“Mathematical Modeling for Drilling Optimization in  

Pre-salt Sections: a Focus on South Atlantic Ocean Operations” 

 

 

 

ANDREAS NASCIMENTO 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 



 
 

 
 

 

ANDREAS NASCIMENTO 

 

 

 

MATHEMATICAL MODELING FOR DRILLING OPTIMIZATION IN  

PRE-SALT SECTIONS: A FOCUS ON SOUTH ATLANTIC OCEAN OPERATIONS 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Guaratinguetá-SP 

2016 



 
 

ANDREAS NASCIMENTO 

 

 

 

 

MATHEMATICAL MODELING FOR DRILLING OPTIMIZATION IN  

PRE-SALT SECTIONS: A FOCUS ON SOUTH ATLANTIC OCEAN OPERATIONS 

 

 

 

 

Thesis presented to the Faculdade de 

Engenharia - Campus de Guaratinguetá 

(FEG), from the Universidade Estadual 

Paulista (UNESP), as part of the fulfillment to 

award the degree of Doctor of Engineering 

(Dr.-Eng.) in Mechanical Engineering with 

focus in Projects. 

 

 

Supervisor: Prof. Dr. Mauro Hugo Mathias (Brazil/ UNESP) 

Co-supervisor: Prof. Dr.mont. Gerhard Thonhauser (Leoben-Austria/ MUL) 

 

 

 

 

 

 

 

 

 

 

 

Guaratinguetá-SP 

2016 



 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
N244m 

Nascimento, Andreas  
     Mathematical Modeling for Drilling Optimization in Pre-salt Sections: 
a Focus on South Atlantic Ocean Operations / Andreas Nascimento - 
Guaratinguetá, 2016 
     135 f : il.  
     Bibliografia: f. 104-109 
      
     Tese (doutorado) - Universidade Estadual Paulista, Faculdade de 
Engenharia de Guaratinguetá, 2016. 

Orientador: Prof. Dr. Mauro Hugo Mathias 
Coorientador: Gerhard Thonhauser 
 
1. Pré-sal  2. Otimização matemática 3. Perfuração estratigráfica   I. 
Título 
 

CDU 622.323(043)                                                                   
 
 

 

 

 

 

 



 
 

 
 

ANDREAS NASCIMENTO 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 
 

 
 

 

 

 
 

 

 
 

 
 

 
 

 

 

February 2016 



 

CURRICULUM INFORMATION 

ANDREAS NASCIMENTO 
 

BIRTH - Date: 30th January 1984; 

- Place: Seeheim-Jugenheim, Hessen, Germany. 

FILIATION - Mother: Marta Leite da Silva Nascimento; 

- Father: Nazem Nascimento. 

2000/ 2004 - Degree: Technician (Tech.) in Industrial Computer Science; 

- Technical School: Industrial Technical College of Guaratinguetá 

- Colégio Técnico Industrial de Guaratinguetá (CTIG) - Brazil. 

2003/ 2008 - Degree: Engineer (Eng.) in Computer Engineering with focus in 

Petroleum Engineering and Energy; 

- University: Federal University of Itajubá - Universidade Federal 

de Itajubá (UNIFEI) - Brazil; 

- Scholarship: Brazilian National Agency of Petroleum, Natural 

Gas and Biofuels - Agência Nacional do Petróleo, Gás Natural e 

Biocombustíveis (ANP). 

2008/ 2010 - Degree: Master of Science (M.Sc.) in Energy Engineering with 

focus in Exploration of Rational Usage of Natural Resources and 

Energy; 

- University: Federal University of Itajubá - Universidade Federal 

de Itajubá (UNIFEI) - Brazil; 

- Scholarship: Brazilian Institute of Petroleum, Gas and Biofuels - 

Instituto Brasileiro de Petróleo, Gás e Biocombustíveis (IBP). 

2008/ 2012 - Degree: Diploma Engineer (Dipl.-Ing.) in International Study in 

Petroleum Engineering with focus in Drilling Engineering; 

- University: Mining University of Leoben - Montanuniversität 

Leoben (MUL) - Austria. 

2011/ 2014 - Position: Drilling & Measurement General Field Engineer; 

- Employer: Schlumberger Oil Field Services - Angola. 

2014/ 2016 - Position: University Assistant/ Visiting Researcher; 

- Hoster: São Paulo State University - Universidade Estadual 

Paulista (UNESP) - Brazil and Mining University of Leoben - 

Montanuniversität Leoben (MUL) - Austria; 

- Scholarship: ANP and CAPES BEX 0506/ 15-0. 



 

DEDICATORY 

  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I dedicate this work to my family and to all that have instilled in me trust, confidence and a 

drive to succeed. 

 

 



 

ACKNOWLEDGMENT 

 

To my parents and brother, for the education, love, advice and teachings. To my relatives for 

their understanding and assistance. 
  

To the Vice-director of the Faculty of Engineering - Campus of Guaratinguetá - Faculdade de 

Engenharia - Campus de Guaratinguetá (FEG) of the São Paulo State University - 

Universidade Estadual Paulista (UNESP) - Brazil and Supervisor, Prof. Dr. Mauro Hugo 

Mathias, for the guidance, teaching, assistance and patience in developing this research. To 

Prof. Dr. Luiz Roberto Carrocci, Prof. Dr. Mauro Pedro Peres, Prof. Dr. João Andrade de 

Carvalho Júnior and to Prof. Dr. José Elias Tomazini for the support, suggestions and 

discussions. 
 

To Prof. Dr.mont. Gerhard Thonhauser from the Department Petroleum Engineering (DPE) of 

the Mining University of Leoben - Montanuniversität Leoben (MUL) - Austria, who accepted 

me for a Doctoral exchange, Co-supervising and enabling a greater depth of research. 
 

To the Brazilian National Agency of Petroleum, Natural Gas and Biofuels - Agência Nacional 

do Petróleo, Gás Natural e Biocombustíveis (ANP) by means of the PRH48-ANP program, and 

to the Brazilian Federal Agency for the Support and Evaluation of Graduate Education - 

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) by means of the BEX 

0506/ 15-0 scholarship, for the financing support provided. To the Mechanic Department - 

Departamento de Mecânica (DME) from UNESP and to the Post-graduation technical session 

of FEG (in special Regina, Maria Cristina, Renata and Rodrigo), for all the assistance provided. 
 

To the Chair of Drilling and Completion Engineering (CDC) from MUL and to the Data Base 

of Exploration and Production (BDEP) from ANP,  for providing information and support in 

terms of data acquisition and analysis. 
 

To my friends and colleagues from Itajubá - Brazil, including the Student House Casa Amarela, 

(in special Zé, Colombia, Pedrão, Kebrado, Vitim, Santiago, Rafa and Tosco), friends from 

Guaratinguetá (in special Galão and Cabecinhas), and also friends from Leoben - Austria 

(Mathias, Danyari, Cohen, Lupo, Asad, Lamik, Daniel, Abbas, Rahman, Roman, Ramsauer, 

Gunnar and Rita). 
 

And to all colleagues, employees, servants, technicians and professors from MUL and UNESP 

who supported me throughout this important step of my life. 



 

EPIGRAPH 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

“The knowledge we learn from the masters and 

books. The wisdom one learns with life and 

with the humble...” 

Cora Coralina. 
 

“…and strong we have to be in this arduous 

necessity of proving knowledge…” 

 

 



 

NASCIMENTO, A. Mathematical Modeling for Drilling Optimization in Pre-salt Sections: 

a Focus on South Atlantic Ocean Operations. 2016. 135 p. Doctorate Thesis (Doctorate in 

Mechanical Engineering). Faculdade de Engenharia - Campus de Guaratinguetá, Universidade 

Estadual Paulista, Guaratinguetá-SP, 2016. 
 

ABSTRACT 
 

Pre-salt basins and their exploration have become more and more frequently mentioned over 

the years, not just for their potential reserves, but also for the implicit challenges in terms of 

operations to face in order to make these fields commercially viable. Several research efforts 

aimed at addressing these related barriers, in which drilling optimization and efficiency are 

presented as a considerably complex area. The problematic is concentrated in the low 

drillability and in the high cost involved when drilling the pre-salt carbonates. 
 

The outcome of this research is based in studies performed on top of eight pre-salt wells, 

addressing drilling operational time savings referenced by benchmarks and drilling mechanics 

parameters choosiness. The studies were based on simulations performed with penetration rate 

(ROP) modeling combined with specific energy (SE). The Bourgoyne Jr. and Young Jr. (1974) 

ROP model was used given the high errors presented for the other models, higher than 40% 

and, in terms of SE, the formulations from Teale (1965) and Pessier et al. (1992) were used. All 

these classic literature are still present in the industry and the software Oracle Crystal Ball was 

used as a supportive tool for the simulations. 
 

This research yielded four important results: 1) the polycrystalline diamond compact (PDC) is 

the most suitable drill-bit choice for pre-salt, presenting the lowest teeth-cutters wear rate, 0.28 

[%/ m]; 2) the possible spare in operational time encountered for the pre-salt operations 

represent a saving of approximately 13,747,550.00 [USD] for the analyzed pre-salt wells; 3) 

the final mathematical model developed, after the adjustments for pre-salt, foresee an 

improvement dropping the relative error from 36.52% to 23.12% in terms of comparing the 

calculated and modeled ROP with the field measured ROP; 4) the final model yielded from the 

combination of the ROP and SE formulations is the most adequate to be used in the industry, 

since it was possible to foresee an improvement by dropping the relative error even more, from 

23.12% to 21.2%. 
 

KEYWORDS: Drilling. Optimization. ROP. Efficiency. Energy. Pre-salt. 

 



 

NASCIMENTO, A. Modelamento Matemático para Otimização de Perfuração em Seções 

de Pré-Sal: um Foco em Operações no Oceano Atlântico Sul. 2016. 135 f. Tese de 

Doutorado (Doutorado em Engenharia Mecânica). Faculdade de Engenharia - Campus de 

Guaratinguetá, Universidade Estadual Paulista, Guaratinguetá-SP, 2016. 
 

RESUMO 
 

As bacias do pré-sal e sua exploração se tornaram cada vez mais mencionadas ao longo dos 

anos, não apenas por seu potencial de reservatório, mas também devido aos grandes desafios 

implícitos em termos de operações a serem enfrentados para tornar estes campos 

comercialmente viáveis. Várias pesquisas vêm sendo desenvolvidas visando contornar estas 

barreiras, das quais a otimização e eficiência de perfuração se apresentam como uma área 

consideravelmente complexa. A problemática se concentra nas baixas taxas de penetração e no 

alto custo envolvido ao se perfurar as seções dos carbonatos do pré-sal. 
 

Os resultados da pesquisa apresentados nesta tese baseiam-se em análises com oito poços do 

pré-sal, abordando economia de tempo operacional com base em análises referenciadas em 

benchmarks e escolhas de parâmetros mecânicos de perfuração. Os estudos foram baseados em 

simulações realizadas com modelagem de taxa de penetração (ROP) combinadas com energia 

específica (SE). Utilizou-se o modelo de ROP de Bourgoyne Jr.e Young Jr. (1974) face aos 

altos erros apresentados pelos outros modelos, superiores a 40% e, em termos de SE, utilizou-

se o equacionamento de Teale (1965) e Pessier et al. (1992). Todas estas literaturas classicas 

ainda estão presentes na indústria e o software Oracle Crystal Ball foi utilizado como uma 

ferramenta de apoio para as simulações. 
 

Os resultados deste trabalho mostraram quatro conclusões importantes: 1) a broca de perfuração 

do tipo polycrystalline diamond compact (PDC) é a mais adequada para o pré-sal, apresentando 

uma taxa de desgaste de dentes-cortadores de 0.28 [%/ m]; 2) a possível diminuição de tempo 

de operação encontrada após análises de performance de operação pode resultar em uma 

economia de aproximadamente 13,747,550.00 [USD] para os poços do pré-sal analisados; 3) o 

modelo matemático final desenvolvido, após os ajustes para o pré-sal, pode garantir uma 

melhoria do erro relativo de 36.52% para 23.12% em termos de comparação entre o ROP 

calculado e o ROP medido durante a atividade no campo; 4) o modelo final como resultado da 

junção do equacionamento de ROP e SE é o mais adequado para a indústria, uma vez que foi 

possível garantir uma diminuição ainda maior do erro relative, de 23.12% para 21.2%. 
 

