RISK ANALYSIS OF DRILLING OPERATIONS IN DEEPWATER

RESERVOIRS

Nuno Filipe Salsa da Silva Ferreira

Thesis to obtain the Master of Science Degree in

Mechanical Engineering

Supervisors: Professor Amílcar de Oliveira Soares Professor Tânia Alexandra dos Santos Costa e Sousa

Examination Comittee

Chairperson: Professor Mário Manuel Gonçalves da Costa Supervisor: Professor Amílcar de Oliveira Soares

Member of the Committee: Professor Maria João Correia Colunas Pereira

November 2014

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ACKNOWLEDGMENTS

It has been a journey that now ends with lot of expectations about the future and the feeling of

accomplishment. I would like to express my gratitude to all the people who gave the contribute to this master

thesis, Professor Tânia for accepting me as a master thesis student and the unquestionable support along this

master thesis theme pursuit, to Professor Amílcar for his incisive support that unblock many doubts I had and

Leonardo for his priceless support in all sort of details that make this thesis what it is.

This thesis was a constant metamorphosis work with continuous improvement and, from my point of view, a

remarkable work is now presented. This dissertation was also an opportunity to combine the knowledge I

acquired from my both Mechanical and Petroleum Masters courses as I had to manage and develop technical

skills from both areas.

Obviously I want to give a word for my friends and family, my parents Luís Filipe and Ana Maria, to my brothers

Ricardo José, Inês Maria and Luís Miguel and my nephews Santiago, Sebastião, Simão and to the new one that

come next year.

Finally, I would like to leave a word of remembrance to Prof. José Miguel C. Mendes Lopes and to Prof. João

Luis Toste de Azevedo for their guidance since the beginning of this journey either as professors and tutors.

“Prediction is very difficult, especially if it’s about the future”, Niels Bohr (1885-1962)

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ABSTRACT

The Oil&Gas industry faces tremendous structural changes due to the growing energy demand of

emerging countries and the increasingly geological complex reservoirs more difficult to access and exploit. This

reality led to innovative technologies and new assessment methods to proper evaluate the drilling risk.

This thesis focuses on these new approaches to assess the drilling risk by introducing the geological

uncertainties to the stochastic simulation model. This new approach relies in the appliance of the Monte Carlo

Inverse Sampling Transform Method to the formation thickness and drilling performances distributions. A

different approach was used to simulate the non-productive time by analyzing the histogram and capture

significant trends and behaviors as verified with the extreme classes following the Bayesian Sequential

Approach. To perform the simulation, an algorithm model to account for these adjustments was developed and

tested.

It was possible to obtain the convergence and validate the algorithm model with field data achieving

the quantification of the geological risk in a deepwater well simulation. It was also achieved a long term rig

performances based on a single project non-productive time simulation by applying the Bayesian Sequential

Approach. With this outcome it was possible to account geological uncertainties caused by the seismic data

acquisition, processing and interpreting in formations delineation, and a quantitative risk analysis of drilling

operations in deepwater well in the pre-salt region was performed without underestimate these uncertainties.

KEYWORDS: Risk Analysis, Geological Uncertainties, Deepwater Pre-salt Well, Monte Carlo Simulation,

Bayesian Sequential Approach, Drilling Operations.

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RESUMO

A indústria do petróleo está perante novas mudanças estruturais devido ao aumento da procura

energética de países emergentes e a reservatórios geologicamente mais complexos e difíceis de aceder e

explorar. Esta realidade conduziu ao desenvolvimento de tecnologias inovadoras e novos métodos de avaliação

para avaliar o risco de cada projecto.

Esta tese foca estas novas abordagens para avaliar o risco introduzindo incertezas geológicas no

modelo de simulação estocástica. Esta nova abordagem recorre à aplicação do Método de Amostragem por

Transformação Inversa a partir das distribuições de espessura das formações e das performances de

perfuração. Uma abordagem alternativa foi seguida para lidar com o tempo não productivo através da análise

do seu histograma e captação de comportamentos e tendências como verificado nas classes extremas seguindo

a Abordagem Sequencial Bayesiana. Para realizar a simulação foi desenvolvido e testado um algoritmo que

permitisse estes ajustamentos.

Foi possível convergir e validar o modelo com dados históricos obtendo-se a quantificação do risco

geológico numa simulação de um poço de águas profundas. Foi também obtido as performances de longa

duração da plataforma baseado na simulação de tempo não-productivo de um projecto único. Com este

resultado foi possível contabilizar as incertezas geológicas devido à aquisição, processamento e interpretação

sísmica na delineação de formações, e realizou-se uma análise de risco em operações de perfuração num poço

de águas profundas na região do pré-sal sem subestimar estas incertezas.

PALAVRAS-CHAVE: Análise de Risco, Incertezas Geológicas, Poço no Pré-sal Profundo, Simulação de Monte

Carlo, Abordagem Sequencial Bayesiana, Operações de Perfuração

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TABLE OF CONTENTS

ACKNOWLEDGMENTS .............................................................................................................................. i

ABSTRACT ................................................................................................................................................ iii

RESUMO ................................................................................................................................................... v

LIST OF FIGURES ...................................................................................................................................... ix

LIST OF TABLES ........................................................................................................................................ xi

GLOSSARY .............................................................................................................................................. xiii

ACRONYMS ............................................................................................................................................. xv

SIMBOLOGY .......................................................................................................................................... xvii

UNITS SYSTEM CONVERSION ................................................................................................................ xix

1. INTRODUCTION ............................................................................................................................... 1

1.1. SCOPE ...................................................................................................................................... 1

1.2. PROBLEM DEFINITION AND OBJECTIVES ................................................................................. 1

1.3. STRUCTURE OF THE DISSERTATION ........................................................................................ 2

1.4. STATE-OF-THE-ART .................................................................................................................. 3

2. INDUSTRY BACKGROUND ................................................................................................................ 7

2.1. GROWING DEMAND FOR OIL&GAS ......................................................................................... 7

2.2. OIL&GAS INDUSTRY ASSETS EVALUATION .............................................................................. 9

2.2.1. RESERVES CLASSIFICATION AND REPORTING ................................................................ 10

2.2.2. E&P SUSTAINIBILITY INDICATORS .................................................................................. 10

2.3. DEEPWATER DRIVERS ............................................................................................................ 11

2.3.1. DEEPWATER HORIZON ACCIDENT CASE STUDY ............................................................ 13

2.4. DRILLING OPERATIONS .......................................................................................................... 14

2.4.1. RIG DRILLING MARKET................................................................................................... 17

2.4.2. MAIN CHALLENGES ........................................................................................................ 21

3. STOCHASTIC PROJECT EVALUATION ............................................................................................. 27

3.1. RISK ANALYSIS ....................................................................................................................... 27

3.2. MONTE CARLO SIMULATION ................................................................................................. 28

3.3. RANDOM VARIABLES AND CONTINUOUS DISTRIBUTIONS ................................................... 29

4. METHODOLOGY ............................................................................................................................. 31

4.1. DATA ANALYSIS ..................................................................................................................... 32

4.2. DEFINING UNCERTAINTIES .................................................................................................... 32

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4.2.1. PRODUCTIVE TIME UNCERTAINTIES .............................................................................. 32

4.2.2. NON-PRODUCTIVE TIME UNCERTANTIES ...................................................................... 35

4.2.3. DRILLING PERFORMANCE UNCERTAINTIES ................................................................... 37

4.2.4. STANDARD DEEPWATER PRE-SALT WELL ...................................................................... 38

4.2.5. GEOLOGICAL UNCERTAINTIES ....................................................................................... 38

4.3. SIMULATION METHODOLOGY ............................................................................................... 42

4.3.1. GENERAL SIMULATION APPROACH ............................................................................... 43

4.3.2. FIRST SCENARIO APPROACH .......................................................................................... 43

4.3.3. SECOND SCENARIO APPROACH ..................................................................................... 44

4.3.4. THIRD SCENARIO APPROACH ........................................................................................ 45

4.4. SIMULATION ALGORITHM ..................................................................................................... 45

4.4.1. CONVERGENCE OF THE MODEL .................................................................................... 47

5. RESULTS AND DISCUSSION ............................................................................................................ 49

5.1 VALIDATION OF THE MODEL ................................................................................................. 49

5.2. RESULTS FROM DIFFERENT SCENARIOS ................................................................................ 53

5.2.1. SIMULATION RESULTS ................................................................................................... 53

5.2.2. RISK ANALYSIS RESULTS ................................................................................................. 54

5.3. DISCUSSION OF THE RESULTS................................................................................................ 56

6. CONCLUSIONS AND FURTHER DEVELOPMENTS ........................................................................... 59

REFERENCES .......................................................................................................................................... 61

APPENDIX .............................................................................................................................................. 65

APPENDIX A ....................................................................................................................................... 66

APPENDIX B ....................................................................................................................................... 70

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LIST OF FIGURES

Figure 1: Schematic of quantitative risk assessment, Source: Mostafavi et al.(2011) ............................................ 5

Figure 2: World energy consumption, Source: EIA International Energy Outlook (2013)....................................... 7

Figure 3: Oil price analysis, Source: Infield Systems (2013) .................................................................................... 8

Figure 4: Average field sanction point by water depth, Source: Infield Systems (2013) ......................................... 9

Figure 5: Reserves evaluation, Source: Soares (2012) .......................................................................................... 10

Figure 6: Reserves Replenishment Ratio by region, Source: BP statistical review of world energy (2013) .......... 11

Figure 7: World oil supply growth, Source: Infield Systems (2013) ....................................................................... 11

Figure 8: Offshore expenditures in 2014-18 period, Source: Infield System (2013) ............................................. 12

Figure 9: Industry deepwater discovered volumes, Source: IHS EDIN (2006) ....................................................... 13

Figure 10: Standard deepwater well design, Source: Modified from Herriot-Watt (2001) ................................... 15

Figure 11: Rig units forecast, Source: Infield System (2013) ................................................................................. 18

Figure 12: Model relationship between utilization rates and dayrates in three floaters markets (2006-2010),

Source: Kaiser et al. (2013).................................................................................................................................... 19

Figure 13: Rig types classification ......................................................................................................................... 20

Figure 14: Semisubmersible offshore rig (a) and drillship (b), Source: Modified from MMS, USDOI (2000) ........ 21

Figure 15: Disaggregated well costs, Source: Vinod (2013) .................................................................................. 21

Figure 16: Haynesville horizontal drilling wells productivity gains, Source: EXCO Resources (2009) ................... 23

Figure 17: Drilling hazards related to wellbore instability, Source: Modified from Managing the risk,

Schlumberger (1999) ............................................................................................................................................. 25

Figure 18: Disaggregation of average NPT percentage in pre-salt deepwater wells, Source: James K. Dodson

Company (2010) .................................................................................................................................................... 26

Figure 19: Risk analysis based on histogram ......................................................................................................... 27

Figure 20: Inverse sampling transform method ................................................................................................... 28

Figure 21: Methodology approach ....................................................................................................................... 31

Figure 22: Data analysis workflow chart ............................................................................................................... 32

Figure 23: Non-productive time of standard rig B ................................................................................................ 35

Figure 24: Consecutive 0 hours NPT of standard rig B .......................................................................................... 36

Figure 25: Consecutive days of 24 hours NPT of standard rig B ........................................................................... 36

Figure 26: Triangular distributions and histograms of the formation thickness................................................... 40

Figure 27: Geological model developed ............................................................................................................... 41

Figure 28: Geological model distributions and histograms of the formation thickness ....................................... 42

Figure 29: Simulation general approach ............................................................................................................... 43

Figure 30: First scenario approach ........................................................................................................................ 44

Figure 31: Second and Third scenario approach ................................................................................................... 44

Figure 32: Algorithm workflow chart .................................................................................................................... 46

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Figure 33: Convergence of the algorithm ............................................................................................................. 47

Figure 34: Well #8 simulation results (above) and Well #9 simulations results (below) ...................................... 51

Figure 35: Drilling operations time (up left), casing, cementing and others operations time (up right) and drilling

productive time (down) ........................................................................................................................................ 53

Figure 36: Risk analysis for First Scenario results ................................................................................................. 55

Figure 37: Risk Analysis for Second scenario results ............................................................................................. 55

Figure 38: Risk analysis for Third scenario results ................................................................................................ 56

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LIST OF TABLES

Table 1: Rig utilization rate by region, Source: Rigzone (updated on May 9th 2014) ........................................... 19

Table 2: Average dayrate by rig type, Source: Rigzone (updated on September 6th 2014) .................................. 20

Table 3: Days of wellbore instability as a percent of total time, Source: Modified from Pritchard & Kotow (2011)

.............................................................................................................................................................................. 24

Table 4: Comparison between Decision trees and Monte Carlo Simulation, Source: Murtha (1997) pp.17 ........ 28

Table 5: Drilling phases associated with correspondent geological facies ........................................................... 33

Table 6: Drilling phases joint operations statistical parameters ........................................................................... 33

Table 7: Drilling phases individual operations statistical parameters .................................................................. 34

Table 8: Drilling phases rate of penetration statistical parameters...................................................................... 37

Table 9: Standard deepwater pre-salt well characterization ................................................................................ 38

Table 10: Formation thickness .............................................................................................................................. 39

Table 11: Triangular distribution parameters ....................................................................................................... 39

Table 12: Well data for validation test from a different dataset of the standard rig B ........................................ 50

Table 13: Validation results .................................................................................................................................. 52

Table 14: Statistical parameters comparison between scenario 2 and 3 ............................................................. 57

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GLOSSARY Based on Schlumberger Oilfield Glossary

Annulus The space between the wellbore and casing.

