Stratigraphic Characterization of Reservoirs Through Segmentation of Digital Images of Well Cores from Machine Learning

Home , Middle Magdalena Valley, Paja Formation

STRATIGRAPHIC CHARACTERIZATION OF RESERVOIRS THROUGH SEGMENTATION OF DIGITAL IMAGES OF WELL CORES FROM MACHINE LEARNING

Thesis dissertation to obtain the degree of: Geoscientist

By Juan Camilo Burgos Florez

Director Ph.D. Roderick Perez Altamar

Co director Ph.D. Jillian Pearse

UNIVERSIDAD DE LOS ANDES SCIENCE FACULTY GEOSCIENCE DEPARTMENT

Bogota, Colombia November 2018

______Jillian Pearse

______Roderick Perez Altamar

______Juan Camilo Burgos Florez

TABLE OF CONTENTS DEDICATION i

ACKNOWLEDGMENTS ii

ABSTRACT iii

RESUMEN iv

1. INTRODUCTION 1

2. TECTONIC FRAMEWORK, REGIONAL GEOLOGY AND

PETROLEUM GEOLOGY 3

2.1. Tectonic framework 3

2.2. Regional geology 5

2.2.1. La Luna formation 7

2.2.2. Cumbre formation 7

2.2.3. Umir formation 8

2.2.4. Paja formation 8

2.2.5. Tablazo formation 8

2.2.6. Simiti formation 9

2.2.7. Mugrosa formation 9

2.2.8. Cimarrona formation 9

2.3. Petroleum geology 10

3. METHODOLOGY 11

3.1. Cores description 11

3.1.1. Well X 11

3.1.2. Well Y 14

3.1.3. Well Z 16

3.2. Algorithm 21

3.2.1. Convolutional network 21

3.2.1.1. Convolution 21

3.2.1.2. Pooling 23

3.2.1.3. Flatten 24

3.2.1.4. Dropout 24

3.2.2. Classifier 25

3.2.3. Optimizer 26

3.2.4. Model 27

3.2.5. Training phase 29

3.2.5.1. Feedforward training 29

3.2.5.2. Backpropagation error 30

3.2.5.3. Weight adjustment 31

4. RESULTS 33

5. DISCUSSION 42

6. CONCLUSION 44

BIBLIOGRAPHY 45

INDEX OF FIGURES

Figure 1. Localization and boundaries of the studied area. 4

Figure 2. Generalized stratigraphic column of the Middle Magdalena Valley

Basin. 6

Figure 3. Location of the worked wells, well X, well Y and well Z. 11

Figure 4. Stratigraphy of well X with a gap between 4504 feet and 4299 feet. 13

Figure 5. Stratigraphy column of the well Y with a serie of gaps between 5788-

5814 feet, 5817-5861 feet,5864-5902 feet, 5904-6028 feet, 6033-6261 feet and

6262-7078 feet. 15

Figure 6.A Stratigraphy column of the well Z. 17

Figure 6.B Stratigraphy column of the well Z. 18

Figure 7.A. The matrix A represents the information of the input picture 5x5,

the matrix B represents the characteristics, in other words the kernel 3x3. 22

Figure 7.B. Graphic process of the convolution, where both matrices are

multiplied, and it is sum the results of each box. So, they are denominated

convolved feature. 22

Figure 8. General idea of max-pooling into an algorithm. 24

Figure 9. Internal structure of a multilayer model. 28

Figure 10. Example of backpropagation model. 29

Figure 11. Process of feedforward training. 30

Figure 12. Process of backpropagation error. 32

Figure 13. Process of weights adjustment. 33

Figure 14. Graph of loss value. Training phase in the first one and validation

phase in the second one. 34

Figure 15. Graphs of loss value in each loss component of the training phase. 35

Figure 16. Graphs of loss value in each loss component of the validation phase. 36

Figure 17. 0.1 feet of image of well cores segmented. Well X 37

Figure 18. Image segmentation of well core Sandstone and conglomerate

with hydrocarbons were identified. 37

Figure 19. Correlation of image segmentation of well core with the stratigraphic

column 38

Figure 20. 0.1 feet of image of well cores segmented. Well Y 39

Figure 21. Image segmentation of well core. Sandstone was identifying. 39

Figure 22. Correlation of image segmentation of well core with the stratigraphic

column 40

Figure 23. New well core image of a new well. 40

Figure 24. 0.1 feet of image of well cores segmented. New well 41

Figure 25. Image segmentation of well core. Sandstone was identified.

Figure 26. Stratigraphic correlation from electric register like the Spontaneous

Potential (SP) 42

INDEX OF EQUATIONS

Equation 1. Classifier 25

Equation 2. Optimizer 26

Equation 3. Backpropagation errors 31

DEDICATION

To God

For give me the strength and the knowledge to make this work and allow me

to overcome all the adversities. Honor and glory be to him. This work is thanks to

him.

To my family

For supporting me in all the process and to be present when I needed help. To

my mom because she is my inspiration to keep going and to my dad that advised me

in all the moments that I needed it. I love you both.

To my grandmother Herminda and my aunt Elda for always watching and

taking care of me. To my sisters Maria Paula, Letizia and Juanita, you are my reason

to continue and I hope to teach you that everything in life can be achieved with the

help of God. I love you.

ACKNOWLEDGMENTS

I want to acknowledge all the institutions and people that contributed to this

work. Particularly to my directors Roderick Perez and Jillian Pearse to give me all

the advices and recommendations, also, to be present during the entire work.

Furthermore, to the Servicio Geologico Colombiano for supplying all the

information required to realize this work and giving all the support in my thesis with

tips, questions, help of geologists and petroleum engineers. Likewise, to I Oil and

Gas Summit for giving me the opportunity to expose my thesis as a poster and to

have the privilege to receive suggestions and recommendations of big companies,

geologist and petroleum engineers. Moreover, to Rigoberto Blandon for being part

of the process of obtaining information and Maria Paula Castañeda for helping me

with the written part.

Additionally, to my family because they are the inspiration to make this work.

All my friends, especially to David Angulo, Sebastian Duran, Felipe Uribe, Daniel

Diaz, Mateo Rueda, Nathalia Bernal, Valentina Blandon and Mariana Sanchez that

contributed in different moments of the process and supported me through difficult

times.

