STATUS OF THESIS
Title of thesis
EXPERIMENTAL STUDY AND MODELLING OF CO2
INJECTIVITY IMPAIRMENT BY SALT PRECIPITATION AND
FINES MIGRATION
MUHAMMAD ASLAM BIN MD YUSOF
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No 32, Jalan Lakeville 24,
Assoc. Prof. Dr Ismail M Saaid
Bandar Universiti,
32610 Seri Iskandar, Perak
Date : 20/10/2021
Date : 20/10/2021
UNIVERSITI TEKNOLOGI PETRONAS
EXPERIMENTAL STUDY AND MODELLING OF CO2 INJECTIVITY
IMPAIRMENT BY SALT PRECIPITATION AND FINES MIGRATION
By
MUHAMMAD ASLAM BIN MD YUSOF
The undersigned certify that they have read and recommend to the Postgraduate Studies
Programme for acceptance of this thesis for the fulfillment of the requirements for the
degree stated.
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Main Supervisor:
Associate Professor Dr Ismail M Saaid
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Co-Supervisor:
Dr Iskandar B Dzulkarnain
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Head of Department:
Associate Professor Dr Khaled Abdalla
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Elraies
Date
2/11/2021
______________________________________
EXPERIMENTAL STUDY AND MODELLING OF CO2 INJECTIVITY
IMPAIRMENT BY SALT PRECIPITATION AND FINES MIGRATION
by
MUHAMMAD ASLAM BIN MD YUSOF
A Thesis
Submitted to the Postgraduate Studies Programme
as a Requirement for the Degree of
DOCTOR OF PHILOSOPHY
PETROLEUM ENGINEERING
UNIVERSITI TEKNOLOGI PETRONAS
BANDAR SERI ISKANDAR,
PERAK
JULY 2021
DECLARATION OF THESIS
EXPERIMENTAL
Title of thesis
STUDY
AND
MODELLING
OF
CO2
INJECTIVITY IMPAIRMENT BY SALT PRECIPITATION AND
FINES MIGRATION
MUHAMMAD ASLAM BIN MD YUSOF
I ____________________________________________________________________
hereby declare that the thesis is based on my original work except for quotations and
citations which have been duly acknowledged. I also declare that it has not been
previously or concurrently submitted for any other degree at UTP or other institutions.
Witnessed by
________________________________
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Signature of Author
Signature of Supervisor
Permanent address:
Name of Supervisor
No 32, Jalan Lakeville 24,
Assoc. Prof. Dr Ismail M Saaid
Bandar Universiti,
32610 Seri Iskandar
Perak
Date: 20/10/2021
Date: 20/10/2021
iv
_______
DEDICATION
This thesis is dedicated
To my late father, MD YUSOF
My beloved mother, MARSILLA
My dearest wife, NIK KHADIJAH
My beautiful daughters, MARYAM, AUFA & NUHA
My cute son, NAUFAL
My siblings and all my family
v
ACKNOWLEDGEMENTS
In the Name of Allah, the beneficent and the merciful.
First, and foremost, I would like to thank you Allah for everything you have bestowed
upon me. Sincere thanks go to my wife, Nik Khadijah and my children for their
motivation, patience, and for sharing this journey with me throughout my study. Also,
I am very thankful to my beloved mother, brothers, sisters and mother-in law for their
continuous prayers and encouragement to proceed in this PhD program which was a
great but exciting challenge for me.
I would like to express my sincere gratitude to my supervisor AP Dr. Ismail M
Saaid for the continuous support of my PhD study, for his patience, motivation, and
immense knowledge. His excellent guidance and consistent mentoring support after
took in charge as the main supervisor in the middle of PhD program helped me in
research and writing of this thesis. My sincere thanks also go to Emeritus Professor Dr
Ahmad Kamal Idris for being such a supportive mentor. Right from the start, Prof
Kamal has been very enthusiastic, energetic, and consistent in providing me excellent
guidance, encouragement, and infinite mentoring support. I could not have imagined
having a better advisor and mentor for my PhD study.
Many thanks are due to my research members especially Arif, Azfar and Asyraf
who helped me during this research. I must express my respect as well to our laboratory
technologists, Mr. Shahrul Rizzal, Iswadi and Saiful. Your wisdom and humor gave me
a lot of wonderful memory over these years. It has been a great pleasure to work with
you. I would like to acknowledge Universiti Teknologi PETRONAS as the sponsor
which provided the opportunity and support that enabled me to proceed this degree.
Last but not least, I would like to thank all of those friends who accompanied me on the
PhD journey and who were there for me when I needed them.
vi
ABSTRACT
Re-injection of carbon dioxide (CO2) into saline aquifer is highlighted as an
effective technique to permanently secure anthropogenic gas produced from high CO2
gas fields in Malaysia. Unlike typical gas injection for oil recovery, reactive interactions
between CO2, brine, and rock minerals during the continuous injection of CO2 would
trigger injectivity-related issues due to salt precipitation and fines migration
mechanisms initiated in the aquifer. However, the existing models to predict CO2
injectivity change are limited to porosity change by salt precipitation alone, without
considering other CO2, brine, and rock parameters. Moreover, there have been limited
systematic experimental studies to understand the impact of these parameters on the
CO2 injectivity change. This research work explored the application of neural network
(NN) and response surface method (RSM) models to predict the CO2 injectivity change
resulting from the combination of salt precipitation and fines migration. The impacts of
independent and combined interactions between CO2, brine, and rock parameters were
also evaluated by injecting CO2 into brine saturated sandstone. The core samples were
saturated with NaCl brine with salinity between 6,000 ppm to 100,000 ppm. The 0.1,
until 0.5 wt.% of different-sized hydrophilic silicon dioxide particles (0.005, 0.015,
0.03, 0.045, 0.06 and 0.07 µm) were added to evaluate the effect of fines migration on
CO2 injectivity alteration. The experimental results showed that brine salinity has a
greater individual influence on permeability reduction as compared to the influence of
particles (jamming ratio and particle concentration) and CO2 injection flow rate.
Moreover, the presence of both fines migration and salt precipitation during CO2
injection was also found to intensify the permeability reduction by 10%, and reaching
up to threefold with increasing brine salinity and particle size. The evidence of
permeability alteration has been examined through FESEM-EDX analysis of the rock
physical changes and collected particles. It was both statistically found that the NN
model gives better CO2 injectivity change prediction than RSM model for training,
validation and testing data sets. NN model as overall is considered as efficient statistical
tools in predicting the CO2 injectivity change of the sandstone rock after exposed with
dynamic injection of scCO2 at different brine salinity, injection flow rate, particle size
and particle concentration.
vii
ABSTRAK
Penyuntikan semula karbon dioksida (CO2) ke dalam akuifer air masin merupakan
teknik yang berkesan untuk menyimpan CO2 yang dikeluarkankan dari lapangan gas
yang memiliki kandungan CO2 yang tinggi di Malaysia. Tidak seperti suntikan gas yang
biasa diamalkan untuk pengeluaran minyak, tindak balas reaktif antara CO2, air garam
dan batuan semasa suntikan CO2 secara berterusan akan mencetuskan masalah yang
berkaitan dengan kebolehsuntikan kerana pemendakan garam dan pergerakan partikel
yang terbentuk dalam akuifer air masin. Walau bagaimanapun, model yang sedia ada
untuk menjangkakan perubahan suntikan CO2 terhad kepada perubahan keliangan oleh
pemendakan garam sahaja, tanpa mempertimbangkan parameter lain seperti CO2, air
garam dan batuan. Tambahan lagi, kajian eksperimen secara sistematik untuk
memahami kesan CO2, air garam dan batuan ini terhadap perubahan suntikan CO agak
terhad. Karya penyelidikan ini meneroka penerapan model neural network (NN) dan
kaedah permukaan tindak balas (RSM) untuk meramalkan perubahan suntikan CO2
akibat gabungan pemendakan garam dan pergerakan partikel. Kesan interaksi antara
parameter CO2, air garam, dan batuan juga dinilai dengan menyuntik CO2 ke dalam
batu pasir berisi air garam. Sampel batu telah diisi dengan air garam NaCl dengan
kemasinan antara 6,000 ppm hingga 100,000 ppm. Partikel silika dioksida dengan
kepekatan 0.1 hingga 0.5 wt% dan saiz yang berbeza (0.005, 0.015, 0.03, 0.045, 0.06
and 0.07 µm) turut ditambah untuk menilai kesan pergerakan partikel terhadap
perubahan suntikan CO2. Hasil eksperimen menunjukkan bahawa kemasinan air garam
mempunyai pengaruh yang lebih besar terhadap penurunan kebolehtelapan
dibandingkan dengan pengaruh partikel (nisbah jamming dan kepekatan partikel) dan
kadar aliran CO2. Di samping itu, kehadiran gabungan pergerakan partikel dan
pemendakan garam semasa suntikan CO2 telah meningkatkan pengurangan
kebolehtelapan sebanyak 10%, dan mencapai tiga kali ganda dengan peningkatan
kemasinan air garam dan ukuran partikel. Analisis FESEM-EDX turut menyokong
perubahan kebolehtelapan disebabkan perubahan fizikal batuan and pergerakan
partikel. Statistik menunjukkan bahawa model NN memberikan ramalan perubahan
suntikan CO2 yang lebih baik daripada model RSM pada perubahan kemasinan air
garam, kadar aliran, ukuran partikel dan kepekatan partikel.
viii
In compliance with the terms of the Copyright Act 1987 and the IP Policy of the
university, the copyright of this thesis has been reassigned by the author to the legal
entity of the university,
Institute of Technology PETRONAS Sdn Bhd.
Due acknowledgement shall always be made of the use of any material contained
in, or derived from, this thesis.
© Muhammad Aslam Bin Md Yusof, 2021
Institute of Technology PETRONAS Sdn Bhd
All rights reserved.
ix
TABLE OF CONTENT
ABSTRACT.................................................................................................................vii
ABSTRAK ..................................................................................................................viii
LIST OF FIGURES .................................................................................................... xiv
LIST OF TABLES ...................................................................................................... xix
LIST OF ABBREVIATIONS ..................................................................................... xxi
LIST OF SYMBOLS .................................................................................................xxii
CHAPTER 1 INTRODUCTION ................................................................................... 1
1.1 Background of study .......................................................................................... 1
1.2 Problem statement ............................................................................................. 4
1.3 Objectives .......................................................................................................... 5
1.4 Scope of study.................................................................................................... 6
1.5 Contributions and significance of study ............................................................ 7
1.6 Thesis outline ..................................................................................................... 8
CHAPTER 2 LITERATURE REVIEW ...................................................................... 10
2.1 The geological carbon sequestration (GCS) in saline aquifer ......................... 10
2.2 CO2 injectivity elements for sequestration ...................................................... 14
2.3 Factors affecting CO2 injectivity impairment .................................................. 16
2.4 Mineral dissolution and secondary mineral precipitation ................................ 21
2.5 Salt precipitation .............................................................................................. 25
2.5.1 Mechanism of salt precipitation .......................................................... 26
2.5.2 Factors affecting salt precipitation during CO2 injection in saline
aquifer .............................................................................................. 28
2.6 Fines migration during CO2 injection .............................................................. 30
2.6.1 Injection flow rate ............................................................................... 30
2.6.2 Clay content......................................................................................... 31
2.6.3 Jamming ratio ...................................................................................... 32
2.6.4 Particle concentration .......................................................................... 34
2.6.5 Hydrodynamic condition of carrier fluid............................................. 35
2.7 Field reports on CO2 injectivity impairments .................................................. 36
x
2.8 Experimental observations on CO2 injectivity impairments ............................ 37
2.8.1 Analyzing methods .............................................................................. 42
2.8.2 Types of core sample........................................................................... 44
2.8.3 Saturation fluid type and properties .................................................... 44
2.8.4 Testing parameters .............................................................................. 45
2.8.5 Changes on physical rock properties ................................................... 45
2.9 Analytical model for prediction of CO2 injectivity impairments .................... 47
2.9.1 Development of the Kozeny-Carman model ....................................... 48
2.9.1.1 The Zeidouni, Pooladi and Keith model .................................. 49
2.9.1.2 Tang et al. model...................................................................... 49
2.9.2 Development of the power law model ................................................ 50
2.9.3 Development of the Hagen-Poiseuille model ...................................... 50
2.9.3.1 The Verma and Pruess model .................................................. 51
2.9.3.2 The Ott, Roles and De Kloe model .......................................... 53
2.9.3.3 The Giorgis, Carpita and Battistelli model .............................. 54
2.9.4 Comparison of theoretical models for prediction of CO2 injectivity .. 54
2.10 Theory and application of Neural Network ................................................... 57
2.11 Response Surface Methodology (RSM) ........................................................ 60
2.12 Summary and highlighted remarks ................................................................ 62
CHAPTER 3 METHODOLOGY ................................................................................ 63
3.1 Materials .......................................................................................................... 65
3.1.1 Rock properties ................................................................................... 65
3.1.1.1 Physical properties ................................................................... 66
3.1.1.2 Topography and mineral composition ..................................... 66
3.1.2 CO2 properties ..................................................................................... 68
3.1.3 Brine .................................................................................................... 68
3.1.4 Fines particles ...................................................................................... 69
3.2 Measurement and analysis ............................................................................... 69
3.2.1 Porosity and permeability measurement ............................................. 70
3.2.2 Mercury Injection Capillary Pressure (MICP) .................................... 70
3.2.3 Petrographic and mineralogy analysis ................................................. 71
3.2.4 Effluent analysis .................................................................................. 72
xi
3.2.5 Core flooding unit ............................................................................... 72
3.3 Experimental work and procedures ................................................................. 74
3.3.1 Semi-static batch experiment .............................................................. 74
3.3.1.1 Experimental procedures ......................................................... 75
3.3.1.2 Taguchi Design of Experiment ................................................ 77
3.3.2 Core- flooding experiment .................................................................. 78
3.3.2.1 Core preparation....................................................................... 78
3.3.2.2 Fluids and fines particles preparation ...................................... 80
3.3.2.3 Core- flooding setup and procedures ....................................... 81
3.3.2.4 Determination of injectivity alteration ..................................... 84
3.4 CO2 injectivity modelling ................................................................................ 86
3.4.1 Assessing the existing theoretical model ............................................ 88
3.4.2 Development of the RSM model ......................................................... 89
3.4.3 Development of the regression model using machine learning .......... 90
3.4.4 Comparison study and model testing .................................................. 91
3.4.5 Statistical evaluation ........................................................................... 91
3.4.5.1 Average Absolute Percentage Error (AAPE) .......................... 91
3.4.5.2 Sum of the Squares due to Error (SSE) ................................... 92
3.4.5.3 Root Mean Square (RMSE) ..................................................... 92
3.4.5.4 Coefficient of Determination (R2) ........................................... 93
3.4.5.5 Adjusted R2 .............................................................................. 93
CHAPTER 4 RESULTS AND DISCUSSION ............................................................ 94
4.1 Screening the brine-rock parameters affecting sandstone rock physical
changes ......................................................................................................... 94
4.1.1 Signal-noise ratio and analysis of ANOVA ........................................ 94
4.1.2 pH analysis .......................................................................................... 98
4.1.3 Rock physical changes of sandstone before and after CO2 reaction
by FESEM-EDX analysis .............................................................. 100
4.1.3.1 Mineral dissolution and precipitation .................................... 101
4.1.3.2 Fines migration and entrapment............................................. 103
4.1.3.3 Effect of different brine systems ............................................ 105
4.2 Effects of CO2-brine-rock parameters on CO2 injectivity ............................. 108
xii
4.2.1 Changes of produced brine chemistry ............................................... 109
4.2.2 Characterization of migrated fines particles ...................................... 112
4.2.3 The effect of CO2 injection scheme .................................................. 116
4.2.4 The effect of injection flow rate ........................................................ 119
4.2.5 The effect of brine salinity ................................................................ 122
4.2.6 Effect of the brine system.................................................................. 124
4.2.7 The effect of initial rock permeability ............................................... 126
4.3 Combined impact of salt precipitation and fines migration on CO2
injectivity .................................................................................................... 127
4.3.1 Effect of brine salinity ....................................................................... 128
4.3.2 Effect of injection flow rate. ............................................................. 129
4.3.3 Effect of particle size ......................................................................... 131
4.3.4 Effect of particle concentration ......................................................... 132
4.4 CO2 injectivity change relationship due to salt precipitation and fines
migration .................................................................................................... 134
4.4.1 Analysis of existing model ................................................................ 134
4.4.2 Evaluation of regression model using the machine learning
approach ......................................................................................... 143
4.4.2.1 Screening of regression machine learning models................. 143
4.4.2.2 Optimization of neural network model .................................. 144
4.4.2.3 Validation of neural network model ...................................... 148
4.4.2.4 Evaluation of effects of CO2-brine-rock parameters on CO2
injectivity changes, using the NN model ............................... 150
4.4.3 Evaluation of the RSM model ........................................................... 153
4.4.3.1 Training and validation of the RSM model ........................... 153
4.4.3.2 Evaluation of effects of CO2-brine-rock parameters on CO2
injectivity changes, using the RSM model ............................ 159
4.4.4 Testing of new CO2 injectivity models ............................................. 164
4.4.4.1 Trend analysis of NN and RSM models ................................ 164
4.4.4.2 Comparison between NN and RSM models .......................... 167
4.4.4.3 Testing the models using actual data from published works . 168
CHAPTER 5 CONCLUSION AND RECOMMENDATIONS ................................ 173
xiii
5.1 Conclusion ..................................................................................................... 173
5.2 Recommendations.......................................................................................... 174
APPENDIX A CORE FLOOD EXPERIMENTAL DATA ...................................... 187
APPENDIX B GOOGLE COLAB CODE ................................................................ 190
LIST OF FIGURES
Figure 2.1 Types of geological storage options [45]. .................................................. 11
Figure 2.2 Plotted pressure and temperature data based on compiled large scale CCS
projects in saline aquifer. ............................................................................................. 12
Figure 2.3 Relevant properties of CO2 as functions of temperature and pressure: (a)
CO2 phase diagram, (b) variation of liquid CO2 density as a function of temperature
and pressure and (c) viscosity of the liquid and supercritical phases [61]................... 16
Figure 2.4 Different factors that controlling CO2 injectivity impairment. .................. 17
Figure 2.5 pH, water and gas saturation explained as segregated region from wellbore
during CO2 sequestration process (modified from Andre et al., 2007). ...................... 19
Figure 2.6 Aerial view of a typical interaction region of CO2 geo-sequestration in
saline aquifer. ............................................................................................................... 20
Figure 2.7 A typical occurrence of salt precipitation region of CO2 geo-sequestration
in saline aquifer [11]. ................................................................................................... 25
Figure 2.8 Aerial schematic illustration of different physical mechanisms contributing
to the process of salt precipitation [11] ........................................................................ 27
Figure 2.9 Image of micromodel after scCO2 flooding under SEM [87]. ................... 28
Figure 2.10 Pressure drop profiles of injection of fresh water and supercritical CO2
into Berea Sandstone cores [17] .................................................................................. 42
Figure 2.11 SEM images taken from the same spot on a rock sample before and after
flooding. The markings on the images indicate fines migration and mineral
precipitation [124]. ....................................................................................................... 43
Figure 2.12 Comparison of theoretical models to predict permeability changes as a
function of porosity changes. ....................................................................................... 56
Figure 2.13 A schematic diagram of a typical fast-forward NN architecture. ............. 58
Figure 2.14 A schematic diagram of a typical backpropagation NN architecture. ...... 59
xiv
Figure 3.1. Summary of research methodology. .......................................................... 64
Figure 3.2 XRD spectrum of three sandstone core selected for this research shows
comparable mineralogical composition ....................................................................... 68
Figure 3.3 POROPERM Equipment set-up. ................................................................ 70
Figure 3.4 RPS core- flooding set-up. ......................................................................... 73
Figure 3.5 Schematics of the experimental set-up used for CO2 core- flooding
experiments. ................................................................................................................. 73
Figure 3.6 Experimental setup for semi-static CO2-brine-rock. ................................. 76
Figure 3.7 XRD mineral points matching for Berea sandstone. .................................. 79
Figure 3.8 XRD mineral points matching for Kirby sandstone. .................................. 80
Figure 3.9 Diagram of CO2 injectivity modeling process............................................ 87
Figure 4.1 Main effect of S/N ratio on weight change percentages. ............................ 96
Figure 4.2 pH value measurement on brine samples. .................................................. 99
Figure 4.3 FESEM images of Berea sandstone saturated with 30000 ppm of NaCl
show the pore space enlargement due to dissolution causing an increase on pore
connectivity (red circles)............................................................................................ 102
Figure 4.4 Newly- formed kaolinite mineral filled in the gap between the particles
after CO2 exposure. .................................................................................................... 103
Figure 4.5 Migrated silica particle trapped at the pore throat. ................................... 104
Figure 4.6 Newly- formed siderite particle formed between the pore spaces. The
mineral was confirmed with the EDX analysis.......................................................... 105
Figure 4.7 Comparison of images before and after the CO2 exposure for sandstone
saturated with 30,000 ppm CaCl2, NaCl and KCl. The green circles indicate newlyformed material on the grain surface and the red circles highlight the enhanced pore
spaces due to dissolution and missing particles. ........................................................ 107
Figure 4.8 ICPAES analysis of the produced brine and initial brine. ........................ 110
Figure 4.9 Samples of brine before and after the CO2 flooding experiment. ............ 111
Figure 4.10 The FESEM image of collected fine particles collected from the produced
effluent (Berea core saturated with 30000 NaCl brine), showing the range of size and
shape. ......................................................................................................................... 113
Figure 4.11 The FESEM image of precipitated salt attached to the surface of particles
(showing the range of size and shape). ...................................................................... 114
xv
Figure 4.12 Detached kaolinite particles scattered around the main kaolinite stack
(found attached to the stable quartz grains) ............................................................... 114
Figure 4.13 Schematic diagram of mineral dissolution, salt precipitation and fines
migration mechanisms during CO2 injection into saline aquifer. .............................. 115
Figure 4.14 The effect of CO2 injection schemes on modifications in permeability
which was evaluated on the core samples before and after the core flood studies. ... 117
Figure 4.15 Compared images of sandstone core samples before and after each CO2
injection scheme......................................................................................................... 118
Figure 4.16 The Pressure profiles during scCO2 injection at different flow rates. .... 120
Figure 4.17 The effect of injection flow rate on alteration in permeability percentages
measured on core samples before and after the core flood studies. ........................... 121
Figure 4.18 The effect of increasing NaCl brine concentration on the alteration in
permeability percentages measured on core samples before and after core flood
studies. ....................................................................................................................... 122
Figure 4.19 A schematic view of the effect of salt precipitation on reducing the
crossflow area in the bundle-of-tubes model. ............................................................ 123
Figure 4.20 The effect of different brine systems on the alteration of permeability
percentages measured on core samples before and after core- flooding studies. ...... 124
Figure 4.21 FESEM images of Berea sandstone core samples saturated with 30000
ppm of (a) NaCl and (b) KCl, before and after CO2 injection schemes. Precipitated
salts partly and fully covered the surface of the particle and filled in the pore spaces
(green circles)............................................................................................................. 125
Figure 4.22 The FESEM image shows enhanced pore space in core sample saturated
with 30000 ppm of CaCl2. ......................................................................................... 126
Figure 4.23 Estimated relative injectivity change of CO2 as a function of initial rock
permeability ............................................................................................................... 127
Figure 4.24 RIC measured as a function of salinity................................................... 128
Figure 4.25 RIC measured as a function of CO2 injection flow rate. ........................ 130
Figure 4.26 RIC measured as a function of particle size. .......................................... 131
Figure 4.27 RIC measured as a function of particle concentration............................ 133
Figure 4.28 Comparison plot of the predicted RIC values against corresponding
experimental data for brine salinity range between 0 and 100,000 ppm. .................. 136
xvi
Figure 4.29 Comparison plot of the predicted RIC values against corresponding
experimental data for injection flow rate range between 2 and 10 cm3/min. ............ 137
Figure 4.30 Comparison plot of the predicted RIC values against corresponding
experimental data for different jamming ratio between 0 and 0.06. .......................... 138
Figure 4.31 Comparison plot of the predicted RIC values against corresponding
experimental data for 0.015 μm particle size at increasing concentration from 0 to
0.5wt%. ...................................................................................................................... 139
Figure 4.32 Actual and predicted value for the effect of brine salinity. ................... 140
Figure 4.33 Actual and predicted value for the effect of injection flow rate. ........... 141
Figure 4.34 Actual and predicted value for the effect of jamming ratio. .................. 141
Figure 4.35 Actual and predicted value for the effect of particle concentration. ..... 142
Figure 4.36 Number of hidden layers and neurons versus accuracy of R2 values. .... 145
Figure 4.37 Alpha parameter versus accuracy of R2 values. .................................... 146
Figure 4.38 Initial learning rate versus accuracy of R2 values. ................................ 147
Figure 4.39 Momentum versus accuracy of R2 values. ............................................ 148
Figure 4.40 Validation of actual experimental data against corresponding predicted
data using NN regression model. ............................................................................... 149
Figure 4.41 Absolute percentage error between the measured and calculated RIC at
increasing brine salinity using the NN model. ........................................................... 151
Figure 4.42 Absolute percentage error between the measured and calculated RIC at
injection flow rate from 2 cm3/min to 10 cm3/min using the NN model. .................. 151
Figure 4.43 Absolute percentage error between the measured and calculated RIC at
various particle sizes using the NN model. ................................................................ 152
Figure 4.44 Absolute percentage error between the measured and calculated RIC by
the NN model using 0.015 μm at different particle concentrations. .......................... 152
Figure 4.45 Weightage of experimental parameters on RIC response evaluated using
the NN model. ............................................................................................................ 153
Figure 4.46 Predicted RIC versus experimental data................................................. 156
Figure 4.47 Validation of the RSM model using 20% excess experimental data
showing high accuracy of the model with R–square of 0.985. .................................. 158
Figure 4.48 Absolute percentage error between the measured and calculated RIC at
increasing brine salinity using RSM model. .............................................................. 160
xvii
Figure 4.49 Absolute percentage error between the measured and calculated RIC at
injection flow rate from 2 cm3/min to 10 cm3/min using the RSM model. ............... 161
Figure 4.50 Absolute percentage error between the measured and calculated RIC at
various particle sizes using the RSM model. ............................................................. 161
Figure 4.51 Absolute percentage error between the measured and calculated RIC by
the RSM model using 0.015 μm at different particle concentrations. ....................... 162
Figure 4.52 3D response surface plot of RIC: a) effects of brine salinity and jamming
ratio; b) effects of brine salinity and particle concentration; c) effects of injection flow
rate and jamming ratio; d) effects of particle concentration and injection flow rate. 163
Figure 4.53 Brine salinity trend analysis of the NN model and RSM model. ........... 165
Figure 4.54 Injection flow rate trend analysis of the NN model and RSM model. ... 166
Figure 4.55 Particle size trend analysis of the NN model and RSM model. ............. 166
Figure 4.56 Particle concentration trend analysis of the NN model and RSM model.
.................................................................................................................................... 167
Figure 4.57 Predicted RIC versus reported data from the literature for the NN model
and the RSM model. .................................................................................................. 170
Figure 4.58 Predicted RIC using the NN and the RSM models versus actual data from
training, validation, and testing data sets. .................................................................. 172
xviii
LIST OF TABLES
Table 2.1 Summary of mineral with complete dissolution after CO2-brine-sandstone
interactions ................................................................................................................... 23
Table 2.2 Summary of dissolved minerals after CO2-brine-sandstone interactions with
newly formed secondary minerals ............................................................................... 23
Table 2.3 Occurrence of pore plugging/piping due to different jamming ratios [37].. 33
Table 2.4 Summary of the experimental studies for petrophysical changes induced by
CO2 injection................................................................................................................ 38
Table 2.5 Laboratory flow rates based on distance to the wellbore [126] ................... 45
Table 2.6 Comparison of theoretical models used for prediction of CO2 Injectivity
changes ......................................................................................................................... 55
Table 3.1 Summary of core samples’ physical properties ........................................... 66
Table 3.2 XRF results for Berea, Kirby and Idaho sandstones ................................... 67
Table 3.3 XRD results for Berea, Kirby, and Idaho sandstones .................................. 67
Table 3.4 Control factors and levels of the orthogonal test ......................................... 77
Table 3.5 Summary of experimental parameters for core flooding ............................. 83
Table 3.6 Prediction of CO2 injectivity models by previous researchers .................... 88
Table 4.1 Experimental L9 (34) orthogonal array and S/N results .............................. 95
Table 4.2 The average effects of different factors on each level ................................. 97
Table 4.3 ANOVA table .............................................................................................. 98
Table 4.4 Statistical parameter values for RIC data fitting using existing model ..... 135
Table 4.5 Different n values for power law at various experimental conditions ....... 140
Table 4.6 Summary of R2 and RMSE for all regression methods in screening stage
using Microsoft Azure. .............................................................................................. 144
Table 4.7 Goodness of fitting for the NN Regression Model to predict the 20% excess
experimental data. ...................................................................................................... 149
Table 4.8 Evaluated models for responses on RIC by Design Expert software. ....... 154
Table 4.9 ANOVA results of quadratic model for RIC response. ............................. 155
Table 4.10 Goodness of fitting for the RSM model to predict the 20% excess
experimental data ....................................................................................................... 159
xix
Table 4.11 Comparison between NN model and RSM model. ................................. 168
Table 4.12 Summary of data used for model testing. ................................................ 169
Table 4.13 Statistical data of the NN Model and the RSM Model to predict the
reported data from published literature ...................................................................... 171
xx
LIST OF ABBREVIATIONS
AAPE
Absolute average percentage error
CO2
Carbon dioxide
CaCl2
Calcium Chloride
FESEM
Field emission scanning electron microscopy
NaCl
Sodium Chloride
KCl
Potassium Chloride
KC
Kozeny-Carman
HP
Hagen- Poiseuille
ML
Machine learning
NN
Neural network
ppm
parts per million
RIC
Relative injectivity change
RSM
Response surface method
R2
R-squared
RMSE
Root mean square error
scCO2
supercritical carbon dioxide
SSE
Sum of squared deviations
SST
Total number of squares
xxi
LIST OF SYMBOLS
𝑐𝐻
Empirical coefficient
𝑑10
Empirical coefficient
𝜇
Viscosity
𝐼
Injectivity index
𝐼𝑖
Initial injectivity index
𝐼𝑓
Final injectivity index
𝑞
injection flow rate
𝑞𝑖
initial injection flow rate
𝑞𝑓
final injection flow rate
∆𝑃
Pressure drop
∆𝑃𝑖
Initial pressure drop
∆𝑃𝑓
Final pressure drop
𝑘
Initial permeability
𝑘𝑖
Initial permeability
𝑘𝑓
Final permeability
𝜙
Porosity
𝜙𝑜
Initial porosity
𝜙𝑐
Critical porosity
𝐷
Diameter
𝐿
Length
𝑇
Temperature
𝑃𝑃
Pore pressure
𝑂𝑃
Overburden pressure
𝑚𝐷
milidarcies
𝑑𝑝
Pore size diameter
𝐷
Diameter
𝑟
Radius
𝛾
Surface tension of mercury
𝜃
Model response
xxii
𝑃𝑐
External pressure
𝛽0
Constant value
𝛽𝑖
Regression coefficient
𝐴𝑡
Measured data
𝐹𝑡
Predicted data
𝑒
Error
xxiii
CHAPTER 1
INTRODUCTION
1.1 Background of study
Carbon capture and storage (CCS) also known as carbon capture and sequestration;
is a process that involves capturing the CO2 at its large source, transporting it to the
disposal site and storing it before its release to the atmosphere. In Malaysia, there has
been an emphasis to reduce the emission from its high CO2 offshore gas fields by the
re-injection of produced CO2 after its separation from the gas stream into the available
saline aquifer in the geological formation [1]. There is an estimated of 37 Tscf of
natural gas that remains undeveloped in Malaysia’s gas fields, in which the CO2
contents exceed 10% volumetric of produced acid gas [2]. Most of these gas fields were
not economically viable in the past due to large presence of high CO2 and are always
associated with potentially high corrosion risks to the surface facilities and pipelines.