PALAVRAS-CHAVE: Perfuração. Otimização. ROP. Eficiência. Energia. Pré-sal. 



 

LIST OF FIGURES 

 

Figure 1 - Energy matrix forecast between 2012 and 2050. .................................................. 24 

Figure 2 - Energy demand forecast per energy source till 2050. ............................................ 25 

Figure 3 - World petroleum-related production and demand forecast to 2030. ...................... 25 

Figure 4 - Pre-salt layer break-down and details of its remoteness. ....................................... 26 

Figure 5 - Pre-salt formation details and similarity between Brazil and Angola. ................... 27 

Figure 6 - South America and Africa continents early period fitting and main basins. .......... 28 

Figure 7 - Pre-salt carbonate samples with highlights of silica nodes in dashed red marks. ... 30 

Figure 8 - Basic schematic with major components of a drilling-rig. .................................... 32 

Figure 9 - Diamond impregnated (a) and polycrystalline diamond compact (PDC) drill-bit (b).

 ............................................................................................................................................ 34 

Figure 10 - Milled tooth (a) and tungsten-carbide-insert (TCI) drill-bit (b). .......................... 34 

Figure 11 - General example of a hybrid drill-bit with PDC and TCI features together. ........ 35 

Figure 12 - ROP versus rotary speed in atmospheric (a) and overbalance (b) conditions. ...... 38 

Figure 13 - Torque relation versus WOB. ............................................................................. 39 

Figure 14 - ROP versus WOB (a) and drill-bit OD (b). ......................................................... 40 

Figure 15 - ROP versus depth (a), compaction (b) and pore pressure (c). .............................. 43 

Figure 16- ROP versus differential pressure (a) and Reynolds Number (b). .......................... 45 

Figure 17 - ROP versus drill-bit teeth-cutters wear. .............................................................. 46 

Figure 18 - Schematic of flow and the three definition zones. ............................................... 47 

Figure 19 - Influence of total jet impact force in the ROP. .................................................... 48 

Figure 20 - ROP versus WOB for different overbalance pressures. ....................................... 49 

Figure 21 - Brief schematic of a translational axial and rotational movement of a drill-bit while 

drilling. ................................................................................................................................ 53 

Figure 22 - Graphics showing the convergence of specific energy to rock crushing strength. 55 

Figure 23 - Relationship between torque and penetration per revolution. .............................. 55 

Figure 24 - SE and drill-bit sliding friction factor under atmospheric (a) and overbalanced (b) 

conditions. ........................................................................................................................... 58 

Figure 25 - Graph showing a common drill-rate test curve and improvements possibilities. .. 60 

Figure 26 - Separated histogram of pre-salt historical GR for the wells # A, B, C, D, E and F 

under analysis. ..................................................................................................................... 64 

Figure 27 - Grouped and cumulative histogram of pre-salt historical GR for all wells # A, B, C, 

D, E and F. ........................................................................................................................... 64 

Figure 28 - Pre-salt returning fluids samples with traces of limestone (a) and claystone (b). . 65 



 

Figure 29 - Pre-salt caving (a) and cuttings (b) examples retrieved from related operations. . 65 

Figure 30 - Historical pressures profiles for the pre-salt wells # A, B, C, D, E, F, G and H. .. 69 

Figure 31 - Historical overburden pressures for the pre-salt wells # A, B, D, E, G and H. ..... 70 

Figure 32 - Historical temperatures for the pre-salt wells # B, D, E, G and H. ...................... 71 

Figure 33 - Historical drilling operational performance indicator for POOH. ........................ 74 

Figure 34 - Historical drilling operational performance indicator for RIH............................. 75 

Figure 35 - Historical drilling crew operational performance indicator for W2W connection.

 ............................................................................................................................................ 75 

Figure 36 - Historical performance analysis and benchmark for POOH activity. .................. 77 

Figure 37 - Historical performance analysis and benchmark for RIH activity. ...................... 77 

Figure 38 - Historical performance analysis and benchmark for surveying. .......................... 78 

Figure 39 - Historical performance analysis and benchmark for W2W connection time. ....... 78 

Figure 40 - Historical performance indicator for M/U of BHAs + SHT. ............................... 79 

Figure 41 - Historical distribution of drill-bits usage for the pre-salt wells # A, B, C, D, E, F, G 

and H. .................................................................................................................................. 86 

Figure 42 - Historical teeth-cutters characteristics after having drillined pre-salt sections. .... 88 

Figure 43 - Histogram distribution of ROPs per pre-salt used drill-bit. ................................. 89 

Figure 44 - Histogram distribution of footage per drill-bit type used in the pre-salt wells. .... 90 

Figure 45 - Histogram distribution of ROPs per pre-salt used drill-bit type and its dullness. . 90 

Figure 46 - Example of a simulation run with the software Oracle Crystal Ball. ................... 92 

Figure 47 - Field ROP versus modeled ROP using Cunningham (1960) model. .................... 93 

Figure 48 - Field ROP versus modeled ROP using Maurer (1962) model. ............................ 93 

Figure 49 - Field ROP versus modeled ROP using Bourgoyne Jr. and Young Jr. (1974) model.

 ............................................................................................................................................ 93 

Figure 50 - Simulation result for the (a) Cunningham (1960), (b) Maurer (1962) and (c) 

Bourgoyne Jr. and Young Jr. (1974) models. ........................................................................ 94 

Figure 51 - Field versus modeled ROP after BYM model adjustments. ................................ 95 

Figure 52 - Raw drilling mechanics parameters with highlights to the rotary speed. ............. 96 

Figure 53 - Field versus modeled ROP after BYM model adjustments for the group with rotary 

speed of 150 [rpm]. .............................................................................................................. 97 

Figure 54 - Field ROP and field MSE with highlights in black dashed lines for the UCS 

presented for the 150 [rpm] rotary speed group. ................................................................... 98 

Figure 55 - Field versus modeled MSE for group with rotary speed of 150 [rpm]. ................ 98 

Figure 56 - Re-built of drill-rate curve. ................................................................................. 99 

Figure 57 - Simulation for optimum drilling mechanics choosiness. ................................... 100 



 

LIST OF TABLES 

 

Table 1 - Historical drill-bit performance and cost for pre-salt sections from the literature. .. 36 

Table 2 - Bourgoyne Jr. and Young Jr. (1974) coefficients and model details. ...................... 42 

Table 3 - BYM ROP model details from Bourgoyne Jr. and Young Jr. (1986). ..................... 51 

Table 4 - BYM ROP model details from Eren (2010). .......................................................... 51 

Table 5 - BYM ROP model details from Irawan et al. (2012). .............................................. 52 

Table 6 - Historical pre-salt well costs, sizes, intervals, water depths, and coastal distance. .. 62 

Table 7 - Wells historical hydraulics and pressure related information. ................................ 68 

Table 8 - Historical drilling contractor performance for the wells # A, B, C, D, E, F, G and H.

 ............................................................................................................................................ 73 

Table 9 - Data performance analyses from for M/U BHA and SHT as per Figure 40. ........... 79 

Table 10 - Operational efficiency analysis for POOH and RIH speed for the wells # A, B, C, D, 

E, F and H. ........................................................................................................................... 81 

Table 11 - Wells drilling contractor efficiency analysis for W2W connection and surveying for 

the wells # A, B, C, D, E, F and H. ....................................................................................... 82 

Table 12 - Historical total potential savings for the pre-salt wells under analysis. ................. 83 

Table 13 - Historical parameters boundaries from equipment and drilling programs. ............ 84 

Table 14 - Historical pre-salt PDC drill-bit performance and record. .................................... 86 

Table 15 - Historical pre-salt TCI drill-bit performance and record. ..................................... 87 

Table 16 - Historical pre-salt hybrid drill-bit performance and record................................... 87 

Table 17 - Historical pre-salt diamond impregnated drill-bit performance and record. .......... 87 

Table 18 - Simulation results for the different ROP models in reference. .............................. 92 

Table 19 - Simulation results for the modeled ROP BYM model adjustments. ..................... 96 

Table 20 - Details of the drilling mechanics parameters limitation after simulation. ........... 100 

Table 21 - Historical ROP and drilling parameters for the well # A - runs # 1, 2 and 3. ...... 110 

Table 22 - Historical ROP and drilling parameters for the well # B - runs # 1, 2 and 3. ...... 111 

Table 23 - Historical ROP and drilling parameters for the well # C - runs # 1, 2 and 3. ...... 112 

Table 24 - Historical ROP and drilling parameters for the well # C - runs # 4 and 5. .......... 113 

Table 25 - Historical ROP and drilling parameters for the well # D - runs # 1, 2, 3, 4 and 5.

 .......................................................................................................................................... 114 

Table 26 - Historical ROP and drilling parameters for the well # D - runs # 6 and 7. .......... 115 

Table 27 - Historical ROP and drilling parameters for the well # E - runs # 1, 2, 3, 4, 5 and 6.

 .......................................................................................................................................... 116 

Table 28 - Historical ROP and drilling parameters for the well # E - runs # 8, 9 and 10. ..... 117 



 

Table 29 - Historical ROP and drilling parameters for the well # F - run # 1. ...................... 118 

Table 30 - Historical ROP and drilling parameters for the well # F - run # 2. ...................... 119 

Table 31 - Historical ROP and drilling parameters for the well # H - runs # 1, 2, 3, 4, 5 and 6.

 .......................................................................................................................................... 120 

Table 32 - Historical ROP and drilling parameters for the well # H - runs # 7, 8 and 9. ...... 121 

Table 33 - Drill-bit performance and record for the well # A - runs # 1, 2 and 3. ................ 123 

Table 34 - Drill-bit performance and record for the well # B - runs # 1, 2 and 3. ................ 124 

Table 35 - Drill-bit performance and record for the well # C - runs # 1, 2 and 3. ................ 125 

Table 36 - Drill-bit performance and record for the well # C - runs # 4 and 5. .................... 126 

Table 37 - Drill-bit performance and record for the well # D - runs # 1, 2 and 3. ................ 127 

Table 38 - Drill-bit performance and record for the well # D - runs # 4, 5, 6 and 7. ............ 128 

Table 39 - Drill-bit performance and record for the well # E - runs # 1, 2 and 3. ................. 129 

Table 40 - Drill-bit performance and record for the well # E - runs # 4, 5 and 6. ................. 130 

Table 41 - Drill-bit performance and record for the well # E - runs # 7, 8, 9 and 10. ........... 131 

Table 42 - Drill-bit performance and record for the well # F - runs # 1 and 2. ..................... 132 

Table 43 - Drill-bit performance and record for the well # G. ............................................. 132 

Table 44 - Drill-bit performance and record for the well # H - runs # 1, 2 and 3. ................ 133 

Table 45 - Drill-bit performance and record for the well # H - runs # 4, 5 and 6. ................ 134 

Table 46 - Drill-bit performance and record for the well # H - runs # 7, 8 and 9. ................ 135 

 

  



 

LIST OF ABBREVIATIONS AND INITIALS 

 

ANP 

 

BHA   

BHP   

BMK  

BYM   

CAPES  

 

 

CDC 

Connec. 

CTIG  

 

D 

DME  

DD 

Diamond impreg. 

DOC 

DR  

Drill. prog. 

