Developing Intelligent Synthetic Logs Application to Upper Devonian Units in PA.pdf

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Developing Intelligent Synthetic Logs:

Application to Upper Devonian Units in PA

Luisa F. Rolon

Thesis submitted to the

College of Engineering and Mineral Resources

at West Virginia University

in partial fulfillment of the requirements

for the degree of

Master of Science in

Petroleum & Natural Gas Engineering

Committee:

Professor Samuel Ameri, Chair

Dr. Shahab Mohaghegh

Dr. Razi Gaskari

Dr. Daniel Della-Giustina

Department of Petroleum and Natural Gas Engineering

Morgantown, West Virginia

2004

Keywords: Reservoir, Well logs, Upper Devonian, Pennsylvania, Artificial Neural

Network



ABSTRACT

Developing Intelligent Synthetic Logs: Application to Upper Devonian Units in PA

Luisa F. Rolon

A methodology to generate synthetic wireline logs is presented. Synthetic logs

can help to analyze the reservoir properties in areas where the set of logs that arenecessary, are absent or incomplete. The approach presented involves the use of Artificial

Neural Networks, as the main tool, in conjunction with data obtained from conventional

wireline logs. Implementation of this approach aims to reduce operation costs tocompanies.

Development of the neural network model was completed using a General

Regression Neural Network, and four wells that included gamma ray, density, neutron,and resistivity logs. Synthetic logs were generated through two different exercises.

Exercise one involved four wells for development and training of the network.Subsequently verification was carried out using each of the wells that were used to train

the network. The second exercise used three wells for training and development of thenetwork. A fourth well that was not used during training and calibration, was selected for

verification. Three combinations of inputs/outputs were chosen to train the network. In

combination “A” the resistivity log was the output and density, gamma ray, and neutronlogs, and the coordinates and depths (XYZ) the inputs. In combination “B” the density

log was output and the resistivity, the gamma ray, and the neutron logs, and XYZ were

the inputs, and in combination “C” the neutron log was the output and the resistivity, thegamma ray, and the density logs, and XYZ were the inputs.

After development of the neural network model, synthetic logs with a reasonabledegree of accuracy were generated. Results indicate that the best performance was

obtained for combination “A” of inputs and outputs, then for combination “C”, and

finally for combination “B”. In addition, it was determined that accuracy of syntheticlogs is favored by interpolation of data.

As an important conclusion, it was demonstrated that quality of the data plays a

very important role in developing a neural network model. A recommendation for future

works is to do a very careful quality control of the data before a neural network model is built. Conversely it was concluded that lithologic heterogeneities in the reservoir do not

affect performance of a neural network model in generation of synthetic logs.



Acknowledgments

First I thank God for giving me the capability and the courage to finish my thesis and

complete my MS in Petroleum and Natural Gas Engineering.

I don’t have the words to express my thanks and appreciation to Dr. Sam Ameri, chair of

my committee, who brought me to the Petroleum and Natural Gas Engineering

Department and encouraged me to complete my master's degree. I wouldn’t be ableaccomplish this without his support and advise, not only during this work but also

throughout the time I spent at the department.

I want to extend my sincere appreciation and gratitude to my research advisor Dr. Shahab

Mohaghegh, for introducing me to the fascinating area of Neural Networks, for his

friendship, and for his continuous guidance, encouragement, support and patiencethroughout this work.

Special thanks to Dr. Razi Gaskari and Dr. Daniel Della-Guistina for being in my

committee and for the enriching contributions and comments to this work.

My deepest gratitude to Mr. Richard Goings and Dominion Exploration and Production,

Inc. for providing me the data I used for this study. Without this valuable information thiswork couldn't have be completed.

Thanks to my colleagues and friends Nikola Maricic, Emre Artun, Jalal Jalali, BoydHuls, Miguel Tovar and Clay Blaylock, for keeping my morale high and for helping me

when I needed them. Thanks a lot guys, you are the best!

Special thanks to Beverly Matheny for her assistance and enthusiasm during every

semester spent in the department.

Finally, I want to dedicate this thesis to my parents Silvio and Dilma and my husband

Bret, who always gave me their support and encouragement, and most importantly, their

love. It kept me going during some of the difficult moments of this work. Thank you somuch, I love you.

iii



TABLE OF CONTENTS

1. INTRODUCTION ……………………………………………………………………..1

2. BACKGROUND ……………………………………………………………………5

2.1. Geological Setting ……………………………………………………………………..5

2.1.1. Description of the Murrysville & 100 Foot Sands ……………………………62.1.2. Description of the Gordon Sandstone ………………………………………...7

2.1.3. Description of the 2nd

Bradford Sand and the Speechley Sands ……………...7

2.1.4. Structural Geology ……………………………………………………………8

2.2. Well logs fundamentals ……………………………………………………………92.2.1. Gamma-ray log ……………………………………………………………….9

2.2.2. Porosity logs ………………………………………………………………...12

2.2.3. Spontaneous potential (SP) log ……………………………………………..142.2.4. Resistivity log ……………………………………………………………….16

2.2.5. Sonic log …………………………………………………………………….16

2.3. Fundamentals on Artificial Neural Networks ……………………………………172.3.1.Mechanics of neural networks ……………………………………………….192.3.2. Learning mechanisms for Artificial Neural Networks ………………………21

2.3.3. Training the network ………………………………………………………...24

2.3.4. General Regression Neural Network ………………………………………..25

3. LITERATURE REVIEW …………………………………………………………….274. METHODOLOGY …………………………………………………………………...28

4.1. Data Preparation …………………………………………………………………30

4.2. Neural network model development ……………………………………………..31

4.2.1. Exercise 1: Four Wells Combined …………………………………………..31

4.2.2. Exercise 2: Three Wells Combined, one well out …………………………...335. RESULTS …………………………………………………………………………….34

5.1. First Attempt: Data set from Buffalo Valley Field (New Mexico) ………………36

5.2. Southern Pennsylvania Logs: Upper Zone (1000’ to 2000’) …………………….485.2.1. Exercise 1 ……………………………………………………………………48

5.2.2. Exercise 2 ……………………………………………………………………49

5.3. Southern Pennsylvania Logs: Lower Zone (2500’ to 3500’) …………………….50

5.3.1. Exercise 1 ……………………………………………………………………505.3.2. Exercise 2 ……………………………………………………………………50

6. DISCUSSION ……………………………………………………………………….101

7. CONCLUSIONS ……………………………………………………………………106

REFERENCES ………………………………………………………………………...108

APPENDIX A: Calibration results (Southern Pennsylvania data set) ………………...110

APPENDIX B: Training results (Southern Pennsylvania data set) ……………………111

APPENDIX C: Neural network model results (Buffalo Valley Field data set) ………..112

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LIST OF FIGURES

Page

Figure 1. Location of the study area and wells analyzed (157, 168, 169,

174). A-A’ represents the line of the cross-section.

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Figure 2. Gamma Ray correlation of 2nd Bradford (distributary channel –deep).

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Figure 3. Gamma Ray correlation of Murrysville / 100 Foot Sands

(Braided Stream – Shallow).

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Figure 4. Cross-section of the Acadian clastic wedge, showing the

relationship of the Price-Rockwell and Catskill delta complexes.

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Figure 5. Structural map of the area, showing Structural Axes inSouthwestern PA.

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Figure 6. Gamma ray and sonic logs from the Alberta basin, and their

response to different lithologies.

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Figure 7. Gamma ray emission spectra of K-40, uranium, and thorium

series.

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Figure 8. Relationship between gamma-ray deflection and proportion of

shale.

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Figure 9. Example of SP and resistivity logs from the Alberta basin. 15

Figure 10. Sketch of a biological neuron. 17

Figure 11. Structure of a simple artificial neuron. 18

Figure 12. Architecture of a multilayer perceptron. 22

Figure 13. Supervised and Unsupervised scheme. 23

Figure 14. Training and verification curve. 25

Figure 15. Segment of the matrix prepared for well 157. 30

Figure 16. Cartoon to show distribution of wells used for training /testing

and Production dataset through exercise 1.

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Figure 17. Different combinations of inputs/ outputs used fordevelopment of neural network model.

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Figure 18. Combinations of wells for training, testing and verification

used in exercise 2.

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Figure 19. Location of the Buffalo Valley Field area and the wells used in

the first attempt.

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Figure 20. .tif files and the resulting Gamma Ray curve afterdigitalization. Well 219 Buffalo Valley Field

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Figure 21. .tif files and the resulting Density curve after digitalization.

Well 219 Buffalo Valley Field

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Figure 22. .tif files and the resulting Resistivity curve after digitalization.Well 219 Buffalo Valley Field

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Figure 23. .tif files and the resulting Neutron Porosity curve after

digitalization. Well 219 Buffalo Valley Field

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Figure 24. .tif files and the resulting Gamma Ray curve after


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Page

Figure 25. .tif files and the resulting Density curve after digitalization.


