A SURVEY ON THE METHODS TO PREDICT RATE OF

EASTERN MACEDONIA AND THRACE INSTITUTE OF TECHNOLOGY

FACULTY OF ENGINEERING

DEPARTMENT OF PETROLEUM AND NATURAL GAS TECHNOLOGY

MSc in OIL AND GAS TECHNOLOGY

MASTER THESIS

A SURVEY ON THE METHODS TO PREDICT RATE OF PENETRATION IN DRILLING PROJECT

PANAGIOTIS ILIOPOULOS B.Sc. Mechanical Engineer

SUPERVISOR: VASILEIOS GAGANIS

KAVALA 2015

A survey on the methods to predict rate of penetration in drilling project

By

Iliopoulos Panagiotis

Submitted to the Department of Petroleum and Natural Gas Technology,

Faculty of Engineering

in Partial Fulfillment of the Requirements for the Degree of

Masters of Sciences in the Oil and Gas Technology

at the

Eastern Macedonia and Thrace Institute of Technology

APPROVED BY:

Thesis Supervisor: Vasileios Gaganis

Committee member:

Committee member:

Date defended:

EASTERN MACEDONIA AND THRACE INSTITUTE OF TECHNOLOGY

FACULTY OF ENGINEERING

DEPARTMENT OF PETROLEUM AND NATURAL GAS TECHNOLOGY

MSc in OIL AND GAS TECHNOLOGY

MASTER THESIS

A SURVEY ON THE METHODS TO PREDICT RATE OF PENETRATION IN DRILLING PROJECT

PANAGIOTIS ILIOPOULOS B.Sc. Mechanical Engineer

SUPERVISOR: VASILEIOS GAGANIS

KAVALA 2015

EASTERN MACEDONIA AND THRACE INSTITUTE OF TECHNOLOGY FACULTY OF ENGINEERING DEPARTMENT OF PETROLEUM AND NATURAL GAS TECHNOLOGY © 2013 This Master Thesis and its conclusions in whatsoever form are the property of the author and of the

Department of Petroleum and Natural Gas Technology. The aforementioned reserve the right to

independently use and reproduce (partial or total) of the substantial content of this thesis for teaching

and research purposes. In each case, the title of the thesis, the author, the supervisor and the

department must be cited.

The approval of this Master Thesis by the Department of Petroleum and Natural Gas Technology does

not necessarily imply the acceptance of the author’s views on behalf of the department.

--------------------------------------------------------------

The undersigned hereby declares that this thesis is entirely my own work and it has been submitted to

the Department of Petroleum and Natural Gas Technology in partial fulfillment of the requirements for

the degree of Masters of Sciences in the Oil and Gas Technology. I declare that I respected the

Academic Integrity and Research Ethics and I avoided any action that constitutes plagiarism. I know

that plagiarism can be punished with revocation of my master degree.

Signature

Panagiotis Iliopoulos

ABSTRACT

For the purpose of this thesis we will first refer to the efforts of oil and gas industries

for development. We start from the beginning of the 20th century until today with a

historical retrospection in order to classify the operating period in accordance with

the rate of penetration (ROP) prediction methods. An extensive literature survey on

drilling optimization was conducted for this research study that presents all the

drilling optimization models and the main factors that participate in the drilling

activity influenced the penetration rate. Entire models which predict the rate of

drilling penetration as a function of available parameters and which are used from

the industry such as perfect cleaning theory, cutting removal model, best constant

weight, rotary speed and multiple regression process will be analyzed extensively in

order to make clear the relationship between drilling parameters. Also the terms cost

and time, which are directly connected with the models performance, are evaluated,

offering to the reader a full understanding of the optimization process. In addition,

we will analyze a real time optimization process as this technique is going to be

widely used in future drilling activities reducing drilling cost. Finally new advanced

simulation methods used from the industry, based on real time data, are evaluated

and we should pay attention to their beneficial and economic point of view.

SUBJECT AREA: Rate of penetration prediction in drilling project

KEYWORDS: Mathematical studies, Multiple regression, Real time methods,

Simulation models

ΠΕΡΙΛΗΨΗ

Για τους σκοπούς της παρούσας διατριβής πρώτα θα αναφερθούμε στην ανάγκη για

την ανάπτυξη των βιομηχανιών πετρελαίου και φυσικού αερίου. Ξεκινάμε από τις

αρχές του 20ου αιώνα μέχρι σήμερα, κάνοντας μια ιστορική αναδρομή, θέλοντας να

χαρακτηρίστει η περίοδος λειτουργείας σύμφωνα με το ποσοστό διείσδυσης (ROP)

των μεθόδων πρόβλεψης. Μια εκτεταμένη βιβλιογραφική έρευνα για τη

βελτιστοποίηση γεωτρήσεων πραγματοποιήθηκε για αυτήν την ερευνητική μελέτη

παρουσιάζονται όλα τα μοντέλα βελτιστοποίησης γεωτρήσεων και τους κύριους

παράγοντες που συμμετέχουν σε γεώτρησης δραστηριοτητες, επηρεάζοντας το

ρυθμό διείσδυσης. Ολόκληρα τα μοντέλα που προβλέπουν το ρυθμό διείσδυσης

γεωτρήσεων ως συνάρτηση των διαθέσιμων παραμέτρων και χρησιμοποιείται από τη

βιομηχανία, όπως η τέλεια θεωρία καθαρισμού, απομάκρηνση θραυζμάτων μοντέλο,

καλύτερα σταθερές βάρος - ταχύτητα περιστροφής και πολλαπλής βελτιστοποίησης

διαδικασια αναλύονται εκτενώς, προκειμένου να γίνει κατανοητή η σχέση μεταξύ των

παραμέτρων γεώτρησης. Επίσης, οι όροι του κόστους και των χρόνου συνδέονται

άμεσα με την επίδοση των μοντέλων που αξιολογήθηκαν, δίνοντας στον αναγνώστη

μια πλήρη κατανόηση της διαδικασίας βελτιστοποίησης. Επιπλέον θα αναλυθεί μια

διαδικασία βελτιστοποίησης σε πραγματικό χρόνο διότι η τεχνική αυτή πρόκειται να

χρησιμοποιηθεί ευρέως στο μέλλον σε δραστηριότητες γεώτρησης μειώνοντας το

κόστος διάτρησης. Τέλος οι νέες προηγμένες μεθόδους προσομοίωσης που

χρησιμοποιούνται από τη βιομηχανία και βασίζονται σε πραγματικού χρόνου

δεδομένα, αξιολογούνται ενώ θα πρέπει να δώσουμε προσοχή στα ωφέλοι από

οικονομικής μεριάς.

ΘΕΜΑΤΙΚΗ ΠΕΡΙΟΧΗ: Πρόβλεψη ρυθμού διείσδυσης σε γεώτρησης

δραστηριότητα

ΛΕΞΕΙΣ ΚΛΕΙΔΙΑ: Μαθηματική μελέτες, πολλαπλή βελτιστοποίηση, μεθόδους σε

πραγματικό χρόνο, μοντέλα προσομοίωσης

This thesis is dedicated to my lovely parents.

ACKNOWLEDGEMENTS

I want to thank my supervisor Vasileio G. for his cooperation and effort in terms of

providing all the needed information and for his immediate response to my questions

during this study. I would also like to give very sincere thanks to my friends, pieces

of advice which were more than helpful for the completion and success of this

project. Above all, I want to express my gratitude to my parents who shared their

support, financially and physically through my graduate study.

TABLE OF CONTENTS

Contents

1. CHAPTER 1 INTRODUCTION ............................................................................. 15

1.1 INTRODUCTION ........................................................................................... 15

1.2 HISTORY OF DRILLING OPTIMIZATION ....................................................... 17

1.3 FACTORS AFFECTING RATE OF PENETRATION............................................ 19

1.4 OBJECTIVE OF THIS STUDY ......................................................................... 20

2. CHAPTER 2 LITERATURE OVERVIEW .............................................................. 21

2.1 DRILLING ACTIVITY PARAMETERS .............................................................. 21

2.1.1 DESCRIPTION OF CONTROLLABLE PARAMETERS THAT

INFLUENCE RATE OF PENETRATION ........................................................... 21

2.1.2 DESCRIPTIONS OF MEASURABLE PARAMETERS ................................... 23

2.2 DRILLING OPTIMIZATION RESEARCH .......................................................... 24

2.2.1 RATE OF PENETRATION OPTIMIZATION STUDIES ............................... 24

2.2.2 RATE OF PENETRATION SIMULATION MODELS ................................... 30

2.2.3 STUDIES OF REAL TIME DRILLING OPTIMIZATION ............................. 32

3. CHAPTER 3 COMMON OPTIMIZATION MODEL THEORY ................................. 35

3.1 MAURERS PERFECT CLEANING THEORY .............................................. 35

3.2 WARREN CUTTING REMOVAL MODEL .......................................................... 38

3.3 GALLE AND WOODS BEST CONTANT WEIGHT AND ROTARY SPEED........... 42

3.3.1 THREE FUNDAMENTAL EQUATIONS ..................................................... 43

3.3.2 ADDITIONAL CALCULATION EQUATION ............................................... 45

3.3.3 CALCULATION OF CONSTANTS ............................................................. 45

3.4 BOURGOYNE AND YOUNGS MULTIPLE REGRESSION MODEL ...................... 47

3.4.1 FORMATION STRENGTH FUNCTION ..................................................... 48

3.4.2 FORMATION COMPACTION FUNCTION ................................................. 49

3.4.3 DIFFERENTIAL PRESSURE FUNCTION .................................................. 49

3.4.4 BIT DIAMETER AND WEIGHT FUNCTION ............................................. 50

3.4.5 ROTARY SPEED FUNCTION ................................................................... 50

3.4.6 TOOTH WEAR FUNCTION ..................................................................... 50

3.4.7 HYDRAULIC FUNCTION ......................................................................... 50

4. CHAPTER 4 ANDANCED OPTIMIZATION METHODS ..................................... 52

4.1 REAL TIME DATA .......................................................................................... 52

4.1.1 MEASURE WHILE DRILLING PIPING ..................................................... 52

4.1.2 REAL TIME TECHNICAL CENTERS ......................................................... 55

4.2 REAL TIME BIT WEAR .................................................................................. 55

4.3 ROP PREDICTION USING FUZZY K MEANS .................................................. 58

4.4 ROP PREDICTION TECHNOLOGIES BAZED ON NEURAL NETWORK ............. 61

4.4.1 UNDERSTANT AND LEARN CONCEPT .................................................... 61

4.4.2 DRILLING OPTIMIZATION ANN ............................................................. 62

4.4.3 ELM AND RBF TECHNOLOGIES ............................................................. 63

5. CHAPTER 5 CONCLUSIONS ............................................................................... 65

5.1 TOPICS DISCUSSED ..................................................................................... 65

5.2 GENERAL CONSIDERATION .......................................................................... 66

ABBREVIATIONS – INITIALS ................................................................................... 68

REFERENCES ............................................................................................................... 69

LIST OF FIGURES

Figure 2.1: Drilling operation centers time line of significant initiatives .......................... 32

Figure 3.1: Crater formation mechanism ....................................................................... 34

Figure 3.2: Crater volume VS impact energy................................................................. 35

Figure 3.3: General rate of penetration equation ........................................................... 47

Figure 4.1: Simplified MPT system description ............................................................. 52

Figure 4.2: MPD setup with wired drill pipe and the resulting control volumes .............. 53

Figure 4.3: Schematic shows how PDC and roller cone bit types cutters have

measured ....................................................................................................................... 56

Figure 4.4: Framework of prediction procedure ............................................................. 58

Figure 4.5: Artificial neural network ............................................................................... 60

Figure 4.6: Drilling optimization ANN ............................................................................. 61

LIST OF TABLES

Table 2 1: Fluid type characteristics .............................................................................. 21

CHAPTER 1: INTRODUCTION

Panagiotis Iliopoulos - 15 - 2015

1. CHAPTER 1

INTRODUCTION

1.1 INTRODUCTION

In recent years the increasing demand for energy research from the ground has

forced operators to develop a subject of survey ensuring that well drilling is realized

in a more efficient manner. For that reason oil and gas companies tend to find

different methods with different consideration on drilling activities in order to reduce

cost, increase performance and overcome possible difficulties. There is no doubt that

energy sources are reducing day by day and the oilfield exploitation will be more

difficult in the future. These entail that the future project should improve productivity

and make well construction cost effective. New methods which improve drilling

operations have been based in technological advantages that maximize the desired

goals.