BOP A large valve design to prevent influx of hydrocarbons in the risers above the wellhead.

Christmas Tree The set of valves, spools and fittings connected to the top of a well to direct and control

the flow of formation fluids.

Casing String An assembled length of steel pipe configured to suit a specific wellbore.

Core Cylindrical sample of target formation rock.

Contractors Service companies hired to perform a specific task.

Cuttings Small pieces of rock that break away due to the action of the bit teeth.

Drillpipe Tubular steel conduit which connects the rig surface equipment with the bit.

Liner Casing string that does not extend to the top of the wellbore but instead is suspended

from the inside the bottom of the previous casing string.

Packer A device used to isolate the annulus and anchor or secure the bottom of the production

string.

Risk Is associated with the probability of total loss.

Tubing String A continuous length of low-alloy steel carbon steel tubing which employed into a

wellbore for manipulation of tools.

Uncertainty Is associated with the description of the range of possible outcomes.

Wellhead The system of spools, valves and assorted adapters that provide pressure control of a

control production well.

Wellbore The drilled hole or borehole, including the openhole or uncased portion of the well.

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ACRONYMS

AAPG American Association of Petroleum Geologists

BP British Petroleum plc

BOP Blow Out Preventer

boe Barrels of Oil Equivalent

boed Barrels of Oil Equivalent per Day

bbl Oil Barrel

CDF Cumulative Distribution Function

ECDF Experimental Cumulative Distribution Function

E&P Exploration and Production

HIIP Hydrocarbons Initially In Place

IADC International Association of Drilling Contractors

IOC International Oil Company

M&A Mergers and Acquisitions

NOC National Oil Company

O&G Oil and Gas

PDF Probability Density Function

RRR Reserves Replenishment Ratio

SPE Society of Petroleum Engineers

SPEE Society of Petroleum Evaluation Engineers

WD Water Layer Depth

WPC World Petroleum Council

USD United States Dollar

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SIMBOLOGY

Uppercase Latin

AvgNPT% Average non-productive time percentage

DT Drilling time

NPT Non-productive time simulated value

NPTf Non-productive time marginal cumulative distribution function

NPT% Non-productive time percentage

NPT0 0 hours non-productive time simulated value

NPT0f 0 hours non-productive time conditional cumulative distribution function

NPT24 24 hours non-productive time simulated value

NPT24f 24 hours non-productive conditional cumulative distribution function

P1 First drilling phase time

P2 Second drilling phase time

P3 Third drilling phase time

P4 Fourth drilling phase time

PC&O Phase casing, cementing and others operations time

PD Phase drilling operations time

PT Productive time

ROP Rate of penetration

Th Formation thickness

VarNPT% Variance non-productive time percentage

𝑍 Random variable

𝑍 ∼ Distribution of a random variable

Lowercase Latin

𝑛 Length of a sample set

𝑠 Skewness coefficient

𝑧 Sample value

𝑧𝑠 Simulated value

Lowercase Greek

𝜇 Mean

𝜎 Standard deviation

𝜎2 Variance

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UNITS SYSTEM CONVERSION

Oilfield Units Conventional System Units International System Units

1 bbl 158.9873 l 158.9873x10-3

m3

1 boe 5.8615 GJ 5.8615x109 J

1’ (ft) 0.3048 m 3.048x10-1

m

1‘’ (in) 2.54 cm 2.54x10-2

m

1 million (mm) 106 -

1 billion (bn) 109 -

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1. INTRODUCTION

1.1. SCOPE

The Oil&Gas industry is changing into a new era in which maintaining oil production and sustainability

involves unprecedented high risks, raising costs and reducing profitability. On the other hand the increasing

demand and the robust oil prices provide the Oil&Gas companies investment capability to sustain these high

costs.

To maintain reserves indicators companies have increasingly turned to deepwater and unconventional oil

resources in the face of the declining of the conventional onshore and shallow offshore fields. This trend leads

to high capital expenditures involving decisions under uncertainties. In order to assess, analyze and manage

this risk, simulations are performed based in technological uncertainties to obtain trustworthy results. The

main task of these companies is correctly allocating its capital expenditures in profitable ventures so project

evaluations are carried out to characterize each venture.

1.2. PROBLEM DEFINITION AND OBJECTIVES

The main objective of this dissertation is to enrich a model base (Farinha, 2013) by adding and

analyzing new uncertainties and approaches and performing simulations using an own developed algorithm,

instead of a “black box” commercial software where adjustments to the simulation model cannot be

performed. This thesis pretends to achieve these goals:

Perform a stochastic risk analysis in a deepwater pre-salt well drilling operation;

Development of a risk analysis simulation software using the Monte Carlo Inverse Transform Sampling

method;

Enrichment of the simulation model by incorporating geological uncertainties;

Validate and converge the simulation model.

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1.3. STRUCTURE OF THE DISSERTATION

This dissertation intends to perform a logical chain to describe the state-of-the-art, the causes and the

author’s methodology to perform a stochastic risk analysis of deepwater pre-salt drilling operations based in

available field data.

In Chapter 1, the scope of the dissertation, its problem definition and objectives and a literature review of the

state-of-the-art analysis are presented, focusing the main issues addressed and the solutions applied.

In Chapter 2 a background industry study is made to assess the main causes to perform risk analysis in

deepwater drilling operations, focusing in the key drivers and describing the operations and its limitations. A

case study related to the subject is discussed.

In Chapter 3 the theoretical foundations of stochastic project evaluation focusing in the Monte Carlo simulation

(MC) and risk analysis principles and definitions are presented. The probability distribution functions are also

adressed.

Chapter 4 focuses the method used to define the simulation model and the uncertainties. The algorithm model

is defined and the convergence established.

Chapter 5 presents the results and discussion from the simulation and its impacts in the outcome, by

performing a risk analysis. The model validation is checked.

Finally Chapter 6 draws the conclusions and the key findings and proposes further developments.

Due to the large amount of information that references and supports this dissertation a References and

Appendix chapters were added.

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1.4. STATE-OF-THE-ART

According to Coelho et al. (2005) the concept of risk connotes the possibility of loss and the chance or

probability of that loss. Risk can be assessed and analyzed to identify the problem, specify the objectives and

constrains, model the uncertainties and perform sensitivity analysis which lead to a decision. Risk management

connotes a second stage where decision maker seek protection from unfavorable situations mitigating the risk

(Murtha, 1997).

Risk analysis is a tool to maximize the possibility of adopting, under uncertain conditions, the correct decision.

Due to the nature of significant capital expenditure under highly uncertain engineering and geological

conditions drilling operations risk analysis is extensively used by the industry as focused in Peterson et al.

(1995): “Risk analysis methods have recently gained wide-spread acceptance (…) as companies realize the

importance of quantifying alternative choices competing for limited budgets.”

This concept has been introduced by Newendorp & Root (1968) which summarized its advantages. With the

use of this method, the effects of unlimited number of variables on drilling operations can be analyzed,

sensitivity analysis can be conducted and variables highly affecting the final outcome can be proper and

individually scrutinized.

Later in 1975 Newendorp & Campbell emphasized the advantages of using decision analysis methods and the

definition of an entire range of possible outcomes which define and compare different options with different

levels of risk and uncertainties.

Cowan (1969) focused on the superiority of applying probabilistic methods compared with deterministic

methods and proposed a model for risk assessment in the development of hydrocarbon production, however

not aimed specifically and only for drilling operations. His model was able to carry out analysis in five different

phases: “exploration period”, “drilling the wild cat”, “delineating the field”, “developing” and “producing the

field” which opened the scope of this method application.

Newendorp in 1983 pointed out different levels of risk analysis due to the increasing trend of exploration

activities towards small and complex structures in a challenging environment. He considered five levels, the

first three as discrete-outcome models and the latter two as continuous-outcome models. He stated that the

increasing level depends on the data availability or the discrete-continuous transition being beyond the five

possible reserves outcomes, which the model should be converted to a continuous model to characterize the

entire reserves distribution. The last level relies on the Monte Carlo simulation analysis which evaluates the risk

based in a given set of drilling parameters.

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Ostebo et al. (1991) published, after the Piper Alpha accident, a study where qualitative and quantitative risk

assessment were implemented in a broader way. With the issue of tight new regulations in offshore operations

it was defined a method, Concept Safety Evaluation (CSE), to quantify risk analysis which was intended to

determine and evaluate the areas where problems may occur reducing the possibility of accidents.

Focusing in the probabilistic analysis that uses Monte Carlo simulation with time dependent variables Peterson

et al. (1993) pointed out that the simulation were better predictors of the actual days than the conventionally

generated estimates, offered more insight of problem-free and problem days contribution to the total days,

and emphasized the uncertainty associated with drilling operations. The simulation has the ability to be

expanded as the quality of the historical data permits.

According to Peterson et al. (1995) methodology, and as defined in this dissertation, the variables are

separated in input and output and statistical analysis is used to define them. They include an estimate of time

to perform the various operations: total problem-free time, total problem time and the sum of them, the total

time. The author pointed out that the routines presented allow reproducibility of time estimates as they

incorporate historical data, more representativity of stochastic estimates and the flexibility to improve as more

data is obtained.

Referencing Bilgesu et al. (1997) developed a new approach to modelling the parameters that affect the bit

performance, such as ROP, torque, rotational speed and lithology. The work was based in laboratory data and a

neural approach was performed resulting in bit wear distribution output.

Later in 2005, Peterson et al. presented best practices for applying risk management, risk analysis and

uncertainties analysis.

Akins et al. (2005) described a probabilistic approach to developing drilling/completion time and cost model

that can be used throughout the well construction life cycle, from conception to project review. A step by step

risk analysis is undertaken in each operational sequence and a review is made to identify and define

contingency steps. The disaggregated step by step distribution variables are inputs to a Monte Carlo simulator

and its outcome include a more comprehensive time and cost probability distribution. This process allows a

non-biased approach for time and cost outcomes as its inherent risks and sensitivity.

Coelho et al. (2005) compared two different methodologies for the total time assessment in drilling and

completion operations, the Monte Carlo Simulation and the Neural Network Approach. In order to represent

uncertainties a hybrid model with competitive feedforward and probabilistic neurons was proposed. The

authors concluded that this last methodology must be complemented with traditional simulation techniques,

although this approach offers more information to the decision maker based on low level information

availability to estimate total time.

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Mostafavi et al. (2011) developed an approach based on simulation of drilling performances (rate of

penetration) to estimate the cost uncertainties. Variations of operational parameters (Figure 1) are applied to

provide the probability distribution of ROP, time and cost of the operations using a reliable model through

Monte Carlo Simulation. To generate time and costs from ROP distributions the author used data based in a

single well and pointed out the importance of the lithology uncertainties.

Figure 1: Schematic of quantitative risk assessment, Source: Mostafavi et al.(2011)

Farinha (2013) analyzed the time and cost estimation for drilling operations in a deepwater well under the pre-

salt region relying in a Monte Carlo simulation to define an authorization for expenditure (AFE) based in a risk

assessment. The non-productive time (NPT) was generated from a distribution of NPT percentage on a daily

basis obtaining more realistic results. A full shut down (24 hours of NPT) consecutive days distribution was

defined from the data and fed to the simulator.

The present thesis pretends to further expand this approach by considering all the extreme relevant

phenomena building the NPT distribution, capture the behavior and generate individual times for each

operative day and developing a risk analysis model using an own made software and particularly evaluate the

uncertainties in a sequential approach. The main pretension is to incorporate geological uncertainties and

analyze the associated risk by simulating drilling performances (ROP) and formation thickness to achieve time

and cost distributions.