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Figure 26. .tif files and the resulting Resistivity curve after digitalization.


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Figure 27. .tif files and the resulting Neutron Porosity curve after


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Figure 28. Synthetic resistivity log Well 157, southern Pennsylvania area(lower zone). Exercise 1 and combination A of inputs and outputs.

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Figure 29. Synthetic resistivity log Well 168, southern Pennsylvania area

(lower zone). Exercise 1 and combination A of inputs and outputs.

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Figure 32. Synthetic density log Well 157, southern Pennsylvania area(lower zone). Exercise 1 and combination B of inputs and outputs. 57

Figure 33. Synthetic density log Well 168, southern Pennsylvania area(lower zone). Exercise 1 and combination B of inputs and outputs.

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Figure 34. Synthetic density log Well 169, southern Pennsylvania area

(lower zone). Exercise 1 and combination B of inputs and outputs.

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Figure 36. Synthetic neutron log Well 157, southern Pennsylvania area(lower zone). Exercise 1 and combination C of inputs and outputs.

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Figure 38. Synthetic neutron log Well 169, southern Pennsylvania area

(lower zone). Exercise 1 and combination C of inputs and outputs.

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Figure 45 Synthetic density log Well 168, southern Pennsylvania area


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Figure 53. Synthetic resistivity log Well 168, southern Pennsylvania area(lower zone). Exercise 1 and combination A of inputs and outputs. 78


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Figure 73. Synthetic neutron log Well 168, southern Pennsylvania area(lower zone). Exercise 2 and combination C of inputs and outputs. 98


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Figure 76. R 2 values obtained for the upper zone of the Southern

Pennsylvania data set, through exercise 1.

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Figure 77. R 2 values obtained for the lower zone of the Southern


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viii



LIST OF TABLES

Page Table 1. Common values of matrix density for different type of rocks. 13

Table 2. Common activation functions. 20

Table 3. Results for exercise 1 and combinations A, B, and C of inputs

and outputs. Buffalo Valley field data set.

46


and outputs. Buffalo Valley field data set.

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Table 5. Results for exercise 1 and combinations A, B, and C of inputsand outputs. Southern Pennsylvania area data set (upper zone). 48


and outputs. Southern Pennsylvania area data set (upper zone).

49


and outputs. Southern Pennsylvania area data set (lower zone).

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and outputs. Southern Pennsylvania area data set (lower zone).

52

ix



1. INTRODUCTION

Well logging, a geophysical technique that has been in use for almost one century, plays

an essential role in the determination of production potential in hydrocarbon reservoirs.

The well logging process involves lowering a number of instruments into a borehole,

which measures formation properties as function of depth. The collected data

measurements broadly fall into three categories: electrical, nuclear and acoustic. After

measurement, the log analyst interprets the data from the log in order to determine the

petrophysical parameters of the well. Therefore, logs constitute a very important tool in

the process of exploration and development of any petroleum field.

However, for economical reasons, companies do not always posses all the logs that are

required to determine reservoir characteristics.

This study presents a methodology that can help to solve the aforementioned problem by

generating synthetic wireline logs for those locations where the set of logs that are

necessary to analyze the reservoir properties, are absent or are not complete. Data used

were provided by Dominion E&P. The study area is located in southern Pennsylvania

(figure 1). The approach presented involves the use of artificial neural networks, as the

main tool, in conjunction with data obtained from conventional wireline logs.

During the last few years, artificial neural networks, a multi-dimensional-interpolation

system, have proven to be an efficient tool for prediction of reservoir properties. Actual

data are used to train the network; then the system can develop the best correlation

scheme between different properties of the reservoir and predict the same properties at

points where they are unknown.

1



AAr r mmssttr r oonngg CCoo..

CCr r oossss--SSeeccttii

A

174

SSoouutthhwweesstteer r nn PPeennnnssyyllvvaanniiaa,,

AAr r mmssttr r oonngg CCoo..

Figure 1. Location of the study area and wells analyzed (157, 168, 169, 174). A-A’ represents the line of the cross

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Figure 3. Gamma Ray correlation of Murrysville / 100 Foot Sands (Braided Stream – Shallow)

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The sequence of rock recorded through the set of logs used here belong to the Upper

Devonian of southern Pennsylvania (the Venango and Bradford plays), which have been

producing natural gas in the area since the late 1800s. The names of the units involved

from bottom to top are the following: 2nd

Bradford, Speechley, Gordon, 100 Foot, and

Murrysville (figures 2 and 3).

This work demonstrates that by following the methodology presented, synthetic logs can

be generated with a reasonable degree of accuracy. The intention of the technique used

here is not to eliminate well logging in a field but it is only meant to become a tool for

reducing costs for companies whenever logging proves to be insufficient and/or difficult

to obtain. This technique in addition, can provide a guide for quality control during the

logging process, by prediction of the response of the log before the log is acquired.

2. BACKGROUND

2.1. Geological Setting

The sequence of rocks involved in this study were deposited during the Devonian period,

when through the assemblage of the Laurussian continent.

This tectonic event, known in Appalachian area as the Acadian orogeny, led to

establishing of several river systems and a large prograding alluvial plain during Late

Devonian time. The mentioned sedimentary complexes are known as the Catskill and the

Price-Rockwell delta complexes (Boswell and Donaldson, 1988; Kammer and Bjerstedt,

1988).

The Catskill delta complex is composed of marine, transitional, and terrestrial clastic

rocks (Boswell and Donaldson, 1988). The lower portion, consisting from bottom to top

5



of the 2nd

Bradford, and the Speechley intervals (names assigned by local drillers), was

deposited in a variety of deltaic environments, related to the delta front. These units

constitute a sedimentary wedge that has been named the Bradford Play. The upper

portion, known as the Venango Play, comprises from bottom to top the Gordon, the 100

Foot and the Murrysville intervals (names assigned by local drillers). The environments

in this interval range from barrier-island complex in the Gordon Sandstone (McBride,

2004), to a complex of fluvial-braided river deposits in the 100 Foot and the Murreysville

zones. Figure 4 shows the Acadian wedge, and the relationship between the Bradford

and the Venango plays, as well as the relationship between the Catskill and the Price-

Rockwell deltas.

2.1.1. Description of the Murrysville & 100 Foot Sands

The Murrysville and 100 Foot sands are generally fine-to-coarse grained, quartz

cemented sandstones and conglomerates. The two formations, where developed, are

generally separated by a shale 30 to 40 foot shale interval. However, as with channel

deposits, this shale can often be scoured into by the younger Murrysville braided sands,

making the division between the two difficult to discern. For both units, much of the

primary porosity is intergranular with secondary porosity developed by mineral

dissolution and replacement, or from fracture porosity in areas with structural control.

Log correlation is often difficult in this interval due to rapid sediment changes within the

braided river environment. Often there is no clearly defined channel, but rather multiple

channels that are laterally discontinuous due to the high sediment load combined with

intermittent water movement, mainly during flooding events. Sand/conglomerate

channel lenses that interfinger with shale from overbank deposits often characterize the

6



two units. Variation in gamma ray, density, and resistivity values taken from well logs

can vary greatly from location to location, even in wells that are close offsets,

approximately 1000 ft apart (figure 2).

2.1.2. Description of the Gordon Sandstone

The Gordon sandstone is composed of a series of conglomerate, sandstone, and shales.

The sandstones of this facies are fine- to medium-grained, well sorted, well rounded, and

have good porosity and permeability. Log porosity has be measured up to 25% and

permeabilities have been measured up to 250 mD (McBride, 2004). The conglomerate

and coarse-grained sandstone of the upper upper shoreface and the foreshore tend to have

more cement and therefore a lower porosity and permeability (McBride, 2004). Gamma

ray, density, and resistivity values are more or less constant, although changes in

thickness occur from location to location (figure 2).

2.1.3. Description of the 2nd

Bradford Sand and the Speechley Sands

The 2nd

Bradford and the Speechley sands are quartz and feldspar cemented sandstone-

and-siltstone reservoirs. In general, these reservoirs have similar characteristics in all the

logs used, with little discontinuity among wells. There is no discernable water leg in

much of the area, and the dominant trapping mechanism is mostly structural with some

influence from stratigraphic changes. Gamma ray, density, and resistivity values are

relatively constant among wells in the study area. The Speechley interval is considerably

finer-grained than the 2nd Bradford (figure 3).

7



Figure 4. Cross-section of the Acadian clastic wedge, showing the relationship of thePrice-Rockwell and Catskill delta complexes (adopted from Boswell et al, 1996).

