Response surface optimization for operating conditions in comprehensive sagd performance

The SAGD performance was investigated based on the variables of reservoir properties such as thickness, porosity, permeability, oil saturation, viscosity, rock thermal conductivity, alon

Response Surface Optimization for

Operating Conditions in Comprehensive

SAGD Performance

NGUYEN XUAN HUY

The Graduate School of Sejong University Department of Energy and Mineral Resources Engineering

Response Surface Optimization for

Operating Conditions in Comprehensive

SAGD Performance

NGUYEN XUAN HUY

A Doctoral Thesis Submitted to the Department of Energy and Mineral Resources Engineering and Graduate School of Sejong University

in partial fulfillment of the requirements for the degree of Doctor of Engineering

May 2012

Approved by Prof Wisup Bae Major Advisor

This certifies that the dissertation of Nguyen Xuan Huy

is approved

Professor Taewoong Chung

Professor Wisup Bae

Professor Jonggeun Choi

Professor Kyungiun Jun

Professor Myung Jin Nam

The Graduate School of Sejong University May, 2012

Dedication

To

my parents and my younger sister and brother

Acknowledgment

My name is Huy Xuan Nguyen I have over 10 years experience in the area of petroleum geology and reservoir simulation in the oil and gas industry I hold B.Eng (2001) and M.Eng (2004) degrees in petroleum engineering and MBA degree (2008) in petroleum economic from Ho Chi Minh University of Technology as considered the top university with the high quality education in Vietnam I have positioned the lecturer in teaching undergraduate and science research at Faculty of Geology and Petroleum Engineering, Ho Chi Minh City University of Technology since 2003 In 2009, I received the PhD scholarship program in petroleum engineering from Sejong University under the supervisor of Professor Wisup Bae

Currently, my research interested in the section of petroleum economic management, chemical EOR flooding, thermal oil recovery processes, particularly the oil recovery improvement on SAGD process and the application innovative technologies to exploit the unconventional resources based on electromagnetic heating, nuclear energy, single-well SAGD, and operation optimization I am author and coauthor of more than 20 technical papers including SCI Journals, SPE, AAPG and international conferences around the world

I would like to express my special appreciation to my supervisor Prof Wisup Bae for kind support and academic valuable suggestions throughout my work

I also would like to express my sincere thank to the members of petroleum lab in Sejong University Ngoc T B Nguyen, Cuong Dang, Taemoon Chung, Tho N Tu, and Danh

H Nguyen for their generosity and suggestions Their assistances are essential in performing

my research successfully and have made my studying life here more enjoyable and priceless

By the fact of completing this thesis, I am immensely indebted to my parents, Nguyen Xuan Lang and Tran Thi Tuyet Nhung younger sister and brother They have encouraged and

nurtured in the development of my personality and support any decision and future career direction

Last but not least, I would like to express my sincere thank to my friends in Vietnamese Students Association in Korea for their generosity and help during study time in Korea

Abstract

The steam assisted gravity drainage (SAGD) process has proven to be an effective thermal recovery method for heavy oil and bitumen production However, there has been much dispute over the question of technical and economical risks The technical efficiency of the SAGD process depends on two important factors: reservoir properties and operating conditions The SAGD performance was investigated based on the variables of reservoir properties such as thickness, porosity, permeability, oil saturation, viscosity, rock thermal conductivity, along with operating variables as including preheating, injector/producer spacing, injection pressure, steam injection rate and subcool temperature In addition, the economic risks associate to the cost of initial investment for building ground facilities, operating costs, and the uncertainties of oil and gas prices The integration of economic and technical aspects for SAGD performance plays an important role in field operation Main problems to solve are how to design optimal operating conditions for a reasonable steam requirement with certain injection pressure to maximize economic feasibility under reservoir conditions

Recently, some innovative techniques based on the background SAGD operation have been applied such as conventional SAGD, Fast-SAGD, Hybrid SAGD, FA-SAGD Most previous literatures implemented sensitivity analysis and optimization of SAGD performance

by classical methods based on numerical simulations lead to a lack of confidence level and ignored interactions effects between considered parameters, which may cause low efficiency issues in a field operation In addition, the SAGD economic models have not fully information with limited consideration on few factors These restrictions can be avoided by the application design of experiment and response surface methodology to determine the optimal operating conditions for the production prediction Then, discontinuous SAGD technique was operated to control the amount of injected steam at several specific injection time intervals

The results showed that the effect of reservoir parameters on SAGD performance is the most important with order ranking as porosity, thickness, oil saturation, permeability, viscosity, and then interaction factors of reservoir properties Subsequent to injection pressure and steam injection rate have a greatest effect in operational parameters The results of this study showed uncertainties ranking of reservoir and operational parameters are a target for best choice on oil sand projects

The new concept of the discontinuous SAGD process is applied to three major formations of Alberta’s oil sands after optimal operation conditions based on response surface methodology The results showed that both oil recovery factor and economic profit are much higher than other techniques of Fast-SAGD and conventional SAGD process, especially the effective at deeper burial reservoirs of Clearwater and Bluesky formations Moreover, amount of steam injection rate and cumulative steam oil ratio (CSOR) reduced significantly to cause lower operating costs as steam cost, led to increase NPV as well as minimal environmental damages This study will help to improve heavy oil recovery with the minimal environmental damages and with lower production cost