I appreciate you all very much and once again thanks for everything!

iii

ABSTRACT

The purpose of the present work is to generate an algorithm that allows an

automatic segmentation of images of well cores from machine learning. The

motivation for the use of this type of analysis is to look for an application of neural

networks in the petroleum industry, as a support tool for geologists that allows to

specify the descriptions of possible structures and patterns that are not identified by

the human eye.

Whence, it was used information of three wells of the Middle Magdalena

Valley Basin to know the lithologies and stratigraphic sequence to do a core

description. Then, they were recollected 1966 images of core with a size of 0.1 feet

to training the algorithm. So, 983 images were used to feed the training phase, and

the rest to feed the validation phase with the aim to realize a supervised training. The

final results were a training loss value of 1.0709 and a validation loss value of

1.0804, which shows that the images had a good segmentation but present some

mistakes that are product of different aspects that are mention in the discussion.

Thus, this research work will be divided into three parts: the first part will be

the description of the geological context of the study area and description of the

images of the cores. The second part will be the generation of codes and creation of

algorithms for the segmentation of the images. The third part, will be to prove the

algorithm for the segmentation of cores not used in the training and validation phase.

RESUMEN

El propósito del presente trabajo es generar un algoritmo que permita una

segmentación automática de imágenes de núcleos de pozo mediante machine

learning. La motivación es buscar una aplicación de redes neuronales en la industria

del petróleo como una herramienta de apoyo para los geólogos que permita

especificar las descripciones de posibles estructuras y patrones que no se identifican.

Por lo tanto, se utilizó la información de tres pozos de la Cuenca del Valle del

Magdalena Medio para conocer la secuencia estratigráfica para su descripción.

Despues, se recolectaron 1966 imágenes de núcleo con un tamaño de 0.1 pies para

entrenar el algoritmo. De ahi, se utilizaron 983 imágenes para alimentar la fase de

entrenamiento, y el resto para alimentar la fase de validación. Los resultados finales

fueron un valor de pérdida de entrenamiento de 1.0709 y un valor de pérdida de

validación de 1.0804, que muestra que las imágenes tuvieron una buena

segmentación, pero presentan algunos errors en donde se analizaran en la discusión.

Por lo tanto, este trabajo de investigación se dividirá en tres partes: la primera

será la descripción del contexto geológico del área de estudio y la descripción de las

imágenes de los núcleos. La segunda parte será la generación de códigos y la

creación de algoritmos para la segmentación de las imágenes. La tercera parte, será

probar el algoritmo para la segmentación de núcleos no utilizados en la fase de

entrenamiento y validación.

I. INTRODUCTION

The present research work shows the new advances in machine learning and

neural networks in the image processing. Since, the main characteristic of this

process is that “it has been used in a wide range of fields, including in medical

diagnostics, stock exchange, robot control, transportation, aviation, heavy industries,

toys and games” (Hernández,2017). This technology is based on “how humans can

learn by simply observing the world and formulating consistent explanation”

(Zhengqi, 2018). Therefore, the purpose is to implement and to apply those concepts

in the stratigraphic characterizations of reservoirs through the use of core images

and establish their correlation with the stratigraphic column. Whence, in the image

analysis it is possible to detect characteristics and patterns that for the human eye are

harder to perceive.

Currently, there are tools of open code for the implementation of neural

networks such as Tensorflow, “a software library for high-performance numerical

calculation. Its flexible architecture allows for an easy implementation of

computing” (Tensorflow, 2018), and it can be complemented by other software

library as it is Keras. These tools will be used for the generation and calibration of

the model, and the model will be trained through the segmentation of images of well

cores within a supervised classification. Furthermore, it will be correlated with their

stratigraphic column because “the field of pattern recognition is concerned with the

2 automatic discovery of regularities in data through the use of computer algorithms

and with the use of these regularities to take actions such as classifying the data into

different categories” (Bishop, 2006).

In the same way, machine learning is an application of artificial intelligence

(AI) that provides systems the ability to automatically learn and improve from

experience without being explicitly programmed. Machine learning focuses on the

development of computer programs that can access data and use it learn for

themselves, whence, there exists many applications within different industries

(Varone,2018). For example, in medicine ML “predict prognosis empower

healthcare officials to allocate resources optimally and physicians to select better

treatment options for patients” (Guy and Chan, 2017), in biology in the

“understanding of brain functioning, obtaining models of the retina.” (Martínez,

2017), also in geoscience as climate informatics, earth and space informatics, study

of tectonics plates, study of the soils, among others. (Karpatne, 2017).

Therefore, the motivation for this kind of analysis is to search an application

for the neural networks in the oil industry as support tool to the geologists, and to

allow accurate description of lithology and sedimentary structures that are not easy

to detect by human eye. In that case if the available data is enough to train the

network, and the prediction rate is high, it is expected that the model could predict

the correct segmentation of new images of cores that are not included within the

3 phase of calibration and training. Hence, the dataset will be constructed with 88

images of cores where each picture will be cut in sizes of one inch, 50% of those

will be intended to the training phase and the other 50% will be destined to the testing

phase to prove the functionally of the model.

Regarding the ideas previously mentioned, this work is going to be divided in

three parts, the first part will be the description of the regional geology of the studied

area and the description of the images of cores, the second part will be the process

of how the algorithm was created for the image segmentation. Finally, the model

will implement new images to analyze and discuss the results like advantages and

disadvantages of the process of machine learning.

2. TECTONIC FRAMEWORK, REGIONAL GEOLOGY AND

PETROLEUM GEOLOGY

2.1 TECTONIC FRAMEWORK

The Colombian Andes are a composition of three major mountains structures

known as Eastern, Central and Western Cordilleras. The images of cores were

recollected in the Middle Magdalena Valley Basin (MMVB) between the Central

and Western Cordilleras (Lozano & Zamora, 2014)(Figure 1). Their boundaries are

to the north and south by the Espíritu Santo fault system and the Girardot foldbelt,

to the northeast is limited by the Bucaramanga-Santa Marta fault system and to the

southeast by the Bituima and La Salina fault systems, and the western limit is defined

4 by the westernmost onlap of the Neogene basin fill into the Serranía de San Lucas

and the Central Cordillera basement (Barrero, Pardo, Vargas, & Martínez, 2007).