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2. INDUSTRY BACKGROUND

In this chapter an industry background is made to scrutinize the main reasons for the Oil&Gas industry

to perform risk analysis in drilling operations. The key questions that will be answered are the need for these

companies to endorse new project ventures based in the actual world increasing need for energy, the

economics of an Oil&Gas company that forced the companies to continually invest in these high cost/risk

ventures and the complexity of drilling operations in deepwater pre-salt in terms of technological challenges,

market availability and undesired costs.

2.1. GROWING DEMAND FOR OIL&GAS

According to EIA (International Energy Outlook, 2013), shown in the figure below, the forecast for

2040 indicates a growing demand for energy pressuring the companies to further development its assets by

improving recovery factors on actual fields or investing in exploration of new ventures with high risks, like

deepwater and ultradeepwater.

Figure 2: World energy consumption, Source: EIA International Energy Outlook (2013)

The forecast above shows the increasing demand for energy mainly by the non-OECD in the last years and also

in the future causing the recent and expected increase in the world oil price. These high prices (Figure 3)

provide International Oil Companies (IOC) the capability to review their assets and investing into developing

new reserves leading to the escalade in the deepwater exploration.

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For companies to maintain a certain sustainability ratios in investing and developing the new high risk

areas of the deepwater and utradeepwater, this economical context of growth in demand for the next decade,

the oil price should be around the 110 USD per barrel mark. A base price of 90 USD per barrel will spur oil

producing countries like Saudi Arabia, to sustain its budget (219 billion USD in 2012) and the further

expenditure increase (+19% in 2013 budget) which requires this minimum oil price. A high price of 120 USD per

barrel has already boosted the explorations and development of new resources such as the deepwater and

ultra-deepwater.

Figure 3: Oil price analysis, Source: Infield Systems (2013)

In the figure below (Figure 4) is shown that the oil price is capable to sustain offshore developments while

shallow water reserves clustered between 10 to 30 USD per barrel to be developed, deepwater and

ultradeepwater fields with the actual technology need an oil price range between 36 to 80 USD/bbl to sustain

their development (Infield Systems, 2013). This price range is needed due to the increasing water-depths,

complex well development and the high utilization rates of the offshore rigs in some regions.

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Figure 4: Average field sanction point by water depth, Source: Infield Systems (2013)

2.2. OIL&GAS INDUSTRY ASSETS EVALUATION

Regarding Howard & Harp (2009) the primary assets of an Exploration and Production (E&P) company

are its proven reserves, that is, hydrocarbons below the surface that have not yet been produced and are

economically viable to extract with the existing technology. These companies are unique in that their primary

asset base is depleting and therefore must be continually replaced through either investing in new ventures or

by mergers and acquisitions (M&A).

According to Kaiser (2013) assessing these reserves relies in indirect methods that are expensive to perform

meaning that reserves estimation is uncertain. The reserves reporting is a critical activity for the industry – for

instance the National Oil Companies’ (NOC) reserves reporting is consider state secret – leading the regulatory

bodies to define regulations prescribing how volumes are classified.

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2.2.1. RESERVES CLASSIFICATION AND REPORTING

The 2007 SPE/WPC/AAPG/SPEE Petroleum Resources Management System (PRMS) is an industry

standard for classifying and reporting the reserves and is adopted by most of the E&P companies. This

classification categorizes, at a given date, the resources in: Reserves – known recoverable accumulations,

Contingent Resources – potentially recoverable from known accumulations not currently considered

commercially recoverable and Prospective Resources – potentially recoverable from undiscovered

accumulations (Guerreiro, 2012).

Figure 5: Reserves evaluation, Source: Soares (2012)

2.2.2. E&P SUSTAINIBILITY INDICATORS

The international Oil&Gas industry has entered in a stage where maintaining production and

sustainability involves unprecedented risk and increasing costs (Stockman et al., 2011).

A standard tool to evaluate E&P companies’ sustainability is the Reserves Replacement Ratio (RRR), which

measures the amount of proved reserves added to a company’s reserves portfolio during a year relative to the

amount of oil and gas produced at the same time.

Drilling operations performance and innovation is providing the solution for the continue assurance of

reserves, by assessing the risk of these operations and providing reliable prediction of time duration and costs.

11

As seen in the figure below (Figure 6) nowadays the RRR is under the 100% in almost all world regions except

South and Central America. This was caused by the investments in the Golf of Mexico and in the Brazilian pre-

salt since this indicator is the main driver to the capital expenditures performed by the Oil&Gas companies in

these higher risk prospects – Deepwater – in the last decade.

Figure 6: Reserves Replenishment Ratio by region, Source: BP statistical review of world energy (2013)

2.3. DEEPWATER DRIVERS

World offshore crude oil production started in the 1940’s and has grown from a modest 1 mmboed in

the 1960’s to nearly 24 mmboed in 2009, representing roughly one third of oil output (Figure 7). In fact,

offshore production has been the main source of growth for world oil supply in the last two decades.

Figure 7: World oil supply growth, Source: Infield Systems (2013)

12

The deepwater exploration and production has developed over the past 40 years from the early

origins in Brazil, although with a remarkable performance in the last 15 years. As the production of onshore

and shallow waters fields declines, the sustainability ratios decreases and, as mentioned before, the growing

demand associated with a robust oil price have boosted the development of deepwater exploration.

It is expected that both deepwater and ultradeepwater plays will be major contributors to global supply, as

Daly (2010) stated the industry has plans to double the actual production of 9 mmboed by 2020. To accomplish

that, deepwater expenditure is expected to increase by 130% totaling 260 billion USD in this period (Douglas

Westwood, 2014), mainly in the Americas and Africa which will account for 80% of the capital expenditure. In

Africa the forecast is a greater growth in the East African natural gas while South America (Brazil) will remain

the biggest market and North America (Gulf of Mexico) is expected to experience the least growth. The figure

below shows the capital expenditure for the next 4 years (2014-2018) in offshore and as pointed out before the

Americas and Africa will continue to be the center of the offshore expenditure.

Figure 8: Offshore expenditures in 2014-18 period, Source: Infield System (2013)

In the figure below, we can see that the discovered deepwater assets being the South Atlantic pre-salt the

major area with an estimate of 50 bnboe in discovered volumes. These resources were known a long time ago

but technological and investment barriers had lead the companies to invest in other projects.

13

Figure 9: Industry deepwater discovered volumes, Source: IHS EDIN (2006)

2.3.1. DEEPWATER HORIZON ACCIDENT CASE STUDY

On the evening of April 20, 2010, a well event allowed hydrocarbons to escape from the Macondo well

onto Transocean’s Deepwater Horizon offshore rig, resulting in explosions and fire aboard. Eleven people lost

their lives, and 17 others were injured. The fire, which was fed by hydrocarbons from the well, continued for 36

hours until the rig sank. Hydrocarbons continued to flow from the reservoir through the wellbore and the BOP

for 87 days, causing an oil spill of national significance affecting the environment, the populations and the

economy of the entire Gulf of Mexico and setting the stage for dramatic changes to the deepwater exploration

industry.

According to Graham et al. (2011) the chain of events was consecutively miss of the safety procedures such as

testing the cement and the wellbore pressure. Although the main root cause of the event was the delay of 43

days by the contractors (Transocean and Halliburton) to complete the well and the 21 billion dollars

overbudget. The impact of the accident was assessed (Goosens, 2012) with BP maximum losses of 54.6% in

market capitalization corresponding to 101.59 billion USD and Transocean share price declined because of

uncertainty associated with its future liability (Kaiser et al., 2013) being overcome by the second largest

contractor in value – Seadrill – with only half the revenue and one-third the fleet size of Transocean. Due to this

accident the insurance and legal costs increased. Regarding Moody’s Investor Service (2010) repricing the risk

results of rising by 50% in the insurance of drilling rigs. Due to the regulatory changes this legal costs increased

also.

This accident emphasizes the level of risk involved in drilling in deepwater and set a new era where the need to

proper assess the risk in the drilling operations and perform reliable prevision is crucial.

14

2.4. DRILLING OPERATIONS

The purpose of this chapter is to characterize the drilling operations: the main challenges, the rig

drilling market and rig types. It is intended to briefly review the casing, cementing, logging and

completion/workovers operations.

There are three types of wells: exploration wells, used to find and confirm hydrocarbons evidences,

appraisal wells used to delineate and define the boundaries of the reservoir and development wells used for

production. Drilling operations must adjust at each well type for their distinct objectives, by adjusting the

trade-off drilling fast versus drilling properly.

Drilling operations comprise separately operations: drilling, casing, cementing and others, such as

setting BOP or the abandonment. During drilling, the rig bores a hole in the earth using a drillbit which is

connected to and turned by a drillpipe. Drilling fluid passes down the drillpipe through the bit where it

lubricates the bit, controls the hydrostatic pressure inside the well and carries the cuttings back up to the rig

through the annulus between the drillpipe and the borehole. Wells are drilled in stages and when the bottom

of a stage is reached, the open hole is cased off using steel pipe (casing operations) and cemented (cementing

operations).

Casing operations are intended to prevent the hole from collapsing on the drill pipe while cementing

operations fill the annulus space, between the casing and the wellbore, with cement in order to avoid fluid

escapes that can cause environmental hazards.

Logging operations comprise the data acquisition through the life time of the field. Before the

production stage logging defines the geometry and the anisotropy of the reservoir and cap rock (thickness,

fractures, faults), as the lithology and properties for the evaluation reserves (net-to gross ratio) and

petrophysical properties (porosity, permeability, fluid saturation). During the production phase logging is used

to evaluate the fluid movement across the reservoir rock, assess residual oil and saturation changes and

determine borehole integrity. During the drilling phase it is used for geosteering in deviated wells.

There are five acquisition types of logging: wireline logging is performed after the well is drilled in

cased or open hole; tough logging conditions (TLC) through drillpipe used mainly in horizontal wells; logging

while drilling (LWD) or a simple form measuring while drilling (MWD) usually perform for geosteering in

deviated wells; continuous down hole sensing (DTS) which measures continually properties along the borehole,

and mudlogging which measures fluid and cuttings properties with surface sensors.

Completion operations are intended to set production casing across the reservoir interval and the

blowout preventer is replaced by the wellhead, finally the production casing (liner) is perforated and the

reservoir is stimulated if necessary. Workover operations are mainly to repair or stimulate a production well in

order to restore or enhance the production.

15

Offshore well usually have three to four casing strings before reaching the target formation. In this

thesis we define a standard deepwater pre-salt well with four phases. A descriptive characterization of the

standard pattern is presented below.

Figure 10: Standard deepwater well design, Source: Modified from Herriot-Watt (2001)

First Phase - Installing the 30’’ Conductor (P1)

The first stage in the operation is to drive a large diameter pipe, usually called casing or in this case because it is

the first casing installed, named conductor. The purpose of this casing is to prevent the unconsolidated surface

formations from collapsing at the same time as drilling get deeper. This conductor typically has an outside

diameter of 30 in and when it is in place, the full sized drilling rig is brought onto the site, and set up over the

conductor, and preparations are made for the next stage of operations.

Second Phase - Drilling and Casing the 26’’ hole (P2)

The second phase of the drilling is marked by drilling the borehole section with a drill bit of 26’’, with a smaller

diameter than the inner diameter of the previous casing conductor. This 26’’ hole will be drilled down through

the consolidated formations.

16

The ideal case would be to drill the entire well from surface to the reservoir in only one hole section. However,

this is generally not possible because of pressure gradients and different geological formations faced while

drilling. As a result, wellbore diameter gets smaller and smaller while the well is drilling in sections, with casing

being used to isolate the problem formations, preventing the collapse of the well. When 26’’ section is being

drilled, drilling fluid known as mud, is circulated down the drillpipe, across the surface of the drillbit, and up the

annulus between the drillpipe and the borehole, carrying the drilled cuttings from the face of the bit to the

surface. At the surface, the cuttings are removed in mud pits, before the mud is circulated back down the

drillpipe, helping to better understand the geological formations crossed. When the drill bit reaches the bottom

of this section, the drill string is pulled out of the hole and the surface casing is run into the hole. This second

casing, for this particular study, has normally a 20’’ outside diameter and is delivered to the rig in equal joints

with threaded connections at end of each joint. This casing is pulled down into the wellbore, joint by joint, until

it reaches the bottom of the hole. Afterwards, cement is then pumped into the annular space between the

casing and the borehole. This cement covers acts as a seal between the casing and the borehole, restricting the

fluid movement between formations and also supports the casing. Once the cement has solidified, wellhead is

attached to the top of 20’’ casing. The sub-sea wellhead is a pressure-containing vessel that helps to suspend

and support the weight of subsequent casing string. This wellhead also provides a profile to handle the Blowout

Prevention (BOP). In this way, access to wellbore is secure in a pressure-controlled environment. BOP is a set of

valves whose main functions are: to confine the well fluids to the wellbore, to provide means to add drilling

fluids to the wellbore and to allow controlled volumes of fluid to be withdrawn from the wellbore. Moreover,

BOP is used to monitor and regulate the wellbore pressure, shut down the well in case of an emergency,

preventing the flow of formation fluid or influx from the reservoir into the wellbore. The BOP valves are

designed to close around the drillpipe, sealing off the annular space between the drillpipe and the casing.

