Application of deep learning and random forest algorithms in a machine learning-based well log analysis for a small data set of a sand zone
PETROLEUM EXPLORATION & PRODUCTION
PETROVIETNAM JOURNAL
Volume 6/2020, pp. 4 - 14
ISSN 2615-9902
APPLICATION OF DEEP LEARNING AND RANDOM FOREST
ALGORITHMS IN A MACHINE LEARNING-BASED WELL LOG
ANALYSIS FOR A SMALL DATA SET OF A SAND ZONE
Ruwantha Ratnayake1, Pham Huy Giao1,2
1Asian Institute of Technology (AIT)
2Vietnam Petroleum Institute (VPI)
Email: hgiao@ait.asia/giaoph@vpi.pvn.vn
Summary
Artificial intelligence (AI) and machine learning (ML) have the potential to reshape the oil and gas exploration and production
landscape. Once viewed as a promising novelty, AI and ML are not far away from becoming mainstream for all exploration and production
companies. Earlier many researchers have worked on using intelligent analyses such as Artificial Neural Network (ANN), deep learning
(DL), Fuzzy, Genetic Algorithm (GA) in well log interpretation, which are supposed to be effective for large data sets. Random forest (RF)
algorithm so far has not been much applied for well log analysis. In this research, a code in Python language was developed for DL and
RF analyses for well log interpretation. To highlight the advantages of the RF-based well log analysis we applied the new code for a small
data set over a 50 m depth zone consisting of clay and sand zones.
Porosity, permeability and water saturation of the reservoir zone were predicted by the RF analysis, compared with those obtained
by the DL analysis and validated with the core measurements. It was found that there is a significant improvement in the analysis running
time and the accuracy of the RF-predicted well log answers compared to those results by DL analysis. It is therefore recommended that
more applications of RF-based well log analysis be done for clastic reservoirs in Vietnam in the future.
Key words: Machine learning (ML), Python, random forest (RF), well log analysis, sand reservoir.
1. Introduction
RF is a classifier that evolves from decision trees. To
The RF algorithm is a supervised learning model, it uses
labelled data to “learn” how to classify unlabelled data.
The RF algorithm is used to solve both regression and
classification problems, making it a diverse model that is
widely used by engineers [1].
classify a new instance, each decision tree provides a
classification for input data; RF collects the classifications
and chooses the most voted prediction as the result. The
inputofeachtreeissampleddatafromtheoriginaldataset.
In addition, a subset of features is randomly selected from
the optional features to grow the tree at each node. Each
tree is grown without pruning. Essentially, RF enables a
large number of weak or weakly-correlated classifiers to
form a strong classifier.
1.1. Earlier developments to RF
Ho proposed a method to overcome a fundamental
limitation on the complexity of decision tree classifiers
derived with traditional methods [2]. Such classifiers
cannot grow to arbitrary complexity without sacrificing
the generalisation accuracy on unseen data.The proposed
method uses oblique decision trees which are convenient
for optimising training set accuracy. The essence of the
method is to build multiple trees in randomly selected
subspaces of the feature space. The trees generalise their
classification in complementary ways, and their combined
classification can be monotonically improved.
The RF algorithm is composed of different decision
trees, each with the same nodes, but using different data
that leads to different leaves. It merges the decisions
of multiple decision trees in order to find an answer,
which represents the average of all these decision trees.
Amit and Geman proposed a shape recognition
approach based on the joint induction of shape features
Date of receipt: 22/11/2019. Date of review and editing: 22/11 - 24/12/2019.
Date of approval: 5/6/2020.
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and tree classifiers [3]. Because of virtually infinite number
of features, they reached the conclusion that no classifier
based on the full feature set could be evaluated as it was
impossible to determine a priori whose features were
informative. Due to the number and nature of features,
standard decision tree construction based on a fixed
length feature vector was not feasible. An alternative
approach would be to entertain a small random of
sample features at each node, constrain their complexity
to increase with tree depth, and grow multiple trees.