Moreover, the MMVB is divided by the Cimitarra fault in the north of

Barrancabermeja and it is possible identify two regions known as MMV north and

MMV south in fact those areas are important for the hydrocarbon industry

(Sarmiento, Puentes, & Sierra, 2015). Due, they present a “compressive tectonics

with reverse and/or low angle faulting is restricted to the eastern portion” (Mojica

and Franco, 1990) and this characteristic stimulate the creation of traps to hold oil,

water and gas.

Figure 1. Localization and boundaries of the studied area. Taken from Lozano & Zamora (2014)

The MMVB was the result of the different tectonic processes as the lifting of

Central Cordillera and Western Cordillera starting from an intra arc evolution and

intra mountain evolution respectively (Lozano & Zamora, 2014). First, “the

5 opening that begun in the Mesozoic is characterized by efforts of course with

perpendicular extensional component, which produces a deformation in the

lithosphere and thinning in the crust, giving rise to the opening to the E of the

Cordillera Central” (Lozano & Zamora, 2014). Then, in the Cretaceous the continent

collided against the oceanic crust and produced a compressional stress, this fact

helped the lifting of the Central Cordillera and the creation of the mega forearc basin

(Lozano & Zamora, 2014)

In other hand, the Western Cordillera uprising was after the medium Miocene

with the reactivation and inversion of the normal faults of old extensional basins,

furthermore the exhumation in western flank of the cordillera was product of the

contractational deformation started 25 Ma ago (Caballero, Parra, & Mora, 2010).

Whence, the MMVB represents an asynchronous tectonic depression with two

different margins, in the occident a passive border and in the western a compressive

margin with a continuous deformation. (Mojica & Franco, 1990)

2.2 REGIONAL GEOLOGY

The description of the regional geology of the MMVB will be of the

unconventional petroleum system base on the primary exploration reservoirs as

Cenozoic continental, transitional clastic reservoirs and the Cretaceous source rock

because are the new targets for unconventional exploration and production (Spickert,

2014) their lithology is showed in the figure 2.

Figure 2. Generalized stratigraphic column of the Middle Magdalena Valley Basin.

Taken from Agencia Nacional De Hidrocarburos (2012)

2.2.1 La Luna Formation

This stratigraphic unit was subdivided in three members Salada, Pujamana

and Galembo (Sarmiento, Puentes, & Sierra, 2015). The geology of Salada member

are black mudstones, black shales, black calcareous claystone, concretions with

pyrite, and black limestone layers (Torres et.al.,2015). According to Spickert (2014),

the Pujamana member is composed of claystone, mudstone, gray shale, and chert.

The geology of Galembo member are calcareous shales with limestone layers and

nodules (Torres et.al.,2015). Furthermore, “the Galembo member generally contains

minor to trace amounts of carbonate (2,4%), in contrast, the Pujamana and Salada

members are carbonate-rich (43,2% and 40,4%)” (Quintero & Ríos, 2016)

2.2.2 Cumbre Formation

The geology of this unit are “a set of dark gray sandstones with intertwined

stratification, alternating with black pyrite shales, which emerge between Arcabuco

and Moniquira” (Pulido, Ulloa, & Rodriguez, 1986). So it is possible to identify

according to Spickert (2014) the change from continental deposition to shallow

marine deposition with a grain size of “claystone and greenish siltstones, quartz

sandstones, of medium grain and a calcareous level towards the base ” (Pulido,

Ulloa, & Rodriguez, 1986)

2.2.3 Umir Formation

This unit are composed by shales gray to black, carbonaceous, micaceous,

with ferruginous concretions and abundant intercalations towards the roof of lithic

sandstones, gray siltstones and the presence of exploitable carbon mantles.

(Sarmiento, Puentes, & Sierra, 2015). Particularly, base to ceiling sandstones have a

compositional increase in lithic components varying from sublitharenites to

lithoarethites (Sarmiento, Puentes, & Sierra, 2015) and their formation it is in the

upper Cretaceous (Spickert, 2014)

2.2.4 Paja Formation

It is composed by shales dark gray to blue, fossiliferous, laminated with

intercalations of fine grained yellowish gray sandstones or gray fossiliferous

limestones, locally sandy. (Sarmiento, Puentes, & Sierra, 2015). Furthermore, their

deposition took place in an open sea, epicenter-like environment with restricted

influence of terrestrial material. (Sarmiento, Puentes, & Sierra, 2015) and their

formation is in the Creataceous (Caballero, Parra, & Mora, 2010)

2.2.5 Tablazo Formation

Tablazo Formation is the uppermost unit in the basal calcareous group. It is

composed mostly of biomicrites, calcareous shales, and fossiliferous sandstones

(Spickert, 2014), and quartzites and siltstones of light color with a gravel size

(Caballero, Parra, & Mora, 2010). The age is estimated between “the upper Aptian

9 and the lower Albian, by comparison with the supra and infra-lying formations.”

(Sarmiento, Puentes, & Sierra, 2015)

2.2.6 Simiti Formation

The unit consists of shales carbonaceous, gray to black, laminated and soft,

locally calcareous with concretions commonly fossiliferous impregnated with oil

that form a thickness of 410m (Sarmiento, Puentes, & Sierra, 2015). Furthermore,

“It is estimated that 70% could be fissile claystones with flat parallel lamination,

forming sets of very thick layers. In the middle part there are intercalations of

calcareous sandstones with fossiliferous concretions and micritical layers towards

the ceiling.” (Sarmiento, Puentes, & Sierra, 2015)

2.2.7 Mugrosa Formation

The unit consists varicolored mudstones where reddish and yellow colors

predominate over gray tones. In these are interspersed in a much smaller proportion

layers of very coarse grain to conglomeratic sandstones, decreasing grain and with

moderate lateral continuity. Furthermore, the characteristics correspond to fluvial

systems of alluvial plains and meander rivers. (Sarmiento, Puentes, & Sierra, 2015)