Nowadays, due to rapid development of CCS technology, it attracts a possibility to
develop of up to 80% of the amount of high CO2 gas field in the region of South-East
Asia [3, 4].
CO2 injection into saline aquifer for sequestration is gaining attention by
researchers with respect to mitigation potential [5, 6]. Studies indicated that saline
aquifer can provide huge storage capacity compare to other types of reservoir such as
depleted oil and gas reservoir or enhanced oil recovery [7]. This has encouraged
researchers to investigate the potential of saline aquifer to permanently store the CO2
produced from high CO2 gas fields [8, 9]. Unlike typical gas injection for oil recovery,
the injection of a large volume of reactive CO2 fluid would disrupt the thermodynamic
equilibrium of the fluid-rock system near the wellbore to cause formation damage.
Previous studies highlighted that mineral dissolution and precipitation are two
main geochemical mechanisms because of interactions between CO2, brine and rock
formation [10, 11]. During the CO2 injection, the water nearby the wellbore would
evaporate into the CO2 stream to form a dry out zone during continuous injection, which
leads to salt precipitation. Meanwhile CO2 nearest to the formation brine fronts would
gradually dissolve in the brine to form carbonic acid, which is highly reactive to rock
minerals, especially carbonates [12, 13]. The existence of carbonic acid could lower the
pH to about 3-4 where the impact of such acidic environment on the rock properties is
significant [14-16]. The acid reacts with rock carbonate minerals, leading to iondissolution-precipitation as well as generating secondary minerals in the form of fine
particles into the pore fluid.
Although the dissolution of carbonate mineral, such as calcite, might be a
beneficial phenomenon, it could result in detachment of several less reactive minerals
from the original place, followed by migration and placement in narrow pore channels,
which reduce the porosity and permeability. This phenomenon is generally called as
CO2 injectivity impairment and measured by ratio of initial permeability and final
permeability of the formation rock [17, 18]. The permeability alteration due to
particulate process near wellbore would have direct effect on the CO2 injectivity. The
combination of salt precipitation and fines migration would lead to severe permeability
impairment, as proven in laboratory experiments [19, 20].
While previous work on CO2-brine-rock experiments attempted to elaborate on the
mechanism and effect of CO2-brine dissolution, most of the experiments were limited
to the individual storage physical conditions and their effects on injectivity impairment.
The high variation of brine compositions, rock properties and injection flow rates in
the literature lead to challenges in gaining an understanding of the impact of the
parameters on the physical changes in the rock [21-23]. Researchers normally used
brine salinity and type, which was specifically designed based on formation brine of
storage sites. Therefore, it is almost impossible to quantify the individual contribution
of each salt type on the petro physical changes of the rock after exposed with CO2.
The injection scheme is possibly the most controversial parameters in CO2-brinerock experimental work. Despite the number of articles debating the impact of the
injection scheme [24, 25], no experimental attempt has been performed. While some
researchers injected carbonated brine believing it to be the most damaging sequence in
the flooding process, other researchers perceived that the intermediary front of
carbonated brine between the unaffected brine and scCO2 was too short to alter the
initial rock conditions. However, the impacts of the two sequences were derived from
different mechanisms. To be specific, while carbonated brine would dissolve minerals
and cause fines migration, injection of scCO2 would dry the core and cause salt
precipitation.
In existence of fines migration, the particulate process in porous media is subjected
to various factors during transport, attachment, and detachment mechanisms. Once
entrained by the fluids in porous media, the particles will migrate through the
preferential tortuous flow pathways available in the porous media. Then, the particles
are subjected to capture, retain and deposit process within the porous matrix. The
particle plugging in porous media is depending on characteristics of fine particles,
porous medium, and carrier fluid [26-28]. Among the important parameters are particle
and porous media grain diameters, and concentration in pore space, density and
viscosity of the carrier fluid and convective velocity (velocity of particles that is
normally assumed equal to injection rate). While the previous work focused only on the
water/brine and oil phase system that normally found in oil and gas industry, the unique
combination of gas-like viscosity and liquid-like density of supercritical CO2 could
influence fines transport. Therefore, a study on the effect of particle properties in CO2brine system is critically required in order to quantify the injectivity impairment during
CO2 injection. However, there is a limited number of experimental studies has been
reported on fines migration and the effect of fines particle properties on injectivity
impairments during CO2 injection.
Currently, the most widely used porosity-permeability model to predict CO2
injectivity in current numerical simulations are Kozeny-Carman model, HagenPoiseuille model and Power law model [8, 29]. The models are ascribed by porosity
3
change due to pore modification and several parameter values were derived from the
fitting of experimental data [8, 30-33]. In many cases, the salt precipitation has
completely dominated the modelling of CO2 injectivity without considering the
alteration contributed by the migration of particles. In 2011, Sbai and Azaroual
developed a mathematical model based on the double layer expansion theory to predict
permeability alteration due to fines migration and retention during CO2 sequestration.
Meanwhile, recent work by Xie, et al. [35] implemented the surface force concept
combined with the hydrodynamic effect to illustrate the migration of fines during CO2
injection. However, the prediction of permeability alteration due to salt precipitation
and fines migration did not include the overall impact of CO2, brine, rock, and fines
migration components on the permeability changes/alteration of the rock sample. Later,
Sokama-Neuyam [20] attempted to model the coupled effect of fines mobilization and
salt precipitation on CO2 injectivity. The model, however, has some drawbacks as it
does not consider the varying sizes of mobile particles and failed to represent the pore
bridging and multi-particle blocking in the fine trapping mechanism.
1.2 Problem statement
The injection of CO2 produced from high CO2 gas fields into saline aquifer for
sequestration would trigger injectivity-related issues due to mineral dissolution,
precipitation and fines migration mechanisms initiated in the aquifer. These
mechanisms would have direct implications on the CO2 injectivity and has been
reported in field observations and laboratory studies. Although multiple studies have
been performed to evaluate the impact of these mechanisms on petrophysical changes
of the rock properties, there have been limited studies on the influence of individual
parameter of CO2, fluids, rock, and migrated particles on the injectivity damage
presented by permeability alteration. As a result of different conditions used in each
study, especially brine type, brine salinity, rock permeability, injection flow rate, and
CO2 injection scheme, direct comparisons between permeability alterations in different
studies became peerless. Moreover, the existing prediction of CO2 injectivity changes
are ascribed by porosity, while certain relations used to fit experimental data are often
4
simple exponential or power functions. All of these modeling studies, however, have
been focusing on the salt precipitation effect of CO2 injectivity alteration without
considering the alteration contributed by the fines migration. The existing models also
do not consider the effect of varying particles sizes, particle concentration and has not
been able to simulate different plugging mechanisms which normally occurs in porous
media. Having said that, the special properties of CO2 at supercritical condition and
complex interactions between various elements of the fluids-rock system demand an
extension of conventional findings to understand the impact of fines migration in
context of CO2 injection. Therefore, a comprehensive study to evaluate the influence of
individual component of CO2, brine, rock, and particles on the CO2 injectivity changes
is essential in order to develop a reliable model to predict the relative importance of
each component in CO2 injectivity changes.
1.3 Objectives
The general objective of this study is to investigate the combined effect of salt
precipitation and fines migration on CO2 injectivity changes. In order to achieve the
general aim of this study, the following specific objectives are presented below;
1. To evaluate the individual and combined effect of salt precipitation and fines
migration on CO2 injectivity at various CO2, brine, rock, and particles
parameters through experimental work.
2. To assess the applicability of the existing CO2 injectivity models at various CO2,
brine, rock, and particles parameters using the generated experimental data.
3. To develop new predictive modelling for CO2 injectivity model using RSM and
neural network.
5
1.4 Scope of study
This study is based on semi-static batch experiment and core flood experiment. The
pressure of 1800 psi (12.4 MPa) and temperature of 60°C (140oF) was selected to
represent a potential geological storage in the Malaysia [36]. At this condition, the
injected CO2 was in supercritical CO2 condition (critical limit for CO2 is at 31.1oC and
1070 psi). Petrographic analysis such as XRF, XRD, FESEM and EDX and effluent
analysis were used to support the analysis. Three types of high-quartz sandstone cores
were used as porous media in these series of experiment to represent ubiquitous saline
aquifers that have the potential for CO2 geological storage sites namely Kirby, Berea,
and Idaho. The three types of core samples were selected based on variation in porosity,
permeability, and pore sizes.
In the experiment, different salinities from 6000 parts per million (ppm) to 100000 ppm
NaCl brine were prepared to evaluate the influence of brine salinity on injectivity
changes. Furthermore, a constant salinity of 30000 ppm was used to understand the
impact of different brine systems, injection flow rate, jamming ratio and particle
concentration. The injection flow rate was set between 2 cm3/min and 10 cm3/min to
represent the flowing condition at near wellbore. To control the amount and fines sizes,
0.005, 0.015, 0.03, 0.045, 0.06 and 0.07 µm of silica oxide particles were used to
represent the moving fines particles. The selected particle sizes would give jamming
ratios (pore throat to particle diameter ratio) from 0.004 to 0.04. This is to give
difference pore plugging occurrence suggested by Khilar and Fogler [37]. Then, the
concentration of the particles was varied from 0.1 wt% to 0.5 wt%.
The CO2 injectivity is measured using Relative Injectivity Change equation proposed
by Sokama-Neuyam, et al. [17]. It compares the percentage difference between final
permeability and initial permeability of the sandstone rock after being injected with
CO2 at changing CO2, brine, rock, and fines particles parameters. Results from the
experiments were used to develop new predictive model using RSM and neural network
regression.
6
1.5 Contributions and significance of study
The research project was sponsored by YUTP research grant with a primary aim to
evaluate the impact of salt precipitation and fines migration on CO2 injectivity at
varying CO2-brine-rock parameters. The other objectives are to assess the existing CO2
injectivity prediction models and to develop a new model which consider the effect of
salt precipitation and fines migration mechanism.
This research contributes to the current understanding of how brine salinity, CO2
injection flow rate, particle size and particle concentration, precisely, water-wet silica
particles could affect CO2 injectivity which presented by permeability change. The
findings were supported by experiments such as semi-static batch experiment,
petrographic characterization, fluid and particle analysis and core flood experiments.
This study added to the existing research by assessing the individual and combined
impact of salt precipitation and fines migration mechanisms at changing CO2-brinerock parameters on CO2 injectivity which has not been adequately emphasized in the
previous literatures. The final developed model has contributed to the existing CO2
injectivity change model in the petroleum and CO2 sequestration industry, which was a
lack in giving an accurate and precise prediction in the presence of fines migration and
changing CO2 injection flow rate.
The following contributions have been successfully achieved:
•
This research found that the injection of scCO2 would lead to more
permeability reduction compared to the injection of CO2-saturated brine in
sandstone core samples which were saturated with constant NaCl brine. The
cumulative damage by both injection schemes was almost equivalent to
permeability alteration in similar sandstone injected with CO2-saturated
brine followed by scCO2.
•
This research observed that rock with higher permeability tended to receive
more damage due to greater pore channel size and longer residence time
between CO2-brine-rock.
7
•
This study indicates that increasing brine salinity, particle size and particle
concentration have increased the permeability reduction.
•
This study observed that there was a critical injection flow rate which acts
a turning point which beyond this would lead to lower injectivity
impairment.
•
This research found that the existing porosity-permeability model (KozenyCarman and Hagen-Poiseuille) are incapable of predicting the CO2
injectivity change at changing injection flow rates and the presence of fines
particles.
•
This research revealed that applicability of Power law model depends on the
value of constant ‘n’ for different experimental conditions. The equation for
different conditions were summarized in Chapter 4 (Table 4.5).
•
This research established a new model by using ANN and RSM in
predicting the CO2 injectivity changes at varying CO2 (injection flow rate),
brine (salinity), rock and particles (jamming ratio and particle
concentration) parameters.
•
Although the new model was developed based on experimental datasets, the
other cases studies which are operating in the range of experimental
conditions still can use this model. This was proven in the testing part of the
model by using data from published case studies.
1.6 Thesis outline
•
Chapter 1: Introduction
Chapter 1 covers the introduction of the CO2 injection for sequestration in saline
aquifer. Moreover, problem statement, research objectives, scope of research
study, novelty and thesis outline are introduced in this chapter.
8
•
Chapter 2: Literature Review
Chapter 2 contains a concise literature review of current research within the
scope of this study. Firstly, concept and elements of CO2 injectivity for
sequestration have been introduced and various process modifying pore spaces
during CO2 injection is summarized. An extensive review on previous field
observations, laboratory findings and existing models to predict CO2 injectivity
are also discussed in some details.
•
Chapter 3: Methodology
This chapter presents the materials, equipment, and experimental works used in
determining the properties and performance of the studied CO2, brine, rock and
fines particles parameters. Semi static batch and core flooding setup and
procedures are also explained in this chapter. Modelling works to predict CO2
injectivity change is also described in this chapter.
•
Chapter 4: Results and Discussion
Chapter 4 presents a comprehensive discussion with full details on data and
results that were obtained from the laboratory experiments and modelling
works.
•
Chapter 5: Conclusion and Recommendations
Lastly, this chapter summarizes the study and findings that can be achieved from
the experimental results and discussions. Relevant recommendations for future
work are also included in this chapter.
9
CHAPTER 2
LITERATURE REVIEW
This chapter reviews the relevant theory and previous studies on CO2 injectivity
impairment due to salt precipitation and fines migration during sequestration. It begins
with explanation of CO2 geosequestration in saline aquifer. Then, the concept and
theory to measure CO2 injectivity during sequestration are presented. The next section
explains the main mechanisms that contributes to the CO2 injectivity impairments
which are mineral dissolution, mineral precipitation, salt precipitation and fines
migration. The field observations and laboratory studies were critically reviewed. In
the final part of this chapter presents a review of existing analytical model to predict
CO2 injectivity and application of neural network as a better prediction tool.
2.1 The geological carbon sequestration (GCS) in saline aquifer
The United Nations Intergovernmental Panel on Climate Change (IPCC), in
numerous studies, has assessed the increase in the earth temperature due to the
anthropogenic CO2 emissions [38, 39]. Scientists found the carbon capture and storage
(CCS) technology as the main solution to reduce CO2 in the atmosphere by separating
it from the atmosphere and injecting it into geological storage sites. CCS is the only
practical solution to bending the curve or, in other words, to achieve negative carbon
emission the carbon in the air must be captured and stored in any tank or reservoir [40].
It is estimated that CCS has the potential to make up between 10% and 55% of the total
carbon mitigation effort until the year 2100 [41]. Currently, the technology is able to
capture and store the anthropogenic gas in the range of a few kt- CO2 per year up to 1
or 2 Mt- CO2 per year based on different tank or reservoir sizes and other technological
limitations [42]. Therefore, to meet the key indicator to capture and store 20 Gt-CO2 by
2050, it requires the current largest project scale to be multiplied by a factor of five and
deployed 200 times in the next 10-20 years.
An integrated CCS system consists of three main parts; capturing and separating
CO2 from other gases, transporting the CO2 to the disposal site and injecting the CO2
in identified storage sites [42]. Originally, in the last step of the CCS system, CO2
storage included a few types of media such as ocean storage, geological storage, and
mineral carbonation (Figure 2.1). However, current and many ongoing CCS research
and commercial operations mainly cover geological storage [43]. Other storage options
such as ocean storage and mineral carbonation gained less attention owing to
environmental implications or intense energy requirements [44].
Figure 2.1 Types of geological storage options [45].
Geological Carbon Sequestration (GCS) in saline aquifers is a recent approach to
store and mitigate CO2 before it is released into the atmosphere. This is considering the
available option of potential water aquifers that are technically feasible and
economically viable for the CCS project [5]. Studies indicated that saline aquifers can
provide huge storage capacity compared to other types of reservoirs [7, 45]. This has
11
encouraged researchers to investigate the potential and suitability of saline aquifers for
CO2 storage [46, 47]. For example, the reinjection of CO2 into the saline aquifer is
considered an option to permanently secure the anthropogenic gas produced from the
high CO2 gas field in the region of South East Asia [4]. Despite the high potential for
CO2 storage, relative to other geological sites such as coal seams and depleted oil and
gas reservoirs, relatively less information is available about the CO2 storage properties
of saline aquifers.
At present, there are about 30 active CCS fields for saline aquifers type of
geological storages that are operating around the world. Figure 2.2 shows the pressure
and temperature data tabulation for selected CCS projects that inject CO2 into saline
aquifers for storage. The data was compiled based on available field reports and
published literature. North America has the largest number of CCS projects where most
of the operations take place in the United States (US). There are another 15 projects
located outside the US, namely Canada, Brazil, UAE, Japan and Saudi Arabia. The
injection rate varies between projects; the lowest is 0.8 kt/day and the maximum is 23
kt/day.
Figure 2.2 Plotted pressure and temperature data based on compiled large scale CCS
projects in saline aquifer.
12
In Norway, there are two large CCS projects, Sleipner and Snohvit CO2 storage
projects which have been injecting million tonnes of CO2 into saline aquifers for
storage. The Sleipner project is the first commercial CCS to inject into a saline aquifer
and this is largely prompted by having an adequate price on carbon that has been
introduced by the Norwegian government. The other commercial CCS projects for
saline aquifers are the In Salah project in Algeria and the Gorgon project in Australia.
Others are still either in the demonstration stage or pilot scale. Most of this kind of
geological storages are sandstone with only two locations that have carbonate as the
reservoir rock. The majority of the formation have good porosity from 12% to 38% that
yield an average porosity of 19%. However, the permeability of the formation between
the projects shows a wide range that can be sorted into three main groups; low
permeability (less than 100 mD) has 4 CCS projects, medium permeability (100 mD –
500 mD) has 12 projects and high permeability (more than 500 mD) has 9 projects.
Based on the plotted diagram, the injection and disposal of CO2 into the saline aquifers
is mostly made at supercritical conditions (31.1oC and 1070 psi), in order to avoid
adverse effects of prior separation of CO2 into liquid and gas phases in the injection
system [48-50].
In Malaysia, there is a growing interest to meet the global demand of reducing CO2
emission by sequestering the produced CO2 from high CO2 offshore gas fields into
available saline aquifer in the geological formation [1, 4]. Sukor, et al. [2] reported that
there are about 37 Tscf of natural gas is yet to be developed in Malaysia’s gas fields.
This mainly because of high CO2 content (above 10%) which could give corrosive
problems to the surface facilities and pipelines. Recently, the ongoing development of
CCS technology would give a potential hope for these gas fields with high CO2 content
to be developed by adopting the advanced offshore CO2 separation and sequestration
into saline aquifer.
13
2.2 CO2 injectivity elements for sequestration
Injecting a large amount of CO2 into geological storage would encounter three
critical problems on storage capacity, containment efficiency and proper injectivity
[51]. Proper estimation of storage capacity in a saline aquifer is a big challenge. In a
hydrocarbon reservoir, the calculation is straightforward because the completed
reservoir intervals are well defined, and the capacity estimation is based on the material
balance concept; conservation of mass in a reservoir by the observation that the amount
of mass leaving a control volume is equal to the amount of mass entering the volume
minus the amount of mass accumulated in the volume can be used for CO2 storage.
However, estimation of CO2 storage in saline aquifers is difficult because of their
different trapping mechanisms that act at different rates,
and CO2 solubility in
continuous aquifer volumes [52, 53].
For injectivity, a significant volume of CO2 would be injected into the storage at an
acceptable rate through a minimum number of wells due to economic reasons [54]. The
attainable rate of CO2 injection into the formation without fracturing the formation can
be expressed in terms of the injectivity index (I), defined as the ratio of volumetric
injection flow rate (q) to the pressure drop [55, 56]:
𝐼=
𝑞
∆𝑃
(2.1)
In the laboratory scale, fluid injectivity is normally conducted by injecting CO2 at
certain flow rate into a core sample in a core flood unit. The pressure drops before and
after the experiment are measured throughout the experiment to calculate the injectivity
value. In order to estimate the injectivity impairment during the injection process, a
Relative Injectivity Change (RIC) index (𝛽) is being used by researchers [57]. It is a
ratio of the injectivity index of initial injection condition (𝐼𝑖 ), to final injection
condition (𝐼𝑓 ), at a constant injection flow rate (𝑞𝑖 = 𝑞𝑓) assuming that the viscosity of
the fluid (𝜇), core area (𝐴) and length (𝐿) used in the measurement are considered
constant, 𝐶 = 𝐴⁄𝜇𝐿. Therefore, RIC can be defined as
14
𝐼𝑖 =
𝑞
= 𝑘𝑖 . 𝐶
∆𝑃𝑖
(2.2)
𝐼𝑖 =
𝑞
= 𝑘𝑓 . 𝐶
∆𝑃𝑓
(2.3)
𝑘𝑓
∆𝑃𝑖
)= 1−( )
∆𝑃𝑓
𝑘𝑖
(2.4)
𝑅𝐼𝐶 = 1 − (
Any pore plugging would reduce the flow area (𝐴) and increase the pressure drop
across the core, ∆𝑃. Therefore, it would give ∆𝑃𝑓 > ∆𝑃𝑖 and 𝑘𝑖 > 𝑘𝑓 because of
permeability impairment. A positive RIC value indicates injectivity impairment and
vice versa. The RIC value is normally presented in percentage, and it is an indirect
method for estimating injectivity impairment, independent of chemical properties that
occur in the core during injection.
For the normal range of pressures and temperatures found in the reservoir rock, the
injected CO2 could be in a gas, a liquid, or the supercritical phase subject to its unique
thermodynamic properties (Figure 2.3). CO2 is a stable gas, heavier than air, at normal
atmospheric conditions and it will turn to a supercritical phase once temperature and
pressure reach above 31.1oC and 1070 psi respectively [48, 49]. Due to the risk of
buoyancy-driven leakage and to avoid the adverse effects of prior separation of CO2
into liquid and gas phases in the injection system, the injection and disposal of CO2 into
the saline aquifers would ideally be made at supercritical conditions[58]. In this
condition, CO2 behaves still like a gas by filling all the available volume, but has a
“liquid” density that increases, depending on pressure and temperature, from 200 to 900
kg/m3, thus approaching water density [59, 60].
15
Figure 2.3 Relevant properties of CO2 as functions of temperature and pressure: (a) CO2
phase diagram, (b) variation of liquid CO2 density as a function of temperature and
pressure and (c) viscosity of the liquid and supercritical phases [61].
Injection of CO2 into aquifers includes a variety of strongly- coupled physical and
chemical processes as multiphase flow, solution-dissolution kinetics, solute transport,
and hydrodynamic instabilities due to the displacement of less viscous brine with more
viscous CO2 (viscous fingering), and the upward movement of CO2 due to gravity
(gravity override) [46]. Therefore, careful attention must be given to these mechanisms
in order to measure accurate CO2 injectivity changes.
2.3 Factors affecting CO2 injectivity impairment
Continuous injection of massive amounts of CO2 can potentially alter the porosity
and the permeability of a porous medium at near wellbore. Lombard, et al. [62],
Azaroual, et al. [63], Torsæter and Cerasi [64] and many others have described the
various problems encountered when injecting CO2 into formation rock saturated with
16
saline water. Firstly, Lombard, et al. [62] classified the processes modifying pore spaces
during CO2 injection into three types: (a) geochemical effects such as mineral
dissolution and salt precipitation, (b) transport effects such as mobilization of fines, and
(c) geomechanical processes. Among these threats to injectivity, the damage
mechanism contributed by salt precipitation has been focused on in recent years [46,
65, 66].
Later, Azaroual, et al. [63] added another type; injection scheme to consider the
effect of injection pressure, temperature, flow rate and displacement methods which
can trigger different mass and heat transfer mechanisms. Figure 2.4 shows the overview
of factors controlling the CO2 injectivity impairment during sequestration in saline
aquifer. The integration of all four key factors is critical to determine the success of a
GCS project. The understanding of these phenomena on the basis of scientific and
technical knowledge will reduce the uncertainty about injectivity and the predictive
results of numerical simulations on CO2 storage sustainability and safety.
Figure 2.4 Different factors that controlling CO2 injectivity impairment.
17
During the lifetime of CO2 sequestration, the migration process and interactions can
be categorized into several regions from the injection well to the furthest affected region
depending on the time of sequestration and the initial permeability of the formation
rock. The moment CO2 injection starts, usually in the supercritical form, scCO2 will
dissolve and interact with the nearest reactive material; formation brine. Due to
continuous injection, two initial processes will take place; while the prevailing scCO2
pushes the formation brine further into the formation leaving dry salts behind, the
scCO2 nearest to the formation brine fronts will slowly dissolve in the brine and
dissociate into carbonic acid [67]. Thus, the interaction region can be categorized into
five regions as depicted in Figure 2.5 and Figure 2.6.
1. Region 1 – Nearest to the well where extreme conditions of capillarity and
dehydration reactions occur where CO2-cement interaction occurs which may
disturb the initial integrity of the well.
2. Region 2 –The initial aqueous phase of the formation is totally removed and the
porous medium now contains only scCO2 and a small quantity of metastable
and capillary water in the fine pores and micro cracks. This region is also known
as the dried region.
3. Region 3 – Multiphase region. The porous media in this region contains both
the scCO2 and the aqueous phase including water, salts, and aqueous CO2. The
pH and the composition of the aqueous phase vary with water saturation with a
drying trend of the rock and creating conditions for capillarity.
4. Region 4 – Acidified region. This region contains the aqueous phase of salt and
CO2. pH in this region is extremely low due to the dissociation of aqueous CO2
into carbonic acid. This region is also where mineral dissolution and
precipitation occur, inducing non-reactive materials to be discharged in the flow
path.
5. Region 5 – Non- affected region. The porous medium in this region contains
only the initial aqueous solution. The pores are saturated with water (initial
18
state) under conditions of thermodynamic equilibrium between minerals of the
rock matrix and pore water.
Figure 2.5 pH, water and gas saturation explained as segregated region from wellbore
during CO2 sequestration process (modified from Andre et al., 2007).
As shown in Figure 2.5 and Figure 2.6, an obvious difference between CO2
injection and the conventional injection of hydrocarbon gas is the geochemical
interactions between CO2, brine, and rock formation that drive the changes in rock flow
and petro- physical properties.
19
Figure 2.6 Aerial view of a typical interaction region of CO2 geo-sequestration in saline
aquifer.
In summary, the formation damage in the CO2 injection well occurs due to the
following interactions between the fluid-fluid and the fluid-rock systems:
1. CO2-brine behavior; for example, multiphase flow conditions that affect
relative permeability and pH reduction due to carbonic acid creation after CO2
dissolves in brine.
2. CO2-wellbore interactions; for example, interfaces between cement and CO2
can lead to fluid pathways that allow fluid to escape.
3. Pure CO2-rock minerals; for example, mobilization of trace metals by dry
supercritical CO2, the relatively rapid carbonation of silicate minerals by waterbearing supercritical CO2 and some carbonation by dry CO2.
4. Mixed CO2-rock; for example, contaminant gas such as SO2 can cause heavy
quartz dissolution.
5. CO2 saturated brine-rock; for example, mainly due to rapid mineral dissolution
and precipitation mechanisms.
20
6. Clay shrinking and swelling; for example, dispersive clay such as kaolinite is
subjected to the lifting off from other particles, and sudden water extraction
from clay minerals to dry CO2 can lead to shrinking in size.
This study focused on the permeability alteration that is mainly caused by the CO2brine-rock interactions in the pore spaces near the wellbore region. Therefore, three
primary mechanisms that contribute the most are the mineral dissolution and
precipitation, salt precipitation and fines migration. The mechanism of the reactions
and their effects are described in more detail in the following sections.
2.4 Mineral dissolution and secondary mineral precipitation
Mineral dissolution and precipitation during the reactive injection of CO2 are
among the main mechanisms that occur due the alteration of the geochemical
equilibrium between rock-forming minerals and formation waters [68, 69]. Mineral
dissolution occurs when the acidic condition resulting from the dissociated CO2 in
brine dissolves the carbonate mineral and other minerals in the formation rock [70, 71].
Meanwhile, mineral precipitation occurs when cations, initially available in the
formation water, react with the aqueous bicarbonates and form new insoluble secondary
minerals.
When carbon dioxide is dissolved in the formation brine, basically two types of
reactions may occur: pH-buffered (reactions that change the acidity level of the
formation) and non-pH buffered [72], and the rates of these reactions may vary from
formation to formation and buffer pH at different levels depending on the mineralogical
and fluid compositions in the aquifer. In general, during the injection of CO2 into a
saline aquifer, the pH may change from its initial condition of ~7 (Region 5 in Figure
2.6) to around ~3 (Region 3 in Figure 2.6). Furthermore, without considering the salt
precipitation effect, the dissolution of formation rock minerals may cause the rock mass
porosity and permeability near the injection well to be significantly increased [72]. In
contrast, precipitation of carbonate minerals from any of these reactions may create a
negative influence on aquifer permeability in the early stages of the geochemical
21
reactions. Therefore, the process is complex, and holistic understanding is necessary
before putting it into practice.
Depending on salinity, brine composition, pressure and temperature, CO2 could
dissolve in aqueous solution until equilibrium is established. The ions in the solution
could dissociate into HCO3+ and CO3- which may induce the formation of carbonic acid.
According to Fang et al. (2010) about 1% of the dissolved CO2 exists as carbonic acid.
Regardless of the rock composition, the progressive dissolution of CO2 in the brine
(formation water) leads to a reduction in pH to about 3-4 [73-75]. Although small in
amount, the carbonic acid in formation could dissolve cementing materials that hold the
grains together. Theoretically, in the absence of dynamic forces, mineral dissolution
could increase effective porosity and permeability by etching new pore spaces or
widening narrow pore channels, thus temporarily increasing the injectivity [11, 76].
Cementing materials are usually made up of clay and carbonate minerals. While
only some clay minerals can be dissolved in acidic conditions, carbonate minerals are
very susceptible to dissolution upon dissociation of CO2 into carbonic acid. Table 2.1
summarizes the dissolution reactions of common minerals in acidic conditions. While
this may sound beneficial, dissolution of cementing materials may result in the
mobilization of fines particles which may travel along with the carbonated brine. These
fines particles could agglomerate and plug pore throats, reducing the permeability of
the formation rock. Moreover, the bicarbonates could react with cations in the rock and
formation water to form stable carbonates which later could aggregate into small
particles or form a scale on the pore walls.