Terminal nodes contain estimates of the corresponding
posterior distribution over shape classes. By sending the
image down and aggregating the resulting distribution,
the image can be classified.
majority voting where each classifier casts one vote for its
predicted class label, then the class label with the most
votes is used to classify the instance.
Decision tree: Figure 1 shows a schematic decision tree
that is a structure used in decision making process. This
structure starts with a root node, which then branches to
another decision node, repeating this process until a leaf
is reached. A node asks a question in order to help classify
the data. A branch represents the different possibilities
that this node could lead to.
Some of the basic terminology related to decision
trees are given below:
Root node: It represents entire population or
sample and this further gets divided into two or more
homogeneous sets.
In another paper by Ho [4], he proposed a method
to solve the dilemma between overfitting and achieving
maximum accuracy. This was done by constructing
a decision-tree-based classifier that maintained the
highest accuracy on training data and, at the same
time, improved on generalisation accuracy as it grows
in complexity. The classifier consisted of multiple
trees constructed systematically by pseudo-randomly
selecting subsets of components of the feature vector,
that is, trees constructed in randomly chosen subspaces.
When empirically tested against publicly available data
sets, the subspace method proved its superiority when
compared to single-tree classifiers and other forest
construction methods. The next section introduces RF
which is an ensemble method that combines existing
techniques in order to construct a collection of decision
trees with controlled variation.
Splitting: It is a process of dividing a node into two or
more sub-nodes.
Decision node: When a sub-node splits into further
sub-nodes, then it is called decision node.
Leaf node: Node which does not split is called leaf or
terminal node.
Pruning: When a sub-node of a decision node is
removed, this process is called pruning. It is the opposite
process of splitting.
Branch/Sub-tree: A sub section of an entire tree is
called branch or sub-tree.
Parent and Child node: A node, which is divided into
sub-nodes is called parent node of sub-nodes whereas
sub-nodes are the child of parent node.
1.2. RF algorithm
Splitting decision trees: Breiman. [5] introduced
additional randomness during the construction of
RF is an ensemble learning method used for
classification and regression. Developed by Breiman
[5], the method combines Breiman’s bagging sampling
approach [6] and the random selection of features,
introduced independently by Ho [2, 4] and Amit and
Geman. [3], in order to construct a collection of decision
trees with controlled variation. Using bagging, each
decision tree in the ensemble is constructed using a sample
with replacement from the training data. Statistically, the
sample is likely to have about 64% of instances appearing
at least once in the sample. Instances in the sample are
referred to as in-bag instances, and the remaining instances
(about 36%) are referred to as out-of-bag instances. Each
tree in the ensemble acts as a base classifier to determine
the class label of an unlabelled instance. This is done via
Root
Node
Branches
Decision
Node
Decision
Node
Branches
Branches
Leaf
Node
Leaf
Node
Leaf
Node
Leaf
Node
Figure 1. Decision tree.
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decision trees using the classification and regression trees
(CART) technique. Using this technique, the subset of
features selected in each interior node is evaluated with
the Gini index heuristics. The feature with the highest Gini
index is chosen as the split feature in that node. Gini index
has been introduced by Breiman et al. [7]. However, it has
been first introduced by the Italian statistician Corrado
Gini in 1912.The index is a function that is used to measure
the impurity of data, i.e. the uncertainty of the data. In
classification, this event would be the determination of
the class label [8]. The general form of Gini index is shown
below:
needs to be done. The data does not need to be rescaled
or transformed.
- Parallelable: They are parallelisable, meaning that
we can split the process to multiple machines to run. This
results in faster computation time. Boosted models are
sequential in contrast and would take longer to compute.
- Quick prediction/training speed: It is faster to train
than decision trees because we are working only on a
subset of features in this model, so we can easily work
with hundreds of features. Prediction speed is significantly
faster than training speed because we can save generated
forests for future uses.