MurrysvilleAnticline

Figure 5. Structural map of the area, showing Structural Axes in Southwestern PA

8



2.1.4. Structural Geology

All of the wells in the study area fall within the Valley and Ridge Province of

Southwestern Pennsylvania. More specifically, the four wells analyzed in this work, are

located along the crest of the Murrysville anticline, a southwest / northeast trending

structural feature, which constitutes one of many low amplitude folds throughout

Southwestern Pennsylvania (figure 5). The observed structural features are

Pennsylvanian in age and formed during the Alleghenian orogeny, a tectonic event

correlated with the collision of the North American Plate with other continental plates, in

the late Paleozoic (Middle Ordovician to Permian).

2.2. Well logs fundamentals

2.2.1. Gamma-ray log

This log (figure 6) measures the natural gamma-ray emission of the various layers

penetrated in the well, a property related to their content of radiogenic isotopes of

potassium, uranium and thorium.

The tool may detect gamma ray energies of less than 0.5 to more than 2.5 millivolts.

Figure 7 shows the individual emission spectra for thorium, uranium, and potassium.

These elements (particularly potassium) are common in clay minerals and some

evaporites. In terrigenous clastic successions the log reflects the “cleanness”(lack of

clays) or “shaliness” (high radioactivities) (see figures 6 and 8) on the API scale of the

rock, averaged over an interval of depth. Because of this property, gamma-ray log

patterns mimic vertical sand-content or carbonate-content trends

9



It must be emphasized that the gamma-ray reading is not a function of grain size or

carbonate content, only the proportion of radioactive elements, which may be related to

the proportion of shale content. For example, clay free sandstones or conglomerates with

any mix of sand and pebble-clast sizes generally give similar responses, and lime

mudstone gives the same response as grainstone (Cant, 1992). The concentration of

radioactive elements in shale increases with compaction, so the shale line should be

readjusted if a thick section is being studied.

The Gamma Ray (GR) tool emits gamma rays into sedimentary formations to an average

penetration of approximately one foot. When gamma rays pass through a formation, they

experience successive Compton-scattering collisions with formation atoms (Cant, 1992).

These collisions cause gamma rays to lose energy (Bassiouni, 1994). Subsequently,

formation atoms absorb this energy through the photoelectric effect.

The amount of absorption is a function of the formation density. Therefore, the

radioactivity level shown on the GR log will be different for two formations that have the

same amount of radioactive material per unit volume but with different densities. The

lower density formation will appear to be more radioactive.

Cased hole use is an important application of the GR Log because the tool can be run in

completion and work-over operations. The GR log also can be used as a substitute for the

SP log in cased holes or open holes where the SP resolution is poor. When run with

casing collar locator logs, the GR also allows for a very accurate positioning of

perforating guns. GR logs are also used in locating source beds as well as in the

interpretation of depositional environment (Ameri, 2004).

10



Figure 6. Gamma ray and sonic logs from the Alberta basin, and their response

to different lithologies (adopted from Cant, 1992).

Figure 7. Gamma ray emission spectra of K-40, uranium, and thorium series

(adopted from Bassiouni, 1994)

11





Rock Type Matrix density (g/cm3)

Sand or Sandstone 2.65

Limestone 2.71

Dolomite 2.87

Anhydrite 2.98

Table 1. Common values of matrix density for different type of rocks.

The formula for calculating density porosity is :

)(

)(

f ma

bma

den ρ ρ

ρ ρ φ

−−

=

whereden

φ is density derived porosity,ma

ρ is the matrix density,b

ρ is the bulk density,

and f

ρ is the average density of the fluids in pore spaces.

Density of formation water ranges from 0.95 g/cc to 1.10 g/cc approximately depending

on temperature, pressure and salinity. Average density of oil is slightly lower than these

values and varies over an equally wide range. According to Bassiouni (1994), the

investigation ratio of the tool is shallow, therefore it investigates the invaded zone and

f ρ can be expressed by:

h xomf xo f )S 1( S ρ ρ ρ −+=

,

wheremf

ρ is the mud-filtrate density, S xo is the mud filtrate saturation in the invaded

zone, and h ρ is the invaded zone hydrocarbon density. In water-bearing zones where S xo

is equal to 1,h

ρ can be assumed to be equal tomf

ρ . For gas-bearing formations, it is

13



reasonable to assume thatmf

ρ is equal to 1.00. Therefore for practical reasons, 1.00 can

be used as a general value for the term f

ρ (Bassiouni, 1994).

2.2.2.2. Neutron Log

The neutron, a particle constituent of the atom, exhibits a high penetrating potential

because its lack of electric charge. Because of its penetration power, the neutron plays an

important role in well logging applications.

Because hydrogen is responsible for most of the slowing-down effect, measuring the

concentration of epithermal neutrons indicates the hydrogen concentration in the

material. In shale-free, water-bearing formations, the hydrogen concentration reflects the

porosity and lithology.

The neutron log measures the hydrogen concentration or hydrogen index in the rock. The

tool emits neutrons of a known energy level, and measures the energy of neutrons

reflected from the rock. Because energy is lost most easily to particles of similar mass,

the hydrogen concentration can be delineated.

2.2.3. Spontaneous potential (SP) log

This log records the electric potential between an electrode pulled up the hole and a

reference electrode at the surface. This potential exists because of electrochemical

differences between the waters within the formation and the drilling mud, and because of

ionic selection effects in shales (the surfaces of clay minerals selectively allow passage of

cations compared to anions). The potential is measured in millivolts relative to shale the

line (figure 9).

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Figure 8. Relationship between gamma-ray deflection and proportion of shale

(adopted from Cant, 1992).

Figure 9. Example of SP and resistivity logs from the Alberta basin, (adopted from

Cant, 1992).

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In shaly sections the maximum SP response to the right from normal, depending on the

salinity of the drilling mud. The best test of the reliability of the SP log in determining

lithology is to calibrate the log against cores and cuttings.

SP log is useful for detection of permeable beds, location of bed boundaries for

correlation purposes, determination of formation water resistivity, and indication of

formation shaliness.

2.2.4. Resistivity log

This log records the resistance of interstitial fluids to the flow of an electric current, either

transmitted directly to the rock through an electrode, or magnetically induced deeper into

the formation from the hole, as it is the case with induction logs (figure 9). The term

“deep” refers to horizontal distance from the well bore. Varying the length of the tool and

focusing the induced current measure resistivities at different depths into the rock.

Several resistivity and induction curves are commonly shown on the same track (figure

9).

Resistivity logs are used for evaluation of fluids within formations. They can also be used

for identification of coals (high resistance), thin limestones in shale (high resistance) and

bentonites (low resistance). In turn, for wells where few types of logs have been run, the

resistivity log may be useful for picking tops and bottoms of formations, and for

correlating between wells. Freshwater-saturated porous rocks have high resistivities, so

the log can be used in these cases to separate shales from porous media (sandstones and

carbonates).

2.2.5. Sonic log

This log (figure 6) measures the velocity of sound waves in rock (Ameri, 2004).

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Velocity depends on 1) lithology 2) amount of interconnected pore space, and 3) type of

fluid in the pores.

The log is useful for delineating beds of low-velocity material such as coal (figure 6) or

poorly cemented sandstones, as well as high-velocity material such as tightly cemented

sandstones and carbonates or igneous basement. Sonic logs are also important in

understanding and calibrating seismic lines.

2.3. Fundamentals on Artificial Neural Networks

An artificial neural network is a computing parallel scheme based on the biological

neural system configuration (Mohaghegh, et al., 2002; Poulton, 2002, Faucett, 1994,

White et al., 1995). A neuron in the brain (figure 10) is a unique piece of equipment that

consists of three types of components called dendrites, cell body or soma, and axon.

Dendrites are the sensitive part of neuron that receive signal from other neuron. Soma

calculates and sums the signals and transmitted to other cells through axon. The

biological neuron carries information and transfers to other neuron in a chain of

networks.

Soma

Axon

Dendrite ofanother Neuron

Synaptic

Gap

Dendrite

Axon of

another Neuron

Soma

Axon

Dendrite ofanother Neuron

Synaptic

Gap

Dendrite

Axon of

another Neuron

Figure 10. Sketch of a biological neuron (adopted and modified from

Faucett, 1994).

17



The process of growing and learning in the human brain is one of creating neural

connections through an associative process based on patterns received from the senses.

The artificial neuron imitates the functions of the three components of the biological

neuron and their unique process of learning.

The process of learning in an artificial neural network is similar to the process that is

performed in the human brain. Artificial neural networks are systems mathematically

designed to receive, process, and transmit information. Information processing occurs at

the neurons. The simple neuron (figure 11) consists of an input layer, activation function,

and output layer. The input layer receives signals from the external environment (or other

neuron). The activation function is the internal neuron that calculates and sum the input

signals.

weights

Figure 11. Structure of a simple artificial neuron (adopted and modified from

Faucett, 1994)

These signals are then transmitted to an output layer and retransmitted. The input layer,

activation function, and output layer in artificial neuron are similar to the function of

18



dendrites, soma, and axon in the biological neuron. Still, as seen in figure 11, an artificial

network has many inputs but only one output.