These BOPs have a large internal diameter in order to be easy to run in hole all the necessary drilling tools.

Third Phase - Drilling and Casing the 14-3/4” hole (P3)

After the installation of BOP, it has to be tested and afterwards the drilling of the third phase starts with a drill

bit 14-3/4’’ down to the next target depth. This phase represents the drilling of the salt layer. Once the salt

layer has been drilled, formations are isolated behind another string of casing with 10-3/4’’ (intermediate

casing). This casing is run into the hole in the same way as the 20’’ casing and it is sustained by wellhead while

it is cemented in place.

Fourth Phase - Drilling and Casing the 8-1/2” hole (P4)

This phase represents the drilling of the reservoir, and it comprehends many risks and cautions in order to

prevent damage to the reservoir, otherwise all efforts to drill the well would be lost. While drilling this

formation, oil will be visible on the cuttings being brought to surface by mud. If gas is presented in the

formation, it will be detected on surface by gas detectors placed above the mud flowline connected to the top

of BOP stack. When the total depth is reached, the drill string is pulled out of the hole and several tools can be

used to measure petrophysical proprieties as explaned before in the logging operations.

17

Some logs are run to measure for instance: the bulk density of the rock (indicating the porosity of the rock); the

electrical resistance of the fluids in the rock (indicating the presence of water/hydrocarbons); or the natural

radioactive emissions from the rock (indicating the presence of shales). These tools are not essential for drilling

a well, and their application depends on the purpose of the well, and on how much one wants to know about

the reservoir.

For a more accurate study of the reservoir, it may be required to retrieve a large cylindrical sample of rock

known as core. This operation is called coring, and the conventional bit must be pulled from the borehole. A

donut shaped bit is then attached to a special large diameter pipe known as core barrel and it is run in the hole

on the drillpipe. This coring assembly allows the core to be cut from the rock and retrieved. Porosity and

permeability measurements can be showed on this core sample in the laboratory.

When these tests are completed, another casing string called liner is run in the hole and consequently

cemented to the wellbore. Liners do not extend back to the wellhead but, instead, they are suspended from

another casing string. The liner is used instead of full casing strings to reduce costs, allow the use of larger

tubing above the liner top, to improve hydraulic performance when drilling deeper and not to represent a

tension limitation for a rig.

If all the evidences from tests indicate good results, then the oil company will decide to complete the well. To

produce oil and gas effectively, the well has to suffer some interventions called completion operations. In most

cases, the first step is to run and cement production casing, the tubing through which the production flows.

Afterwards, the casing has to be perforated below the tubing, in the completion operations, so the oil and gas

can flow through the reservoir to the surface. The annulus between the production casing and the production

tubing is sealed off by a device known as packer. This device is run on the bottom of the tubing and it is set in

place by hydraulic pressure or mechanical manipulation of the tubing string. After these operations, BOP is

then removed and replaced by a set of valves known as Christmas Tree installed on the top of the wellhead.

The Christmas Tree is used to control the flow of hydrocarbons flowing into the wellbore and up to the surface.

2.4.1. RIG DRILLING MARKET

Regarding Kaiser et al. (2013), E&P firms lease rigs from drilling contractors to drill wells,

approximately 120.000 wells have been drilled offshore since 1955, and from 2000 to 2010, approximately

3500 offshore wells have been drilled each year with a growing percentage in deepwater as shown in the figure

below.

18

Figure 11: Rig units forecast, Source: Infield System (2013)

For instance in 2010 the E&P firms paid approximately 43 billion USD to drilling contractors, which 67% coming

from deepwater drilling although deep and ultradeepwater wells represented only a small share of the total

amount of offshore wells drilled. As the forecast show (Figure 11) from 2013 to 2021 the growth in rig units in

ultradeepwater will raise 60%.

2.4.1.1. Contract Drilling Market

According Kaiser et al. (2013), the contract drilling market is described in dayrates, utilization and fleet

size. Dayrate is the daily rental fee charged by the drilling contractor and includes the use of the rig and labor

costs, but does not include other costs associated with well construction. Dayrates behave according to

demand and supply conditions and as rig demand exceeds supply, dayrates generally rise (Figure 12). Demand

for contract drilling, as mentioned in chapter 2.2, is driven by the capital spending of E&P companies, which, in

turn, is based on companies’ assets valuation and performances. Dayrates are indicator of market conditions as

drivers of the rest of the offshore service companies (e.g. support vessels, logistics, cementing, wireline

logging).

As shown in the figure below, there is a positive exponential correlation, as expected, between the utilization

rate (%) and the dayrate (USD/day).

19

Figure 12: Model relationship between utilization rates and dayrates in three floaters markets (2006-2010), Source:

Kaiser et al. (2013)

The rig utilization rate by region is shown in the table below. As seen the utilization rate is high and Brazil (pre

salt) with the development of the deepwater fields accounts the maximum rate of 96.7%.

Table 1: Rig utilization rate by region, Source: Rigzone (updated on May 9th 2014)

Region Utilization Rate

West Africa 77.8%

Southeast Asia 75.0%

North Sea 90.6%

Mediterranean 81.3%

Persian Gulf 78.4%

Mexico 81.7%

US Golf of Mexico 75.0%

Brazil 96.7%

Average 82.1%

20

The average dayrate by rig type is presented in the table below (Table 2). The high dayrates are achieved by

ultradepwater (4000+ ft), mainly caused by the high utilization rates, which elevate the costs.

Table 2: Average dayrate by rig type, Source: Rigzone (updated on September 6th 2014)

Rig Type Average Dayrate

Drillship < 4000 ft WD 259,000 USD/day

Drillship 4000+ ft WD 516,000 USD/day

Semisubmersible < 1500 ft WD 284,000 USD/day

Semisubmersible 1500+ ft WD 346,000 USD/day

Semisubmersible 4000+ ft WD 437,000 USD/day

2.4.1.2. RIG TYPES

Rig types are classified mainly due to the field operations followed by their specifications (Figure 13). It

is quite needed for the drilling contractor to choose the right rig according to its operative conditions and

drilling specifications such as the water depth or the power needed.

Figure 13: Rig types classification

21

Mobile offshore drilling units (MODU) are ocean-going vessels (Semisubmersible and Drillship) use to

drill, complete and workover wellbores in marine environments. Typically in deepwater and ultra-deepwater

operations are performed by semisubmersibles (Figure 14a) and drillships (Figure 14b).

Bottom supported units included jackups, platforms and submersibles, being the last two used in inland waters.

Jackups however are used in shallow waters (<500 ft WD) being commonly used around the world.

Floating units include semisubmersibles and drillships and are used for deepwater drilling (3000-7500 ft WD).

Floaters can operate in deeperwaters than bottom-supported units since the only physical connection with the

seabed is the anchoring system.

Figure 14: Semisubmersible offshore rig (a) and drillship (b), Source: Modified from MMS, USDOI (2000)

2.4.2. MAIN CHALLENGES

According to Vinod (2013) the main costs associated with drilling a well are mainly due to the rig costs

in which are considered the inefficient costs due to several causes explained below.

Figure 15: Disaggregated well costs, Source: Vinod (2013)

22

The main challenges of drilling operations are avoiding losses of drilling equipment or drilling process

continuity, i.e. non-productive time (NPT) due the impact in the total cost of a well. These challenge are even

greater when drilling in deepwater and through salt layers due to the particular conditions of high pressures

and mobile formations.

Drilling through the salt layer, there is a degree of uncertainty related to the salt movement (halokinesis) and

also a wrong prediction of the lithology and pore pressures, indeed the plastic flow under subsurface

temperatures and pressures along with low permeability present unique challenges for drilling operations as

mobile salt formations hazards.

The non-productive time represents high costs, 150 million USD per year for each drilling contractor, which is

due to these categories of issues in order of occurrence (Athens Group, 2010):

Surface equipment failure;

Subsea equipment failure;

Other (unplanned, waiting, unknown);

Bottom hole problems related to the physical environment;

Rig repairs;

Weather;

Bottom hole equipment failure;

Personnel;

Stuck pipe;

Accident/Incident;

One of the examples is the experience of the personnel which increases rig efficiency as shown below (Figure

16).

23

Figure 16: Haynesville horizontal drilling wells productivity gains, Source: EXCO Resources (2009)

The time needed to drill wells reduces considerably (around 50%) with the increasing experience of the rig

crew. For further development of this thesis, it is intended to model this uncertainty to proper quantify and

evaluate without underestimate the cost.

Another critical factor according to Pritchard & Kotow (2011) is the wellbore instability in deepwater drilling

since any event of wellbore instability has the potential of becoming a well event. These events are generated

due to the miss-predicting lithology and stratigraphy originating abnormal pressures and movable formations

during drilling. The table below summarizes time spent on deepwater wells both in pre-salt and non-pre-salt

regions specifically due to wellbore hazards.

24

Table 3: Days of wellbore instability as a percent of total time, Source: Modified from Pritchard & Kotow (2011)

Events related to wellbore

instability

Pre-salt Wellbores

WD > 3000 ft

Non-pre-salt Wellbores

WD > 3000 ft

Stuck pipe 2.90% 0.70%

Wellbore stability 2.90% 0.90%

Loss circulation 2.40% 2.00%

Kick 1.90% 0.80%

Total [%] 10.10% 4.40%

Total Wellbore Instability [days] 9.80 2.38

Total NPT [days] 29 9

Instability % of NPT days 33.78% 26.40%

Average days to Drill 97 54

As shown in the Table 3 the wellbore instability hazards in deepwater pre-salt wells accounts for 33.78% of the

NPT time and 10.10% of the total drilling time and compared with non-pre-salt wells the time spent is over four

times more (2.38 to 9.80 days).

This issue highlights the need to incorporate in the drilling operations simulation the geological uncertainties to

mitigate this risk which ultimately leads to well events as it happened in the Macondo’s blowout.

In the figure below are some examples of wellbore instability hazards.

25

Figure 17: Drilling hazards related to wellbore instability, Source: Modified from Managing the risk, Schlumberger

(1999)

Referencing Pritchard & Kotow (2011), it is shown the disaggregation of losses of drilling continuity by causes

(Figure 18). The main causes are due to rig failure (6.3%), equipment failure (5.9%) and the wellbore instability

hazards (2.9%), the first two cases more related to the rig age and maintenance and the last with miss-

predicting the geology of the prospect area which can result in severe consequences shown in the figure below.

26

Figure 18: Disaggregation of average NPT percentage in pre-salt deepwater wells, Source: James K. Dodson

Company (2010)

Reducing drilling costs is one of the implications of improved efficiency. As verified in the figure above (Figure

18) the NPT percentage of deepwater pre-salt wells accounts for 30% of the drilling time/costs representing

key concern for operators. According to Cochener (2010), to minimize the drilling costs these drilling rigs are

becoming more efficient based in a five points strategy in order of importance:

Minimizing Non-Productive Time (NPT): This concept implies that the rig spends more time working

and less time waiting.

Working faster: By increasing rate of penetrations (ROP).

Working smarter: These strategies comprise sequential activities, parallel operations and utilizing

technology to monitor and avoid problems.

Making better decisions: Since management and planning decisions have significant impact on the

efficiency metrics such as the drilling bit and necessary power (motors) choice.

Improve rig design: Development of special fit-for-purpose rigs for targeted areas such as shale plays,

horizontal drilling and pad-site drilling (capability of a rig to drill several wells from the same location

avoiding time consuming relocations).

All the challenges presented led to the development of rig technology and the decommissioning of old

inefficient rigs being the leading edge of innovation in this area is the development of laser drilling and the

fully automated offshore exploratory rigs.

27

3. STOCHASTIC PROJECT EVALUATION

According to Belaid & De Wolf (2009) the evaluation of an exploration and production investment

project is set to maximize the profit of the company firstly to determine the cash flow requirements and

secondly analyze the risk of each project.

