A parametric study of machine learning techniques in petroleum reservoir permeability prediction by integrating seismic attributes and wireline data

Accepted Manuscript A parametric study of machine learning techniques in petroleum reservoir permeability prediction by integrating seismic attributes and wireline data Fatai Anifowose, Abdulazeez Abdulraheem, Abdullatif Al-Shuhail PII:

S0920-4105(19)30124-X

DOI:

https://doi.org/10.1016/j.petrol.2019.01.110

Reference:

PETROL 5754

To appear in:

Journal of Petroleum Science and Engineering

Received Date: 7 September 2018 Revised Date:

29 January 2019

Accepted Date: 30 January 2019

Please cite this article as: Anifowose, F., Abdulraheem, A., Al-Shuhail, A., A parametric study of machine learning techniques in petroleum reservoir permeability prediction by integrating seismic attributes and wireline data, Journal of Petroleum Science and Engineering (2019), doi: https:// doi.org/10.1016/j.petrol.2019.01.110. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

ACCEPTED MANUSCRIPT 1 2 3 4

A PARAMETRIC STUDY OF MACHINE LEARNING TECHNIQUES IN PETROLEUM RESERVOIR PERMEABILITY PREDICTION BY INTEGRATING SEISMIC ATTRIBUTES AND WIRELINE DATA

5

Fatai Anifowosea, Abdulazeez Abdulraheemb, Abdullatif Al-Shuhailc The Research Institute, Center for Petroleum and Minerals, b

7

Department of Petroleum Engineering, c

8 9 10

Department of Earth Sciences,

RI PT

a

6

King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia. a

[email protected], [email protected], [email protected]

11

One of the recipes for the big data and artificial intelligence paradigms is multi-dimensional

13

data integration for improved decision making in petroleum reservoir characterization.

14

Various machine learning (ML) techniques have been applied. However, there is still ample

15

room for improvement. This paper carries out a rigorous parametric study to investigate the

16

comparative performance of common and sophisticated ML techniques in the estimation of

17

the permeability of a carbonate reservoir in the Middle East. The study integrates seismic

18

attributes and wireline data for improved permeability prediction. The effects of tuning

19

hyperparameters on the performance of the techniques are also studied. The techniques are

20

evaluated on two versions of the seismic-log integrated data: globally-averaged and depth-

21

matched. The results show that using the depth-matched dataset gives marginal improvement

22

on the permeability prediction as reflected in the higher correlation coefficient and lower

23

errors than the globally-averaged version. The outcome of this study will assist users of ML

24

techniques to make informed choices on the appropriate ML techniques to use in petroleum

25

reservoir characterization for more accurate predictions and better decision making especially

26

when faced with limited and sparse data.

27 28 29 30

Keywords: Computational intelligence; reservoir characterization; seismic attributes; wireline log; depth-matching; global averaging.

31

1.

32

Over the years, machine learning (ML) has attracted keen attention in various areas of

33

petroleum engineering and geosciences applications. Many successful implementations of

34

this science with real oil/gas industry cases have encouraged considerable application of these

35

techniques to predict reservoir permeability in uncored wells. Some of the areas in which ML

36

techniques have been successfully utilized in the petroleum industry include reservoir

37

characterization, seismic pattern recognition, reservoir properties prediction, lithofacies

AC C

EP

TE D

M AN U

SC

12

INTRODUCTION

1

ACCEPTED MANUSCRIPT identification, well production prediction, and various reservoir portfolio management (Duch

2

et al. 1997; Hosmer and Lemeshow 2000; Guojie 2004; Salah et al. 2005).

3

Permeability is an important reservoir property and a major ingredient of reservoir

4

characterization and simulation processes. It is part of the inputs used to determine

5

hydrocarbon production rate, estimation of recovery, optimal well placement, downhole

6

pressure, fluid contact evaluation, etc. A more accurate prediction of reservoir permeability

7

will lead to an integral improvement in the exploration and development of a field. More

8

accurate prediction of permeability in uncored reservoirs has remained a challenge in the

9

petroleum industry.

RI PT

1

The most reliable estimation of reservoir permeability is the special core analysis (SCAL)

11

performed on core samples in the laboratory. Both the coring process and the consequent

12

SCAL process are expensive and require huge manpower. Core samples are only available

13

over limited reservoir intervals. The reservoir simulation process requires that SCAL

14

measurements are available for the whole length of a reservoir. Hence, there has been the

15

need to develop relationships based on existing and abundant wireline and SCAL data that

16

can be used to predict reservoir permeability for uncored wells. The utility of ML techniques

17

in petroleum reservoir characterization is one of the alternative methods to reduce the need for

18

extensive coring. Traditional methods of permeability estimation are based on statistical

19

regressions and empirical equations that use correlations between wireline data and SCAL.

20

The linear regression techniques assume and establish a linear relationship between the input

21

and target variables. This may not be valid for a robust permeability prediction as the

22

variables are believed to be highly nonlinear. The empirical equations are derived based on

23

local experiments that may not be applicable in different locations.

24

The recent advancement in seismic attributes derivation from seismic volumes has given a

25

boost to the reservoir characterization process (Brahmantio et al. 2012; Maity and Aminzadeh

26

2012). This has allowed the integration of such diverse data in history matching for improved

27

reservoir simulation (Kazemi and Stephen 2010; Jin et al. 2011), with production data for

28

improved reservoir portfolio management (Nalonnil and Marion 2010; Liang et al. 2011;

29

Suman et al. 2011), and with stratigraphic data for improved forward modeling

30

(Lertlamnaphakul et al. 2012). Previous studies have investigated the prediction of reservoir

31

permeability from seismic attributes (Behzadi et al. 2011; Liang et al. 2011). This is the

32

rationale for this study. We aim to extend the existing effort of predicting reservoir

33

permeability by integrating seismic attributes and well logs to achieve improved results.

34

Leveraging recent developments in ML and seismic attributes extraction along with the

35

wireline data currently being used can have potential utility in improving the prediction of full

36

permeability profile in a given reservoir where seismic attributes and wireline data are

37

available without recourse to an extensive coring process. Artificial Neural Networks (ANN)

AC C

EP

TE D

M AN U

SC

10

2

ACCEPTED MANUSCRIPT and other traditional ML techniques have over some decades been used to predict reservoir

2

permeability and other petroleum reservoir properties. Such techniques, however, have

3

various disadvantages that impose structural and technical limitations that affect their

4

predictive performance. In the recent time, some more sophisticated ML techniques have been

5

successfully applied in other fields. It is essential for such techniques to be explored for

6

improved petroleum reservoir characterization through a rigorous comparative study that

7

assesses their applicability and performance in different data scenarios.

8

This study explores the comparative performance of traditional and more sophisticated ML

9

techniques in the prediction of petroleum reservoir permeability using integrated seismic

10

attributes and wireline data. The choice of these methods is based on their common use in the

11

petroleum industry literature and research community, and to demonstrate their comparative

12

performance as professionals transit from the traditional to the more sophisticated methods.