Table of Contents

Abstract

List of Figures

List of Tables

List of Nomenclature and Abbreviations

Chapter 1 Introduction……… 1

1.1 Overview 1

1.2 Description of the problems……….2

1.3 Research objective and methodology……… 3

1.4 Literature Review………4

1.4.1 Geological characteristics in Alberta oil sands……….4

1.4.2 Athabasca oil sands……… …6

1.4.3 Cold Lake oil sands……… …7

1.4.4 Peace River oil sands………8

1.4.5 Lloydminster oil sands……….8

1.4.6 A review of the development of thermal recovery technology……….9

1.4.6.1 SAGD technique……… 9

1.4.6.2 Fast-SAGD technique……….…11

1.4.6.3 Hybrid SAGD technique……….13

1.5 The control of operating parameters under reservoir conditions………14

Chapter 2 Design of Experiment and Response Surface Methodology 2.1 Response surface methodology………18

2.2 Two-Level Factorial Designs………20

2.3 Two-Level Fractional Factorial Designs………20

2.4 Central Composite Design (CCD)……… …21

2.5 Box-Behnken design……… …22

2.6 Face Centred Central Composite Design (FCCD)………24

2.7 D-optimal design………24

2.8 Model adequacy checking ………25

2.8.1 Test for significant of regression………26

2.8.2 Residual analysis……….28

2.8.3 Scaling Residuals……… 29

2.8.4 Lack of Fit Test………31

2.9 Optimization….……… 32

Chapter 3: Effects of Reservoir Properties and Operating Conditions on SAGD Performance 3.1 The application D-Optimal design and RMS for sensitivity analysis……….36

3.2 Effects of reservoir variables………38

3.2.1 Porosity……….…38

3.2.2 Thickness ……….……39

3.2.3 Oil saturation….………39

3.2.4 Permeability….………40

3.2.5 Viscosity…….……… …40

3.2.6 Rock thermal conductivity……… 41

3.3 Effect of operational parameters……….…41

3.3.1 Vertical well spacing (IPS)……… 41

3.3.2 Injection Pressure………42

3.3.3 Steam Injection Rate……….……… 42

3.3.4 Subcool Temperature……… ……… …42

3.4 Conclusions……….……… ………43

Chapter 4 : Response Surface Optimization for Operating Conditions in Three Major Reservoirs of Alberta’s Oil Sand 4.1 Athabasca oilsands………52

4.1.1 Application of central composite face-centred design for optimizing the operating conditions….………52

4.1.2 Effect of operating parameters on the NPV.………55

4.1.3 Optimization of operating conditions by response surface methodology………56

4.1.4 Verification of predictive model……… …57

4.1.5 Comparison and the best choice for operating conditions in conventional SAGD process 4.1.6 Optimization for Fast-SAGD performance……….58

4.1.7 Optimization for discontinuous SAGD performance……… 60

4.2 Cold Lake oilsands………64

4.2.1Application of Box-Behnken design for optimizing the operating conditions….64 4.2.2 Effect of operating parameters on the NPV………66

4.2.3 Optimization of operating conditions by response surface methodology………… 68

4.2.4 Verification of predictive model……….69

4.2.5 Comparison and the best choice for operating conditions in conventional SAGD process……… 69

4.2.6 Optimization for Fast-SAGD performance……… 70

4.2.7 Optimization for discontinuous SAGD performance……… 72

4.3 Peace River oilsands………77

4.3.1Application of central composite face-centred design for optimizing the operating… 77

conditions 4.3.2 Effect of operating parameters on the NPV………79

4.3.3 Optimization of operating conditions by response surface methodology………81

4.3.4 Verification of predictive model………81

4.3.5 Comparison and the best choice for operating conditions in conventional SAGD process 4.3.6 Optimization for Fast-SAGD performance……….82

4.3.7 Optimization for discontinuous SAGD performance………85

Chapter 5: Summary, Conclusions and Recommendations………90

5.1 Summary ………90

5.2 Conclusions………91

5.3 Recommendations for future work……….93

References

List of Figures

1.1 The regions of Albertan Oil Sands, cross section and stratigraphic succession, 2008, AAPG

1.2 Typical viscosities of bitumen in three majors oil sands

1.3 The production mechanism of SAGD horizontal well pairs (NEB, 2004)

1.4 Operation of injection and production in SAGD process (NEB, 2004)

1.5 The Fast – SAGD process

1.6 Arrangement of wells in HSAGD and Fast-SAGD system

2.1 Sample experimental designs (a) 22 factorial design, (b) 32 factorial design, (c) central composite design and (d) face-centred cubic design