2.2.8 Cimarrona Formation

The unit was divided into 4 Members units, The Fría, Level of Sandstones and

Shales, Zaragoza Member and Primavera Member where the lithology is

conglomerates of quartz, siliceous siltstone, cherts, feldspathic sandstones with

10 coarse grained, shales with intercalations of sandstones and siltstone. Furthermore,

the total thickness of the formation is 424 meters. (Melo, 1988)

2.3 PETROLEUM GEOLOGY

A century of exploration history in the basin has lead to the discovery of about

1,900 MMBO, 2.5 TCF and a total of 41 fields (Barrero, Pardo, Vargas, & Martínez,

2007). The source of the hydrocarbons comes from the total organic carbon (TOC)

values and the most important source rock is the Cretaceous limestones and shales

of the La Luna and the Simiti-Tablazo formations and their TOC are high (1-6%)

(Barrero, Pardo, Vargas, & Martínez, 2007). Furthermore, 97 % of the reservoirs

proceed from the “continental paleogene sandstones (Paleocene-Miocene), Lisama,

Esmeraldas-La Paz, and Colorado-Mugrosa formations, with average porosities 15-

20% and average permeability 20-600 md.” (Barrero, Pardo, Vargas, & Martínez,

2007)

3. METHODOLOGY

3.1 CORES DESCRIPTION

The cores used to feed the algorithm are belonging to three wells called well

X, well Y and well Z. While the well X presents 52 images of cores, the Y well

registers 26 images of cores, and the Z well shows 111 images of cores. In all cases

each image corresponds to one feet of core. The locations of the wells are showed in

the figure 3. The X and Y well belong at Mugrosa Formation and Z well to

Cimarrona Formation

Figure 3. Location of the worked wells, well X, well Y and well Z. Taken from Servicio

Geologico Colombiano (2018)

3.1.1 Well X

The well X is divided in two type of rock, metamorphic and sedimentary rocks

(Figure 4). The first section corresponds to fresh metamorphism as basement, and it

is a gray schist with white bands, biotitic with internal variations with probable areas

of gneiss with many and thick quartz veins. On the other hand, there are areas with

muddy sedimentary appearance or phyllite. Many ptygmatic folds are found locally

with “fluids” structures, and mostly present faults with hydrocarbon. (Servicio

Geologico Colombiano, 2018)

The second section are the sedimentary rocks where the base is a sandy

conglomerate in a supported matrix with pebbles up to 2 cm of schist and milky

quartz, towards the top are the conglomeratic sandstone and the greenish gray

sandstone due to alteration with moderate and bad selection impregnated of

hydrocarbons. Compositionally it is a sublitharenite with schist among 10% and

15%. Furthermore, in a depth of 4490 feet there is presence of sandy siltstone with

a color greenish gray and a mottle reddish yellow and dark red. The fraction of sand

oscillates between 30% and 40% with grains fine, sub-angulars and bad to moderate

sphericity. In some areas there is a transition to muddy sand with pebbles up to 4 or

5 mm of milky quartz (Servicio Geologico Colombiano, 2018)

Likewise, in a depth of 4489 feet the base is a sandy conglomerate with

supported matrix, schist pebbles, milky quartz and large muddy intraclasts. In the

13 top part it exists a transition to muddy sandstone with good to moderate selection,

grains sub-rounded to sub-angulars and good to moderate sphericity.

Figure 4. Stratigraphy of well X with a gap between 4504 feet and 4299 feet. Taken from

Servicio Geologico Colombiano (2018)

Compositionally it is a lithic sandstone with schists between 20% to 25%, high

bioturbation and traces of muscovite (Servicio Geologico Colombiano, 2018).

The depositional environment begun with a floodplain from of a river

depositing small grain size as sandy siltstone. Then, the flow of the river returned to

be normal and it begun to transport and to deposit big sediments that resulted in

rocks in facies of bioturbated massive sandstones, conglomeratic sandstones and

conglomerate with supported matrix (Servicio Geologico Colombiano, 2018). After

that, the environment was a floodpain again and deposited small sediments generated

siltstones. However, there was a crevasse complex depositing sandstones, and just

after, occurred an event that formed a floodplain that deposited many sediments to

generate a sandy siltstone. Finally, the environment was a river with high energy,

but as time passed the energy decreased resulting in a grain decreasing sequence.

3.1.2 Well Y

The stratigraphy of the well Y (Figure 5) starts with a feldespatic sandstone

yellowish gray, sub-angular and sub-rounded with a good selection, moderately hard

and it presents traces of muscovite and biotite <1%. Then, in a depth between 6259

and 6262 feet there is feldespatics sand, light olive gray, sub-angular and sub-

rounded with a moderate selection and traces of muscovite. Furthermore, an

arcosalitic, light olive gray colored with a composition of 70% quartz, 20%

15 feldespar, 10% lithic, sub-angular with a moderate selection, presence of bioturbation and cross stratification in tundish.

Figure 5. Stratigraphy column of the well Y with a serie of gaps between 5788-5814 feet, 5817-

5861 feet,5864-5902 feet, 5904-6028 feet, 6033-6261 feet and 6262-7078 feet. Taken from

Servicio Geologico Colombiano (2018)

In a depth of 6030 feet there is a feldespatic sandstone with a composition of

70% quartz, 15% lithic and 15% feldspar and it is slightly calcareous, yellowish

gray, sub-angular with moderate selection. (Servicio Geologico Colombiano, 2018).

At the depth of 5903 feet, it presents a lithic feldespatic sandstone slightly calcareous

with a yellowish gray color to light olive gray, sub-angular, moderate selection and

differential cementation, the sedimentary structures are bioturbation and cross

stratification. At the top, there is feldespatic sandstone with poor to moderate

selection, a feldespatic sandstone slightly calcareous with composition of quartz

70%, feldspar 20% and lithic 10%, sub-angular and sub-rounded with good selection

and presence of muscovite. (Servicio Geologico Colombiano, 2018)

The deposition environmental of all stratigraphy column was fluvial due to

good a moderate selection of the grains, the presences of bioturbation, traces of

muscovites and biotite, yellow and gray color characteristics of river environment

and the same lithology during almost 35 feet.