13

The outcome of this study will assist researchers in the petroleum industry to decide on which

14

set of ML techniques to use in cases of different operational and data scenarios such as with

15

limited and high-dimensional data.

16 17

2.

18

INTELLIGENCE

19

One of the most fundamental equations used to calculate permeability is the generalized

20

Kozeny-Carman equation (Duch et al. 1997) that approximates the fluid flow in porous media

21

as given in equation 1.

26 27 28 29 30 31

where k is in µm2 and Sgv is in µm-1.

……………..(1)

is a function that characterizes the

geology of porous media and variations in pore geometry (Blasingame 2008, Orodu et al. 2009).

is the shape factor, is tortuosity, and

is the specific area.

Equation 1 can be rewritten as follows:

0.0314

32 33 34 35

=

AC C

25

EP

23

TE D

PERMEABILITY PREDICTION AND COMPUTATIONAL

22

24

M AN U

SC

RI PT

1

=

where k is in mD.

3

……………..(2)

ACCEPTED MANUSCRIPT In addition to the independent terms in the equations above, reservoir permeability has been

3

predicted separately from log measurements and seismic attributes. Details of log

4

measurements and their relationship with various reservoir properties such as permeability are

5

found in a number of geophysical literatures such as Sengel (1981), Etnyre (1989), Darling

6

(2005), Schlumberger Oil Field Glossary (2018), and while those of seismic attributes have

7

been well documented in Taner et al. (1979), Chen and Sidney (1997), Walls et al. (1999),

8

and Brown (2001).

9

The utility of ML techniques has been widely reported in various fields including petroleum

10

engineering and the geosciences. This interdisciplinary collaboration has succeeded in

11

creating the necessary synergy among computer scientists, petroleum engineers, and

12

geoscientists in improving the petroleum reservoir characterization process. ML is the

13

computational aspect of artificial intelligence (AI) that deals with algorithms that

14

automatically learn from data without explicit programming. More details about the AI field

15

and the related subfields of computational intelligence and ML have been extensively

16

discussed in Fulcher (2008). Details of the various ML techniques that have been applied to

17

predict various reservoir properties can be found in Duch et al., (1997), Hosmer and

18

Lemeshow (2000), Guojie (2004), Salah et al. (2005), Lauría and Duchessi (2006), and El-

19

Sebakhy (2011). Such reservoir properties include PVT, drive mechanism, well spacing, well-

20

bore integrity, structure and seal, diagenesis, porosity and permeability while such ML

21

techniques include K-Nearest Neighbor, Multilayer Perceptrons, Logistic Regression, Radial

22

Basis Function, Naïve Bayes, Random Forests, Functional Networks, Bayesian Belief

23

Networks, Support Vector Machines, Probabilistic Neural Networks, Adaptive-Neuro Fuzzy

24

Systems, Artificial Neural Networks, and Decision Trees.

25

The main objective of this study is to investigate some of these traditional techniques as well

26

as the more sophisticated ones with respect to their performance on limited and integrated

27

data scenarios for the possibility of obtaining improved predictive performance of such

28

models. In addition to demonstrating the capability of the proposed methods in the petroleum

29

industry, they are essentially relevant to handle the sparse and limited datasets we handle in

30

the petroleum industry. Core measurements are limited to few samples in the entire length of

31

a reservoir due to their huge cost, enormous time consumption, and excessive manpower

32

requirement. The utility of seismic datasets is also limited due to their low resolution.

33

The following sections give brief overviews of the ML techniques that are implemented and

34

evaluated in this study.

AC C

EP

TE D

M AN U

SC

RI PT

1 2

35

4

ACCEPTED MANUSCRIPT 3.

MACHINE LEARNING TECHNIQUES IMPLEMENTED

2

3.1

ARTIFICIAL NEURAL NETWORKS

3

Artificial neural networks (ANN) is a machine learning technique developed in an attempt to

4

mimic the way the human brain works. It consists of an array of processing units called

5

neurons that communicate with other neurons by sending weighted signals. They have been

6

successfully applied to build various models for pattern recognition, signal processing,

7

robotics, control, and decision making (Ali 1994). The most widely used neural network

8

architecture for handling prediction and regression problems is the multilayer perceptron

9

(MLP) with back-propagation. The MLP architecture produces its output by learning the

10

patterns embedded in the data. More details of ANN, its different architectures, and

11

underlining mathematical bases can be found in Petrus et al. (1995).

12 13

3.2

14

Functional networks (FN) is a generalization of ANN. It is similar to ANN by consisting of

15

different layers of neurons connected by links but different in that each computing unit or

16

neuron performs a simple calculation typically a scalar, typically monotone, function f of a

17

weighted sum of inputs. The function associated with each neuron is fixed and the weights are

18

learned automatically from data using some common algorithms such as the least-squares

19

fitting (Castillo et al. 2001). FN ensures that the weights are suppressed when the functions

20

are undergoing learning. The functions can be multivariate or composed of single variables.

21

Solving the system of equations leads to a great simplification of the initial functions f

22

associated with the neurons (Castillo et al. 2001; El-Sebakhy 2011). The FN architecture can

23

be mathematically defined as:

SC

RI PT

1

TE D

M AN U

FUNCTIONAL NETWORKS

Assume that we have a neuron with s inputs: (x1,…, xs) and k outputs: (y1,…, yk), then

26

we assume that there exist k functions Fj; j = 1,…, k, such that yj = Fj(x1,…, xs); j =

27

1,…, k.

AC C

28

EP

24 25

29

More details about the FN architecture can be found in Castillo et al. (2001), El-Sebakhy

30

(2011), and Anifowose and Abdulraheem (2011).

31 32 33

3.3

34

Support vector machines (SVM) is a supervised learning method that belongs to the class of

35

generalized linear classifiers and a special case of Tikhonov Regularization. It was initially

36

developed for classification until Vapnik et al. (1995) developed a new ε-sensitive loss

37

function technique that seeks to minimize an upper bound of the generalization error ideal for

SUPPORT VECTOR MACHINES

5

ACCEPTED MANUSCRIPT 1

regression problems. It is founded on the statistical learning theory and follows the principle

2

of structural risk minimization. It maps input vectors to a higher dimensional space where a

3

maximal separating hyperplane is constructed (Peng and Wang 2009; Anifowose et al.

4

2014). SVM has been reported to exhibit excellent predictive performance. The kernel

5

functions that are commonly used in SVM are:

6

8 9

Linear:

RI PT

7

……………..(3)

RBF:

SC

……………..(4)

Polynomial:

12 13

M AN U

10 11

……………..(5)

where param is the kernel parameter in the SVM file.