Subsequent growth of secondary minerals, especially clay and carbonate minerals,
occur following the reactions between CO2-brine-rock. The phenomena are controlled
by reactive fluid transport processes, fluid pH and the availability of metal cations in
the complex fluid-rock interactions. The growth of carbonate minerals in the system
has been recognized as a method for long- term CO2 storage known as mineral
carbonation. Table 2.2 shows the list of minerals that react during CO2 injection and
produce the newly formed secondary mineral.
22
On the other hand, as studies from literature show, CO2 dissolution in formation
brine could only reduce the pH to as low as 3-4; a major mineral in sandstone, like
quartz, is known to be unreactive towards this condition. Quartz, as the main silicate,
only dissolves at higher pH (pH > 7) and extremely low pH (pH < 2) [77]. Therefore,
it can be concluded that quartz dissolution is negligible during CO2 injection [25, 78]..
Table 2.1 Summary of mineral with complete dissolution after CO2-brine-sandstone
interactions
Mineral
Reaction
name
Kaolinite
𝐴𝑙2 𝑆𝑖2 𝑂5(𝑂𝐻)4 (𝑠) + 6𝐻 + (𝑎𝑞) → 5𝐻2 𝑂 + 2𝑆𝑖𝑂2 (𝑎𝑞) + 2𝐴𝑙 3+ (𝑎𝑞)
𝐼𝑙𝑙𝑖𝑡𝑒 + 8𝐻 + (𝑎𝑞)
→ 5𝐻2 𝑂(𝑙) + 0.6𝐾 + (𝑎𝑞) + 0.25𝑀𝑔2+ (𝑎𝑞)
Illite
+ 3.5𝑆𝑖𝑂2 (𝑎𝑞) + 2.3𝐴𝑙 3+ (𝑎𝑞)
𝐶𝑎0.6 𝑁𝑎0.4 𝐴𝑙1.6 𝑆𝑖2.4 𝑂8 + 5.4𝐻 + (𝑎𝑞) + 𝐶𝑂2 (𝑎𝑞)
→ 0. 6𝐶𝑎2+ (𝑎𝑞) + 𝐻𝐶𝑂3− (𝑎𝑞) + 2.2𝐻2 𝑂(𝑙)
Labradorite
+ 0.4𝑁𝑎+ (𝑎𝑞) + 1.6𝐴𝑙 3+ (𝑎𝑞) + 2.4𝑆𝑖𝑂2 (𝑎𝑞)
𝐶𝑎𝐶𝑂3(𝑎𝑞) + 𝐻 + (𝑎𝑞)
Calcite
Dolomite
→ 𝐶𝑎2+ (𝑎𝑞) + 𝐻𝐶𝑂3− (𝑎𝑞) , 𝑎𝑡 ℎ𝑖𝑔ℎ 𝑝𝐻 𝑣𝑎𝑙𝑢𝑒𝑠 𝑜𝑛𝑙𝑦
𝐶𝑎𝑀𝑔(𝐶𝑂3 )2(𝑠) + 2𝐻 + (𝑎𝑞) + 𝑀𝑔2+ (𝑎𝑞) + 𝐻𝐶𝑂3− (𝑎𝑞)
Table 2.2 Summary of dissolved minerals after CO2-brine-sandstone interactions with
newly formed secondary minerals
Mineral
Reaction
name
Secondary
minerals
𝐶𝑎2+ (𝑎𝑞) + 𝐶𝑂32− (𝑎𝑞) → 𝐶𝑎𝐶𝑂3(𝑠)
Calcite
𝐹𝑒 2+ (𝑎𝑞) + 𝐶𝑂32− (𝑎𝑞) → 𝐹𝑒𝐶𝑂3 (𝑠)
Siderite
𝑀𝑔2+ (𝑎𝑞) + 𝐶𝑂32− (𝑎𝑞) → 𝑀𝑔𝐶𝑂3 (𝑠)
Magnesite
𝐶𝑎2+ (𝑎𝑞) + 𝑆𝑂42− (𝑎𝑞) → 𝐶𝑎𝑆𝑂4 (𝑠)
Anhydrite
23
𝐾 + (𝑎𝑞) + 3𝐴𝑙 3+ (𝑎𝑞) + 2𝑆𝑂42− (𝑎𝑞) + 6𝐻2 𝑂(𝑙)
Alunite
→ 𝐾𝐴𝑙3 (𝑆𝑂4 )2 (𝑂𝐻)6 (𝑠) + 6𝐻 + (𝑎𝑞)
𝐶𝑎2+ (𝑎𝑞) + 𝑀𝑔2+ (𝑎𝑞) + 2𝐻𝐶𝑂3− (𝑎𝑞)
Dolomite
→ 𝐶𝑎𝑀𝑔(𝐶𝑂3 )2 (𝑠) + 2𝐻 + (𝑎𝑞)
Albite
𝑁𝑎𝐴𝑙𝑆𝑖3 𝑂8 (𝑠) + 𝐶𝑂2 (𝑔) + 𝐻2 𝑂(𝑎𝑞)
→ 𝑁𝑎𝐴𝑙(𝐶𝑂3 )(𝑂𝐻)2 (𝑠) + 3𝑆𝑖𝑂2 (𝑠)
K-feldspar
𝐾𝐴𝑙𝑆𝑖3 𝑂8 (𝑠) + 𝑁𝑎+ (𝑎𝑞) + 𝐶𝑂2 (𝑔) + 2𝐻2 𝑂(𝑙)
→ 𝑁𝑎𝐴𝑙(𝐶𝑂3 )(𝑂𝐻)2 (𝑠) + 3𝑆𝑖𝑂2 (𝑠) + 𝐾 + (𝑎𝑞)
Calcite
𝐶𝑎𝐶𝑂3 (𝑠) + 𝐻 + (𝑎𝑞)
Dawsonite,
quartz
Dawsonite,
quartz
Complete
dissolution
→ 𝐶𝑎2+ (𝑎𝑞)
+ 𝐻𝐶𝑂3− (𝑎𝑞) , 𝑎𝑡 ℎ𝑖𝑔ℎ 𝑝𝐻 𝑣𝑎𝑙𝑢𝑒𝑠 𝑜𝑛𝑙𝑦
Glauconite
𝐺𝑙𝑎𝑢𝑐𝑜𝑛𝑖𝑡𝑒 + 14𝐻 + (𝑎𝑞)
Quartz
→ 1.5𝐾 + (𝑎𝑞) + 2.5𝐹𝑒 3+ (𝑎𝑞) + 0.5𝐹𝑒 2+ (𝑎𝑞)
+ 𝑀𝑔2+ (𝑎𝑞) + 1.0𝐴𝑙 3+ (𝑎𝑞) + 7.5𝑆𝑖𝑂2 (𝑎𝑞)
+ 9𝐻2 𝑂(𝑙)
Annite
𝑎𝑛𝑛𝑖𝑡𝑒 + 3𝐶𝑂2 ↔ 3𝑠𝑖𝑑𝑒𝑟𝑖𝑡𝑒 + 𝐾 − 𝑓𝑒𝑙𝑑𝑠𝑝𝑎𝑟
Siderite,
K-feldspar
Chlorite
𝐶ℎ𝑙𝑜𝑟𝑖𝑡𝑒 + 20𝐻 + (𝑎𝑞)
Aluminium
→ 5𝐹𝑒 2+ (𝑎𝑞) + 5𝑀𝑔2+ (𝑎𝑞) + 4𝐴𝑙(𝑂𝐻)3 (𝑎𝑞)
hydroxide
+ 6𝐻4 𝑆𝑖𝑂4 (𝑎𝑞)
Subsequent growth of secondary minerals, especially clay and carbonate minerals,
occur following the reactions between CO2-brine-rock. The phenomena are controlled
by reactive fluid transport processes, fluid pH and the availability of metal cations in
the complex fluid-rock interactions. The growth of carbonate minerals in the system
has been recognized as a method for long- term CO2 storage known as mineral
carbonation. Table 2.2 shows the list of minerals that react during CO2 injection and
produce the newly formed secondary mineral.
On the other hand, as studies from literature show, CO2 dissolution in formation
brine could only reduce the pH to as low as 3-4; a major mineral in sandstone, like
24
quartz, is known to be unreactive towards this condition. Quartz, as the main silicate,
only dissolves at higher pH (pH > 7) and extremely low pH (pH < 2) [77]. Therefore,
it can be concluded that quartz dissolution is negligible during CO2 injection [25, 78]..
2.5 Salt precipitation
Salt precipitation due to brine vaporization during scCO2 injection into a saline
aquifer is a distinct phenomenon. In microscopic discussion, salt precipitation in porous
media will reduce its porosity and permeability while in macroscopic discussion,
reduction in porosity and permeability will affect further injection of scCO2 into an
aquifer [11, 33, 79-81].
Figure 2.7 A typical occurrence of salt precipitation region of CO2 geo-sequestration in
saline aquifer [11].
Figure 2.7 shows the typical occurrence of salt precipitation at near wellbore region
of CO2 geo-sequestration in saline aquifer. During the injection of scCO2 into a saline
aquifer, there is a mutual solubility between the CO2 stream and the formation water,
where formation water eventually evaporates and the molar fraction of the water in the
CO2 stream increases. In the meantime, as vaporization of the formation water
25
progresses, the concentration of dissolved salt in the brine builds up and when the salt
concentration exceeds its solubility limit under the thermodynamic state of a given
reservoir, the excess salt will precipitate out of the aqueous phase (salting-out) and alter
the porosity and permeability of the formation [73, 82].
2.5.1 Mechanism of salt precipitation
Miri and Hellevang [11] provided a comprehensive review on the mechanism of
salt precipitation affecting CO2 in a saline aquifer. They stated that the progression of
dry-out and the extent of precipitation were the consequences of the interplay between
several physical mechanisms. These mechanisms are:
1. Two- phase displacement of formation brine away from the injection well
by viscous force imposed through the flowing CO2 stream.
2. Evaporation of formation brine into the flowing CO2 stream.
3. Capillary-driven backflow of aqueous phase toward the injection point due
to capillary pressure gradients and salt enhancing.
4. Molecular diffusion of dissolved salt from the aqueous phase.
When CO2 is injected into a saline aquifer, the formation can be divided into several
regions as depicted in Figure 2.6. However, for simplicity, this part of the discussion is
only interested in the different phase regions divided by the flooding front (formation
brine side) and the shocking front (CO2 plume side) as depicted in Figure 2.8 (a). In
between those regions, a two-phase flow region forms where both an aqueous phase
and a CO2-rich phase are present. This process is referred to as the
two-phase
displacement where a primary drainage, owing to the viscous displacement, pushes
brine away from the injection well [33, 81, 83].
As the flooding front moves further into the aquifer, a zone is left behind wherein
residual brine is trapped in several configurations such as thin wetting films
surrounding the grain surfaces, liquid bridges and/or pools of brine in the pores [84].
26
Immediately and simultaneously this drained region is exposed to the constant flow of
scCO2 with low water vapor pressure, initiating an evaporation regime and resulting in
formation dry-out. In addition, as water is evaporated, the relative permeability of CO2
increases allowing for further evaporation.
While most of the water mass has been pushed away from the injection well, the
water in the two-phase region is left sticking on the rock grains due to mineral
wettability. The saturation gradient resulting from this phenomenon creates a capillary
pressure gradient towards the drying front which eventually overcomes the injection
pressure gradient (Figure 2.8 (b)). Thus left-over water will imbibe towards the drying
front, supporting more evaporation [33, 81, 83].
As the water is evaporated into the CO2 stream, salt concentration in the trapped
brine increases which results in salt diffusion near the water-CO2 face (Figure 2.8 (c))
[83, 85]. Once the salt concentration in the trapped brine reaches it solubility limit due
to the constant evaporation process, salt will precipitate out of the aqueous phase. The
solubility of CO2 depends on many factors including pressure, temperature and salt
types and their combinations [86]. The precipitated salt has a significant affinity toward
the aqueous solution, which means it can imbibe water from a large distance towards
the evaporation front. This process will result in further salt precipitation [84].
Figure 2.8 Aerial schematic illustration of different physical mechanisms contributing
to the process of salt precipitation [11]
27
In pore scale observation, Kim, et al. [87] observed that salt precipitate forms by
two mechanisms which are large bulk crystal (Figure 2.9) formed early within the
trapped brine phase, and a more distributed polycrystalline aggregated structure formed
late in the evaporation process. Miri, et al. [84], then discovered that the existence of
the large bulk crystal is due to the self-enhancing effect of the precipitated salt. Salt
precipitate which is hydrophilic in nature has the ability to imbibe more water to
compensate the evaporation process. The net outcome of the imbibition and the
evaporation process results in salt accumulation in the CO2 pathways.
Figure 2.9 Image of micromodel after scCO2 flooding under SEM [87].
2.5.2 Factors affecting salt precipitation during CO2 injection in saline aquifer
There is a general assumption that higher brine salinity would give rise to a higher
amount of salt precipitate. For example, the Ketzin storage site in Germany is a
reservoir with high salinity of around 25wt% and intermediate permeability of about
100 mD. It has been reported that salt precipitation is the main reason for pressure buildup in the course of CO2 injection [79]. However, this relationship is still debated as it
seems to be dependent on other factors as well because there are reports that show
severe salt precipitation despite having intermediate brine salinity. Some researchers
28
have suggested that the relationship between salinity and the severity of salt
precipitation may also depend on the injection rate.
Even though there are reports describing the dependence of salt precipitation on the
injection rate [82, 88-90], its direct relationship is still in question. This is because it
lacks generality as most reports are case dependent. Kim, et al. [91], in their simulation,
for example have attributed the effect of injection rate to the localization of salt
precipitate. They observed that salt precipitation would cause pressure to build up at
the bottom hole as the injection rate increases for low permeability reservoirs. In high
permeability reservoirs however, the trend would be reversed as they simulated that the
combination of a low injection rate and high permeability produced the most severe
case of salt precipitation.
Among all the parameters governing the precipitation process, the most
controversial results have been reported for the effect of the CO2 injection rate. Keeping
in mind the determinative role of the flow rate in the injectivity calculation, explaining
these differences can be an essential step to improve the understanding of the physics
of the precipitation process. Some research suggest that a high injection rate will induce
a higher-pressure gradient, thus suppressing the capillary backflow towards the
evaporation surface [31, 68, 83, 91]. The reduced capillary flow, in turn, reduces the
possibility of intensive salt accumulation. Utilizing an analytical model for the
vaporization-precipitation process, Zeidouni, et al. [92] showed that the extent of salt
precipitation is determined by the combined effect of the aqueous phase mobility and
the vaporization rate. An increase in the injection pressure will slow down the plume
mobility owing to the increased viscosity of the scCO2 phase, but further evaporation
at higher injection pressures will increase the amount of precipitation. In other words,
their results show that an increase in the evaporation rate is more significant than a
decrease in the capillary backflow, which seems to contradict previous findings.
Irrespective of the actual physical impact of the injection rate, many attempts have been
made to define the relationship for the critical velocity above which the massive salt
accumulation corresponding to the capillary drying regime can be avoided. Most of
these studies, however, lack a theoretical basis, and findings strongly depend on the
29
thermodynamic conditions and rock properties of the tests [31, 33, 68]. As a result, the
findings of such studies are case dependent and lack generality.
2.6 Fines migration during CO2 injection
Dissociation of CO2 into carbonic acid could cause a reaction between the aqueous
phase and the host rock causing some of the minerals to be dissolved into water soluble
bicarbonates [71, 93]. As a result, unreactive minerals could be detached from its
original position called fines. Fines are typically defined as mobile particles of an
equivalent diameter smaller than 40 μm [64]. Theoretically, in the absence of dynamic
forces, the dissolution of minerals would create more pore spaces that would increase
effective porosity and permeability, thus increasing the injectivity [11, 62, 76].
Based on previous studies, there are several factors which are affecting fines
migration during scCO2 injection in saline aquifer such as injection flow rate, clay
content, jamming ratio, particle concentration and hydrodynamic condition of carrier
fluid.
2.6.1 Injection flow rate
As stated earlier, fines migration only happens in the presence of dynamic forces.
Thus, fluid velocity is a huge factor in the process of mobilization, migration, and
entrapment of fines particles. Investigation of fluid velocity is a crucial factor in
studying the fines migration phenomenon. This is because at a high flow rate, fines
suspended in fluids will exhibit Brownian motion, creating random particle movement
and induce heterogeneous plugging. The high energy also could dislodge particles
bridging at the pore channels which could open some of the plugged channels [17]. For
example Xie, et al. [94] found that migratory clay particles especially kaolinite particles
could not detach from the grain (quartz) surface unless the fluid velocity increased to 2
cm/s (equivalent to 1200 ml/hr using core plugs with 38 mm in diameter) and higher.
At such velocity, the particles would exhibit positive total interaction force as a result
30
of the increase of tangential force. At a velocity lower than 2 cm/s, the acidic
environment due to CO2 dissolution in formation brine, triggers the surface force to
become less negative. Therefore, kaolinite particles were unlikely to detach from the
grain surface; rather, they were detached from themselves because the double layer
expansion between kaolinite/quartz is much lower than that of the kaolinite/kaolinite
during the CO2 injection.
Some researchers even suggested that a high injection rate, above that certain
critical velocity, will induce higher permeability increment [95, 96]. For example
Mohamed, et al. [97] observed that at high flow rate (5 and 10 mL/min) permeability
increased between 2-4%. Similar findings were reported by Sokama-Neuyam, et al.
[17] who found permeability increment up to 14% when they increased the injection
rate from 2 mL/min to 10 mL/min.
On the contrary, below the certain flow rate, permeability could be unchanged or
reduced because the carried particles might also drift, but with a speed that is
significantly lower than the velocity of the carrier fluid, the particles could settle down
at the bottom of the pore space [94]. This is supported by Mohamed, et al. [97]. A
reduction in the core permeability was reported after CO2 injection. Similar findings
were also reported on permeability reduction of between 10% and 17% at the inlet and
up to 20% at the outlet because of the migration of clay particles plugging the pore
throat [47, 98]. Furthermore, Izgec, et al. [76] highlighted that the duration of the CO2rock contact time and the surface contact area seem to have a more pronounced effect
compared to the rate effect. At high flow rates, the contact time between CO2 and brine
is lesser, leading to a smaller amount of dissolved minerals or vice versa [97]. The
determination of the critical flow rate and its relationship to the mineral dissolution rate
are yet to be established and require further consideration.
2.6.2 Clay content
Clay is a mineral group whose behaviour under CO2 flooding is poorly understood.
It can be divided into four different types on the basis of mineralogy and reactivity,
31
namely kaolinite, illite, chlorite and smectite [84]. Smectite is swelling clay while illite,
kaolinite and chlorite are non-swelling clay. Also, while illite and kaolinite are known
as emigrational fines problem clay; smectite is known as the least stable and the most
susceptible to hydration and diagenetic alteration among clay minerals [85]. It is
broadly accepted in literature that clay minerals stay quite stable in acidic environments
and solutions with high ionic strength. The existence of Na+ and K+ inhibiting ions
within the dead brine solution causes low clay reaction activities [86].
However, several researchers found that the detachment and migration of clay
minerals was the main contributing factor for permeability reduction in sandstone core
samples even at the latter condition [99, 100]. Luquot, et al. [58] added that precipitation
of clay mineral (kaolinite, muscovite and smectite) is higher at lower injection rates. A
study conducted by Al-Yaseri, et al. [95] on Berea sandstone (low clay content) and
Bandera Gray sandstone (high clay content), found that the quantity of clay was not
the sole controlling factor on permeability changes due to pore plugging. They
highlighted that salt type and concentration, acidity, and distribution/structure of clay
minerals within the rock are other factors that need to be considered. The dispersed clay
minerals on the pore wall (pore surface coating), are much likely to be detached and
mobilized in the bulk fluid compared to the structural embedded clay within the rock
grains. Most of the studies, however, were conducted on different types of sandstone
core samples with various ranges of clay mineral content. As a result, the findings of
such studies are case dependent and lack generality.
2.6.3 Jamming ratio
Pore media grain diameter (pore throat size) and particle diameter (size) are two
main parameters determining whether entrapment or piping would occur. In a pore
network, pore throat acts like an entrance that connects the pore areas. Pore throat size
distribution and interconnectivity would affect the particulate process. Probability of
particle entrapment is relatively high in the porous media having small pore throat size.
For example, plugging resulting from particle entrapment is likely to occur in naturally
consolidated porous media such as sandstone because of its small pore throat size (1
32
µm) compared to unconsolidated porous media such as soil mass and packed bed that
are more susceptible to piping because of their relatively large pore throat size [37].
While moving through the pore throat, particles could be trapped because of size
exclusion or direct interception or better known as the jamming ratio (pore throat to
particle diameter ratio, β) [37, 101-104]. If the particle size is equal to or greater than
the pore throat size, then entrapment or plugging will certainly take place. On the other
hand, if the particle size is smaller than the pore throat size, piping or particle passing
through will occur. Different critical jamming ratio values were introduced to explain
pore throat entrapment occurrence.
Table 2.3 presents qualitative results on the particle plugging phenomenon due to
the jamming ratio; dependence of pore plugging or piping on the ratio of particle size
to pore throat size. For example, no plugging or piping will occur if the particle size is
very small, and the jamming ratio value is less than 0.01. Likewise, single plugging or
size exclusion would occur when the particle size is comparable to the pore throat size,
normally in the case of the jamming ratio being larger than 1.00. However, when the
ratio value is between 0.1 and 0.001, either surface deposition, bridging or multiparticle blocking can occur. The particle plugging occurrence, however, is subject to
other conditions such as particle concentration, flow rate and properties of the carrier
fluid.
Table 2.3 Occurrence of pore plugging/piping due to different jamming ratios [37]
Jamming ratio
Occurrence
≥1.00
Plugging due to blocking or size exclusion
0.10 to 0.60
Plugging due to bridging and multi-particle blocking
0.04 to 0.10
Plugging due to surface deposition, bridging and multiparticle blocking
0.01 to 0.04
Surface deposition and multi-particle blocking
< 0.01
Piping
In laboratory work, the particle plugging phenomenon has been reported by several
researchers. For example Al-Yaseri, et al. [24] tested two Bandera Gray sandstone
33
(permeability 15-21 mD) at a pressure of 2175 psi and a temperature of 175oF. They
concluded that due to the low size of pore throat within the high clay content of the
Bandera Gray sandstone (particle size 0.16, pore throat size 0.10, jamming ratio 1.6),
the migration of fines clay particles was limited. Moreover, Sokama-Neuyam, et al.
[17] reported that permeability impairment reduced by 24 percentage points on the
Berea sandstone (pore throat size of 2 µm) when particle size increased from 0.08 µm
(jamming ratio, 0.04) to 0.14 µm (jamming ratio, 0.07). Interestingly, permeability
impairment also increased when they increased particle concentration from 0.3 wt% to
0.5 wt%. They also found that permeability impairment was higher in the Berea
sandstone (64 mD) compared to the lower permeability of the Kirby sandstone (9 mD).
Good understanding of the relationship between pore geometry (size, connectivity) and
moving fine particles is important to evaluate the particle entrapment process. However,
each experimental work was limited to the core flooding experiment without any further
detailed micromodel experiment to confirm the plugging mechanism.
2.6.4 Particle concentration
While particle size to pore throat size is an important parameter, it is believed that
the concentration of the suspension could play an important role in plugging. This is
because as particle concentration increases, the distance between the suspended
particles shortens, enhancing multi-particle blocking of the invaded pores [15]. Particle
concentration plays a greater role when the jamming ratio is in the range of 0.01 and
0.1. At a higher jamming ratio, straining occurs, while at a much lower ratio, there may
even exist a critical particle concentration (CPC) beyond which plugging may occur
[105].
34
2.6.5 Hydrodynamic condition of carrier fluid
Hydrodynamic forces acting on the released particles affect the particulate process
at the pore constrictions. Among all parameters, the most common variable used to
monitor the impact on permeability impairment is injection flow rate. Explaining the
determinative role of the CO2 injection rate can be an essential step to improve the
understanding of the permeability impairment mechanism. At low velocity the particle
size and density are large. The sedimentation force has control on the trajectory of the
particle to lead them to settle at the bottom wall of the pore space. Likewise, if the size
and density of the particle are small, the particle tends to follow the streamline of the
flow [37].
The flow velocity can also indirectly affect the plugging process in the porous
media. The flow velocity controls the rate of particle release which leads to the
concentration of the particles in suspension. The effect of particle concentration on the
plugging phenomenon has been explained in the previous section. Moreover, when the
jamming ratio is between 0.04 and 0.60, the particles have a tendency to form bridges
at pore constrictions (Table 2.2). The structure of the bridge and the rate of the
formation depend on the hydrodynamic conditions of the flow [106]. At high flow
velocity, there will be a high drag force acting on the bridge to cause it to break apart.
In this condition, it will introduce the Brownian motion that creates random particle
movement and induces heterogeneous plugging. The high energy also could dislodge
articles bridging at the pore channels which could open some of the plugged channels
[17]. However, at low flow velocity, it helps the number of bridges formed to be greater.
Some researchers suggest that a high injection rate, above that certain critical velocity,
will induce a higher permeability increment. For example, Mohamed, et al. [107]
observed that at high flow rate (5 and 10 mL/min) permeability increased between 24%. Similar findings were reported by Sokama-Neuyam, et al. [17] They found
permeability increment up to 14% when they increased the injection rate from 2
mL/min to 10 mL/min. On the contrary, below the certain flow rate, permeability could
be unchanged or reduced because the carried particles might also drift, but with a speed
that is significantly lower than the velocity of the carrier fluid, the particles could settle
35
down at the bottom of the pore space [35]. This is supported by Mohamed, et al. [107]
who reported a reduction in the core permeability after CO2 injection. Similar findings
were also reported on permeability reduction of between 10% and 17% at the inlet and
up to 20% at the outlet because of the migration of clay particles plugging the pore
throat [47, 108]. Furthermore, Izgec, et al. [49] highlighted that the duration of the CO2rock contact time and the surface contact area seems to have a more pronounced effect
compared to the rate effect. At high flow rates, contact time between CO2 and brine is
lesser, leading to smaller amounts of dissolved minerals or vice versa [107]. The
determination of the critical flow rate and its relationship with the mineral dissolution
rate is yet to be established and requires further consideration.
2.7 Field reports on CO2 injectivity impairments
Fines migration is one of the long-standing issues in the oil and gas industry. The
chemical damage adverse interactions between external fluids and formation rock or
fluid could trigger several damage mechanisms such as clay swelling, formation
dissolution and wettability alteration. Later, these mechanisms will alter the internal
movement of fine particulates within a rock’s pore structure resulting in the bridging
and plugging of pore throats [109, 110]. It gives a critical effect on the hydraulic
properties and consequently on production or the performance of the injection wells. A
comprehensive compilation of formation damage by fines migration can be found in
Civan [111]. The study of formation damage and fines migration in the context of CO2
injectivity in saline aquifers is a new topic, but evidence of the phenomenon has been
encountered at several CO2 fields.
Hadlow [112] reported the loss of injectivity in six different EOR fields in which
the reservoir permeability average was less than 10 mD. It appears that an average CO2
project will experience about 20% injectivity loss compared to the waterflood
injectivity at similar reservoirs. A significant reduction in well injectivity from 10 to
100% was reported in the Weyburn field in Canada. It was a sandstone reservoir where
CO2 was injected for the EOR purpose. Raistrick, et al. [113] reported that the produced
36
brines showed an increase in Ca2+, Mg2+, K+, SO42-, HCO3- and CO2 concentrations due
to the dissolution of calcite, dolomite, and K-feldspars. The minerals were carried out
by the flood and clogged the narrow pore channels.
In the context of the CCS operation in the saline aquifer, existence of salt
precipitation has been reported in the Snohvit field in Norway and the Ketzin field in
Germany [79, 114]. Zettlitzer, et al. [115] shared their experience in handling the
injectivity impairment of the CO2-injection well in Ketzin, Germany; an onshore saline
aquifer CO2-storage site. They reported that fines migration from the weakly
consolidated Stuttgart formation could be the main problem that caused the injectivity
impairment. Later, Zemke, et al. [116] analysed that the dissolution/precipitation of
minerals and possible textural modifications (shale mobilisation, cement, porous
network) induced important changes in both the physical (e.g. evolution of the porosity
and permeability) and mechanical behaviours of the reservoir rocks. However, the
mechanism is not yet understood in detail. Furthermore, in the Montmiral field, a
natural CO2 field in France, detailed mineralogical and fluid characterisation combined
with numerical modelling show that the dissolution of feldspars is the main reaction
and that the porosity has increased by less than 3% and precipitation of dolomite has
been reported at the site [117].
2.8 Experimental observations on CO2 injectivity impairments
An obvious difference between CO2 injection and conventional hydrocarbon gas
injection is the geochemical interactions between CO2, brine and formation rock that
lead to modifications of the rock flow and petrophysical properties [118]. Petrophysical
properties, especially near wellbore porosity and permeability can significantly impact
injectivity. The porosity and permeability evolution induced by the flow of reactive
fluid has been extensively studied in the past to better model the formation damage at
near wellbore [111] and more recently in the context of geological CO2 storage [46].
Table 2.4 gives a comprehensive list of experimental studies along with summarized
conclusions conducted for assessing petrophysical changes during CO2 injection.
37
Table 2.4 Summary of the experimental studies for petrophysical changes induced by CO2 injection
Rock properties
Fluid
properties
Sayegh, et al.
[119] (1990)
Five Pembina Cardium
sandstone
k = 0.023-0.091mD, 𝜙 =
0.09-0.14%, D = 1.5in L =
2.75in
5 wt% NaCl
Yu, et al.
[108] (2012)
Qing 1 sandstone, China
k = 120-530 mD,
𝜙 = 12-15 %, D = 1 in
L = 7 in
Synthetic brine
Mangane, et
al. [120]
(2013)
Mondeville carbonate,
France
k = 120-530 mD, 𝜙 = 12.6
%, D = 0.35 in L = 0.62 in
Synthetic brine
Luquot, et al.
[121] (2016)
Heletz sandstone, Israel
k = 10-40 mD, 𝜙 = 15-24 %,
D = 0.28 in L = 0.55 in
Gypsum based
and Heletz
formation brine
38
Reference
Injection
condition
T = 113 F
PP = 2000 psi
q = 0.3 and 0.25
mL/min
Fluid = carbonated
brine
T = 212 F
PP = 3480 psi
OP = 3480 psi
q = 0.05 mL/min
Fluid = CO2
saturated brine
T = 212 F
PP = 1740 psi
OP = 1740 psi
q = 1.0 mL/min
Fluid = CO2
saturated brine
T = 140F
PP = 2175 psi
OP = 2175 psi
q = 0.05-0.3 mL/min
Analyzing
method
Permeability
measurement,
XRD, SEM,
Chemical
analysis
Remarks
- Dissolution of carbonate cementing material
resulted in enlargement of pore bodies.