2.2 The points distribution of a Central Composite Design

2.3 Box- Behnken design

2.4 Geometry of Face Centred Central Composite for three variables

2.5 Normal probability plot of residuals

2.6 The desirability curve for the goal as minimum

2.7 The desirability curve for the goal as maximum

2.8 The desirability curve for the goal as maximum

2.9 The desirability curve for the goal as Within range

3.1 The order ranking of variables

3.2 Normal probability plot of NPV response

3.3 Effects of reservoir and operational parameters on NPV responses

4.1 The order ranking of factors affecting on NPV, Athabasca oilsands

4.2 Effects of operating conditions on NPV, Athabasca oilsands

4.3 Response surface plots, Athabasca oilsands

4.4 Cumulative oil in Athabasca oil sands

4.5 Cumulative SOR in Athabasca oil sands

4.6 Oil rates in Athabasca oil sands

4.7 The order ranking of factors affecting on NPV, Cold Lake Oilsands

4.8 Effects of operating conditions on NPV, Cold Lake oilsands

4.9 Surface response map, Cold Lake oilsands

4.10 Optimal operating conditions of CSS well in Fast SAGD, Cold Lake oil sands 4.11 Response Surface plots in Fast-SAGD, Cold Lake oil sands

4.12 Cumulative oil in Cold Lake

4.13 Cumulative steam oil rate in Cold Lake

4.14 Oil rate in Cold Lake

4.15 The order ranking of factors affecting on NPV, Peace River oilsands

4.16 Effects of operating conditions on NPV, Peace River oilsands

4.17 Surface response map in SAGD process, Peace River oilsands

4.18 Optimal operating conditions of CSS well in Fast SAGD, Peace River oil sands 4.19 Response Surface plots in Fast-SAGD, Peace River oilsands

4.20 Cumulative Oil in Peace River Oilsands

4.21 Cumulative SOR in Peace River Oilsands

4.22 Oil rates in Peace River Oilsands

List of Tables

1.1 Geological features of Cold Lake in Alberta (National Energy Board, 2000)

2.1 Coded factor levels for Box-Behnken designs for optimizations involving four and five factors

2.2 Comparison of efficiency of central composite design and Box-Behnken design

3.1 Variables and D-optimal design levels

3.2 The D-optimal design with 10 independent variables

3.3 ANOVA for response surface quadratic model

3.4 Regression coefficients of the predicted quadratic polynomial model.e surface quadratic model

4.1 Reservoir properties

4.2 Variables and CCF design levels, Athabasca oilsands

4.3 The CCF design with four independent variables, Athabasca oilsands

4.4 ANOVA for Athabasca oilsands

4.5 Estimated regression coefficients for NPV by using coded units

4.6 Optimization of operating conditions in conventional SAGD process, Athabasca Oilsands 4.7 Optimization of operating conditions in Fast SAGD process, Athabasca Oilsands

4.8 Steam injection mode in discontinuous SAGD process in Athabasca oilsands

4.9 Variables and experimental design levels, Cold Lake oilsands

4.10 Box-Benhken design with four independent variables, Cold Lake oilsands

4.11 ANOVA for Cold Lake Oilsands

4.12 Estimated regression coefficients for NPV by using coded units

4.13.Optimization of operating conditions in conventional SAGD process, Cold Lake Oilsands

4.14 Variables and experimental design levels in CSS well, Cold Lake

4.15 Full factorial design of CSS well in Fast-SAGD

4.16 Estimated regression coefficients for CSS well, Cold Lake oilsands

4.17 Optimal operating condition of CSS well, Cold Lake oilsands

4.18 Optimization of operating conditions in Fast SAGD processes, Cold Lake Oil sands

4.19 Steam injection mode in discontinuous SAGD process in Cold Lake oilsands

4.20 Variables and experimental design levels Peace oilsands

4.21 The CCF design with four independent variables, Peace River oilsands

4.22 ANOVA for Peace River oilsands

4.23 Estimated regression coefficients for NPV by using coded units, Peace River oilsands 4.24 Optimization of operating conditions in conventional SAGD process, Peace River Oilsands 4.25 Variables and experimental design levels in CSS well, Peace River Oilsands

4.26 Full Factorial design of CSS well in Fast-SAGD

4.27 Estimated regression coefficients for NPV by using coded units, Peace River oilsands 4.28 Optimal operating condition of CSS well

4.29 Optimization of operating conditions in Fast SAGD processes, Peace River Oilsands 4.30 Steam injection mode in discontinuous SAGD process in Peace River Oilsands

List of Nomenclature and Abbreviations

CMG Computer Modeling Group

CSS Cyclic Steam Stimulation

CSOR Cumulative Steam-Oil-Ratio

DOE Design of Experiment

dSAGD Discontinuous SAGD

FA-SAGD Foam-assist SAGD

Kv/Kh Vertical permeability/ Horizontal permeability

IP Injection Pressure

IPS Injector Producer spacing

MCS Monte Carlo Simulation

MSIR Maximum Steam Injection Rate

NPV Net Present Value

PERM Permeability

Poro Porosity

RSM Response Surface Methodology

SAGD Steam Assisted Gravity Drainage Process

Strap Subcool Temperature

of operating condition in oil sand projects

1.1 Overview

The vast reserves of oil sands deposits are trapped in shallow Alberta’s oil sands, with an estimated 1.7 trillion bbls of bitumen in place, as the third-largest proven crude oil reserve in the world, next to Saudi Arabia and Venezuela The estimated remaining recoverable from bitumen resource is only about 10% with current techniques