14 3.4

TYPE-2 FUZZY LOGIC SYSTEM

16

Type-2 fuzzy logic system is a generalization of the Type-1. Details about Type-1 fuzzy logic

17

system can be found in Zadeh (1975) and Lee (1990). Fuzzy sets (FS) enable modeling in

18

uncertain and ambiguous data conditions. They are capable of solving ill-posed problems.

19

Each element in a FS is mapped to [0,1], a set of real numbers between 0 and 1 (inclusive) by

20

a membership function. A type-2 FS allows the incorporation of uncertainty about the

21

membership function into fuzzy set theory. It would be noted that in the absence of

22

uncertainties, a type-2 FS reduces to a type-1 FS, which is similar to probability reducing to

23

deterministic approaches when unpredictability vanishes. The membership function of a type-

24

2 FS is three-dimensional where the third dimension is the value of the membership function

25

at each point on its two-dimensional domain. This is referred to as the footprint of uncertainty

26

that provides new design degrees of freedom for handling uncertainties (Karnik and Mendel

27

1999; Mendel and John 2002). Further details of type-2 FS and its successful applications

28

can be found in Mendel (2006).

29 30

3.5

31

Decision tree (DT), also known as classification or regression tree, is a machine learning

32

technique that uses the principle of information gain theory to map observations about a

33

problem to conclusions about the problem's target value. In the DT structure, leaves represent

AC C

EP

TE D

15

DECISION TREES

6

ACCEPTED MANUSCRIPT the outcome classes and branches represent conjunctions of features that lead to the outcome

2

classes. DT learning is a commonly used data mining method that is capable of creating

3

models that predict the value of a target variable based on one or more input features (White

4

and Liu 1994). The DT algorithm learns by splitting the input features into subsets based on a

5

value test. This process, called recursive partitioning, is repeated on each derived subset in a

6

recursive manner. The recursion is stopped when further splitting no longer adds value to the

7

predictions or when the subset at a node has the same value of the target variable. More

8

details about the DT algorithm can be found in Sherrod (2008).

9 10

3.6

11

Extreme learning machine (ELM) is a unified framework of generalized single-layer feed-

12

forward networks (SLFFN). ELM runs much faster than conventional methods. It

13

automatically determines all the network parameters by randomly choosing the input weights

14

and analytically estimating the output weights of the SLFFN. This gives it the capability to

15

avoid trivial human intervention and makes it efficient in online and real-time applications. It

16

was proposed to overcome the drawbacks of gradient-based algorithms such as ANN and

17

SVM (Han et al. 2006). Mathematically, the output function of an ELM model with L hidden

18

nodes can be given as:

M AN U

SC

EXTREME LEARNING MACHINES

RI PT

1

19

"

TE D

!" # = $ %& ℎ& # &(

22 23 24 25 26 27

The output function of the ith hidden node is further given as:

EP

21

where %& is the output weight and ℎ& is the output function of the ith hidden node.

AC C

20

……………..(6)

ℎ& # = ) *& , ,& , #

……………..(7)

where *& and ,& are the parameters of the ith hidden node.

The output of the hidden layer is expressed as:

28 ℎ # = [) ℎ # , ℎ # , … , ℎ" # ]

29 30

Finally, with N samples the output matrix of the hidden layer is given as:

31

7

……………..(8)

ACCEPTED MANUSCRIPT ℎ 3 ℎ 2 0=2 2 2 1ℎ

# ) * , , , # ) * , , , # … ) *" , ," , # 7 3 # ) * , , , # ) * , , , # … ) *" , ," , # 6 2 . 6 2 . . . = . 6 2 . . . . 6 2 . . . #4 5 1) * , , , #4 ) * , , , #4 … ) *" , ," , #4

7 6 6 6 6 5

……………..(9)

1 3

……………..(10)

More details about this technique can be found in Huang et al. (2004, 2006)

6

M AN U

4 5

9 39 7 2.6 8=2 . 6 2 6 2.6 194 5

RI PT

and the training data target matrix is given as:

SC

2

4.

METHODOLOGY

8

4.1.

DESCRIPTION OF DATA

9

Seismic attributes and wireline data from 17 wells in a Middle East carbonate reservoir are

10

used to design and evaluate the models. The seismic data are available in four intervals: 10ms,

11

20ms, 30ms, and 40ms corresponding to four seismic zones. Both datasets were prepared,

12

processed, and checked to the highest level of quality. The major sources of uncertainty in

13

wireline log data are depth shifting, hole cleaning condition, borehole size, cycle-skipping,

14

stuck logging tools, and mud filtrate invasion. For the seismic data, a major source of

15

uncertainty is the presence of noise data (coherent, such as ground roll, and incoherent, such

16

as scattering by near-surface sources). Others include the presence of artifacts (such as gain,

17

NMO stretch, and frequency filtering), and wavelet phase changes caused by natural sources

18

such as absorption, deconvolution, and zero phasing. Correcting such uncertainties and

19

anomalies requires estimating all parameters contributing to the uncertainties and then adding

20

them together in a way that displays the confidence level. We ensured that both the seismic

21

and wireline data used in this study are corrected against all these uncertainties and

22

anomalies. Details of the steps taken to ensure the highest quality standard of the datasets are

23

beyond the scope of this paper.

24

Table 1 and 2 show the seismic attributes and wireline logs forming the integrated dataset.

25

Table 3 shows the result of the statistical analysis comprising eight parameters namely

26

average, median, minimum, maximum, kurtosis, skew, standard deviation and variance of the

27

combined seismic-log data.

AC C

EP

TE D

7

28

8

ACCEPTED MANUSCRIPT 1 2 3

Abbreviation IP IF AL HE RMSA

4 5 6 7

Full Meaning Instantaneous Phase Instantaneous Frequency Arc Length Half Energy RMS Amplitude

RI PT

Table 1. Seismic attributes used in this study.

Table 2. Wireline logs used in this study.

M AN U

8 9 10 11

Full Meaning Neutron Porosity Log Density Log Caliper Log Gamma Ray Water Saturation Deep Resistivity

SC

Abbreviation NPL RHOB CT GR SWT DT

IF

HE

AA

AL

Average

33.96

43.99

1.56

1.06

-2.89

0.17

2.48

0.12

18.35

0.48

64.49

Median

32.70

42.85

1.40

1.05

-32.40

0.18

2.47

0.08

15.26

0.44

64.75

Minimum

16.32

16.16

0.63

1.00

-171.19

0.06

2.32

0.01

2.78

0.07

54.37

Maximum

61.84

88.85

2.93

1.16

178.92

0.25

2.67

0.59

160.26

0.99

74.75

Kurtosis

TE D

Table 3. Basic Statistics of the Integrated Data. IP

NPL

RHOB

CT

GR

SWT

DT

0.23

-1.05

-0.95

-1.50

-1.01

-0.90

3.33

51.57

-0.93

-1.01

0.33

0.49

0.37

0.49

0.17

-0.30

0.19

1.82

6.88

0.25

0.03

STD

10.44

15.43

0.65

0.04

110.23

0.05

0.09

0.12

19.14

0.25

5.54

108.90

238.05

0.43

0.00

12150.40

0.00

0.01

0.01

366.26

0.06

30.69

Variance

EP

-0.33

Skew

It should be noted that the seismic attributes were extracted from the seismic cubes of the

15

respective wells using equations that are well established in literature. Details of such

16

equations are not the focus of this paper. Also, both the seismic and wireline log datasets were

17

cleaned and quality-checked by the relevant department before using them for this work.