3.1.3 Well Z

The well Z (Figure 6.A and 6.B) begins with clay and sandy siltstone, slightly

calcareous with a gray color and moderate bioturbation. Also, it presents thin

intercalations of very fine quartz sandstones with an intense bioturbation. It is

possible to identify trace of pyrite and glauconite (<1%), parallel lamination

predominant, locally waved ripple with ichnofacies of Cruziana. 30 feet closer to the

17 surface it is possible to find very fine quartz sandstones gray, slightly muddy and

calcareous, with relicts of parallel lamination and remains of shell. (Servicio

Geologico Colombiano, 2018).

Figure 6.A Stratigraphy column of the well Z. Taken from Servicio Geologico Colombiano

(2018)

Figure 6.B Stratigraphy column of the well Z. Taken from Servicio Geologico Colombiano

(2018)

At a depth of 6992 feet there is gray claystones and siltstones slightly

calcareous, with traces of glauconite and pyrite (<1%), intensely bioturbated but

with relicts of parallel lamination and presence of ichnofacies of Cruziana. In a depth

of 6980 there is presence of very fine sandstone and quartz siltstones some muddy

and gray calcareous, intense bioturbation, ichnofacies of Cruziana, less of 1% of

glauconite in the top of the layer and rounded quartz pebbles. After that, there is

muddy, very fine, gray siltstones and quartz sandstones, slightly calcareous intensely

bioturbated, the lower contact is bioturbated and there is presence of ichnofacies

type Cruziana and Glossifungites. Likewise, some feet up there is presence of sandy

conglomerate supported calcareous matrix with many benthic foraminifera and

sporadic planktonic, intense bioturbation, lower contact bioturbated and ichnofacies

type Glossifungites. (Servicio Geologico Colombiano, 2018)

On the other hand, in a depth of 6954 feet there is gray siltstone, dark gray

claystones and sandstone quartz very fine slightly calcareous, low bioturbation, and

in the middle part there is siderite nodules with intervals of glauconite traces.

Moreover, there is presence of oligomitic sandy conglomerates, supported

calcareous matrix and muddy sandstone of quartz with a moderate bioturbate,

parallel and ripples lamination with a ichnofacies of Cruziana. Then, at the depth of

6932 feet, there is gray siltstone with thin intercalations of light gray very fine quartz

sandstones. In the low middle, bioturbation is intense while at the top it is low.

Moreover, there are traces of glauconite and pyrite <1%. After that, there is a

oligomitic conglomerate, clast supported in the base and supported matrix towards

the roof, olive gray colored, massive for bioturbation, many benthonic foraminifera

and sporadic planktonic, the matrix is very fine with traces of glauconite and pyrite.

At the top in a depth of 6922 feet, there is olive gray colored foraminifera grainstone,

with sand sheets as fine as muddy, few planktonic foraminifera, very rounded

pebbles of quartz smaller than 1 cm, traces of glauconite and pyrite less than 1% and

presence of faults that are stuffed of calcite and hydrocarbons. (Servicio Geologico

Colombiano, 2018)

The environmental deposition was coastal and it begun in the shoreface where

the fine grain size was deposited due to the fact that there was presence of ichnofacie

as skolithos. Afterwards, the tide went up and deposited grain size silts, generating

wave ripples, that lasted a long time because the lithology is 27 feet thick, if it is

inferred that the gaps between the depth of 7003 and 7029 feet are the same

lithology. Then, the tide went down and it deposited fine and very fine grain size and

this loop lasted a long time due to the presence of a sequence of sandstone and

siltstone. But, at the depth of 6958 feet there is presence of sandy conglomerate

whence their deposition was in a beach zone and then the tide loop begun again

generating a sequence of sandstone and siltstone. At the top of the stratigraphy

column, it is possible to find a sequence of conglomerate and grainstone as a result

21 of the depositional environment which was in a distal beach, and then the tide went

up in turbulent conditions to generate a grainstone with calcite filled fractures.

(Servicio Geologico Colombiano, 2018)

3.2 ALGORITHM

3.2.1 Convolutional network

The main purpose of the convolutional networks is to reduce the

computational weight when the algorithm is working with arrays of any image.

However, when the arrays contain a lot of information or are too big, the process of

the algorithm and the computational performance could slow down. Consequently,

the convolutional network extracts the most significant characteristics of an image

in order to decrease the matrices of characteristics (Martínez, 2017). Moreover, “the

outputs of the convolutional units form the inputs to the subsampling layer of the

network” (Bishop, 2006)

3.2.1.1 Convolution

Convolution process is the main step within a neural network, the purpose of

this layer in the network is to extract the characteristic of an input image because

each picture is an array (Martínez, 2017). The main idea is to have two arrays or

matrices, where one contains the information of the image and the other is the kernel

or filter that contains the characteristics of interest. So, the process behind the

convolution is to move the kernel upon the image matrix with a jump of one pixel.

In each position, the multiplication between the two matrices is calculated and the

results are added to obtain an integer as shown in figure 7.A and 7.B (Martínez,

2017). Moreover, it is important to mention that depending of the values of the

kernel, the algorithm will follow different aspects or patterns into the picture, and

the number of filters depend on the number of characteristics of interest. Principally,

the characteristics are determinated with the value of the pixel in the case of the

figure 7.A the regions of interest are the ones with a number one.

7.A.1 7.A.2

Figure 7.A. The matrix A represents the information of the input picture 5x5, the matrix B

represents the characteristics, in other words the kernel 3x3. Taken from Martínez (2017)

Figure 7.B. Graphic process of the convolution,

where both matrices are multiplied , and it is

sum the results of each box. So, they are

denominated convolved feature. Taken from

Martínez (2017).

3.2.1.2 Pooling

The purpose of this layer is to reduce the dimensions of the image while

holding the important information. Some examples of pooling are max-pooling,

average-pooling, sum-pooling among others. (Martínez, 2017). Similarly to the

convolution, the pooling extracts the most important characteristic of the image

reducing its size, depending only on the relative spatial coordinates (Shelhamer,

Long, & Darrell, 2016), in other words, pooling depends on the move of a certain

window. This window checks the values of the image and depending on the type of

pooling it extracts the characteristics. As result, the pooling “converts smaller and

more manageable input representations, reduces the number of parameters and

calculations in the network. Therefore, controls overfitting, makes the network

invariant to small transformations, distortions and translations in the image of entry”

(Martínez, 2017)

In this work, the algorithm of the convolutional network is the max pooling.