- Fine were released and mobilized during
flood, collecting at pore network.
- Porosity decreased by 0.87% to 1.8% and
permeability reduced by 10% to 20%.
- Permeability damage contributed by
precipitation of new mineral (kaolinite and
solid phase), migration of released clay
particles after cement dissolution that move
in fluid flow path/accumulate at pore throat.
Permeability
- Porosity increased because of dissolution
measurement, Xprocess.
ray
- However, permeability decreased due to
microtomography
clogging of pore area by particles
(rearrangement of detached undissolved
particles).
Permeability
- Dissolution process is homogenous at higher
measurement,
flow rate while more localized (wormholeXRD, SEM
like at low flow rate.
- Permeability increases for all samples. But,
at high flow rate some particles dragged to
Permeability
measurement,
SEM, XRD,
Fluid = CO2
saturated brine
-
39
Pudlo, et al.
[122] (2015)
Altmark sandstone, Germany
k = 10-40 mD, 𝜙 = 15-24 %,
D = 0.28 in L = 0.55 in
Synthetic brine
T = 248F
PP = 2900 psi
Duration = 4-6
weeks
Fluid = CO2
Static batch
experiment, thin
section,
microCT,
FESEM, EDX,
EMPA, XRD, N2
gas adsorption,
SCAL, NMR T2,
ICP-OES
Saeedi, et al.
[47] (2016)
South West Hub sandstone,
Western Australia
k = 120-530 mD, 𝜙 = 12-15
%, D = 1.45 in L = 2.95 in
NaCl at 30000
ppm
T = 142 - 157 F
PP = 2760 - 3600
psi
OP = 6230 - 8170
psi
Q = N/A
Fluid = scCO2 +
CO2 saturated brine
T = 142 - 157 F
PP = 2760-3600 psi
OP = 6230-8170 psi
q = 2, 3, 3.33
mL/min
Fluid = scCO2 +
CO2 saturated brine
Permeability
measurement, Xray CT images,
NMR, XRD
Xie, et al.
[35] (2017)
South West Hub sandstone,
Western Australia
k = 120-530 mD, 𝜙 = 12-15
%, D = 1.45 in L = 2.95 in
NaCl at 30000
ppm
-
Permeability
measurement,
SEM and XRD
cause temporary decrease in permeability
due to local plugging.
Precipitation of secondary mineral
(kaolinite, muscovite, smectite) and Kfeldspar is larger at low flow rate.
Comprehensive microscopic, petrophysical,
tomographic and chemical analytics for 150
samples.
Dissolution of calcite and anhydrite caused
an increase in porosity while fine migration
deteriorate the permeability.
Clay fine release and pore throat plugging,
formation new pore space, and evolution of
new pathway are affecting the reservoir
injectivity.
25%-60% reduction in permeability but
negligible changes in porosity.
Mineral precipitation and fines migration
contributed to the permeability reduction.
Study on effect of pH and brine salinity on
kaolinite is required.
- Continuation paper from A. Saeedi (2016).
- Permeability reduction between 25% and
52% due to fines migration (kaolinite).
- Low permeability samples with high clay
have high tendency for damage.
Al-Yaseri, et
al. [24]
(2017)
SokamaNeuyam, et
al. [57]
(2017)
Berea sandstone
k = 209-219 mD, 𝜙 = 18-20
%, D = 1.2 in L = 2-2.3 in
Bandera GraySsandstone
k = 15-21 mD, 𝜙 = 18 %,
D = 1.2 in L = 2.37 in
Bentheimer sandstone
k = 1200-2000 mD, 𝜙 = 2224 %, D = 1.5 in L = 7.87 in
T = 175.7 F
PP = 1450 psi
OP = 2175 psi
q = 1, 5, 10 mL/min
Fluid = CO2
saturated brine and
scCO2
T = 140 F
PP = 1160 psi
OP = 1160 psi
q = 0.25, 0.5, 1.0
mL/min
Fluid = CO2
saturated brine and
scCO2
Permeability
- Applied CO2 injection rate did not affect the
measurement and
permeability significantly.
SEM
- Salt type, salt concentration, acidity, and
types of clay mineral (dispersed clays) are
controlling factors affecting permeability.
- Pore throat of hosting rock define the
bridging blocking mechanism.
Permeability
- Permeability impairment up to 26% by fines
measurement,
migration.
SEM, EDX
- Salt precipitation could reduce flow area and
increase jamming ratio. Higher brine salinity
gives more salt and reduced flow area. Even
smaller particles easily trapped.
- No obvious correlation between rock
permeability and injectivity impairment.
- Permeability reduced with increasing
injection rate.
Synthetic brine
T = 122 F
PP = 1160 psi
OP = 2175 psi
q = 2, 5, 10 mL/min
Fluid = scCO2
Permeability
measurement
Synthetic brine
T = 149 F
PP = 2900 psi
OP = 3900 psi
q = N/A
Permeability
measurment,
XRD, EDX,
NMR T2,
Medical CT
5 wt% NaCL +
1 wt% KCl
Synthetic brine
Kipton Berea sandstone
k = 90-120 mD, 𝜙 = 17-19
%, D = 1.5 in L = 7.87 in
40
SokamaNeuyam, et
al. [17]
(2017)
Khather, et
al. [123]
(2017)
Bandera Gray sandstone
k = 4-10 mD, Φ = 19-21 %,
D = 1.5 in L = 7.87 in
Berea sandstone
k = 209-219 mD, 𝜙 = 18-20
%, D = 1.5 in L = 7.87 in
Bandera Gray sandstone
K = 15-21 mD, 𝜙 = 18 %, D
= 1.2 in L = 2.37 in
Carbonate (vuggy, fractured
and tight)
k = 0.11-528 mD, 𝜙 = 6-40
%, D = 1.5 in L = 1.8-2.7 in
- Included Al2O3 as fines particles inside
core samples.
- Particle concentration greatly affect CO2
injectivity.
- 0.3 wt% particle concentration induced twofold injectivity compared to 10 wt% of
dissolve salt.
- Permeability enhancement is due to
dissolution and removal of dolomite and
anyhydrite minerals.
Fluid = CO2
saturated brine
Scanner and
Effluent analysis
41
Khather, et
al. [124]
(2018)
Carbonate (91 wt% calcite)
k = 0.4-288 mD, 𝜙 = 9.1-31
%, D = 1.5 in L = 2.3-3.2 in
Synthetic brine
T = 149 F
PP = 2900 psi
OP = 3900 psi
q = N/A
Fluid = CO2
saturated brine
Permeability
measurement, XRay CT, SEM
Othman, et
al. [25]
(2018)
Berea sandstone
k = 250 mD, 𝜙 = 20 %,
D = 1 in, L = 2.03 in
1 wt% NaCl
Permeability
measurement,
ICPOES,
FESEM
Edem, et al.
[125] (2020)
Berea sandstone
k = 294 mD, 𝜙 = 19.98 %,
D = 1 in, L = 3 in
5,15,25 wt%
NaCl
T = 122 F
PP = 1450 psi
OP = 2030 psi
q = N/A
Fluid = CO2
saturated brine and
scCO2
T = 104-113 F
PP = 1000 psi
OP = 2500 psi
q = 1-3 ml/min
Fluid = CO2
saturated brine and
scCO2
Permeability
measurement,
SEM
- Reduced permeability can be attributed to
combined effect of mineral precipitation of
calcite and mineral compaction.
- Dissolution is more intense at inlet, results
in dissolution pattern and wormholes.
- Continuation paper from M. Khather et al
(2017).
- Reaction rate between calcite and carbonic
acid is highest followed by dolomite and
quartz.
- Permeability reduction by 12% in longest
sample is due to fines migration originating
from mineral dissolution. SEM image
indicated possible sign of fines migration.
- Investigate bloackage due to fines migration
and dissolution during CO2 injection.
- Mobilized fines are clay, quartz, and
cement.
- scCO2 is not reliable for permeability
measurement due to fluctuation.
- Porosity and permeability decrease at
increasing salinity.
- Higher injection rate caused higher salt
precipitation and higher porosity and
permeability reduction.
2.8.1 Analyzing methods
Researchers have used different equipment and methods to evaluate the
petrophysical changes of the core samples and to monitor the injectivity changes
throughout the experiment. The analyzing methods can be divided into two groups:
permeability analysis and petrographic analysis. The .core flooding unit is widely used
by researchers for permeability analysis [35, 119]. During the experiment, the pressure
at the inlet of the core sample, the pressure at the outlet of the core sample and the
overburden (confining) pressure are all measured using individual pressure transducers.
Likewise, the differential pressure across the core is measured and recorded every 30
seconds or 1 minute. Then, the recorded data is translated into graphs to calculate the
permeability value (Figure 2.10). Details of various core flooding units and the
recommended procedure have been discussed in detail by Civan [111].
Figure 2.10 Pressure drop profiles of injection of fresh water and supercritical CO2
into Berea Sandstone cores [17]
42
The petrographic analysis allows in- depth investigation of the chemical and
physical features of a particular rock sample. Typical equipment to be used for the
microscopic analysis includes X-ray diffraction (XRD), X-ray fluorescence (XRF) and
scanning electron microscope (SEM) with energy dispersive X-ray microbeam (EDX).
The XRF gives information on the chemical composition of the samples (elemental
analysis) while the XRD identifies and measures the presence and amount of minerals
in the samples (compound analysis). On the other hand, SEM/EDX provides structural
information or material composition information. The evaluation of SEM images for
pre- and post-flood samples can provide microstructural changes which may occur to
the samples (Figure 2.11). Recently, advanced visualisation techniques such as X-ray
CT and Micro X-Ray Ct have been adopted to capture the pore-scale event but they are
limited to rendering time and presenting dynamic process during the analysis.
Figure 2.11 SEM images taken from the same spot on a rock sample before and after
flooding. The markings on the images indicate fines migration and mineral precipitation
[124].
43
2.8.2 Types of core sample
Experimental works were conducted on sandstone and carbonate core samples
which represent the main geological type of reservoir rock in CCS operations. For
sandstone, all of the measurements hail from low range permeability (0.023 mD- 60
mD) to middle range permeability (100 mD – 530 mD) with an exceptional case of high
permeability for the Bentheimer sandstone (1200 mD – 2000 mD) [15]. SokamaNeuyam, et al. [57], observed higher permeability reduction in the Berea sandstone
compared to the low permeability Kirby sandstone (9 mD). Both core samples were
initially saturated with 0.5 wt% particle solution with an average size of 0.08 µm and
then injected with supercritical CO2 at 5 ml/min. They opined that sandstone rock with
high permeability would release more particles (which led to pore plugging) because of
the improved contact area between the carbonated brine and the rock minerals.
However, their work was limited to only the core flood experiment. Since the majority
of the CCS field has medium to high permeability formation, further work on core flood
experiment is required to study permeability alteration by using different types of high
permeability sandstone core samples supported by detailed petrographic analysis and
micromodel study.
2.8.3 Saturation fluid type and properties
Moreover, laboratory work mainly used NaCl and synthetic brine to saturate the
core samples. The concentration of brine or brine salinity ranged between 30,000 ppm
and 50,000 ppm for NaCl while for the synthetic brine, a larger range of brine salinity
from 10,600 ppm to 105,500 ppm was reported. Brine salinity has a significant role in
changing the injectivity of the rock. It controls the CO2-brine solubility which leads to
different CO2-brine-rock interactions at near wellbore [49]. Increasing brine salinity
causes reduction in water solubility in the CO2 phase. Therefore, the phenomenon
creates CO2 and brine phases which govern the drying and salt precipitation processes
[46]. It is generally accepted that higher salinity gives rise to a higher amount of salt
precipitation which later reduces the porosity and permeability reduction. However,
44
since this project focused on the application of CO2 sequestration in the Malaysian
offshore condition, the brine salinity was considered low at a range of 6,000 ppm to
30,000 ppm [126].
2.8.4 Testing parameters
For experimental conditions, the important variables to control the CO2 injection
process can be summarized as follows: injection flow rate, injection pressure,
overburden pressure, temperature, and mode of injection. Different variables were used
to represent the reservoir condition and the required testing parameters. It is important
to highlight that all experiments were conducted at pressures and temperatures higher
than the supercritical CO2 borderline to represent the actual CO2 injection. The range
of temperature was between 68-248 and 1160 psi to 3600 psi for the pressure. Yu, et
al. [108] carried out a core flood experiment at 212oF and injection pressure of 3480 psi
to study the CO2-brine-rock interactions in sandstone core samples. The pressure and
temperature conditions were comparable with the Qing 1 formation reservoir in China.
Furthermore, the three modes of injection that were used in the experiments were CO2
saturated brine only, supercritical CO2 only, and CO2 saturated brine with supercritical
CO2. The CO2 was injected at different flow rates between 0.5 mL/min and 50 mL/min
to represent a flow rate representative of a different distance to the wellbore (Table 2.5).
Table 2.5 Laboratory flow rates based on distance to the wellbore [126]
Distance from wellbore (m)
0
1
2
4
6
11
15
100
10
5
4
2
1
0.5
Flow rate (mL/min)
2.8.5 Changes on physical rock properties
Laboratory results demonstrated that the modification of the rock structure can
either improve or impair the porosity and permeability values depending on two main
driving geochemical processes: dissolution and precipitation, which are functions of the
45
rock fabric (pore shapes, distribution and connectivity), brine composition,
thermodynamics conditions and precipitate distribution. The dissolution of minerals in
both the carbonates and the sandstone core samples occurs a short period after the CO2
injection, followed by precipitation and the transformation of minerals. The experiment
by Yu, et al. [108] showed that K-feldspar, albite, calcite and ankerite dissolved during
the CO2 flooding experiment. They found that calcite dissolution was the fastest
followed by ankerite, and feldspar minerals showed the least sign of dissolution.
Moreover, the rate of dissolution depended on temperature and the injection flow rate.
Mohamed, et al. [107], conducted an experiment at 68, 95 and 122oF and found that
calcite dissolution was faster at high temperature but with less precipitation. At a high
injection rate, it gives lower contact time between CO2 and brine, resulting in lower
dissolution and less precipitation. Luquot, et al. [121], highlighted that dissolution rates
were homogenous at high flow rates whereas the dissolution pattern was more localized
(wormhole) at lower injection rates. The dissolution was more intense at the inlet of
the core which resulted in the formation of the dissolution pattern and wormholes in the
area [123].
Researchers also confirmed that precipitation occurred during the CO2 injection
because of the CO2-brine-rock interaction. For instance, Yu, et al. [108] studied CO2 brine-rock interactions at 212oF and 3480 psi by using the core flooding experiment.
XRD and chemical analyses after the experiment indicated that the calcite content in
the sandstone core sample dropped to zero and a significant amount of clay minerals
(kaolinite) precipitated after the CO2 injection. The carbonate and silicate mineral
dissolution as well as the precipitation of secondary minerals (kaolinite, muscovite, and
smectite) were observed through the change in the solution chemistry as reported by
Luquot, et al. [121]. The precipitation of kaolinite is often linked to the dissolution of
K-feldspar while smectite precipitation is controlled by the availability of Fe and Mg
released from the ankerite solution. The existence of both precipitated minerals was
captured in SEM images. It is important to emphasize that the dissolution and
precipitation of minerals would result in porosity and permeability changes. However,
researchers are inconsistent in relating the effect of these mechanisms to the severity of
petrophysical changes.
46
2.9 Analytical model for prediction of CO2 injectivity impairments
This section reviews the development of the theoretical model to predict
permeability change with the focus on CO2 injectivity. As mentioned earlier, the
continuous injection of reactive CO2 into geological storage sites would cause several
processes that would modify the pore spaces (mainly due to mineral dissolution),
precipitation and fines migration. Therefore, Hommel, et al. [29] in their review work
stated that a reliable approach to calculate the change in permeability during the
injection of reactive fluid should fulfil the following requirements:
1. The relationship should only rely on available parameters.
2. It should consider the physical processes changing the porosity.
3. It should fit experimental observations.
4. It is able to calculate at reasonable computational time and expenses.
In their work, they presented a comprehensive collection of permeability change
relations for evolving pore space due to reactive transport processes via precipitation,
dissolution and biogeochemical.
In the early days, permeability changes were quantified through using estimating
techniques by using easily measurable properties such as porosity, grain size
characteristics or pore geometry of certain materials. An example of this is , Hazen
[127] relates the hydraulic conductivity, 𝑘 in cm/s of a sand unit to the particle diameter,
𝑑10 in cm, as follows;
2
𝑘 = 𝑐𝐻 𝑑10
(2.5)
where 𝑐𝐻 is an empirical coefficient value ranging from 1 to 1000. However, due to
a limited range of particle diameters, 0.01 cm < 𝑑10 <0.3 cm, plus the variety of 𝑐𝐻 , it
makes the proposed relationship impractical for general use.
47
Then, further development of modelling the injectivity changes within this vicinity
is largely determined by the flow physics such as the porosity-permeability relationship.
The porosity-permeability relationships have been developed from a different set of
backgrounds. They are relations based on mathematical or geometrical parameters
which normally require a simplification of the porous media structure while certain
relations used to fit experimental data are often simple exponential or power functions
[111].
In the context of CO2 injectivity, the potential variation in permeability changes
can be computed from a common continuum scale of porosity-permeability
relationships including the Kozeny-Carman model and the bundle-of-tubes model
derived from the Hagen-Poiseuille model and the power law model [8, 128]. Moreover,
Zhang and Liu [129] in their review, added power law as another analytical model to
predict the permeability change due to salt precipitation during CO2 sequestration. The
power law model is flexible because it can be simply modified by changing the
exponential value to fit the experimental data. On the other hand, Sokama-Neuyam, et
al. [57] proposed a conceptual model to predict the CO2 injectivity change based on the
coupled effect of salt precipitation and fines migration. Still, no experimental work has
been done to prove the concept. The following sections describe the development of
the analytical model to predict the CO2 injectivity changes.
2.9.1 Development of the Kozeny-Carman model
The Kozeny-Carman (KC) model is the widely used approach to calculate the
pressure drop, ∆𝑃, required for fluid flow at the velocity, 𝑣, through a packed bed of
solids length, 𝐿. It was first introduced by Kozeny [130] and was later modified by
Carman [131]. The equation is as follows;
∆𝑃 180𝜇 (1 − ∅)2
= 2 2
𝑣
𝐿
∅𝑠 𝐷𝑝
∅3
48
(2.6)
Equation 2.6 can be rewritten to calculate permeability by using Darcy’s equation as
follows:
𝑘𝐾𝐶 =
∅3
𝜏(1 − ∅)2 𝑆 2
(2.7)
where 𝜏 is the tortuosity, 𝑆 represents surface area and ∅ is the porosity of the
porous media. Due to ease of use, the KC equation was applied in models describing
porosity and permeability changes due to mineral precipitation. The following
subsection explains the relations derived from the classic KC model to be used for
predicting the CO2 injectivity changes.
2.9.1.1 The Zeidouni, Pooladi and Keith model
Zeidouni, et al. [92], used the simple Kozeny-Carman grain model based on spheres
to calculate the permeability changes after the CO2 exposure due to changes in porosity.
The relationship is shown in Equation 2.8.
𝑘
𝜙 3 1 − 𝜙𝑜
)
=( ) (
𝑘𝑜
𝜙𝑜
1−𝜙
2
(2.8)
2.9.1.2 Tang et al. model
Tang, et al. [89] modified the Zeidouni, et al. [92] model by including the
exponential coefficient that was demonstrated through the data regression with
minimum deviation. The exponential value was determined as 2.4. This is shown in
Equation 2.9.
2
𝑘
𝜙 𝐶 1 − 𝜙𝑜
)
=( ) (
𝑘𝑜
𝜙𝑜
1−𝜙
where 𝐶 is the exponential coefficient.
49
(2.9)
2.9.2 Development of the power law model
The classic KC model can be simplified by assuming 𝑆 ∝ ∅𝑝 [132]. The exponent
can be assumed by using the constant 𝑛 so that the given power law equation would be,
𝑘
∅ 𝑛
=( )
𝑘𝑜
𝜙𝑜
(2.10)
The equation is widely used to describe permeability changes and modelling studies
[133-135].
Experimentally, Carroll, et al. [136] and Hao, et al. [137] found that the 𝑛 value
was
depending on mineral heterogeneity and pore space distribution. For more
heterogeneous vuggy limestone, they fitted 𝑛 from 6 to 8 while for the more
homogeneous Marly dolostone, the value of 𝑛 was fitted at 3. The lower 𝑛 is associated
with homogeneous dissolution and the higher 𝑛 is often related with the increasingly
heterogenous dissolution pattern in carbonate rocks. Similar findings were also found
by Menke, et al. [138] and Menke, et al. [139].
On the other hand, the value of 𝑛 was observed to vary with time as the dissolution
progressed. In a labwork Al-Khulaifi, et al. [140], observed that the permeability and
porosity changes were dependent on the dissolution phase. The fitted 𝑛 value of three
different samples of carbonate rock were changed from a high value at the beginning
of the experiment to a lower intermediate value and increased to a high value at the end
of the experiment.
2.9.3 Development of the Hagen-Poiseuille model
The Hagen-Poiseuille (HP) model was experimentally derived independently by
Jean Léonard Marie Poiseuille in 1838 and Gotthilf Heinrich Ludwig Hagen to relate
the pressure drop in an incompressible and Newtonian fluid in laminar flow flowing
through a long cylindrical pipe of constant cross section [141]. By assuming constant
fluid density and a cylindrical geometry, the HP model relates the pore radius, 𝑟, the
50
fluid’s viscosity, 𝜇, and the pressure gradient over a length of the pore,
∆𝑝⁄
𝐿, to the
flow rate, 𝑄𝐻𝑃 , through that core as follows:
𝑄𝐻𝑃 =
𝜋𝑟 4 ∆𝑝
8𝜇𝐿
(2.11)
Using Darcy’s equation and given the circular cross-sectional area as 𝜋𝑟 2 ,
permeability can be calculated by using the following equation:
𝑘𝐻𝑃 =
𝑟2
8
(2.12)
The HP model was derived and used widely in many industrial applications. The
following subsection summarizes the equations that were modified based on the HP
model as a function to predict the permeability change during CO2 injection.
2.9.3.1 The Verma and Pruess model
In 1988, Verma and Pruess [142] proposed a porosity-permeability relation which
considered the highly idealized model of permeable media to correlate the relative
changes in permeability to the relative changes in porosity caused by mineral
precipitation. The pore network was represented by a bundle of non-intersecting flow
tubes with either circular tubular or planar cross sections. For a set of straight, parallel,
infinite tubes with radius, 𝑟 and a density of 𝑁𝑡 tubes per unit cross-sectional area, the
effective continuum permeability is
𝑁𝑡 𝜋 4
𝑟
8
(2.12)
𝜙𝑡 = 𝑁𝑡 𝜋𝑟 2
(2.13)
𝑘𝑡 =
while the porosity is given by
51
By combining Equations (2.12) and (2.13), the following expressions for
permeability as an explicit function of porosity can be obtained:
𝑘𝑡 =
𝜙𝑡 2
8𝜋𝑁𝑡
(2.14)
The discussion above applies to flow channels with uniform cross-sectional areas.
In many permeable media, flow channels consist of ‘wide’ and ‘narrow’ segments
(corresponding to pore bodies and pore throats), whose lengths are of the order of a
pore diameter. The Verma and Pruess [142] relation assumes that a fraction, 𝛤 of the
total length of a capillary tube has a radius, 𝑅, while the remainder, 1 − 𝛤 has a smaller
radius 𝑟. Assuming all tubes to be identical, the porosity–permeability relationship can
be obtained by considering the case of a single tube per unit area. Initial porosity, ∅𝑜
and permeability, 𝑘𝑜 are given by
𝜙𝑜 = 𝜋[𝛤𝑅 2 + (1 − 𝛤)𝑟 2 ]
(2.15)
1 8 𝛤 1−𝛤
= [ + 4 ]
𝑘 𝜋 𝑅4
𝑟
(2.16)
and
If a volume, 𝛬 is deposited per unit length, porosity becomes 𝜙 = 𝜙0 − 𝛬. The
flow channel will become completely clogged and permeability will become zero when
𝛬 = 𝜋𝑟 2 , at which time we still have finite porosity 𝜙𝑐 = 𝜙𝑜 − 𝜋𝑟 2. Denoting the radii
of the tube segments after deposition of 𝛬 by 𝑅∝ and 𝑟∝ respectively, the porosity and
permeability are given by
𝜙 = 𝜋[𝛤𝑅∝2 + (1 − 𝛤)𝑟∝2 ]
(2.17)
1 8 𝛤 1−𝛤
= [ + 4 ]
𝑘 𝜋 𝑅∝4
𝑟∝
(2.18)
and
52
Introducing the normalized porosity given by,
𝜃=
𝜙 − 𝜙𝑐
𝜙𝑜 − 𝜙𝑐
(2.19)
with 𝜙𝑐 = 𝜋𝛤(𝑅 2 − 𝑟 2 ) and the ratio of cross-sectional areas of the tube segments,
𝜔 = (𝑅 ⁄𝑟)2, we obtain
𝑘
1 − 𝛤 + 𝛤 ⁄𝜔2
2
=𝜃
𝜃
𝑘𝑜
1 − 𝛤 + 𝛤 (𝜃 + 𝜔 − 1)
(2.20)
This equation can be well fit by a power law with an exponent of 2 as follows when
𝛤 = 0.8, 𝜙𝑟 = 0.9:
𝑘
𝜙⁄𝜙𝑜 − 𝜙𝑟
=(
)
𝑘𝑜
1 − 𝜙𝑟
2
(2.21)
Equation 2.21 and the given parameter values were used by Pruess and Müller [83].
The 𝜙𝑟 being 0.9 means that when porosity is reduced by 10% due to mineral
precipitation, permeability will decrease to zero. The value was decided similar to what
was used in another study of permeability changes due to the precipitation of
amorphous silicate at a geothermal injection well, with the exponential term being equal
to 2 and the critical porosity equal to 0.9 [143]. Later, André, et al. [68] slightly changed
the 𝜙𝑟 value to 0.91 to accommodate their study.
2.9.3.2 The Ott, Roles and De Kloe model
Moreover, Ott, et al. [144] improved the Verma and Pruess [142] model to fit their
experimental data, but introduced a new term which was the critical value to which
permeability can be reduced by mineral precipitation. They also reduced the critical
porosity, 𝜙𝑟 = 0.8 because they argued that the maximum pore volume that can be filled
by the precipitate was the volume corresponding to the residual brine concentration (in
53
their case it was 0.2). Using these parameters, they found a larger exponential term
equal to 10.1. Their porosity-permeability can be presented as below:
10.1
𝑘
𝜙⁄𝜙𝑜 − 𝜙𝑟
=(
)
𝑘𝑜
1 − 𝜙𝑟
(1 −
𝑘𝑐
𝑘𝑐
)+
𝑘𝑜
𝑘𝑜
(2.22)
2.9.3.3 The Giorgis, Carpita and Battistelli model
Meanwhile, another research by Giorgis, et al. [31] used the bundle-of-tubes model
as a regression function to fit their extended Verma and Pruess model. They also
decided the exponential term equal to 4.1 and the critical porosity of 0.3. Equation 2.23
shows that the porosity-permeability relationship can be summarized as:
4.1
𝑘
𝜙⁄𝜙𝑜 − 𝜙𝑟
=(
)
𝑘𝑜
1 − 𝜙𝑟
(2.23)
2.9.4 Comparison of theoretical models for prediction of CO2 injectivity
The published models that were discussed in the previous sections to predict CO2
injectivity changes were motivated by analytical, mathematical, or geometrical
derivations. Table 2.6 summarizes the theoretical models and the features they offer to
adapt to specific requirements. Among the distinguished characteristics are their
consideration of threshold values such as critical porosity and the dominant pore space
modifying mechanism. As mentioned earlier, the injection of CO2 into sandstone rock
saturated with brine would cause precipitation, dissolution, and fines migration.
Therefore, the selection of a suitable model should consider the dominant pore space
modifying process. As shown in Table 2.6, the theoretical models to consider the
combination of dissolution and precipitation used Kozeny-Carman. When only
dissolution was considered, the power law was the only choice and the HagenPoiseuille model was used when precipitation was considered, with varying exponents
or slight adaptations. However, the impact of fines migration was neglected in all
models.
54
Table 2.6 Comparison of theoretical models used for prediction of CO2 Injectivity
changes
Source
Relation
Equation
Application
type
Zeidouni, et
Kozeny-
al. [92]
Carman
Tang, et al.
Kozeny-
[89]
Carman
Luhmann, et
Power law
𝑘
𝜙 3 1 − 𝜙𝑜
)
=( ) (
𝑘𝑜
𝜙𝑜
1−𝜙
2
precipitation
2
𝑘
𝜙 2.4 1 − 𝜙𝑜
)
=( ) (
𝑘𝑜
𝜙𝑜
1−𝜙
𝑘
∅ 𝑛
=( ) ,
𝑘𝑜
𝜙𝑜
al. [133]
Dissolution,
1.93 ≤ 𝑛
Dissolution,
precipitation
Dissolution
≤ 9.03
Al-Khulaifi,
𝑘
∅ 𝑛
=( ) ,
𝑘𝑜
𝜙𝑜
Power law
et al. [140]
3.2 ≤ 𝑛
Dissolution
≤ 12.8
Pruess [145]
2
Hagen-
Precipitation
𝑘
𝜙⁄𝜙𝑜 − 𝜙𝑟
=(
) ,
𝑘𝑜
1 − 𝜙𝑟
Poiseuille
𝜙𝑟 = 0.9
Ott, et al.
Hagen-
[33]
Poiseuille
10.1
𝑘
𝜙⁄𝜙𝑜 − 𝜙𝑟
=(
)
𝑘𝑜
1 − 𝜙𝑟
−
𝜙𝑟 = 0.8,
Giorgis, et
Hagen-
al. [31]
Poiseuille
Precipitation
𝑘𝑐
𝑘𝑐
)+
𝑘𝑜
𝑘𝑜
𝑘𝑐
= 3.5 × 10−3
𝑘𝑜
𝑘
𝜙⁄𝜙𝑜 − 𝜙𝑟
=(
)
𝑘𝑜
1 − 𝜙𝑟
55
(1
4.1
Precipitation
Ratio of reduced to initial permeability
1.0
Pruess and Muller (2009)
0.9
Ott et al. (2015)
0.8
Giorgis et al. (2007)
0.7
Zeidouni et al. (2009)
0.6
Tang et al. (2015)
0.5
Power law (n=3)
Power law (n=6)
0.4
Power law (n=35)
0.3
0.2
0.1
0.0
0.5
0.6
0.7
0.8
Ratio of reduced to initial porosity
0.9
1.0
Figure 2.12 Comparison of theoretical models to predict permeability changes as a
function of porosity changes.