18

Hence, the quality of the data is assured. It is well known that quality of data affects the

19

performance of models especially those based on machine learning.

20 21

4.2

22

The datasets are integrated in two ways following the two schools of thought on seismic

23

attributes and wireline data integration. One school postulated that only globally averaging

AC C

12 13 14

DATA PRE-PROCESSING

9

ACCEPTED MANUSCRIPT the log data according to the seismic zones without considering the exact well locations is

2

sufficient while the other school suggests that both data should be matched and averaged at

3

the exact points where the well locations intercept the seismic zones. The integrated data

4

arising from the former, with no depth precision, is named Seismic_Log#1. The one arising

5

from the latter led to a loss of a number of samples as those data points fell outside of the

6

seismic zones, hence having no match. This is named Seismic_Log#2. In each case, the

7

stratified sampling approach applied in some previous studies such as El-Sebakhy (2004,

8

2011), Anifowose and Abdulraheem (2010), and Anifowose et al. (2011) is used to divide the

9

dataset into training and validation subsets. With this stratification approach, a randomly

10

selected 70% of the integrated dataset was reserved for training while the remaining was used

11

for validation. The choice of the 70:30 stratification strategy is motivated by the

12

recommendation of Anifowose et al. (2016). This random selection is preferred over the

13

conventional fixed stratification strategy because it gives each data sample an equal chance of

14

being selected for either purpose. This ensures fairness and gives more credence to the results

15

of the study.

M AN U

SC

RI PT

1

16 4.3

CRITERIA USED FOR PERFORMANCE EVALUATION

18

The performance of the proposed ML techniques is evaluated using commonly used statistical

19

model evaluation criteria: correlation coefficient (R2), root mean squared error (RMSE), and

20

mean absolute error (MAE).

21

The R2 is a statistical measure of the strength of a relationship and the trend between n pairs

22

of two variables, x and y. It is mathematically expressed as:

TE D

17

23

EP

25

: =

AC C

24

; ∑=

; ∑ =>

∑=

∑= ∑> ; ∑>

∑>

……………(11)

26

The RMSE is a measure of the degree of spread between the actual x values around the

27

average of the predicted y values. It can be expressed as:

28

:? @ =

∑B ACD =A >A ;

……………..(12)

29

The MAE is the mean of the absolute errors of the predicted y values relative to the actual x

30

values and is given by:

31 32

?E@ = ; ∑;&( |#& − H& |

10

……………..(13)

ACCEPTED MANUSCRIPT 1 4.4

PARAMETRIC STUDIES

3

The six proposed ML techniques were implemented on the integrated seismic and wireline

4

log dataset. The development environment is MATLAB 2018a installed on a 64-bit Core i7

5

2.8 GHz processor running on a Window 10 operating system with a RAM of 16 GB. The

6

general principle employed in the determination of the optimal parameters for the six

7

proposed methods is presented in the following pseudocode:

8 9

RI PT

2

1. For each parameter Pi belonging to a set of parameters P1, P2, …, Pn, do the following. 2. Establish a reasonable search range for the selected parameter, Pi.

11

3. For each value Ni in the search range sequentially

12

4. Note the effects on the model performance using the evaluation criteria.

13

5. Continue the next parameter Ni until Nn.

14

6. Determine the value within the search range that gave the best model performance

16

M AN U

15

SC

10

according to the model evaluation criteria.

7. Using the best value for N, continue the next parameter Pi until Pn.

17

A number of runs were carried out with each technique to ascertain the optimal model

19

parameters as presented in the pseudocode above. Representative results of the various runs

20

with both versions of the dataset are presented in Figures 1 through 9. The objective of this

21

exercise is to obtain optimal models that completely avoid the challenges of overfitting and

22

underfitting. Overfitting is indicated by an increasingly wider gap between the training and

23

testing curves as the search progresses from the low end of the range to the high. Underfitting

24

is indicated by both training and testing curves moving together in low performance in terms

25

of low CC or high RMSE and MAE.

26

Figure 1 shows the results of searching for the optimal number hidden neurons for ANN over

27

a range of 1 to 50. The choice of the limit of 50 neurons follows the work of Beale et al.

28

(2015) which suggested that no more than 50 neurons is sufficient for ANN to solve any

29

problem. This suggestion is found to be valid as there is no sign of convergence after 50

30

neurons but rather a continuation of the same erratic pattern. The two datasets demonstrate

31

and confirm the erratic behavior of ANN as reported in the literature. ANN suffers from local

32

optima as several points (such as 6, 14, 27, and 40 for Run 1 and 6, 23, and 33 for Run 2)

33

could qualify for optimality. With this observed erratic pattern, it would be preferred to go for

34

a lower number of neurons that give the same level of performance than a higher one.

35

For the SVM model, Figure 2 shows the results of the search for the optimal regularization

36

parameter, C, for SVM over a range of 0 to 15000 for Run 1 (a) and Run 2 (b). From the

AC C

EP

TE D

18

11

ACCEPTED MANUSCRIPT plots, it could be confirmed that there was no further improvement in the model performance

2

beyond 15000. Rather there is increased overfitting. It is observed that the point of optimality

3

for each model Run is where the training plot meets the testing. Before this point is

4

underfitting and after it is overfitting. As mentioned earlier, the goal of any machine learning

5

project is to maintain a balance between these two extremes. Figure 3 shows the results of the

6

search for the optimal error goal, lambda, another hyperparameter for SVM. It was also

7

confirmed that going beyond the experimented range does not improve the model

8

performance but rather indicates increased overfitting. Figure 4 shows the results of the search

9

for the optimal penalty for overfitting, epsilon, over a range of 0 to 5. It is also confirmed

10

from the plot that there was no improvement on the model performance beyond 5 as

11

overfitting increases. Figure 5 shows that the SVM model’s kerneloption hyperparameter

12

does not have any effect on the model’s performance.

13

Figure 6 shows the result of the search for the T2FLS’s learning rate, Alpha, over a range of 0

14

to 5. There was no sign of possible improvement in the model performance going beyond 5. It

15

rather indicates that the lower the value, the better for the model. The same was observed for

16

the two Runs 1 and 2. For DT, the results of the search for the optimal number of tree splits

17

are shown in Figure 7. The plots confirmed that there is no gain in performance improvement

18

beyond 50. Similar to the Alpha parameter of SVM, the search result indicates that the lower

19

the value of K, the better for the model.