The conventional SAGD process is applied the most popular as technically effective of thermal recovery method (Butler, 2001) By using two horizontal wells are located at the bottom of reservoir, one injector located above the oil producer at short vertical distance, the heat from steam

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injected of injector can transfer upward to the top and sideways of reservoir effectively and production recovery mechanism based on the gravity driving force affecting on heated bitumen The Fast-SAGD process comprised two full SAGD well pairs and two CSS wells (Polikar, 2000), uses offset wells, which are placed horizontally about 50m away from the SAGD producer and each offset well These offset wells are operated alternatively as injector and producer When the steam chamber reaches up the top reservoir after operating SAGD well pairs, the CSS operation

is started at the first offset well The CSS operation at other offset wells will be started later with a certain schedule after the CSS operation at the first offset well

Discontinuous SAGD technology (dSAGD) is new concept based on the background of conventional SAGD process (Huy, 2012) In SAGD conventional technique, the injectors are continuously injecting steam into reservoir and continuously producing from the producers Instead

of continuing injected steam, injectors are operated the following Cyclic Steam Stimulation mode with certain difference standby time intervals as called discontinuous SAGD technique, while producers still keep working after preheating connection spacing between the wells

1.2 Description of the problems

The SAGD process is an effective thermal recovery method for heavy oil and bitumen production utilizing two parallel horizontal wells, one injector located above the oil producer at short vertical distance However, the high uncertainties of reservoir properties and operating conditions affected significant to oil recovery factor and profit Hence, both reservoir properties and operating parameters must be investigated clearly for making decision the best choice of oil sands project as well as operating conditions

Polikar (2000), Gong (2002) and Shin (2007) have conducted the optimization of SAGD process

by classical methods based on their numerical simulations and experiments However, there is a lack of confidence level in the optimized conditions because they didn’t determine the significance level of operational parameters and ignored interactions effects between considered parameters,

3

which may lead to low efficiency issues in a field operation These limitations of the classical method can be avoided by application design of experiment (DOE) and response surface methodology (RSM) that involves statistical design of experiments in which all factors are varied together over a set of experimental runs

In addition, there has been much dispute over the question of economic efficiency due to high capital investment, operating costs as steam cost, and the uncertainties of oil and gas prices The economic models in previous studies were not comprehensive enough and backward with limited consideration on only three factors such as steam cost, low bitumen price and discount rate That approach could significantly reduce the accuracy of economic evaluations and make it very difficult

to predict the best selection of process performance The integration of economic and technical aspects for SAGD operation plays an important role for success in field operation

Recently, some innovative techniques based on the background SAGD operation have been applied such as conventional SAGD, Fast-SAGD, Hybrid SAGD, FA-SAGD However, in practical, an increase oil recovery is not remarkable and, so using conventional SAGD process is still as common approach In this study, the author established a new operating process based on the background of SAGD called as discontinuous SAGD (dSAGD) The injectors are operated at specific difference time intervals in dSAGD The result proved that the dSAGD performance worked better than others were, the best way to maximize oil recovery, and minimal steam requirements and heat loss

1.3 Reaseach objective and methodology

This study describes the application of DOE and RSM to investigate the effect level of reservoir properties and operating parameters on the oil recovery factor and net present value Based on the economic perspective, the optimization of operating parameters is identified under uncertainties of reservoir conditions in three oil sands areas in Alberta: Athabasca, Cold Lake, and Peace River areas It was aimed to mitigate the risk of incomprehensive economic assessment on the process

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operation The study started with the using of DOE to screen the independent variables, and then insignificant variables were excluded from model before developing the optimal design by response surface methodology The main objective need to do as follow:

1 The appropriate DOE types were selected to design the initial numerous samples Reservoir simulation scenarios were run by CMG’s Star to estimate the amount of oil recovery, cumulative steam oil ratio (CSOR), produced water

2 The economic model was built on Excel spreadsheet with the input parameters of reservoir simulation results, the prices of oil and gas, capital costs, operating costs, non-gas cost and discount rate of 10%

3 Based on the net present value of analysis of variance in mathematic statistics, screening of the reservoir and operating parameters are conducted to chose the most significant variables and the sensitivity analysis The RSM was employed to search for promising designs The uncertainties of NPV were evaluated, and the optimization of operating conditions in SAGD and Fast-SAGD process was identified by building a surface response map

4 Comparison and evaluation the effect of low and high injection pressure in SAGD and SAGD and propose the best solutions for operating options

Fast-5 Subsequently, the most appropriate of these operating conditions are used for the optimization dSAGD process to find the optimal the specific intervals of steam injection time and standby time for the target of maximum oil recovery and minimum heated loss

6 Among of the conventional SAGD, Fast-SAGD and dSAGD process, let compare and select the best operating condition in three majors Alberta’s oil sands

1.4 Literature review

1.4.1 Geological characteristics in Alberta oil sands

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Canada’s resources of crude bitumen occur entirely within the province of Alberta and found in sand and carbonate sedimentary formations in three regions defined as the Athabasca, Cold Lake and Peace River Oil Sands Areas (Figure 1.1) These areas cover a minimum of 4.3 million hectares, 729 thousand hectares and 976 thousand hectares respectively The Athabasca formation including Grand Rapids formation are buried at upper depth ranges of 200-400 m and lower depth ranges of 270-470 m, Wabiskaw or McMurray formation are buried at Mineable depth ranges of 0-