The basic principle for all operations is the relation between cost and time, which are

two interdependent amounts. It is understood that when time expands, cost

increases and vice versa. From the beginning of the 20th century, oil and gas

companies have realized how important is to minimize drilling operation cost. As a

result, all efforts aim to increase drilling speed in order to accelerate penetration rate

(ROP) [1]. It is generally accepted that there are many factors referred to as

performance qualifiers (PQ) which influence ROP. Some of them are more important,

some other less and all together make the relationship complex, as they require the

development of mathematical models in order to be determined. Consequently, only

when all parameters affecting ROP are met to the greatest extent possible, they give

the best combination of drilling operating conditions. Hence, during the drilling

process the main objective is to conduct all the activities in the most economic way

[2].

MASTER THESIS DEPARTMENT OF PETROLEUM AND NATURAL GAS TECHNOLOGY


Nowadays, many countries lack resources and hire oil and gas operator companies in

order to have energy providers. On the other hand, companies wish to have mass

production and develop techniques which give them the capability to drill many

different wells from one location, when these wells belong to the same reservoir.

Therefore with the directional drilling method, companies avoid construction and cost

for each new well, while at the same time drillers by using PC based systems have

the opportunity to collect data from close wells and gain years of knowledge [3].This

is very useful because knowing the structure from the same geological area and the

operation parameters from nearby wells, the driller can estimate and optimize all the

factors which have impact in drilling operations. The problem is that there are many

variations on drilling data and it is impossible to find the suitable combination without

using a mathematical model. There were many mathematical models attempting to

combine all relations of drilling factors. Most of these models aim to calculate the

best selection of weight on the bit (WOB) and rotary speed so as to achieve optimal

time and cost reduction [4].

It is remarkable that structure and properties formation is one of the most important

factors on drilling process. However, it is considered one of the most difficult factors

to estimate because the ground does not present a uniform geological structure. For

this reason geologists try to illustrate the real conditions of subsoil and provide as

accurate data as possible. The data do not guarantee success because in many cases

the ground presents helical structure, cracking, salt dome and other geological

phenomena [5]. It is common to have different geological allocation between two

wells which are close to each other and this is exactly the reason why we can never

be sure and we should always consider the uncontrollable factors.

There are controllable factors such as bit types, fluid properties, WOB, horsepower,

hydraulics and rotary speed. While the driller follows the good drilling practice, he

has the opportunity to select and determine the factors using suitable models which

predict the rate of penetration.

The scope of this study is to analyze all models that have been used for ROP

predictions during the drilling operation from the initial method at the beginning of

the previous century until today.



1.2 HISTORY OF DRILLING OPTIMIZATION

If we go back to the beginning of drilling activities we observe the need for

knowledge. The development of all suitable and important techniques took place in

the first 20 years, such as rotary drilling bits, fluid dynamics, casing installation,

cement. During this first period all methods and tools improved, hence it was named

development period. After this period there is a gap for about thirty years as oil

companies did not invest large amounts of money on drilling research. From 1948 to

1968 oil companies started to perceive the importance of research. During these

years the scientific period took place and consequently the total cost increased. The

thought for optimized drilling is one of the most important assumptions of the

scientific period but in reality it started in 1968. It should be mentioned that many

researchers spend endless time studying all parameters included in drilling and the

relation between them. The period after the 1970s is known as automation period. At

that time the first computer systems were created which performed operations

improving drilling. Most of oil and gas companies started to use automated rig

systems, based on closed-loop computer system that controlled drilling variables and

had complete planning of well drilling from spud to production [6].

Looking at the chronological axis some dates are worth mentioning as they are

considered landmarks of drilling optimization. The Graham and Muenh study in 1959

can be regarded as the first integrated model which approached and included the

most important drilling factors. More precisely this mathematical model evaluated the

correlation between WOB and rotary speed, as well as the shelf life of bit.

Summarizing, drilling rate was predicted combining depth, rotary speed and WOB.

Four years later, another research was carried out. In 1963 Galle and Woods created

special arranged graphs which indicated the best combination of drilling parameters

[7]. So far the most important model on which all modern studies have relied is the

linear penetration model by Bourgoyne and Young. This model uses multiple

regression analysis in order to achieve the best selection of drilling parameters.

Consequently, model’s equation is developed for different formations. Their basic

purpose was to create a model able to calculate maximum penetration rate with the

minimum cost, taking into account all technical specifications [8-9]. During the next

decade, no significant changes occurred in drilling optimization so petroleum industry



kept using past mathematical approaches in order to assess drilling activities. The

need for a more accurate project led one of the biggest industries, named SHELL, to

develop a new concept named “drill the limit” (DTL). Actually through methodology

they discovered the removal time, that is the difference between real well time and

theoretical well duration. The main objective was to increase rig time efficiency, by

finding the best critical path between parallel works [10-11]. At the end of the

millennium the real time monitoring was a very promising method. A drilling

procedure brought to light tools which had the opportunity to give additional

information from the bottom hole during the drilling operation in real time. This way,

companies had a better understanding of the factors that influence the penetration

rate and increase the drilling cost. The basic advantage of this evolution is that it

allows drilling parameters monitoring from many different locations [12,64]. Therefore

real time operation centers were established in the next years so that the companies

have a more integrated information system. The initial idea is quite simple; the

drilling data is stored and transferred in real time. In the coming years the

technological development and the new improved tools which communicate directly

with the computers, provided the possibility to have better control and optimization

service including additional measurement, such as pressure control and rock strength

[13].

Drilling optimization from 1950 until today:

Scientific period

1950 – Expansion of drilling research

– Beginning of drilling optimization

1952 – Jet type of roller cone bits

1959 – First drilling optimization model by Graham and Muench

1963 – Galle and Woods model

Automation period

1970 – Beginning of automation period

1974 – Multiple regression model by Bourgoyne

1986 – Real time drilling optimization at Chevron rig site

1999 – Real time drilling monitoring

2003 – Real time operation centers Shell and Halliburton



2005 – Real time monitoring at ExxonMobil rig site

2006 – Real time transfer centers by Statoil

1.3 FACTORS AFFECTING RATE OF PENETRATION

It has been observed that the rate of penetration depends on many factors. These

factors are distinguished in two basic categories as to whether they can change or

not. So the first category is named controllable factors, such as WOB, hydraulics and

drill string rotary speed which can be influenced by the user where it is necessary.

On the other hand, there are environmental factors characterized as uncontrollable

that can be measured but not changed, that’s why we adjust our project always

based on them. The geological structure and the formation properties is an

understandable example. However, additional factors essential for a normal drilling

operation such as the bit type, downhole pressure, temperature, cutting

transportation, horsepower from pumps and general auxiliary equipment influence

drilling operations [14]. It should be mentioned that all previous factors can be applied

regardless of whether the well is horizontal or inclined, but there is no doubt that the

degree of difficulty is greater in the second case.

Cutting removal is the factor that requires particular attention in order to have the

best possible bottom hole cleaning. The efficiency of cutting removal is one of the

most important factors of drilling penetration rock, because only at that time the fluid

from the nozzle will achieve fracturing and the drilling process will continue [15].

It is remarkable that there are soft geological formations which are very easy to be

drilled but there are also hard geological formations which require more expensive

bit and more time. Since the trip time increased, the well cost also increased enough,

while the trip time takes a major part of the well operation. This is contrary to

efficiency because time is money in drilling operation and the main objective of the

industry is to operate with the lowest cost per foot. Also, it should be mentioned

that if we change some factors and improve ROP, this shall not entail improvement

of drilling efficiency [16].



1.4 OBJECTIVE OF THIS STUDY

The methods to predict rate of penetration (ROP), used from oil and gas industry,

have proved to be a valuable tool that with continuous improvement, ensure a

smoother and more economic operation. The primary objective is the models to be

as close as possible to the recording data. If this assumption is confirmed, the

method can be considered accurate for new predictions.

This survey presents a theoretical approach to the drilling problem based on the

main factors that influence the drilling process. The objective of this research is to

analyze and explain all models which have been used until now and to estimate the

efficiency of each one.

Subject area

Presentation of the results from laboratory drilling experiments

Determination of parameters which influence rate of penetration

Presentation of the drilling rate equations

Analysis of mathematical models constants

Comparison between the most common ROP prediction models

Presentation of the optimum drilling conditions which minimize the drilling cost

Introduction of new advanced techniques

This survey uses existing studies and industry knowledge in order to correlate all

current parameters during the drilling process and present the effect to the rate of

penetration. This survey is also an attempt to make the term “cost per foot” more

understandable when the rate of penetration increases dramatically.

CHAPTER 2: LITERATURE OVERVIEW


2. CHAPTER 2

LITERATURE OVERVIEW

2.1 DRILLING ACTIVITY PARAMETERS

A brief reference to parameters involved in the drilling process is required in order to

explain how the rate of penetration is influenced. Another important point which

should be understood is how these parameters interact, accelerating or slowing the

drilling activity. In addition there are parameters that can be characterized as

measurement parameters as they describe the specifications and the amount of

recorded data either during the drilling process or before.

2.1.1 DESCRIPTION OF CONTROLLABLE PARAMETERS THAT INFLUENCE

RATE OF PENETRATION

WOB: By the term “weight on the bit” we refer to the total weight exerted on the bit

from the drilling string. This amount of weight in practice can be measured using the

drilling line tension. That means that a sensor is applied in drilling line, recording the

unique value that is converted to weight. With this tool we calculate the overall

weight including the weight of the block. This calculation requires particular attention

in order not to have to incorrect results. In addition, the new technology tools (MWD

collars) can measure the axial force exerted to the collars and transfer the

information [17].