20

In Figure 8, the results of the search for the optimal number of hidden neurons for the ELM

21

model are presented. Similarly, the plots confirmed that there is no gain in the performance

22

improvement going beyond the limit of 50. Both search results show progressive increase in

23

the training performance but erratic pattern in the testing. This behavior is similar to that of

24

ANN. This is not surprising since ELM is a special case of ANN with a single hidden layer.

25

Several points (such as 24, 31, 36, 45, and 48 for Run 1, and 26 and 43 for Run 2) also quality

26

for optimality. This confirms that ELM overfits with the data used for this study.

27

A summary of the optimal parameters obtained from the two Runs for the six methods is

28

presented in Table 4. The points of optimality were obtained by taking the value of the

29

parameter corresponding to the points on the plots where the R2 (labeled as CC) of the

30

training performance are the closest to those of the testing. This implies points of no or the

31

least overfitting.

AC C

EP

TE D

M AN U

SC

RI PT

1

32 33 34 35 36

12

ACCEPTED MANUSCRIPT 1 2 3

Table 4. Summary of the Optimized Parameters for All Models. Technique

Values of the Optimized Parameters Run 1 • Number of Hidden Layers = 2 • Number of Neurons in each layer = 40 Run 2 • Number of Hidden Layers = 2 • Number of Neurons in each layer = 33 ● Degree of Polynomial = 1 Run 1 • Regularization Parameter, C = 8000 ● Error Allowance, Lambda = 0.008 ● Penalty for Overfitting, epsilon = 0 ● Type of Kernel = Polynomial ● Kernel Step Size = Constant

RI PT

ANN

SC

FN

M AN U

SVM

Run 2 • Regularization Parameter, C = 7000 ● Error Allowance, Lambda = 0.002 ● Penalty for Overfitting, epsilon = 2 ● Type of Kernel = Polynomial ● Kernel Step Size = Constant ● Learning Rate, Alpha = 0.3 ● Learning Algorithm = Gini ● Minimum Number of Tree Splits = 7 Run 1 • Number of Hidden Neurons = 36 ● Activation Function = Sigmoid

DT

Run 2 • Number of Hidden Neurons = 43 ● Activation Function = Sigmoid

AC C

4 5

EP

ELM

TE D

T2FLS

6

After the models have been optimally trained, they could be used to predict the permeability

7

for new/uncored wells. The input data should be composed of the same integrated set of

8

seismic and wireline logs in the same order they were presented to the models during the

9

training. This is to ensure that the coefficients or weights generated for each input feature are

10

used for the same feature during the prediction phase.

11 12

5.0

13

The optimized parameters obtained from the exhaustive search conducted and reported in

14

section 4.3 are used to build the six CI models and their performance results are compared.

RESULTS AND DISCUSSION

13

ACCEPTED MANUSCRIPT 1

The comparative results obtained on the Seismic_Log#1 dataset are presented in Table 5

2

while the representative comparative results of training and validation are shown in Figures 9

3

and 10. Those obtained on the Seismic_Log#2 dataset are presented in Table 6 and similar

4

representative training and validation comparative performances are shown in Figures 11 and

5

12.

6 7 R

RMSE Test

Train

Test

Train

ANN

0.69

0.64

0.68

FN

0.75

0.70

SVM

0.78

0.73

MAE

Min Error Test

Train

Test

Train

0.76

0.52

0.61

-1.70

-1.86

0.59

0.56

0.47

0.42

-1.4

-1.26

0.56

0.51

0.46

0.39

-1.21

-1.16

0.74

0.35

0.63

0.90

0.45

0.67

-2.07

DT

0.95

0.55

0.24

0.78

0.14

0.57

-0.61

ELM

0.45

0.23

0.86

1.09

0.67

0.84

-1.43

8 9

Exec. Time (s) Test

Train

1.86

1.35

1.32

0.001

1.17

0.70

0.06

0.001

1.29

0.58

0.25

0.001

-2.2

0.67

1.33

0.98

0.3

-1.93

1.08

1.30

0.17

0.001

-2.67

2.44

1.88

0.03

0.031

M AN U

T2FLS

Max Err Test

Train

SC

ML Tech.

RI PT

Table 5. Results of Permeability Prediction using Seismic_Log#1. 2

Table 6. Results of Permeability Prediction using Seismic_Log#2. 2

Technique

R Train

RMSE Test

Train

Test

MAE Train

Min Error

Test

Train

Test

Max Err

Train

Test

Exec. Time (s) Train

Test

0.64

0.42

0.70

1.02

0.34

0.82

-3.66

-2.38

0.78

0.81

1.15

0.001

FN

0.84

0.76

0.40

0.567

0.32

0.47

-1.02

-1.16

0.84

0.70

0.062

0.001

0.37

-1.12

-0.14

0.70

0.57

0.33

0.001

TE D

ANN SVM

0.84

0.85

0.41

T2FLS

0.87

0.57

0.45

0.77

0.48

0.34

0.24

0.64

-0.57

-1.44

1.42

1.62

0.655

0.280

DT

1.00

0.73

0.00

0.60

0.00

0.46

ELM

0.71

0.41

0.53

0.60

0.42

0.48

0.00

-1.03

0.00

1.36

0.17

0.001

-1.34

-1.006

0.96

1.64

0.031

0.001

From the results of the permeability prediction using the Seismic_Log#1 dataset shown in

13

Table 5, the DT model exhibit the highest training R2 but gave a poor testing performance

14

(Figure 9). This is a demonstration of overfitting. T2FLS also overfitted the data. However,

15

ELM showed underfitting as both the training and testing R2 values were poor. The SVM

16

model outperformed the ANN and FN models. It shows acceptable performance without

17

overfitting. A similar performance trend was demonstrated by the models in terms of the other

18

performance measures such as the mean absolute error (MAE) (Figure 10). The T2FLS, DT

19

and ELM models gave higher error values relative to the other models. ANN, FN and SVM

20

show more stability with the dataset as they do not show signs of overfitting or underfitting.

21

The performance of SVM in terms of MAE agrees with that of the CC by exhibiting the least

22

errors, thereby emerging as the best model for this dataset.

AC C

EP

10 11 12

14

ACCEPTED MANUSCRIPT In terms of execution time, the dataset could not clearly show the difference among the

2

models as they mostly executed at closely the same amount of time. However, T2FLS showed

3

that it took the most time to execute compared to the ELM model that took the least (Table 5).

4

The results obtained in this work agree perfectly with the performance of each of the models

5

as reported in the literature. FN (Castillo et al 2001; El-Sebakhy 2011) and SVM (Shawe-

6

Taylor & Cristianini 2004) are generally known to be computationally stable and fast in

7

execution. ANN takes more time especially when it has to handle large dataset (Petrus et al.

8

1995). DT (Sherrod 2008) and ELM (Han et al. 2006) have also been described as light-

9

weight techniques but susceptible to overfitting with small datasets while T2FLS (Mendel

10

2003) took the most time due to its complex algorithm involving a gradient descent method of

11

optimizing its performance and the conversion between Type-1 and Type-2 fuzzy sets during

12

its input and output processes.