ECD 

EMW  

EOR   

ESD   

FDP   

FEG   

 

FLOW  

FIT 

FP   

GR   

HSE   

HT   

Brazilian National Agency of Petroleum, Natural Gas and Biofuels 

(Agência Nacional do Petróleo, Gás Natural e Biocombustívei); 

Bottom-hole-assembly; 

Bottom-hole pressure; 

Benchmark; 

Bourgoyne Jr. and Young Jr. model; 

Brazilian Federal Agency for the Support and Evaluation of Graduate 

Education (Coordenação de Aperfeiçoamento de Pessoal de Nível 

Superior); 

Chair of Drilling and Completion Engineering; 

Connection; 

Technical Industrial College of Guaratinguetá (Colégio Técnico 

Industrial de Guaratinguetá); 

Deviated; 

Mechanic Department (Departamento de Mecânica); 

Directional drilling; 

Diamond impregnated; 

Depth-of-cut; 

Drilling rate; 

Drilling program; 

Equivalent circulating density; 

Equivalent mud weight; 

Enhanced oil recovery; 

Equivalent static density; 

Fast drill program; 

Faculty of Engineering - Campus of Guaratinguetá (Faculdade de 

Engenharia - Campus de Guaratinguetá); 

Flow-rate; 

Formation integrity test; 

Fracturing pressure; 

Gamma-ray; 

Health-safety-environment; 

High temperature; 



 

IBP   

 

ILT   

IT 

LOT 

LWD  

MMbbd 

MSE   

MUL  

MWD  

M/U 

n/a 

NPT   

OIM   

OD   

OP 

Op. c. 

PDM  

PDC  

POOH  

PP   

PU  

RAB   

RIH   

ROP   

rpm   

RSS   

S. 

SE   

SHT  

SO 

SPP_off  

SPP_on  

TBRT 

TCI  

Brazilian Institute of Petroleum, Gas and Biofuels (Instituto Brasileiro 

de Petróleo, Gás e Biocombustíveis); 

Invisible lost time; 

Information technology; 

Leak-off test; 

Logging-while-drilling; 

Millions of blue barrel per day; 

Mechanical specific energy; 

Mining University of Leoben (Montanuniversität Leoben); 

Measuring-while-drilling; 

Making-up; 

Not available; 

Non-productive time; 

Offshore installation manager; 

Outer diameter;  

Overburden pressure; 

Operational counts; 

Positive displacement motors;  

Polycrystalline diamond compact; 

Pull-out-of-the-hole; 

Pore pressure; 

Pick-up weight; 

Rotary free weight;  

Running-in-hole; 

Rate of penetration;  

Rotation per minute; 

Rotary steerable systems; 

Sampling; 

Specific energy; 

Shallow-hole-testing;  

Slack-off weight;  

Stand pipe pressure off bottom; 

Stand pipe pressure on bottom; 

Tool/ drill-bit below rotary table; 

Tungsten-carbide-insert; 



 

Temp.  

TH 

TOR_on  

TOR_off 

Temperature; 

Tripping-in/ out-of-hole; 

Torque on bottom;  

Torque off bottom; 

UCS 

USD 

UNESP 

UNIFEI  

USS 

V 

W2W  

WOB   

Ultimate compressive strength; 

United States dollar; 

São Paulo State University (Universidade Estadual Paulista); 

Federal University of Itajubá (Universidade Federal de Itajubá); 

Ultimate shear strength; 

Vertical; 

Weight-to-weight; 

Weight-on-bit. 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 



 

LIST OF SYMBOLS 

 

푇푖푚푒   Total rotating/ drilling time [h]; 

푇푖푚푒   Total time spent in connections [h]; 

푇푖푚푒  Total time spent in drill-string tripping [h]; 

퐶표푠푡  Final cost per drilled meter [USD/ m]; 

퐶표푠푡   Drill-bit cost [USD]; 

퐶표푠푡   Drill-rig operational cost per hours [USD/ h]; 

푀퐷   Final depth taken into account [m]; 

푀퐷   Initial depth taken into account [m]; 

푇푉퐷 True vertical depth [ft]; 

푅푂푃   Rate of penetration [ft/ h]; 

푅푃푀     Rotary speed [rev/ min] [rpm]; 

푊푂퐵    Translational axial force acting in the drill bit [lbf]; 

푂퐷  Outer drill-bit diameter [in]; 

퐾   Constant dependent drill-bit dullness, formation and drilling conditions [1]; 

푊푂퐵    Translational axial force threshold necessary to initiate rock fracture [lbf]; 

푎  Formation strength and drilling fluid properties coefficient [1]; 

푎   Normal compaction trend coefficient [1]; 

푎   Under-compaction and pore pressure coefficient [1]; 

푎   Differential pressure coefficient [1]; 

푎   Constant dependent on drilling conditions and WOB behavior [1]; 

푎   Constant dependent on drilling conditions and rotary speed behavior [1]; 

푎   Teeth-cutters wear coefficient [1]; 

푎   Hydraulic coefficient [1]; 

ℎ  Fractional tooth height that has been worn away [1]; 

푆  Rock drillability or crushing strength [psi]; 

푢   Apparent drilling fluid viscosity [cP]; 

푂퐷   Drill-bit nozzle diameter [in]; 

퐸푃푃 Formation pore pressure [ppg]; 

퐸퐶퐷  Equivalent circulating density [ppg]; 

퐸푀푊 Equivalent mud weight [ppg]; 

푅푂푃   Calculated ROP using ROP models [ft/ h]; 

푅푂푃   ROP retrieved from field data - observed one [ft/ h]; 



 

푥   Related temporary parameters; 

푅   Regression index correlation [1]; 

푟  Residual error [1]; 

퐹   Jet impact force used to characterize level of bit hydraulics [lbf]; 

퐹   Jet impact force adjusted by the reduction factor [lbf]; 

훾  Fluid specific gravidity [1];  

퐾 , 퐾 , 퐾    Drill-bit constants present in the Warren (1987) model [1]; 

푉  Average velocity of jet nozzle [ft/ s]; 

퐴   Ratio of nozzle jet velocity to return back-flow velocity [1]; 

푘  Junk slot area in percentage of total drill-bit diameter [1]; 

푉   Total return back-flow velocity [ft/ s]; 

푄   Nozzle flow-rate [gal/ min] [gpm]; 

푄   Total nozzles flow-rate [ft3/ s]; 

푄   Total return back-flow flow-rate [ft3/ s]; 

푛   Number of active bit nozzles [1]; 

퐴    Nozzle cross-section area [in2]; 

휏    Total work performed by the forces acting in the drill bit [in-lbf]; 

휏   Work performed by rotational force acting in the drill bit [in-lbf]; 

휏   Work performed by translational axial force acting in the drill bit [in-lbf]; 

퐹     Translational axial force acting in the drill-bit [lbf]; 

퐹   Rotational force acting in the drill-bit [lbf]; 

푇    Drill-bit torque [in-lbf]; 

푑푡   Infinitesimal time range [min]; 

푑휃    Infinitesimal rotary angle [o]; 

푑푣     Infinitesimal drill-bit velocity equivalent to the ROP [in/ min]; 

푑푠     Infinitesimal drill-bit displacement [in]; 

푁     Total revolution taken into account [1]; 

푆퐸   Drill-bit SE in terms of energy per volume of rock [lbf/ in2]; 

퐴     Drill-bit cross section area [in2]; 

푑푉    Infinitesimal volume of rock drilled per minute [in3/ min]; 

    Total revolution per time equivalent to the rotary speed [rev/ min]; 

푆퐸   Drill-bit MSE in terms of energy per volume of rock [lbf/ in2]; 

휇  Drill-bit sliding friction factor [1]; 



 

푀푆퐸   Adjusted MSE to represent down-hole energy [lbf/ in2]; 
푀푆퐸   Raw MSE in terms of surface energy per volume of rock [lbf/ in2]; 

퐸퐹퐹    MSE efficiency in terms of percentage transmitted to the drill-bit [1]. 
 
 

 



 

TABLE OF CONTENT 

 

1 INTRODUCTION ............................................................................................... 21 

1.1 OBJECTIVES ........................................................................................................ 22 

1.2 THESIS STRUCTURE .......................................................................................... 22 

2             LITERATURE REVIEW ................................................................................... 24 

2.1 THE PRE-SALT .................................................................................................... 24 

2.1.1 South Atlantic Ocean coasts similarity ............................................................... 27 

2.1.2 General geology and drilling information .......................................................... 29 

2.2 DRILLING OPERATIONS ................................................................................... 30 

2.2.1 Activities and equipments ................................................................................... 30 

2.2.2 Drilling activity and costs .................................................................................... 35 

2.3 ROP MODELING CONCEPT ............................................................................... 37 

2.3.1 ROP Model evolution .......................................................................................... 37 

2.3.2 BYM ROP Model applicability ........................................................................... 50 

2.4 SPECIFIC ENERGY CONCEPT ........................................................................... 52 

2.4.1 Specific energy knowledge evolution .................................................................. 52 

3             PRE-SALT DATA ANALYSIS ........................................................................... 61 

3.1 GENERAL WELL INFORMATION AND COSTS............................................... 61 

3.2 RESERVOIR CHARACTERIZATION ................................................................. 62 

3.3 RELATED HYDRAULIC CHARACTERIZATION AND ANALYSIS ................ 66 

3.4 DRILLING OPERATIONAL PERFORMANCE ANALYSIS ............................... 71 

3.5 DRILLING MECHANICS PERFORMANCE AND ANALYSIS .......................... 83 

3.6 DRILL-BIT PERFORMANCE AND ANALYSIS ................................................. 85 

4            OPTIMIZATION MODELING AND RESULTS ............................................... 91 

4.1 ROP MODEL CHOOSINESS ............................................................................... 91 

4.2 SPECIFIC ENERGY CROSS-ANALYSIS WITH ROP MODEL .......................... 97 

4.3 OPTIMIZATION DETERMINATION METHODOLOGY ................................... 98 

5            CONCLUSION ................................................................................................... 101 

REFERENCES ................................................................................................................ 104 

APPENDIX A - HISTORICAL PRE-SALT ROP AND DRILLING PARAMETERS 110 

APPENDIX B - HISTORICAL PRE-SALT DRILL-BIT RECORD ............................ 122 

 

 



21 
 

1 INTRODUCTION 

Pre-salt basins and their exploration have become more and more frequently mentioned over 

the years, not just for their potential reserves, but also for the implicit challenges in terms of 

general operations (downstream and upstream) addressed to make these fields commercially 

viable. Several research efforts aimed at addressing these related barriers, but the known 

challenges of drilling optimization and efficiency resulted from considerably low drillability 

throughout the pre-salt carbonates is still present. The pre-salt market trend has been frequently 

explored over the years in Brazil and in Angola and, considering these countries’ potential in 

terms of oil and natural gas, these reserves have a considerable importance in each country’s 

economy and energy outlook. Moreover, since one of the barriers still faced is the high 

operational cost and the downside of drilling related events, by boosting directly or indirectly 

the drilling activities, the possibility of having these fields coming through economically is 

enhanced. Thus, studies are still under performance in several related research areas in order to 

model a way to allow reliable forecast and drilling parameters choosiness for efficiency 

assurance while performing drilling operations.  
 

In this sense, this thesis is based in the analysis of the pre-salt carbonates operations focusing 

in operations that was carried in the South Atlantic Ocean. Considering the low oil prices and 

the also Petrobras scandal in Brazil, it is fair to say that any improvements that may result in 

cost savings can help even more in making these pre-salt fields to come through.  

 

Thus, the originality of this research can be seen firstly by the pre-salt wells statistical study 

presented, from which an identity was drawn to refer numerically to these layers, allowing 

analysis to be developed. Subsequently, the research novelty was presented by a new 

methodology of ROP and SE models combination aiming drilling optimization. From the 

determination of operational time savings, of the best drill-bit to be used in these regions, of 

drill-bit teeth-cutters wear rate, up to in-situ geothermal and pressure profiles, a ROP model 

was modified accordingly, in order to reflect specifically the pre-salt wells. After the ROP 

model adjustments, it was combined with the SE formulations, yielding as a final result a path 

for determining the best set of drilling mechanics parameters, aiming to support the industry 

for an efficient and optimized operation, and so, potentializing costs reduction. 