120 m and In situ with depth ranges of 80-750 m The Cold Lake formations including Grand Rapids, Clearwater and McMurray are buried at depth ranges from 275-525 m, 370-500 m and 420-

600 m, respectively The Athabasca oil sands are composed of approximately 70% sand and clay, 10% water and from 0 to 18% heavy oil or bitumen (Deutsch and McLennan, 2003)

As result of the estimation of Canadian oil sands reserves, 44% of Canadian oil production was from oil sands, with an additional 18% being heavy crude oil, while light oil and condensate had declined to 38% of the total Oil sands represent as much as two-thirds of the world's total liquid hydrocarbon resource, with at least 1.7 trillion barrels in the Canadian Oil Sands (assuming a 10% recovery)

The characteristics of the bitumen and the reservoir properties of the oil sands is in large part a function of the degree of biodegradation that took place For the Peace River deposits, the oil migrated the shortest distance and were subjected to only a moderate degree of biodegradation, while for the Athabasca and the Cold Lake deposits, the migration distance was considerably farther and therefore these deposits were subjected to a greater degree of biodegradation (NEB, 2000) Some of the distinguishing characteristics of the three areas are:

+ The Peace River deposits contain bitumen in Mississippian carbonates, as well as in the Permian and Cretaceous sandstones;

+ The Athabasca deposit has the largest areal extent and contains bitumen in the Devonian carbonates and the Cretaceous sandstones; and,

6

+ The Cold Lake deposits contain bitumen only in the Cretaceous sandstones

1.4.2 Athabasca oil sands

The Athabasca oil sands deposit is the largest petroleum accumulation in the world, covering an area of about 46,000 km2 Most of the bitumen deposits are found within a single contiguous reservoir, the lower cretaceous McMurray-Wabiscaw interval (Mossop, 1980) The McMurray Formation lies over Devonian Formation, which is a layer of limestone, and is overlain by the Wabiscaw Member of the Clearwater Formation The Clearwater Formation is itself overlain by the

Figure 1.1 The regions of Albertan Oil Sands, cross section and stratigraphic succession, 2008,

AAPG

1.4.3 Cold Lake oil sands

The Cold Lake oil sands deposit in northern Alberta contains over 40 x 109 of bitumen in place

(Beattie, 1991) There are three formations starting from the bottom to up: McMurray, Clearwater, and Grand Rapids, belong to the members of the lower Cretaceous Mannville group All three formations contain bitumen, but the most laterally extensive and homogeneous deposits are in the Clearwater formation (MossoP et al., 1980) Southward from Athabasca, the relatively deep-water Clearwater shales change facies to a near-shore deltaic and foreshore/shoreface complex The most prospective targets include stacked distributary mouth bar sequences and non-marine fluvial and high-energy tidal sand flats deposits (Gingras, 2004) Upper Grand Rapids deposition largely represents brackish water near shore deposition overlying more normal marine conditions of the lower Grand Rapids and upper Clearwater (Benyon and Pemberton 1992)

The Clearwater sands are unconsolidated, clean, well-sorted, fine to medium grained, and have porosity between 14% and 35% The absolute permeability ranges of 0.5 – 2.0 D and oil saturation average of 70% PV The in-situ viscosity of the bitumen is about 100,000 cp (Figure 1.2) and is buried at depth ranges from 275-525 m, 370-500 m and 420-600 m, respectively (Table 1.1) Steam injection rates requires the high injection pressures to cause both localized fracturing and widespread PV increases in the formation

1.4.5 Lloydminster Area

The Lloydminster area of Alberta and Saskatchewan has been the focal point of heavy oil development for many years and geographically is the largest prospective area Heavy oil production is from the Mannville Group sediments, with the entire suite of Mannville Formation’s being prospective targets

of the uncertainty can be quantified by using the DOE and RSM in the geological site The distribution in a range of variables requires to be known

1.4.6.1 SAGD Technique

The SAGD is one of the most relevant in situ heavy oil recovery techniques in western Alberta owing to the huge amount of oil reserves accessible with this technique The conventional SAGD, introduced by Butler et al (1981) as shown in Figure 1.3, uses two horizontal wells, one injector

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and one producer Usually the producer is placed as low in the reservoir as possible, and the injector

is located several meters above the producer The horizontal wells have a length range from

500-1000 m SAGD depends on the combustion of natural gas that is used to generate steam The initial heating or preheating of the cold oil (heavy oil or tar) is very important to form the steam chamber The heat is transferred by conduction, convection and by latent heat of steam to the formation through injector and producer during the preheating period The heating is maintained from only the injector after putting the producer to normal operation

The injected steam will reduce the bitumen viscosity, and then the heated bitumen and condensed steam will flow down into the producer by gravity force The ceiling drainage can be seen during the steam chamber rise period The injected steam rises to the top of the reservoir and reduces bitumen viscosity, and the mobile bitumen and condensed water flow down into the producer