The comparison of all the theoretical models are presented in Figure 2.12. Verma
and Pruess [142] and Ott, et al. [144] predicted that permeability decreases to zero when
porosity is filled with about 10% of mineral precipitation. This is due to the new term
they introduced which was the lowest value to which permeability can be reduced by
precipitation. They argued that the amount of salt precipitate must be dependent on the
residual brine saturation. Thus, Verma and Pruess [142] used critical porosity, ∅𝑟 as 0.9
and Ott, et al. [144] used 0.8 by assuming the residual water saturation at 0.1 and 0.2
respectively. The other HP based model presented by Giorgis, et al. [31] predicted a
higher permeability change value because it used lower critical porosity value at 0.3.
Moreover, the KC based models show a lower permeability reduction trend
compared to the HP- based models. The models published by Zeidouni, et al. [92] and
Tang, et al. [89] require a porosity reduction of approximately 50% to achieve the same
reduction in the permeability predicted by the HP- based models. Lastly, regardless of
the complexity of the HP and the KC- based models, the flexible power law model
behaves almost similarly with suitable exponents (3 ≤ 𝑛 ≤ 35). For example, the
56
Giorgis, et al. [31] is very similar to the power law with 𝑛 = 6 while the KC- based
model can be approximated relatively well by simply using a lower 𝑛. Furthermore, the
power law equation is easy to use as it only needs the porosity and provides 𝑛 as the
fitting factor. However, it is often criticized for not accurately representing the complex
processes that change the pore structure.
2.10 Theory and application of Neural Network
Machine learning (ML) as a branch of artificial intelligence can be described as the
study of computer algorithms that allow computer programs to automatically improve
through experience [146]. Neural Network (NN) is one type of regression model under
ML algorithm umbrella which normally used to predict output y values by estimating
the relationship between different range of input x values. The NN model is a system
that has been developed to process information similar to the characteristics of the neural
systems on the human brain, where it can process complex information. The advent of NN
for its accuracy and the ability to develop complex nonlinear models has seen a significant
growth of its use in various discipline in petroleum engineering including exploration,
field development, reservoir engineering and others. [147].
The explanation of NN concept can perhaps be started by linking it to the functions
of neurons connectivity in the human brain for analyzing the information. The brain’s
neuron functions are replicated by large sets of algorithms representing the artificial
neural networks which are capable of establishing relationships amongst highly
anomalous nonlinear variables and producing sophisticated, accurate and reliable
results to complex problems through learning and training. The ANN works like the
neuron connections in the brain with multiple interconnections where each node (point)
is linked to each other in the form of a pathway for interaction with each other.
The connections between neurons with neurons have formed three different pattern
layers that are called architecture. The first layer is the input layer that functions as a data
receiver from the external stimuli. This data will be sent to the next layer wherein this layer,
57
and the neurons can be more than one. The third layer is the hidden layer that receives the
electric signal from the input layer and will process the signals by using the functions. The
processed data will be passed to the output layer, where it will determine the validity of the
data based on the existing limits in the activation function.
There are two types of NN which are Feed-Forward Neural Network (FFNN) and
Feedback Neural Network (FBNN) popularly called the Back-Propagation NN
(BPNN). The FFNN is straightforward NN approach that consists of a multilayer
interconnection of per-node where the output layer does not form a loop for feedback
connections or recurrent networks but in a forward unidirectional flow. The basic
concept of FFNN is shown in Figure 2.13. For BPNN, it has similar architectural
structure like FFNN except that it allows the creation of loop where the erroneous
information is sent back for iterative altering of weight values until error can no longer
improve to achieve a more accurate output value. Figure 2.14 shows a typical backpropagation neural network architecture which showing the error being looped back
through network for weight (bias) tuning.
Figure 2.13 A schematic diagram of a typical fast-forward NN architecture.
58
Figure 2.14 A schematic diagram of a typical backpropagation NN architecture.
The NN can work with a single hidden layer [148] to assign weights to each node
in a neural structure. The training phase feeds the input data as vectors through a neural
network framework. The output error is computed and looped back, into the network
for the iterative altering of the weights using gradient descent to be done to reduce the
error based on experience until it can no longer be improved. This process is repeated
until a bias value that gives a more accurate prediction is obtained. The mathematical
equation of the error function derivative used to update the weights by gradient descent
is represented as [149];
∆𝑤(𝑡) = 𝜂∇𝐸(𝑡) + 𝛼∆𝑤(𝑡 − 1)
Where ∆𝑤 is the weight update, 𝐸 is the observed error between the measured input
and predicted output, 𝜂 is the learning rate, 𝛼 is the momentum parameter (range below
than 1).
Moreover, the leaning process of NN can be divided into two categories. The first
one is the supervised learning system. The supervised learning system including spam
classifiers of e-mail, face recognizers over images, and medical diagnosis systems for
patients, is to study the collection of input data and the goal is to make predictions about
future data points. The signals will be propagated along with the network until the last
layer of neurons in the output layer. This output pattern will be compared with the desired
output pattern. If the error occurs during the process comparison, then the process will be
modified to adjust the weights so that the actual output is following the desired output.
Another type of learning process is unsupervised learning system, whereby the target output
59
is not being provided during the process. The objective of this type of learning process is
to organize the data in some way or to describe its structure. The network will put the
sample in any way until the response has similar characteristics with the input that will
result in a new code. The BPNN approach is widely used in supervised learning.
The ability of NN to mimic human way of thinking in solving classification problems
by creating complex dynamic estimation of functions provide a greater advantage and
prediction performance over other algorithms. A robust regression analysis helps to
model the relationship that exists between a dependent and one or several independent
variables showing significant relations between them and the change of the dependent
value because of a change in the independent variables. Over the years, the reputation
of neural networks in making better prediction accuracy of complex problems have
grown substantially in regression modelling. Most traditional regression models show
some difficulties in obtaining an adequate fit with complex data whereas ANN offers
complex mathematical structures that generate higher accuracy and can fit any
regression function hence its superiority. Within the scope of CO sequestration, NN is
commonly used as highly effective supervised machine learning method to solve
classification problems of storage efficiency [150], sealing and trapping mechanisms
[151, 152], and predicting permeability changes [153]. For example, a recent work by
Yan, et al. [153] used different hybrid models to predict the coal permeability changes
after injected with CO2 for sequestration. However, as far as author’s knowledge is
concerned, no attempt has been made to use NN model for predicting permeability or
CO2 injectivity changes in the context of CO2 sequestration in saline aquifer.
2.11 Response Surface Methodology (RSM)
Response surface methodology (RSM), as one type of Design of Experiment
(DOE) methods, is an approach that couple experimental designs with mathematical
and statistical methods aimed at developing an empirical model relating between
several independent variables and one or more responses [154]. The RSM method is
based on the fit of mathematical models (linear, square polynomial functions and
60
others) to the experimental results generated from the designed experiment and the
verification of the model obtained by means of statistical techniques.
Experimental design technique especially RSM is appropriate for analyzing
individual and interactive effects of different parameters. RSM uses a strong statistical
method based on the least square method that fits of the estimated values obtained from
experiment/simulation to the quadratic polynomial model of RSM. To predict the
system behavior, the quadratic or higher-order polynomial model is applied in many
industrial applications. Dependent on the behavior of the model, the polynomial equation
can be of a linear or non-linear formula. The relationship can be described in a first-order
model if the relationship is linear. The second-order model is used for curvature
relationship. The established polynomial function can only be used to describe the
relationship within the range of the independent variables specified during the development
of the function. The second order (quadratic) polynomial equation of RSM is expressed
as a general form:
𝑛
𝑛
𝑛
𝑛
𝑌 = 𝛽0 + ∑ 𝛽𝑖 𝑥𝑖 + ∑ 𝛽𝑖𝑖 𝑥𝑖2 + ∑ ∑ 𝛽𝑖𝑗 𝑥𝑖𝑗 + 𝑒
𝑖=1
𝑖=1
𝑖=1 𝑗=1
Where 𝑌is the modelled response, 𝛽 is the regression coefficient, 𝑥 is the
independent variables, and 𝑒 is the error. 𝛽0 is a constant value while 𝛽𝑖 𝑥𝑖 and
𝛽𝑖𝑖 𝑥𝑖2 represent linear terms (first-order effect of variables) and quadratic terms
(second-orer effects of variables), respectively, and 𝛽𝑖𝑗 𝑥𝑖𝑗 is a two-factor interaction
term. This equation does not take the interaction between three factors or more into
account. The equation may be simplified to linear equation by setting 𝛽𝑖 and 𝛽𝑖𝑖 as zero.
Moreover, a two-factor interaction (2FI) model can be derived from the model by
setting 𝛽𝑖𝑖 as zero.
To confirm that the designated polynomial equation best signifies the model, a least
square method is used to minimalize the residual error measured by the sum of square
deviations between the actual and the predicted responses. This includes the calculation of
estimates for the regression coefficients. The calculated coefficients of the model equation
require to be tested for statistical significance. This is thru analysis of variance approach
61
(ANOVA), where tests for significance of the regression model, significance of individual
model coefficient, and lack of it are performed. RSM has been widely applied in the
industry by numerous researchers for optimization [155-157] and predictions [158, 159]
purposes.
2.12 Summary and highlighted remarks
A review of the current literature indicates that dissolution, precipitation and fines
mobilization mechanisms occur during CO2 injection. Dissolution of carbonate
minerals due to CO2-brine-rock reactions is dominant and it could increase the porosity
and permeability of sandstone core samples. On the other hand, detachment,
precipitation of salt and clay mineral, especially kaolinite and deposition of fines
particles, would decrease permeability and even clog the flow paths despite net
dissolution. The effect of these two opposing processes on CO2 injectivity has been
clearly demonstrated through numerous experimental studies supported by field
reports. However, the results are case dependent and lack generality in terms of
quantifying the petro physical damage. There are many parameters indicating positive
or negative impacts on CO2 injectivity. Therefore, it is recommended to perform an
integrated study for the determination of the major and minor factors affecting the
impairment mechanism in any CO2 condition. Moreover, the previous theoretical
models are limited to predict the permeability changes contributed by mineral
precipitation and mineral dissolution. The impact of fines migration is not well reported
in all models. On the other hand, the unique capability of neural network model and
RSM provides a great potential to develop an alternative model for predicting the CO2
injectivity changes. In the context of CO2 injectivity, most of the previous work were
conducted using carbonate rock samples. There is only a limited number of studies on
using sandstone rock sample.
62
CHAPTER 3
METHODOLOGY
This chapter describes details of the experimental stages, materials, equipment, and
procedures used in this study. The research started with understanding the subject
matter through a review of the literature, field reports, previous experimental works,
and simulations. After that, a suitable experimental approach was identified, and a
proper methodology was selected. The experiment started with a semi-static batch
experiment to identify the basic parameters that control the CO2-brine-rock interactions.
With these studies, the dominant parameters that contribute the most to the rock
physical changes were selected for further analysis in dynamic core flooding
experiments. In the core- flood experiments, CO2-brine-rock parameters were varied to
evaluate their effects on CO2 injectivity changes. Extensive results of CO2 injectivity
changes were used to develop new CO2 injectivity model and were compared with the
published results of previous authors for validation. Figure 3.1 summarizes the
methodology used to complete the research project.
Figure 3.1. Summary of research methodology.
64
3.1 Materials
The materials that were used throughout the project consisted of rock core samples,
carbon dioxide, brine, and colloidal particles. The materials were carefully determined
after a thorough analysis of the literature review, technical capability or laboratory
equipment and their market availability.
3.1.1 Rock properties
Three types of high-quartz sandstone cores were used as porous media in these series
of experiments to represent ubiquitous saline aquifers that have the potential for CO2
geological storage sites, namely Kirby, Berea, and Idaho. These three types of core
samples were selected because of the variation in porosity, permeability, and pore size.
The coring of each core sample was ensured to be from the same block and similar
direction so that it was composed of similar mineral and physical properties. The cores
were originally 12 inches (30.48 cm) in length and 1.5 inches (3.81 cm) in diameter.
Due to the capability of the available porosity and permeability test unit (VINCI,
France) that could only accommodate cores up to 3 inches (7.62 cm) in length, the cores
were cut with a diamond saw, using the dry cutting technique, into shorter cores to
avoid any reaction between the reactive clay in the sample and water. In addition, the
core samples were also cut into small cube samples of 1 cm3 from the original size of
the cylindrical plugs of about 3-inches in length and 1.5-inches in diameter. The surface
fines that resulted from the process of cutting the cores into cubes, were cleaned by
immersing them in ethanol in open beakers in a ventilated ultrasonic bath for 15 minutes
without any heat applied. Ethanol was chosen instead of water, as ethanol is insensitive
towards clay within the rock samples, it was chosen to preserve the mineral composition
as much as possible. Then the samples were dried in an oven at 60 °C (140 °F) for 48
hours.
65
3.1.1.1 Physical properties
Three types of physical properties analysis were carried out on the core samples,
which were porosity and permeability analysis, helium porosity test and mercury
injection capillary pressure.
Table 3.1 Summary of core samples’ physical properties
Avg. permeability
Avg. surface area
Avg. pore throat
(mD)
(m2/g)
diameter (µm)
21
55
0.320
0.81
Berea
22
195
0.399
1.42
Idaho
40
1318
0.436
3.84
Core
Avg. porosity (𝝓)
Kirby
3.1.1.2 Topography and mineral composition
The quantitative results of XRF and XRD for both types of sandstone core samples
are presented in Table 3.2 and Table 3.3. The results indicate that the Kirby, Berea and
Idaho sandstone core samples contained the highest composition of silicon oxide
followed by Fe2O3, Al2O3, K2O, MgO, TiO2 and ZrO2. The analysis was correlated with
the qualitative analysis presented in Figure 3.2. The XRD results showed that all the
three types of sandstone samples were composed of a high percentage of silicon oxide
or better known as quartz. In addition, the samples also showed quite a high content of
potassium aluminium silicate (k-feldspar) and potassium aluminium silicate hydroxide.
The other compounds found in the samples were potassium iron magnesium silicate
hydroxide (biotite), zirconium dioxide, aluminium silicate, and calcium carbonate.
The texture and composition of both samples were properly sorted with loosely
packed grains. The detrital grains, which were sand-sized quartz, feldspar, and lithic
fragments with minor mica consisted of muscovite, biotite, undifferentiated mica, and
opaque grains, while the grain shapes were sub-rounded to sub-angular.
66
Table 3.2 XRF results for Berea, Kirby and Idaho sandstones
Compound
Composition (wt%)
Berea
Kirby
Idaho
SiO2
90.27
91.97
85.29
Fe2O3
3.84
2.43
3.31
Al2O3
3.44
3.31
5.57
K2O
1.65
1.60
4.52
TiO2
0.69
0.69
1.31
ZrO2
0.11
Table 3.3 XRD results for Berea, Kirby, and Idaho sandstones
Compound
Name
Chemical formula
Berea
Kirby
Idaho
Silicon oxide
SiO2
92.074
95.815
90.431
Potassium
aluminium
silicate (Kfeldspar)
KAlSi3O8
1.789
1.801
6.867
Potassium
aluminium
silicate
hydroxide
KAl2(Si3AlO10)(OH)2
4.463
2.383
2.703
Potassium iron
magnesium
silicate
hydroxide
K0.78Al1.35Fe0.85Mg1.63N
a0.22Si2.84Ti0.33O12H
0.468
-
-
Zirconium
dioxide
ZrO2
0.145
-
-
Aluminium
silicate
Al2SiO5
1.062
-
-
Calcium
carbonate
CaCO3
-
0.002
-
67
Figure 3.2 XRD spectrum of three sandstone core selected for this research shows
comparable mineralogical composition
3.1.2 CO2 properties
The purity of the CO2 used in the experiment amounted to 99.9%. The pressure of
1800 psi (12.4 MPa) and temperature of 60°C (140oF) were selected to represent a
potential geological storage in Malaysia [36]. In this condition, the injected CO2 was
in supercritical CO2 condition (critical point for CO2 is at 31.1oC and 1070 psi).
3.1.3 Brine
Ultrapure deionized water was mixed with NaCl, KCl, and CaCl2, which
represented a simple system of formation water. These are the prevalent salts which are
normally found in the saline aquifer system for storage [86]. Different salinities of 6000
parts per million (ppm), 30000 ppm, 60,000 ppm, 80,000 ppm and 100000 ppm NaCl
brine were prepared to evaluate the influence of brine salinity on injectivity changes.
Furthermore, a constant salinity of 30000 ppm was used to understand the impact of
different brine systems.
68
3.1.4 Fines particles
In actual conditions, during the continuous injection of scCO2 into the sandstone
rock, previous findings reported that fines particles are mobilized due to the dissolution
of reactive minerals and they are migrated together with the flowing scCO2. These
mobile particles are highly subjected to particle plugging when moving through
slimmer pore throats [25, 160]. However, the amount and sizes of fines particles
detached, migrated, and entrapped are very much unknown and uncontrollable. Thus,
as a method of controlling the variables, artificial fines are introduced into the system
during brine injection.
To control the amount and fines sizes, 0.005, 0.015, 0.03, 0.045, 0.06 and 0.07 µm
of silica oxide particles were used to represent the moving fines particles. The selected
particle sizes would give jamming ratios (pore throat to particle diameter ratio) from
0.004 to 0.04 for an average pore throat size of 1.4 µm (based on mercury intrusion
capillary pressure analysis). This was to give different pore plugging occurrences
suggested by Khilar and Fogler [37]. Silicon dioxide particles were selected for this
study because of their similar physical and chemical properties to quartz. On top of that,
silicon dioxide is highly water-wet which would form a very stable dispersion.
3.2 Measurement and analysis
Different analytical equipment were used in this research. The main equipment was
the core- flooding unit, and the micromodel unit was used to inject the carbon dioxide.
In order to run a detailed analysis of the pore media before and after the flooding
experiment, petrographic analysis equipment such as XRF, XRD and SEM were
utilized. The following section explains in more detail the capability and requirement
of all the equipment that were used in this research.
69
3.2.1 Porosity and permeability measurement
The core samples were measured for their Pore Volume (PV) and Permeability (k)
using the POROPERM instrument by the VINCI Technologies FRANCE.
The
apparatus, which was available in the Core Analysis Lab, Block 15 met the
requirements of MS ISO/IEC 17025:2005.
The instrument has the capability to
measure wide ranges of permeability and porosity effectively: (0.001 to 20,000 mD and
0.1 to 40% respectively). The type of medium used for the direct measurement was
Helium which is inert. The dimensions of the core were determined accurately using
the digital calliper. Figure 3.3 shows the set-up of the equipment.
Figure 3.3 POROPERM Equipment set-up.
3.2.2 Mercury Injection Capillary Pressure (MICP)
The pore size distribution of the sandstone sample was measured by using the MICP
equipment, that is available in Chemical department, UTP. The technique is a
commonly used method for pore system characterization based on porosity and pore
size distribution. It determines the pore volume by calculating the volume of intruded
mercury into the pore system under increasing injection pressure up to the limit of the
equipment. Mercury intrudes through pore throats of a specific size at a specific
pressure.
70
The governing equation to measure the pore size diameter relationship between
pressure and pore throat diameter is defined by Washburn's equation:
𝑑𝑝 =
−4𝛾 cos 𝜃
𝑃𝑐
(3.1)
𝑑𝑝 = pore size diameter
𝛾= surface tension of mercury
𝜃= contact angle
𝑃𝑐 = external pressure
3.2.3 Petrographic and mineralogy analysis
The mineralogical characterization of the rock samples was performed using the Xray fluorescence (XRF) and the X-ray diffraction (XRD). Essentially, the XRF is
performed to determine and measure the concentrations of elements and oxides in a
substance. The Bruker XRF S8 Tiger is used in the XRF analysis. After the sample was
scanned, the XRF software evaluated the data, while the results were displayed in the
form of normalized percentage concentration for each oxide. XRD, on the other hand,
is a physical phenomenon as well as an experimental method for the characterization
of materials, especially crystalline materials. XRD analysis was performed in the scan
range of 2° to 90° with a step size of 0.01°/2θ and an exposure time of five seconds per
step using the PANalytical X’Pert3 Powder and the Empyrean Powder XRD at the
Centralized Analytical Laboratory (CAL) in Universiti Teknologi PETRONAS (UTP).
Following that, mineral identification was interpreted using the PANalytical X’Pert
Highscore plus for the qualitative and the Rietveld Refinement analyses.
The topography, morphology and elemental composition of the samples were
analyzed using a Variable Pressure Field Emission Scanning Electron Microscope (VPFESEM) Zeiss Supra55 equipped with an Energy Dispersive X-ray spectroscope,
(EDX) located in the Centralized Analytical Laboratory (CAL) in Universiti Teknologi
71
PETRONAS (UTP). During the sample preparation, the uncoated samples were
mounted on a grid holder and spin-coated with gold to enhance electron conductivity.
Accelerating voltages of 5kV and 20kV were used on the samples to view the highresolution microstructure images and for the EDX analysis respectively.
3.2.4 Effluent analysis
Outlet fluid from the core flood rig was collected in a conical flask. Then, it was
analysed for geo- and hydro- chemical investigation on concentrations of Si, Ca, Mg,
Al, K and Fe by using the Inductively Couple Plasma-Optical Emission Spectrometry
(for cation concentrations) (ICP-AES) [58, 122, 161].
3.2.5 Core flooding unit
The core flooding experiment was conducted in order to meet the first and second
objectives of the research. At the macro-level, the intention was to conduct experiments
on the core samples simulated in conditions close to the natural environments. The
results of the core- flooding experiments, would enable one to predict how different
fluids or gases would move through the sampled area. Experimental work was
conducted by using the core -flooding unit known as the Relative Permeability System
Unit (RPS) by Temco, Inc. Tulsa, Oklahoma, that was available in the Core Analysis
Lab, Block 15, UTP. This was because it used Hastelloy for its tubing and core holders
that can handle corrosion that may arise because of injecting CO2 and particles. The
experimental set-up and the schematic diagram of the equipment are shown in Figure
3.4 and Figure 3.5 respectively.
72
Figure 3.4 RPS core- flooding set-up.
Figure 3.5 Schematics of the experimental set-up used for CO2 core- flooding
experiments.
The equipment is designed for testing core samples, at in-situ conditions of pressure
and temperature. The core holder supplied as part of this system allowed fluids to be
injected by the face of the core (simulating flow through the borehole, across the
formation rock face). Test conditions can be up to 10,000 psig flowing pressure, and up
10,000 psig overburden (confining) pressure, at 150°C (302°F). The pressure at the inlet
of the core sample, the pressure at the outlet of the core sample and the overburden
(confining) pressure were all measured using individual pressure transducers.
73
Likewise, the differential pressure across the core was measured with a differential
pressure transmitter. Leak-off fluids produced through the core sample were collected
in a beaker, which sat on a balance. The fluids that flowed by the face of the core,
without leaking off through it, were collected in another beaker. The system was also
designed for the measurement of liquid permeability. A single phase of the liquid was
injected through the core sample. The produced liquid was collected in a beaker that sat
on a balance.
3.3 Experimental work and procedures
The experimental work was divided into two main stages, namely semi-static batch
experiment and core flood experiment. The following sections describe in detail the
parameters and the required procedures to accomplish the overall research objectives.
3.3.1 Semi-static batch experiment
The objective of this experimental work was to identify the influence of CO2-brinerock factors that contribute to the dissolution and precipitation mechanisms. This
experiment acted as the preliminary work to evaluate the dominant parameters that
control the physical rock changes after the CO2 exposure. Four controllable parameters;
pore surface area, exposed time, brine type, and brine concentration were analysed in
the semi-static batch CO2-brine-rock experiments as functions of physical rock
changes. Moreover, another aim of this experiment was to provide evidence of mineral
dissolution, mineral precipitation and fines migration due to CO2-brine-rock
interactions. Experimental influence parameters were identified using the Taguchi
experimental design method to decrease the number of experiments while evaluating
each factor independently.
74
3.3.1.1 Experimental procedures
Three high-silica sandstone samples, Kirby, Berea and Idaho with comparable
mineral content were used in this study. Porosity and permeability tests conducted on
these sandstone samples showed that core sample Kirby had an average porosity almost
similar to the core sample Berea of 22% and 21% with much lower permeability; 55
mD for Kirby while 195 mD for Berea and an average pore surface area of about 0.32
m2/g and 0.399 m2/g respectively. Core sample Idaho represented a very high porosity
and permeability rock sample with 40% porosity, 1318 mD permeability and 0.436
m2/g average pore surface area.
Petrographic and mineralogical characterisation of these rock samples were carried
out before and after the static batch CO2-rock-brine test. Prior to the static batch CO2rock-brine test, the core samples were cut into small cube samples of 1 cm3 from the
original size of the cylindrical plugs of about 7.62 cm in length and 3.81 cm in diameter.
The surface fines that resulted from the core cutting process into cubes were cleaned by
immersing them in ethanol in open beakers within a ventilated ultrasonic bath for 15
minutes without any heat applied. Ethanol was chosen instead of water because it is
insensitive towards clay within the cube samples in order to preserve the mineral
composition of the rock sample as much as possible. Then the samples were dried in
the oven at 60°C for 48 hours [162].
The topography, morphology and elemental composition of the samples were
analysed using a Variable Pressure Field Emission Scanning Electron Microscope
(FESEM) Zeiss Supra55 equipped with an Energy Dispersive X-ray spectroscope
(EDX), located in the Centralized Analytical Laboratory (CAL) in Universiti Teknologi
PETRONAS (UTP). During the sample preparation, the uncoated samples were
mounted on a grid holder and spin-coated with gold to enhance electron conductivity.
Accelerating voltages of 5kV and 20kV were used on the samples to view the highresolution microstructure images and for the EDX analysis, respectively.
The semi-static batch CO2-rock-brine test was carried out under the conditions of
the potential geological storage in the Malay Basin and the Luconia Basin which are
75
located in the South China Sea [36]. Therefore, the experiments were conducted at a
temperature of 60°C under pressure of 1800 psi, by exposing the samples to CO2
saturated synthetic formation brine composed of 6,000 ppm, 30,000 ppm or 50,000 of
either sodium chloride (NaCl), potassium (KCl) or calcium chloride (CaCl2) during a
time period of 1-4 weeks. The experimental duration represented the estimated time
required for CO2 diffusion in brine to allow changes near the wellbore region during
the initial CO2 flooding with formation brine by Kampman, et al. [163] and was the
variation of time used by Dawson, et al. [164] and Pudlo, et al. [99].
The dry weight of each individual cube sample was measured before and after the
experiments in order to quantify the mass change which would give insight on the
porosity change of the samples which is directly related to the dissolution process that
might take place during the static CO2-rock-brine experiments. The cube samples were
saturated with the intended brine samples that were to be used in the experiments, in a
vacuum desiccator for four (4) hours prior to the experiments. The pH of the brine
samples was measured before and after the experiments to monitor the changes. Aging
cells (Fann Intrument, Texas, USA) were used to contain the cubes, the brine and the
CO2. A high precision twin syringe pump (Teledyne ISCO 1000D, Nevada, USA) was
used to pressurise the CO2 supplied from a CO2 tank in an accumulator to 1800 psi
before pumping it into the aging cells placed in an oven that had been preheated to 60°C
through a pressure line of the oven. The aging cells were then left in the oven for a
period of 1 week to 4 weeks as depicted in Figure 3.6.
Figure 3.6 Experimental setup for semi-static CO2-brine-rock.
76
3.3.1.2 Taguchi Design of Experiment
In this study, the Taguchi experimental design method was used to identify the
degree of dominance by four controllable parameters: pore surface area, exposed time,
brine type, and brine concentration as functions of physical rock changes. Under the
Taguchi method, the four factors were presumed to be autonomous. Thus, it enabled
analyses that prioritized the relative effects of these factors on physical changes before
and after the interactions. Moreover, three different levels of each factor represented
the high, the intermediate and the low levels of brine and rock properties under typical
CO2 storage reservoir conditions.
As shown in Table 3.4, the selected salt type and concentration were to represent
the typical saline aquifer in the study area and major CO2 saline aquifer storage sites
around the world [126, 165]. In addition, the NaCl, KCl and CaCl2 brine types were
chosen because they are the main salt components that are normally found in a saline
aquifer. Therefore, the L9 (34) orthogonal array was selected based on the Taguchi
design concept and the experimental conditions were acquired by combining the data
given in Table 3.4, and the L9 (34) orthogonal array [166]. For all possible combinations
of these variables, if the experiment were to be performed using a complete factorial
experimental design, it would have involved 81 (34) trial runs. In comparison, the
Taguchi orthogonal array L9 experimental design only needed 9 simple and effective
trial runs which significantly reduced the experimental cost and time.
Table 3.4 Control factors and levels of the orthogonal test
No
Factor
Level 1
Level 2
Level 3
1
Surface area (m2/g)
0.320
0.399
0.436
2
Brine type
NaCl
KCl
CaCl2
6000
30000
100000
1
2
4
3
4
Brine
salinity
(ppm)
Duration (week)
77
3.3.2 Core- flooding experiment
The dynamic injection of CO2 into the sandstone rock sample saturated with brine
is conducted using core- flooding experiments to simulate the actual process that takes
place in the reservoir, as closely as possible. The experiments were designed to examine
the sensitivity of the various types of CO2-brine-rock parameters while analyzing the
extent of the injectivity alteration. Two parts of the core flood experiment were
conducted to meet the first and second objective of this research. The first part
investigated the effect of the CO2 injection scheme, rock permeability, brine type and
salinity on CO2 injectivity, which was presented by permeability alteration. In the
second part, the effect of particle properties on CO2 injectivity was evaluated by varying
the particle sizes, particle concentration and type. Core -flooding experiments were
applied through the Relative Permeability Test equipment for the CO2 injection in the
Core Analysis Laboratory, Universiti Teknologi PETRONAS.
3.3.2.1 Core preparation
Two types of sandstone core samples with similar porosity and mineralogical
composition, namely Kirby and Berea were used in this study. These samples were
extracted from the outcrop sandstone formation containing no oil. Furthermore, they
were received as cylindrical plugs, which were 7.62 cm in length and 3.81 cm in
diameter. It was found from the porosity and permeability tests that the Kirby cores had
an average porosity of 20% which was similar to Berea, while the permeability for
Kirby and Berea were 55 mD and 183 - 203 mD respectively. Based on the Mercury
Injection Porosimeter (MICP) analysis, Kirby had a narrower pore channel (average
value of 0.898 μm) and a smaller average pore surface area of 0.32 m2/g compared to
Berea which had an average pore size of 1.418 μm and an average pore surface area of
0.399 m2/g. The mineralogical characterization of the rock samples was performed
using X-ray fluorescence (XRF) and X-ray diffraction (XRD). Essentially, the XRF
was performed to determine and measure the concentrations of elements and oxides in
a substance. The Bruker XRF S8 Tiger was used in the XRF analysis. After the sample
was scanned, the XRF software evaluated the data, while the results were displayed in
78
the form of normalized percentage concentrations for each oxide. XRD, on the other
hand, is a physical phenomenon as well as an experimental method for the
characterization of materials, especially crystalline materials. The XRD analysis was
performed in the scan range of 2° to 90° with a step size of 0.01°/2θ and an exposure
time of five seconds per step using the PANalytical X’Pert3 Powder and Empyrean
Powder XRD at the Centralized Analytical Laboratory (CAL) in Universiti Teknologi
PETRONAS (UTP). Following that, mineral identification was interpreted using the
PANalytical X’Pert Highscore plus for the qualitative and the Rietveld Refinement
analyses.