22 
 

1.1 OBJECTIVES 

The main objective of this research is to identify, characterize, and suggest changes in technical 

exploration of petroleum-related hydrocarbons carried in South Atlantic Ocean. Thus, develop 

and mold mathematically a drilling optimization model aiming performance improvement and 

drillability enhancement. This thesis was developed based on the following specific objectives: 
 

- Address the geological similarity of the South Atlantic Ocean’s coasts; 

- Study techniques and new researches concerning drilling optimization with regard to rate of 

penetration (ROP) modeling, specific energy (SE) surveillance, and analysis of drilling 

mechanics parameters; 

- Analyze these studies using combined pre-salt field operational information and data sets, 

proposing performance improvements;  

- Suggest possible alternatives to improve drilling efficiency by combining ROP modeling and 

SE surveillance techniques/ 

- Dissert a final methodology linked to mathematical modeling, based in the studied literature 

and suggestions to enhance the drillability and performance in pre-salt sections. 

1.2 THESIS STRUCTURE  

The thesis is structured in five chapters organized as following: 
 

In this first Chapter - Introduction - relevancies related to the thesis development are addressed, 

specifying the organization, layout, purpose, and a brief background of the subjects with their 

relative importance to the present topic under research. 
  

Chapter two - Literature review - presents a literature review of important concepts used 

throughout the thesis that help understanding the relevancies of the pre-salt to the world 

energetic scenario, and the methodology used behind the optimization models to develop and 

gather the data used for the studies. 
 

Chapter three - Pre-salt data analysis - presents the data set used throughout the thesis and its 

combination results for providing relevant information useful for progressing with the 

performance analysis and subsequent optimization appliance. It starts addressing the general 

pre-salt wells information and costs, detailing then the reservoir and hydraulic characterization. 



23 
 

Subsequently, the operational performance analysis is presented, followed by the drilling 

mechanics and drill-bit performance analysis, respectively. 
 

Chapter four - Optimization modeling - presents the methodology for choosing the best 

optimization model, the step-by-step of modifications and set-up applied to the best chosen 

model with the information yielded from chapter three, and the final developed mathematical 

model for drilling optimization followed by its implementation with help of one pre-salt well 

data-set as a case study.  It starts with the choosiness of the best ROP model to be used, detailed 

by fitting graphs, findings tables and regression relative error analysis. Subsequently, the step-

by-step for modeling the SE based in ROP models is presented, followed by a case study where 

optimization simulations with the developed mathematical model are run, defining the 

optimized drilling mechanics parameters by means of best efficiency.    
 

Chapter five presents a consolidation of results in form of conclusion and perspectives for future 

researches. 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 



24 
 

2         LITERATURE REVIEW 

This chapter covers a literature review of the main topics addressed in the thesis, encompassing 

information about petroleum-related energy market, drilling operations and related 

optimization researches. 

2.1 THE PRE-SALT 

The needs to meet increasing energy demands has allowed room for fossil energy sources to 

play a very important role within the context of the world energy matrix. Though constantly 

pitted against renewable energy sources, forecasts have shown that the increase in energy 

demand has consequently pushed the demand for fossil fuels, even though constantly losing 

position as a primary energy source versus renewable sources. Figure 1 highlights specific 

countries and continents, projecting energy source usage in year 2050; oil and natural gas may 

have their representation decreased in approximately 36% against an increase in more than 

200% for renewable energy sources when comparing the scenarios between the years of 2012 

and 2050 in a global reference. Figure 2 provides a view of how petroleum will still be in 

demand in the following years, even if losing space as a primary source of energy (WWF, 2011; 

EIA, 2015).  
 

Figure 1 - Energy matrix forecast between 2012 and 2050.  

Source: (EIA, 2015). 
 



25 
 

Figure 2 - Energy demand forecast per energy source till 2050. 

 
Source: (WWF, 2011). 
 

Since petroleum still have a significant impact on the energetic matrix, it is necessary to 

guarantee that their production meets expected demand. The actual scenarios and forecasts 

(Figure 3) show that the industry could face a deficit of petroleum-related hydrocarbon 

production of about 83 [MMbbd] by 2030 (PETROBRAS, 2009).  
 

Figure 3 - World petroleum-related production and demand forecast to 2030. 

 
Source: (PETROBRAS, 2009). 
 



26 
 

Hence, to asses this issue and to be able to meet the world demand, the oil and natural gas 

industry has to focus on implementing new technologies and incorporating new exploitable 

reserves. New technologies and techniques include increasing the enhanced oil recovery (EOR) 

of existing fields (known in the industry as the implementation of various techniques for 

increasing the amount of oil and natural gas that can be extracted from a reservoir), and reaching 

unconventional hydrocarbon reservoirs. It is in this scenario that the pre-salt reserves come to 

play a very important role. These fields are known to be located in remote regions considerable 

far from the coast, in ultra-deep water environments (known in the industry as water depths 

greater than 1,500 [m]), where geological and drilling challenges are common (thick salt layer 

and a very hard and abrasive carbonate rock reservoir). These are schematized in the Figure 4, 

where the evaporites layer drawn in white are basically a sedimentary rock saline deposit 

formed by crystallization and chemistry precipitation of salts dissolved in the sea aqueous 

medium (FRAGA et al., 2015; PINHEIRO et al., 2015). The hydrocarbon reserve discoveries 

off the Brazilian and Angolan coasts exhibit the potential to help fill this energy deficit based 

on the considerable supply potential these countries may have in terms of pre-salt reserves 

(PETROBRAS, 2009; GAFFNEY, 2014). 
 

Figure 4 - Pre-salt layer break-down and details of its remoteness. 

 
Source: (Adapted from: FRAGA et al., 2015; PINHEIRO et al., 2015). 



27 
 

2.1.1 South Atlantic Ocean coasts similarity 

The pre-salt layers are geological formations that were laid down before the evaporites layer 

(also nicknamed as salt layers in the industry) accumulated above them during the 

Pangaea supercontinent separation which started around 200 million years ago. More evidenced 

between the Jurassic and the Cretaceous period (between 150 and 65 millions of years ago), the 

evaporite layers were formed along the South Atlantic Ocean sides of the now a days known as 

South American and African continents, as shown in Figure 5 (NASCIMENTO, 2010; 

KONING, 2015). 
 

Figure 5 - Pre-salt formation details and similarity between Brazil and Angola. 

 
Source: (Adapted from: KONING, 2015). 
 

During the separation of the Gondwanaland (known as the south supercontinent existent 

between the Jurassic and Cretaceous periods formed after the separation of the Pangea), some 

gulfs were originated between the continent parts, which, combined with the restricted water 

fluxes and the climate in the equatorial line, guaranteed favorable conditions for the deposits. 

And, due to the same origin continental emigration, geological similarity can be to date 

evidenced in the Brazilian and African coasts, with highlights for Angola, as shown in Figure 

6 (NASCIMENTO, 2010; KONING, 2015; PINHEIRO et al., 2015). 

  



28 
 

Figure 6 - South America and Africa continents early period fitting and main basins. 

 
Source: (Adapted from: KONING, 2015). 

 
Thus, the known pre-salt reservoirs and main barriers encountered on the side of one continent 

are commonly found on the other continent and vice-versa. Generally, the pre-salt explorations 

have taken place in remote locations in terms of depth and coastal distance. In order to reach 

these locations in some regions, the activities have to be performed up to 300 [km] from the 

coast and at a water depth of about 2,000 [m] (classified as ultra-deep water environment, being 

the depth of 1,500 [m] the boundary). The evaporite layers have shown to be, in some locations, 

up to 2,000 [m] thick and the pre-salt reservoir to be located up to 7,000 [m] deep, as 

schematized in Figure 4 (FRAGA et. al., 2015; PINHEIRO et al., 2015). 



29 
 

2.1.2 General geology and drilling information 

Mostly of the oil and natural gas accumulations in these pre-salt reserves are trapped in a rock 

type classified as carbonate. Known as a class of sedimentary rock (formed when particles of  

materials are deposited from bodies of water in the earth’s surface), their primary compound 

are carbonate minerals; typically encountered and spread within the pre-salt layers are primary 

the limestones (CaCO3) and secondarily the dolomites, which is chemically represented as 

CaMg(CO3)2 (NASCIMENTO, 2010; NASCIMENTO, 2012). The pre-salt has been defined to 

be heterogeneous in some extensions due to the non-uniform porosity, permeability, and the 

presence of silica nodes in it (MUNIZ, 2013), resulting in a very hard and abrasive formation 

(PEIXOTO et al., 2010). 
 

The hardness can be understood, effectively, as the driver for slowing down the ROP, and the 

abrasiveness, together with the silicate presence (Figure 7), responsible for drill-bit teeth-cutters 

breakage, dullness, and wear progression, affecting the ROP considerably. A cumulative issue 

in it is that, at a certain point, not much improvement in terms of excavate hole can be noticed 

while drilling; activity drops to a low efficiency level, and, in some cases, leads to under-gaged 

holes (known in the industry as when the hole size diameter is less than the nominal diameter 

of the drill-bit). These under-gaged end-run edges need to be reamed before allowing the new 

drill-bit to go straight, to guarantee section gauge and smoothness. But, among several factors 

that affect drilling efficiency, the downside drilling events can be broken-down into different 

responsible agents, in which each one has its own degree of influence on the process. Also 

important to notice are the difficulties faced in spotting the base of the evaporites for optimum 

casing set linked to some early section drilling fluid (known in the industry as drilling mud) 

loss events when entering the pre-salt carbonates (PEIXOTO et al., 2010; MUNIZ, 2013; 

HBAIEB et al., 2013).  

  



30 
 

Figure 7 - Pre-salt carbonate samples with highlights of silica nodes in dashed red marks. 

a)  
 

b)  
 

Source: (FORMIGLI, 2008; PEIXOTO et al., 2010). 
 

All these information are important to help understanding the reasons behind the low 

performance frequently evidenced when drilling pre-salt. Recent researches have shown that 

the average drilling performance through these formations, historically, has stayed between 0.5 

and 6 [m/ h] (HBAIEB et al., 2013). 

2.2 DRILLING OPERATIONS 

This sub-chapter contextualizes information about drilling operations and how the drilling 

activities are conducted, linking those to pre-salt operations.  

2.2.1 Activities and equipments 

The drilling operations conducted in specific regions are accomplished by using different 

machineries with specific functionalities, combined into several systems working together in a 

so called drilling platform or drilling-rig (Figure 8). The whole system can be divided into four 

main parts: the hoisting, the rotary, the power and the circulating system. The power system 

(composed of generators, engines, and frequency converters) provides power to the drilling 



31 
 

system machineries; the power is transmitted from gas or diesel generators. The hoisting system 

(composed of drill-lines, draw-works, crown-block, travelling-block, derrick, and the top-drive 

set) is the key to raising and lowering the whole drill-string, casing, and other subsurface 

equipment, from and into the wellbore, respectively; this system is responsible for controlling 

the weight being transmitted to the drill-bit while drilling, also known as weight-on-bit (WOB). 

The rotary system (composed of top-drive set, drill-string, and other main compounds) is 

responsible to transmit a clock-wise rotation to the drill-string, and consequently, to the drill-

bit, providing the so-called rotary speed and necessary torque to advance the excavating 

process. The circulating system (composed of mud pumps, flow-lines, drill-string, drill-bit 

nozzles, mud tanks, mixing equipment, and contaminant removal equipment) has the function 

of filtrating and cleaning the drilling mud, via a recycling process, for its continuous reusing 

throughout the drilling operations. The circulating system transmits the drilling mud through 

the drill-string to the drill-bit. After passing through the drill-bit, the drilling mud transports the 

cuttings to the surface via the annulus (known as the space formed with the borehole wall 

outside of the drill pipe) and into the return line. The drilling mud is cleaned of cuttings and 

then recirculated to provide down-hole equipment cool down and hydraulic energy. Figure 8 

summarizes the main components, providing in a schematic view of how drilling-rigs are 

configured in general, highlighting also the main system’s components just detailed.  