13

The signs of overfitting/underfitting are further graphically shown in Figure 9 with the wide

14

gap between the training and testing performance curves of the T2FLS, DT, and ELM

15

models. However, the competitive performance of ANN, FN and SVM are also shown with

16

SVM demonstrating the best performance in the overall with the highest R2 (labeled as CC)

17

This relative performance of the models complemented Figure 10 which shows a similar trend

18

with SVM exhibiting the most stability, highest R2 and the lowest error indices.

19

On the Seismic_Log#2 dataset, the performance of the models follows a trend similar to that

20

of the Seismic_Log#1 dataset. The T2FLS, DT and ELM models also exhibit the

21

characteristics of overfitting. ANN showed less performance on this dataset than on the

22

previous. However, FN and SVM improved in their competitive performance with SVM

23

remaining in better performance. Despite that the DT model overfitted the dataset, the

24

performance on this dataset is better than on the former. The error measures are in good

25

agreement with the R2 results as the T2FLS, DT, and ELM models have the highest errors

26

while the FN and SVM models showed the least. In the overall, the SVM model kept the best

27

performance in both data conditions.

28

These performance demonstrations are in perfect agreement with literature as discussed

29

earlier. The reduction in the performance of ANN on this dataset agrees with its reported

30

unstable behavior (Petrus et al. 1995). This is due to its often being trapped in the local

31

optimum. The reduction in the number of samples also affect the performance of the ANN

32

model. ANN has been shown to require more data points for effective generalization. The FN

33

and SVM models, on the other hand, have the capability to handle small data. However, the

34

improvement in the performance of the other models can be attributed to the improvement in

35

the quality of the dataset. It would be recalled that this dataset (Seismic_Log#2) is more

36

rigorously pre-processed than the former (Seismic_Log#1). The Seismic_Log#1 dataset was

37

simply a result of the global averaging of each of the four seismic zones. However,

AC C

EP

TE D

M AN U

SC

RI PT

1

15

ACCEPTED MANUSCRIPT Seismic_Log#2 takes into consideration the proper depth matching ensuring that the same

2

depth locations in the log data correspond to the same locations in the seismic traces.

3

In terms of execution time, the trend follows that of the former dataset as the T2FLS model

4

continued to show its complexity as it took more time to execute for training and testing than

5

the others. Figure 11 confirms the emergence of the SVM model as the best performing

6

technique in terms of training and validation R2 while Figure 12 follows the same trend by

7

showing SVM with the least mean absolute error. Other models either showed signs of

8

overfitting or generally poor performance (underfitting).

9 6.

11

In this study, we have presented the results of a rigorous and comprehensive parametric study

12

to investigate the comparative performance of six traditional and state-of-the-art ML

13

techniques and the effects of tuning hyperparameters on them in the estimation of

14

permeability from integrated seismic attributes and wireline datasets. This study is

15

implemented on the integration of six wireline logs and five seismic attributes extracted from

16

17 wells in a giant reservoir located in the Middle East. The method of integrating the datasets

17

led to the emergence of two different versions: one globally averaged without regard to the

18

exact depth matches with wells; and the other depth-matched at the exact well locations. The

19

objective of this study is to investigate the effect of these datasets on the performance of six

20

ML techniques in the prediction of reservoir permeability.

21

After a rigorous comparative study and analysis of the results, the following conclusions are

22

drawn: •

TE D

M AN U

SC

10

23

CONCLUSION

RI PT

1

Certain techniques have hyperparameters with optimal values beyond which no further performance improvement will be achieved. These techniques are

25

consequently better suited for certain data and other processing scenarios.

27 28 29 30

•

Of all the runs of the study, SVM demonstrated the most acceptable performance with the highest R2 and the lowest error measures.

AC C

26

EP

24

•

Bringing together the best performing techniques from each of the data conditions on

a comparative scale, we found that SVM performed better on the Seismic_Log#2 than the Seismic_Log#1 dataset. This indicates that the effort made on the depth-matching

31

process and the consequent higher precision made a significant difference. On a field-

32

wide scale, this difference could make a big positive impact in exploration efficiency

33

and production capacities.

34 35

•

ANN and FN demonstrated a competitive strength by having a close match to the performance of SVM but with ANN showing more overfitting than FN.

16

ACCEPTED MANUSCRIPT 1 2

•

DT and ELM showed the most sensitivity to the datasets by exhibiting clear overfitting.

3 4 Acknowledgement The authors would like to acknowledge the support provided by King Abdulaziz City for

7

Science and Technology through the Science & Technology Unit at King Fahd University of

8

Petroleum & Minerals for funding this work under Project No. 11-OIL2144-04 as part of the

9

National Science, Technology and Innovation Plan.

10

RI PT

5 6

REFERENCES

12 13 14

Ali JK (1994) Neural networks: a new tool for the petroleum industry? In: Proceedings of the European Petroleum Computer Conference, Aberdeen, U.K., March.

15 16 17 18 19

Anifowose FA, Abdulraheem A (2010) A functional networks-type-2 fuzzy logic hybrid model for the prediction of porosity and permeability of oil and gas reservoirs. Paper #1569334237, In: Proceedings 2nd International Conference on Computational Intelligence, Modeling and Simulation, Bali, September 28 – 30, IEEEXplore, pp. 193 – 198.

20 21 22

Anifowose FA, Abdulraheem A (2011) Fuzzy logic-driven and SVM-driven hybrid computational intelligence models applied to oil and gas reservoir characterization, Journal of Natural Gas Science and Engineering, 3: 505 – 517.

23 24 25 26

Anifowose F, Khoukhi A, Abdulraheem A (2016) Investigating the Effect of Training-Testing Data Stratification on Soft Computing Techniques: An Experimental Study, Journal of Experimental and Theoretical Artificial Intelligence, 29:(3): 517 – 535.

27 28 29 30 31 32 33 34 35

Anifowose FA, Labadin J, Abdulraheem A (2011) A hybrid of functional networks and support vector machine models for the prediction of petroleum reservoir properties. Paper #45, In: Proceedings of 11th International Conference on Hybrid Intelligent Systems, Meleka, Malaysia, 5-8 December, IEEExplore, pp. 85 - 90. Anifowose FA, Adeniye S, Abdulraheem A (2014) Recent advances in the application of computational intelligence techniques in oil and gas reservoir characterization: a comparative study. Journal of Experimental & Theoretical Artificial Intelligence, 26(4): 551 – 570.

36 37 38

Behzadi H, Alvarado V, Padhi A, Mallick S (2011) CO2 saturation, distribution and seismic response in 2D dimensional permeability model. Paper Presented at the SEG 2011 San Antonio Annual Meeting.