RPM: This term describes the rotation speed of the drill string per minute. The

rotation motion starts from the rotation machine, which in some cases is a rotary

table, in other cases it is a top drive system and it is transferred through drill string

on the bit. The data are obtained by an electronic device and are considered quite

accurate [17-18].



PUMP PRESSURE: The pump pressure is directly linked to the term WOB while it

influences the total force which is exerted in the formation from the drill bit. When

the pump pressure increases the nozzle has more strength and as a result the rate of

penetration increases. A large amount of pump power is consumed on the bit. Flow

meters are used as pressure detection at the entrance and exit of the fluid [19].

BIT ENERGY: The three previous factors are considered bit energy parameters while

the amount of weight, speed and pressure is converted to energy strength. In other

words we are talking about the energy created between bit and rock [20].

FLUID PROPERTIES: This thesis focuses on the use of liquid drilling fluid (oil, water,

synthetic) while there are gas-liquid mixtures (foam, aerated water) and gases (air,

natural gas). The mud properties such as density, viscosity, are considered the two

most important rheological parameters for a safe drilling operation without risk for

kick and with an effective cutting removal. Also the mud properties are responsible

for other functions such as bit bailing, bit coiling, high torque and stuck pipe.

Nowadays, there are sensors which measure the mud weight and fluid viscosity in

real time, accelerating the process. The following table indicates the three different

types of liquid mud [20-21].

Table 1.1 Fluid type characteristics

HOLE CLEANING: Maybe there are the most important parameters for the bit drilling

and the increase of well depth. The cutting removal and consequently the hole

cleaning depend from many things. The most significant are the hole angle, cutting



size, annular size, bit specifications, fluid flow regime, fluid velocity and fluid

properties [15, 22-23].

2.1.2 DESCRIPTIONS OF MEASURABLE PARAMETERS

TORQUE: This is a down hole drilling measurement which describes the fatigue of

the drill string while it rotates. They are also referred to as rotational friction which

entails the interaction between the bit and the formation. This measurement

indicates if the bit is damaged and cannot be used again. It is a clear indication that

protects the bit from premature wear [17, 24].

DRILL STRING PROPERTIES: This term includes all the specifications that all parts

which constitute the drill string should have. Pipes must be designed to resist loads

such as buckling and axial forces. The parts that accept huge forces are designed to

be more durable [25].

VIBRATION: The term vibration describes the axial, torsional and lateral motions at

the bit. Such effects, such as a slip/stick, a bit whirl and bit bounce, have as a result

a faster cutter damage, shortening the life expectancy. After many experiments, it

has been proved that a diamond bit (anti-vibration bit) is able to sustain controlled

frequency vibrations increasing the ROP [26-28].

BIT BALLING: This is a phenomenon happening during the drilling process, that

occurs both on roller cone bits and PDC bits. As a consequence the rate of

penetration decreases continuously while the bit loses the performance. New

techniques such as electro-osmosis have focused on reducing bit balling and

increasing ROP [29-30].

ROCK STRENGTH: Rock strength should be defined for similar types of drilled rock

using the same bit and under the same conditions. Recorded database such as

formation drillability catalog provides a useful indication for the prediction of power

requirements for a particular drilling operation. When the rock strength is immense,

the required drilling conditions have negative effect on the penetration rate [31].

INCLINATION: This parameter referred to the directional drilling methods is

conducted with different tools. This advantageous equipment can take



measurements while drilling (MWD) that are continuously updated and send the

information in real time [32].

2.2 DRILLING OPTIMIZATION RESEARCH

When the industries perceived the main factors that influence the drilling operation it

was necessary to study the interaction between them. Following this consideration

and having as ultimate purpose to improve the process, the first research studies

were performed. For oil and gas companies the drilling optimization is accompanied

with two elements, rate of penetration increase and cost per foot reduction.

It was clear that the most significant factor which could guarantee improvement of

the drilling rate was the hydraulic maximization. For this reason companies tried to

improve the bit characteristics by doing tests and spending money.

However, we should mention that most of the trials were conducted in laboratories

and most of the studies describe the static optimization process. After that, the

advantageous communication system was a determining factor for the real time

drilling optimization period. There are two different categories of models which

optimize the drilling. The optimization was achieved using analytical methods such as

Warren model and statistical methods such as (Bourgoyne and Youngs) multiple

regression models.

Early drilling optimization models and recent real time optimization methods

constitute the subject of this assignment.

2.2.1 RATE OF PENETRATION OPTIMIZATION STUDIES

Bourgoyne and Youngs study is considered one of the most widespread models. It

became an accurate tool for the ROP predictions while it was a standard model on

which many of next researches are based. They used data from twenty five wells in

order to enact the constants. Taking into account eight different variables such as

formation strength, formation compaction, pressure differential, bit diameter- bit

weight, tooth wear, bit hydraulics and rotary speed, they established a linear



penetration model using multiple regression analysis in order to find the best WOB,

RPM and bit hydraulics characteristics. In addition, they claim that a simpler drilling

optimization model is possible to reduce the total costs by about 10% [8].

John W. Speer in 1959 wanted to create a chart which would indicate the best

correlation between five drilling parameters knowing the minimum of previous data.

Using personal experience he tried to determine the combination of WOB, RPM,

hydraulic horsepower and drillability formation which have the best result with

minimum drilling cost [33].

Garnier and Lingen focused on the formation characteristics and conducted

laboratory experiments with soft drag bits and roller cone bits on rock type with

different strength and permeability. They observed that there is a reduction of the

penetration rate when the formation strength is larger due to the dispute between

mud and pore pressure. They also supported that the cuttings due to pressure

differentiation in many cases remain at the bottom and the rocks are less drillable

[34].

Graham and Muench supported that if the optimum combination between bit weight

and rotary speed is found, the drilling cost will decrease while the rate of penetration

will increase. On the other hand, they noted that if the rate of penetration increases

due to greater bit weight and rotary speed, the cost of making round trip and bit cost

increases while the bit life expectancy decreases. It was clear that changes on WOB

and RPM, which increase or decrease the drilling efficiency, should be determined at

any drilling conditions by a mathematical analysis [7].

Galle and Woods are some of the first researchers who assumed that ROP is affected

only by two parameters and developed a mathematical relation between weight on

the bit and rotary speed in order to find the best combination of these constants.

They created a model which predicts the ROP and includes parameters such as

weight on bit, rotary speed, bit tooth wear and type of formation. They presented a

graph which indicates that the drilling cost can be minimized using the suitable

combination of drilling parameters. At the end they used the previous model and

established the drilling rate equation (2.1) rate of dulling equation (2.2) and bearing

life equation (2.3) [35].



𝑑𝐹

𝑑𝑡= 𝐶𝑓𝑑

𝑊𝑘 𝑟

𝑎𝑝 (Drilling rate equation) (2.1)

𝑑ℎ

𝑑𝑡=

1

𝐴𝑓

𝑖

𝑎𝑚 (Rate of dulling equation) (2.2)

𝐵 = 𝑆𝐿

𝑁 (Bearing life equation) (2.3)

Maurer studied the rate of penetration equation for roller cone bit from rock cratering

mechanisms. This equation has as general consideration the perfect cleaning which

means that all the rock scraps between teeth are removed. Also he established the

correlation of rate weight speed (RWS) and created the following formula (2.4) as a

function of depth which proves that failure in bottom hole cleaning is an important

factor reducing the rate of penetration with depth [36].

𝑑𝐹

𝑑𝑡=

4

𝜋𝑑𝑏2

𝑑𝑉

𝑑𝑡 (2.4)

Where:

F = the distance drill by bit

V = is the volume of rock removed

db = is the bit diameter

Langston presented a way for allocation, recording and usage of existing information

with day to day competitive drilling circumstances. These factors are all those

involved in drilling operation and must be optimized in order to have successful

results [37].

Eckel conducted an experimental study and observed a reduction in drilling rate due

to the changes from water to mud. He claims that viscosity is one of the most

important factors affecting drilling rate while influencing the cleaning effect [38].

Subsequently, he performed a microbit study showing that the drilling rate may be

expressed as an exponential function of a pseudo Reynolds number involving flow

rate, nozzle size, fluid viscosity and density [39].

R= k (Re)0.5 , 5 a<Re a<100 (2.5)



Young invented the development of a computer control system that will collect,

record and analyze the data. The system used the data as input information to solve

minimum cost drilling formulas and control the drilling parameters. More analytically,

the minimum cost solution is accompanied by four different equations, i.e., drilling

rate, bit tooth wear rate, bit wearing rate and drilling cost [40].

Lummus supported that drilling fluid and hydraulics are the most important factors

affecting drilling rate. He also classified the data required for optimized drilling in

three categories: data needed as input, day by day data which determine the

efficiency of optimization and data for better future optimization. However, he said

that it is possible to face problems when the drilling optimization programs have

difference requirements than the ones actually supplied from the rig equipments,

i.e., rig pump is not enough to provide adequate hydraulics. As a result, the

difference in rig equipments should affect the weight, rotary speed, mud and

hydraulics programs. In order to avoid this, the drilling programs should be planned

to be as much flexible as possible so that they adapt to rig equipments and satisfy

the optimum recommendation [41].

Wilson and Bentsen in 1972 presented a drilling optimization study which has as a

primary objective to minimize the drilling cost. This model presupposed that all the

parameters which affect the drilling process are restricted to two basic ones, WON

and RPM, while all others have been preselected. Due to complexity it is necessary to

develop three different methods: firstly minimize the cost per foot, secondly minimize

a cost of a selected interval and thirdly the cost over a series of interval [42].

Reed method predicted the best combination of factors, such as weight on the bit

and rotary speed, taking into consideration two different cases, when all other

variables were constant and when they were fluctuated. This method reached the

same result as Galle and Wood method, but is considered more accurate because it

has resolved the Monte Carlo Scheme. It should also be mentioned that this method

presented effective advantages in connection with field application [43].

Bizanti and blick did many laboratory experiments because they wanted to study the

factors which influence the cutting removal. During the trials they observed that

parameters such as nozzle diameters, cutting size, mud density, mud viscosity, yield



point, flow rate, rotary speed, bottom hole pressure, pressure drop through the

nozzles and inclination angle were responsible for the variations of a regression

analysis. The previous parameters were expressed as dimensional parameters such

as Reynolds number and Froude number in regression equations, where combining

these with a chart was a useful tool for cutting removal and ROP optimization [44].

Tanseu in 1975, using heuristic approach from several bit runs regression equation,

wanted to predict penetration rate and bit life. He considered the weight on the bit,

rotary speed and bit hydraulic horse power as controllable variables. These variables

impose the maximum drilling rate while the drilling cost is minimized over these

variables. Also he introduced an online optimization scheme for updates with each

new bit run [45].