 

When a well is being drilled, which happens in stages, it is regularly cased after each drilled 

section, avoiding possible contaminations and collapse of the just-opened hole (meaning avoid 

getting closed back up). This casing operation is carried out by lowering a steel pipe (casing) 

into the hole under its own weight, or pushed down by the hoisting system (mainly in deviated 

paths) with subsequent cementing outside the casing. The casing has an outer diameter (OD) 

smaller than the nominal drill-bit diameter (or hole diameter), which basically allows enough 

room for lowering the casing and pumping cementing slug around it. The cementing fills up the 

gap in the annulus between the casing OD and the formation, providing support for the axial 

and vertical loads while maintaining an integral isolation. 

 

 

 

 

 

 



32 
 

Figure 8 - Basic schematic with major components of a drilling-rig. 

 
Source: (Adapted from BONITRON, 2015). 

 

 

Schematically, a well is normally divided into sections, in which the sections’ diameter 

decreases as the well gets deeper. These sections are determined mainly based on an off-set 

well’s formation geology and pressure correlation, specific strategic needs, and unforeseen 

events arise during the operation. Each section can be accomplished by one or more drill-bit 

runs; main factors driving the number of drill-bit runs include drill-bit wear, bottom-hole-

assembly (BHA) tool failure and operation limitations such as overpressure zones, drill-string 

sticking, drilling mud losses, and strategic changes governed by the decision maker.  
 

In order to recover underground oil and natural gas, the process requires not just hardware, but 

also manpower as important drivers. The field personnel (or rig crew), are the main determinant 

to ensure that operations are carried out safely, correctly, and in a timely manner. The three 

main groups are the operators crew (block owner), the drilling contractor crew (rig owner and 

contracted by the operators), and the service companies crew (specialized services and 

contracted by the operators). The service companies offer services like logging-while-drilling 

(LWD), measuring-while-drilling (MWD), directional drilling (DD), cementing, fluid 



33 
 

engineering, drilling optimization, among others. The drilling contractor offers the drilling-rig 

services, sub-contractors and staff, and stays mainly on top of the main drilling-rig operations 

with the offshore installation manager (OIM), ship captain (when in a floating drilling-rig), 

engineer supervisors, drilling personnel, information technology (IT) personnel, logistic 

personnel, health-safety-environment (HSE) personnel and catering services. The operators 

also have important staff in the drilling-rig to ensure that all is carried out as planned, while 

supervising activities and operations being performed by drilling contractors and service 

companies; the main representatives are the company man, the geologist, the fluid engineer, 

and the drilling engineer. 
 

Details are crucial in all drilling activity such as: how will the drilling mud be designed, how 

will drill-string BHA be configured, which drill-bit will be used, how will the measuring tools 

be programmed to provide the desired lithology data, how will the directional drilling tools be 

adjusted in order to provide desired direction and target, among others. Communication plays 

a very important role since, for example, service companies have to deliver according to the 

wishes of the operators, but counting on the drilling contractors in mutual and friendly 

cooperation. The configuration, designs, and decision have, for the most part, already been 

defined in the drilling program from the main office or headquarters; however, the operations 

are always susceptible to adjustments in which responses are expected to be made and 

implemented as quickly as possible and directly from the field. 
 

The measuring tools allows a close eye on the drill-bit, making possible to known exactly where 

it is, as well as measure and retrieve information from the down-hole regarding the environment 

and formation such as: pressure, temperature, formation porosity, formation permeability, 

drilling mechanics data, among others. This information from the drilling mechanics data is 

used (consider also surface sensing information) by the field personnel to analyze how the 

operation is progressing, and evaluate trends; the information are used to determine and adjust 

drilling mechanics parameters such as flow-rate, rotary speed, WOB and torque, always looking 

for ways to enhance drilling efficiency by optimizing the rate of penetration (ROP) and 

improving the operational efficiency.   
 

Still, the details of the configuration and the selection of components to be used in the BHA are 

extremely important to guarantee optimized operation. For instance, the right placement of the 

stabilizers and the drill-collars ensure the drill-string will work with less probability of stick-



34 
 

slip, vibration and buckling. No less important, the drill-bit is the ultimate responsible for 

making the hole and effectively drill formation.  
 

Different types of drill-bits are offered on the market. The main groups are the drag bits (mostly 

in use for pre-salt operations) and the roller-cutter bits (HBAIEB et al., 2013). Drag bits consist 

of fixed cutters blades that are integrated with the body of the drill-bit, rotating as a unit with 

the drill-string; roller-cutter bits consist of two or more cones (normally three) which have the 

cutting elements attached to it and rotate about the axis of the cones as the drill-bit rotates at 

the bottom of the hole. Figure 9 and Figure 10 show these two types of drill-bits, respectively. 
 

Figure 9 - Diamond impregnated (a) and polycrystalline diamond compact (PDC) drill-bit (b). 

a)                b)    

Source: (BAKER, 2013). 
 

Figure 10 - Milled tooth (a) and tungsten-carbide-insert (TCI) drill-bit (b). 

a)                b)       

Source: (BAKER, 2013). 

 

As a new tendency, hybrid bits are being manufactured, showing some improvements in pre-

salt drilling (Figure 11). These information are important since statistical analysis will take 

place in later chapters in a sense of showing which drill-bit allows better performance when 

drilling pre-salt formation. 
 

 



35 
 
 

 

 

Figure 11 - General example of a hybrid drill-bit with PDC and TCI features together. 

 
Source: (BAKER, 2013). 

2.2.2 Drilling activity and costs 

Going beyond the technical description of the activities, there is an important parameter that 

has to be taken into account when planning and executing a well; the costs involved in each 

stage, since the drilling operations of a specific well do not guarantee the existence of petroleum 

accumulations. If the drilling activity concerns a producing well or an exploratory well in an 

area with the exploratory activity already advanced, the chances of a dry-hole (known in the 

industry when no accumulation is found) are considerably diminished. From exploratory wells, 

studies are performed in order to guarantee a delimitation in which the reserves can be defined 

as proven. Moreover, a dry-hole may not signify an unsuccessful operation since the geological 

and drilling information acquired, together with the knowledge gained, are used in subsequent 

operations as a basis for improving subsequent activities (THOMAS et al., 2002; COOPER et 

al., 2009). 
 

In general, is common and has been fairly considered in the petroleum industry that the 

probability of encountering oil and natural gas accumulations from a wild-cat (the first drilled 

exploratory well from a field) is, in general, 30%. For the development of an entire field, 10 to 

20% of the costs can be related to the exploration phase while 50% concerns the development 

phase. The remaining is related to the production phase and logistics portion necessary to the 

operations, representing approximately 30 to 40% of the costs. And, from this exploratory 

phase, 40 to 80% of the costs are specifically related to the drilling itself, representing 4 to 16% 

of a field’s total cost (THOMAS et al., 2002; LEFFLER et al., 2003; THONHAUSER, 2009). 
 



36 
 

From a historical break-down of drilling activities, it is considered reasonable to say that just 

25 to 35% of the operational time is related to effective drilling activity, while the other portion 

is related to drill-rig movement (approximately 35%), tripping operation, supportive activities 

and non-productive time (NPT), from which 40% are related to wellbore instability and pressure 

balance issues, while up to 10% is related to equipment failure (LEFFLER et al., 2003; 

THONHAUSER, 2009). 
 

In this context, the pre-salt wells do not show to be different. Since the activities are developed 

in unconventional regions and since the industry considers itself to be still within the learning 

phase of analog operations, the relative cost of these wells have been considerably high. Table 

1 summarizes historical information from the literature in terms of drill-bit performance 

(considerably low) and costs (considerably high) experienced when drilling pre-salt carbonates 

in the past years (HBAIEB et al., 2013). This low range necessitates performance improvement 

and seeks potential value from new surveillance methods and application tools (DUPRIEST et 

al., 2005). 
 

Table 1 - Historical drill-bit performance and cost for pre-salt sections from the literature. 
Drill-bit type Footage  [m/ run] Average ROP [m/ h] Cost [USD/ m] 

TCI 100 - 250 1 - 3 > 30,000 
Diamond 

impregnated 400 - 500 1 - 3 15,000 - 20,000 

PDC 20 - 250 0.5 - 6 long run < 10,000 
short run > 50,000 

 

Source: (HBAIEB et al., 2013). 
 

Drilling costs tend to increase considerably with depth; it is a good practice study past data and 

information from previous wells to address time and costs of future drilling operations in similar 

regions. When good and reliable data are available for a specific region or location, it is possible 

to predict the relationship between costs and depth, which are reduced as more successful wells 

are drilled in nearby regions. This improvement is related to the learning process, 

mathematically described by learning curves, and, with a minimal amount of gathered data, a 

curve can be drawn for, e.g., drilling engineers to predict well costs for subsequent wells. A 

method used in the industry to estimate the cost involved per length drilled (Table 1) considers 

a calculation accounting for the drill-bit cost per specific run (퐶표푠푡 ), the average drill-rig 

cost per day (퐶표푠푡 ), the initial and final depth in order to account to the length drilled for the 

proper cost calculation (푀퐷  and 푀퐷 ), and the operational time in order to allow 

estimating the time length and so, the final costs over the time-frame of activity (푇푖푚푒 ,  



37 
 

푇푖푚푒 , 푇푖푚푒 ) as per equation (1). Thus, any activity that relates to a more 

effective drilling operation with less NPT and delivers each well safely and economically is 

important in all of these contexts, including then also pre-salt wells, the focus of the thesis 

(RABIA et al., 1985; MITCHELL, 2011). 
 

퐶표푠푡 =
퐶표푠푡 + 퐶표푠푡  . (푇푖푚푒 + 푇푖푚푒 + 푇푖푚푒 )

푀퐷 −푀퐷  (1) 

2.3 ROP MODELING CONCEPT 

Rate of penetration (ROP) modeling has been in use in the industry for decades as a tool to 

quantitatively reduce drilling costs by drill-bit selection and by determining the optimal 

combination of mechanical and hydraulic operating parameters to be used while drilling to 

guarantee optimum activity. This sub-chapter summarizes the main research developments in 

terms of ROP modeling from 1960 to date, highlighting the main classical literature which are 

still used as reference in the industry. 

2.3.1 ROP Model evolution 

Cunningham (1960) addressed a way to represent rate of penetration (ROP) as a function of 

two specific drilling parameters, running several tests under atmospheric and overbalanced 

conditions with roller-cutter drill-bits in shale and granite formation types. The drilling 

conditions applied on the tests were 15 to 50 [psi] hydrostatic pressure, 50 to 400 [rpm] rotary 

speed, 20 to 700 [lbf] weight-on-bit (WOB), weighted brine and tap water as drilling fluid, with 

1.25 and 7.875 [in] OD drill-bits. The final ROP equation relation (푅푂푃 ) was empirically 

derived from the graphs behaviors, presented in Figure 12, by means of its relation to the WOB 

over the outer drill-bit diameter   used (directly proportional to it) and to the rotary 

speed (푅푃푀 ) applied (squarely and directly proportional to it). The constant 푎  was defined, 

for this specific case and experiments, to be around 0.45 and always less than or equal to 1 

(MAURER, 1962). The constant 퐾, regardless of not having been defined, was stated to be a 

general constant dependent on drill-bit dullness not varying much, since the formations used in 

the test are considered to be non-abrasive. Equation (2) details the mathematical relationship of 

these detailed findings (CUNNINGHAM, 1960). 
 



38 
 

푅푂푃 = 퐾.
푊푂퐵
푂퐷 . (푅푃푀 )  (2) 

 

Figure 12 - ROP versus rotary speed in atmospheric (a) and overbalance (b) conditions. 

 

 
Source: (CUNNINGHAM, 1960). 
 

A few years after, Maurer (1962) derived two equations for ROP as a function of rotary speed, 

WOB, drill-bit OD and rock drillability strength, accounting also for down-hole cleaning 

conditions. Was concluded that the rock drillability strength (푆) of the rock, has a relation, not 

simply to the ultimate compressive strengths (UCS) of the rock, but with the ultimate shear 

strength (USS) as well, being quadratically and inversely proportional to the ROP 푅푂푃 ∝  . 