AC C

EP

TE D

M AN U

SC

11

17

ACCEPTED MANUSCRIPT Blasingame TA (2008) The characteristic flow behavior of low-permeability reservoir systems. In: Proceeding of the SPE Unconventional Reservoirs Conference held in Keystone, Colorado, U.S.A., 10–12.

4 5 6 7

Brahmantio R, Kusuma A, Bertini F, Dufour J, Paternoster B, Leclair S (2012) Seismic amplitude loss compression for future seismic characterization studies in Peciko Field-Indonesia. Paper IPTC 14412 Presented at the International Petroleum Technology Conference held in Bangkok, Thailand, 7-9 February.

8 9

Beale M, Hagan M, Demuth H (2015) Neural network toolbox user’s guide. The MathWorks, Inc., Apple Hill Drive, Natick, US.

10 11

Brown AR (2001) Calibrate yourself of your data! A vital first step in seismic interpretation. Geophysical Prospection 49:729–733.

12 13

Castillo E, Gutiérrez JM, Hadi AS, Lacruz B (2001) Some applications of functional networks in statistics and engineering. Technometrics 43:10–24.

14 15

Chen Q, Sidney S (1997) Seismic attribute technology for reservoir forecasting and monitoring. The Leading Edge 16:445-456.

16

Darling T (2005) Well Logging and Formation Evaluation. Oxford, UK: Elsevier.

17 18 19

Duch W, Adamczak R, Jankowski N (1997) Initialization and optimization of multilayered perceptrons. In: Proceedings of the Third Conference on Neural Networks and their Applications, Kule, Poland.

20 21 22 23

El-Sebakhy EA (2004) Functional networks training algorithm for statistical pattern recognition. In Proceedings of the Ninth International Symposium on Computers and Communications 2004 Volume 2 (ISCC"04) - Volume 02, IEEE Computer Society Washington, DC, USA.

24 25 26

El-Sebakhy EA (2011) Functional networks as a novel data mining paradigm in forecasting software development efforts. Expert Systems with Applications 38(3):2187-2194.

27 28

Etnyre LM (1989) Finding oil and gas from well logs. Kluwer Academic Publishers. 249 pages.

29 30 31

Fulcher J (2008) Computational Intelligence: An Introduction. In: Fulcher J., Jain L.C. (eds) Computational Intelligence: A Compendium. Studies in Computational Intelligence, vol 115. Springer, Berlin, Heidelberg.

32 33

Guojie L (2004) Radial basis function neural network for speaker verification. A Master of Engineering thesis submitted to the Nanyang Technological University.

34 35 36

Han F, Li X, Lyu MR, Lok T (2006) A modified learning algorithm incorporating additional functional constraints into neural networks. International Journal of Pattern Recognition and Artificial Intelligence 20(2):129-142.

AC C

EP

TE D

M AN U

SC

RI PT

1 2 3

18

ACCEPTED MANUSCRIPT Hosmer D, Lemeshow S (2000) Applied logistic regression. John Wiley and Sons, 392 pages.

3 4 5

Huang GB, Zhu QY, Siew CK (2004) Extreme learning machine: a new learning scheme of feedforward neural networks. In: Proceedings of the international joint conference on neural networks, Budapest, Hungary.

6 7

Huang GB, Zhu QY, Siew CK (2006) Extreme learning machine: theory and applications. Neurocomputing 70:489-501.

8 9 10 11 12

Jin L, Alpak FO, Hoek P, Pirmes C, Fehintola T, Tendo F, Olaniyan E (2011) A comparison of stochastic data-integration algorithms for the joint history matching of production and time-lapse seismic data. Paper SPE 14618 Presented at the SPE Annual technical Conference and Exhibition held in Denver, Colorado, USA, 30 October - 2 November.

13 14

Karnik NN, Mendel J (1999) Type-2 fuzzy logic systems. IEEE Transactions on Fuzzy Systems 7(6):643-658.

15 16 17

Kazemi A, Stephen KD (2010) Optimal parameter updating in assisted history matching of the nelson field using streamlines as a guide. In: Proceedings of the SPE EUROPEC/EAGE Annual Conference and Exhibition, 14-17, Barcelona, Spain.

18 19

Lauría EJM, Duchessi P (2006) A bayesian belief network for IT implementation decision support. Decision Support Systems 42(3): 1573-1588.

20 21 22

Lee CC (1990) Fuzzy logic in control systems: fuzzy logic controller. I. In: Proceedings of the IEEE Transactions on Systems, Man, and Cybernetics 20(2): 404418.

23 24 25 26 27

Lertlamnaphakul P, Thanaitit U, Al-Busaidi SM, Russell WR, Seusutthiya K (2012) Integrated well log electrofacies and seismic facies modeling for stratisgrahic trap identification in carbonate reservoirs, North Oman. Paper IPTC 14806 Presented at the International Petroleum Technology Conference held in Bangkok, Thailand, 7-9 February.

28 29 30 31 32

Liang L, Abubakar A, Habashy TM (2011) Improved estimation of permeability from joint inversion of time-lapse crosswell electromagnetic and production data using gradient-based method. Paper SPE 146526 Presented at the SPE Annual technical Conference and Exhibition held in Denver, Colorado, USA, 30 October - 2 November 2011.

33 34 35 36

Maity D, Aminzadeh F (2012) Reservoir characterization of an unconventional reservoir by integrating microseismic, seismic and well log data. SPE Paper 154339 presented at the SPE Western Regional Meeting held in Bakersfield, California, USA, 19-23 March.

37 38

Masters T (1993) Practical neural network recipes in C++. Morgan Kaufmann, 493 pages.

AC C

EP

TE D

M AN U

SC

RI PT

1 2

19

ACCEPTED MANUSCRIPT Mendel JM (2006) Interval type-2 fuzzy logic systems made simple. IEEE Transactions on Fuzzy Systems 14(6):808-821.

3 4

Mendel JM, John RI (2002) Type-2 fuzzy sets made simple. IEEE Trans. on Fuzzy Systems 10:117-127.

5 6

White AP, Liu WZ (1994) Bias in information-based measures in decision tree induction. Machine Learning 15:321-329.

7 8 9

Nalonnil A, Marion B (2010) High resolution reservoir monitoring using crosswell seismic. Paper SPE 132491 Presented at the SPE Asia pacific Oil and Gas Conference and Exhibition, Brisbane, Queensland, Austria, 18-20 October.

10 11 12

Orodu OD, Tang Z, Fei Q (2009) Hydraulic (flow) unit determination and permeability prediction: a case study of block Shen-95, Liaohe oilfield, north-east China. Journal of Applied Sciences 9:1801-1816.

13 14

Peng X, Wang Y (2009) A normal least squares support vector machine (NLS-SVM) and its learning algorithm. Neurocomputing 72:3734-3741.

15 16

Petrus JB, Thuijsman F, Weijters AJ (1995) Artificial neural networks: an introduction to ANN theory and practice. Berlin, Germany, Springer.