Al-Betairi applied Bourgoyne and Young model using statistical analysis system and

observed that there are parameters which are not estimated in their model. The

purpose of his study was to find the correlation between the unknown drilling

parameters from the result of statistics, but the estimation is not more accurate due

to the presence of multicollinearity [46].

Reza and Alcocer created a new mathematical drilling optimization model that

consisted of three different equations which predicted the rate of penetration (2.6),

rate of bearing wear (2.7) and the rate of bit dulling (2.8) just as Galle and Woods

had done. These equations include factors such as WOB, RPM, mud density, mud

viscosity, rock hardness, fluid flow rate, pressure differential, temperature and heat

transfer coefficient. However, the determination of coefficient is very difficult in

laboratory using data from actual deep well [47].

𝐹

𝑁𝑑𝑝= 0.33 [

𝑁𝑑𝑝2

𝑢]

0.43

[𝑁𝑑𝑝

3

𝑄]

−0.68

[𝐸𝑑𝑝

𝑊]

−0.91

[𝛥𝑝𝑑𝑝

𝑊]

−0.15

(2.6)

𝐵

𝑁= 0.05 [

𝑡ℎ𝑑𝑝

𝑊𝑁]

0.51

[𝑢

𝑁𝑑𝑝2]

0.4

[𝑄

𝑁𝑑𝑝3]

−0.5

(2.7)

𝐷

𝑁𝐷𝑏= 0.001 [

𝑄

𝑁𝐷𝑏3]

0.56

[𝑊

𝐸𝐷𝑏2]

0.26

[𝐷𝑏

𝑄]

−0.03 (2.8)



Hoover and Middleton performed laboratory experiments wishing to determine the

bit performance and bit wear characteristics correlating the results with bit design

options. The experiments were conducted at 100 and 500 rpm with different bit

design in three types of rock: Nugget sandstone, Crab Orchard sandstone, and Sierra

White granite. They observed that as the bit wear has large wear flat, the torque

presented more variables when changed the weight on the bit [48].

In 1984, Warren wanted to determine a torque relationship based on a force balance

concept, using laboratory drilling tests and field data. He claimed that the torque was

determined by the weight on the bit and the depth of the tooth while the new model

is not influenced from parameters such as formation type, bit hydraulics and mud

characteristics [49]. Three years later he presented the rate of penetration model of

roller cone bit by cutting removal process which comprised of two terms. The first

includes the weight on the bit effect without depth of the tooth when the rate of

penetration is calculated and the other term includes the tooth effect [50].

Miska and Ziaja focused on evaluating the formation strength and formation

abrasiveness. They performed an experimental model with a verified rate of

penetration equation considering that it will confirm the reduction in penetration rate

due to the bit wear. The results were as expected while they achieved a perfect

matching with the theoretical model. This method can indicate the index of rock

strength [51].

Maidla and Ohara developed a drilling model, using previous drilling data. They

wanted to find the suitable bit bearing, weight on the bit and rotary speed. They had

as a basic ambition to reduce the drilling cost. The results from this drilling model

compared with the Bourgoyne and Young model. They supported that the drilling

rate could be predicted if we analyze the coefficient from previous drilling data and

added that the drilling model accuracy depends on the quality of these data [52].

Brett and Millheim method was a practice based on data from previous well which

had been drilled in a specific area. They created a method which was named drilling

performance curve (DPC). This method is a useful tool, while it gives all the

information from a variety of wells for the drilling process. This model was



considered a simple model because it restricted all the value of constants to three

[53].

Wojtanowicz and Kuru in 1987 developed a new mechanism model which includes all

the constants and functions of the drilling process. The validity of the constants was

tested using some field and laboratory data. Also the concept of maximum bit

performance (UBP) curve was taken into consideration. The curve indicates the

maximum values of the average drilling rates for various values while it was analyzed

for both roller cone bits and PDC bits [54].

Fear’s methods used foot based mud logging data, geological information and bit

characteristics in order to determine the correlations between controllable drilling

parameters. These correlations were used to generate recommendations for

maximizing ROP in drilling process [55].

Samuel and Miska in 1998 studied the optimization of motor performance and the

effect of drilling parameters. They performed a new test called wear off test to

establish an operating benefit from optimization of positive displacement motors

either on roller cone bit or on diamond bit. This study proves that the PDC

optimization accelerates the rate of penetration without aggravating motors

efficiency [56].

2.2.2 RATE OF PENETRATION SIMULATION MODELS

Pessier and Fear performed a full scale simulation test and developed an energy

balance model for boreholes drilling under hydrostatically pressurized conditions. The

basic elements are mechanical specific energy input, drilling efficiency and a

minimum specific energy equal to the rock strength. As a result they acquired better

and more accurate methodologies for WOB, ROP evaluation while supporting that the

drilling bearing problem is more reliable by continuously monitoring Es and μ,

equations [57].

𝐸𝑠 = 𝑊𝑂𝐵 (1

𝐴𝑏+

13.33𝜇𝑠𝑁

𝐷𝐵𝑅𝑂𝑃) (2.9)



𝜇 = 36𝑇

𝐷𝐵𝑊𝑂𝐵 (2.10)

Cooper created a drilling software that gives the opportunity to a student or engineer

to simulate and optimize the drilling process. Consequently, the program should run

either as a training program or as a simulator of a real project. The simulator

contains an algorithm which determines the rate of penetration, the rate of wear of

the bit and finds other accidental conditions such as well kick as drilling continues.

Also, it provided analytical indicator for cost per foot during drilling, while the user

could perform all the functions that are included in a real project [58].

Baraggan created a program which was based on the heuristic approach in order to

find the optimum drilling conditions using Monte Carlo Simulation and developing

numerical algorithm. In this study we have analyzed five different rate of penetration

equations (Moore, Maurer, Bingham, Cunningham, Eckel, Galle) having as a main

purpose to prove that drilling optimization of well phase is more economical than the

optimization by single bit runs. It is mentioned that the heuristic approach accepts

easily the constrain values to the drilling parameters [59].

Dubinsky and Baecker performed a computerized drilling simulation study. They used

the PC based simulator to determine dynamic behavior of the bit for various drilling

conditions. This was an attempt to simulate many of the major drilling dynamic

functions such as bit bounce, vibration, bottom hole assembly, torque shocks, stick

slip and torsional oscillation. However, they supported that the model required self

learning and practical experience in order to achieve the on line drilling optimization.

On the other hand, the program should be used as a training tool for MWD operator

[60].

Millheim and Gaeble created a new concept in order to reduce drilling cost and

increase the performance, which was called Virtual Experience Simulation (VES) for

drilling. This new concept was based on heuristics and exploited unused data

accumulations which are processed from specific data sets in specific geographical

and geological environments, such as geology, tripping, cementing, logging and ROP.

Very good ROP isomeric maps as well as 3D graphs were illustrated in the outcomes

of their work. They supported that these new data are valuable while they give the



user access to virtual drilling experience. VES offers a way that can provide

knowledge from others as virtual experience [61].

2.2.3 STUDIES OF REAL TIME DRILLING OPTIMIZATION

Simmons study is considered as the first study of real time drilling optimization.

Initially, Simmons used each available technology and engineering model that could

predict and evaluate the drilling process. These two concepts open new horizons

while the drilling supervisor on location using experience and usable technology,

which provides real time drilling performance, has the ability to determine the drilling

optimization parameters. Following Simmons’ study a combination of current

technology, engineering knowledge and real time drilling optimization can improve

drilling efficiency and save on overall drilling costs [62].

Zachariah John created a new advance data transmission system named InterACT

Web Witness (IWW) and could transfer data from remote drilling well sites in real

time. This procedure is 10-20 times quicker than the conventional system FTP. The

main advantage of real time system is that drilling experts have the opportunity to

exploit real time information in order to provide more effective support to the well

site staff especially when critical decisions should be taken [63].

Rommetveit and team created an innovative system for drilling automation and

simulation which was named drilltronics. This advance system had the capacity to

collect all available drilling data in real time and therefore to optimize the drilling

process. In reality the combination of equipment contributed in this project. The

system is constituted by a software modeling based on algorithm; using models that

drive drilling data in real time. This integrated drilling simulator develops the models

simultaneously comparing the ROP. Moreover, with the operations use such as

automatic control and automatic detection it warns for problems that may arise.

Consequently, this innovative system can detect unwanted event, improve drilling

data and automate a critical process [65].

J.E. Booth describes the coordinated effort from an operator and service oil and gas

companies to establish real time operation centers (RTOC) in order to improve



drilling efficiency. The evolution of drilling centers is divided into two periods. The

first drilling operation centers focus on data management and distribution and make

ambitious attempts to change the drilling process and provide a new work process

for managing and supporting remote operations, using data from different locations

of operation. The following timeline illustrates the chronology of the events [64].

Figure 2. 1 Drilling operation centers timeline of significat initiatives

Dupriest and Koederitz performed a new system which was called Navigation

Optimization (NAVO) and was based on (MSE) mechanical specific energy theory.

This innovative system monitors all dynamic drilling parameters during drilling

operations in real time, having as basic principle the ROP maximization and drilling

cost reduction [66].

Iversen and team created an integrated drilling monitoring system which promised

better optimization in drilling operation. This new system consisted of computer

controlled machinery and advanced computer modeling which are continuously



updated in real time data. Having all information for fluid flow we can detect

unwanted occurrences which exceed the safe limit for the drilling process. Operations

such as the cover tripping and reaming, pump start up, friction tests, stick slip

prevention, bit load optimization and monitoring are included in this process [67].

Milter studied the project on real time data, transferred from offshore facilities to

land support centers. The data were collected not only from one site but from any

place/site with high speed internet communication while piped data cover all the

necessary information in order to facilitate remote support. They ascertained that

this system of real time data transmission can minimize the number of unforeseen

event during drilling process [68].

Strathman and other member of Statoil team in 2007 were able to make a step

change in drilling activities. They supported that time needed for data extraction is

the main factor for an effective analysis, unlike the usual way for optimal operation

which focused on depth.

A data system included up to 200 parameters while the data frequency were derived

every 5 seconds from 20 different wells. The basic advantage of this system was the

effective optimization without having the experts on the rig [69].

Iversen and other member of Stavanger international institute (IRIS) presented in

2008 a new drilling controlled system for real time data optimization and automation

control which was installed into the rig control mechanism in order to pipe signal

from sensor in a real time basis. However the test showed that data transfer

credibility was not sufficient but measures have been taken to solve this problem. At

the end they concluded that parameters can be calculated and verify the quality of

safeguard calculations while the system functionality depends on data and correct

system setup [70].

CHAPTER 3: COMMON OPTIMIZATION MODEL THEORY


3. CHAPTER 3

COMMON OPTIMIZATION MODEL THEORY

Many optimization studies have been performed in order to determine the parameters

which influence the drilling rate, most of these aiming to reduce the total drilling cost

and increase the efficiency. The objective of this chapter is to present and analyze the

basic principle of the most common model which has been used from the industries

and that gave the stimulus to further research. There are four common drilling rate of

penetration models which are: Maurer’s [36], Warren’s [49-50], Galle and Woods’ [35] and

Bourgoyne & Young’s theories [8].