First, a window or neighborhood is defined, and the elements or high values of the

matrix image are taken. Then, the window does move to a next zone to take a new

high element, this process lasts until the image array is finished (Figure 8) (Martínez,

2017)

3.2.1.3 Flatten

In general, the flatten layer is used at the end of the neural network because its

purpose is to compress the final information of the picture after going through a

series of convolutional and max pooling layers. For example, at the end of the

process, the final image is too small for the convolutional and max pooling layers

but it is too deep for other filters along the process. As a result, the flatten layer

reduces all the layers or information of them in a single layer.

Figure 8. General idea

of max-pooling into an

algorithm. Taken from

Martínez (2017) .

3.2.1.4 Dropout

The dropout layer usually is the last layer of the neural networks before the

final result, because its function is to configure the number of neurons that will learn.

If the algorithm used all neurons between layers, the neural network will just learn

one way to recognize patterns and its learning rate will be low. On the other hand, if

25 it randomly it uses a determined amount of neurons, the system will learn many

possibilities to detect different patterns of the image, and the probability of neural

network learning better will increase.

3.2.2 Classifier

In the machine learning there exists many classifiers that are regressions, and

each regression depends on the purpose of the neural network. In this case, the

classifier is the softmax regression or normalized exponential (Bishop, 2006). The

softmax regression belongs to the exponential family and it is an expansion of the

logistic function (Martínez, 2017). Thus, its based on the classification of objects

into two or more families or classes.

The purpose of the softmax regression is to estimate the probability � (� =

�|�) for each value �=(1, 2,…,K). As a consequence, a vector K-dimensional is

obtained when the sum of all the probabilities of each class is equal to 1

(Martínez, 2017). The expression of softmax function derivatives of the

multinomial distribution in the equation 1 (shown below).

Equation 1. Taken from Bishop (2006)

However, when used the softmax regression, it is necessary to calculate the

function of cost that indicates if the neural networks train properly. Basically, a

26 function of cost is “a measure of how wrong the model is in terms of its ability to

estimate the relationship between X and y.” (McDonald, 2017) and the main idea is

to reduce the cost function to zero. Theoretically, the learning rate is inversely

proportional to cost function whereby its expected that while the neural networks

learn to increase the learning rate, the cost function tends to cero.

3.2.3 Optimizer

The optimizer is the function that regulates the weights between layers in each

iteration. In the present work, the optimizer is the Stochastic Gradient Descent(SGD)

or also known as sequential gradient descent. This optimizer works with a little

training data and based on that, reduces the cost function. If the cost function

comprises a sum over data points E= ΣnEn , then, after presenting pattern n, the

stochastic gradient descent algorithm updates the w vector parameter using the

equation 2 (Bishop, 2006).

Equation 2. Where τ denotes the iteration number, and η is a learning rate parameter.

Taken from Bishop (2006)

Moreover, the SGD purpose is to work with little data, because it helps to

“reduce the variance in the update of the parameters and this allows a more stable

convergence, allowing the use of linear algebra for the efficient calculation of cost

and gradient” (Martínez, 2017). It is important to take into account that in SGD the

27 way in which data is presented to the algorithm will affect its performance, since, if

in neural network “if data are presented in any order, this can introduce an offset in

the gradient and lead to a poorer convergence” (Martínez, 2017). As a consequence,

the neural network will not learn properly and give wrong results.

3.2.4 Model

In general, the algorithm consists of a multilayer model that contains an input

layer and output layer. Also, there exists one or more intermediate hidden layers that

receive the name of hidden neurons (Figure 9) (Hernández, 2017). In this context,

the specific visual model is the Fully Convolutional Network (FCN) that is a deep

learning. It consists of a multilayer model that has been used to create different

networks to classify, to segment images, to detect objects and a semantic

segmentation. Besides, the general idea of the model is to take all pixels, in which

each pixel is labeled with the class of its enclosing object or region. Some examples

of this model are Vgg16, Vgg19, Resnet50, among others. The differences are the

pixel accuracy and the learning rate of the model.

The Fully Convolutional Network used in this work is Vgg16 model. Their

structure is based on six blocks, the first two blocks contain 3 layers, the third and

fourth blocks are 4 layers, then, block number five has 8 layers and finally, the sixth

block consists of 4 layers. Furthermore, between each layer it can be found a scalar

number that configures the next layers. In general, the majority of blocks are

28 composed by two essential layers, convolutional layer and maxpooling layer.

Moreover, each block can have two convolutional layers or more, with the purpose

of extracting the features of the image that will be an array with more accuracy.

Afterwards, the last block contains a flatten and dropout layers with a softmax

regression as the activation function that prepares the final image to be shown.

Figure 9. Internal structure of a multilayer model. Taken from Hernández (2017)

Likewise, within the above structure there also exists two fundamental

structures: (i) the Faster-RCNN (Faster Region based Convolutional Neural

Network) and (ii) Mask-RCNN (Mask Region Convolutional Neural Network). The

first one has two stages where it begins with the Region Proposal Network (RPN)

and it function is to provide a candidate object framing it with boxes. Then, the

following stage is the classification and framing box regression in two different

steps. Mask-RCNN presents the same structure mentioned before. The RPN and the

classification and framing box regression, but in this case the last step is executed

29 simultaneously. Furthermore, Mask has other characteristics, such as the

segmentation of each class. (He, Gkioxari, Dollár, & Girshick, 2018)

3.2.5 Training phase

The training phase is the most important step in the neural network because in

this part the network will learn all the characteristics of the data. From this

perspective, the training model is the backpropagation and its objective is that “the

errors of the units of the hidden layers are determined by backpropagation of errors

of the units of the output layer.” (Hernández, 2017). So, the structure of the

backpropagation model can be divided in three parts: the first one, is the feedforward

training; the second one, are the errors of backpropagation; the last one, is th

weights adjustment (Figure 10).