The quantitative results of XRF and XRD for both types of sandstone core samples
are presented in Table 3.2 and Table 3.3. The results indicate that Kirby and Berea
sandstone core samples consisted of nearly identical compounds with up to 95% of
quartz and a minor composition of K-feldspar and muscovite. While less muscovite was
found in the Kirby sandstone compared to Berea, there was no presence of kaolinite,
biotite, and zirconia in it. The analysis was correlated with the qualitative analysis
presented in Figure 3.7 and Figure 3.8.
Figure 3.7 XRD mineral points matching for Berea sandstone.
79
Figure 3.8 XRD mineral points matching for Kirby sandstone.
3.3.2.2 Fluids and fines particles preparation
To represent a simple system of formation water, three (3) brine salinities were used
which were 6000, 30000 and 100000 ppm using only sodium chloride (NaCl) and
ultrapure deionised (DI) water with a resistivity ≥9.6 MΩ (PureLab Flex, Elga, United
Kingdom). Meanwhile, the CO2 used was 99.8% pure. The preparation of the CO2saturated brines utilised a gas-tight piston accumulator filled with 800 mL of NaCl brine
and pressurising it with CO2 to 800 psi (5.51 MPa).
To control the amount and fines sizes, an artificially introduced mono-dispersed
colloid suspension was prepared at 0.3 wt% using silicon dioxide of 0.005 µm and 0.015
µm (Sigma-Aldrich, Missouri, USA). Silicon dioxide was selected for this study
because of its similar physical and chemical properties with quartz. On top of that,
silicon dioxide in its raw state is highly water-wet, which would form a very stable
dispersion.
80
3.3.2.3 Core- flooding setup and procedures
CO2 injection was done through core- flooding experiments using the Relative
Permeability System-800-10000 HTHP (Temco, Oklahoma, USA) in the Core Analysis
Laboratory, UTP. A simplified experimental set-up of the equipment is shown in Figure
3.5. The core flooding unit was equipped with Hastelloy tubing and hassler type core
holder which allowed high-pressure, high-temperature test as well as resistance to
corrosion that might arise from CO2 exposure. The cylindrical core sample, wrapped in
a tight fluoroelastomer rubber sleeve, was loaded into the core holder. A confining
pressure of 2500 psi (17.2 MPa) was applied in the annular space between the rubber
sleeve and the core holder. The pressure at the inlet/outlet of the core sample and the
overburden (confining) pressure were all measured using individual pressure
transducers. Likewise, the differential pressure across the core was measured with a
differential-pressure transmitter. A continuous-flow high precision twin syringe pump
(Teledyne ISCO 1000D, Nevada, USA) was used to deliver either designated brine,
CO2-saturated brine or scCO2 from dedicated piston accumulators.
The core samples were initially dried in an oven at 60 °C for at least 24 hours to
remove any moisture. The experiment consisted of the following steps:
1. Measurement of gas porosity and permeability of each core sample using the
Poroperm equipment.
2. Static saturation of core with designated brine samples without fines particles
using a vacuum desiccator.
3. Core- flooding set-up and dynamic saturation of core with designated brine
samples without fines particles. Confining pressure: 2500 psi (17.2 MPa);
temperature: 60 °C (140 °F).
4. Core flooding of CO2 saturated brine with or without fines particles at 1800 psi
(12.4 MPa).
5. Supercritical CO2 flooding.
6. Measurement of final permeability with designated brine samples without fines
particles.
81
7. Drying core in an oven at 60 °C for at least 24 hours.
8. Measurement of gas porosity and permeability of each core sample.
In the first step of the experiment the core samples were initially saturated with the
designated brine for 30 pore volumes injected (PVI) to remove the gas possibly trapped
inside the core samples, and the initial permeability measurement. The permeability
measurement was not done using the scCO2 in the core- flooding system due to extreme
pressure fluctuations observed during the scCO2 flooding. Similar pressure fluctuations
were also observed by Yusof, et al. [167] and Othman, et al. [25] which they attributed
to straining and the subsequent release of fines.
To investigate the effect of the CO2 injection scheme, the fourth step of the
experiment was varied with either CO2-saturated brine, scCO2 or CO2-saturated brine
followed by scCO2 with a constant injection of 2 cm3/min until the core was injected
for 135 PVI. For the last injection scheme, CO2-saturated brine was injected into the
core sample for 65 PVI followed by 70 PVI of scCO2 injection. Then, in order to
understand the impact of the injection flow rate, brine salinity, brine system, rock
permeability and particle properties on permeability changes, the experiment with the
injection scheme of CO2-saturated brine followed by scCO2 was repeated.
To evaluate the effect of the injection flow rate, the flow rate of the scCO2 injection
part was increased to 5 cm3/min and 10 cm3/min. Specifically, the high flow rates were
selected to represent the approximate fluid flow velocity at the vicinity of the near
wellbore. Moreover, the shift from low to high velocity was predicted to lead to a
viscous force impact on the fluid-rock interactions in the core samples. Furthermore,
three different salinities of NaCl and another two types of salt, (KCl and CaCl2) were
used to study the effects of different brine salinity and brine type. Then, the Berea
sandstone was replaced with a sandstone with lower permeability to investigate the
effect of initial rock permeability on permeability alteration.
In order to evaluate the effect of fines migration on CO2 injectivity, silica oxide,
particle sizes of 0.005, 0.015, 0.03, 0.045, 0.06 and 0.07 µm at different concentrations
ranging from 0.1 to 0.5wt% were initially saturated in the Berea sandstone before being
82
injected with the scCO2. The selected particle size would yield an average jamming
ratio (particle size/pore size) of 0.004 to 0.04. Moreover, the brine salinity was also
increased between zero salinity (fresh water) to 100000 ppm to evaluate the
compounding effect of salt precipitation and fines migration on CO2 injectivity. Since
the particulate process is heavily influenced by the flowing medium, the scCO2
injection flow rate was varied at 2 cm3/min, 3.5 cm3/min, 5 cm3/min, 6 cm3/min, 7
cm3/min, and 10 cm3/min.
Lastly, the final permeability was measured by injecting the designated brine into
the core sample for 30 PVI. The differential pressure between the face of the core inlet
and the outlet was recorded every 30 seconds during the injection series. The
experimental conditions is presented in Table 3.5 and all manipulated variables tested
in this study is summarized in Appendix A.
Table 3.5 Summary of experimental parameters for core flooding
Parameters
Conditions
Confining pressure
2500 psi (17.2 MPa)
Injection pressure
1800 psi (12.4 MPa)
Temperature
60 °C (140 °F)
Porosity
20 ± 5 %
Permeability
185 ± 20 mD
Injection scheme
CO2-saturated brine -> scCO2
Salt type
Sodium chloride
Flow rate
2, 3.5, 5, 6, 7, and 10 cm3/min
Brine salinities
Fresh water, 6,000, 30,000, 60,000, 80,000 and
100,000 ppm
Fines sizes
0, 0.005, 0.015, 0.03, 0.045, 0.06 and 0.07 µm
Besides, the core samples and collected fines from the produced effluent were sent
out for characterization using the Variable Pressure Field Emission Scanning Electron
Microscope (FESEM) Zeiss Supra55, which was equipped with an Energy Dispersive
83
X-ray spectroscope (EDX) in the Centralised Analytical Laboratory (CAL) in
Universiti Teknologi PETRONAS (UTP). The analysis was conducted on the highresolution microstructure images and semi-quantitative chemical determinations on the
minerals of the samples. The samples were mounted on a grid holder and gold-coated
to enhance the conductivity of electrons. To view the microstructure images of the
cubes, an accelerating voltage of 5 kV was used. Lastly, post-injection, porosity, and
permeability of the core samples were measured and compared with the pre-injection
data to monitor changes.
3.3.2.4 Determination of injectivity alteration
Following economic factors, a significant volume of CO2 would be injected into the
storage at an acceptable rate through a minimum number of wells [54]. The attainable
rate of CO2 injection without fracturing the formation could be expressed in the form
of the injectivity index (I) below, which is defined as the ratio of volumetric injection
flow rate, (q), to the pressure drop [55, 56].
𝐼=
𝑞
∆𝑃
(3.2)
The petrographic analysis, such as FESEM, X-ray scanning, pore-scale imaging,
and other advanced analytical methods may provide detailed information on pore scale events and physical features of the rock sample in the laboratory scale [47, 124,
126]. However, these methods were limited to highlight the most important parameter
in the present work, which was the resistance developed in the fluid flow through the
physical changes in the porous media during CO2 injection. This parameter could be
determined by measuring the changes in the fluid injectivity, which is normally
conducted by injecting non-reactive fluid into the core sample in a core- flood unit at a
certain flow rate. In this case, water or brine injection is normally used [18, 24].
Assuming that the core previously had a constant absolute permeability, 𝑘𝑖 , the initial
fluid injectivity (𝐼𝑖 ) the final fluid injectivity (𝐼𝑓 ) could be expressed from Darcy’s law
as follows after the CO2 exposure, 𝑘𝑓 :
84
𝐼𝑖 =
𝑞
= 𝑘𝑖 . 𝐶
∆𝑃𝑖
(3.3)
𝐼𝑖 =
𝑞
= 𝑘𝑓 . 𝐶
∆𝑃𝑖
(3.4)
The constant, 𝐶, is defined as 𝐶 = 𝐴⁄𝜇𝐿 for the use of similar fluid properties
(viscosity, 𝜇) and the constant core area, 𝐴, and length, 𝐿. At a constant injection flow
rate in the measurement of injectivity (𝑞𝑖 = 𝑞𝑓) , a dimensionless ratio between final
permeability, 𝑘𝑓 , and initial permeability, 𝑘𝑖 , can be used to reflect the injectivity
changes during the injection process (Al-Yaseri et al., 2017; Othman et al., 2019), given
by:
𝑘
Permeability ratio = 𝑘𝑓
(3.5)
𝑖
To give a quantitative value of how much the injectivity changes after the CO2
exposure, the injectivity impairment can be presented in terms of the Relative
Injectivity Change (RIC) [57], which is as follows:
𝐼𝑖 − 𝐼𝑓
)
𝑅𝐼𝐶 = (
𝐼𝑖
(3.6)
Substituting Equation (3.3) and (3.4) into (3.6) yields
𝑘𝑖 − 𝑘𝑓
𝑘𝑓
𝑅𝐼𝐶 = (
)= 1−( )
𝑘𝑖
𝑘𝑖
(3.7)
Provided that any pore plugging would reduce the total flow area (𝐴) and enhance
the core pressure drop, ∆𝑃, ∆𝑃𝑓 > ∆𝑃𝑖 and 𝑘𝑖 > 𝑘𝑓 would occur due to permeability
impairment. A positive RIC value indicates injectivity impairment or vice versa. The
RIC value is normally viewed as a percentage and an indirect way of calculating
injectivity damage, which takes place in the core sample during the injection regardless
of the chemical properties.
85
3.4 CO2 injectivity modelling
This subchapter presents the methodology to develop a new model to predict CO2
injectivity change in sandstone. Data obtained from the porosity and permeability
measurements were utilized to predict the CO2 injectivity change using theoretical
equations, newly developed equations using the Response Surface Method and
Regression from the Machine Learning (ML) method. The theoretical models were
selected from the porosity-permeability relationship of published works that were used
to evaluate the CO2 injectivity change. Meanwhile, the RSM uses the multiple linear
regression analysis which correlates independent parameters to provide a new
mathematical model that fits the estimated values obtained from the experiment.
Moreover, the several regression techniques from the machine learning approach have
also been developed to forecast the injectivity changes. The efficiency of the newly
developed RSM model and the regression model using ML were validated with the
experimental results and published field reports and publications from different CO2
sequestration fields. The comparison of the models was made in terms of the Average
Absolute Percentage Error (AAPE), sum of the squares due to error (SSE), R2, adjusted
R2 and Root Mean Square (RMSE). A cross-plot analysis was also presented to show
the fitness of the new models with the validation data. Figure 3.9 presents a flow
diagram of the development of the CO2 injectivity model.
86
Figure 3.9 Diagram of CO2 injectivity modeling process.
87
3.4.1 Assessing the existing theoretical model
The existing theoretical model to predict the CO2 injectivity changes was then
compared with the experimental results. The models were selected based on their
relation type; for example the Hagen-Poiseuille relation type is presented by Pruess and
Müller [83], André, et al. [68], Ott, et al. [33], and Sokama-Neuyam, et al. [57] while
Tang, et al. [88] and Zeidouni, et al. [91] represent the Kozeny-Carman relation type.
A flexible power law model was also used to predict the injectivity changes. Summary
of each model is summarized in Table 3.6. The statistical error analysis is calculated
and discussed in the next chapter.
Table 3.6 Prediction of CO2 injectivity models by previous researchers
Model
Equation
Pruess and Muller
𝑘
𝜙⁄𝜙𝑜 − 𝜙𝑟
=(
)
𝑘𝑜
1 − 𝜙𝑟
Hagen-Poiseuille
2
Hagen-Poiseuille
(2009)
Relation type
2
model
Andre et al. (2014)
𝑘
𝜙⁄𝜙𝑜 − 𝜙𝑟
=(
)
𝑘𝑜
1 − 𝜙𝑟
Tang et al. (2015)
𝑘
𝜙 2.4 1 − 𝜙𝑜
=( ) (
)
𝑘𝑜
𝜙𝑜
1−𝜙
Zeidouni et al.
(2009)
Power law (2016)
𝑘
𝜙 3 1 − 𝜙𝑜
=( ) (
)
𝑘𝑜
𝜙𝑜
1−𝜙
𝑘
𝜙 𝑛
=( )
𝑘𝑜
𝜙𝑜
88
model
2
2
Kozeny-Carman
model
Kozeny-Carman
model
Power law
3.4.2 Development of the RSM model
In this work, the total number of core flooding experimental data used to design the
model was 80, of which 80% were chosen to train the algorithm and 20% for the
validation of the model. The D-optimal design, as one of the common RSM designs,
was applied in this study. The experimental design technique, especially RSM was
appropriate for analyzing the individual and the interactive effects of the different
parameters. RSM uses a strong statistical method based on the least square method that
fits the estimated values obtained from experiments/simulations to the quadratic
polynomial model of RSM. In order to predict the system behavior, the quadratic or
higher-order polynomial model is applied in many industrial applications. For modeling
the CO2 injectivity change according to the CO2-brine-rock and fines particle
parameters, the second order (quadratic) polynomial equation of RSM is expressed as
a general form:
𝑛
𝑛
𝑛
𝑛
𝑌 = 𝛽0 + ∑ 𝛽𝑖 𝑥𝑖 + ∑ 𝛽𝑖𝑖 𝑥𝑖2 + ∑ ∑ 𝛽𝑖𝑗 𝑥𝑖𝑗 + 𝑒
𝑖=1
𝑖=1
𝑖=1 𝑗=1
(3.8)
where 𝑌is the modelled response, 𝛽 is the regression coefficient, 𝑥 is the
independent variables, and 𝑒 is the error. 𝛽0 is a constant value while 𝛽𝑖 𝑥𝑖 and
𝛽𝑖𝑖 𝑥𝑖2 represent linear terms (first-order effect of variables) and quadratic terms
(second-order effects of variables) respectively, and 𝛽𝑖𝑗 𝑥𝑖𝑗 is a two-factor interaction
term. This equation does not take the interaction between three factors or more into
account. The equation may be simplified to a linear equation by setting 𝛽𝑖 and 𝛽𝑖𝑖 as
zero. Moreover, a two-factor interaction (2FI) model can be derived from the model by
setting 𝛽𝑖𝑖 as zero.
For the optimizing step, the requirements for the response and the factors need to
be established. Then, a set of operating conditions was found at which all responses
were optimized or in the accepted range.
89
3.4.3 Development of the regression model using machine learning
The screening of the suitable regression technique was conducted using the
Microsoft Azure Machine Learning. Using the given Microsoft Azure guideline, the
supervised learning approach was selected considering that the aim of this project was
to make predictions of future data points. Then, different types of regression techniques
were developed to make forecasts of CO2 injectivity changes based on the relationship
between the input parameters. Like the RSM model, the 80 core -flood data was divided
into 80% for training and 20% for validation. The statistical results from all regression
techniques were compared using given statistical parameters from the software, namely
RMSE and R2.
Based on results, Neural Network (NN) model was found to be the best regression
technique with the highest R2 value of 0.969 with the lowest RMSE of only 5.83, which
suggest that it would give the highest accuracy of forecast data as compared to other
regression methods. NN model is a forecasting technique focused on basic brain
mathematical models. It is a well-known regression model that is used in several deep
learning applications and forecasting methods. Even for non-linear and complex
relationships, they work admirably in mapping the response variable to its predictions.
Using a learning algorithm, the model correctly weights each input variable and its
importance to the output as it passes across multiple layers of nodes in an iterative and
converging manner. It is a powerful model, particularly when dealing with multiple
different inputs, each of which behaves differently towards the observed result, as in
the case of the CO2-brine-rock-particle parameters and the measured RIC. The
supervised NN model used in this project was generated using the sci-kit-learn module
from the Python library and hosted in the Google Colab notebook, an interactive
platform to execute the arbitrary python code for machine learning and data analysis.
The model was then optimized by varying the hyperparameters to get the best-fit model
for predicting the actual data.
90
3.4.4 Comparison study and model testing
The performance of the theoretical model, the RSM model and the regression model by
ML were first tested with the experimental data. Then, the efficacy of the newly
developed RSM model and the regression model were tested with the reported CO2
injectivity data from the field report and experimental works of previous researchers.
The results were evaluated using the statistical error analysis and graphical error
analysis.
3.4.5 Statistical evaluation
For the statistical error analysis, the five main parameters were AAPE, SSE, RMSE, R2
and adjusted R2. These parameters were used as a guide to indicate the performance of
the models in assessing the theoretical model, training, validation and testing of the
newly developed models.
For graphical analysis, the measured experimental data and the predicted data from the
model were plotted in a linear relationship to form a cross- plot diagram. The
distribution of the predicted data against the actual data could be observed from this
analysis.
3.4.5.1 Average Absolute Percentage Error (AAPE)
AAPE measures the mean or average of the absolute percentage errors of forecasts.
Error is defined as the actual or the observed value minus the forecasted value. Also,
because absolute percentage errors were used, the problem of positive and negative
errors canceling each other out was avoided. The value was expressed in percentage
and was defined as:
𝑛
1
𝐴𝑡 − 𝐹𝑡
𝐴𝐴𝑃𝐸 = ∑ |
|
𝑛
𝐴𝑡
𝑡=1
91
(3.9)
where 𝑛 represents the number of data, 𝐴𝑡 is the measured data and 𝐹𝑡 is the predicted
data. The lower the value of AAPE, the better agreement between the estimate and the
forecast.
3.4.5.2 Sum of the Squares due to Error (SSE)
The sum of the squares due to error, also known as SSE, is the sum of the squares
of the residuals (deviation predicted from actual data). It is a measure of difference
between the observed value and the predicted value. A small SSE implies a tight fit of
the prediction model to the actual data. The SSE can be found using the formula below:
𝑛
𝑆𝑆𝐸 = ∑(𝐴𝑡 − 𝐹𝑡 )2
(3.10)
𝑖=1
3.4.5.3 Root Mean Square (RMSE)
Root Mean Square or RMSE is another way to measure the error of the model in
predicting actual data. The formula is defined as follows:
𝑛
(3.11)
(𝐴𝑡 − 𝐹𝑡 )2
𝑅𝑀𝑆𝐸 = √∑
𝑛
𝑖=1
RMSE measures the residuals (prediction errors), of how the spread of these residuals
from the regression line data points. It other words, it tells how concentrated the
predicted data is around the best of fit line. Typically, a lower RMSE is better than a
higher one.
92
3.4.5.4 Coefficient of Determination (R2)
The coefficient of determination, denoted by R2, is a measurement used to explain
how much the variability of one factor can be caused by its relationship to another
related factor. This correlation, known as the "goodness of fit," is represented as a value
between 0.0 and 1.0. The value can be determined by using Equation 3.12:
𝑅2 = 1 −
𝑆𝑆𝐸
𝑆𝑆𝑇
(3.12)
where 𝑆𝑆𝐸 is the sum of the squares of errors and 𝑇𝑆𝑆 represents the total sum of
the squares. The higher the value of R2 the smaller the degree of scatter; thus, the
accuracy is higher.
3.4.5.5 Adjusted R2
Adjusted R2 is a modified R2 that has been adjusted for the number of predictors in
the model. Essentially, it can provide a more precise view of whether additional input
variables are contributing to the model. Adjusted R2 can be calculated using the
following formula:
𝑆𝑆𝐸⁄
(𝑛 − 𝐾)
𝐴𝑑𝑗𝑢𝑠𝑡𝑒𝑑 𝑅 = 1 −
𝑆𝑆𝑇⁄
(𝑛 − 1)
(3.13)
2
where K is the number of parameters. Importantly, its value increases only when
the new term improves the model fit more than what is expected by chance alone. The
adjusted R2 value decreases when the term does not improve the model fit by a
sufficient amount.
93
CHAPTER 4
RESULTS AND DISCUSSION
This chapter provides a comprehensive description and clarification of the results
obtained from the experimental works that were presented in Chapter Three. The results
and discussion presented in this chapter are divided into the preliminary study of the
basic parameters that control the CO2-brine-rock interactions, evaluation of the CO2brine-rock parameters on CO2 injectivity in the dynamic core -flooding experiments,
and the development of the prediction model to predict CO2 injectivity changes.
4.1 Screening the brine-rock parameters affecting sandstone rock physical
changes
In this study, the Taguchi experimental design method was used to identify the
degree of dominance by four controllable parameters: pore surface area (different rock
permeability), exposed time, brine type, and brine concentration as functions of
physical rock changes.
4.1.1 Signal-noise ratio and analysis of ANOVA
Table 4.1 shows the results of the nine trial conditions, with three runs per trial
condition. The physical changes were measured in terms of weight changes (%). In the
Taguchi analysis, there are three types of quality characteristics with regard to target
design, namely lower is better, nominal is better and larger is better [166].
Table 4.1 Experimental L9 (34) orthogonal array and S/N results
Factor
Try
Brine
S/N
Surface area
Brine type
1
Low (K)
NaCl
6000
1 week
47.61
2
Low (K)
KCl
30000
2 weeks
52.24
3
Low (K)
CaCl2
50000
4 weeks
36.27
4
Medium (B)
NaCl
30000
4 weeks
45.85
5
Medium (B)
KCl
50000
1 week
44.59
6
Medium (B)
CaCl2
6000
2 weeks
51.04
7
High (I)
NaCl
50000
2 weeks
44.83
8
High (I)
KCl
6000
4 weeks
62.37
9
High (I)
CaCl2
30000
1 week
41.78
salinity
Duration
This study was to identify which experimental factor contributed to the highest
changes on the physical weight of the rock. Therefore, the larger value of weight
changes was desirable, and it was categorized in the ‘larger is better’ quality
characteristics. The results were transformed into the S/N ratio in which ‘signal (S)’
means output characteristics of desirable data (mean) and the term ‘noise (N)’ denotes
the undesirable data of output characteristics. The signal to noise ratio (S/N) was
calculated as follows [168]:
𝑆
1
= −10 𝑙𝑜𝑔 [ ∑ 𝑦𝑖2 ]
𝑁
𝑛
(4.1)
where “yi” is the observed performance characteristic data in the ith experiment and
i = 1, 2, 3, and “n” is the number of trial runs. In this study “y” indicates the weight
change of the sample.
The experimental results were converted to the S/N ratio and presented in Table
4.1. The contribution value of each individual factor is important to define the nature
of the process. Therefore, the average effect of each factor at every level was computed
95
to determine the most dominating parameter. The average S/N ratio of the influencing
factors pore surface area, brine type, brine salinity and CO2-brine-rock contact time are
shown in Figure 4.1. It can be observed that there has been an increase in the average
effects starting from level 1 to 3 for the brine salinity factor and a decrease in the
average effects for the pore surface area factor. This indicated that the weight change
percentage would increase when the brine concentration became higher. On the
contrary, when the pore surface area increased, there would be a lower effect on the
weight change percentages.
Level
1
2
3
-40.00
Mean of S/N ratio
-45.00
-50.00
-55.00
-60.00
Surface Area
Brine Type
Brine Salinity
Duration
Figure 4.1 Main effect of S/N ratio on weight change percentages.
There were no obvious changes in the S/N values at level 1 and level 3 for the
duration factor. However, there was a slight drop at the level 2 value when the
experiment duration was 2 weeks. A similar trend was observed in the Brine type factor
as it changed the salt type between NaCl, KCl and CaCl2. The maximum weight change
percentage after the experiment was found at the medium size pore surface area
(sandstone sample B), 50000 ppm NaCl and 4 weeks’ experiment duration. On the other
hand, the minimum effect on weight changes was observed at the high pore surface area
96
factor, 50000 ppm KCl brine and 2 weeks’ experiment duration. The mean value of the
S/N ratio is presented in Table 4.2.
Table 4.2 The average effects of different factors on each level
Column
Factors
1
Level number
1
2
3
Surface area
-47.63
-47.41
-52.58
2
Brine type
-45.77
-55.98
-45.87
3
Brine salinity
-54.49
-50.36
-42.76
4
Duration
-48.75
-50.28
-48.59
Different factors influence the varying degrees of deposition. The comparative
impact of the various factors can be achieved by decomposing the total variation into
suitable components, frequently referred to as the analysis of variance (ANOVA). The
ANOVA statistic is commonly applied to the experiment data to establish the
relationship between experimental parameters and output results [169, 170]. The
analysis is able to evaluate the most dominating parameters which affect the response
parameter [171]. The results of the ANOVA are shown in Table 4.3. The sum of the
squares for every factor was calculated based on the corresponding level in Table 4.2
by using the following equation [172]:
𝑆𝑆𝑖 = 3(𝑀1𝑖 − 𝑀)2 + 3(𝑀2𝑖 − 𝑀)2 + 3(𝑀3𝑖 − 𝑀)2
(4.2)
where 𝑀1𝑖 , 𝑀2𝑖 𝑎𝑛𝑑 𝑀3𝑖 refer to the average effects corresponding to each factor
for each level as listed in Table 4.3. Each factor's variance was calculated by dividing
the sum of the square for each factor with its degree of freedom (DOF). The DOF for
any factor equals to one less than the number of levels. For example, in the case of a
factor with three levels, level 2 can be contrasted with level 1 and level 3 but not with
level 2 itself. The variance ratios of the pore surface area, brine type, brine salinity and
duration of experiment were calculated as 25.72, 103.13, 106.19 and 2.62 respectively.
Lastly, the degree of dominance or the percentage of contribution of an individual
parameter on the physical rock change can be calculated by using the following
equation [173]:
97
𝐿𝑒𝑣𝑒𝑙 𝑜𝑓 𝑑𝑜𝑚𝑖𝑛𝑎𝑛𝑐𝑒 (%) =
𝑆𝑆𝑖
× 100
∑ 𝑆𝑆𝑖
(4.3)
Table 4.3 ANOVA table
Column
Factors
DOF
1
Surface area
2
Sum of squares
(SS)
51.44
2
Brine type
2
3
Brine salinity
4
Duration
Total
Variance
Percent (%)
25.72
10.82248
206.26
103.13
43.39256
2
212.39
106.19
44.68149
2
5.25
2.62
1.103461
8
475.34
100.00
The summary of the ANOVA shows that brine type and brine salinity are the
principal factors that contribute to the largest weight change percentages after the CO2brine-rock interactions with 43.4% and 44.7% respectively. Since the contribution of
the exposure duration is the smallest, that is less than 10%, it is considered as
insignificant. This is probably because in the semi-static experiment the contacted fluid
was not being replaced and the movement of the reactive ions were decreasing over
time. Moreover, no obvious trend is seen on the rock’s physical changes as the reactive
pore surface area increases. The difference in the pore surface area between all the
samples is too small to produce a huge impact on the sandstone rock alteration.
According to this approach, brine salinity is the most dominating factor for the physical
weight changes of the rock, followed by the brine type and the contacted pore surface
area.
4.1.2 pH analysis
Under all likely conditions for CO2 storage, CO2 and water are immiscible even
without any presence of dissolved salts. At the range of conditions relevant for reservoir
storage, CO2 solubility is almost independent of temperature but has strong pressure
dependency. It is further influenced by the brine composition in natural reservoirs. The
mechanism of the reaction between CO2 and brine to form carbonic acid and
subsequently bicarbonate can be represented schematically as:
98
𝐶𝑂2 + 𝐻2 𝑂 ⇆ 𝐻2 𝐶𝑂3 ⇄ 𝐻𝐶𝑂3 − + 𝐻 +
(4.4)
Figure 4.2 shows the pH value measurement on different brine samples for four
weeks of experiment. As expected, the progressive dissolution of CO2 in the brine leads
to a sudden reduction in pH from 7.4 to about 5 after one week, confirming the
comparatively reactive nature of the injected CO2. As can be seen, the pH reduction is
bigger in KCl followed by NaCl and CaCl2. As the experimental duration extended up
to four weeks, the pH measurement gradually dropped to the lowest point at 4.8 for
NaCl and slightly above 5 for KCl and CaCl2 because of the longer contact time
between CO2 and brine. The effect of different pH reduction in different brine types
could be explained by the solubility of CO2 in the salt solution. At the same pressure,
temperature and salt concentration, the solubility of CO2 in the aqueous solution of
CaCl2 is slightly lower than that in the NaCl brine, and both are considerably lower than
that in the KCl solution [174].
8
NaCl
KCl
CaCl2
pH value
7
6
5
4
0
1
2
Duration (week)
3
4
Figure 4.2 pH value measurement on brine samples.
Previous studies have emphasized the relevance of this CO2 dissolution in brine for
the storage of injected CO2 to solubility trapping in saline formation [43, 175]. The
dissolution process is not only important for storage reasons; it also significantly affects
the mineral reactivity, because free H+ ions released into the pore fluid would react
99
with the available rock minerals, dissolving them and eventually changing the
composition and structure of the rock formation. However, at a certain level, the effect
of fluid-mineral interactions is almost invariably to neutralize the carbonic acid acidity,
resulting in a smaller pH reduction to no change in pH for longer experimental
durations. Provided the pH remains below the apparent first constant of carbonic acid
(pH = 6), the dominant aqueous carbonate species remain as CO2 and H2CO3, and
mineral dissolution has little effect on the total dissolved inorganic carbon. If the
reactions caused a rise in pH above the critical point, significant additional CO2 may
enter the solution as bicarbonate, enabling additional CO2t to be stored through
solubility trapping. The effect of CO2 on the physical changes of the rock for this study
is explained in the next section.