3.1 MAURERS PERFECT CLEANING THEORY

Maurer’s drilling rate formula is based on the perfect cleaning theory whereby all of

the rock scraps have been removed between teeth. This formula for roller cone bits,

which is derived from rock catering mechanism, consists from two main operations.

Initially is created a crater under the big teeth and immediately after this, the cuttings

is removed from the craters.The following picture illustrates the crater formation

mechanism to the overall drilling operation.

Figure 3. 1 Crater formation mechanism



When the bit tooth comes in contact with rock, its surface creates a deformed force,

which develops until its power overcomes the crushing strength of the rock. Exactly at

this point, a wedge of crushed rock is formed below the tooth and the crushed

material is compressed, creating high lateral forces around it. As a result, when the

force is higher than the limit of the rock, the fracture is transmitted from the point

under the tooth to the surface of the rock [71-72].

As demonstrated in the previous picture, the volume that arises from the fracture

should be removed, in order to continue the drilling process. This volume (V0),

depends on the following equation:

𝑉0 ∝ 𝐸𝐶 − 𝐸0 (3.1)

Where:

EC = energy imparted to the rock during formation of a single crater

E0= threshold energy required to initiate cratering

In case that there is a second free face to which crater the volume of material that

removed is larger and the relation between VO and E0 is a linear in order to slope

which presented the next picture. The new relationship is 𝑉0 ⋉ 𝐸𝐶 .

Figure 3. 2 Crater volume VS impact energy

It is remarkable that wedge or cones with larger included angles should be considered

as more effective, because they have the ability to crush larger volume. On the other

hand, it has been ascertained that smaller included angles have a greater penetration



depth. However, after many experiments, it was obtained that the previous

consideration is verified for angle ranking from 30 degrees to about 90 degrees, which

is the most effective point. That is because it creates a larger number of deeper lying

cracks that are more difficult to complete back to the rock surface to form fragments.

After this point, for tool angles greater than 90 degrees, the effectiveness decreases

rapidly [36, 71]. The drilling rate formula can be expressed as:

𝑅 =4

𝜋𝐷𝑏2

𝑑𝑉

𝑑𝑡 (3.2)

Where:

V = is the volume of rock removed

Db = is the bit diameter

When all of the broken rock is removed from the craters between impacts:

𝑉 = 𝑛 𝑉𝐶 (3.3)

Where:

n = is the number of the impacts

The total volume of each crater is independent of time and the equation (3.3)

transfomes to:

𝑑𝑉

𝑑𝑡=

𝑑𝑛

𝑑𝑡 𝑉𝐶 (3.4)

The rate at which teeth are impacting is:

𝑑𝑛

𝑑𝑡=IN (3.5)

Where:

I=is the number of impacts per revolution

N= rotary speed

When the effect force and the previous parameters are included, the drilling rate formula is:



𝑅 ∝𝐼𝑁(𝑊−𝑊0)2

𝑛𝑖2𝐷2𝑆2 for 𝑊 ≥ 𝑊0 (3.6)

𝑅 = 0 for 𝑊 ≤ 𝑊0 (3.7)

Where:

W= is the weight on the bit

W0= is the threshold weight required before the teeth penetrate the rock

Ni= is the number of teeth in contact with the rock when there is maximum force per tooth

S= is defined as the drillability strength of the rock

W0 depends on the type of the formation, for example, we assume that W0 is small

compared to W when the formation is very soft while low strengths are observed for

this kind of formations. According to perfect cleaning theory, the penetration per

revolution (R/N) should be independent of the rotary speed [73]. When the weight on

the bit has a very high value, the R/N ratio decreases very rapidly, as the rotary speed

is increased due to cleaning problem, which is occurred from high drilling rates. This

problem is considered as one of the majors problems during the drilling process. In

this case, the equations (3.6) reduce to:

𝑅 = 𝑘𝑁𝑊2

𝐷2𝑆2 (3.8)

Equation (3.8) indicates the good correlation of rate, weight and speed (R, W, N)

under perfect cleaning conditions. However, it should be mentioned that the data

relationships derived, apply only to the specific conditions under which they were

obtained, while it is very difficult to create a formula for imperfect cleaning conditions

[36].

3.2 WARREN CUTTING REMOVAL MODEL

Warren’s observation doesn’t depart from Maurers theory. After laboratory test, he

remarked that the ROP reduction at high bottom hole pressure is the effect from

insufficient cleaning. Warren created a model making an effort to represent all the

parameters of the physical process in one equation. The ROP depend by either the



cutting generation process or the cutting removal process, because under steady state

drilling condition the cutting removal is equal to the rate which new chips are formed.

The perfect cleaning model includes parameters such as rate of penetration, weight

on the bit, rotary speed, rock strength and bit size. The initial equation is the

imperfect cleaning model, which is the following [50,74].

𝑅 ≡ (𝑎𝑆2𝑑𝑏

3

𝑁𝑏𝑊2 +𝐶

𝑁𝑑𝑏)

−1

(3.9)

Where:

a,c=dimensional constants

Nb=bit rotary speed

S= rock strenght

W= weight on the bit

The first fraction on the equation is based on the assumption that the WOB is

supported by a fixed number of teeth and is independent from the teeth depth. On

the other hand, the second term describes the WOB distribution for more teeth as the

WOB is increased and the teeth penetrate deeper into the rock. Equation (3.9)

includes the bit size effect, WOB, rotary speed and rock strength. However, this

equation can’t predict the ROP without modification to account imperfect cleaning,

because the cutting removal is an important obstacle to the process [50].

At this point, it should be mentioned that the relation between WOB and ROP is not

standard and present different value under different conditions. In order to make the

previous relation more understandable, it’s very important to mention the

phenomenon which conducted in the inflection point. At low WOB the ROP increases

at an increasing rate as WOB to be increased up to a point. After this point WOB

continue to increase but a decrease rate. Exactly this point is called “inflection point”,

which has been observed that it occures when using bits with long teeth, which

increase the ROP, but it doesn’t occure when using bits with sort teeth [50].



Hydraulics flow is considered the most critical factor for the bottom hole cleaning.

When the level of hydraulics is increased the bit has more weight. As a result, the ROP

is decreased due to the mud properties which contribute to poor cleaning.

At this point, it is necessary to estimate the hydraulic energy which is developed under

the bit and available for the cutting removal. Warren, relying on this assumption,

calculated the impact pressure in order to evaluate the ability of the jet stream to

transfer energy to the bottom of the hole. The next equation indicates the impact

pressure:

𝑝𝑚 =50

1.238,6𝑠2 𝑝𝑑𝑛2𝑣𝑛

2 (3.10)

Where:

1.238,6 becomes 7991 when expressed in SI metric values

p=fluid density

dn= nozzle diameter

vn= nozzle velocity

s= distance from jet to impact point

The impact pressure measured under the bit, indicate a part of the energy has been

lost due to the jet flow into a confined space and the counterflow, which is the return

flow of fluid from under the bit. Making theoretical approach to impact pressure,

which should be independent of the nozzle size for a fixed bit size, the calculated

impact force can be found by the following equation:

𝐹𝑗 = 0.000516𝑝𝑞𝑣𝑛 (3.11)

Where:

0.000516 becomes 0.061S3 when expressed in SI metric values

p=fluid density

q=flow rate

vn=nozzle velocity



The maximum impact pressure is considered to be more suitable measurement for the

hydraulic cleaning ability of various hydraulic conditions, than the impact force is. The

reverse flowing fluid is a function of the ratio of the jet velocity to the return fluid

velocity while the volumetric flow rate through the jets is the same as the return flow

rate [76]. In order to calculate the velocities, it is very important to know the nozzle

cross sectional area and the cross sectional area around the bit. The function below

gives the ration between the two velocities [50, 75, 76]:

𝐴𝑣 =𝑉𝑛

𝑉𝑓 (3.12)

For roller cone bit with three jets it is assumed that, the area available for fluid return

flow is 15% of the total bit area and the previous equation is transformed to:

𝐴𝑣 =𝑉𝑛

𝑉𝑓=

0.15𝑑𝑏2

3𝑑𝑛2 (3.13)

Where:

Vn=nozzle velocity

Vf=return fluid velocity

db=bit diameter

dn= nozzle diameter

In the equation (3.10), the impact pressure for the various bit calculate,

𝑝𝑚 = (1 − 𝐴𝑉−0.122)

50

1.238,6𝑠2 𝑝𝑑𝑛2𝑣𝑛

2 (3.14)

and the impact force when is affected the same as the impact pressure.

𝐹𝑗𝑚 = (1 − 𝐴𝑉−0.122

) 𝐹𝑗 (3.15)

The improved ROP model that originates from the equation (3.9) is combined with the

impact force and mud properties in order to account the cutting removal. The

following equation describes the process from cutting generation to cutting removal as

the controlling factor to ROP [50].



𝑅 ≡ (𝑎𝑆2𝑑𝑏

3

𝑁𝑏𝑊2 +𝐶

𝑁𝑑𝑏+

𝑐𝑑𝑏⋎𝑓𝜇

𝐹𝑗𝑚)

−1

(3.16)

The first and second term has been analyzed previously; the third fruction includes the

following parameters:

C=dimensional constants

db= bit diameter

⋎𝑓=fluid specific gravity

μ=plastic viscosity

Fjm=modified jet impact force

The equation indicates that when the cutting size is increased, an increase from the

impact force is required, to maintain a particular level of cutting removal.

Nevertheless, when the cutting size is huge, the nozzle size used generally becomes

less important. Additional to this, it should be mentioned that hydraulic cleaning can’t

be improved by increasing the fluid density, which increases the impact force [76, 77, 78].

3.3 GALLE AND WOODS BEST CONTANT WEIGHT AND ROTARY SPEED

Galle and Woods study is focused on the best selection effect of weight on the bit and

rotary speed, for lowest drilling cost on the roller cone bits. There is a consideration

which supports that, when the weight on the bit and the rotary speed are constant

during the procedure, the total cost is higher than, when the two previous factors are

varied. According the above consideration, we can distinguish the next categories:

The best combination of constant weight and rotary speed

The best constant weight for any given rotary speed

The best constant rotary speed for any given weight

In the first case, the rig equipment permits the use of any WOB and rotary speed.

When there are limitations from the rig on the rotary speed we apply the second case.

The third case describes situations in which ther is the maximum weight, for example

overstress of drill string.



In order to found the best constant WOB and rotary speed for lowest drilling cost, the

following eight cases were examined for each of three categories individually. [35]

Case 1 Teeth limit bit life.

Case 2 Bearings limit bit life.

Case 3 Bearings and teeth wear out simultaneously.

Case 4 Drilling rate limits economical bit life.

Case 5 Drilling rate and bearings limit bit life simultaneously.

Case 6 Drilling rate and teeth limit bit life simultaneously.

Case 7 Drilling rate, teeth and bearings limit bit life simultaneously.