17 18

Salah A, Rahman S, Nath K (2005) An enhancement of k-nearest neighbor classification using genetic algorithm. MICS.

19 20 21

Schlumberger Oil Field Glossary (2018) Well logs. Available online: http://www.glossary.oilfield.slb.com/Display.cfm?Term=porosity. Accessed on September 12.

22 23

Sengel EW "Bill" (1981) Handbook on well logging. Institute for Energy Development, Oklahoma City, Oklahoma, 168 pages.

24

Sherrod PH (2008) DTREG: predictive modeling software. User Manual, pp. 197.

25 26 27

Suman A, Fernandez-Martinez JL, Mukerji T (2011) Joint inversion of time-lapse seismic and production data for Norne field. Paper Presented at the SEG San Antonio 2011 Annual Meeting.

28 29

Taner MT, Koehler F, Sheriff RE (1979) Complex seismic trace analysis. Geophysics 44:1041-1063.

30

Vapnik V (1995) The nature of statistical learning theory. Springer-Verlag, London.

31 32 33 34

Walls JD, Taner MT, Guidish T, Taylor G, Dumas D, Derzhi N (1999) North Sea reservoir characterization using rock physics, seismic attributes, and neural networks: a case history. In proceedings of the 69th Ann. International Mtg., Soc. Expl. Geophys., Expanded Abstracts, 1572-1575.

35 36

Zadeh LA (1975) The concept of a linguistic variable and its application to approximate reasoning - I. Information Sciences 8(3):199-249.

AC C

EP

TE D

M AN U

SC

RI PT

1 2

20

ACCEPTED MANUSCRIPT

AC C

EP

TE D

M AN U

SC

RI PT

1 2

21

ACCEPTED MANUSCRIPT List of Figures

2

Figure 1. Optimal Number of Hidden Neurons for ANN with (a) Run 1 and (b) Run 2.

3

Figure 2. Optimal Regularization Parameter for SVM with (a) Run 1 and (b) Run 2.

4

Figure 3. Optimal Error Goal for SVM with (a) Run 1 and (b) Run 2.

5

Figure 4. Optimal Overfitting Penalty for SVM with (a) Run 1 and (b) Run 2.

6

Figure 5. Optimal Kernel Step Size for SVM with (a) Run 1 and (b) Run 2.

7

Figure 6. Optimal Learning Rate for Type-2 Fuzzy Logic.

8

Figure 7. Optimal Number of Splits for DT with (a) Run 1 and (b) Run 2.

9

Figure 8. Optimal Number of Hidden Neurons for ELM with (a) Run 1 and (b) Run 2.

SC

RI PT

1

Figure 9. Comparative R2 of 6 AI Techniques on Data Seismic_Log#1.

11

Figure 10. Comparative Mean Abs. Error of Six AI Techniques on Data Seismic_Log#1.

12

Figure 11. Comparative R2 of Six AI Techniques on Data Seismic_Log#2.

13

Figure 12. Comparative Mean Absolute Error of Six AI Techniques on Data Seismic_Log#2.

M AN U

10

AC C

EP

TE D

14

22

AC C

EP

TE D

M AN U

SC

RI PT

ACCEPTED MANUSCRIPT

AC C

EP

TE D

M AN U

SC

RI PT

ACCEPTED MANUSCRIPT

AC C

EP

TE D

M AN U

SC

RI PT

ACCEPTED MANUSCRIPT

AC C

EP

TE D

(a)

M AN U

SC

RI PT

ACCEPTED MANUSCRIPT

(b)

ACCEPTED MANUSCRIPT

Optimal Training/Testing Parameters for SVM 0.8 0.75 0.7

0.6

RI PT

CC

0.65 Training Testing

0.55

SC

0.5 0.45 0

5000

10000

M AN U

0.4

15000

C

(a)

Optimal Training/Testing Parameters for SVM 0.85 0.8 0.75

EP

0.65

AC C

CC

0.7

0.6 0.55 0.5 0.45 0.4

Training Testing

TE D

0.9

0

5000

10000

C

(b)

15000

ACCEPTED MANUSCRIPT

Optimal Training/Testing Parameters for SVM 0.74 0.72 0.7

CC

RI PT

0.68 0.66

0.6

0

0.002

0.004

0.006

0.008

0.01

M AN U

Training Testing

0.62

SC

0.64

0.012

0.014

0.016

0.018

0.02

Lambda (a)

Optimal Training/Testing Parameters for SVM

TE D

0.75

0.74

EP

0.72

AC C

CC

0.73

0.71

0.7

0.69

Training Testing

0

0.002

0.004

0.006

0.008

0.01

0.012

Lambda

(b)

0.014

0.016

0.018

0.02

AC C

EP

TE D

(a)

M AN U

SC

RI PT

ACCEPTED MANUSCRIPT

(b)

AC C

EP

TE D

(a)

M AN U

SC

RI PT

ACCEPTED MANUSCRIPT

(b)

ACCEPTED MANUSCRIPT

Optimal Training/Testing Number for T2F 1 Training CC Testing CC

0.8

RI PT

0.6

SC

0.2 0

-0.4 -0.6

0

0.5

1

1.5

2

M AN U

-0.2

2.5

EP

TE D

Alpha

AC C

CC

0.4

3

3.5

4

4.5

5

ACCEPTED MANUSCRIPT Optimal Training/Testing Parameters for DT 1 Training Testing

0.9 0.8 0.7

RI PT

CC

0.6 0.5 0.4

SC

0.3 0.2

0

0

5

10

15

20

25

M AN U

0.1

30

35

40

45

50

K, Node Split Threshold

(a)

Optimal Training/Testing Parameters for DT 0.9 0.8

EP

0.7 0.6 0.5

AC C

CC

Training Testing

TE D

1

0.4 0.3 0.2 0.1 0

0

5

10

15

20

25

30

35

K, Node Split Threshold

(b)

40

45

50

ACCEPTED MANUSCRIPT Optimal Training/Testing Parameters for ELM 1

0.8

0.6

RI PT

0.4

CC

0.2

0

-0.2

SC

Training Testing

-0.4

-0.8

0

5

10

15

20

25

M AN U

-0.6

30

35

40

45

50

40

45

50

# of Hidden Neurons

(a)

Optimal Training/Testing Parameters for ELM

TE D

1

0.8

EP

0.6

0.2

AC C

CC

0.4

0

-0.2

Training Testing

-0.4

-0.6

0

5

10

15

20

25

30

# of Hidden Neurons

(b)

35

AC C

EP

TE D

M AN U

SC

RI PT

ACCEPTED MANUSCRIPT

ACCEPTED MANUSCRIPT Parametric study to investigate the comparative performance of ML techniques.

•

Study is applied to the estimation of petroleum reservoir permeability.

•

Seismic and log data are integrated for improved permeability prediction.

•

Outcome assists users to make informed choices on the appropriate techniques.

AC C

EP

TE D

M AN U

SC

RI PT

•