3.1. RISK ANALYSIS

Risk analysis is a very powerful tool for certain engineering processes where decision under

uncertainty is involved by attempting to quantify the associated risk.

Deterministic approaches apply a single point values for parameters (geological, technical and economic) to

obtain results, although is well known that those parameters are associated with a broad level of uncertainty. It

was common, in the industry, to perform deterministic models using the worst case parameters and absorb the

impact of the uncertainties, minimizing the risk with higher investment costs.

A probabilistic approach relies on a Monte Carlo method to provide broad outcome results accommodating

various risk levels, intended in risk management stage. Ultimately this analysis, by having a full scope of the

outcome, can answer the following question: what is the risk (p) to obtain a time/cost greater than x?

Figure 19: Risk analysis based on histogram

A comparison table of a deterministic approach using a decision tree, and a probabilistic approach obtained

with a Monte Carlo simulation, is provided in the table below (Table 4):

28

Table 4: Comparison between Decision trees and Monte Carlo Simulation, Source: Murtha (1997) pp.17

Decision Tree Monte Carlo Simulation

Objectives make decisions quantify uncertainty

Inputs discrete scenario distributions

Solution driven by Expected Value run many cases

Outputs choice and Expected Value distributions

Dependence limited treatment rank correlation

Due to the nature of the problem defined on the chapter 1.2, e.g. drilling time, a stochastic approach was

follow using the Monte Carlo simulation with the Inverse Sampling Transform method.

3.2. MONTE CARLO SIMULATION

The Monte Carlo Simulation is a statistics-based analysis method that yields probability versus value

relationship. Monte Carlo was a “code word” to describe sampling-based methods for neutron scattering

computations developed in the 40’s and associated with Manhattan Project being nowadays one of the most

used technic to deal with decisions and risk under uncertainty (Murtha, 1997). This method is based on inverse

transform sampling based in a random number generator of the input distributions creating multiple

realizations of the model generating an output distribution. The algorithm follows the next pattern, defining zs

the simulated value from a random variable distribution function FZ.

Figure 20: Inverse sampling transform method

1. Generate a random value u from a

uniform distribution function, U, in the

interval [0, 1]

𝑢 ∶ 𝑈 ∈ [0,1] (1)

2. Inverse transformed value from the

cumulative distribution function

𝑧𝑠 = 𝐹𝑍−1(𝑢) (2)

29

3.3. RANDOM VARIABLES AND CONTINUOUS DISTRIBUTIONS

Since the random variables that will be analyzed are continuous (time, rates and thickness) is defined a

distribution function FZ(z) of the continuous random variable Z as a non-decreasing monotonous function

continuous in ℝ.

𝐹𝑍(𝑧) = ∫𝑓𝑍(𝑡)𝑑𝑡

𝑥

−∞

(3)

Being fZ(t) the correspondent probability density function (PDF) verifying the following statements:

0 ≤ 𝐹𝑍(𝑧) ≤ 1 (4)

𝐹𝑍(−∞) = lim𝑧→−∞

𝐹𝑍(𝑧) = 0 (5)

𝐹𝑍(+∞) = lim𝑧→+∞

𝐹𝑍(𝑧) = 1 (6)

The Normal distribution was introduced by the french mathematician Abraham de Moivre (1667-1754)

in 1733 and it was used to approximate binomial probability events. It is curious to note that the work was

“lost” for some time, until Karl Friedrich Gauss (1777-1855) derived the normal distribution in 1809. The most

common alternative name is Gaussian distribution. The normal distribution reflects the larger probability of

occurrence near the mean and the diminishing in the extreme classes. It is defined a random variable Z which

follows a normal density function fZ(z):

𝑍~𝑁𝑜𝑟𝑚𝑎𝑙 (𝜇, 𝜎2) (7)

𝑓𝑍(𝑧) =1

√2𝜋𝜎𝑒−(𝑧−𝜇)2

2𝜎2 (8)

The Triangular distribution is a continuous distribution function based in a minimum (a), maximum (b)

and most likely value, mode (c), due to the lack of data available. It is defined a random variable Z which

follows a triangular density function fZ(z):

𝑍~𝑇𝑟𝑖𝑎𝑛𝑔𝑢𝑙𝑎𝑟(𝑎, 𝑐, 𝑏) (9)

𝑓𝑍(𝑧) =

{

2(𝑧 − 𝑎)

(𝑏 − 𝑎)(𝑐 − 𝑎), 𝑓𝑜𝑟 𝑎 ≤ 𝑧 < 𝑐

2

𝑏 − 𝑎, 𝑓𝑜𝑟 𝑧 = 𝑐

2(𝑏 − 𝑧)

(𝑏 − 𝑎)(𝑏 − 𝑐), 𝑓𝑜𝑟 𝑐 < 𝑧 ≤ 𝑏

(10)

30

The minimum is the minimum value of the dataset, the mode is the most likely value of the dataset, i.e. the

highest probability value to occur and the maximum is the maximum value of the dataset.

With the data available constrains for some variables, experimental cumulative distribution functions (ECDF)

were define and assumed by the software (Matlab) sourcing the Kaplan-Meier method.

The statistical parameters analyzed were determined as defined below.

The mean (µ) is an equal weighted average of data.

𝜇 =1

𝑛∑𝑧𝑖

𝑛

𝑖=1

(11)

The variance (σ2 or var) is a measure of data dispersion around the mean, it’s determined by the sum of the

square differences of the sample value (zi) and the mean along the samples set (n). The square root of the

variance is named standard deviation (σ or stdv).

𝜎2 =1

𝑛∑(𝑧𝑖 − 𝜇)

2

𝑛

𝑖=1

(12)

Skewness (s or skew) is a measure of the asymmetry of data around the sample mean. For posistive skewness

the data are sread out more to the right and negative skewness the data are spread out more to the left of the

mean. The nule skewness represents a perfectly symmetric distribution around the mean. It is determine by

the following equation.

𝑠 =

1𝑛∑ (𝑧𝑖 − 𝜇)

3𝑛𝑖=1

𝜎3

(13)

31

4. METHODOLOGY

As stated the main objective of this master thesis is to enhance the simulation model by adding

geological uncertainties. Following Peterson et al. (1995) the methodology applied in this thesis considers that

the total drilling time is disaggregated into productive and non-productive time in order to better understand

the impact of each one in the final total time duration.

Figure 21: Methodology approach

The methodology proposed follows the sequential simulation approach, by summing the simulated random

variables (time). Those random variables are considered independent (productive time based on each drilling

phase distributions) or dependent (conditional distributions based on non-productive time extreme classes)

being generated as explained below.

Independent random variables simulation:

𝑧𝑠𝑡 = 𝑧𝑠1 + 𝑧𝑠2 +⋯+ 𝑧𝑠𝑛 (14)

Being the zSn a simulated value from a continuous random variable distribution, F(zn), and the zSt the sum of all

simulated values.

Dependent random variables simulation based on the Bayesian Sequential Simulation:

𝐹(𝑧1, 𝑧2, … , 𝑧𝑛) = 𝐹(𝑧1) ∙ 𝐹(𝑧2|𝑧1) ∙ … ∙ 𝐹(𝑧𝑛|𝑧1, 𝑧2, … , 𝑧𝑛−1) (15)

Defining the random variables z1,z2,…,zn joint distributions F(z1,z2,…,zn) and conditional distributions

F(zn|z1,z2,…,zn-1).

In order to apply these methodology uncertainties will be defined by adjusting a distribution function, defining

its parameters and a global simulation approach will be followed applying the concepts presented. It will be

defined three case scenarios and at the end is expected to generate a cumulative distribution function (CDF),

histogram and statistical metrics of the outcome.

32

4.1. DATA ANALYSIS

In order to perform a data analysis quantification and qualification of the data available is a critical factor.

In this thesis it was used the dataset presented in Farinha (2013) namely:

Total depth and duration of each drilling phase disaggregated in processes of wells in a representative

pre-salt field (Table A-1);

Drilling performances statistics of wells in a representative pre-salt field (Table A-2).

Sampled data of non-productive time per operative day in a standard rig in an offshore pre-salt well

drilled (Table A-3);

Total non-productive time per rig (percentage) operating in a representative pre-salt field (Table A-4).

From this historical data statistical trends and behaviors are captured and disaggregated information is defined

as input variables for the simulation as shown in the workflow (Figure 22).

Figure 22: Data analysis workflow chart

4.2. DEFINING UNCERTAINTIES

In this chapter the uncertainties, their distributions and parameters used as inputs to the simulator

will be defined. Due to the data availability constrains a normal distribution was used for the input parameters

and the experimental cumulative distribution function (ECDF) for some scarce data variables.

4.2.1. PRODUCTIVE TIME UNCERTAINTIES

It is defined productive time as the problem-free time to fulfill an operation. As defined in the chapter

2.4 the operations to drill a well consists in four phases, each of them is disaggregated on individual operations.

Phase one (P1) consist in drilling 36’’ borehole, setting the 30’’ casing typical 10 m above and cemented the

annulus space. The second phase (P2) is defined as drilling operation of 26’’ borehole and the 20’’ casing is set

and cemented. Also the BOP is installed along with a riser. Phase three (P3) consist in drilling a 14-3/4’’

borehole and cased and cemented with a 10-3/4’’ diameter casing. In the last fourth phase (P4) a 8-1/2’’

33

borehole is drilled and a 7’’ liner is set and cemented finishing with the well abandonment operation. For each

phase was also associated to a correspondent geological facies, presented in the Table 5.

Table 5: Drilling phases associated with correspondent geological facies

Phase Operation Geological Facies

1st phase (P1)

Drilling 36’’ bit

Unconsolidated sediments

Po

st-s

alt

Set and cement 30’’ csg

2nd phase (P2)

Drilling 26’’ bit

Consolidated sediments Set and cement 20’’ csg

Set riser & BOP

3rd phase (P3)

Drilling 14-3/4’’ bit

Salt layer Set and cement 10-3/4’’

csg

4th phase (P4)

Drilling 8-1/2’’ bit

Carbonated reservoir

Pre

-sal

t

Set and cement liner 7’’

Abandonment

Assuming each phase as a single operation it was defined following a normal distributed behavior the Table 6

with the distribution parameters, mean and standard deviation.

Table 6: Drilling phases joint operations statistical parameters

Phase Time [days]

Joint Operations Mean Stdv

1st phase (P1) 4.49 0.49

2nd phase (P2) 16.23 1.83

3rd phase (P3) 39.69 9.77

4th phase (P4) 47.66 10.69

34

These values were calculated by averaging the mean and the standard deviation for each individual operation

based on Table A-1.

It was also defined the individual operations metrics by disaggregation of each phase into drilling operations

(PD) and casing, cementing and others operations (PC&O). Again these variables were defined as normally

distributed and it was determined the mean and standard deviation based in Table A-1 and presented in the

Table 7.

Table 7: Drilling phases individual operations statistical parameters

Phase Operation

Time [days]

Mean Stdv

P1

P1D Drilling 36’’ bit 2.54 0.44

P1C&O Casing 30’’ &

Cementing 1.94 0.26

P2

P2D Drilling 26’’ bit 6.56 1.13

P2C&O Casing 20’’ &

Cementing & Set BOP 9.67 2.18

P3

P3D Drilling 14-3/4’’ bit 24.41 7.76

P3C&O Casing 10-3/4’’ &

Cementing 15.27 8.14

P4

P4D Drilling 8-1/2’’ bit 37.63 10.21

P4C&O Set and cement liner 7’’

& Abandonment 10.03 1.85

35

4.2.2. NON-PRODUCTIVE TIME UNCERTANTIES

This time is related with a variety of unexpected events as focus in the Chapter 2.4.2. To define these

uncertainties an experimental cumulative distribution function (ECDF) and a histogram were generated based

in the non-productive time by productive day in a well project on a standard rig (Figure 23).

Figure 23: Non-productive time of standard rig B

Based on historical data (Table A-3) of wells drilled in the pre-salt region the behavior for the non-productive

time of one well drilled was characterized (Figure 23). It was noted the behavior of the NPT histogram extreme

classes, namely the problem-free phenomena of 0 hours of NPT and the total shutdown phenomena of 24

hours of non-productive time.

Analyzing the NPT data set (Table A-3) a continuity of these extreme phenomenon along the days was stressed

out. In order to capture this behavior, distributions of consecutive days of each phenomenon where defined by

building 0 hours non-productive time consecutive days and 24 hours non-productive time consecutive days

histograms (Figure 24 and Figure 25). Experimental distribution functions (ECDF) were generated to represent

these variables cumulative functions.