Figure 1.3: The production mechanism of SAGD horizontal well pairs (NEB, 2004)

The most expensive part of the SAGD operation is the steam generation Figure 1.4 shows the steam flow through the injector and as the bitumen is heated up, the oil is pumped through the producer to the surface

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Figure 1.4 Operation of Injection and production in SAGD process (NEB, 2004)

The steam-oil-ratio (SOR) is a measure of the thermal efficiency in SAGD High SOR results

in more natural gas combustion to generate the required steam, which has economic ramifications Optimizing the steam injection rate to reduce the SOR is imperative in any SAGD project Steam quality is another important factor that should be kept as high as possible, as low steam quality forms more condensate that flows toward the producer delivering only small amounts of heat to the oil During the preheating phase, the steam zone is expected to grow laterally Oil is drained down along the oil/steam interface to the production well

Some parameters influence the SAGD processes including reservoir depth, length of the horizontal drilling, vertical spacing between the well pair, steam injection rate, steam temperature, steam pressure and the pressure drop between the well pair,…The success of a SAGD project depends on the controlling these parameters to minimize the CSOR and maximize the COP

1.4.6.2 Fast-SAGD technique

The Fast-SAGD technique are combining the CSS and SAGD processes, uses offset wells, which are placed horizontally about 50 m away from the SAGD producer (Figure 1.5) and each

12

offset well These offset wells are operated alternatively as injector and producer When the steam chamber reaches the top of the reservoir after the SAGD operation, the CSS operation is started at the first offset well The CSS operation at other offset wells will be started later with a certain schedule after the CSS operation at the first offset well Shin (2005) suggested that there are at least two cycles of CSS at the offset wells, and each cycle is composed of three phases: injection period

of several months, soak period of a few weeks, and production period of several months Steam is injected at higher pressure and rate than those used in the SAGD operation, but the pressure is below the fracturing pressure of the formation

The Fast-SAGD process has the following features:

a The CSS operation from the offset well propagates the SAGD steam chamber sideways and also speeds up the recovery of bitumen;

b The high pressure steam injection at the offset well results in enhanced bitumen recovery from the SAGD producer due to steam drive effect caused by pressure difference between the SAGD injector and the offset well;

Figure 1.5 The Fast – SAGD process

1.4.6.3 Hybrid SAGD technique

Coskuner (JCPT, 2009) proposed a novel process called Hybrid SAGD The HSAGD process borrows the well configuration from the Fast-SAGD process However, the wells are operated very differently That is, initially CSS is conducted in a staggered pattern in both the SAGD injectors and the offset wells Because these wells now operate at the same pressure, the tendency for steam to bypass the reservoir between the wells is greatly reduced This initial staggered CSS operation is similar to an earlier investigation where it was observed that staggered horizontal wells with CSS exhibited improved performance compared to in-line horizontal wells with CSS

Once the steam chambers of individual wells (i.e offset wells and SAGD injectors) come into contact with each other, which occurs during the third cycle in the current study, the SAGD process commences by continuously injecting steam into the SAGD injectors and continuously producing from the SAGD producers and offset wells It is observed that HSAGD performs better than CSS in the Clearwater Formation, as will be shown later

The SAGD stage in the HSAGD process starts after a small number of CSS cycles (three cycles in this case) At this point, CSS alone could still continue to be an economically viable process, however, HSAGD produces more bitumen in less time, thereby increasing the economic attractiveness of the project

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Figure 1.6 Arrangement of wells in HSAGD and Fast-SAGD system

1.5 The control of operating parameters under reservoir conditions

As mentioned above, the SAGD performances depend on the uncertainties of reservoir properties and the reasonable controlling of operating parameters affected to production recovery The variables of reservoir properties such as thickness, porosity, permeability, oil saturation, viscosity, rock thermal conductivity, along with operating variables as including preheating, injector/producer spacing, injection pressure, steam injection rate and subcool temperature In order

to manage the uncertainties of oilsands project, the authors estimated hierarchical correlations between parameters on returns The clear understanding of reservoir characterization allows the engineers to the making decision for the best choice reservoirs to avoid risks in operating process Then, the reasonable design of operating conditions are how to achieve maximum NPV response

Shin (2007) have conducted optimization of SAGD process by classical methods based on their numerical simulations and economic indicators The operating conditions of Athabasca reservoirs were designed as I/P spacing of 5 m, steam injection rate of 700 m3/d at a maximum injection pressure of 1,500 kPa For Cold Lake reservoirs were determined to be: I/P spacing of 15 m and steam injection rate of 400 m3/d at a maximum injection pressure of 3,100 kPa For Peace River reservoirs were calculated to be: I/P spacing of 15 m and steam injection rate of 600 m3/d at a maximum injection pressure of 4,500 kPa Actually, the design spacing between injector and