Case 8 Neither drilling rate, nor teeth, nor bearings limit bit life.

3.3.1 THREE FUNDAMENTAL EQUATIONS

Galle and Woods presented graphs for each of three procedures which indicate that

the drilling cost can be minimized using the following fundamental equations, which

are denoted by an identifying seven digit number on each of the graphs.

Drilling rate equation

𝑑𝐹

𝑑𝑡= 𝐶𝑓

�̅�𝑘

𝑟

𝑎𝑝 (3.17)

Where:

F=distance drilled by bit

Cf=formation drillability parameter

W=equivalent bit weight

a=0.928135D2+6.0D+1 (function of dullness)

k=1.0 for most formations and 0.6 for very soft formations

p=0.5 for self-sharpening or chipping-type bit tooth wear

r= rotary speed to a fraction power

This equation gives us detailed information about rate of penetration. We observe that

ROP increases with drillability, weight and rotary speed, while decreases with dullness.



Also, we should have in mind that the drillability parameter (Cf) includes all the effects

of bit types, hydraulics, drilling fluid and formation [35, 80].

Rate of dulling equation

𝑑𝐷

𝑑𝑡=

1

𝐴𝑓

𝑖

𝑎𝑚 (3.18)

Where:

D=bit tooth dullness, fraction of original tooth height worn away

Af= formation abrasiveness parameter

a=0.928135D2+6.0D+1 (function of dullness)

i= N+4348 x 10-5 N3

m= 1359.1-714.19log10W

In this equation the abrasiveness constant includes all the effects from factors such as

bit type, hydraulics, drilling fluid and formation. It is clear that the rate of wear

increases as the abrasiveness, weight and rotary speed increase. On the other hand, it

decreases as the dullness is increases [80].

Bearing life equation

𝐵 = 𝑆𝐿

𝑁 (3.19)

Where:

S= value of drilling fluid

L= tabulated function of W used in bearing life equation

N= rotary speed

It should be noted that, when the weight and rotary speed are increased, the bearing

life is decreased. The only factor which can contribute to the bearing life increases, is

the drilling fluid factor (S) [80].

As discussed before, the use of graph is necessary in order to determine the equation

constant. There are three different sets of graphs each identified by a seven digit

number, for example (2 075 060). The first number indicates the type of tooth wear



obtained on the bit. After this, the first three digit denotes the drilling rate to rotary

speed and the second three digit indicates the drilling rate to weight [35].

3.3.2 ADDITIONAL CALCULATION EQUATION

Total rotating time equation

𝑇𝑅𝑇 = [𝑆𝑛∗𝐿

𝑁] 𝐴𝑓 When teeth or drilling rate limit bit life (3.20)

𝑇𝑅𝑇 = [𝑆𝑛𝐿

𝑁] 𝐴𝑓 When bearings limit bit life (3.21)

Calculation cost per foot

Cost per foot = 𝐾(𝑟𝑖𝑔 𝑐𝑜𝑠𝑡 𝑝𝑒𝑟 ℎ𝑜𝑢𝑟)

𝐶𝑓 (3.22)

Calculation of total footage

𝐹𝑓 =𝐴𝑛+

𝑆𝑛∗𝐿

𝑁

𝐾 𝐴𝑓𝐶𝑓 When teeth or drilling rate limit bit life (3.23)

𝐹𝑓 =𝐴𝑛+

𝑆𝑛𝐿

𝑁

𝐾 𝐴𝑓𝐶𝑓 When bearings limit bit life (3.24)

3.3.3 CALCULATION OF CONSTANTS

Calculation of formation constants Af and Cf

Af is a constant which measures the abrasiveness and Cf is a constant which measures

the drillability of the formations. Using the values of N, W, D and the Galle and Woods

table, which indicates the correlation between constants, we can find the values of i, r,

m, L, U, V in order to calculate these constants [80].

𝐴𝑓 =𝑇𝑓 𝑖

�̅� 𝑈 (3.25)

𝐶𝑓 =𝐹𝑓 𝑖

𝐴𝑓 𝑟 �̅� 𝑚 𝑉 When using (2 075 100) or (2 043 100) (3.26)



𝐶𝑓 =𝐹𝑓 𝑖

𝐴𝑓 𝑟 �̅�6𝑚 𝑉 When using (2 075 060) (3.27)

�̅� =788𝑊

𝐻 (3.28)

H=hole or bit diameter

W= bit weight

Ff= final distance drill by bit

Tf= final rotating time

Calculation of drilling fluid constant (S)

High value of S means very good drilling fluids and the opposite low value of S entail

bad quality of drilling fluid. The determination of this factor is necessary in order to

calculate the bearing life. The bearing life is affected from S, weight and rotary speed.

The following equation gives the drilling fluid value: [35, 80]

𝑆 =𝑇𝑓 𝑁

𝐵𝑥𝑓 𝐿 (3.29)

Calculation An and Sn

𝐴 =𝑏𝑖𝑡 𝑐𝑜𝑠𝑡

𝑟𝑖𝑔 𝑐𝑜𝑠𝑡 𝑝𝑒𝑟 ℎ𝑜𝑢𝑟+ 𝑡𝑟𝑖𝑝 𝑡𝑖𝑚𝑒, ℎ𝑟 (3.30)

𝐴𝑛 =𝐴

𝐴𝑓 (3.31)

𝑆𝑛 =𝑆

𝐴𝑓 (3.32)

Sn*=∫𝑁𝑚𝑎

𝐿𝑖

𝐷𝑓

0 𝑑𝐷 (3.33)

Special attention is required when we want to determine the value of the constant,

because we should read the corresponding set of graph that applies in the right case

[35, 79].



3.4 BOURGOYNE AND YOUNGS MULTIPLE REGRESSION MODEL

Bourgoyne and Youngs’ model is the most widespread model in the industry while it is

considered to be one of the most complete mathematical drilling models for the

penetration rate prediction. It is a linear penetration model, which is consisted from

controllable and uncontrollable drilling variables. The following formula is considered

as a general linear rate of penetration equation for roller cone bit [8].

𝑑𝐹

𝑑𝑡= 𝑒{𝑎1+∑ 𝑎𝑗𝑥𝑗8

𝑗=2 } (3.34)

The constants can be determined by a multiple regression analysis of field data which

are caused from the formation strength effect, compaction effect, differential pressure

effect, bit diameter and bit weight effect, rotary speed effect, tooth wear effect and

bit hydraulic effect [81].

A multiple regression model is configured based on controllable variables in the

general ROP equation, such as bit weight and rotary speed, whoms function influence

the other uncontrollable data from regression cycle. The past drilling data from other

wells is essential condition in order to determined the constants which given in the

previous equation.

A complete description of the controllable and uncontrollable drilling variables is given

from the following equation and is represented by the following figure. [8, 81, 82]

𝑑𝐹

𝑑𝑡= 𝐸𝑥𝑝 {𝑎1 + 𝑎2(8000 − 𝐷) + 𝑎3𝐷0.69(𝑔𝑝 − 9) + 𝑎4𝐷(𝑔𝑝 − 𝑝𝑐) +

𝑎5𝐿𝑛 {

𝑤

𝑑𝑏−0.02

4−0.02} + 𝑎6𝐿𝑛 (

𝑁

60) + 𝑎7(−ℎ) + 𝑎8

𝑝𝑞

350𝜇𝑑𝑛} (3.35)



Figure 3.3 General rate of penetration equation

3.4.1 FORMATION STRENGTH FUNCTION

The constant a1 represents the effect of formation strength. This means that the value

of the constant is proportionate with ROP. For very low value of this constant, we

have low penetration rate and vise versa. Also, the formation strength function

includes the effect of other drilling parameters, such as drilling cuttings, which have

not been modeled mathematically. Additional factors could be introduced as new

function, influencing the general ROP equation. The following term of the general

equation indicates the drillability of the formation which is the same with ROP as

exponential function [81-82].

𝑓1 = 𝑒𝑎1 (3.36)



3.4.2 FORMATION COMPACTION FUNCTION

The two next terms of the general equation (a2, a3) describe the compaction effect.

There are two different compaction effects, which are depended from the formation

properties. It is very common that the rock strength is increased as the depth is

getting larger. In this case, the formation compaction effect is called normal

compaction while it is observed an exponential decrease in penetration rate with

increasing depth [8].

𝑓2 = 𝑒𝑎2𝑋2 = 𝑒𝑎2(8000−𝐷) (3.37)

The second term of the formation compaction function, which is defined as (a3),

describes the under compaction effect. This effect is conducted when we have

abnormally pressured formations, where the rate of penetration shows an increasing

behavior to the depth. Therefore, the equation of this function indicates an

exponential increase in penetration rate because the pore pressure gradient is higher

[8].

𝑓3 = 𝑒𝑎3𝑋3 = 𝑒𝑎3𝐷0.69(𝑔𝑝−9) (3.38)

3.4.3 DIFFERENTIAL PRESSURE FUNCTION

The pressure differential factor is considered to be an inhibiting factor, because the

penetration rate is reduced when there is a pressure difference. The term which

includes the differential pressure is defined as (a4) and it indicates an exponential

decrease in ROP when it excesses the bottom hole’s pressure. In other words, when

the pressure between the bottom hole and the formation is zero, the effect of this

function is equal to 1 [82].

𝑓3 = 𝑒𝑎4𝑋4 = 𝑒𝑎4𝐷(𝑔𝑝−𝑔𝑐) (3.39)



3.4.4 BIT DIAMETER AND WEIGHT FUNCTION

The term a5 determines the function of bit diameter and weight, since it is the term

that has direct effect on penetration rate. The exponential term is normalized to equal

1.0 for 4000lb pert inch of bit diameter which is the requirement tooth force in order

to the fracture begins. This force is called threshold force [8, 81].

𝑓5 = 𝑒𝑎5𝑥5 = 𝑒𝑎5𝐿𝑛{

𝑤𝑑𝑏

−0.02

4−0.02}

(3.40)

3.4.5 ROTARY SPEED FUNCTION

The next term of the general equation (a6) represents the effect of rotary speed. The

relation is similar with the weight function while the term ea6x6 is normalized to be

equal to 1.0 for 100 rpm. Also the rotary speed reported value is ranging from 0.4 for

very hard formation to 0.9 for very soft formation [8].

𝑓6 = 𝑒𝑎6𝑥6 = 𝑒𝑎6𝐿𝑛(

𝑁

60) (3.41)

3.4.6 TOOTH WEAR FUNCTION

The function for the tooth wear is defined by coefficient (a7). The tooth wear function

is usually expressed as a fraction of tooth height (h) of an inch. The value of this

function depends on the bit type and the formation type. The following tooth wear

exponent equation intimates that this functions equals to 1 when the h or a7 is zero [8,

81].

𝑓7 = 𝑒𝑎7𝑥7 = 𝑒𝑎7(−ℎ) (3.42)

3.4.7 HYDRAULIC FUNCTION

The function for the hydraulic effect is defined by coefficient (a8). The effect of bit

hydraulics is based on microbit experiments performed by Eckel, who found that ROP



was proportional to a Reynolds number group raised to the 0.5 power while μ is

defined as the apparent viscosity measured at 10,000 seconds -1 [81].