36

Figure 24: Consecutive 0 hours NPT of standard rig B

Figure 25: Consecutive days of 24 hours NPT of standard rig B

4.2.2.1. BAYESIAN SEQUENTIAL APPROACH FOR THE NON-PRODUCTIVE TIME

The Bayesian Sequential Approach consists in a simulation of values based on marginal distributions

and sequentially on conditional distributions and it was applied to obtain the non-productive time variables as

defined below.

The simulated value zS, which represents the simulation of the total non-productive time results of the sum of

the simulated zS1, zS2 and zS3:

𝑧𝑆 = 𝑧𝑆1 + 𝑧𝑆2 + 𝑧𝑆3 (16)

The simulated value zS1 is obtained from the marginal distribution F1(z), NPT cumulative distribution function,

which model the non-productive time by day:

𝑧𝑆1 = 𝐹1−1(𝑢) (17)

37

The sequential simulated values, zS2 and zS3, are obtained from the conditional cumulative distributions

functions F2(z) and F3(z) respectively, which model the consecutive days of the problem-free and total shut-

down conditions:

𝑧𝑆2 = {

𝐹2−1(𝑢|𝑧𝑆1 = 0)

0 , 𝑖𝑓 𝑧𝑆1 ≠ 0

(18)

𝑧𝑆3 = {

𝐹3−1(𝑢|𝑧𝑆1 = 24)

0 , 𝑖𝑓 𝑧𝑆1 ≠ 24

(19)

The F2(z) CDF represents the consecutive days of 0 hours of NPT (NPT0) and the F3(z) CDF represents the

consecutive days of 24 hours of NPT (NPT24).

4.2.3. DRILLING PERFORMANCE UNCERTAINTIES

A typical drilling performance is the rate of penetration (ROP) that measures the drilled depth (ΔD) per

time to perform it (Δt), in meters per day.

𝑅𝑂𝑃 =∆𝐷

∆𝑡 (20)

Based on the ROP statistical data an input was defined as normal distribution random variable for each phase

associated with each geological facies and shown in the table below (Table 8), by determine the mean and the

standard deviation based on Table A-2.

Table 8: Drilling phases rate of penetration statistical parameters

Phase

Rate of Penetration [m/day]

Mean Stdv

1st phase (P1) 37.01 12.06

2nd phase (P2) 141.14 19.77

3rd phase (P3) 88.82 24.90

4th phase (P4) 15.47 6.44

38

4.2.4. STANDARD DEEPWATER PRE-SALT WELL

It was defined a standard deepwater pre-salt well by depths (meters) regarding the data available. The

depths of each phase by the drilling bit size used were obtained by averaging the depths of all wells in the pre-

salt region as shown in the following Table 9.

Table 9: Standard deepwater pre-salt well characterization

Borehole section [in] Average depths [m]

Water depth 2162

36’’ 2258

26’’ 3178

14-3/4’’ 5206

8-1/2’’ 5750

4.2.5. GEOLOGICAL UNCERTAINTIES

The pay thickness is based on seismic data which contains uncertainties. This uncertainty is not only

due to the acquisition and processing of the seismic data, but also to the seismic interpretation which relies

entirely in the subjective of the technician based on his geological model.

Regarding Chambriard (2010) the uncertainty associated horizon’s formation delineation in pre-salt region

reservoirs is between -22 to +26 meters range. Since it was the only available uncertainty range it was defined

for all the formations under this region. The formation thickness (Th) is obtained by subtracting the bottom

(BtmFm) and the top of the formation (TopFm) according with the next equation:

𝑇ℎ = 𝐵𝑡𝑚𝐹𝑚 − 𝑇𝑜𝑝𝐹𝑚 (21)

The formation thickness was calculated based on the Table 9 and is presented below.

39

Table 10: Formation thickness

Phase Borehole section

[in] TopFm [m] BtmFm [m] Th [m]

1st phase (P1) 36’’ 2162 2258 96

2nd phase (P2) 26’’ 2258 3178 920

3rd phase (P3) 14-3/4’’ 3178 5206 2028

4th phase (P4) 8-1/2’’ 5206 5750 544

And the uncertainty associated with it is the double in order to accommodate the entire possible range,

respectively -44 to 52 meters. Based on the average thickness of Table 10 and the uncertainty associated

triangular distribution parameters were defined:

Table 11: Triangular distribution parameters

Formation Thickness Minimum [m] Mode [m] Maximum [m]

Formation 1 (Th1) 52 96 148

Formation 2 (Th2) 876 920 972

Formation 3 (Th3) 1984 2028 2080

Formation 4 (Th4) 500 544 596

The histograms and triangular cumulative distribution functions are presented below.

40

Figure 26: Triangular distributions and histograms of the formation thickness

For a further complexity case scenario of the formation thickness a geological model was built in geophysics

modeling and interpretation with the software Petrel® (©2014 Schlumberger Ltd.) by using the average depth

of the datasets for a standard deepwater well (Table 9). This model generates surfaces using a fractal artificial

algorithm (defined in the software) to obtain a distribution for the thickness in each formation. The geological

model generated is shown in the figure below (Figure 27).

41

Figure 27: Geological model developed

The fractal algorithm is intended to generate the uncertainties associated with the horizons delineation. In

Figure 28 the thickness distribution functions and histograms as well as its descriptive statistics for each

formation are presented.

42

Figure 28: Geological model distributions and histograms of the formation thickness

4.3. SIMULATION METHODOLOGY

Three scenarios were defined with increasing complexity. The first scenario was made to allow the

model to convergence based in a standard well simulation for drilling operations time.

A second scenario was built to validate the model and to incorporate standard geological uncertainties from

the literature based uncertainties on the delineation of formation horizons.

A third complex scenario was set out to incorporate geological uncertainties based in a geological model

defined in seismic interpretation software according to the depths of the field data.

43

4.3.1. GENERAL SIMULATION APPROACH

The general approach (Figure 29) defined for the simulation was to obtain the productive time (in

days) and then sequential generate a non-productive time (in hours per day) for each productive day. The way

each productive time is generated differentiates each scenario, being either directly sampled (Scenario 1) or

obtained as a result of the sampling of other variables (Scenarios 2 and 3)

The non-productive time is generated from a marginal CDF and for the cases stated a conditional distribution is

used following the Bayesian Sequential Approach.

Figure 29: Simulation general approach

4.3.2. FIRST SCENARIO APPROACH

This scenario relies in a typical well simulation based in the uncertainties distribution for the different

drilling phases joint operations time. Assuming independency between each drilling phase the sum up of the

partial productive days of each phase generates the drilling time. Then the non-productive time is generated

for each productive day following from this point the general approach.

44

Figure 30: First scenario approach

4.3.3. SECOND SCENARIO APPROACH

For the second scenario the approach was to simulate drilling performances, rate of penetrations,

which are sampled along with the formation thickness from the triangular distributions (Figure 31) defined

above. This approach introduces the geological uncertainties based in the formation thickness distributions.

Figure 31: Second and Third scenario approach

To obtain the drilling operations time (PD), in days, equation 22 is applied.

𝑃𝐷 =𝑇ℎ

𝑅𝑂𝑃 (22)

As defined before each phase was disaggregated in individual operations. In order to model the casing

cementing & others operations time (PC&O) it was generated a time for these operations based on the

distributions defined by the parameters presented in Table 7.

The productive time (PT) is obtained by summing all the individual operations time following Equation 23. It is

assumed the independency between the random variables, PD and PC&O.

𝑃𝑇 = 𝑃𝐷 + 𝑃𝐶&𝑂 (23)

45

From this point on the general non-productive time generation approach was followed.

4.3.4. THIRD SCENARIO APPROACH

This approach follows in all manners the second approach except the way how the thickness

distribution was obtained. In this scenario the thickness distribution was obtained from the geological model

defined in the seismic interpretation software. This geological model was characterized based on the average

depths of the standard deepwater pre-salt well (Table 9) defining the formation horizons, then by the

application of Equation 21 the formation thickness was obtained. A geological model was defined based in this

depth and in order to introduce the uncertainties a software defined fractal algorithm was applied and the

thickness distribution generated. From this step on this scenario follows the Scenario 2 approach by sampling

the ROP and the PC&O variables to generate the productive time. The non-productive time methodology was

applied as defined before.

4.4. SIMULATION ALGORITHM

As focused before a software model was developed in Matlab® (©2014 The MathWorks Inc.) by this

thesis author to allow for the modelling of parameters that could not be adjusted using a commercial software

(e.g. @Risk) available in the market.

The main stream algorithm cycle relies in the generation of productive days (PT variable) followed by the

generation of non-productive hours for each of those days (NPT variable). In each scenario the productive time

is generated, as mentioned before, by direct input variables distributions (first scenario) and indirectly by

sampling other input variables (Thickness, ROP and Casing, Cementing & Others) to achieve the productive

time (second and third scenario).

The non-productive time generation relies in conditional distributions for specific cases where the NPT

variables assume the value of 0 (0 hours NPT) and 24 (24 hours NPT). For this the algorithm generates

consecutive days for each case (NPT0 and NPT24 variables) from conditional distributions (NPT0f and NPT24f

CDF’s). The productive time (PT) and all the non-productive time (NPT, NPT0 and NPT24) are sum to define the

drilling time (DT). From one cycle outputs NPT percentage (NPT%) is determined and from the simulation cycle

(nsimulations) an average of NPT percentage (AvgNPT%) is obtained. At the end of the iteration cycle

(niterations) DT histograms and cumulative distribution functions are generated and variance of NPT

percentage is calculated.

The algorithm workflow is presented below (Figure 32).

46

Figure 32: Algorithm workflow chart

47

4.4.1. CONVERGENCE OF THE MODEL

In order to check the convergence of the model a series of runs were performed and convergence

parameters were evaluated.

The parameter chosen to evaluate the convergence was the variance of the non-productive time average

(VarNPT%) that reflects the stationarity of the first order momentum, the mean (AvgNPT%). This variance was

determined at the end of the simulation, and the convergence study was performed by increasing the number

of simulations (nsimulations) for a fix number of iterations (niterations=100) as shown in the Figure 32. The

choice for fixing the number of iterations was the continuous divergence due to the continuous increasing of

histogram classes, so in order to avoid a fixed number of the evaluated classes was set. The convergence

evaluation was based on the decreasing variance at some point that the computational cost versus the benefit

of the extra simulations is not worthy. The full results report is presented in Table B-1.

Figure 33: Convergence of the algorithm

From the graphical analysis it was set 10,000 simulations (log10(nsimulations)=100) as the reference number of

Monte Carlo cycles necessary to produce trustworthy results. The relation between cycles, simulations and

iterations is the following:

𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑐𝑦𝑐𝑙𝑒𝑠 = 𝑛𝑖𝑡𝑒𝑟𝑎𝑡𝑖𝑜𝑛𝑠 × 𝑛𝑠𝑖𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛𝑠 (24)

48

49

5. RESULTS AND DISCUSSION

In this chapter is presented the validation of the model, the main achievements of the simulation

through comparison between different scenarios results and the risk analysis performed.

5.1 VALIDATION OF THE MODEL

In order to perform the validation of the proposed methodology were considered two test cases: two

wells (Well #8 and Well #9) from a different dataset but drilled by the same standard rig B and the broader

average of non-productive time percentage (AvgNPT%) of the same rig.

For the first case it is intended for the simulation to achieve the range of the well data, drilling time and non-

productive time, knowing that these two wells are independent realizations. To feed the simulator formation

thickness input values were defined based on drilled depths (ΔD). Drilling performances (ROP) and the casing,

cementing and others operations (PC&O) were generated based on distribution described above, and also

defined as inputs for the simulation. For instance for the first phase the drilled depth (ΔD) was 64 m, being this

the depth difference between the starting point, sea bottom (WD=2162 m), and the ending point of drilling

phase one (2226 m). The well data is presented in the table below (Table 12).

50

Table 12: Well data for validation test from a different dataset of the standard rig B

Phase Operation

Well #8 Well #9

Depth [m] ΔD [m] Depth [m] ΔD [m]

1st Phase

Drill 36’’ 2226

64

2236

74

Set Csg 30’’ 2216 2226

2nd Phase

Drill 26’’ 3009

783

3325

1089 Set Csg 20’’ 2999 3315

Set BOP 2135 2184

3rd Phase

Drill 14-3/4’’ 4769

1760

4987

1662

Set 10-3/4’’ 4759 4977

4th Phase

Drill 8-1/2’’ 5001

232

5459

472 Set Liner 7’’ 4991 5449

Abandonment 2135 2184

Total Drilled Depth [m] 2839 3297

Total Duration [days] 158.0 137.0

NPT [days] 41.7 43.0

NPT% 26.1% 31.4%

As the convergence study suggests 10,000 simulations were run and the drilling time histogram and cumulative

distribution function are presented below (Figure 34). It is also shown the simulation statistical parameters: the

number of samples (#Samples); the drilling time mean (Mean); the drilling time standard deviation (Stdv); the

maximum (Max) and the minimum (Min) values in the drilling time sample set; the drilling time sample set

percentiles 10, 50 and 90 (P10, P50 and P90); the average percentage of non-productive time (AvgNPT%).