2.3.1.Mechanics of Neural Networks

Artificial neural networks are generalizations of mathematical models of human

cognition (Faucett, 1994). They function based on the following assumptions:

Information processing occurs at many simple elements (neurons).−

−

−

−

Signals are passed between neurons over connection links.

Each connection link has an associated weight, which, in a typical neural net,

multiplies the transmitted signal.

Each neuron applies an activation function to its net input to determine its output

signal.

Assume we have n input units, X i ,…,X n with input signals x1 ,…,xn. When the network

receive the signals ( xi) from input units ( X i), the net input to output ( y_in j) is calculated by

summing the weighted input signals as follows:

∑=

n

1iiji

w x

The matrix multiplication method for calculating the net input is shown in the equation

below:

∑=

=n

1iiji j

w xin _ y

where wij is the connection weights of input unit xi and output unit y j.

The network output ( y j) is calculated using the activation function f(x). In which y j = f(x),

where x is y_in j. The computed weight from the training is stored and will become the

19



information for the future application. Table 2 shows the most common types of

activation functions.

Neural networks can be divided into three architectures, namely single layer, multilayer

network and competitive layer. The number of layers in a net is defined based on the

number of interconnected weights in the neuron. A single layer network consists only of

one layer of connected weights, whereas, multilayer networks consist of more than one

layer of connection weights. The network also consists of an additional layer called a

hidden layer.

Function Definition Identity x Logistic

X e−+1

1

Hyperbolic

Exponential

Softmax

Unit sum

Square root

Sine sin( x)

Table 2. Common activation functions.

Multilayer networks can solve more complicated problems than those solved by a single

layer network. Both networks are also called “feed forward” networks where the signal

flows from the input units to the output units in a forward direction. For example, a

recurrent network is a feedback network with a closed-loop signal from the unit back to

itself.

20



Figure 12 shows the architecture of a simple network, a multilayer perceptron (MPL),

where the basic parts are the neurons (also known as nodes), layers and connection

weights. Input and output layers are trained with user supplied data. The hidden layer

performs a mapping from the input to the output layer. The architecture of different

networks is defined by the connection strategy between neurons and layers (Poulton

2002).

2.3.2. Learning mechanisms for Artificial Neural Networks

Human beings are capable of learning with the aid of a teacher or on their own. The first

case is considered supervised learning, the latter is unsupervised learning. In supervised

learning, a teacher supplies both the material to be learned and corrects the student when

the response to the material is incorrect. In unsupervised learning, the student receives the

material to be learned and has to drawn his/her own conclusion as to what the material

means. The most basic division of artificial neural networks is whether they learn in a

supervised or unsupervised mode. In supervised mode, common in most applications, the

user supplies a set of patterns that the neural network should learn. These patterns are

then associated with responses dealing with a classification or an estimation of a

parameter value. In the unsupervised mode, the network is supplied with the set of

patterns to learn, but it is not supplied with a prior classification or parameter value

(Poulton, 2002).

While the architecture is important in defining how the network will function, the specific

learning algorithm used to train the network defines how it will learn. The learning

algorithm involves the input signals, the weights, the activation function (table 2), and the

21





Network, which uses the Backpropagation-learning algorithm. Backpropagation

algorithm is one of the well-known algorithms in neural networks. Backpropagation

algorithm has been popularized in 1980s as a euphemism for generalized delta

rule. Backpropagation of errors or generalized delta rule is a decent method to

minimize the total squared error of the output computed by the net (Faucett, 1994).

2.3.2.2. Unsupervised Learning

Unsupervised learning (figure 13) method is not given any target value. A desired output

of the network is unknown. During training the network performs some kind of data

compression such as dimensionality reduction or clustering. The network learns the

distribution of patterns and makes a classification of that pattern where, similar patterns

are assigned to the same output cluster. Kohonen network is the best example of

unsupervised learning network. According to Sarle (1997) Kohonen network refers to

three types of networks that are Vector Quantization, Self-Organizing Map and Learning

Vector Quantization

Figure 13. Supervised and Unsupervised scheme (adopted and modified from Jaeger,

2002)

outout

ii

out

i

Mod

unknoIn utCorre

:out

Unsupervised B.

Mod

:Teach

A. Supervised

23



2.3.3. Training the network

Training the network is time consuming. It usually learns after several epochs, depending

on how large the network is. Thus, a large network requires more training time than a

small one. Basically, the network is trained for several epochs and stopped after

reaching the maximum epoch. For the same reason minimum error tolerance is

used provided that the differences between network output and known outcome is

less than the specified value (see for example Pofahl et al., 1998). We could also

stop the training after the network meet certain stopping criteria.

During training the network might learn too much. This problem is referred to as

overfitting. Overfitting is a critical problem in most all-standard neural networks

architectures. Furthermore, neural networks and other artificial intelligence machine

learning models are prone to overfitting (Lawrence et al., 1997). One of the solutions is

early stopping (Sarle, 1995), but this approach needs more critical intention, as this

problem is harder than expected (Lawrence et al., 1997). The stopping criterion is also

another issue to consider in preventing overfitting (Prechelt, 1998). To crack this problem

during training, a validation set is used instead of a training data set. After a few epochs,

the network is tested with the verification data. The training is stopped as soon as the

error on verification set increases rapidly higher than the last time it was checked

(Prechelt, 1998). Figure 14 shows that the training should stop at time t when verification

error starts to increase.

24



E r r o r

verification

training

Timet

2.3.4. General Regression Neural Network

Figure 14. Training and verification curve (adopted from Prechelt, 1998)

The general regression neural network (GRNN) is Donald Specht's term for a neural

network invented by him in 1990 (Specht, 1991). The general regression neural network

(GRNN) is a memory-based network that provides estimates of continuous variables and

converges to the underlying regression surface. GRNNs are based on the estimation of

probability density functions, feature fast training times and can model non-linear

functions.

The GRNN is a one-pass learning algorithm with a highly parallel structure. It is that,

even with sparse data in a multidimensional measurement space, the algorithm provides

smooth transitions from one observed value to another. The algorithmic form can be used

for any regression problem in which an assumption of linearity is not justified.

GRNN can be thought as a normalized RBF (Radial Basis Functions) network in which

there is a hidden unit centered at every training case. These RBF units are usually

probability density functions such as the Gaussian. The only weights that need to be

learned are the widths of the RBF units. These widths are called "smoothing parameters.

The main drawback of GRNN is that it suffers badly from the curse of dimensionality.

25



GRNN cannot ignore irrelevant inputs without major modifications to the basic

algorithm. So GRNN is not likely to be the top choice if there are more than 5 or 6 no

redundant inputs.

The regression of a dependent variable, Y, on an independent variable, X, is the

computation of the most probable value of Y for each value of X based on a finite

number of possibly noisy measurements of X and the associated values of Y. The

variables X and Y are usually vectors.

In order to implement system identification, it is usually necessary to assume some

functional form. In the case of linear regression, for example, the output Y is assumed to

be a linear function of the input, and the unknown parameters, ai, are linear coefficients.

The procedure presented in Donald F. Specht’s article (Specht, 1991) does not need to

assume a specific functional form.

A Euclidean distance is estimated between an input vector and the weights, which are

then rescaled by the spreading factor. The radial basis output is then the exponential of

the negatively weighted distance.

The GRNN equation is:

∑

∑

=

=

−

−

=n

1i2

2

i

n

1i2

2

i

i

2

Dexp

2

DexpY

) X ( Y

σ

σ

The estimate Y(X) can be visualized as a weighted average of all of the observed values,

Yi, where each observed value is weighted exponentially according to its Euclidian

distance from X. Y(X) is simply the sum of Gaussian distributions centered at each

training sample. However the sum is not limited to being Gaussian.

26



In this theory, σ is the smoothing factor and can be seen as the spread of the Gaussian

bell.

3. LITERATURE REVIEW

Artificial neural networks have been broad used in reservoir characterization because

their ability to extract nonlinear relationships between a sparse set of data (Banchs and

Michelena, 2002). The most common architecture used is the backpropagation artificial

neural network (BPANN). Studies in this subject have used wireline measurement logs,

and seismic attributes to predict reservoir properties such as effective porosity, fluid

saturation and rock permeability, and to define lithofacies and predict log responses, i.e.

generation of synthetic logs. In all cases it was demonstrated that ANN are powerful tool

for recognition-pattern, system identification, and prediction of any variable in the future

with a better correlation coefficient (R 2) over traditional statistical analysis like linear

regression.