4.1.3 Rock physical changes of sandstone before and after CO2 reaction by
FESEM-EDX analysis
In whatever rock composition, the injection of CO2 into the brine leads to a series
of physical and chemical reactions (CO2-brine-rock interactions), changing the physical
rock properties. The reactions occurring in sandstone rocks generally include
dissolution of silicates like quartz (SiO2), feldspar (CaAl2Si2O8 − NaAlSi3O8 −
KAlSi3O8), pyroxene ((Mg, Fe)2Si2O6-Ca(Mg,Fe)Si2O6) or olivine ((Mg,Fe)2SiO4),
carbonates, for instance calcite (CaCO3), dolomite (CaMg(CO3)2), or magnesite
(MgCO3),
and/or
clay
minerals
like
kaolinite
(Al2Si2O5(OH)4),
illite
(K0.65Al2Al0.65Si3.35O10(OH)2), or smectite group minerals (e.g. montmorillonite
(Na,Ca)0.3(Al,Mg)2Si4O10(OH)2∙nH2O) to name a few [176, 177]. Meanwhile, the
produced bicarbonates, due to messy reactions, can react with the available cations
present in the liquid in order to form stable carbonates based on the following reactions:
𝐻2 𝑂 + 𝐶𝑂2 + 𝐶𝑎𝐶𝑂3 ⇄ 𝐶𝑎(𝐻𝐶𝑂3 )2
(4.4)
𝐻2 𝑂 + 𝐶𝑂2 + 𝑀𝑔𝐶𝑂3 ⇄ 𝑀𝑔(𝐻𝐶𝑂3 )2
(4.5)
𝐻2 𝑂 + 𝐶𝑂2 + 𝐹𝑒𝐶𝑂3 ⇄ 𝐹𝑒(𝐻𝐶𝑂3 )2
(4.6)
100
The process can be the combination of mineral dissolution, precipitation and finally
the fines migration [84, 120, 178].
4.1.3.1 Mineral dissolution and precipitation
The physical rock changes of sandstone samples before and after the reactive
exposure with CO2 and brine were studied with the help of the FESEM-EDX analysis.
Figure 4.3 shows the FESEM images of the quartz-rich Berea sandstone core samples
saturated with 30 000 ppm NaCl. The comparison of the FESEM images taken pre- and
post-experiments showed that quartz particles remained intact, but dissolution of
carbonate as a cementing material and feldspar occurred in all experiments. Quartz
dissolution [177] is given by:
𝑆𝑖𝑂2 + 4𝐻 + ⇄ 𝑆𝑖 + + 2𝐻2 𝑂
(4.7)
However, at low pH, the effect of quartz dissolution is negligible and has not been
observed in short- term laboratory tests. Moreover, the acidic environment of CO2-brine
dissolution only reduced the pH value to about 4 in this experiment and would not lower
the pH below 3 [16, 74]. Therefore, it can be assumed that quartz dissolution is
negligible throughout this experiment.
By detailed spot analyses of the marked areas in the samples, the pore space growth
due to carbonate dissolution was traceable in defined areas. The mechanism ranged
from a total to a partial dissolution of carbonate and to almost unaltered ones. In certain
parts, other minerals such as K-feldspar and clay also reacted and dissolved after the
CO2-brine exposure as can be seen in Figure 4.3. In general, feldspars dissolve
congruently in acid and alkaline pH, and are incongruent at neutral pH based on the
following reaction [108]:
𝐾𝐴𝑙𝑆𝑖3 𝑂8 + 𝑁𝑎+ + 𝐶𝑂2 + 2𝐻2 𝑂 ⇄ 𝑁𝑎𝐴𝑙(𝐶𝑂3 )(𝑂𝐻)2 + 3𝑆𝑖𝑂2 + 𝐾 +
(4.8)
This matched with our observation on the EDX analysis where there was a
significant reduction of 𝐾 + in its original concentration. Clay mineral and kaolinite
101
were also found to migrate and fill the gaps between the stable quartz grains and were
found in the FESEM image (Figure 4.4). The dissolution of these minerals accompanied
by an enlargement of the pore size and generation of newly- formed pores led to a
possible reduction of the total weight of the samples. Similar effects of increasing the
pore space and rock porosity due to mineral dissolution are also described by Dawson,
et al. [162], Kaszuba, et al. [176], Pearce, et al. [179].
Figure 4.3 FESEM images of Berea sandstone saturated with 30000 ppm of NaCl show
the pore space enlargement due to dissolution causing an increase on pore connectivity
(red circles).
102
Figure 4.4 Newly- formed kaolinite mineral filled in the gap between the particles
after CO2 exposure.
4.1.3.2 Fines migration and entrapment
The dissolution of the intergranular cement material which formerly bound and
covered the particle grains and clay minerals will not only result in the enhancement of
rock porosity but will also release the grains and expose the clay minerals to the
dynamic formation fluids. This exposure enables fluid-rock interactions and particulate
migration. The flowing particles can mechanically or geochemically plug the narrow
pore throats through bridging and size exclusion processes.
The submicroscopic studies by FESEM indicated that silica and clay particles
(chlorite group) had migrated and been captured at smaller pore throat areas (Figure
4.5). The silica particle SiO2 is easy to be identified in EDX where it clearly shows high
peaks of Si and O elements. In Figure 4.5, the original debris of particles on the stable
quartz grains were cleared after the experiment. Later, it was found that a new silica
particle was trapped in between the narrow pore spaces. While moving through the pore
throat, particles could be trapped because of size exclusion or direct interception or
better known as the jamming ratio (particle diameter to pore throat ratio, β) [180]. If
the particle size is equal to or greater than the pore throat size, entrapment or plugging
will certainly take place. On the other hand, if the particle size is smaller than the pore
throat size, piping or particle passing through will occur. Most important, this confirms
103
that the fines migration phenomena has occurred after the CO2-brine-rock interactions
experiment.
Figure 4.5 Migrated silica particle trapped at the pore throat.
In Figure 4.6, the newly stable carbonate particle such as siderite, based on equation
(7), also formed, and filled in the available pore space and these phenomena were
confirmed by the EDX analysis. Such behaviors also observed and discussed by
Sokama‐Neuyam and Ursin [66], Pudlo, et al. [99] and Xie, et al. [35] were attributed
to the varying fluid and rock conditions. The mechanism resulted in the decline of pore
space and connectivity.
104
Figure 4.6 Newly- formed siderite particle formed between the pore spaces. The
mineral was confirmed with the EDX analysis.
4.1.3.3 Effect of different brine systems
Figure 4.7 presents the FESEM images taken on the surface of the Berea sandstone
saturated with 30,000 ppm of CaCl2, NaCl and KCl. Clearly, the sandstone saturated
with CaCl2 appears to have clean but enhanced pore spaces with a larger number of
missing particles (Figure 4.7a). This disappearance is likely due to heavy dissolution of
carbonate materials which caused the particles to be released from the grain bindings.
In the CaCl2 brine system, the carbonic acid that reacts with calcium ions to produce
calcium carbonate and hydrochloric acid [181] is given by:
𝐶𝑎𝐶𝑙2 + 𝐻2 𝐶𝑂3 ⇄ 𝐶𝑎𝐶𝑂3 + 2𝐻𝐶𝑙
(4.9)
The newly- formed hydrochloric acid may react with the calcite and other carbonate
cement materials and cause a heavy dissolution effect. That is the possible reason why
the dissolution effect was found dominant in the CaCl2 brine system compared to the
NaCl and the KCl brine systems.
105
Moreover, from the FESEM images in Figure 4.7b and Figure 4.7c, the appearance
of salt precipitation is more severe for monovalent salt types (NaCl and KCl) than for
the divalent salt of CaCl2 after the CO2 exposure experiment. The microscopic images
show most of the surface area covered by the precipitated salt. The amount is higher as
the brine salinity increases. The formerly existing pores shown in the green circles in
Figure 4.7 went missing and were partly reduced in size after the experiment. This is in
agreement with the findings of Pruess and Müller [182] and Peysson, et al. [183], who
explained the formation of the dry-out and salt precipitation phenomenon after the
injection of CO2 into the sandstone rock saturated with monovalent salt types. The salt
precipitation which has been widely reported as the major contributor to the
permeability reduction at near wellbore caused a drastic reduction in CO2 injectivity
impairment [114, 115].
By applying various components of CO2-brine-rock parameters and the Taguchi
methods, this study was able to systematically examine the degree of influence by brine
type, brine salinity, reactive pore surface area and contact time on the alteration of the
physical rock properties and pH changes. This study provides a new insight into the
principal dominance of brine type, salinity and exposed area which significantly affect
the pore space growth and pore network due to dissolution, precipitation, and fines
mobilization mechanisms. The brine type and salinity are among the listed parameters
that significantly affect the CO2 injectivity calculation based on the porositypermeability relationship modelling [129, 145]. These findings will be useful in
understanding the practical applications and the overall control of key fluid-rock
parameters during CO2 sequestration, particularly those related to porosity and
permeability rock changes in saline aquifer. However, careful consideration must be
given to the details of the statistical assumptions and limitations involving no crossterm effects while using the Taguchi methods.
106
Figure 4.7 Comparison of images before and after the CO2 exposure for sandstone
saturated with 30,000 ppm CaCl2, NaCl and KCl. The green circles indicate newlyformed material on the grain surface and the red circles highlight the enhanced pore
spaces due to dissolution and missing particles.
107
From the ANOVA analysis, it was observed that brine salinity was the most
significant parameter for physical weight changes of the rock, followed by brine type
and exposed area. The brine factors are four times more dominant compared to the other
factors towards the weight- change percentage of the sandstone rock core samples. The
exposure time was also found to be less significant to alter the physical changes of the
rock. The presented pH analysis depicts a low pH for all brine samples after being
injected with CO2 due to the dissolution of CO2 in brine. The acidified brine dissolves
the rock minerals, especially the carbonate material, feldspar, and clay minerals. The
continuation of the chemical reaction also contributed to the precipitation of new clay
minerals and salt precipitation.
The FESEM images and the EDX analysis confirm that the combination of mineral
dissolution, salt precipitation and finally the fines migration had taken place on the
sandstone core samples. At constant brine salinity, the FESEM image comparison
analysis indicates that pore spaces and connectivity in sandstone saturated with KCl are
heavily damaged because of extreme salt precipitation. However, core saturation with
CO2-CaCl2 brine has greatly improved the pore spaces due to cement and sensitive
minerals dissolution. It enlarges the available pore network, and new pore spaces also
have been created after the particles had been released. Therefore, a better
understanding of the influence of the brine parameter (salinity and type) on the
magnitude of the petro physical changes should be the focus of future research.
4.2 Effects of CO2-brine-rock parameters on CO2 injectivity
This section presents the findings of the core -flooding experiments, focusing on
the effect of CO2, brine, and rock parameters on the injectivity impairment presented
by permeability alteration. The three significant parameters highlighted from the
previous semi-static batch experiment, which were brine salinity, brine type and surface
area (represent rock permeability) were evaluated under a dynamic scCO2 injection
series. Additional experimental parameters, namely the CO2 injection scheme and the
injection flow rate were also studied. Supplementary analysis of produced water
108
chemistry, microscopic analysis of migrated fines particles and pressure plot profiles
are also presented.
4.2.1 Changes of produced brine chemistry
Inductively Coupled Plasma Atomic Emission Spectrometry (ICP-AES) of the
produced effluent collected from the outlet of the core -flooding unit during the
injection series showed an increase in dissolved Ca, Mg, K, Si, Al and Fe concentrations
(Figure 4.8). These ions were entirely absent during the injection of different
concentrations of NaCl brine. However, after the injection of the CO2 saturated brine
followed by scCO2, the concentration of these elements increased considerably.
Dissolution of the injected scCO2 in brine results in the creation of a low acidic
medium: carbonic acid in the pore fluid, given by:
𝐶𝑂2 + 𝐻2 𝑂 → 𝐻2 𝐶𝑂3 → +𝐻𝐶𝑂3−
(4.10)
The carbonic acid in brine can dissolve the available cementing material in the Berea
sandstone, CaCO3, which results in the production of Ca, given by;
𝐶𝑎𝐶𝑂3 + 𝐻 + → 𝐶𝑎2+ + 𝐻𝐶𝑂3−
(4.11)
Moreover, the experimental findings are in agreement with available literature
which indicates that the CO2 dissolution in formation brine could reduce the pH only at
4. Therefore, quartz, as the major component of sandstone rock is known to be
unreactive in this condition. Quartz, as the main silicate dissolves only at higher pH
(pH > 7) and extremely low pH (pH < 2) (Brady & Walther, 1990). Recent findings by
Zhang, et al. [184] also indicated that quartz particle migration is unlikely because of
unchanged strong water-wet after being exposed with CO2 injection. Therefore, it can
be concluded that quartz dissolution is negligible during CO2 injection.
109
60
Concentration (mg/L)
50
40
30
20
10
0
Mg
Ca
Fe
Initial brine
Al
Mn
Si
K
Produced brine
Figure 4.8 ICPAES analysis of the produced brine and initial brine.
The observation of the Si element in the produced samples is probably a result of
the dissolution of K-feldspar and clay minerals, muscovite and kaolinite which are
reported in the XRD analysis. The dissolution of K-feldspar, muscovite and kaolinite
are given by [70]:
K-feldspar,
𝐾𝐴𝑙𝑆𝑖3 𝑂8 + 𝑁𝑎+ + 𝐶𝑂2 + 2𝐻2 𝑂 → 𝑁𝑎𝐴𝑙(𝐶𝑂3 )(𝑂𝐻)2 + 3𝑆𝑖𝑂2 + 𝐾 +
(4.12)
Muscovite,
𝐾𝐴𝑙2 (𝑆𝑖3 𝐴𝑙𝑂10 )(𝑂𝐻)2 + 10𝐻 + → 3𝐴𝑙 3+ + 3𝑆𝑖𝑂2 + 𝐾 + + 6𝐻2 𝑂
(4.13)
Kaolinite,
𝐴𝑙2 𝑆𝑖2 𝑂5 (𝑂𝐻)4 + 6𝐻 + → 5𝐻2 𝑂 + 2𝑆𝑖𝑂2 + 2𝐴𝑙 3+
(4.14)
It can be seen from the above equations that, a part of the Si element, the dissolution
of K-feldspar and muscovite also contributed to the increase of K ion. This finding is
consistent with the earlier observation in the semi-static batch experiment to describe
110
the dissolution of K-feldspar in the Berea sandstone (Figure 4.3). Furthermore, the
increase of Al can be explained by the dissolution of clay minerals, muscovite and
kaolinite.
Additionally, the dissolution of the biotite mineral is probably the main cause for
the increment of Mg, Fe and Al ions concentrations. The reaction also produced a new
kaolinite mineral, given by:
𝐾𝑀𝑔3 (𝐴𝑙𝑆𝑖3 𝑂10 )(𝑂𝐻)2 + 7𝐻 + + 0.5𝐻2 𝑂
(4.15)
→ 𝐾 + + 3𝑀𝑔2+ + 2𝐻4 𝑆𝑖𝑂4 + 0.5𝐴𝑙2 𝑆𝑖2 𝑂5 (𝑂𝐻)4
Lastly, the comparison of the visual observation between the initial brine and the
produced brine after the CO2 injection in the core- flooding system is shown in Figure
4.9. Clearly, the initial transparent brine sample (Figure 4.9a) has changed to a
yellowish colour with some yellowish-red sediments (Figure 4.9b), settled down at the
bottom of the beaker. A few amounts of particles were also directly observed. These
particles were believed to have been released from the sandstone core during the
continuous injection of CO2-saturated brine followed by scCO2. This finding was also
reported by [185].
Figure 4.9 Samples of brine before and after the CO2 flooding experiment.
111
The overall analysis of the produced water chemistry suggested that there were
some reactive interactions between the fluid and the rock minerals during the CO2
injection series. An implication of these reactions contributes to mineral dissolution,
precipitation and fines migration mechanisms which may alter the porosity and
permeability of the sandstone.
4.2.2 Characterization of migrated fines particles
This characterization activity aimed to evaluate the properties of the fines particles,
which were released or passed through the core samples. The injection of scCO2 into
the sandstone rock saturated with brine led to a series of physical and chemical
reactions, which changed the physical rock properties. The interactions that occurred in
the sandstone rocks generally included mineral dissolution, mineral precipitation, and
fines migration.
Figure 4.10 shows the FESEM images of the collected fine particles with their
estimated sizes and shapes. The size of the collected fine particles was in the range of
0.1 μm to 200 μm and with different irregular shapes. Based on the EDX analysis, most
of the collected fines particles were quartz particles, the existence of which was most
likely due to the particle detachment process. This observation is consistent with that
of Othman, et al. [25] who found that migrated fines are quartz and minor minerals
present in sandstone rock including kaolinite and muscovite. While quartz was found
to be stable in a low pH condition, the quartz particles migration was probably due to
detachment after the dissolution of the intergranular cementing material (CaCO3) in the
acidic environment. In the disorganized reactions of the CO2-brine-rock, CaCO3
normally dissolved and reacted with the available cations present in the liquid to form
stable carbonates [93], as shown in Equation 4.4.
The dissolution of CaCO3 allowed the release of particles such as stable quartz material
to flow with the fluid during the scCO2 injection.
112
Figure 4.10 The FESEM image of collected fine particles collected from the produced
effluent (Berea core saturated with 30000 NaCl brine), showing the range of size and
shape.
Precipitated salt and dispersed kaolinite particles were also found in the effluent
with a small number of cement materials (CaCO3). Specifically, precipitated salt was
attached to the surface of the silica grain during the injection of scCO2, as shown in
Figure 4.11. This finding was indicated by the size of the salt ranging from 0.5 μm to
almost 2 μm. Moreover, the precipitated salt on the surface of the released particles was
found to enhance the fines particle size and surface area. This also suggests that salt
precipitation first occurred on the particle surface area before it migrated along with the
scCO2 flow. Following that, Figure 4.12 indicates that the kaolinite mineral remained
intact with the migrated quartz particles, while parts of the kaolinite and other particles
were scattered around. The increase in the kaolinite’s surface particles detachment, in
this study, supports evidence from a previous observation [184], which found that
Kaolinite was water-wet weak at raising temperature (above 55oC), which then was
more easily dislodged from the rock surface during the CO2 injection in brine.
113
Figure 4.11 The FESEM image of precipitated salt attached to the surface of particles
(showing the range of size and shape).
Figure 4.12 Detached kaolinite particles scattered around the main kaolinite stack
(found attached to the stable quartz grains)
114
In this experiment, the dissolution mechanism enhanced the pore networks and was
able to release fines particles. During continuous CO2 injection, the released particles
flowing through the porous medium could either be attached to the flow without being
captured or be attached in the restricted pore channels. The salt precipitation, which
was found to cover the surface of the grains and filled in the pore spaces, would reduce
the permeable path. This would result in a reduction in the porosity and the permeability
of the sandstone core sample. A schematic diagram to present the mineral dissolution,
salt precipitation and fines migration mechanisms during the CO2 injection into saline
aquifer is depicted in Figure 4.13. The particulates processed in the porous media were
subjected to the physical properties of fine particles, porous media and carrier fluid [37,
186]. The important parameters included the particle and porous media grain diameters,
the density and viscosity of the carrier fluid and the convective velocity of particles,
which are commonly assumed to be equal to the injection flow rate.
Figure 4.13 Schematic diagram of mineral dissolution, salt precipitation and fines
migration mechanisms during CO2 injection into saline aquifer.
115
In a realistic scenario of CO2 sequestration, the ideal disposal of CO2 into deep
saline aquifer would be made by injecting scCO2 into a limited number of wells at the
highest possible flow rate due to economic reasons and maximum storage. Under these
conditions, the impacts of salt precipitation might be the dominant cause of injectivity
deficiency in a region near the wellbore and the released particles due to high drag
forces which were more likely to be pushed further into the formation. Consequently,
the distribution of pore plugging will depend on the amount of the generated particles
as a result of CO2-brine-rock interactions. Additionally, the unique characteristics of
CO2 in the supercritical situation and the complex relationships between different
components of the fluids-rock scheme require an expansion of conventional findings to
gain an understanding of the processes of fines mobilization in the CO2 injection
context.
4.2.3 The effect of CO2 injection scheme
The effect of CO2 injection schemes on permeability alteration was investigated
using three Berea sandstone cores. Figure 4.14 presents the permeability change of
experiments performed on the Berea sandstone after being injected with different CO 2
injection schemes. The units are measured in RIC percentages. According to the chart,
the permeability reduction created by the injection of scCO2 alone was higher at 7.4%
as compared to the injection of CO2-saturated brine at 4.7%. On top of that, the highest
permeability reduction was at 13.6% which was observed on the Berea sandstone core
injected with CO2-saturated brine followed by scCO2. The injection of CO2 into a
porous medium saturated with aqueous solution would lead to the production of
carbonic acid based on Equation 4.4.
These reactions occurred with the minerals constituting the porous media, which
led to mineral dissolution and/or precipitation. Although mineral dissolution would
increase porosity, the subsequent mechanism of precipitation and fines migration
during the continuous injection of CO2 would reduce the permeability. Schaef and
McGrail [14] stated that in many cases a higher petro physical alteration was expected
when the core sample was injected with CO2-saturated brine due to the higher carbonic
116
acid volume in the pre-generated fluid (pH 3-4). Relatively, the injection of scCO2 into
brine required a longer time for solubility to take place [25]. Additionally, it was also
expected that a low amount of carbonic acid would form in a short dynamic coreflooding experiment.
Figure 4.14 The effect of CO2 injection schemes on modifications in permeability
which was evaluated on the core samples before and after the core flood studies.
As can be seen from Figure 4.14, the damage created by injecting scCO2 was higher
compared to the injection of CO2-saturated brine. To illustrate this finding, the CO2saturated brine injection into the brine was a single-phase mixture, leading to an acidic
environment, which led to possible permeability damage through mineral dissolution
and a small amount of migrated fines. This finding is consistent with that of Othman,
et al. [18] who reported that although the injection of CO2-saturated brine led to a
decrease in the permeability of core samples with the content of high-salinity brine, it
led to an increase in the permeability of core samples with a low-salinity of brine.
Comparatively, the injection of scCO2 into the brine would lead to two conditions,
in which a portion of CO2 dissolved in brine, while the flow of another portion of scCO2
enabled the brine evaporation process. As a result, an accumulation of salt precipitation
was observed on the surface of the core sample injected with scCO 2 while no
117
precipitated salt was found on the other core injected with CO2-saturated brine (Figure
4.15). Furthermore, precipitated salt particles were also found together with other
migrated particles based on the collected effluent during the scCO2 injection as
discussed in the characterization of the migrated fines particles section. Therefore, the
development of salt precipitation during the scCO2 injection resulted in a more
significant permeability reduction compared to the injection by CO2-saturated brine.
Figure 4.15 Compared images of sandstone core samples before and after each CO2
injection scheme.
Lastly, the injection scheme with CO2-saturated brine followed by scCO2 yields the
highest permeability reduction. This is because, in this injection scheme, the
permeability damage during the CO2-saturated brine is amplified by the precipitation
of salt combined with the fines migration during the continuous injection of scCO2. As
the injected scCO2 displaces the low-pH CO2-saturated brine laterally, the interfacial
force between CO2-brine can dislodge the fines particles along the flow direction. Then,
the migrated particles have a higher tendency to impair the permeability because of the
narrower pore channels rendered by the salt precipitation. As displayed in Figure 4.15,
118
salt precipitation covered a larger area after being injected with CO2-saturated brine
followed by scCO2 as compared to the other CO2 injection schemes. Taken together,
these results suggest that there is an association between the CO2 injectant condition
(CO2-saturated brine and scCO2) and the permeability alteration of sandstone rock
samples.
4.2.4 The effect of injection flow rate
Figure 4.16 illustrates the profile of the pressure differences across the core samples
during the scCO2 injection flow rate from 2 to 10 cm3/min. As depicted in Figure 4.16,
the change in the scCO2 flow rate strongly influenced the pressure drop profiles. At a
lower flow rate, the value of the pressure increased was less significant although a
longer duration was required to reach the breakthrough point compared to the higher
flow rate. As the flow rate increased from 2 cm3/min to 10 cm3/min, the pressure drop
value increased by approximately 80 kPa. Similar findings were recorded by SokamaNeuyam, et al. [17], who presented a notable increase in the pressure up to 517 kPa
with the injection of a similar CO2 flow rate into the Berea sandstone. However, their
core sample was initially saturated with a higher brine salinity of 100000 ppm and 0.5
wt% of a mono-disperse particle with an average particle of 0.08 μm. Therefore, a
higher amount of precipitated salt and pore plugging by the particles was recorded,
which possibly reduced the larger flow area and increased the pressure drop value.
119
Figure 4.16 The Pressure profiles during scCO2 injection at different flow rates.
Furthermore, various peaks of pressure drop fluctuations were developed in the last
stage of the scCO2 injection possibly due to pore jamming and the subsequent opening
by the migrated fines particles. The peaks were also slightly higher with a high flow
rate of 10 cm3/min compared to the low flow rate of 2 cm3/min. Similar pressure
fluctuations were observed by Mohamed, et al. [187] and Othman, et al. [25], in which
fines straining and subsequent release indicated a fluctuation in the pressure difference
profile. As a result of the reaction during the scCO2 injection, the measurement of a
reliable permeability value similar to the conventional brine, oil, or non-reactive gases
injection was impossible as a constant pressure drop profile was required.
Moreover, the relative injectivity change in the porous media as a result of different
scCO2 injection flow rates are presented in Figure 4.17. The experimental results of the
solid line indicate that the increase in the scCO2 injection flow rate from 2 cm3/min to
5 cm3/min led to approximately 10% of permeability reduction. Notably, the highest
permeability reduction of 23.6% was observed when scCO2 was injected at 5 ml/min.
This was followed by a decrease in the permeability changes by approximately 5% at
the highest flow rate of 10 cm3/min.
120
Relative Injectivvity Change (%)
30
20
10
0
2
4
6
8
10
Injection flow rate (cm3/min)
Figure 4.17 The effect of injection flow rate on alteration in permeability percentages
measured on core samples before and after the core flood studies.
A similar trend was also found in the study by Sokama-Neuyam, et al. [17] which
recorded an increase in the permeability reduction from 24% to 28% with the increase
in scCO2 injection flow rate from 2 cm3/min to 5 ml/min. Meanwhile, the study by
Jeddizahed and Rostami [188] recorded a decrease in permeability reduction values
when the Berea sandstone was injected at a high flow rate of 5 cm3/min, 10 cm3/min,
and 20 cm3/min. Overall, these findings suggest that a critical scCO2 injection flow rate
or injection velocity was present, which led to the deviation of permeability impairment
from the increasing trend to the lower permeability damage. Moreover, the critical
value to obtain the highest injectivity impairment was around 5-6 cm3/min. Any scCO2
injection flow rate beyond this critical point would lead to lower injectivity impairment,
which is beneficial in any CO2 sequestration project. This finding broadly supports the
work of other studies in this area linking the CO2 injection rate with permeability
impairment by salt precipitation [31, 145].
121
4.2.5 The effect of brine salinity
Figure 4.18 displays the permeability changes of three Berea sandstone core
samples saturated with salinity of between 0 and 100000 ppm NaCl brine after being
injected with CO2-saturated brine followed by scCO2. The effect of the brine salinity
can be seen clearly in the plotted data. The permeability reduction, which was
represented by RIC values, increased gradually from 6% to 27.3% with the rise in brine
salinity. The effect of brine salinity on injectivity changes was indicated through the
formation of salt precipitation during the subsequent injection of scCO2 into the brine.
Relative Injectivity Change (%)
30
20
10
0
0
20000
40000
60000
80000
100000
Salinity (ppm)
Figure 4.18 The effect of increasing NaCl brine concentration on the alteration in
permeability percentages measured on core samples before and after core flood studies.
The precipitated salt was most likely formed on the surface of the available grains
or filled in the available pore space area, which reduced the porosity and effective flow
area. This was found on the injected face of the core samples and the collected fines
particles from the effluent sample. A higher amount of precipitated salt covered the
surface of the 100000 ppm core sample compared to the cores saturated with a lower
brine salinity of 30000 ppm and 6000 ppm. The increase in the salt precipitation, 𝑆𝑠
with the increasing brine salinity, 𝑋𝑠 is based on the following mass balance equation
previously presented by Pruess [145] as:
122
𝑆𝑠 = (1 − 𝑆𝑔,𝑑 )
𝜌𝑎𝑞 𝑋𝑠
𝜌𝑠
(4.15)
As shown in Figure 4.19, the effective pore spaces for liquid and gas flow in natural
reservoir rocks could be represented by a bundle of parallel cylindrical tubes with
various diameters between non-porous masses which indicate the rock matrix [142,
189]. At higher brine salinity, the thickness of the deposited salt in each capillary tube,
∆𝑟𝑠
increased
according to Equation (11) by Sokama-Neuyam and Ursin [19].
Therefore, the presence of more precipitated salt reduced the presence of the cross-flow
area within the pore flow (Figure 4.20). As a result, lower injectivity value was formed
at higher brine salinity.
∆𝑟𝑠 =
2 𝑆𝑠 𝑟𝑖
3 𝑙𝑑
(4.16)
These results indicate that there is a direct correlation between the brine salinity,
which determines the amount of precipitated salt, and the permeability alteration of
sandstone after being injected with CO2-saturated brine followed by scCO2.
Figure 4.19 A schematic view of the effect of salt precipitation on reducing the
crossflow area in the bundle-of-tubes model.
123
4.2.6 Effect of the brine system
A thorough understanding of the solubility of CO2 in brine is essential in the
estimation of permeability alteration in the acidic environment during CO2 injection.
Figure 4.20 shows the effect of the NaCl, KCl and CaCl2 brine systems on the alteration
of permeability percentages measured on core samples before and after the core flooding studies. The experiments indicated that the core samples injected with
monovalent salt systems exhibited a reduction in permeability after the CO2 flooding
experiment. As shown in Figure 4.21, the image analysis of sandstone core samples
indicates the CO2 dry-out effect on samples saturated with NaCl and KCl. It was found
that the precipitated NaCl and KCl salt partly covered the surface of the stable quartz
and filled in the pore spaces. This is in line with the findings by Pruess [145] and
Peysson, et al. [183], who explained the formation of the dry-out and the salt
precipitation phenomenon after the injection of CO2 into the NaCl and KCl brines.
Figure 4.20 The effect of different brine systems on the alteration of permeability
percentages measured on core samples before and after core- flooding studies.
Furthermore, the enhanced permeability effect was recorded in the sample saturated
with CaCl2. Specifically, the increase in permeability was mainly due to the dissolution
of the calcite-cemented material during the injection of CO2-saturated brine. The pH of
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the brine was measured to reduce the pH range of 3.5 to 4. Moreover, it was found from
the physical pore-image analysis that certain pore areas increased significantly to form
dissolution channels and offer better flow areas and connectivity (Figure 4.22).
Meanwhile, a small amount of precipitated CaCl2 salt on the rock surface was observed
at the injection inlet. Compared to the limited salt precipitation, the increase in the
dissolution-related permeability led to an increase in the lead permeability by 6.9% after
the CO2 injection series. Overall, these results were in line with the data recorded by
Mohamed [190], who found that at a brine salinity lower than 50000 ppm, the core
saturated with CaCl2 brine exhibited an increase in permeability, while a negligible
change of permeability was found in the NaCl saturated core.
Figure 4.21 FESEM images of Berea sandstone core samples saturated with 30000 ppm
of (a) NaCl and (b) KCl, before and after CO2 injection schemes. Precipitated salts
partly and fully covered the surface of the particle and filled in the pore spaces (green
circles).
