRISP-DM Methodology
In Machine Learning, the quality and volume of
data influence the accuracy of predictive models. To
guarantee the model's applicability, it is also crucial
to validate the model and understand the findings.
Iterations and tweaks may be necessary in this
procedure based on the validation findings. Since
this study involves regression, the machine learning
(ML) approach of support vector machines with
several kernel types (linear, polynomial, and RBF
radial basis functions) was applied. Equation (2)
presents the general equation for Support Vector
Machines (SVM).
Equations (3), (4), and (5) illustrate the various
kernel types: polynomial, linear, and RBF. The
kernel function is represented by K, the intercept by
b, the dual coefficients by Alphas, and the
optimization parameters by C, γ, r, and d.
(2)
Lineal Kernel
(3)
RBF Kernel
(4)
Polynomial Kernel
d
(5)
5 Results and Discussion
Table 4 depicts the correlation matrix, illustrating
the interrelationships among eight variables denoted
as V1 to V8. The correlation coefficients within the
range of -1 to 1 signify the strength and direction of
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associations, with a value of 1 denoting a flawless
positive correlation, -1 indicating a flawless
negative correlation, and 0 signifying the absence of
correlation.
Table 4. Correlation matrix
V1
V2
V3
V4
V5
V6
V7
V8
V1
1,00
V2
-0,03
1,00
V3
0,04
-0,08
1,00
V4
-0,03
-0,05
0,03
1,00
V5
-0,03
0,09
0,09
0,05
1,00
V6
0,03
-0,02
-0,03
0,14
0,00
1,00
V7
0,06
-0,02
0,04
0,13
0,16
0,12
1,00
V8
-0,04
-0,08
-0,02
-0,02
-0,02
0,04
-0,03
1,00
Note: V1 = API Gravity, V2 = Gas Oil Ratio, V3 =
Samplig Deth TVDES, V4 = Test Temperature, V5 =
Test Pressure, V6 = X, V7 = Y, V8 = Viscosity.
These correlations provide insights into the
linear relationships between pairs of variables. Keep
in mind that correlation does not imply causation
and other statistical methods may be needed for a
more comprehensive analysis.
Table 5 presents the results of the different
trained models, Accuracy, Recall, precision, and F1-
Score metrics were calculated. The fit tests were R²,
MSE, and MAE. The polynomial kernel performed
better than the other two (higher R² and lower MSE
and MAE).
Table 5. Results
Metrics
SVM
Kernel
Lineal
SVM
Kernel
RBF
SVM
Kernel
Polynomial
R²
0.879
0.826
0.947
MSE
1450.51
2088.98
631.21
MAE
25.82
24.15
15.16
The Support Vector Machine (SVM) model
with a polynomial kernel has shown a remarkably
superior performance in terms of fit metrics
compared to other models evaluated. This finding
implies that the complexity and nonlinear
interactions seen in the examined data have been
well captured by the kernel selection.
6 Conclusion
There is a clear relationship of viscosity concerning
temperature, viscosity decreases critically with
increasing temperature, but concerning depth
viscosity increases. This is because the change in
viscosity at reservoir conditions responds more to a
change in fluid density than to in-situ temperature.
Viscosity information is dependent on many
other characteristics apart from geographical
position and depth. For future research, it is
suggested that more information is suggested to
correlate viscosity behavior with more chemically
influential characteristics.
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_US
WSEAS TRANSACTIONS on COMPUTERS
DOI: 10.37394/23205.2023.22.31
Gil Vera Victor Daniel
E-ISSN: 2224-2872
283
Volume 22, 2023