𝑓8 = 𝑒𝑎8𝑥8 = 𝑒𝑎8

𝑝𝑞

350𝜇𝑑𝑛 (3.43)

At this point, it should be mentioned that Bourgoyne and Youngs’ method is

considered to be the most suitable method for real time drilling optimization since it is

based on evaluation of the past drilling parameters from many wells that are

introduced continuously in linear penetration equation in order to conduct the multiple

regression analysis. The basic advantage of multiple regressions method is that it has

the capacity to estimate the rate of penetration as a function of independent drilling

parameters. In other words, the controllable variables monitored -in respect to the

depth and any deflection from the initial model due to uncontrollable variables, such

as formation characteristics- are taken into consideration in order to achieve the

regression.



4. CHAPTER 4

ANDANCED OPTIMIZATION METHODS

Many advanced optimization practices have been performed the last years from oil

and gas industries in order to minimize the drilling problems and to achieve the

reduction of drilling cost. Nowadays, all the advanced optimization methods use a

database which is based in real time information from different drilling sites. The

objective of this chapter is to present the way which drilling data are collected and

shipped and to analyze some of the modern ROP optimization models.

4.1 REAL TIME DATA

After 1980, emerged the need from petroleum industries for using innovative

systems and tools that measure petrophysical properties while drilling and monitor in

real time critical downhole parameters, which influence the penetration rate. As a

result of this necessity, the following years new advanced logging tools (LWD) which

come to cover the needs replace the wireline logging. Real time technology centers

started to be established in order to evaluate, manage, analyze and share the

informations [83-84].

4.1.1 MEASURE WHILE DRILLING PIPING

Measure While Drilling tools provide a volume of informations about the drilling

function which are very useful for the real time engineers in order to optimize the

drilling conditions. At this stage, it is very important to examine the way on which

these informations transfer from the downhole to the surface of the rig and after this

to real time technology centers. There are three ways to transmit data from the

downhole to the surface and will be analyzed below [93].

CHAPTER 4: ADVANCE OPTIMIZATION METHODS


Mud pulse telemetry (MPT)

This is a tool which transmits informations from downhole to the surface, introduced

in the industries in the early 60’s. Valves that exist in the BHA, regulate the flow of

the mud in order to produce pressure fluctuations that correspond to the transmitted

information. The pulses are propagated within the mud inside the drillstring towards

the surface where computers decode them into binary bits. The following represent

the MPT process [85-87].

Figure 4.1 Simplified MPT system description

Electromagnetic telemetry (EM)

There is a potential to have underbalanced drilling or extreme lost circulation

conditions. In this case, the mud pulse telemetry -as a way for data transmission-

could not have application, so electromagnetic telemetry is used as an alternative

solution. In practice, in an electromagnetic system the drillstring is used as an

antenna to transmit signal to the surface. This method uses low-frequency

electromagnetic waves that are transmitted through the formation, transferring the

encoded data [88-89].



Wired drill pipes

This system has higher cost from the previous telemetry systems. This technology

(WDP) is considered as the fastest way to send data to the surface. In this method,

the measurements are transmitted to the surface through electrical wires that are

well housed inside every single pipe of the drillstring [90]. Also this system contributes

to evaluation of kick, because it has pressure sensors along the string that divide the

annulus into control volumes. Using this volume technique the gas kick can be

estimated [91-92].

Figure 4.2 MPD setup with wired drill pipe and the resulting control volumes



4.1.2 REAL TIME TECHNICAL CENTERS

Drilling reports are typically created and transferred from the rig site on a daily basis.

The main operational data that are critical for real-time centers, which are disclosed

through daily reports, are:

Mud rheology

Drilling activity details

Bottom hole assembly components

Bit type and configuration

Crew information

Well risks

The state of the art is the connection in real time data directly with the required

report information in order to facilitate the drilling process [94]. When the drilling

measurements reach in real time centers, the data are stored and the optimization

process starts. The new advanced softwares are valuable tools for the real time

engineers, because monitoring and visualizing the data, provides them the ability to

reduce the project risk, which arises from the time that it is spended by comparing

the real-time data with the operations data. The software matches historical data

from other wells, so the users can correlate previous data as reference for current

well. When data are analyzed, regression coefficients should be determined in order

to be used in calculating the predicted rate of penetration and find the optimum

parameters [93, 95].

4.2 REAL TIME BIT WEAR

Having analyzed the real time data transfer mechanism, it is very important to study

the way on which these advanced tools contribute in ROP prediction. This module

presents a new method to combine the mechanical specific energy (MSE) and ROP

model, in order to calculate real time bit wear. The mechanical specific energy

method is defined as the work needed to destroy a given volume of the rock. On the

other hand, the rate of penetration model is used in order to predict the drilling

process measurements, such as formation drillability calculating, the effect of drilling



parameters, bit design and bit wear. The combination of these two methods can

optimize the drilling operation, showing the bit wear status during drilling, which is a

determining factor to take decisions. Bourgoyne and Youngs’ ROP prediction model

has been extensively analyzed in the previous chapter [96-97].

Bourgoyne and Youngs ROP model

We remind that this model is a linear penetration model, which includes controllables

and uncontrollables drilling variables, such as the effect of formation strength, the

compaction, the differential pressure, the bit diameter and bit weight, the rotary

speed, the tooth wear and the bit hydraulic effect. The model has been

mathematically expressed as: [8, 81]

𝑅𝑂𝑃 = 𝑓1 × 𝑓2 × 𝑓3 × 𝑓4 × 𝑓5 × 𝑓6 × 𝑓7 × 𝑓8 (4.1)

The above equation indicates that the rate of penetration is determined from eight

functions, which can be inverted in order to occure the formation drillability (f1).

𝑓1 =𝑅𝑂𝑃

𝑓2×𝑓3×𝑓4×𝑓5×𝑓6×𝑓7×𝑓8 (4.2)

Mechanical specific energy (MSE)

Using the mechanical specific energy could optimize the drilling parameters, since it

gives the ability to monitor the process and detect changes in drilling efficiency. The

MSE is measured as input energy, which is required to destroy a given volume of the

rock to the ROP. Taking into consideration this assumption, the following MSE

equation can be expressed as: [96]

𝑀𝑆𝐸 =𝑊𝑂𝐵

𝐴𝐵+

120𝜋×𝑁×𝑇

𝐴𝐵×𝑅𝑂𝑃 (4.3)

Where:

AB=bit surface area

N=rotary speed

T= measured torque



The torque can be determined as a measurement while drilling, but, in many cases

the torque is expressed as a function of the weight on the bit and bit sliding friction

coefficient from the following formula:

𝑇 = 𝜇𝐷𝐵×𝑊𝑂𝐵

36 (4.4)

In order to be calculated, a bit sliding friction coefficient which is a constant with the

same value both the roller cone and the PDC bit, it is necessary to conduct

laboratory measurement using torque and WOB. From the previous equations (4.2)

and (4.3) results the modified formula [97]:

𝑀𝑆𝐸𝑀𝑂𝐷 = 𝑊𝑂𝐵 (1

𝐴𝐵+

13.33×𝜇×𝑁

𝐷𝐵×𝑅𝑂𝑃) (4.5)

Real time bit wear developed model

If we combine the formation drillability and MSE, we have the following relationship:

𝑀𝑆𝐸 = 𝐾1 × (1

𝑓1)

𝐾2 (4.6)

Fractional bit wear is simplified and it is considered as a linear decreasing trend vs

depth, using the following equation [98]:

ℎ =(𝐷𝐸𝑃𝑇𝐻𝐶𝑈𝑅𝑅𝐸𝑁𝑇−𝐷𝐸𝑃𝑇𝐻𝐼𝑁)

(𝐷𝐸𝑃𝑇𝐻𝑂𝑈𝑇−𝐷𝐸𝑃𝑇𝐻𝐼𝑁)×

𝐷𝐺

8 (4.7)

Where:

DG= reported bit wear dullness

Figure 4.3 Schematic shows how PDC and roller cone bit types cutters have measured



The bit wear value starts at the point of T1, at the beginning of each bit run and is

decreasing throughout the bit run. The model used to estimate bit wear is based on

the approach developed by Rashidi [98] which included rock confined compressive

strength (CCS). General form of the equation is showed below:

𝑛𝑜𝑟𝑚𝑎𝑙𝑖𝑧𝑒𝑑 = (1

𝐾1) = 1 − ℎ𝐵 (4.8)

Where:

B= is a constant

K1= is the ratio of the MSE to the inverse rock drillability for each meter of the

drilled wells

The MSE, which incorporates the effect of bit wear, can be used in combination with

the CCS from ROP models, to back out real time fraction bit wear. Bit wear fraction

can be obtained using the following equation for the roller cone and the PDC bits: [98]

𝑊𝑓 = 1 − 𝑎 = (𝛥𝐵𝐺

8)

𝑏 (4.9)

Where:

ΔBG=8*h when fractional scale of bit grading from 0 to 8

This developed model is the basis of the creation of software that receives the data

from an online server and estimates real time bit wear. It should be mentioned that

the constant K1 are calculated manually for each bit run in order to have better bit

wear trend. This software improves the drilling operation while it has been observed

that achieves better match between calculating and reporting bit wear out value. As

a result, we can say that, using bit wear software, can minimize drilling cost by

reducing tripping time [95, 97].

4.3 ROP PREDICTION USING FUZZY K MEANS

It is perceived that ROP prediction is a complex phenomenon, because it depends

from many factors. Bourgoyne and Youngs ROP model which has been analyzed in

the previous chapter, it is used from the most petroleum industries during last



decades. However, it is not considered enough accurate method because it computes

coefficients using multiple regression analyses, which may have negative or zero

values that are completely absurd. For example, if the weight on the bit coefficient is

negative, it illustrates that increasing the WOB will decrease the penetration rate.

The main purpose of this section is to present a new method based on fuzzy K-

mean clustering -a computer simulation method- that predict the drilling rate

accurately. As mentioned before, there are uncertain parameters which influence

ROP. However, this simulation system receives the main variables, considering the

ROP as a nonlinear function g(x) with eight following inputs: true vertical depth (D),

weight on bit (W), bit diameter (db), rotary speed (N), pore pressure gradient (gp),

equivalent mud density (ρc), fractional bit tooth wear (h), jet impact force (Fj). For

every Fuzzy simulated annealing (SA) in real continuous functions g(x), there is a

fuzzy system f(x) such that [98]:

𝑠𝑢𝑝|𝑓(𝑥) − 𝑔(𝑥)| < 𝜀 (4.10)

Fuzzy simulated annealing algorithm provides an estimator f(x) to approximate g(x)

while predict undetermined parameters with minimum error.