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producer has significant affected on the reasonable control of injection pressure and steam injection rate to maximize oil recovery Therefore, the 10 kPa of difference between steam injection pressure and reservoir pressure is not enough for success for SAGD operation that proved insignificant incremental bitumen recovery lead to poor economic (Huy, 2011) However, a lack of reliability in optimal conditions due to do not determine the significance level of variables and ignored interactions effects between variables, which may lead to low efficiency issues in a field operation The Fast-SAGD process presented by Polikar et al (2000) that combines the SAGD and CSS processes CSS accelerates the growth of the steam chamber sideways Shin (2006) implemented the optimization of Fast-SAGD mentioned that the shallow Athabasca reservoirs should not applied for Fast-SAGD technique due to uneconomic, The Cold Lake and Peace River reservoirs could be conducted the Fast-SAGD with a minimum thickness of 15 m and 20m, respective However, based

on the reservoir thickness has not really reflected the comprehension the nature of Fast-SAGD operation instead of specific reservoir properties, especially the attention to the width of reservoir Compared to conventional SAGD, the Fast-SAGD process proved insignificantly incremental bitumen recovery as well as economic efficiency in Peace River oilsands (Huy, 2011)

The application of experimental design techniques in reservoir engineering studies is no longer new; numerous applications can read in the technical literature, especially road map the uncertainty

of some variables that measures the reservoir performance The selected model can also be used as a quick reference of comparison between the parameters of SAGD performances (Vanegas,2008)

C.Yang et at proposed a optimization method based on global optimization, Box-Behnken experimental design, response surface generation and Monte Carlo simulation technique that was performed to quantify the uncertainty of SAGD forecasts in terms of cumulative probability distribution of the NPV at different values of the SAGD design parameter They concluded that SAGD performance is improved by adjusting steam injection rate and producer liquid withdrawal rate during different SAGD operation period

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Gates and Chakrabarty (2006) used a genetic algorithm together with the STARS™ simulator

to optimize the CSOR by altering the steam injection pressure in a generic two-dimensional McMurray Reservoir model They concluded that the CSOR can be reduced significantly by operating SAGD with a profile of steam injection pressures throughout the life of the process over that of constant injection pressure One limitation of this study is that the results might be particular

to the reservoir model used in this work This is because the optimized strategy is determined by the reservoir’s response to the input variables The reservoir’s response is controlled by the geology of the system

Kisman and Yeung (1995) concluded that operating at low pressure decreased oil production in

a simulation model for the Burnt Lake oilsands conditions Li (2006) suggested that SAGD operation at high pressure induced higher porosity and permeability with higher oil production However, Collins (2007) also shown the failure low pressure SAGD in the Peace River Shell project where SAGD injection was at 2,700kPa and SOR ranging from 5-10 To minimize heat losses, Card (2006) proposed that the change of the operating pressure in two manners: 1) operating at high pressure until steam chamber reach up the overburden, and 2) then operate at low pressure In practice, each reservoir properties will have correspond to various operation modes, typical is the flexible controllable of injection pressure and steam injection rate based on using robust optimization methods

G.Coskuner (2009) proposed a new process combining Cyclic Steam Stimulation and Assisted Gravity Drainage, as called Hybrid SAGD Indeed, based on the well configuration from Fast-SAGD process In HSAGD process, all CSS wells are conducted in a staggered pattern in both the SAGD injectors and the offset wells and operated very differently This study observed that HSAGD performed better than CSS in the Clearwater Formation and produced the most amount of oil recovery in the shortest time and with the least amount of steam compared to SAGD, Fast-SAGD and CSS The results can only proper for investigation in Cold Lake areas without others

Chaodong Yang (2011) presented a robust SAGD optimization methodology, which takes into account geological uncertainties of the reservoir The robust optimization objective consists of two components: the expected value and standard deviation of NPV over the set of representative realizations Robustness of such optimization is validated by applying the obtained optimal well location and operating strategy to the full set of 100 realizations Yet, the results indicated that the optimum solution based on a single realization may lead to worse prediction results for certain realizations Thus, risk analysis following nominal optimization should always be performed to assess the risk of applying the nominal optimal solution

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CHAPTER 2

DESIGN OF EXPERIMENT AND RESPONSE SURFACE

METHODOLOGY

Design of Experiment was first developed by Sir Ronald A Fisher in the 1920s and 1930 It is

a systematic method that is used to determine the relationship between the different factors (input variables or independent variables) affecting a process and the output (response) of that process This method generates a mathematical model, which is a function of defined parameters

Response surface methodology is a gathering of statistical and mathematical techniques used

to develop, improve, and optimize processes Graphical perspective of the response can be generated based on the mathematical model This model is an empirical model obtained from observed data of the system It is an approximating model representing the true response surface

2.1 Response surface methodology

Response surface methodology (RSM), developed by Box and Wilson in 1951, is a collection

of statistical and mathematical methods that are useful for designing experiments, building models, evaluating the effect of factors and searching for optimum conditions for desirable responses The RSM technique can improve product yields and provide closer confirmation of the output response toward the nominal and target requirements In recent years, the RSM has played an important role

in oil field, especially applications in enhanced oil recovery

In most RSM problems, the form of the relationship between the response and the independent variables is unknown Thus, the first step in RSM is to find a suitable approximation for the true functional relationship between the response (Y) and the set of independent variables If the response is well modeled by a linear function of the independent variables, then the

approximation function is the first-order model or multiple linear regression model (Myers, 2008):