(1)
( )
= 1 −
- Handles unbalanced data: RF methods for
balancing error in class population unbalanced data sets.
RF tries to minimise the overall error rate, so when we have
an unbalanced data set, the larger class will get a low error
rate while the smaller class will have a larger error rate.
Where: Gini is the Gini index; pi is the probability of
an object being classified to a particular class; c is the
number of unique labels.
Breiman [5] showed that the RF error rate depends
on correlation and strength. Increasing the correlation
between any two trees in the RF increases the forest
error rate. A tree with a low error rate is a strong classifier.
Increasing the strength of the individual trees decreases
the RF error rate. Such findings seem to be consistent with
a study made by Bernard et al. [9], which showed that the
error rate statistically decreases by jointly maximising the
strength and minimising the correlation.
- Low bias, moderate variance: Each decision tree
has a high variance, but low bias. However, because we
average all the trees in RF, we are averaging the variance
as well so that we have a low bias and moderate variance
model [1].
1.4. General applications of RF algorithm
There are several sectors where the RF can be applied
as listed below:
1.3. Advantages of RF
Banking sector: The banking sector consists of most
users. There are many loyal customers and also fraud
customers. RF analysis can be used to determine whether
the customer is a loyal or a fraud. A system uses a set of
RF, which identifies the fraud transactions by a series of
the pattern.
Key advantages of RF are robustness to noise and
overfitting [5, 10]. Overfitting generally occurs when a
model is constructed in such a way that it fits the data
more than it is warranted. A model which has been overfit
will generally have poor predictive performance, as it does
not generalise well. By generalisation we mean how well
the model will make predictions for cases that are not in
the training set. Hawkins pointed out that overfitting adds
complexity to a model without any gain in performance
or, even worse, leads to poorer performance [11]. A
classifier that suffers from overfitting is likely to have a low
error rate for the training instances (in-bag instances), and
a higher error rate for the out-of-bag instances.
Medicines: Medicines needs a complex combination
of specific chemicals. Thus, to identify the great
combination in the medicines, RF can be used. With the
help of machine learning algorithm, it has become easier
to detect and predict the drug sensitivity of a medicine.
Also, it helps to identify the patient’s disease by analysing
the patient’s medical record.
Stock market: Machine learning also plays role in
the stock market analysis. When it is needed to know
the behaviour of the stock market, with the help of RF
algorithm, the behaviour of the stock market can be
analysed. Also, it can show the expected loss or profit which
can be produced while purchasing a particular stock.
Other advantages of RF can be listed as follows:
- High versatility: Whether the task is regression or
classification, RF is an applicable model for all the needs.
It can handle binary features, categorical features, and
numerical features. There is very little pre-processing that
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Applications of RF algorithm in oil & gas: In a research
done by Chen, he successfully applied ML methods to
predict well productivity and design hydraulic fracturing
parameters in Montney and Duvernay Formations. He
found out that ensemble models such as RF and ExBoost
seem to outperform other types of ML methods (SVM,
ANN) with a higher prediction accuracy [12].
Where: SST is the total variation in the data (sum of
squared total), SSR is the sum of squares regression, yi is
the y value for observation i, is the mean of y values and
is the predicted values of y for observation I, and R2 is
the correlation coefficient.
1.6. Transfer functions
Transfer function is an algorithm process to transfer
weighted sum to the hidden layers and the output layer.
Thetransferfunctionischosentosatisfysomespecification
of the problem that neural network is attempting to solve.
1.5. Grid search method in ML
Grid search is the process of performing hyper
parameter tuning in order to determine the optimum
values for a given model. This is significant as the
performance of the entire model is based on the hyper
parameter values specified. ‘GridSearchCV’ in the sklearn
library of Python is a method which calculates a score
for different hyper parameter combinations based on
accuracy (R2 score), network building time and running
time of the module. The combination which has the R2
highest score is selected as the optimum combination.
The R2 score is calculated by Equations (2 - 4).