Mohaghegh, et al. (1998), describes a methodology developed to generate synthetic

Magnetic Resonance Imaging logs using conventional well logs such as Spontaneous

Potential,Gamma Ray, Caliper, and Resistivity for four wells located in East Texas, Gulf

of Mexico, Utah, and New Mexico. The methodology incorporates a backpropagation

artificial neural network as its main tool. The synthetic Magnetic Resonance Imaging

(MRI) logs were generated with a high degree of accuracy even when the model

developed used data not employed during model development.

Mohaghegh, et al. (1999), Present an approach that involves neural-network-design

software, for low cost/ high effectiveness log analysis in a field scale. The cost reduction

27



is achieved by analyzing only a group of the wells in the field. The intelligent software

tool is built to learn and reproduce the analyzing capabilities of the engineer on the

remaining wells. As part of this study, logs that were missed in several wells and that

were necessary for analysis were generated. The tool used for this procedure was also a

backpropagation neural network

Bhuiyan (2001), developed a backpropagation neural network to generate synthetic

magnetic resonance imaging logs (MRI) in order to provide information about reservoir

characteristics of the Cotton Valley formation. In this work, data preparation previous to

network training, involved fuzzy logic for group well logs together based on similarity

criteria of the reservoir formation and to identify the most influential logs for a well.

Tonn (2002), uses seismic attributes, density and sonic logs to train an ANN in order to

predict the GR response of the Athabasca oil sands in western Canada, in order to solve

the reservoir properties and therefore chose the best location to place injection and

production wells for a steam injection program.

4. METHODOLOGY

The main objective of the study was to develop a systematic approach, that uses an

artificial neural network model, with the aim of generate synthetic wireline logs, from

other conventional wireline logs. Developing of this technique intends to generate

synthetic curves of any nonexistent log at any specific location, which can be necessary

to measure reservoir characteristics such as effective porosity, fluid saturation and rock

permeability. Implementation of this approach will reduce operation costs to companies,

28



by avoiding acquisition of new logs than now will be able to be obtained from already

acquired data.

The methodology applied in this work is based on the approaches presented by Bhuiyan,

(2001), and Mohaghegh et al., (1999).

In order to generate the synthetic logs, an artificial-neural-network-design software,

NeuroShell®2, previously developed by Ward Systems Group®, was used to find the

best model that could be applied to the data set used for this project.

NeuroShell®2 includes a set of procedures for building and executing a complete neural

network application. The software gives users the ability to create and execute a variety

of neural network architectures through different modules that allow the user to input

data, prepare the data for training, built the neural network, apply the model to new data

and examine the outputs. Outputs can be evaluated in terms of R-squared (R 2). R

2is the

relative predictive power of a model. R 2

is a descriptive measure between 0 and 1. The

closer it is to one, the better your model is. R-squared is defined as:

YY

2

SS

SSE 1 R −= , where

∑ −= 2 ) y y( SSE

∑ −= 2

YY ) y y( SS

= y actual value

= y the predicted value of , and y

= y the mean of the values. y

29



R 2 values can be interpreted, as indicators of how good are the results produced by the

network, although they are not the ultimate measure, but is the user who finally decides if

the network is working properly or not.

4.1. Data Preparation

The first step of the data preparation was to identify the depth of the pay zone/s. Five

units are producing in the study area: the Murrysville, the 100 foot, the Gordon, the

Speechely, and the 2nd

Bradford formations, which were included in this study.

Taken in account the sedimentary characteristics of the aforementioned formations, the

studied interval can be divided in two segments with different lithologic and petrophysic

characteristics. In addition breaking of the logs allowed better visualization of the actual

logs and the logs generated by the network. These two intervals are from 1000 to 2000

feet and from 2500 to 3500 feet.

The second step was to prepare a matrix in a spreadsheet to be imported to NeuroShell®.

The matrix for each well contained the well name, the depths, the longitude, the latitude,

and the values of the resistivity (RILD), density (DEN), gamma ray (GRGC), and neutron

(DNND) logs. Figure 15 is an example of the arrangement used to prepare the matrices.

ID DEPTH LAT LONG RILD DEN NPRL GRGC DNND

157 2000 40.5859 79.4719 32.87 2.70 8.79 144.66 15775.31

157 2000 40.5859 79.4719 31.73 2.71 9.08 145.10 15718.19

157 1999 40.5859 79.4719 30.91 2.71 9.38 142.85 15628.33

157 1999 40.5859 79.4719 30.82 2.71 9.58 141.16 15647.24

157 1998 40.5859 79.4719 31.57 2.71 9.61 142.10 15765.67

157 1998 40.5859 79.4719 32.53 2.69 9.43 142.63 15928.85

Figure 15. Segment of the matrix prepared for well 157.

30



4.2. Neural network model development

Development of the neural network model was completed using four wells that included

gamma ray, density, neutron, and resistivity logs. Different training algorithms were

attempted until the best results in terms of R 2 and matching of the synthetic logs

generated by the network versus the actual logs were achieved. The algorithm that has

been most frequently used in previous publications similar to this study, is the

backpropagation (Mohaghegh et al., 1998, Mohaghegh et al., 1999, Bhuiyan, 2001),

however, this work found that the best results were obtained using a General Regression

Neural Network (GRNN).

The network consists of three layers: an input layer made up of 7 neurons, a hidden layer

made up of 7000 neurons, and finally an output layer consisting of only one neuron. The

smooth factor applied was always 0.122 obtained by default from the NeuroShell.

Training, calibration and verification were carried out through two different exercises that

are described as follows:

4.2.1. Exercise 1: Four Wells Combined

In this exercise the entire set of data, consisting of 4 wells, was used during development

and training of the network and then each one of these wells were used to verify the

trained network (figure 16).

The data brought into the network as inputs/outputs were the locations of the wells (in

terms of latitude and longitude), Depths, Deep Induction (RILD) log values, Density

(DEN) log values, Gamma Ray (GRGC) log values, and Neutron (DNND) log values.

31



174

169

168

157

Verification

wells

174

169

168

157

Trainingand

calibrationwells

Figure 16. Cartoon to show distribution of wells used for training /testing and Production dataset through exercise 1.

Combinations of different inputs/outputs were chosen to train the network (figure 17); at

each combination one of the logs aforementioned was predicted from the other

information. In combination “A” the resistivity log was used as an actual output while the

density, the gamma ray, the neutron, and the coordinates and depths (XYZ) were used as

inputs, in combination “B” the density log was used as an actual output while the

resistivity, the gamma ray, the neutron, and XYZ were used as inputs, and in combination

“C” the neutron log was used as an actual output while the resistivity, the gamma ray, the

density, and XYZ were used as inputs. The percentages used for training, calibration and

verification were 80%, 15%, and 5% respectively. There were in total 3 combinations

used for exercise 1.

32



Figure 17. Different combinations of inputs/ outputs used for development of neural network model

Combination C

Combination B

Combination A

XYZ = Coordinates

and Depths

NEU = Neutron

GR = Gamma Ray

DEN = Density

RES = Resistivity

= Inputs

= Actual Output

I

A

III

Z

Y

X

XYZNEURE S GR DEN

AI

IIIA I

Z

Y

X

XYZNEURES GR DEN

III

Z

Y

X

XYZNEURE S GR DEN

AI

4.2.2. Exercise 2: Three Wells Combined, one well out

Differing from exercise 1, this exercise used only three wells for training and

development of the network while the fourth well, never used during training and

calibration, was selected to generate synthetic logs out of the other three wells

33



(verification). Since the verification data set in this exercise consisted of a data set never

used during training, the model was developed only with training and calibration data

sets. The percentages used were distributed 85% for training and 15% for calibration.

Therefore, wells 157, 168, and 169 where combined to generate logs in well 174; wells

157, 168, and 174 where combined to generate logs in well 169; wells 157, 174, and 169

where combined to generate logs in well 168; and wells 174, 169, and 168 where

combined to generate logs in well 157.

Figure 18 represents the combinations of wells used through this exercise (there were in

total four possible combinations). Combinations of inputs/output used in exercise 1 were

repeated for this exercise.

5. RESULTS

As mentioned before, the neural network used in this work to generate the synthetic logs

involved General Regression architecture. During training the network uses a data set

consisting of inputs and outputs. For calibration the data set consists of a similar number

of inputs and outputs, but in this case they are used to validate the network by verifying

how well the network is performing on data that were never seen before during the

training process. In this fashion, the partially constructed network is checked at certain

intervals of training by applying the calibration data set. Finally the verification set is

used to prove the ability of the network to provide accurate results on the unseen data.

Therefore, the values of R 2 obtained for each of the dataset mentioned, reflect the

performance of the network during training, calibration and verification.

34



Verification

well

169

174

157

Training

and

calibration

wells

168

169

Verification

well

174

168

157

Training

and

calibration

wells

157

Verification

well

168

169

174

Training

and

calibration

wells

174

Verification

well

169

168

157

Training

and

calibration

wells

Figure 18. Combinations of wells for training, testing and verification used in exercise 2.