39 
 

Also addressed was the fact that the torque may not vary with respect to rotary speed, but just 

quadratically with respect to the WOB (푇표푟푞푢푒 ∝ 푊푂퐵 ) (Figure 13). The tests were 

performed in sandstone, shale, and concrete formation types with a 4.75 [in] roller-cutter drill-

bit with the following parameters: 50 to 200 [rpm] rotary speed, 0 to 30 [klbf] WOB 

(MAURER, 1962). The mathematical equations developed are representative for perfect 

drilling conditions (equation (3)) and for imperfect cleaning conditions (equation (4)). They 

were developed based on the experiment graph outputs presented by Figure 14 and previous 

researches (Figure 12), defining for this specific experiments 푎  to be positive and 푎  to be less 

than or equal to 0.5. In Figure 14, the experiment drawn with filled small black spheres 

represents good borehole cleaning due to higher flow-rate and the one with triangle, borehole 

with a bad borehole cleaning due to less flow-rate, what directly affects the maximum 

achievable ROP for given WOBs. The parameter 푊푂퐵  represents the minimum thrust load 

necessary to start a rock breakage for initiating the rock fracture. 
 

푅푂푃 = 퐾.
푅푃푀 . 푊푂퐵 −푊푂퐵

푂퐷 .푆
 (3) 

푅푂푃 = 퐾.
푅푃푀 . 푊푂퐵 −푊푂퐵

푂퐷
 (4) 

 

Figure 13 - Torque relation versus WOB. 

 
Source: (MAURER, 1962).  

   



40 
 

Figure 14 - ROP versus WOB (a) and drill-bit OD (b).  

a)  
 

b)  
 

Source: (MAURER, 1962; WARREN, 1987). 
 

But was with some more development and more detailed researches over approximately ten 

years that a more complete and complex model was put together. Bourgoyne Jr. and Young Jr. 



41 
 

(1974) combined as much parameters as possible that may had influence in the ROP, modeling 

it into one equation with eight sub-functions addressing many different behaviors, in which the 

determination of the best fit, with the weighting coefficients (from 푎  to 푎 ), would be the key 

in fitting the mathematical model into specific field data. Table 2 summarizes coefficient 

ranges, related drilling conditions, and equations (equations (5), (6), (7), (8), (9), (10), (11) and 

(12)), in which 푇푉퐷 represents the true vertical depth, 퐸푃푃 the equivalent in-situ pore pressure, 

퐸퐶퐷 the in-situ equivalent circulating density, 퐸푀푊 the equivalent mud weight in use, 푄 the 

flow-rate of the drilling fluid,  푢  the apparent drilling fluid viscosity, 푂퐷  the drill-bit 

nozzle diameter, 푂퐷  the outer drill-bit diameter, 푊푂퐵  the surface applied WOB, 푅푃푀  

the surface applied rotary speed, 푅푂푃  the calculated ROP using the model and the 푅푂푃  

the actual field read ROP while performing the operation. Important to note is that the equation 

takes into account variables in which when equalized to field data would not affect the original 

ROP since the sub-functions would be powered by zero and so, the modeled ROP would be 

multiplied by one. Equation (13), 푅 represents the residual error, which should be as low 

as possible, representing the best fit between the modeled calculated ROP (푅푂푃 ) and the 

field ROP (푅푂푃 ). Equation (14), 푅 , represents the index correlation (0 ≤

R ≤ 1) of a regression, having the best fit as it approaches to one (fitting of 100%). The 

drilling parameters were varied as follows: from 58 to 129 [rpm] rotary speed; 0.81 to 3.76 

[klbf/ in] WOB over drill-bit OD; from 9.5 to 17.7 [ppg] equivalent circulating density (ECD); 

with milled tooth and Tungsten-carbide-insert (TCI) drill-bits varying in OD from 6.125 [in] to 

17.5 [in], and all with different types of mud tested in different porous and permeable sandstone 

formations. The WOB over drill-bit OD threshold necessary to be overcome in order to 

effectively commence drilling a rock was established to be between 0.6 and 2 [klbf/ in], 

representing boundary values suitable for soft up to very hard formation (BOURGOYNE Jr. 

and YOUNG Jr., 1974). 

 

 
 



42 
 

Table 2 - Bourgoyne Jr. and Young Jr. (1974) coefficients and model details. 

Sub-functions Figure Coefficient Coefficient range Affecting 
representation 

n/a n/a 푎  2.71 - 3.78 
Formation strength and 

drilling fluid design 

Equation (6) Figure 15-a 
Figure 15-b 푎  0.00015 - 0.00028 Formation compaction 

Equation (7) Figure 15-b 
Figure 15-c 푎  0.00018 - 0.0009 Formation compaction and 

pore pressure 
Equation (8)  Figure 16-a 푎  0.00004 - 0.000085 Differential pressure 

Equation (9) 
Figure 14-a 
and Figure 

14-c 
푎  0.43 - 2 WOB and drill-bit OD 

Equation (10) Figure 14-b 푎  
0.21 - 0.9 

 (0.21 for hard formations) 
 (0.9 for very soft formations) 

rotary speed 

Equation (11) Figure 17 푎  
0.2 - 1.11 

(0 for TCI drill-bits) 

Fractional teeth-cutters 
wear (more drill-bit and not 
much formation dependent) 

Equation (12) Figure 16-b 푎  0.16 - 0.61 Hydraulics and Reynolds 
number influence 

 

Source: (BOURGOYNE Jr. and YOUNG Jr., 1974). 
 

푅푂푃 = 푒
 .

 (5) 

푥 = 10,000 − 푇푉퐷 (6) 

푥 = 푇푉퐷 . . (퐸푃푃 − 9) (7) 

푥 = 푇푉퐷. (퐸푃푃 − 퐸퐶퐷) (8) 

푥 = ln

⎣
⎢
⎢
⎡
푊푂퐵
푂퐷 −

푊푂퐵
푂퐷

4 −
푊푂퐵
푂퐷 ⎦

⎥
⎥
⎤
 (9) 

푥 = ln
푅푃푀

100  (10) 

푥 = −ℎ (11) 

푥 =
퐸푀푊.푄

350.푢 .푂퐷  (12) 

푅 =  
∑ |푅푂푃 − 푅푂푃 | 

푅푂푃
 

(13) 

 

푅 = 1 −  
푅푂푃 − 푅푂푃

푅푂푃 − 푅푂푃
 (14) 



43 
 

The following Figure 15, Figure 16 and Figure 17, represents outputs from experiments run 

which were also used to derive, empirically, the ROP model defined by Bourgoyne Jr. and 

Young Jr. (1974). Figure 15 shows that the deeper is drilled, the more compacted a specific 

geological layer is and the less pore pressure is present at a specific depth, the more negatively 

would the ROP be influenced. Figure 16, which relates mainly the hydraulics, shows that the 

less differential pressure is present in the bottom of the hole and the higher the Reynolds 

Number or the drill-bit jet impact force is, the higher would be the ROP achieved. Figure 17 

shows the influence of drill-bit dullness in terms of drillability, where the more worn a drill-bit 

teeth-cutters are the less would be the maximum achievable ROP.   
  
Figure 15 - ROP versus depth (a), compaction (b) and pore pressure (c). 

a)   



44 
 

b)  
 

c)  

Source: (MURRAY et al., 1955; COMBS, 1968). 



45 
 

Figure 16- ROP versus differential pressure (a) and Reynolds Number (b). 

a)  
   

b)  

Source: (CUNNINGHAM et al., 1959; ECKEL, 1968). 



46 
 

Figure 17 - ROP versus drill-bit teeth-cutters wear. 

 
Source: (GALLE and WOODS, 1963; EDWARDS, 1964; BOURGOYNE Jr. and YOUNG 

Jr., 1974). 
 

As a next step in the evolution of the ROP modeling development, the researchers started 

focusing themselves on fluid mechanics and the drilling fluid influence in ROP. In this sense, 

Warren et al. (1984) and Warren (1987) presented a modified mathematical model accounting 

for different drilling mechanics specifically for soft formations and roller-cutter drill-bits, 

accounting for the main drilling parameters, as well for the hydraulic jet impact force, 

conducting tests with 7.875 [in] and 12.25 [in] drill-bit sizes, with the following parameters: 48 

to 194 [rpm] rotary speed, 4 to 40 [klbf] WOB, 287 to 460 [gpm] flow-rate, with drilling mud 

weight ranging from 9 to 13 [ppg], with shale, sandstone, and limestone as formation types. 

The studies were conducted verifying the effect of the hydraulic jet impact force and the real 

contribution it may have on rock cutting process. It was determined, through a lot of 

experiments, some interesting characteristics about the fluid velocity ejecting from the drill-bit 

nozzles. Separated in three different regions, the fluid flow from the nozzle in zone I (the free 



47 
 

jet zone) is characterized by a cone of moving fluid that expands along the x-axis (the cone 

angle can vary from 20 to 25 [o]), losing energy as the particles disperse (Figure 18). Zone 2 

(the impingement zone) is where maximum pressure is applied against the formation, as defined 

next. Zone 3 is the radial portion of the fluids and the main driving is the cross flow. It was 

concluded that energy acting in the bottom of the hole would be higher with a greater number 

of smaller jets and also the higher the jet impact force (Figure 19), which may positively impact 

the penetration rate if correctly applied; basically, the greater the nozzle diameter, the lower the 

energy that would reach the stagnation point (MCLEAN, 1964; WARREN et. al., 1984). In 

addition, it was formulated an empirical estimation of the effect of jet dispersion in bottom-hole 

cleaning, so that the final jet impact pressure and force were reduced by a factor driven by the 

ratio of the nozzle jet velocity and the total back-flow velocity (the return flow upwards and 

responsible for carrying the cuttings out of the hole). Since the back-flow is dependent on the 

cross section area of the junk slot of the drill-bit (approximately 15% for roller-cutter drill-bits), 

the equations (15), (16), and (17) show the development in calculating this influencing factor 

(WARREN, 1987). 
 

Figure 18 - Schematic of flow and the three definition zones. 

 
Source: (WARREN et al., 1984).  

 



48 
 
 
 Figure 19 - Influence of total jet impact force in the ROP. 

 
Source: (WARREN et al., 1984).  
 

  퐹 = 0.00126.휌.푂퐷 .푉  = 0.000516.휌.푄 .푉 (15) 

퐴 =
푉

푉 =

푄
푛 .퐴

푄
푘.퐴  

=
푘

100 .푂퐷
푛 .푂퐷

   (16) 

퐹 = (1 − 퐴 ).퐹  (17) 

 

From additional investigation on the hydraulic jet impact force on the bottom of the hole, 

Warren (1987) produced a modified ROP model that differed from his initial findings 

(WARREN et al., 1984), enhancing relationships based on the hydraulics studies performed on 

the influence of overbalance on the ROP and the flow-rate on the ROP, as per equation (18). In 

the following equation, the factor 퐾  has been found to range between 0.0378 and 0.0379, 퐾  

between 0 and 1 and 퐾  between 2.7 and 2.86. In this context Figure 14-a and Figure 20 details 

different behavior of the ROP in terms of WOB for different flow and bottom-hole pressure, 



49 
 

where can be seen that the higher the flow-rate and the lower the bottom-hole pressure, the 

more one let the ROP to be sensitive to changes in WOB. 

 

Figure 20 - ROP versus WOB for different overbalance pressures. 

 
Source: (WARREN, 1987). 
          
Interesting to notice is that the less overbalance is implicit the better the ROP performs and the 

higher the flow-rate is used for pumping the drilling fluid the better the ROP performs, as a 

response of bottom-hole cleaning and also of an increased jet impact force, which, as seen 

previously, influences the ROP positively.   

 

푅푂푃 = 퐾 .
푆 .푂퐷

푅푃푀 .푊푂퐵
+ 퐾 .

1
푅푃푀 .푂퐷 + 퐾 .