2. Methodology
The general workflow adopted in this study is
explained in Figure 2.
2.1. Data collection and preparing the training input
data
The published data set used in this study is taken from
Darling [13] for a clastic reservoir located from 616 to 675
m deep. The well log data consist of gamma ray (GR), deep
resistivity (LLD), sonic (DT), density (RHOB), and neutron
porosity (NPHI). A part of the well data from 616 to 631 m
was used as training data, while the part of well log data
from 631 to 675 m was used for prediction. The target
effective porosity (Φe) was calculated based on density
(ΦD) and neutron (ΦN) porosity as shown in Equations (5)
and (6) [14]:
(2)
(3)
(4)
=
=
(
(
−
−
)
)
=
Table 1. Common transfer functions used in neural networks (ANN and DL analyses)
ꢆctiꢃation function
ꢅꢄuation
ꢂeriꢃatiꢃe
1ꢂ ꢁraꢀh
Linear
( ) =
′( ) = 1
0,
0.5,
1,
< 0
= 0
> 0
Unit step (Heaviside
function)
( )
( )
=
=
′( ) = 0
′( ) = 0
− 1,
0,
1,
< 0
= 0
> 0
Sign (Signum)
1
Logistic (Sigmoid)
′( ) = ( )(1 − ( ))
′( ) = 1 − ( )
( ) =
( ) =
1 +
−
+
Hyperbolic tangent (tanh)
ReLu
0,
< 0
> 0
0,
1,
< 0
> 0
( )
( )
=
=
′
,
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Start
Well log data collection [13]
Develop the DL module
using Python
Develop the RF module
using Python
WL interpretation and
preparation of training data
Run machine learning analysis (DL & RF) and compare
the results
Figure 2. Workflow of the study.
Table 2. Well log-calculated and core petrophysical parameters
ꢄoroꢅitꢆ
ꢉalculated
ꢄermeaꢇilitꢆ ꢂmꢀꢃ
ꢉore ꢉalculated
ꢈater ꢅaturation
ꢀeꢁth ꢂmꢃ
ꢉore
0.02
0.02
0.1105
0.01
0.095
0.156
0.15
0.075
0.105
0.06
0.179
0.156
ꢉalculated
1.0
620.116
622.097
624.078
626.059
628.040
630.022
632.003
634.136
636.118
638.099
640.080
642.061
0.03
0.022
0.11
0.014
0.091
0.16
0.13
0.1
0.08
0.04
0.16
0.155
0.01
0.02
22
0.11
0.05
10.1
1.0
0.042
0.74
0.036
0.018
0.022
0.035
0.04
0.03
10.5
135.6
120
11
0.029
7.12
201.12
68.45
8.27
15.3
0.8
5.42
0.16
1.0
0.025
0.046
350
130
482.71
218.9
−
−
(5)
(6)
=
=
+
2
Where: ρm is the matrix density (g/cc) and is equal to
2.65 g/cc in this case for sandstone, ρ is bulk density (g/
cc), ρf is fluid density (g/cc), ΦD is density porosity, ΦN is
neutron porosity and Φe is effective porosity.
The water saturation of training data set was
calculated using Simandoux (1963)’s method as shown in
Equation (7). Simandoux equation was used because the
zone of analysis includes shaly sand intervals.
×
×
×
5
×
0.4
Figure 3. Calculated petrophysical parameters vs core values.
×
(7)
=
+
−
×
To determine permeability a poro-perm relationship
was developed based on Equation (8) using the core data.
Where: Φ is effective porosity, Rw is resistivity of
water, Vsh is shale volume, Rt is formation resistivity, Rsh
is resistivity of shale, a is an empirical constant and m is
cementation exponent.
(8)
k = 10(k + k × Φ )
a
b
e
Using core porosity and permeability values ka and
kb were determined as -2 and 28.04 respectively. The core
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measurements for this case study are represented in Table 2. The calculated
petrophysical parameters as mentioned above are plotted versus the core
values in Figure 3 that show a very good match.