Although the most important criteria to determine if the network is capable of generating

logs with a certain degree of accuracy is indeed the degree of matching between the plots

of the actual logs with the plots of logs generated by the network. Independently of the

R 2

values obtained, it was observed that the best matching between actual and synthetic

generated logs was obtained when high values of R 2 (higher than 0.7) were obtained.

Oppositely, when poor values of R 2 were obtained, matching was also poor.

35



The following are the results obtained from the neural network models developed for this

work. Models were developed throughout the exercises discussed above and using

different combinations of inputs and outputs (combinations A, B, and C). As mentioned

before, both exercises were completed for the interval from 1000 to 2000 feet and from

2500 to 3500 feet.

Performance of the model is showed in terms of values of the R-squared (R 2), the

coefficient of determination (r 2), and the coefficient of correlation obtained for the

training (TRN), calibration (TST) and verification (PRO) data sets. Log plots are also

included, in order to let the reader visualize the degree of matching between the actual

logs and the logs generated by the network.

5.1. First Attempt: Data set from Buffalo Valley Field (New Mexico)

A first attempt to generate synthetic well-logs was done using a set of logs obtained at the

web page of the New Mexico Energy, Minerals and Natural Resources Department.

(http://www.emnrd.state.nm.us). The data is part of the data used for a project that

intends to characterize the Morrow Formation at Buffalo Valley field, from well logs and

seismic data, using an artificial neural network.

The log data set analyzed consisted of resistivity, gamma ray, density, and neutron-

porosity logs. Logs were originally obtained as images of the hard copies, and were

available in .tif format, therefore they had to be digitized in order to be converted to a

format compatible with excel (.las format). Figure 19 shows the location of the wells and

figures 20 to 27 show the quality of the original .tif files and the resulting curves after

digitalization.

36

http://www.emnrd.state.nm.us/

http://www.emnrd.state.nm.us/



The combinations of inputs and outputs that were used to analyze this set of data

corresponds with the same used for exercise 1 and 2, however, for this case, the neutron

porosity log was used instead of the neutron log, since this last curve was absent in all the

wells. Development of the network models was carried out according with the

methodology steps discussed in exercise 1 and 2.

665

754219

1 mile

321

MEXICO

OKLAHOMA

TEXAS

NEW MEXICO

Figure 19. Location of the Buffalo Valley Field area and the wells used in the first attempt.

37



8 0 0 0

8 1 0 0

8 2 0 0

8 3 0 0

1 0 0 1 5 0 2 0 0

.tif file Digitized log

Gamma Ray (API units)

Figure 20. .tif files and the resulting Gamma Ray curve after digitalization. Well 219 Buffalo Valley Field

38



8 0 0 0

8 1 0 0

8 2 0 0

8 3 0 0

2 . 0 2 . 5 3 . 0


Density (g/ccm)

Figure 21. .tif files and the resulting Density curve after digitalization. Well 219 Buffalo Valley Field

39



8 0 0 0

8 1 0 0

8 2 0 0

8 3 0 0

- 2 0 0 0 2 0 0 4 0 0


Resistivity (ohm-m)

Figure 22. .tif files and the resulting Resistivity curve after digitalization. Well 219 Buffalo Valley Field

40



8000

8100

8200

8300

-0.050.150.35


Neutron Porosity

Figure 23. .tif files and the resulting Neutron Porosity curve after digitalization. Well 219 Buffalo Valley Field

41



8000

8100

8200

8300

0 20 40 60 8 0 100


Gamma Ray (API units)

Figure 24. .tif files and the resulting Gamma Ray curve after digitalization. Well 665 Buffalo Valley Field

42



8000

8100

8200

8300

2. 0 2 . 2 2 . 4 2 . 6 2 . 8


Density (g/ccm)

Figure 25. .tif files and the resulting Density curve after digitalization. Well 665 Buffalo Valley Field

43




Resistivity (ohm-m)

8000

8100

8200

8300

0 10 00 20 00 3000

Figure 26. .tif files and the resulting Resistivity curve after digitalization. Well 665 Buffalo Valley Field

44



8000

8100

8200

8300

-0.100.000.100.200.30


Neutron Porosity

Figure 27. .tif files and the resulting Neutron Porosity curve after digitalization. Well 665 Buffalo Valley Field

45



R 2 values obtained for the verification data set, out of the Buffalo Valley field data, were

fairly good, when the neural network model was developed using four wells for training

and calibration, and one of the wells used during training for verification (exercise 1)

Results are shown in table 3.

COMBINATION A

Inputs: Density, Gamma Ray, Neutron Porosity, XYZ

Outputs: Resistivity

Data Set R 2

TRN 0.9295

TST 0.9188

PRO 0.9124PRO well 219 0.766

PRO well 321 0.9342

PRO well 665 0.7281

PRO well 754 0.8128

COMBINATION B

Inputs: Resistivity, Gamma Ray, Neutron Porosity, XYZ

Outputs: Density

Data Set R 2

TRN 0.9708

TST 0.961

PRO 0.9341

PRO well 219 0.6229

PRO well 321 0.895

PRO well 665 0.735

PRO well 754 0.8199

COMBINATION C

Inputs: Resistivity, Density, Gamma Ray, XYZ

Outputs: Neutron Porosity

Data Set R 2

TRN 0.803

TST 0.769

PRO 0.7173

PRO well 219 0.7974

PRO well 321 0.9387

PRO well 665 0.8552

PRO well 754 0.5801

Table 3. Results for exercise 1 and combinations A, B, and C of inputs and outputs. Buffalo Valley field data set.

46



Conversely, when the network was trained using three wells and was verified using a

fourth well that has not been used during training (exercise 2), extremely poor R 2

values

were observed. Table 4 shows the results obtained throughout exercise 2, for

combinations A, B, and C of inputs and outputs.

COMBINATION A COMBINATION B COMBINATION C

Training wells: 219, 321, 665 Training wells: 219, 321, 665 Training wells: 219, 321, 665

Verification well: 754 Verification well: 754 Verification well: 754

Data Set R 2 Data Set R 2 Data Set R 2

TRN 0.9555 TRN 0.9715 TRN 0.8664

TST 0.9377 TST 0.9603 TST 0.8254

PRO well 754 -0.4601 PRO well 754 -0.1129 PRO well 754 -0.1082Training wells: 219, 321, 754 Training wells: 219, 321, 754 Training wells: 219, 321, 754



TRN 0.9619 TRN 0.9858 TRN 0.8059

TST 0.9627 TST 0.98 TST 0.803

PRO well 665 0.3422 PRO well 665 -1.4643 PRO well 665 0.2685




TRN 0.9459 TRN 0.8674 TRN 0.9504

TST 0.9249 TST 0.801 TST 0.8546

PRO well 321 -11.5431 PRO well 321 -2.6582 PRO well 321 -0.2056



Data Set R 2 Data Set R

2Data Set R

2

TRN 0.7571 TRN 0.9688 TRN 0.8401

TST 0.7162 TST 0.9766 TST 0.807

PRO well 219 -139.6099 PRO well 219 -0.9922 PRO well 219 -1.3319

Table 4. Results for exercise 2 and combinations A, B, and C of inputs and outputs. Buffalo Valley field data set.

47



5.2. Southern Pennsylvania Logs: Upper Zone (1000’ to 2000’)

5.2.1. Exercise 1

Table 5 contains the R 2 values and the correlation and determination coefficients obtained

through exercise 1 for the upper interval of the logs belonging to the Southern

Pennsylvania area.

COMBINATION A

Inputs: Density, Gamma Ray, Neutron, XYZ

Outputs: Resistivity

Data Set R 2

TRN 0.9377

TST 0.9412

PRO 0.9207PRO well 157 0.9264

PRO well 168 0.9619

PRO well 169 0.9102

PRO well 174 0.9262

COMBINATION B

Inputs: Resistivity, Gamma Ray, Neutron, XYZ

Outputs: Density

Data Set R 2

TRN 0.8338

TST 0.8225

PRO 0.8099

PRO well 157 0.8126

PRO well 168 0.8668

PRO well 169 0.831

PRO well 174 0.8161

COMBINATION C


Outputs: Neutron

Data Set R 2

TRN 0.942

TST 0.9291

PRO 0.9234

PRO well 157 0.9299

PRO well 168 0.9398

PRO well 169 0.9331

PRO well 174 0.9506

Table 5. Results for exercise 1 and combinations A, B, and C of inputs and outputs. Southern Pennsylvania area data

set (upper zone).

48



Figures 28 to 39 show the relation between the actual logs and the logs generated by the

neural network model during verification. Training and calibration results are included in

the appendix.

5.2.2. Exercise 2

Results obtained through exercise 1 for the upper zone of the logs of Southern

Pennsylvania area, substantially improved in comparison with the results obtained from

Buffalo Valley data set. However, improvements were more significant when exercise 2

was performed. R 2 values rose from negative values to values over 0.8.