Figure 10. Example of

backpropagation model.

Taken from Shelhamer,

Long, & Darrell (2016)

3.2.5.1 Feedforward training

Feedforward training shows in the figure 11, it can approximate virtually any

function of interest to any desired degree of accuracy, providing enough hidden units

that are available (Bebis & Georgiopoulos, 1994). Thus, “its input nodes are the ones

30 with no arcs to them, and its output nodes have no arcs away from them. All other

nodes are hidden nodes.” (Montana & Davis, 1989). So, when the state of all the

input nodes are set, the values propagates into the network while the other nodes

establish their state. But, when the output node obtains a value, it has to go traverses

a series of arcs, whereby the “n” layer of such a network consists of all nodes which

are “n” arcs traversal from an input node (Montana & Davis, 1989). The last process

of this method is to compare the value of y with the value of data training. In the

case of the images, these are the values of the pixel and the purpose of them is to

propagate the signal back to the beginning of the process of backpropagation error.

Figure 11. Process of feedforward training. Taken from Hernández (2017)

3.2.5.2 Backpropagation error

The backpropagation error is a method to supervise where the machine will

learn of its errors. The general idea is to involve an iterative procedure for

minimizing the error function, with adjustments to the weights made in a sequence

of steps. For this purpose, it is possible to distinguish two stages of the process: the

31 first one is to derivate the error function with respect to the weights that must be

evaluated; the second one is to use the derivates to compute the adjustments that

need to be made to the weights (Bishop, 2006). The general formula of

backpropagation is the equation 3, as shown below.

Equation 3. Taken from Bishop (2006)

In the equation 3, δ is the error in each neuron, �kj is the information of

backpropagation, aj is the information of the input data and h’ the derivation of

activation function. In that order of ideas, this means that “the value of δ for a

particular hidden unit can be obtained by propagating the δ’s backwards from units

higher up in the network” (Bishop, 2006). Furthermore, with the equation 3 the

algorithm calculates the error in each neuron backwards and with this information,

it adjusts the weights of the neurons. (Figure 12)

3.2.5.3 Weight adjustment

The final phase of the method of backpropagation training is the weights

adjustment. In this part the algorithm uses the activation function, in other words, it

uses the optimizer that is the stochastic gradient descent, mentioned before. This

process takes place in the final part of each iteration of the algorithm, where the

variables that affect the weight of the neurons are the following: (i) the derivation of

the activation function or h’, (ii) the coefficient � that affects the velocity of the

learning rate and (iii) the net input � (Figure 13). The value of � is calculated by test

of trial and error. Usually, it uses a high value of � and while the learning process

advances it will decrease that value. Under other conditions, it can begin with a low

value and increase it while the program advances, but in the final phase of the

process, the value decreases again. (Hernández, 2017)

Figure 12. Process of backpropagation error. Taken from Hernández (2017)

Figure 13. Process of weights adjustment. Taken from Hernández (2017)

4. RESULTS

The results were obtained from a computer Mac Air 13’ 2015 with a graphic

processor of 1.6 GHz Intel Core i5. The algorithm was executed with a two different

datasets: the first one was to prove the functionality of the algorithm and consisted

of 15 images of core for training phase and other 15 images for test phase. The first

data set ran with 4 classes (background, fracture, sandstone, siltstone), 10 epochs of

3 iterations and in each iteration the algorithm was fed with 5 images with a size of

238 x 91 pixels. The training phase was 3 hours long with a probability threshold

greater than 0.9.

Then, the second dataset was 1966 core images in total, each one of 0.1 feet

to feed the algorithm with the most amount of images. It ran with 16 classes

(background, fresh metamorphic, hydrocarbon, sandy conglomerate, sandy siltstone,

non-differentiated bioturbation, sandstone, muddy sandstone, clayey siltstone,

siltstone, calcareous claystone, claystone, calcareous sandstone, conglomerate,

calcareous siltstone, grainstone), 30 epochs of 25 iterations, in each step the

algorithm was fed with 8 images with size of 740 × 202 and 272 × 63 pixels. The

training phase was 20 hours long with a probability of threshold greater than 0.3.

The figure 14 shows the total loss value of both datasets, where the orange

indicator belongs to the small data set and the red indicator represents the big dataset.

The first figure, show values of training phase that were 0.602 and 1.0709 for the

34 small and big datasets. The second figure represents the validation phase and their

results were 2.561 and 1.122. However, the loss value is the sum of 5 components,

where these components are indicators of each learning rate and shows the efficiency

of learning the algorithm (Figure 15).

Loss value

Figure 14. Graph of loss value. Training phase in the first one and validation phase in the second

one.

Loss value

Figure 15. Graphs of loss value in each loss component of the training phase

Training components are indicators of the algorithm quality to identify,

classify and segment the images. For example, the mrcnn box loss indicates how

good the capacity of the algorithm to localize objects is. The mrcnn class loss shows

how good is the the ability to classify each object to a class. Else ways, the mrcnn

36 mask loss evidences how good the algorithm segmented each object in a particular

class. However, the graphics of rpn box loss and rpn mrcnn loss, exposed the same

parameters of mrcnn box loss and mrcnn class loss. On the other hand, the difference

stands in the internal structure to differentiate the characteristics of the images, as it

was mentioned before.

Loss value

Figure 16. Graphs of loss value in each loss component of the validation phase

Figure 15 represents a similar behavior in all training phase graphics,

nevertheless, it also presents an anomaly in the mrcnn class loss. The figure 16 shows

the behavior of the loss components to the validation phase where it presents an

unstable graphic of mrcnn class loss in both data sets. It shows a threshold of 0.3 and

0.39 of loss value in the big dataset, while in the small dataset it shows a loss value

of 0.27 and 0.345. Additionally, there is an increase of the orange graphic in the rpn

box loss.