2.3. Developing the RF module
The RF module was developed with
multiple number of decision trees and
also coded in Python programming
language as explained in Section 2.4. The
flowchart of the Python code is shown
in Figure 5. Normally in RF, the accuracy
of the predicted results changes with
the number of decision trees used.
Therefore, in this case the trial and error
method was used to find the optimum
number of decision trees to get the most
accurate results.
2.2. Developing the DL module
DL could be usefully applied in well log analysis as indicated in a
research by Giao and Sandunil [15]. Figure 4 shows the architecture of
the DL network used in this study, which has three main layers, namely,
input layer, hidden layer(s) and output layer. Input values of each hidden
layer is multiplied by a certain weight and the summation is introduced
to a transfer function assigned to each neuron. Training of an DL network
is done using training examples. Grid search method which is an inbuilt
function of sklearn library was used to find out the optimum hyper
parameters for this data set. In this a total of 960 combinations were
tested by varying the number of hidden layers from 1 to 50, neurons from
5 to 100, learning rate from 0.0001 to 0.1 and the transfer function being
linear, unit step, sign, Sigmoid, tanh and Relu. Table 3 shows the best
combination of hyper parameters which had the highest score that was
used in DL code.
2.4. Coding and running the DL and RF
modules in Python language
Python programming language
was used in developing both the
modules due to its ease to learn and the
availability of vast amount of machine
learning libraries. Number of standard
libraries were used as shown in Table 4
in developing the codes.
Table 3. The best combination of hyper parameters
ꢀꢁꢂer ꢂarameter
Gridsearch R2 score
Number of hidden layers
Neurons per hidden layer
Learning rate
ꢃeꢄult
0.952
50
100
An illustration of the Python codes
for DL and RF analysis is shown in Tables
5 & 6. The Python package manager
used in this study was Anaconda.
Anaconda is a free and open-source
distribution of the Python programming
language for scientific computing (data
science, machine learning applications,
large-scale data processing, predictive
analytics, etc.), that aims to simplify
package management and deployment.
In order to create the code Jupyter
Notebook was used [16], which is an
open-source web application that
allows to create and share documents
that contain live code, equations,
visualisations and narrative text.
0.0001
1000
ReLu
Number of iterations
Activation function
Figure 4. Architecture of the DL network employed in this study.
Split the
imported data
into training,
testing,
Build
multiple
decision
trees using
the training
Import the
target data set
and predict
well log results
using trained
Import
machine
learning
libraries and
training data
Compute the
R2 score
between
predicted and
actual well log
validation and
Figure 5. Flowchart of the Python code created for RF module.
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Table 4. Libraries used in the code
ꢀodule
ꢁiꢂrarꢃ
Pandas
Matplotlib
Keras
Sklearn
Pandas
ꢄurꢅoꢆe
Import training and predicting data sets
Plotting the ꢀnal interpretation plots
DL
RF
Building the neural network with desired hyper parameters
Splitting and scaling the training data, calculating the R2 score
Import training and predicting data sets
Matplotlib
Sklearn
Plotting the ꢀnal interpretation plots
Scale the training data and building random decision trees by using training data set
Table 5. Structure of Python codes for DL module
Taꢀk
ꢁꢂthon code
Importing libraries
Building the neural network
Training the network
Testing and validating the network
Running the module for predicting data set and
saving the output
Table 6. Structure of Python codes for RF module
ꢁꢂthon code
Taꢀk
Importing libraries
Splitting the data into training, testing
and validation
Creating decision trees
Training phase
Testing, validating phase
Running the module for predicting data
set and saving the output
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Figure 6. Well log curves [13].