COMBINATION A COMBINATION B COMBINATION CTraining wells: 157, 168, 169 Training wells: 157, 168, 169 Training wells: 157, 168, 169



TRN 0.9498 TRN 0.8612 TRN 0.9366

TST 0.9418 TST 0.8301 TST 0.9267

PRO well 174 0.9091 PRO well 174 0.6002 PRO well 174 0.7854




2 Data Set R

2

TRN 0.9455 TRN 0.8612 TRN 0.9437

TST 0.9530 TST 0.8301 TST 0.9348





TRN 0.9667 TRN 0.8397 TRN 0.9435

TST 0.9675 TST 0.6957 TST 0.9291




Data Set R

2

Data Set R

2

Data Set R

2

TRN 0.9464 TRN 0.8313 TRN 0.948

TST 0.9555 TST 0.8277 TST 0.9299


Table 6. Results for exercise 2 and combinations A, B, and C of inputs and outputs. Southern

Pennsylvania area data set (upper zone).

49



Despite some wells had R 2 values between 0.6 and 0.7, the synthetic logs generated by

the network during verification still showed a high degree of accuracy (figures 40 to 51).

It is important to mention that the first results for the verification dataset at this interval

were not successful. R 2 values obtained for this first effort were relatively low. The

reason for these poor results was that data initially included a log interval that had been

run at a cased segment, hence, the values recorded were highly anomalous and

consequently they did inject a significant error into the network. Once the data were

cleaned of this error, results improved. The final results obtained after cleaning the data

are summarized in table 6. Plots of actual logs versus logs generated by the neural

network model during training and calibration are included in the appendix.

5.3. Southern Pennsylvania Logs: Lower Zone (2500’ to 3500’)

5.3.1. Exercise 1

Values of R2, and correlation and determination coefficients, obtained for the lower

interval of the logs belonging to the Southern Pennsylvania area through exercise 1 were

good in general (over 0.8). Table 7 summarizes these results. The logs generated during

verification are shown in figures 52 to 63. Training and calibration results are included in

the appendix.

5.3.2. Exercise 2

Results obtained through exercise 2 are summarized in table 8. Figures 64 to 75 show the

logs generated during verification. Training and calibration results are included in the

appendix.

50



COMBINATION A

Inputs: Density, Gamma Ray, Neutron, XYZ Outputs: Resistivity

Data Set R 2

TRN 0.9536

TST 0.9388

PRO 0.9426

PRO well 157 0.9582

PRO well 168 0.955

PRO well 169 0.9199

PRO well 174 0.9568

COMBINATION B

Inputs: Resistivity, Gamma Ray, Neutron, XYZ Outputs: Density

Data Set R 2

TRN 0.8118

TST 0.7946

PRO 0.8336

PRO well 157 0.8229

PRO well 168 0.816

PRO well 169 0.7911

PRO well 174 0.8064

COMBINATION C


Outputs: Neutron

Data Set R 2

TRN 0.9313

TST 0.9133

PRO 0.9311

PRO well 157 0.9087

PRO well 168 0.94

PRO well 169 0.9215

PRO well 174 0.9354

Table 7. Results for exercise 1 and combinations A, B, and C of inputs and outputs. SouthernPennsylvania area data set (lower zone).

51



Combination A Combination B Combination C




TRN 0.9511 TRN 0.9511 TRN 0.9303

TST 0.9352 TST 0.8882 TST 0.9185




Data Set R 2


2

TRN 0.9704 TRN 0.8244 TRN 0.9354

TST 0.9413 TST 0.7873 TST 0.9138





TRN 0.9531 TRN 0.8155 TRN 0.9301

TST 0.9416 TST 0.7754 TST 0.9014





TRN 0.9671 TRN 0.81 TRN 0.9461

TST 0.9564 TST 0.8103 TST 0.9328


Table 8. Results for exercise 2 and combinations A, B, and C of inputs and outputs. Southern

Pennsylvania area data set (lower zone).

52



1000

1100

1200

1300

1400

1500

1600

1700

1800

1900

2000

10 100 1000

Resistivity (ohm-m)

D e p t h

( f e e t )

Actual

Network

Figure 28 . Synthetic resistivity log generated during verification through exercise 1 and

combination A of inputs and outputs. Well 157, southern Pennsylvania area (upper zone).

53



1100

1200

1300

1400

1500

1600

1700

1800

1900

2000

10 100 1000

Resistivity (ohm-m)

D e p t h

( f e e t )

Actual

Network



54



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Resistivity (ohm-m)

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( f e e t )

Actual

Network



55



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Resistivity (ohm-m)

D e p t h

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Actual

Network



56



1100

1200

1300

1400

1500

1600

1700

1800

1900

2000

2.5 2.6 2.7 2.8

Density (g/ccm)

D e p t h

( f e e t )

Actual

Network

Figure 32 . Synthetic density log generated during verification through exercise 1 and

combination B of inputs and outputs. Well 157, southern Pennsylvania area (upper zone).

57



1100

1200

1300

1400

1500

1600

1700

1800

1900

2000

2.5 2.6 2.7 2.8

Density (g/ccm)

D e p t h

( f e e t )

Actual

Network



58



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( f e e t )

Actual

Network



59



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( f e e t )

Actual

Network



60



1200

1300

1400

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1700

1800

1900

2000

15000 16000 17000 18000 19000 20000

Neutron (snu)

D e p t h

( f e e t )

Actual

Network

Figure 36 . Synthetic neutron log generated during verification through exercise 1 and

combination C of inputs and outputs. Well 157, southern Pennsylvania area (upper zone).

61



1200

1300

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1700

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1900

2000

15000 16000 17000 18000 19000 20000

Neutron (snu)

D e p t h

( f e e t )

Actual

Network



62



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Neutron (snu)

D e p t h

( f e e t )

Actual

Network



63



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Neutron (snu)

D e p t h

( f e e t )

Actual

Network



64



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Resistivity (ohm-m)

D e p t h

( f e e t )

Actual

Network



65



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Resistivity (ohm-m)

D e p t h

( f e e t )

Actual

Network



66



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Resistivity (ohm-m)

D e p t h

( f e e t )

Actual

Network



67



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Resistivity (ohm-m)

D e p t h

( f e e t )

Actual

Network



68



1000

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1300

1400

1500

1600

1700

1800

1900

2000

2.4 2.5 2.6 2.7 2.8

Density (g/ccm)

D e p t h

( f e e t )

Actual

Network

37 005 27157



69



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( f e e t )

Actual

Network



70



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Network



71



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( f e e t )

Actual

Network



72



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14000 16000 18000 20000 22000

Neutron (snu)

D e p t h

( f e e t )

Actual

Network



73



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Neutron (snu)

D e p t h

( f e e t )

Actual

Network



74



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Neutron (snu)

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Actual

Network



75



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Neutron (snu)

D e p t h

( f e e t )

Actual

Network



76



2500

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3000

3100

3200

3300

3400

3500

10 100

Resistivity (ohm-m)

D e p t h

( f e e t )

Actual

Network

Figure 52. Synthetic resistivity log generated during verification through exercise 1 and

combination A of inputs and outputs. Well 157, southern Pennsylvania area (lower zone).

77



2500

2600

2700

2800

2900

3000

3100

3200

3300

3400

3500

10 100

Resistivity (ohm-m)

D e p t h

( f e e t )

Actual

Network



78



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3100

3200

3300

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Resistivity (ohm-m)

D e p t h

( f e e t )

Actual

Network



79



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Resistivity (ohm-m)

D e p t h

( f e e t )

Actual

Network



80



2500

2600

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2800

2900

3000

3100

3200

3300

3400

3500

2.5 2.6 2.7 2.8

Density (g/ccm)

D e p t h

( f e e t )

Actual

Network

Figure 56. Synthetic density log generated during verification through exercise 1 and

combination B of inputs and outputs. Well 157, southern Pennsylvania area (lower zone).

81



2500

2600

2700

2800

2900

3000

3100

3200

3300

3400

3500

2.5 2.6 2.7 2.8

Density (g/ccm)

D e p t h

( f e e t )

Actual

Network



82



2500

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3100

3200

3300

3400

3500

2.5 2.6 2.7 2.8

Density (g/ccm)

D e p t h

( f e e t )

Actual

Network



83



2500

2600

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3000

3100

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3300

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2.5 2.6 2.7 2.8

Density (g/ccm)

D e p t h

( f e e t )

Actual

Network



84



2500

2600

2700

2800

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3000

3100

3200

3300

3400

3500

15000 16000 17000 18000 19000 20000

Neutron (snu)

D e p t h

( f e e t )

Actual

Network

Figure 60. Synthetic neutron log generated during verification through exercise 1 and

combination C of inputs and outputs. Well 157, southern Pennsylvania area (lower zone).