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Where x1, x2, , xk are the independent variables, 0 the constant coefficient, k the linear

effect of the kth factor coefficients and ε is the error observed in the response y These coefficients

are typically estimated by the method of least squares It chooses the β’s that provides the minimum

sum of the squares of the errors, ε It can be written in matrix notation as:

In case that interaction terms are added to the first-order model The equation can be written

as follows (Myers, 2002):

The model can be represented as a second-order model with interaction terms as shown in Eq (2.4) (Myers, 2002)

where ij represents the quadratic effect of the ith factor, and ij represents the cross product

effect or interaction effect between the ith and jth factors

The selection of the best sampling to use for modelling and optimisation is addressed by appropriate choice of experimental design Three designs commonly used for optimisation are the factorial design, central-composite design and face-centred cubic design Fig.2.1 displays examples

of each design Experiments are then conducted at all possible factor-level combinations The total

number of sampling points is ab, where a represents the number of factor levels (usually 2 or 3) and

b denotes the number of factors For a system involving three variables, each with two levels, a total

of 23 sampling points are needed

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Figure 2.1 Sample experimental designs (a) 2 2 factorial design, (b) 3 2 factorial design, (c)

central composite design and (d) face-centred cubic design

2.2 Two-Level Factorial Designs

Factorial designs are widely used in DOE in which several factors are involved, and it is required to investigate both main effects and interactions This design is useful at the early stage of

a response surface study It is used to screen how much each factor affects the response The factors identified as important would be investigated more thoroughly in subsequent experiments Two-level factorial design is a special case where each of the k factors has only two levels, minimum and maximum The design exactly generates 2k experimental runs for k factors; therefore, it is called 2k

factorial design (Myers, 2008) When many factors are involved, the full factorial design is not

applicable in practice due to too many runs needed For instant, 1024 runs (210) are required based

on 10 independent variables As a result, the concept of two-level fractional factorial design comes into place so that the number of runs could be reduced

2.3 Two-Level Fractional Factorial Designs

As mentioned in the previous section, the number of runs could be reduced by using fractional factorial design In case that the certain high-order interactions can be reasonably negligible, running only a fraction of the complete factorial experiment is good enough to obtain the main effects and low-order interactions (Myers, 2008)

One-half fraction and one-quarter fraction are widely used in the industry A one half fraction

of the 2k design is often called a 2k-1 fractional factorial design, and a one quarter fraction is called a

2k-2 design As a result of using these designs, the one-half design would reduce half of the number

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of runs required for the 2 design, while the one quarter design reduces the number of runs to only one-quarter of its The most appropriate two-level fractional factorial design is the design with the minimum number of runs at the smallest effect from aliasing and the highest possible resolution (Myers, 2008)

2.4 Central Composite Design (CCD)

The central composite design is the most popular design for fitting second-order models It was introduced by Box and Wilson (1951) The total number of tests required for CCD is 2k +2k + n0, including the standard 2k factorial points with its origin at the center, combined with 2k points fixed axially at a distance or star points that allow estimation of curvature; k is the number of independent variables The factorial points are used to estimate linear terms and two-factor interactions; these points play an important role for estimating the interaction terms The axial points contribute to the estimation of quadratic terms, and the center points estimate error (Myers and Montgomery, 2008) Figure 2.2 illustrates the generation of a central composite design for two factors

Figure 2.2 The points distribution of a Central Composite Design

The distance from the center of the design space to a star point is ±α The selection of the axial distance (α) and the number of center points (n) is very important If the minimum and maximum values of design factors are presented as -1 and +1, respectively, the value of α normally

+ A cube that consists of the central point and the middle points of the edges, as can be observed in Fig 2.3a

a The location of points in cube b) Three interlocking 2 2 factorial design

Figure 2.3 Box- Behnken design

+ A figure of three interlocking 22 factorial designs and a central point showed in Fig.2.3b

The number of experiments (N) required for the development of BBD is defined as N= 2k (k−1) +C0, (where k is number of factors and C0 is the number of central points) For comparison, the

number of experiments for a central composite design is N=2 k +2k +C0 Tables 2.1 contain the coded values of the factor levels for BBD on three, four and five factors, respectively

A comparison between the BBD and other response surface designs (central composite design, and three-level full factorial design) are demonstrated that the BBD are slightly more efficient than the central composite design, but much more efficient than the three-level full factorial designs, where the efficiency of one experimental design is defined as the number of coefficients in the estimated model divided by the number of experiments Table 2.2 establishes a

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comparison among the efficiencies of the BBD and other response surface designs for the quadratic model This table demonstrates also that the three-level full factorial designs are costly when the factor number is higher than 2

Table 2.1 Coded factor levels for Box-Behnken designs for

optimizations involving four and five factors

Another advantage of the BBD is that it does not contain combinations for which all factors are simultaneously at their highest or lowest levels Therefore, these designs are useful in avoiding experiments performed under extreme conditions, for which unsatisfactory results might occur Conversely, they are not indicated for situations in which we would like to know the responses at the extremes, that is, at the vertices of the cube

Table 2.2 Comparison of efficiency of central composite design

and Box-Beknken design

Number of experiments Efficiency Factors

(k)

Number of coefficient