Figure 4.4 Framework of prediction procedure



The figure (4.4) indicates the ROP prediction procedure which can be distinguished in

the following three steps [98-99]:

Clustering the training data

The first step maybe is the most significant. The input data should separate by K-

mean clustering approach in eight different clusters. In order to achieve this

classification, rules should be set. The number of rules is equal to the number of

clusters. The basic idea is to create a group of input-output clusters and use one rule

for each cluster. At this point, it is required special attention because it has been

observed that a large number of rules can be producing a complex fuzzy system. On

the other hand, a few rules create a less powerful system.

Setting up a typical Fuzzy system

Each group of input data or cluster is accompanied from a membership function.

Using the simulated annealing (SA) this function is optimized. Example for a common

cluster rule is indicated as follows:

if x1 is A’1 and x2 is A’2……….xi is A’i Then y is B’

Where A’i and B’ are mean and standard deviation of Gaussian with the following membership grade:

ℎ𝑖𝑙(𝑥𝑖) = 𝑒𝑥𝑝 [−

1

2(

𝑥𝑖−𝑐𝑖𝑙

𝜎𝑖𝑙 )

2

] (4.11)

Where 𝑐𝑖𝑙 and 𝜎𝑖

𝑙 are mean and the standard deviation of Gaussian

membership function for I input variable of i Fuzzy rule.

The simulated annealing (SA) is used in order to determine these two parameters of

all membership function of the Fuzzy system and find better estimator f(x).

Determining the parameters of Fuzzy system using SA

We can observe 6 steps into the required estimator f(x) process:

Initializing the parameters of SA (initial temperature, cooling coefficient,

searching time, termination condition)



Set a current solution X for above variables. MSE value of X can obtain by the

simplified Fuzzy inference system.

Randomly search for a neighbor solution set X’, which equals to X augments.

ΔE = MSE(X’) − MSE(X ). If D≤ 0, then the current solution set will be replaced

by the neighbor solution set; otherwise (when ΔE > 0), the winning probability of

the neighbor solution set is F (X’) =exp (-ΔE/T)

Compare X with optimal solution X’ and if X is better replaced with X’

If the maximum searching time is not achieved; go back to step 2

Check the termination condition is reached. If yes the algorithm has finished if

no return the step 3 until the termination condition is fulfilled

After many trials has been observed that new computing approach predicts the

penetration rate with more acceptable accuracy than a conventional method such as

Bourgoyne and Youngs prediction model. Using the root mean square error (MSE)

and standard deviation (SD) of ROP, we have more accurate results [98].

4.4 ROP PREDICTION TECHNOLOGIES BAZED ON NEURAL NETWORK

In the previous section we presented a new simulated method which is based on

Fuzzy K- mean clustering. At this section, we analyze another advanced simulated

method based on the artificial neural network (ANN) technologies, which predict the

penetration rate using MATLAB function codes. The ANN uses the previous data from

offset wells and runs to find the expected ROP, including any change of drilling

conditions as input.

4.4.1 UNDERSTANT AND LEARN CONCEPT

The ANN process requires comprehensive collecting data as input in order the system

to analyze the relationship between input and output. The system provides two

outputs, which are compared continuously until the errors are reduced and the

desired outputs become reasonable close. However, the system is very flexible since

it does not have a static formula that requires full set of data but finds the correlation



between input and output to extrapolate the missing data. In addition, it does not

need reprogramming every time the function is changed but it is required a correct

evaluation of input if we want to build a correct model of the offset wells. The below

figure illustrates the schematic process [101-102].

Figure 4.5 Artificial neural network

4.4.2 DRILLING OPTIMIZATION ANN

The first step in applying ANN system is to build a model of the offset wells using

formation analysis software.

The second stage is to establish the correlation (link) between drilling variables and

the results. A multiple neural network (MNN) consists from three different types of

layer: input layers, output layers and many of hidden layers. Input layers collect data

from databases, the hidden layers develop and analyze the relation between input

and output; the output layers produce the results. As is shown in the next figure

(4.6) every neuron of a layer is connected to each neuron of the next layer [101,103].

Every neuron of input represents a parameter which is received from the network as

input. On the other hand, neurons of hidden indicate the extraction output. The

number of hidden layers and neurons is unlimited while the relations between input

parameters are immeasurable. Each connected link has an associated weight which

is transmitted to a signal. This signal transfer is conducted through neurons over the

connecting links [100-101].



Figure 4.6 Drilling optimization ANN

In the next stage the simulator compares the outputs with the desired outputs.

Certainly, the first outputs will show huge errors, because the weight is calculated

with random way. The error signal transmitted back from the outputs layer to the

intermediate layer; the process is repeated layer by layer. The weight’s update is

based on the error signal until the outputs present the closest value to the desired

outputs value [101-102].

4.4.3 ELM AND RBF TECHNOLOGIES

The extreme learning machines (ELM) and radial basis function network (RBF) are

contained in artificial neural network techniques. Both ELM and RBF are single hidden

layer feedforward networks (SLFN) which use MATLAB function codes in order to find

the best results. It is interesting to examine the simulator outputs for these two

methods, in order to have a comparison between them in terms of accuracy and

processing speed. The following four terms, training time, training accuracy, testing

time and testing accuracy, validate a detailed comparison [103].



The ELM techniques training time are not influenced from small changes in the

number of hidden layers while from the five functions, one spends the most time.

Generally, ELM techniques are considered to be quicker because it is required less

training time than RBF techniques. The RBF are not affected by the speed

parameters but has the same training time at the values of MSE used.

Root mean square error (RMSE) and standard deviation (SD) is used in order to

ascertain the training accuracy of ELM which gives more accurate results comparing

with RBF. The ELM accuracy gets when the number of hidden layer is increased but

the RBF accuracy is set to be two MSE values.

ELM testing time is random and not affected by the number of hidden neurons. On

the other hand, RBF testing time is not affected by the choice of goal training

accuracy. However, the RBF testing time is higher than ELM.

Testing accuracies are compared in terms of (RMSE), of (SD) and of absolute percent

relative error. RBF testing is not accurate when training target MSE is chosen low and

very good when it is chosen close to ELM training accuracy.

The conclusion is that the ELM techniques give more accurate result in processing

time. On the other hand, RBF techniques are considered as more accurate methods

for ROP prediction, but if the speed is very important the ELM is more suitable for

use.

CHAPTER 5: CONCLUSIONS DEPARTMENT OF PETROLEUM AND NATURAL GAS TECHNOLOGY


5. CHAPTER 5

CONCLUSIONS

5.1 TOPICS DISCUSSED

Summarizing the main subjects of this assignment, we widely discussed the rate of

penetration prediction methods, focusing on their application in the petroleum

industry, analyzing the parameters of their methods as well as their benefits and

weaknesses. The assignment can be used as a handbook for someone who wants to

understand the fundamental functions of the drilling process, the ways in which to

predict the penetration rate throughout the chronological duration of drilling

activities. Also, the assignment gives the reader the opportunity to acquire some

advance knowledge about modern prediction methods.

In the beginning of the 20th century when drilling operations first started, the main

issue was to determine the relation between two terms, cost and time. In the

business world time means money and this is the basic consideration on which all the

rate of penetration prediction models were based. At the second chapter we

analyzed the factors which take part in drilling activities while dividing them into two

different categories depending on whether they can be controlled or not. Also, we

proceeded with the presentation of all the rate of penetration models as well as a

survey, in order to have a better estimation of the way basic principles operate, as

well as their historical evolution until today.

Considering the industry as a demanding costumer who wants to use as more

accurate models as possible, we conclude which study from the ROP is more

integrated and gives the minimum error for the corresponding time. In the third

chapter, we analyzed four models about the relation between the parameters which

contribute to rate of penetration prediction. One of these four, the Bourgoyne and

Youngs model is the basis for further developments while at the same time it is a

multiple regression model and suitable for real time optimization.



The Bourgoyne and Youngs model validates the beginning of the automation period

in early 1970. The oil and gas industry exploit the advance technology to transmit

the drilling data in real time and establish the first real time technical centers in order

to have more accurate input data during the drilling optimization process. It is

observed that the new advanced application using simulators which calculate the

constants of the model with minimum errors, gives the same prediction as the

recorded data and is considered much better than traditional multiple regression

methods.

5.2 GENERAL CONSIDERATION

The main goal of the final topics is to present the following conclusion results from

this evaluation. Can ROP prediction model be accurate? This is a fundamental

question that has to be answered, since the primary penetration model was replaced

with the new advanced simulator model.

Having studied the drilling process we can say that there are many

parameters which influence the penetration rate and it is impossible to find a

formula which will be valid under any circumstances.

The constants of the penetration model improve the accuracy while are based

on the observation from the laboratory trials which simulate the process and

the previous drilling process, operating under similar conditions.

However the combinations between the drilling parameters are unlimited and

the drilling measurement is always different.

A Monitoring system needs to be used in order to have reliable data. The

Multiple Regression Analysis procedure can be applied to determine the

regression coefficients present in the rate of penetration equation.

To increase the accuracy of a model, it is necessary to use data from more

than a single well.

Analysis has shown that the simulators improve the evaluation of field data

and find the optimum drilling parameters for a new well to be drilled.

CHAPTER 5: CONCLUSIONS DEPARTMENT OF PETROLEUM AND NATURAL GAS TECHNOLOGY


Different simulators techniques give different results and the decision makers

choose between the suitable techniques depending on their interest at the

time or the accuracy.

The good optimization techniques which enhance the determination of the

drilling parameters can lead to improvement of drilling performance and

drilling cost reduction.

Another important task of this study is the determination of the instant actual

tooth wear on the bit in real time which can contribute in rate of penetration

prediction.

Answering the main question is much more complicated than we can imagine, taking

into account all the previous considerations, it is perceived that one rate of

penetration model that shows very similar results between predicted ROP and actual

ROP should be an accurate model. Obviously, given all the factors and differences

that were discussed in this thesis, the question will probably not be answered in the

near future.

Therefore, the goal of any future research would be to analyze the state of the art

computer optimization using results from real projects. This research requires direct

cooperation with drilling companies in order to have access to the program and the

database that this program uses. The simulator characteristics should be compared

to the other simulation techniques, having as a purpose to evaluate the performance

in terms of accuracy and processing time.



ABBREVIATIONS – INITIALS

ROP Rate Of Penetration

MWD Measuring While Drilling

LWD Logging While Drilling

PQ Performance Qualifiers

WOB Weight On The Bit

RPM Rotary Speed Per Minute

PDC Polycrystalline Diamond Compact

RWS Rate Weight Speed

DPC Drilling Performance Curve

MBP Maximum Bit Performance Curve

VES Virtual Experience Simulation

RTOC Real Time Operation Centers

MPT Mud Pulse Telemetry

EM Electromagnetic telemetry

WDP Wired Drill Pipe

MSE Mechanical Specific Energy

CCS Confined Compressive Strength

SD Standard Deviation

ANN Artificial Neural Network

MNN Multiple Neural Network

ELM Extreme Learning Machines

RBF Radial Basis Function

RMSE Root Mean Squeare Eroors



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