51

Figure 34: Well #8 simulation results (above) and Well #9 simulations results (below)

52

These two wells (Well #8 and Well #9) presented a deviated behavior, as shown in the Table 13. In

Well #8 158 days were spent to drilling a depth of 2839 m with 41.7 NPT days (26.1 NPT%). This well follows

the simulation results P90, 153.2 days which 90% of the outcome falls. The Well#9 is deeper with 3297 m

drilled in 137 days in which 43 are non-productive days (31.4 NPT%). This well follows the median (P50) of the

outcome with 140.6 days. Noting that Well#8 spends more time to drill (158 days) a shorter depth (2839 m)

with less inefficiencies (41.7 NPT days) when compared with Well#9, although this deviated behavior follows

within the simulation results range. The NPT% prediction accounts for all simulation runs representing an

average value. This model cannot reproduce the single project NPT% but only the long term rig performances,

although the wells average NPT% ((26.1% + 31.4%) / 2 = 28.8%) tends to the simulation outcome average

((28.5% + 28.8%) / 2 = 28.7%).

Table 13: Validation results

Statistical parameters

Well data Simulation data

Well #8 Well #9 Well #8 Well #9

AvgDT [days] 158.0 137.0 120.6 150.5

AvgNPT [days] 41.7 43.0 34.7 43.4

AvgNPT% 26.1% 31.4% 28.5% 28.8%

P90 [days] - - 153.2 194.2

P50 [days] - - 116.4 140.6

P10 [days] - - 90.2 110.0

For the second validation case it was taken into account the average non-productive time percentage

(AvgNPT%) of the standard rig B operating in the representative field (Table A-4) and the model output average

of NPT%. In the two years data for the average NPT% of rig B accounts for 29.1% and the simulation output

accounts for an average around 28.9%1.

1 Based on the average percentage of NPT determined on the convergence study for 10,000 simulations.

53

5.2. RESULTS FROM DIFFERENT SCENARIOS

5.2.1. SIMULATION RESULTS

An important result is shown from the drilling operations time (PD), casing cementing and others

operations time (PC&O) and the sum of them drilling productive time (PT) simulation. This is an example for the

second scenario approach in a drilling phase simulation where the geological uncertainties effect can be

observed. It is noted the long right tail for the drilling time representing the long durations caused by

undesirable events mainly due to the drilling performance and geological uncertainty since it was determined

from the quotient of the formation thickness and ROP distributions (Equation 22).

Figure 35: Drilling operations time (up left), casing, cementing and others operations time (up right) and drilling productive time (down)

54

It is shown in the figure above, as explained before, the asymmetry caused by the drilling operations time in

which relies the geological uncertainty.

5.2.2. RISK ANALYSIS RESULTS

As it was mentioned before the objective of risk analysis is to deliver the entire outcome to decision

makers proper evaluate and manage the risk.

According to the results for each case scenario simulations a risk analysis was performed in order to preview

the costs associated with a certain risk. For that an average dayrate (437000 USD/day, Table 2) from the drilling

rig used (semisubmersible standard rig B) to perform the actual wells was considered.

For each scenario a certain number of simulations (Table B-2) were performed and one of them was chosen to

realize the risk analysis2. It is shown on Figures 36, 37 and 38 the well simulation results and its statistical

parameters as the risk analysis results with the time/cost values above which a certain percentage of the

outcomes falls, quantifying by this way the risk.

2 Noting that will be applied both definitions of percentiles, i.e. x is the value below which certain percentage of the outcomes fall (simulation results) and x being the value above which certain percentage of the outcomes fall (risk analysis), e.g. the P90 of the simulation results is equivalent to P10 of the risk analysis.

55

Figure 36: Risk analysis for First Scenario results

Figure 37: Risk Analysis for Second scenario results

56

Figure 38: Risk analysis for Third scenario results

5.3. DISCUSSION OF THE RESULTS

Although the validation wells comprises abnormal behavior the data is within the range of the

simulation outcome validating the model. The lack of data to proper validate the model comprises the

validation.

It is important to point out that the approach followed and explained in the chapter before produces this

broader average near the real average of the study rig, i.e. from the NPT of a single project data (Table A-3) it

was possible to generate the same average NPT% for the two years activity of the rig (Table A-4). This is an

important result since the simulator with a short time frame can forecast the longer time frame of the standard

rig B operations performance, showing the Bayesian Sequential Approach is a reliable method for the NPT

simulation.

57

As expected the simulation results tends to have a normal behavior as a consequence of the input distributions

shape, although it is important to pointed out the asymmetry of the outcome distribution when the geological

uncertainties were added to the model. Both approaches for the introduction of the geological uncertainties

(Scenarios 2 and 3) ended at the same result. When the geological uncertainty was modelled by a geological

framework defined by thickness distribution from a geological model (Scenario 3) compared to the literature

based uncertainty (Scenario 2) the impact on time/costs was minimum although with a more complex

simulation. It may be due to the normal and triangular distribution follow the same trend with most likely

values to be near the mean of the samples, only differing in the extreme values where the probability of

occurrence in the normal case is low. As it is shown on Table 14 the range between the P90-P50 and P50-P10,

the skewness and the mean of the drilling time are almost the same in both scenarios.

Table 14: Statistical parameters comparison between scenario 2 and 3

Statistical parameters Scenario 2 Scenario 3

Mean [days] 166.47 165.91

Stdv [days] 54.84 54.71

Skew 2.49 2.51

P50 [days] 154.38 153.83

P50-P10 [days] 34.15 34.00

P90-P50 [days] 61.00 62.19

Although this identic result of Scenarios 2 and 3 an important synergy can be made by the E&P companies

which for the reservoir characterization need to generate geological models. From this geological models

distribution thicknesses can be retrieved and introduced into the drilling time simulation model potentiate the

inner synergy of these companies.

Overall the risk analysis shows that by introducing uncertainties, from Scenario 1 to Scenario 2 the drilling

time/costs, assuming for instance 10% chances (P90) have increased from 183.96 or more to 215.38 days or

more. It should be noted the right tail in Scenario 2 and 3 (Skew of 2.49 and 2.51) of the histogram is due to the

lithology miss predicting or the worst case drilling performance.

The increasing in time/costs can be quantified being this a remarkable result of this simulation model. For

instance there is a 10% probability (P90) of the well costs 80.39 MMUSD or more in the Scenario 1 and when

the geological uncertainty is introduced this value increases to 94.12 MMUSD or more in the Scenario 2. This

increasing cost represents the added risk that was so far underestimated.

58

The introducing of geological uncertainties assess a risk that can overbudget any project since the extreme

consequences are wellbore control events due to pore pressure miss prediction which are determined based in

horizons delineation and fluid contacts (gas-oil contact and oil-water contact).

59

6. CONCLUSIONS AND FURTHER DEVELOPMENTS

The Oil&Gas industry faces nowadays challenges to maintain its sustainability ratios by adding reserves

to their portfolios in complex exploration ventures where decision makers must decide under uncertain

conditions with high risks associated to the probability of total loss of the investment capital. This thesis

presented a new approach to deal with geological uncertainties which consequences were underestimated so

far, quantifying its risk.

As specified in the objectives for this thesis a final assessment of the achievements is done below:

Development of a simulation algorithm designed in Matlab® validated and convergence study

performed.

Introduction and evaluation of geological uncertainties in well simulations.

Method applied for the NPT simulation (Bayesian Sequential Approach) deliver trustworthy results.

As said before, the introduction of geological uncertainties in a well simulation and its results is the core

achievement of this thesis and enhanced the possibility to integrate all the information, following the actual

trend of Oil&Gas companies to increase intra-company synergies in order to have a broader knowledge of

projects. The introduction of geological uncertainties in a well simulation is a brand new appliance needing to

be more tested and validated with more field data.

Also the methodology applied prompted reliable results by the Bayesian Sequential Approach of the NPT for

the extreme classes proper generate the long term process continuity inefficiencies of the rig in study.

The simulation algorithm developed for well simulation deliver the expected results as any commercial

software, having the capability to be adjustable. To assess the performance of the algorithm a convergence

study and validation was carried out with reliable results.

For conclusion the objectives proposed to develop a risk analysis for a well in a deepwater pre-salt region

considering the geological uncertainties using an own developed algorithm were achieved.

It is specified below further developments for the enhancement of this thesis by enhancing the simulation

model to introduce other uncertainties:

Perform sensitivity analysis to better understand the impact of each uncertainty in the final outcome.

Enhanced the model with more data from other operations such as logging and completion.

60

Take into account in the risk analysis the specification of the type of well simulation for each kind of

well, exploratory, appraisal, development whose objectives changes considerably.

The experience of the crew is a critical factor to reducing the rig inefficiencies so it is important to

consider the staff experience as an uncertainty using learning curves (Figure 16);

To proper validate more data is necessary being this a critical validation limitation;

Since the biggest concern are due the ineffiencies of the drilling rigs it recommended to further

analyze this topic by disaggregate the NPT% in their components (Figure 18) in order to capture its

individual impact using the Bayesian sequential approach.

Introduction of uncertainties defined as conditional distributions for wellbore instability hazards

considering the marginal distribution of a well control event.

61

REFERENCES

Akins, W. M., Abell, M. P., Diggins, E. M. (2005), Enhancing Drilling Risk and Performance Management Through

the Use of Probabilistic Tme and Cost Estimating, paper SPE/IADC 92340, presented at SPE/IADC Drilling

Conference, Amsterdam, Holland.

Belaid, Fateh, De Wolf, Daniel (2009), Stochastic Evaluation of Petroleum Investment Projects using Monte

Carlo Simulation, University of Littoral Côte d’Opale, France.

Bilgesu, H. I., Tetrick, L. T., Mohaghegh, S., Ameri, S. (1997), A New Approach for the Prediction of Rate of

Penetration (ROP) Values, paper SPE 39231, presented at SPE Eastern Regional Meeting, Lexington, KY, USA.

Chambriard, M. (2010), Exame e Avaliação de Dez Descobertas e Prospectos Seleccionadas no Play do Pré-sal

em Águas Profundas na Bacia de Santos, Brasil, Gaffney Cline & Associates Inc., pp 26.

Cochener, Jonh (2010), Quantifying the Drilling Efficiency, Office of Integrated Analysis and Forecasting, EIA.

Coelho, D. K, Roisenberg, M., de Freitas Filho, P. J. & Jacinto, C. M. C. (2005), Risk Assessment on Drilling

Operations in Petroleum Wells using a Monte Carlo and Neural Network Approach, Winter Simulation

Conference.

Cowan, J. V. (1969), Risk Analysis as Applied to Drilling and Developing an Exploration Prospect, paper SPE 2583

presented at 44th SPE Annual Fall Meeting of AIME, Denver, CO, USA.

Cunha, J. C., Demirdal, B., Gui, P. (2005), Use of Quantitative Risk Analysis for Uncertainty Quantification on

Drilling Operations – Review and Lessons Learned, paper SPE 94980, presented at SPE Latin America and

Caribbean Petroleum Engineering Conference, Rio de Janeiro, Brazil.

Daly, Mike (2010), Key Technologies for Finding and Developing Deepwater Resources, World National Oil

Companies Congress, London, UK.

Deepwater Horizon Accident Investigation Report (2010), BP Safety and Operations Commission.

Deepwater Horizon Losses Sting Insurers and Reinsurers as Hurricane Season Looms Report (2010), Moody’s

Investor Services, London.

Farinha, R. (2013), Risk Assessment in Pre-salt Drilling Operations, Master Thesis in Mechanical Engineering,

Instituto Superior Técnico, University of Lisbon.

Ferentinos, Jonh (2013), Global Offshore Oil and Gas Outlook, Infield Systems / Global Offshore Oil and Gas

Outlook, Infield Systems.

62

Goosens, G. J. H. (2012), The Big Oil Spill: The Market Value Consequences of Deepwater Horizon Disaster,

Master Thesis in Finance, Tilburg School of Economics and Management.