푂퐷 .훾 .휇
퐹  (18) 



50 
 

2.3.2 BYM ROP Model applicability 

From the presented formulations for ROP modeling, over the years, considering that much 

drilling operations started to happen in regions and environments where a lot of the drilling 

mechanics parameters would have a certain degree of directly influence on the ROP, some 

researches started pointing to simulations using mainly the Bourgoyne Jr. and Young Jr. (1974 

and 1986) ROP modeling (BYM) formulation (equation (5)), but still, without proposing any 

modification to the main equation or improvements, but just directly field application of the 

methodology for well engineering purposes. Following this idea, from the literature, Table 3 

(BOURGOYNE Jr. and YOUNG Jr., 1986), Table 4 (EREN, 2010) and Table 5 IRAWAN et 

al., 2012), present the BYM applied to specific fields, detailing the normalization factors chosen 

by the researchers and the best coefficients encountered for driving the ROP model in these 

specific regions, followed by the estimated error. As known by the skilled in the art, it is not 

feasible to guarantee a perfect match between the calculated and the field data ROP, so that the 

best solution would be the one allowing the minimum fitting error (or relative error) between 

both data when compared to each other. Interesting wise, from the year 1986 up to 2012, as per 

detailed tables in reference, the BYM has been applied in the industry with minimum changes 

in it, as can be noticed by the boundary values for the coefficients and the normalization factors. 

In this sense, by grouping all the information from Table 3, Table 4 and Table 5, it was possible 

to set a different and wider window for the boundary of the coefficients and also to change the 

normalization factors accordingly, enhancing the modeling together with a reference of 

acceptable relative error for modeling set as approximately maximum 38% (BOURGOYNE Jr. 

and YOUNG Jr., 1986; EREN, 2010; IRAWAN et al., 2012). The abbreviation used in the 

tables in the tables, in this particular case, stands for not applicable. 
 

All these information detailed in the tables will be used in the final chapter, which details the 

optimization methodology, for helping developing the final mathematical model proposed 

throughout this thesis. 

 



51 
 
 
Table 3 - BYM ROP model details from Bourgoyne Jr. and Young Jr. (1986). 

Parameter Normalization factors 
Coefficients 

Lower boundary Upper boundary 
푅푃푀  100 [rpm] n/a n/a 

푇푉퐷  10,000 [ft] n/a n/a 

퐸푃푃  9 [ppg] n/a n/a 
푊푂퐵
푂퐷  4 [klbf/ in] 

 

 

 

n/a 
 

 

 

n/a 
퐹  1,000 [lbf] n/a n/a 

푎  n/a 0.5 1.9 

푎  n/a 0.000001 0.0005 

푎  n/a 0.000001 0.0009 

푎  n/a 0.000001 0.0001 

푎  n/a 0.5 2 

푎  n/a 0.4 1 

푎  n/a 0.3 1.5 

푎  n/a 0.3 0.6 

Relative error n/a n/a 
 

Source: (BOURGOYNE Jr. and YOUNG Jr., 1986). 
 

Table 4 - BYM ROP model details from Eren (2010). 

Parameter Normalization factor 
Coefficients 

Lower boundary Upper boundary 
푅푃푀  60 [rpm] n/a n/a 

푇푉퐷  8,000 [ft] n/a n/a 

퐸푃푃  9 [ppg] n/a n/a 
푊푂퐵
푂퐷  4 [klbf/ in] 

 

 

 

n/a 
 

 

 

n/a 
퐹  1,000 [lbf] n/a n/a 

푎  n/a 1.0006 3.2914 

푎  n/a 0.0002 0.0048 

푎  n/a 0.0004 0.6589 

푎  n/a 0.0001 0.0003 

푎  n/a 0.1029 0.8529 

푎  n/a 0.48 1.6843 

푎  n/a 0.2843 2.5873 

푎  n/a -0.6324 1.0805 
Relative error n/a 0.379 0.5395 

 

Source: (EREN, 2010). 
 



52 
 

Table 5 - BYM ROP model details from Irawan et al. (2012). 

Parameter Normalization factors Coefficients 
Lower boundary Upper boundary 

푅푃푀  100 [rpm] n/a n/a 

푇푉퐷  10,000 [ft] n/a n/a 

퐸푃푃  9 [ppg] n/a n/a 
푊푂퐵
푂퐷

 4 [klbf/ in] 
 

 

 

n/a 
 

 

 

n/a 

퐹  1,000 [lbf] n/a n/a 
푎  n/a 3.91 
푎  n/a 0.0001 

푎  n/a 0.0001 

푎  n/a 0.0009 

푎  n/a 0.37 

푎  n/a 2.23 

푎  n/a 0.025 

푎  n/a 0.67 

Relative error n/a 0.55 
 

Source: (IRAWAN et al., 2012). 

2.4 SPECIFIC ENERGY CONCEPT 

Specific energy, in simple words, is represented by energy per unit mass or unit volume. Also 

known as energy density, it is mainly applied to quantify the amount of stored heat, and in the 

thesis specific case, to quantify the energy necessary to drill a specific unit of rock volume. It 

has been stated that the energy per unit volume is a quantity on the order of magnitude of twice 

the compressive strength of the rock, and that the high energy necessary to advance in drilling 

a specific rock. This sub-chapter summarizes the main research development in terms of SE 

from 1965 to date, which interestingly is still present and started to be more evident in the 

industry for drilling surveillance purposes in the year 2005 (DUPRIEST, 2005). 

2.4.1 Specific energy knowledge evolution 

Teale et al. (1965) analyzed the work done by a drill bit in order to advance into the rock or 

formation when excavating an infinitesimal volume of rock, and consequently, the necessary 

energy in terms of volume removed instead of mass removed, naming it the specific energy 

(SE) necessary in a rock drilling process. It was then established an equation to address the total 



53 
 

work done by the forces acting on the drill-bit, considering its translational axial and rotational 

movement within a specific time range, stating also that the maximum mechanical efficiency 

would occur with a minimum imposed SE. The total work performed by the axial and radial 

force, in order to allow excavating a specific volume of rock, is represented by equations (19)-

(21) (Figure 21) (TEALE et al., 1965). 
 

Figure 21 - Brief schematic of a translational axial and rotational movement of a drill-bit while 
drilling. 

 
 

Source: (Adapted from: TEALE et al., 1965; PESSIER et al., 1992).  
 

휏 = 휏 + 휏  (19) 

휏 = 퐹 .푑푠 = 퐹 .푑푣.푑푡 (20) 

휏 = ∫ 퐹 . .푑휃. = 퐹 . . (푁. 2.휋 − 0) =  푇 .푁. 2.휋  

푁 푖푠 푡ℎ푒 푛  표푓 푟푒푣표푙푢푡푖표푛. 
(21) 

 

Considering a rotary speed of N revolutions per one minute, a rate of penetration (ROP) or 

displacement speed (푑푣) of one inch per one minute, and a volume (푑푉 ) of excavated rock in 

one minute equivalent to the drill-bit surface area 퐴  times the displacement developed with 

the given ROP (equation (22)) and that the SE would be the work performed by an acting force 

divided by the volume of rock, rather than by the rock mass itself, the total SE developed to 

퐹 =
푊푂퐵

휋.푂퐷푏푖푡
2

4

 
푑퐹 = 휇. 푑퐹  



54 
 

excavate the rock in one minute can be expressed, after adjusting equations (23) and (24), as 

per equation (25). 
 

  푑푉 = 퐴 . 푑푠 = 퐴 .푑푣. 푑푡   (22) 

푆퐸 =
휏  

푑푉 =
퐹  .푑푠 
퐴 .푑푠 +

2.휋.푇
퐴 .푑푠  (23) 

푆퐸 =
퐹  

퐴 +
2.휋.푇  .푁
퐴 .푑푣.푑푡  =  

퐹  

퐴 +
2.휋.푇  

퐴 .푑푣  .
푁
푑푡   

(24) 

푆퐸 =
푊푂퐵  
퐴 +

2.휋.푇 .푅푃푀

퐴 .푅푂푃  (25) 

 

Furthermore, it has been highlighted but not entire proven in terms of different drill-bit types, 

formation types, and drilling mechanics parameters, that the minimum achievable SE would 

then be close to the crushing strength of the rock being drilled, said to be equivalent to the 

compressive strength, given the failure mechanism (Figure 22). The tests were performed under 

atmospheric pressure conditions for concrete, shale, and sandstone, making use of 12.25 [in] 

and 1.6875 [in] (slim-hole) roller-cutter bits together with percussion-rotary events. It was 

observed that the torque could be expressed as a linear relationship to penetration per revolution 

(푃 ) and also that the work performed by the translational axial force portion could be 

negligible, if compared to the rotary one, and so, disregarded. Thus, the slope of a torque versus 

penetration per revolution can also directly represent the SE magnitude (Figure 23), exemplified 

by equations (26) and (27). 
  

푆퐸 =
2.휋.푇 .푅푃푀

퐴 .푅푂푃 =  
2.휋.푇  

퐴 .푑푣  .
푁
푑푡  =  

2.휋. 푇 .푁 

퐴 . 푑푠푑푡 . 푑푡
=  

2.휋
퐴 .

푇 .푁
푑푠  

(26) 

 

푆퐸 =
2.휋
퐴 .

푇  

푑푠
푁 

=  
2.휋
퐴 .

푇  

푃  (27) 

 

  



55 
 

Figure 22 - Graphics showing the convergence of specific energy to rock crushing strength. 

 
Source: (TEALE et al., 1965). 
 

Figure 23 - Relationship between torque and penetration per revolution. 

 
Source: (TEALE et al., 1965). 



56 
 

It was recognized that the SE could not be represented accurately by a single number since it 

was dependent on many dynamic and fluctuation variables presented in the drilling process, so 

that approximate and mean values were essentially sufficient to be considered for modeling and 

prediction of drilling performance. It was also emphasized that all the experiments drive and 

converge to an understandable and feasible correlation in terms of SE and the crushing strength 

of the rock, not entirely proving that it may represent just the ultimate compressive strength 

(UCS). The ratios between SE and crushing strength throughout the various experiments and 

analysis stayed between 0.8 and 1.6. 
 

After extensive researches over twenty years, Rabia et al. (1985) simplified the equation for SE 

calculation as per equation (28), stating that the ROP is more sensitive than SE for WOB and 

rotary speed changes. It was concluded that an increase in the SE (dependent on the drill-bit 

type and design rather than just rock properties) results in an increase in the cost per foot, and 

that cumulative cost per foot is directly related to drill-bit performance. The tests were 

conducted three different 12.25 [in] roller-cutter TCI bits in the Middle East; being the 

formation type not detailed throughout the paper (RABIA et al., 1985). 
 

푆퐸 =
20. (푊푂퐵 .푅푃푀 )
푂퐷 .푅푂푃  (28) 

 

Some year after, following the achievement of Rabia et al. (1985), Pessier et al. (1992) 

addressed some interesting studies and summarized, mathematically and theoretically, the 

importance and possibility of converting the torque shown in the SE equation in terms of WOB 

and drill-bit sliding friction factors (considering the drill-bit as a flat cylinder and touching the 

borehole just in the bottom of the hole as per Figure 21). Thus, the SE formulation defined in 

equation (25), developed by Teale et al. (1965), was also validated for hydrostatic pressure 

environments and started to be called mechanical specific energy (MSE) instead of just SE. The 

tests were conducted in grout (construction material - mixture of water cement sand and some 

gravel) and shale cores using water based muds with TCI and PDC drill-bits of the following 

sizes: 7.875 [in], 8.5 [in] and 12.25 [in]. For TCI drill-bits, the friction factors ranged between 

10 and 20%; for PDC, 30 to 50%. This led to the interpretation that PDC bits need less WOB 

to provide the same performance of a TCI. Another important interpretation was that hydraulics 

appear to have a high impact on penetration rate. The deeper the drilling activity, the less 

effective would be the hydraulic energy reaching the bottom of the hole due to pressure losses 

across the drill-string and the BHA. In addition, there is heating as a source of energy loss that 

should not be taken out of consideration on those calculations. The first changes done in the SE 



57 
 

equation accounted for using torque and ROP in field units (units being [ft- lbf] and [ft/ h], 

respectively), as per equation (29). The second changes applied can be seen in equations (30)-

(32), which were based on the schematic shown in Figure 21 and the drawn formulations in it, 

for expressing the torque as a function of WOB and drill-bit sliding friction factor. In order to 

convert the applied torque in terms of WOB, one has to consider the Normal Force (퐹 ) as one 

specific point on the bit, and the total WOB as being uniformly distributed over the whole cross-

section area of the drill-bit (PESSIER et al., 1992). 
 