85



2500

2600

2700

2800

2900

3000

3100

3200

3300

3400

3500

15000 16000 17000 18000 19000 20000

Neutron (snu)

D e p t h

( f e e t )

Actual

Network



86



2500

2600

2700

2800

2900

3000

3100

3200

3300

3400

3500

15000 16000 17000 18000 19000 20000

Neutron (snu)

D e p t h

( f e e t )

Actual

Network



87



2500

2600

2700

2800

2900

3000

3100

3200

3300

3400

3500

15000 16000 17000 18000 19000 20000

Neutron (snu)

D e

p t h

( f e e t )

Actual

Network



88



2500

2600

2700

2800

2900

3000

3100

3200

3300

3400

3500

10 100

Resistiv ity (ohm-m)

D e p t h

( f e e t )

Actual

Network



89



2500

2600

2700

2800

2900

3000

3100

3200

3300

3400

3500

10 100

Resistivity (ohm-m)

D e p t h

( f e e t )

Actual

Network



90



2500

2600

2700

2800

2900

3000

3100

3200

3300

3400

3500

10 100

Resistivity (ohm-m)

D e p t h

( f e e t )

Actual

Network



91



2500

2600

2700

2800

2900

3000

3100

3200

3300

3400

3500

10 100

Resistivity (ohm-M)

D e p t h

( f e e t )

Actual

Network



92



2500

2600

2700

2800

2900

3000

3100

3200

3300

3400

3500

2.5 2.55 2.6 2.65 2.7 2.75 2.8

Density (ccm)

D e p t h

( f e e t )

Actual

Network



93



2500

2600

2700

2800

2900

3000

3100

3200

3300

3400

3500

2.5 2.6 2.7 2.8

Density (gr/ccm)

D e p t h

( f e e t )

Actual

Network



94



2500

2600

2700

2800

2900

3000

3100

3200

3300

3400

3500

2.5 2.6 2.7 2.8

Density (gr/ccm)

D e p t h

( f e e t )

Actual

Network



95



2500

2600

2700

2800

2900

3000

3100

3200

3300

3400

3500

2.5 2.6 2.7 2.8

Density (gr/ccm)

D e p t h

( f e e t )

Actual

Network



96



2500

2600

2700

2800

2900

3000

3100

3200

3300

3400

3500

14000 16000 18000 20000 22000

DNND (snu)

D e p t h

( f e e t )

Actual

Network



97



2500

2600

2700

2800

2900

3000

3100

3200

3300

3400

3500

14000 16000 18000 20000 22000

DNND (snu)

D e p t h

( f e e t )

Actual

Network



98



2500

2600

2700

2800

2900

3000

3100

3200

3300

3400

3500

14000 16000 18000 20000 22000

DNND (snu)

D e p t h

( f e e t )

Actual

Network



99



2500

2600

2700

2800

2900

3000

3100

3200

3300

3400

3500

14000 16000 18000 20000 22000

DNND (snu)

D e p t h

( f e e t )

Actual

Network



100



6. DISCUSSION

Results discussed in chapter 5, for exercises 1 and 2, indicate that the best neural network

model performance was obtained in general for combination “A”. Combination “C” was

ranked second and combination “B” represents the lowest performance (figures 76, 77,

78, and 79).

These results indicate that the most predictable was the resistivity log and the less

predictable was the density log. The inferior response of the neural network model to

combination “B” is reflected in the way that the network captures the deflections of the

log. The high peaks of the log where high contrasts of density are present are captured

with high accuracy, conversely, small changes cannot be captured accurately but in these

cases the network averaged the values. An explanation for the lower degree of

predictability of the density log is due to radioactive fluctuations (relative to the cesium

source) during the logging operation. Hence, radiations can take different ways at each

time and log response can vary from place to place.

For exercise 2 the best results, were obtained, for wells number 168 and 169 (figures 80

and 81 ). The reason is probably because these wells are located at the middle of the cross

section A-A’, so the neural network model can interpolate information from adjacent

wells. An explanation for anomalous results obtained for combination “A” at the upper

zone, could not be resolved by this study. However, it is important to be mention that,

generally speaking, geology in the study area is simple. Therefore, it is possible that for

areas with more complex geology, this condition could change, and the location of the

wells in terms of geometry, could not have any relation with the performance of the

neural network.

101



A very interesting point to discuss in this study is the fact that poor results were obtained

because of the quality of the data, as a consequence of digitalization of the logs in

original .tif format. These poor results are indicative of the high degree of sensitivity that

neural network models have to the quality of the data. It is highly recommended for

future studies involving generation of intelligent synthetic logs, to perform a strict quality

control of data prior to building the neural network model, especially if the logs that will

be used as inputs in the model are not directly obtained from the borehole, but have been

digitized. It was demonstrated that once it was realized that data from Buffalo Valley had

low quality as a result of the imprecise digitizing, and they were replaced by data from

Southern Pennsylvania, the effectiveness of the neural network models in predicting logs

for exercises 1 and 2 improved considerably. Furthermore, before data from the upper

zone of the Pennsylvanian data set were cleaned, the results were poor, once the

anomalous data were detected and cleaned, results improved noticeably.

Finally, it is important to mention that the main reason why logs of the Pennsylvanian

area were split into two intervals was because it was desired to determine if heterogeneity

of the rocks influenced the performance of the network model. It was demonstrated for

all models built in this study that heterogeneities in lithology of the reservoir have low

influence for the networks since R 2 values obtained for both zones were very similar to

each other.

102



Exercise 1 - Upper Zone (1000' to 2000')

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

TRN TST PRO PROwell 157

PROwell 168

PROwell 169

PROwell 174

R - s q u a r e d

Combination A

Combination B

Combination C

Figure 76. R 2 values obtained for the upper zone of the Southern Pennsylvania data set, through exercise 1.

Exercise 1 - Lower Zone (2500' to 3500')

0.0000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1.0000

TRN TST PRO PRO

well

157

PRO

well

168

PRO

well

169

PRO

well

174

R - s q u a r e d

Combination A

Combination B

Combination C

Figure 77. R 2 values obtained for the lower zone of the Southern Pennsylvania data set, through exercise 1.

103



Exercise 2 - Upper Zone (1000' to 2000')

0.0000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1.0000

PRO well 157 PRO well 168 PRO well 169 PRO well 174

R - s q u a r e d

Combination A

Combination B

Combination C


Exercise 2 - Lower Zone (2500' to 3500')

0.0000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1.0000

PRO well 157 PRO well 168 PRO well 169 PRO well 174

R - s q u a r e d

Combination A

Combination B

Combination C

Figure 79. R 2 values obtained for the lower zone of the Southern Pennsylvania data set, through exercise 1.

104



Exercise 2 - Upper Zone (1000' - 2000')

0.0000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1.0000


R - s q u a r e d Well 157

Well 168

Well 169

Well 174


Exercise 2 - Lower Zone

0.0000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1.0000


R - s q u a r e d Well 157

Well 168

Well 169

Well 174

Figure 81. R

2 values obtained for the lower zone of the Southern Pennsylvania data set, through exercise 2.

105



7. CONCLUSIONS

This work demonstrates that generation of synthetic logs with a reasonable degree of

accuracy is possible by using a neural network model and following the methodology

herein described.

Three neural network models to predict resistivity, density, and neutron logs were built

through exercises 1 and 2, as well as using different combinations of inputs and outputs,

namely combination “A” to predict resistivity logs, combination “B” to predict density

logs, and combination “C” to predict neutron logs.

Results indicate that the best performance was obtained for combination “A” of inputs

and outputs, then for combination “C”, and finally for combination “B”. Therefore

performance for combination “A” indicates that the resistivity log was the most

predictable log. On the other hand performance in combination “B” demonstrates that

density log was the least predictable as a consequence of radioactive fluctuations of the

Cs source during the logging operation.

Results demonstrate as well that in areas where geology is simple, as is the case of the

study of this work, accuracy of synthetic logs may be favored by interpolation of data.

Therefore, the best results were obtained for wells located in the central part of the cross

section studied. This condition could change in areas where geology presents more

complexities.

106



It was demonstrated that in studies that involve generation of intelligent synthetic logs

quality of data plays a very important role during the development of the neural network

model. Quality of logs could be defective when logs are not available in digital format

and have to be digitized. Therefore it is highly recommended for future works to perform

a very careful quality control of the data before a neural network model is built.

It was also demonstrated that lithologic heterogeneities in the reservoir do not

significantly affect performance of a neural network model in the generation of synthetic

logs.

107



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APPENDIX A: Training results (Southern Pennsylvania data set)



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Calibration results for combination B of inputs and outputs. Southern Pennsylvania data set, lower zone.

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Documents

Developing Intelligent Synthetic Logs Application to Upper Devonian Units in PA.pdf