Graham, Bob, Reilly, William K., Beinecke, Frances ,Boesch, Donald F., Garcia, Terry D., Ulmer, Fran (2011),

Deep Water: The Gulf Oil Disaster and the Future of Offshore Drilling - Report to the President, National

Commission on BP Deepwater Horizon Oil Spill and Offshore Drilling.

Guerreiro, Luis (2012), Reserves Evaluation, Instituto Superior Técnico, University of Lisbon.

Howard, Alex W., Harp, Alan B. (2009), Oil and Gas Company Valuations, Business Valuation Review, American

Society of Appraisers, Vol. 28, No. 1.

International Energy Outlook (2013), Energy Information Administration, U.S. Department of Energy.

Kaiser, Mark J., Snyder, Brian, Pulsipher, Allan G., (2013), Offshore Drilling Industry and Rig Construction Market

in the Gulf of Mexico, Coastal Marine Institute, U.S. Department of Interior.

Mostafavi, V., Hareland, G., Aadnoy, B. S. (2011), Assessment and Mitigation of Drilling Risks Using ROP Model

Coupled with Monte Carlo Simulation, paper ARMA 11-128, presented at 45th US Rock Mechanics /

Geomechanics Symposium, San Francisco, CA, USA.

Murtha, J. A. (1997), Monte Carlo Simulation: Its Status and Future, paper SPE 37932, presented at Annual

Technical Conference and Exhibition, San Antonio, TX, USA.

Murtha, J. (2001), Risk Analysis for the Oil Industry, Article Supplement to Hart’s E&P.

Newendorp, P. D., Root, P. J. (1968), Risk Analysis in Drilling Investments, Journal of Petroleum Technology, Vol.

20, No. 6, pp. 578-585.

Newendorp, P. D., Campbell, John M. (1975), Risk Analysis – Is it Really Worth the Effort, paper SPE 5578

presented at 50th SPE Annual Fall Meeting, Dallas, TX, USA.

Newendorp, P. D. (1983), A Strategy for Implementing Risk Analysis, paper SPE 11299, presented at the SPE

Hydrocarbon Economics and Evaluation Symposium, Dallas, TX, USA.

Ostebo, R., Tronstad, L., Fikse, T. (1991), Risk Analysis of Drilling and Well Operations, paper SPE/IADC 21952,

presented at SPE/IADC Drilling Conference, Amsterdam, Holland

Peterson, S. K., Murtha, J. A., Schneider, F. F. (1993), Risk Analysis and Monte Carlo Simulation Applied to the

Generation of Drilling AFE Estimates, paper SPE 26339, presented at SPE Annual Technical Conference,

Houston, TX, USA

63

Peterson, S. K., Murtha, J. A., Roberts, R. W. (1995), Drilling Performance Predictions: Case Studies Illustrating

the Use of Risk Analysis, paper SPE/IADC 19364, presented at SPE/IADC Drilling Conference, Amsterdam,

Holland.

Pritchard, David M., Kotow, Kenneth J. (2011), The New Domain in Deepwater Drilling: Applied Engineering and

Organizational Impacts on Uncertainties and Risk, Deepwater Horizon Study Group.

Robertson, S., Westwood, R. (2013), Global Offshore Prospects, presented at Energy Institute, London, UK.

Stockman, L., (2011), Reserves Replacement Ratio in a Marginal Oil World: Adequate Indicator or Subprime

Statistic, Oil Change International.

Suslick, Saul B., Shiozer, Denis, Rodriguez, Monica R. (2009), Uncertainty and Risk Analysis in Petroleum

Exploration and Production, Terrae, Vol. 6, No. 1, pp. 30-41.

The World Deepwater Market Forecast (2014), Douglas-Westwood, London, UK.

The State of NPT on High Specification Offshore Rigs (2010), First Annual Benchmarking Report, Athens Group.

Vinod, A. K., Kundan, Ashani, Kumar, Manoj, Kalpande, Viktrant, Pande, Rakhi (2013), Prediction of Pre-Drill

Well Cost and Scope of NPT Management in Shallow Water, presented at 10th Biennial International

Conference & Exposition, Kochi, India.

World Development Drilling & Production Forecast (2014), News Release, Douglas-Westwood, London, UK.

64

65

APPENDIX

All the data considered for this dissertation is presented in this chapter.

In the Appendix A is presented all field data retrieve from Farinha (2013) and the calculations to achieve some

variables parameters.

In Appendix B are all the convergence study, validation simulation and risk analysis results.

66

APPENDIX A

Table A-1: Depth and time duration for each phase of wells in a representative field

Phase Operation

Well #1 Well #2 Well #3 Well #4 Well #5 Well #6 Well #7

Depth

[m]

Time

[days]

Depth

[m]

Time

[days]

Depth

[m]

Time

[days]

Depth

[m]

Time

[days]

Depth

[m]

Time

[days]

Depth

[m]

Time

[days]

Depth

[m]

Time

[days]

1st Phase Drill 36’’ 2236 2.5 2214 2.5 2254 2.5 2216 1.8 2309 3.3 2313 2.6 2264 2.6

Set csg 30’’ 2226 1.8 2204 1.6 2244 2.3 2206 2.1 2299 2.2 2303 1.7 2254 1.9

2nd Phase

Drill 26’’ 3445 8.0 3096 6.3 2977 7.4 3298 7.3 3091 5.1 3340 6.7 3000 5.1

Set csg 20’’ 3435 4.6 3086 3.8 2967 3.8 3288 6.0 3081 2.4 3330 3.3 2990 3.4

Set BOP 2169 3.8 2140 4.7 2172 3.9 2106 5.9 2120 8.3 2230 3.8 2200 3.4

3rd Phase Drill 14-3/4’’ 6003 22.1 5130 30.5 4912 24.1 4890 19.0 5014 15.7 5395 20.9 5100 38.6

Set csg 10-3/4’’ 5993 30.8 5120 20.7 4902 8.1 4880 10.4 5004 16.4 5385 10.7 5090 9.8

4th Phase

Drill 8-1/2’’ 6773 34.8 5597 27.0 5316 26.6 5501 34.0 5223 51.0 6225 38.6 5618 51.4

Set liner 7’’ 6763 3.7 5587 3.2 5306 3.1 5491 5.9 5213 7.3 6215 4.0 5608 4.2

Abandonment 2169 4.3 2140 4.0 2172 6.1 2106 6.3 2120 4.9 2230 6.7 2200 6.5

67

Table A-2: Drilling performance for each phase of wells in a representative field

Phase Operation Well #1 Well #2 Well #3 Well #4 Well #5 Well #6 Well #7

[m/day] [m/day] [m/day] [m/day] [m/day] [m/day] [m/day]

1st Phase Drill 36’’ 29.60 20.80 36.80 30.00 44.55 58.08 39.23

2nd Phase Drill 26’’ 151.13 140.00 97.70 148.22 153.33 153.28 144.31

3rd Phase Drill 14-3/4’’ 115.75 66.69 80.29 83.79 122.48 98.33 54.40

4th Phase Drill 8-1/2’’ 22.13 17.30 15.19 17.97 4.10 21.50 10.08

Exemplia gratia: Determination of 2nd phase drilling Rate of Penetration (ROP) based on well data (Table A-1).

𝑅𝑂𝑃 =𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑟𝑢𝑛 (𝑚𝑒𝑡𝑒𝑟𝑠)

𝑡𝑖𝑚𝑒 (𝑑𝑎𝑦𝑠)=3445 − 2236

8= 151.13 𝑚/𝑑𝑎𝑦

68

Table A-3: Non-productive time of standard rig B by day

Day NPT(h) Day NPT(h) Day NPT(h) Day NPT(h) Day NPT(h) Day NPT(h) Day NPT(h) Day NPT(h) Day NPT(h) Day NPT(h)

1 4 23 24 45 0 67 2 89 24 111 6 133 0 155 0 177 8 199 2

2 23 24 24 46 0 68 3 90 24 112 0 134 0 156 0 178 0 200 0

3 2 25 24 47 8 69 1 91 24 113 0 135 0 157 0 179 0 201 0

4 0 26 24 48 24 70 0 92 24 114 2 136 9 158 9 180 0 202 0

5 0 27 24 49 24 71 20 93 24 115 0 137 4 159 4 181 0 203 24

6 0 28 24 50 24 72 24 94 24 116 0 138 3 160 3 182 0 204 24

7 0 29 24 51 24 73 24 95 24 117 0 139 2 161 2 183 0 205 0

8 0 30 24 52 24 74 24 96 24 118 1 140 0 162 0 184 1 206 3

9 18 31 24 53 24 75 24 97 24 119 0 141 1 163 0 185 0 207 8

10 6 32 24 54 24 76 24 98 24 120 0 142 0 164 0 186 0 208 12

11 0 33 24 55 24 77 19 99 13 121 0 143 0 165 0 187 3 209 8

12 9 34 24 56 24 78 15 100 0 122 0 144 2 166 0 188 15 210 14

13 19 35 24 57 24 79 6 101 0 123 0 145 1 167 0 189 1 211 4

14 1 36 0 58 24 80 5 102 0 124 2 146 0 168 0 190 10 212 0

15 2 37 14 59 24 81 13 103 3 125 0 147 0 169 0 191 8 213 0

16 0 38 13 60 14 82 24 104 0 126 1 148 1 170 0 192 1 214 0

17 1 39 19 61 4 83 24 105 0 127 2 149 10 171 0 193 2 215 7

18 24 40 24 62 0 84 24 106 2 128 2 150 8 172 1 194 0 216 0

19 10 41 24 63 8 85 24 107 0 129 24 151 0 173 0 195 19 217 1

20 0 42 16 64 1 86 24 108 1 130 17 152 0 174 0 196 2 218 3

21 0 43 3 65 0 87 24 109 0 131 0 153 0 175 16 197 0 219 5

22 18 44 0 66 0 88 24 110 0 132 0 154 1 176 18 198 0 220 11

69

Table A-4: Total non-productive time for each standard rig in a representative field

Rig AvgNPT% 2011 2012

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

A 33.6 100.0 100.0 39.7 10.1 15.5 27.6 4.0 54.1 7.9 44.0 40.3 20.3 67.6 9.5 11.9 47.1 53.3 26.4 5.1 21.1 9.0 31.0 45.0 15.4

B 29.1 8.6 18.0 7.7 9.2 26.3 3.7 9.1 67.7 22.0 16.6 71.2 62.8 64.4 9.4 5.0 14.2 20.0 29.9 38.0 72.2 10.1 21.0 2.0 89.8

C 25.6 9.7 12.3 27.3 4.4 5.3 47.8 30.0 40.4 21.7 54.0 50.3 40.9 48.6 8.3 5.3 7.4 27.8 10.6 18.8 31.9 28.8 10.0 28.0 45.3

D 23.3 25.1 14.4 5.9 46.3 31.3 25.6 59.4 16.3 57.5 30.0 13.3 17.3 16.3 13.9 32.3 6.6 13.9 14.4 12.6 12.2 23.1 22.0 20.0 26.6

E 23.2 - - - - - - - - - - - - - - 1.6 24.4 21.2 6.6 17.2 40.6 13.8 42.7 14.8 49.0

70

APPENDIX B

Table B-1: Convergence of the model

niterations 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100

nsimulations 10 20 30 40 50 60 70 80 90 100 200 300 400 500 600 700 800 900 1000

ncycles 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 20000 30000 40000 50000 60000 70000 80000 90000 100000

AvgNPT% 28.74 28.93 29.00 28.83 28.90 28.85 28.93 28.88 28.94 28.90 28.83 28.90 28.95 28.91 28.90 28.84 28.89 28.87 28.91

VarNPT% 3.4987 1.3955 0.9160 0.6396 0.5680 0.5099 0.3625 0.3233 0.2525 0.2978 0.1604 0.1008 0.0832 0.0474 0.0439 0.0492 0.0434 0.0311 0.0295

71

Table B-2: Simulation results

FIRST SCENARIO SECOND SCENARIO THIRD SCENARIO

72

FIRST SCENARIO SECOND SCENARIO THIRD SCENARIO

73

Table B-3: Risk analysis results

FIRST SCENARIO SIMULATION #1 SECOND SCENARIO SIMULATION #1 THIRD SCENARIO SIMULATION #1

74

FIRST SCENARIO SIMULATION #2 SECOND SCENARIO SIMULATION #2 THIRD SCENARIO SIMULATION #2

75

FIRST SCENARIO SIMULATION #3 SECOND SCENARIO SIMULATION #3 THIRD SCENARIO SIMULATION #3

76

FIRST SCENARIO SIMULATION #4 SECOND SCENARIO SIMULATION #4 THIRD SCENARIO SIMULATION #4