Figure 17. 0.1 feet of image of well cores segmented. Well X

Figure 18. Image segmentation of well core

Sandstone and conglomerate with

hydrocarbons were identified. Taken from

Servicio Geologico Colombiano (2018)

Figure 19. Correlation of image segmentation of well core with the stratigraphic column

The figure 17 presents the class identified by the algorithm, where the orange-

yellow zone corresponds to sandy conglomerate, while the other colors are oil

impregnation with a prediction percentage of 34.2% and values of 47%-51%

respectively. Likewise, the figure 18 shows the correlation of the original images of

well core, and the prediction produced by the algorithm where some zones were not

identified. However, it is possible to relate the segmented core with their

stratigraphic column (Figure 19), because the algorithm gave as a result the lithology

of the stratigraphy.

The figure 20 shows the prediction of the algorithm to a core of well Y, where

the purple-pink color represents a sandstone with an 89% of reliability. It is possible

to observe the presence of a rectangle that identifies an object and classifies it as

39 fracture with 44% of probability but it does not segment it. Then, in the figure 21 the

other colors within the purple region are classifying errors of the algorithm. But, it

is possible to identify that the algorithm segmented with the same color the entire

core where the image is correlated with the stratigraphic column (figure 22). It is

shown that the algorithm segmented a large region of purple-pink color as well as

the sandstone which is the correct answer.

Figure 20. 0.1 feet of image of well cores segmented. Well Y

Figure 21. Image segmentation of well

core. Sandstone was identifying. Taken

from Servicio Geologico Colombiano

(2018)

Figure 22. Correlation of image segmentation of well core with the stratigraphic column

At this point, the algorithm efficiency was proved with a new image of a new

well, where it was not in the training phase or validation phase but its lithology was

founded in other well cores as in well X. According to the Servicio Geologico

Colombiano (2018) this core is a gray siltstone and claystone (figure 23).

Figure 23. New well core image of a new well. Taken from Servicio

Geologico Colombiano (2018)

Figure 24. 0.1 feet of image of well cores segmented. New well

Figure 25. Image segmentation of well core. Sandstone was identified. Taken from Servicio

Geologico Colombiano (2018)

The figure 24 shows two segmentation in the same region of sandy siltstone

with a 37% of dark blue color and muddy sandstone with a 49% of reliability with

light blue. Also, it identifies a fracture with 43.4%, but it does not segment it. In

some regions the algorithm does not classifies them in the left side of the original

picture of the well core. However, in the figure 25, where the segmented total core

42 is located, it is possible to observe that the algorithm classifies most of the core as a

siltstone. Besides, one part of the core was not segmented but it was recognized by

the algorithm.

Figure 26. Stratigraphic correlation from electric register like the Spontaneous Potential (SP)

From the results given by the algorithm it is possible to realize a stratigraphic

correlation as shown in the figure 26. In this case, a facie correlation exists between

the X and Y well with the massive sandstone bioturbated, in the X well this facie is

found in a depth of 4501 ft and in the Y well is in a depth of 6260 ft. Furthermore,

those wells are correlated by their electric records primarly with the spontaneous

potential, given that both records present the same behavior. However, it is only

possible to correlate these two wells because they have a similar formation in this

area.

5. DISCUSSION

The loss values of the training phase and validation phase were similar, but in

their indicators were different specially in the mrcnn class loss. In the training phase

this component presents a normal behavior with a little anomaly in step 17 where it

43 increased its value. This means that the algorithm was trained adequately to identify

objects, classify them as well as to segment them. Although, when the algorithm was

in the validation phase, its results were not good because when it segmented the

validation data and then compare its results with the correct answer given by the

supervisor, those images were not classified correctly. For this reason, the graphic

of mrcnn in the validation phase presented many variations. Furthermore, the orange

graphic in this component showed a similar behavior, so the amount of the dataset

is not the problem in this indicator.

Likewise, the indicator of rpn box loss illustrated an anomaly in the validation

phase and this can be due the process of identification and classification of the image

by steps. Where it accumulates many information that in occasions is similar in some

groups. So, the algorithm does not relate the properties given to extract in each group

and “confuse” the characteristics of one group with other.

On the other hand, the predictions given by the algorithm shows that the

segmentation with the validation dataset (figure 18 and 21) was good. This, because

it classifies the large area of the core in the correct group and this was confirmed

with the stratigraphic column. It also presented some mistakes, so was the case of

the segmentation of fracture group as the areas with oil impregnation, because the

algorithm presented zones where did not existed presence of this group.

Furthermore, in the images of well cores there existed many groups, with a decrease

44 in the reliability percentage as it is the case of the conglomerates in the well X

(Figure 17). Also, it showed an increase only when there is presence of one big group

as the sandstone of well Y (Figure 20).

In the same way, the principal objective of this work was achieved because

the algorithm can segment in a good way an image of well core that was not used in

a training and test phase. However, the algorithm had “doubts” of the classification

of muddy sandstone or sandy siltstone because it presented both groups. The

description of the core confirmed that in this case, it was a gray siltstone whereby

the algorithm hit the right group. In this circumstances the geologist plays a

fundamental roll, because his function is to confirm which of the groups presented

by the algorithm is correct.

In the case of the mistakes in the process of identification, classification and

segmentation of images, the principal factor is the amount of data and the amount of

epochs and iterations generated. First, the datasets used to run the machine learning

usually are more than 5000 images wide to train the algorithm. In this investigation,

there were 1966 images, which in comparison is a small amount of data. Second, the

learning rate will improve if the epochs and iterations are more and if training is

realized with a GPU (Graphics Processing Unit) instead of CPU (Central Processing

Unit). Whereby, the first one executes a specific function because it has a thousand

cores (computer definitions) in less time, while the CPU just runs with few cores a

45 general function and takes longer time, as in this case. Due to this factors, the

learning rate of the algorithm and the image predictions may seem affected.

6. CONCLUSION

Implementation of machine learning focused on the description of digital

images of well cores is a useful tool to complement the geologist work. It can

confirm the characteristics that he sees but also gives more options to describe a

possible aspect difficult to identify in the well core. This information can be

complemented with core tomographies, spectrometry, infrared analysis, etc.

Furthermore, to apply machine learning in the oil industry or geology purpose it

must be an algorithm with an equitable amount of images per group in the training

phase, so the algorithm has the same probability to classify all the groups instead of

focusing in one group to identify correctly. Likewise, the learning rate could improve

and reduce the mistakes, if the computer infrastructure was better and the dataset of

images of well cores was greater.

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