푆퐸 =
푊푂퐵  
퐴 +

2.휋. 푇 .푅푃푀 . 1
12

퐴 .
푅푂푃

1
60

 . 1
12

=  

 

푊푂퐵  
퐴 +

120.휋. 푇 .푅푃푀
퐴 .푅푂푃    

 

(29) 

푇 = 훿  
4.휇.푊푂퐵
휋.푂퐷

푑훿. 푑휃 =  
8.휇.푊푂퐵

푂퐷
.훿 . 푑훿 =  

 

8.휇.푊푂퐵
푂퐷

 .
훿
3 =  

휇.푊푂퐵 .푂퐷
3   

(30) 

푆퐸 =
푊푂퐵  
퐴 +

120.휋.푅푃푀 .
휇.푊푂퐵 .푂퐷

36
퐴 .푅푂푃  =  

 

푊푂퐵 .
1
퐴 +

120.휋.휇.푅푃푀 .푂퐷

휋.푂퐷4 .푅푂푃  .36
= 푊푂퐵 .

1
퐴 +

13.33.휇.푅푃푀
푂퐷 .푅푂푃  

 

(31) 

 

푅푂푃 =
13.33.휇.푅푃푀 

푂퐷 .
푆퐸

푊푂퐵 − 1
퐴

[ft/ h] (32) 

 

Under hydrostatic conditions, it was observed that the drill-bit sliding friction factors had some 

variance, but not something remarkable, while the SE increased drastically. Explanations for 

that were drill-bit balling (interference of energy transmission due to accumulated material 

within the drill-bit teeth-cutters’ structures) and bottom-hole balling (known as chip hold-down 

effect, cuttings accumulate in the bottom-hole by differential pressure interfering in the energy 

transmitted to rock breakage). Figure 24 exemplifies the relationship between SE and ROP, 



58 
 

where can be seen that by increasing the ROP, the SE is decreased in both scenarios, for 

atmospheric and overbalanced conditions. These are very important outcomes since for 

operations where the torque data are not reliable, the WOB measurements would be enough to 

guarantee surveillance analysis and further, the SE final formulation could be simplified by one 

variable, allowing faster simulations and real-time operational responses. 
 

Figure 24 - SE and drill-bit sliding friction factor under atmospheric (a) and overbalanced (b) 

conditions. 

a)  
 

b)  

Source: (PESSIER et al., 1992). 
 

But was from the year 2005 with Dupriest et al. (2005 and 2010), that the surveillance of SE 

started to be effectively used for improving of drilling performance. It was asserted that drill-

bit efficiency lays between 30 to 40% as also per Teale et al. (1965), which stated that calculated 



59 
 

SE’s were roughly three times the rock crushing strength. It was found that this relates to the 

drill-bit depth-of-cut (DOC) in a proportional manner, and that the low drilling-related 

efficiency is a consequence of basically three main factors: drill-bit balling, bottom-hole baling 

and vibration (evidenced when drilling hard formations with high compressive strength and 

using inadequate WOB and rotary speed). Further, it was determined that an adequate 

hydraulics design with decreasing nozzle sizes and a resultant increase in horsepower per square 

inches [hsi] would have a positive impact on drill-bit balling, helping positively in terms of 

drillability. The usage of PDC drill-bits does decrease the problematic of bottom-hole balling 

which is more evidenced in TCI drill-bits type due to its different drill-bit crushing action. In 

terms of vibration, not much was concluded rather than emphasizing that this parameters alone 

is not enough to guarantee a correlation with ROP. Figure 25 represents a drill-rate curve (result 

of a test done just before drilling a specific formation for choosing best set of rotary speed and 

WOB) modified by Dupriest et al. (2005), which relates to the problematic just disserted. 

Region I represents a region dependent on the DOC, region II represents the normal tendency 

of relation between the WOB and ROP in the sense of having the ROP directly proportionally 

increased by increasing the WOB. Region III represents the foundering region, showing that is 

not true to have the ROP infinitely increased by increasing the WOB, and that the maximum 

applicable WOB would be the one representative by the inflection point of the curve. This 

region III inflection point could be shifted allowing a higher achievable ROP by better 

designing the problematics presented in the previous sentences, including the hydraulics.  
 

Furthermore, Dupriest et al. (2005) stated that friction losses are the main error in SE 

determination since the torque measured on the surface is a sort of reactive force or friction 

encountered and may take into account, not just the down-hole torque of the drill-bit, but also 

the whole drill-string friction. Never the less, as a trending and qualitative tool and not as 

quantitative absolute values, it would still be reasonable to be used in drilling operations as a 

reference chart. In this sense, it was suggested that the SE and MSE (푆퐸 ) 

equations, as determined by Teale et al. (1965) and Pessier et al. (1992), should be used after 

adjusting for the already-known drill-bit efficiency (퐸퐹퐹 ), which lays between 30 and 40%. 

The final adjusted mechanical specific energy (푀푆퐸 ) would change the specific energy 

SE curve to fit the rock crushing strength to maximize correlation in its maximum efficiency, 

and be more feasible for the field personnel (known also as rig crew or field population) to 

reference, as per equation (33) (DUPRIEST et al., 2005 and 2010).  
 

푀푆퐸 = 푆퐸 .퐸퐹퐹   (33) 



60 
 

Figure 25 - Graph showing a common drill-rate test curve and improvements possibilities. 

 
Source: (DUPRIEST et al., 2005). 
 

In the second paper (DUPRIEST, 2010), disserted some interesting thoughts related to field 

operation conducted with PDC bits of sizes 17.5 [in], 12.25 [in] and 8.5 [in] in hard anhydrites 

and dolomites (rock strength ranging from 15 to 35 [kpsi]). It was observed that an increase 

horsepower would increase efficiency, achieved by decreasing nozzle sizes or increasing flow-

rate (or hydraulic jet impact force), and that logging-while-drilling (LWD) and measuring-

while-drilling (MWD) tools do not show the low vibration level which may also affect the MSE 

curves, but are designed to accommodate minimum levels that might be harmful for the tools 

itself.  
 

In terms of vibration, it was stated that lateral vibration, or whirl, could be mitigated by 

increasing the WOB, changing motors, bent housing configurations versus more straight ones, 

using near bit stabilizers, using high torque motor, and even increasing the drill-bit gauge 

length. For torsional vibration or stick-slip, efficiency is enhanced by a decrease in torque 

(achieved by reducing the WOB) or an increase in rotary speed (which increases the angular 

momentum). For axial vibration or bit bounce, a reduction in WOB was helpful, considering 

that it is more frequent when encountering stringers (known as small formation layer of 

different geology within a formation type) or drilling hard formations.  



61 
 

3        PRE-SALT DATA ANALYSIS 

In this chapter, the pre-salt wells are detailed from both technical and economic points of view, 

starting with the main general characteristics and information, then deepening through the sub-

chapters into geological, petrophysical, drilling, and performance characterization. 

3.1 GENERAL WELL INFORMATION AND COSTS 

Pre-salt wells have gained exposure world-wide, not just because of their possible profitability, 

but also due to the challenges implicit in their exploration, operations, and well development 

phases. Considerably remote, hundreds of kilometers from the coast, and in environments 

known in the industry as deep- and ultradeep-water (Figure 4), these wells have some degree 

of complexity, one of several factors that make the activities and operations costly. 
 

Table 6 presents a historical summary of information from analogs drilled in the past years in 

which the wells’ locations are shown to vary from 100 to 180 [km] from the coast, in water 

depths averaging more than 1,500 [m] and with reservoirs (pre-salt section) located 

approximately 3.5 to 6 [km] deep.  All these facts, together with some specific information 

provided in the subsequent sub-chapters, helps addressing why the activity in such type of wells 

comes at such considerably expense, with costs estimated to go up to 134,000,000.00 [USD] 

for the entire operation of a pre-salt well. 
 

It can be considered that the efficiency for effectively drill the pre-salt sections has been, in 

average, approximately 28.5 [m/ day] with costs ranging from 641,985.00 to 1,374,755.00 

[USD/ day] (equivalent to 22,525.00 to 48,237.00 [USD/ m]), dependent on the type of drilling 

platform in use and unforeseen events followed by unforeseen operational costs that can arise 

when performing the operation. These costs and average performance for the pre-salt will be 

used in the next chapters for estimating the potential savings hidden in the pre-salt operations 

in terms of operational performance. 
 

Furthermore, with the presented information in Table 6 it is possible to better picture the wells´ 

data set in use for the optimization analysis in the presented thesis, allowing a better 

visualization of which kind of wells are under study. 

 

 



62 
 

Table 6 - Historical pre-salt well costs, sizes, intervals, water depths, and coastal distance. 

Well 
# 

Time [days]/ cost [MM USD] Pre-salt coastal distance [km]/ MD 
drilled interval [m]/ water depth [m] 

Hole 
size 
[in] 

Total well/ 
pre-salt 
interval 

Total well/ 
pre-salt interval 

 

with (NPT [%]) 
Coast 

Depth/ 
time [days]/ 

vertical (V) or 
deviated (D) 

Water 
depth 

A 91.1/ n/a 
29.12/ n/a 

109.32 (20%)/ n/a 
35.34 (21%)/ n/a 

110 3,993 - 4,195/ 
12.79/ (V) 

1,300 8.5 

B 102.5/ 133.5 
35.55/ 45.25 

123 (20%)/ 160 
42.66 (20%)/ 54.32 100 3,405 - 3,872/ 

21.08/ (V) 900 12.25 

C n/a / n/a 
n/a / n/a 

n/a / n/a 
n/a / n/a 120 4,487 - 5,313/ 

35.29/ (D) 1,800 12.25 

D 80.1/ 79.1 
12.29/ 7.89 

96.1 (20%)/ 93.3 
15.14 (23.19%)/ 9.47 130 4,400 - 4,887/ 

20.29/ (V) 1,700 8.5 

E 100/ 101,4 
41.61/ 37.55 

120 (20%)/ 120 
52.69 (27%)/ 45 130 4,665 - 5,475/ 

30.38/ (D) 1,700 10.63 

F n/a / n/a 
n/a / n/a 

n/a / n/a 
n/a / n/a 

100 4,899 - 5,739/ 
15.29/ (D) 

1,600 12.25 

G 
120/ 165 

15.29/ 21.02 
n/a / n/a 
n/a / n/a 100 

5,255 - 5,600/ 
n/a / (V) 1,700 12.25 

H 115/ n/a 
25,65/ n/a 

134 (20%)/ n/a 
30,77 (20%)/ n/a 180 5.050 - 5.840/ 

27,09/ (V) 1,800 12.25 
 

Source: (BDEP, 2010; CDC, 2015). 
 

Due also to the fact most of these operations are still linked to exploratory phases rather than to 

development phases, and considering that a mature experience is still under development, the 

main focus in such wells has been to avoid unexpected or undesired events while learning any 

single task, so that the operation itself is not always just speed oriented, but more learning and 

information gathering oriented, even understanding that the economic factor plays a very 

important role in the operational context. 

3.2 RESERVOIR CHARACTERIZATION 

The pre-salt reservoirs are characterized as carbonate reserves with different and specific key 

features known to present certain challenges. For example, the thickness of the evaporite layers 

on top of the pre-salt, has to be crossed before reaching the pre-salt accumulations. Historically, 

these formations are very hard and abrasive, but for various reasons not detailed here since it is 

considered to be outside of the scope of this research; the hydrocarbon accumulations are of 

good quality, classified as light and containing some presence of H2S (expectation ranging up 

to 250 [ppm]) and CO2 (ranging up to 40%) that forces cautious by applying specific techniques 



63 
 

when in execution of any exploration and production related phases (BELTRAO ET AL., 2009; 

MELLO ET AL., 2011; CEZAR et al., 2015; ANDRADE, 2015; BSUQUET, 2015). 
 
These clastic sedimentary rocks, predominantly microbiological and coquinoid li