Table 7. Log responses and answers interpreted for the zoned layers at the study location [13]
Log Responses
Log Answers
Shale Density Eꢀective Water
volume porosity porosity Saturation
Depth
Zone Lithology interval
(m)
GR
RHOB
PHIN
LLD
(Ω.m)
Permeability
(mD)
(API) (g/cc)
(Vsh )
0.67
0.17
0.65
0.15
0.52
(ФD)
0.01
0.19
0.10
0.15
0.04
(
)
(Sw)
0.85
0.05
0.08
0.18
0.65
Фe
01
02
03
04
05
Shale
Sand
Shale
Sand
616-624
624-637
637-639
639-655
90
35
88
33
74
2.63
2.50
2.60
2.45
2.55
0.07
0.065
0.04
0.09
0.12
11
8
15
2
0.04
0.13
0.07
0.12
0.08
1.83
61.39
104.52
186.29
215.5
Shaly sand 655-668
15
3. Results and discussion
for the public data set were done using both DL and RF
modules developed, and the results are presented in
Figures 7 and 8.
The collected log curves and data, taken from Darling
[13], are shown in Figure 6 and Table 7.
As shown in Table 8, the R2 scores were calculated for
each training, testing and predicting phase and compared
Results from developed Python modules: Analyses
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between two machine learning techniques
that were used in this study, i.e., DL and RF.
It was also observed that the running
time of the RF analysis is significantly lower
compared to that taken by DL module to run
as seen in Table 8 and Figure 9b.
4. Conclusions and recommendations
In this study, two machine learning-
based analysis modules, i.e. DL and RF, were
developed using Python programming
language to perform well log analysis. These
two modules were tested on a small size
public data set of a clastic reservoir [9] and
the accuracy of the results was compared. The
following concluding remarks could be drawn:
Figure 7. Results for the DL module.
- Based on a conventional well log
interpretation on the study data set taken
from Darling [13] a main sand reservoir zone
from 639 to 655 m was identified with an
average effective porosity (ФD+N) of 0.125,
permeability (K) of 123.84 mD, and water
saturation (Sw) of 0.18 that match well with the
core measurements values, i.e. Фcore = 0.13 and
Kcore = 149.24 mD.
- A number of DL analyses were
conducted by varying the hyper parameters,
i.e. number of hidden layer ranges from 1 to
50, number of neuron per hidden layer varies
from 5 to 100, the learning rate varies from
0.0001 to 0.1, and the transfer function being
linear, unit step, sign, Sigmoid, tanh and ReLu
in both input and output layers. A total of 960
DL analyses have been run, out of which the
best analysis was found to be the one having
50 hidden layers, 100 neurons per hidden layer,
learning rate of 0.0001 and the ReLu transfer
function that gave an average porosity of
0.124, permeability of 112.14 mD and water
saturation of 0.14.
Figure 8. Results from RF module.
Table 8. R2 scores for DL and RF modules
Running time
(sec)
2
R score
Well log
answer
Data set
DL
RF
DL
RF
Training
Testing
0.999
0.989
0.904
0.954
0.845
0.754
0.995
0.932
0.786
0.997
0.984
0.939
0.989
0.980
0.894
0.994
0.975
0.997
Porosity
91
3
Predicting
Training
Testing
Water
Saturation
98
5
- Similarly, a number of RF analyses
were run, varying the number of trees from
1 to 10, out of which the analysis with 6 trees
was found the best RF analysis that gave an
average porosity of 0.126, permeability of
122.15 mD and water saturation of 0.19.
Predicting
Training
Testing
Permeability
97
4
6
Predicting
Average
0.814
0.943
95.3
- By comparing the results predicted by
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(a)
(b)
Figure 9. Comparison of (a) R2 score of the predicting phase from two modules, (b) running time of the modules.
DL and RF analyses it was found that those by RF analyses
are better than those predicted by DL analysis (Table 8
and Figure 9a), i.e. better R2 and shorter running time. For
example, the average running time is 6s for RF and 95.3s
for DL, respectively.
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forest-algorithm-for-machine-learning-c4b2c8cc9feb.
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predicting (Table 8).
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hyper parameters have to be tested, i.e. number of hidden
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