125
Figure 4.22 The FESEM image shows enhanced pore space in core sample saturated
with 30000 ppm of CaCl2.
4.2.7 The effect of initial rock permeability
The data of the permeability change of the Berea (189 mD) and the Kirby sandstone
(61 mD) after the injection of CO2-saturated brine followed by scCO2 are presented in
Figure 4.23. It was found that permeability damage was higher in the Berea sandstone
compared to the Kirby sandstone. This finding was surprising because it was initially
predicted that Kirby would exhibit higher permeability damage due to narrower pore
channels compared to Berea and lead to higher susceptibility to pore plugging.
The higher permeability reduction with the increase in rock permeability could be
illustrated by fluid velocity and residence time in the porous media. At a similar flow
rate, Kirby with a significantly lower permeability and size of pore channels would
exhibit higher velocity compared to Berea. Concerning this, Suekane, et al. [191]
presented an experimental and numerical research on the behavior of scCO2 injected
into the porous media with water content, in which a higher flow speed of scCO2 was
found along a narrow channel with water content. It was also found that the condition
of CO2 flow was a strong function of CO2 saturation and contraction in the pore
network.
126
Figure 4.23 Estimated relative injectivity change of CO2 as a function of initial rock
permeability
As a result of the lower flow velocity at a reduced-width pore network, Berea with
higher permeability would exhibit longer residence time. It would also increase the time
for the brine vaporization process in the flowing CO2 stream, which could lead to a
higher amount of salt precipitation developed in the pore spaces. The physical
observation on the injection surface of the core sample indicated that precipitated salt
covered about 85% of the Berea core sample as compared to less than 10% in the Kirby
core sample. This finding was also observed by Kim, et al. [91], in which salt
precipitation was higher at a combination of low velocity and a high permeability zone
as a result of the localized salt precipitation. Additionally, longer residence time
enabled longer fluid-rock interactions, which led to fines mobilization.
4.3 Combined impact of salt precipitation and fines migration on CO2 injectivity
In this section, the effects of both the salt precipitation and the fines migration at
different brine salinity, injection flow rate, particle size, and particle concentration on
injectivity changes were investigated.
127
4.3.1 Effect of brine salinity
Figure 4.24 presents the experimental data on the impact of brine salinity on the
RIC of sandstones which were initially saturated with different particle sizes. Up to
100,000 ppm NaCl, the RIC showed an increasing trend with increasing salinity. The
injection of scCO2 into sandstone saturated with freshwater (0 ppm) and without any
particle gave the lowest RIC value at only 5.3%. The most significant RIC value of
60.4% was observed in the experiment with the maximum salinity of 100,000 ppm and
a large particle size of 0.06 μm.
Figure 4.24 RIC measured as a function of salinity.
Moreover, the RIC increased about 28% for sandstone with no particle when the
brine salinity rose from 0 to 100,000 ppm. The increase in the permeability reduction
with increasing brine salinity content can be explained by the increasing amount of
precipitated salt as reported by several researchers [30, 160, 188]. On the other hand,
the maximum RIC increment with the presence of particles at zero brine salinity was
only about 14.6%. The higher increment of RIC increasing brine salinity indicates that
the influence of brine salinity is larger than the influence of the particles.
Furthermore, the presence of particles during the scCO2 injection has a strong effect
on the final permeability. The addition of particles has enhanced the pore plugging and
128
therefore increased permeability reduction over the whole salinity range explored. It
can be seen from the experiment that with 0.005 µm particle size the RIC increment is
slightly higher at about 1.3% at zero salinity and moderately increased to 2.6% at
100,000 ppm. The increment of RIC is noticeably higher when using larger particle
sizes. For instance, the experiment l using the 0.015 μm particle size shows that the RIC
value is 10.3% higher at 0 ppm, and the value is doubled at 100,000 ppm as compared
to the experiment with no particle.
These results suggest that there is a significant positive correlation between brine
salinity and injectivity impairment after the sandstone core samples are injected with
scCO2.
4.3.2 Effect of injection flow rate.
The results of RIC changes as a function of the scCO2 injection flow rates are
depicted in Figure 4.25. The presented experimental data also compares the influence
of salt and particle on the RIC with the change of injection flow rates from 2 cm3/min
to 10 cm3/min.
In view of the results obtained, all samples showed the RIC values rose between 2
cm3/min and 5 cm3/min but declined gradually as the flow rates increased to 10
cm3/min. In Figure 4.26, the maximum permeability reduction in each RIC trend line
can be observed when the scCO2 was injected at 5 cm3/min, which was equivalent to
2.19 cm/min. Taking the experiment with 30,000 ppm NaCl as an example, at 2
cm3/min, the RIC stood at 13.6% and then rose steadily to reach a high of 23.6% at 5
cm3/min. From 5 cm3/min, there was a small decrease to about 22.5% at 7 cm3/min of
RIC, and the number remained at 19% at the maximum injection flow rate.
Similarly, Sokama-Neuyam, et al. [17] observed an approximately 5% reduction
in permeability when they increased the scCO2 injection flow rate from 2 cm3/min (1.75
cm/min) to 5 cm3/min (2.15 cm/min). On the other hand, Jeddizahed and Rostami [188]
observed that the permeability kept increasing when the flow rate was increased to
above 5 cm3/cm. Although it may seem that there are discrepancies of data in the
129
literature, the results of this research support both phenomena. The results obtained
suggest that there exists a critical scCO2 injection flow rate. The migration of particles
in porous media is subjected to two main forces, hydrodynamic and electrostatic forces.
The electrostatic force attracts the particles to attach to the pore surface while the
hydrodynamic force removes the particle from the pore. At a lower injection flow rate,
it allows a stable progression of salt precipitation and fines particles to deposit at narrow
pore throat channels to cause permeability impairment. However, if there are any
changes in the forces acting in porous media, it would disrupt the growth of salt
precipitation and particle plugging. Since the hydrodynamic force increases with
injection flow rate, there should be a critical point at which these forces are sufficient
to overcome this equilibrium due to pressure distribution and flow reversal. This critical
point acts as a turning point of permeability reduction from increasing trend to lower
permeability reduction. Knowing the critical injection flow rate may benefit any CO2
sequestration project because the CO2 injection beyond this level would lead to lower
injectivity impairment.
Figure 4.25 RIC measured as a function of CO2 injection flow rate.
130
Moreover, the existence of salt and particle in the saturating fluid has a significant
impact on permeability reduction. Among all the samples, the calculated RIC for
sandstone saturated with freshwater was found to be the lowest. For sandstone saturated
with brine, the RIC was slightly higher with an average of 7.5%, mainly due to the
precipitation of salt that filled the pore spaces. The presence of particles in brine
strongly affected permeability reduction and therefore, gave the highest RIC values
over the range of injection flow rates explored. Evidence of the coupled effect of salt
precipitation and fines migration on CO2 injectivity changes is discussed in the next
section.
4.3.3 Effect of particle size
The effect of fines migration on the permeability change of sandstone during scCO2
injection can be analyzed further using particle size as shown in Figure 4.26. The
concentration of particles was kept constant at 0.3 wt%. Generally, it can be seen that
the percentage of permeability change appears to increase with increasing particle size,
rapidly at a low particle size and more slowly after particle size of 0.03 μm. Moreover,
the measured RIC increases significantly as the salinity gets higher.
Figure 4.26 RIC measured as a function of particle size.
131
As can be seen, the increasing trend of RIC with increasing particle size apparently
reflects the difference of pore plugging phenomenon due to the changing jamming ratio.
While moving through a pore network, the jamming ratio is an important parameter
determining whether particle entrapment or piping would occur. The addition of 0.005
μm particle would have minimal influence on permeability change because no plugging
or piping would occur at a jamming ratio below that 0.01. The permeability change at
this range was mainly influence by the damage created by salt precipitation as discussed
in Section 4.3.1.
Moreover, the surge of permeability reduction between 0.005 and 0.045 μm
particle size can be explained by the pore plugging occurrence caused by surface
deposition and multi-particle blocking when the ratio value is between 0.1 and 0.4. One
unanticipated finding was that the permeability reduction was almost constant when
using particle size larger than 0.045 μm. This result may be explained by the fact that
the increased in particle size at this range obstructed some particles to penetrate the
narrow pore throat of Berea sandstone at the inlet during the saturation process.
Therefore, the number of particles to flow through the core samples was limited which
restricted a further increase in permeability change.
Nevertheless, this finding is contrary to that of Sokama-Neuyam, et al. [17] who
found the permeability change to decrease by 24 percent on Berea sandstone (pore
throat size of 2 μm) when the particle size increased from 0.08 μm (jamming ratio of
0.04) to 0.14 μm (jamming ratio, 0.07). However, this possibly due to the use of alumina
latex in their study, which was oil-wet and decreases the chances of pore plugging in
the water-wet porous media of Berea sandstone.
4.3.4 Effect of particle concentration
The permeability change versus particle concentration for Berea sandstone
saturated with fresh water and 30,000 ppm NaCl is shown in Figure 4.27. The particle
concentration of 0.015 m silicon dioxide particles was varied from 0.1 to 0.7 wt percent.
132
While particle size to pore throat size is an important parameter, it is believed that
the concentration of the suspension could play an important role in plugging. This is
because as particle concentration increases, the distance between suspended particles
shortens, enhancing multi-particle blocking of the invaded pores [17]. The particle
concentration plays a more significant role when the jamming ratio is in the range of
0.01 and 0.1. At a higher jamming ratio, straining occurs, while at a much lower ratio,
there may even exist a critical particle concentration (CPC) beyond which plugging
may occur [105]. From Figure 4.27, it is shown that, the particle concentration affects
the RIC values differently. The percentage of RIC appears to increase with increasing
particle concentration until it reached a maximum value and thereafter decreased for
higher particle concentration. The maximum point was in between of 0.2 and 0.3 wt%.
Moreover, samples saturated with NaCl brine has greater permeability reduction over
the whole particle concentration range explored due to existence of salt precipitation.
Figure 4.27 RIC measured as a function of particle concentration.
133
4.4 CO2 injectivity change relationship due to salt precipitation and fines
migration
In this section, the performance of available theoretical models to calculate the CO2
injectivity changes of the experimental data is analysed. Then, the following subsection presents the development of the new model. Lastly, the efficacy of the new
model is evaluated statistically and graphically.
4.4.1 Analysis of existing model
The applicability of the KC-based model (Tang, et al. [88] and Zeidouni, et al. [92]),
the HP-based model (Pruess and Müller [182] and André, et al. [68]) and the power law
model to predict the CO2 injectivity changes in different experimental conditions were
discussed. The comparison was made based on different brine salinity, injection flow
rate, jamming ratio and particle concentration. The statistical parameters, such as
Average Absolute Percentage Error (AAPE), sum of the squares due to error (SSE), R2,
adjusted R-square and Root Mean Square (RMSE) were used and summarized in Table
4.4. The term “error” represents the difference between the predicted and the actual
values. The coefficient of determination, denoted as R2, is a measurement used to
explain how much variability of one factor can be caused by its relationship to another
related factor. This correlation, known as the "goodness of fit," is represented as a value
between 0.0 and 1.0. The higher the value of R2 the smaller the degree of scatter; thus,
the accuracy is higher. Moreover, low SSE and RMSE values, which are lower than
500 and 100 respectively, are desired to indicate a satisfactory prediction. The
deviations between the experimental and the predicted values are also analysed and
presented in comparison plots in the following paragraphs.
134
Table 4.4 Statistical parameter values for RIC data fitting using existing model
AAPE
Power law
Pruess and Muller (2009)
Andre (2014)
Tang (2015)
Zeidouni (2009)
0.713
0.820
0.987
0.462
0.697
Power law
Pruess and Muller (2009)
Andre (2014)
Tang (2015)
Zeidouni (2009)
0.553
0.543
0.547
0.849
0.915
Power law
Pruess and Muller (2009)
Andre (2014)
Tang (2015)
Zeidouni (2009)
0.454
0.444
0.438
0.819
0.898
Power law
Pruess and Muller (2009)
Andre (2014)
Tang (2015)
Zeidouni (2009)
0.452
0.437
0.430
0.816
0.888
R2
Brine salinity
10.886
0.931
7.799
0.935
9.357
0.935
0.769
0.934
0.252
0.934
Injection flow rate
37.119
0.397
39.740
0.377
48.546
0.376
3.592
0.381
1.143
0.383
Jamming ratio
4.707
0.772
4.610
0.769
5.610
0.769
0.425
0.770
0.136
0.770
Particle concentration
12.884
0.261
11.860
0.204
14.405
0.204
1.102
0.204
1.816
0.001
SSE
RMSE
5.018
5.670
6.782
10.736
12.849
13.497
12.908
12.343
17.677
18.702
17.832
17.188
16.404
23.515
24.844
13.962
13.255
12.187
21.313
22.651
A plot of the CO2 injectivity changes as a function of brine salinity predicted by the
existing models is shown in Figure 4.28. Overall, the KC-based models, the HP-based
models and the power law model show an increasing trend similar to the measured
experimental data. The statistical parameter, R2 is considerably high for all models, at
0.93. It signifies that the RIC estimation from the models is in agreement with the
measured experimental data. The fittings also give relatively low SSE and RMSE
values, which indicate good and satisfactory predictions. The KC-based models were
able to get better prediction values at zero salinity with average absolute percentage
135
error of less than 20%. However, the KC-based models underestimated the CO2
injectivity impairment at increasing brine salinity, with the maximum error up to 83%.
On the other hand, the HP-based models and the power law model show better
prediction values when the brine salinity is at 30,000 ppm and 100,000 ppm. Altogether,
it is apparent that the KC-based model is a better model when the brine salinity is below
6,000 ppm, and the HP-based model and the power law model are suggested to predict
the CO2 injectivity change when the salinity is above 30,000 ppm.
40.00
RIC (%)
30.00
20.00
10.00
0.00
0
25000
50000
Brine salinity (ppm)
75000
100000
Actual data
Zeidouni (2009)
Giorgis (2007)
Pruess and Muller (2009)
Andre (2014)
Power law
Figure 4.28 Comparison plot of the predicted RIC values against corresponding
experimental data for brine salinity range between 0 and 100,000 ppm.
Figure 4.29 shows the plots of the predicted RIC for the influence of the injection
flow rate on RIC as calculated using the existing prediction models. The results show
that all models predicted a decreasing trend of RIC when the injection flow rate was
increasing from 2 cm3/min to 10 cm3/min. There was a little difference between the
predicted values and the experimental data at the injection flow rate of 2 cm3/min. The
136
error percentages of the power law model, the André, et al. [68] model and the Pruess
and Müller [182] model are 5%, 22% and 10%, respectively. However, the models were
unable to predict the RIC trends correctly as the injection flow rate increased. This is
supported by the low R2 values calculated for all models, which is only about 0.38. This
implies a weak correlation between the predicted values from the existing models and
the measured experimental data. Moreover, the RIC values estimated by the KC-based
models were found to be lower than for the other models and with a high average error
percentage of 90%. The results suggest that all models are not reliable to predict the
CO2 injectivity changes at the changing injection flow rates.
RIC (%)
30.00
20.00
10.00
0.00
2
4
6
8
10
Injection flow rate (cm3/min)
Actual data
Giorgis (2007)
Andre (2014)
Zeidouni (2009)
Pruess and Muller (2009)
Power law
Figure 4.29 Comparison plot of the predicted RIC values against corresponding
experimental data for injection flow rate range between 2 and 10 cm3/min.
Figure 4.30 presents the variation of RIC versus the jamming ratio which were
calculated using different prediction models. As can be seen, both the André, et al. [68]
model and the Pruess and Müller [182] model together with the power law model were
able to give good estimated values when no particle was included in the experiment.
137
However, the calculated RIC values by the models failed to address the increasing trend
of the actual RIC values as the jamming ratio increased from 0 to 0.06. This is consistent
with the relatively low R2 calculated for all models. In fact, the models predicted
downtrend values of RIC over the whole particle size range explored. Additionally, no
obvious trend of the predicted RIC was seen for the KC-based models as the particle
size changed.
40.00
RIC (%)
30.00
20.00
10.00
0.00
0
0.01
0.02
0.03
Particle size (μm)
0.04
0.05
Actual data
Zeidouni (2009)
Giorgis (2007)
Pruess and Muller (2009)
Andre (2014)
Power law
0.06
Figure 4.30 Comparison plot of the predicted RIC values against corresponding
experimental data for different jamming ratio between 0 and 0.06.
The trends for the influence of particle concentration on RIC when the factors were
varied over different prediction models are shown in Figure 4.31. In general, the
predicted trend for the sandstone containing different particle concentrations is different
compared to the trends observed previously for the effect of brine salinity, injection
flow rate and particle size on RIC. The RIC values predicted by all the existing models
demonstrated no obvious trend with changing particle concentrations.
138
40.00
RIC (%)
30.00
20.00
10.00
0.00
0
0.1
Actual data
Giorgis (2007)
Andre (2014)
0.2
0.3
0.4
0.5
Particle concentration (wt%)
Zeidouni (2009)
Pruess and Muller (2009)
Power law
Figure 4.31 Comparison plot of the predicted RIC values against corresponding
experimental data for 0.015 μm particle size at increasing concentration from 0 to
0.5wt%.
The power law model was re-evaluated using different empirical n values by using
the trial-and-error approach to get the best-fitted values for each experimental
condition. The values of n are summarized in Table 4.5. The empirical value has a huge
range from -7.17 to -22.61, -18.67 to -91.51, -18.67 to -91.48 and -18.20 to -56.68 for
the effect of brine salinity, injection flow rate, jamming ratio and particle concentration,
respectively. The actual and predicted plot for the conditions are plotted in Figure 4.32
(effect of brine salinity), Figure 4.33 (effect of injection flow rate), Figure 4.34 (effect
of jamming ratio) and Figure 4.35 (effect of particle concentration). As expected, when
different values of n were used for each condition, they successfully predicted the actual
data of RIC.
139
Table 4.5 Different n values for power law at various experimental conditions
Brine salinity
(ppm)
0
6,000
30,000
100,000
Flow rate
(ml/min)
Jamming
ratio
Particle
concentration
(wt%)
2
-
-
5
7
10
30,000
2
0
0.005
0.015
0.06
0.011
0.3
0
0.1
0.3
0.5
Value of n
-7.171
-8.331
-18.67
-22.61
-18.67
-53.7
-80.03
-91.51
-18.67
-29.47
-68.3
-91.48
-18.2
-53.38
-42.3
-56.68
RIC (%)
40.00
30.00
20.00
10.00
0.00
0
25000
50000
Brine salinity (ppm)
Actual data
75000
100000
Power law
Figure 4.32 Actual and predicted value for the effect of brine salinity.
140
RIC (%)
30.00
20.00
10.00
0.00
2
4
6
8
10
Injection flow rate (cm3/min)
Actual data
Power law
Figure 4.33 Actual and predicted value for the effect of injection flow rate.
40.00
RIC (%)
30.00
20.00
10.00
0.00
0
0.01
0.02
0.03
Particle size (μm)
Actual data
0.04
0.05
Power law
Figure 4.34 Actual and predicted value for the effect of jamming ratio.
141
0.06
RIC (%)
40.00
30.00
20.00
10.00
0.00
0
0.1
0.2
0.3
Particle concentration (wt%)
Actual data
0.4
0.5
Power law
Figure 4.35 Actual and predicted value for the effect of particle concentration.
According to these results, the existing models show satisfactory predictions of RIC
at increasing brine salinity in sandstone core samples. However, at changing injection
flow rates and the presence of fines particles, the predicted results by all models were
not encouraging. The models were incapable of predicting trends similar to the
experimental data when the injection flow rate, jamming ratio and particle
concentration increased in the range explored. It can, therefore, be assumed that the
existing models are limited to predicting the CO2 injectivity impairment by salt
precipitation alone.
Additionally, the re-evaluated power law model gave the best-predicted value when
different n values were used for each experimental condition. However, this situation
is not practical since each value is only applicable to predict a specific experimental
condition. Therefore, in the conditions where various salt and fines particles are present
in the system, it would be tedious to use the power law model since it needs to be tuned
according to a specific condition before it can produce a reliable prediction. Therefore,
further work, which takes all variables including brine salinity, injection flow rate,
jamming ratio and particle concentration into account, will need to be taken.
142
4.4.2 Evaluation of regression model using the machine learning approach
The regression model, based on the machine learning approach was used to make
a forecast of RIC by estimating the relationship between four experimental parameters:
brine salinity, injection flow rate, jamming ratio and particle concentration. The best
model was selected based on statistical value from Microsoft Azure and further
optimized using Google Colab notebook.
4.4.2.1 Screening of regression machine learning models
Microsoft Azure was used to screen suitable regression methods for predicting
CO2 injectivity changes based on the experimental data. Two linear- based regressions,
namely linear regression (LR) and neural network regression (NN) and two types of
decision-based regressions, which were the decision- forest regression (DF) and the
boosted decision- tree regression (BDT), were trained and compared in order to
determine the most accurate regression method for CO2 injectivity change prediction.
The data of 80 core flooding experiments were splitted into 80:20 ratios for
training and validation of the regression methods. The Train module was used to train
the model; followed by the Score module to make predictions on the validation data
set. Lastly, based on the prediction on the validation data set, the Evaluate module was
used to compute the regression performance for different models.
The software used RMSE and R2 as significant performance indexes to calculate
the precision of the predicted values from each regression method. The best regression
method was achieved with the highest R2 but the lowest RMSE, which predicted data,
was close to the experimental data. Table 4.6 presents the R2 and RMSE values
calculated according to the regression methods. The results indicate that NN produces
the highest R2 value of 0.969 with the lowest RMSE of only 5.83, which suggest that it
would give the highest accuracy of forecast data as compared to other regression
methods.
143
Table 4.6 Summary of R2 and RMSE for all regression methods in screening stage
using Microsoft Azure.
Regression method
RMSE
R2
Linear
17.10
0.738
Neural network
5.83
0.969
Decision forest
18.30
0.700
Boosted decision tree
9.92
0.912
4.4.2.2 Optimization of neural network model
After confirming the best regression method to be used, the reliability and
accuracy of the NN model needed to be verified. The general performance of a neural
NN model is highly dependent on the computational complexity and is indicated by the
precision and robustness of the predicted data. Apart from that, the convergence and
speed of the computational time is also a notable concern when dealing with NN model.
As such, in order to produce a high-performing neural network algorithm, thorough and
critical optimization of the model framework is required. Specifically, the neural
network model operates on a flexible combination of “hyperparameters” that defines
how the algorithm adapts to the input data. For optimization purpose, the
hyperparameter tuning is done for the size of the hidden layers, Alpha, momentum, and
initial learning rate. The accuracy of each hyperparameter is determined based on
highest R2 value.
Figure 4.36 displays the sensitivity analysis to obtain the optimal hidden layer
size and number of neurons for the neural network model. This plot analyses the
different R2 values obtained from different hidden layer arrangements with an
increasing number of neurons and an increasing number of layers going from left to
right. It is apparent from this plot that three hidden layers, with sizes of 5 to 6 neurons
each, yield the highest R Square value of around 0.988. This result agrees with the
general rule of thumb of hidden layer size selection, which states that the number of
hidden layer neurons should be 70 to 90% of the summation of input and output layer
144
neurons [192]. For this analysis, an input of four injection parameters and one
permeability change value (a total of 5 neurons) suits the approximated three hidden
layers. The number of hidden layer neurons should be less than twice the number of
neurons in the input layer. This suggests that around 6 or 7 neurons in each layer, which
is slightly lower to twice of the four input parameters, is a good approximation for our
analysis. Overall, taking both the sensitivity analysis and the general rule of thumb into
consideration, the hidden layer (6, 6, 6) is chosen, which is a three-layered neuron
system containing six neurons each.
1
Accuracy (R2)
0.98
0.96
0.94
0.92
(2,)
(5,)
(5, 5,)
(5, 5, 5,)
(6, 6, 6,)
(7, 6, 5,)
(7, 7, 6,)
Number of neurons in ith hidden layer
Figure 4.36 Number of hidden layers and neurons versus accuracy of R2 values.
Moreover, the testing of for alpha parameters ranging from 1E-2 to 8E-2 versus R2
values is shown in Figure 4.37. Alpha parameter can be described as the model’s
learning rate at where the model “learns” from its previous iteration and adds specific
weighting to converge its value. It ranges from 0 to 1, where when it is close to 0, the
neural net will engage in more conservative weight modifications, and when it is close
to 1, it will make more radical weight modifications. It is apparent that there is a
minimal variance of ±0.0001 in the R Square performance within the given alpha
145
values. Furthermore, there is an obvious peak at the alpha value of 7.75E-2, beyond
which a decreasing trend is observed, and thus, it is chosen as the optimal value.
0.9886
Accuracy (R2)
0.9885
0.9884
0.9883
0.9882
0.9881
0.9880
0.00E+00
2.00E-02
4.00E-02
6.00E-02
Alpha parameter
8.00E-02
Figure 4.37 Alpha parameter versus accuracy of R2 values.
The effect of changing initial learning rate parameter on R2 values is depicted in Figure
4.38. Generally, there is a sudden increase in R2 performance stemming from the initial
learning rate of 0.0001 up to 0.001 before it starts to gradually decrease until 0.003.
This controls the starting value at which the model takes the weighting of the input
parameters into consideration throughout the neural network algorithm. Neural network
models can drastically vary in performance by deciding on a small or large initial
learning rate value [193]. Although a small initial learning rate allows for faster training
and better test performance initially, the large learning rate achieves better
generalization soon after the learning rate is annealed. This is dependent on the
difficulty of generalizing the input parameters and fitting patterns. For this specific
project, the highest performing initial learning rate of 0.001 is decided to be utilized in
the neural network model.
146
1.000
0.980
Accuracy (R2)
0.960
0.940
0.920
0.900
0.880
0.860
0
0.0005
0.001
0.0015
0.002
Initial learning rate
0.0025
0.003
Figure 4.38 Initial learning rate versus accuracy of R2 values.
The last hyperparameter that was analyzed is the momentum. Momentum controls
how much the previous update influences the current weighting update. The effect of
changing the momentum value on R2 is presented in Figure 4.39. Based on the graph,
the momentum, which is also a parameter that ranges from 0 to 1, shows a clear trend
of increasing fitting in the R Square value up to a value of 0.9. This seems to be the
optimal momentum at which the neural network model operates, as a further increase
in momentum seems to yield a decrease in performance.
The sensitivity analysis on the hidden layer size, alpha parameter, initial learning
rate, and momentum provides great guidance towards the optimal hyperparameter
settings for the neural network model based on the input datasets that are being
analyzed. Following the hyperparameters tuning process of the neural network model,
the model is then statistically assessed with the same datasets as for the Microsoft Azure
model. As anticipated, there is a significant increase in the R2 value as compared to the
original NN model given by Microsoft Azure, where a striking value of 0.9882 and 3.83
for RMSE is recorded. This is a great indicator that the model is able to fit the data with
minimal variance to the actual value.
147
1.00
0.98
Accuracy (R2)
0.96
0.94
0.92
0.90
0.88
0.86
0.8
0.82
0.84
0.86
0.88
0.9
Momentum
0.92
0.94
0.96
Figure 4.39 Momentum versus accuracy of R2 values.
4.4.2.3 Validation of neural network model
The comparison plot of the validation data set and the prediction results from the
NN model are shown in Figure 4.40. The results show that all the points are very close
to the diagonal line. The statistical parameter, which is R2 and the adjusted R2 for the
validated data, is very high at 0.995 and 0.994. The calculated error is also quite low,
for example the AAPE and RMSE are only 0.103 and 1.888, respectively. This indicates
that the selected NN model is in agreement with the results produced by the
experimental work. In addition, the considerably low SSE value also indicates good
prediction by the NN regression model. Summary of the statistical parameters between
the experimental and the predicted data using the NN model for validation purpose is
presented in Table 4.7.
148
100
Prediction data (RIC %)
80
60
40
R2 = 0.995
AAPE = 0.103
20
0
0
20
40
60
Actual data (RIC%)
80
100
Figure 4.40 Validation of actual experimental data against corresponding predicted
data using NN regression model.
Table 4.7 Goodness of fitting for the NN Regression Model to predict the 20% excess
experimental data.
Goodness of fit
Values
AAPE
0.103
SSE
22.503
R2
0.995
Adjusted R2
0.994
RMSE
1.888
149
4.4.2.4 Evaluation of effects of CO2-brine-rock parameters on CO2 injectivity
changes, using the NN model
The deviations between the experimental and the predicted values using the NN
model for each CO2 (injection flow rate), brine (salinity), rock and fines migration
(jamming ratio and particle concentration) parameters are presented in Figure 4.41,
Figure 4.42, Figure 4.43, and Figure 4.44. Generally, the percentage error analysis
suggests that the NN model is reliable in predicting the CO2 injectivity changes
represented by RIC values. This is indicated by the relatively low absolute percentage
error of 18.2%. However, the low absolute percentage error is not seen at the lower
range of experimental parameters for sandstone rock saturated with lower brine salinity
and small fines particles.
As shown in Figure 4.41, the high absolute percentage error above 20% is
apparent for the predicted RIC for sandstone saturated with brine salinity lower than
6,000 ppm and particles of below than 0.005 μm. Similar patterns are also observed in
Figure 4.42, Figure 4.43 and Figure 4.44. Moreover, for all the brine salinity, injection
flow rate, particle size and particle concentration parameters, the absolute percentage
errors decrease with increasing parameter values. Based on these findings, it therefore,
can be suggested that the NN model provides better prediction for sandstone saturated
with NaCl brine and fines particles, particularly at the higher range of the experimental
parameters explored.
150
Absolute Percentage Error (%)
80
60
40
20
0
0
25000
50000
Brine salinity (ppm)
No particle
0.005
0.015
75000
100000
0.06
Figure 4.41 Absolute percentage error between the measured and calculated RIC at
increasing brine salinity using the NN model.
Absolute Percentage Error (%)
80
60
40
20
0
0
2
Fresh water
4
6
Injection flow rates (cm3/min)
30,000 ppm NaCl
8
10
30,000 ppm NaCl + 0.3 wt% 0.015 μm
Figure 4.42 Absolute percentage error between the measured and calculated RIC at
injection flow rate from 2 cm3/min to 10 cm3/min using the NN model.
151
Absolute Percentage Error (%)
80
60
40
20
0
0.00
0.01
No particle
0.02
0.03
Particle size (μm)
6,000 ppm NaCl
0.04
30,000 ppm NaCl
0.05
0.06
100,000 ppm NaCl
Figure 4.43 Absolute percentage error between the measured and calculated RIC at
various particle sizes using the NN model.
Absolute Percentage Error (%)
60
40
20
0
0
0.1
0.2
0.3
Particle size (μm)
Fresh water + 0.3 wt% 0.015 μm
0.4
0.5
30,000 ppm NaCl + 0.3 wt% 0.015 μm
Figure 4.44 Absolute percentage error between the measured and calculated RIC by the
NN model using 0.015 μm at different particle concentrations.
152
Figure 4.45 shows the weightage results for the effect of brine salinity, injection
flow rate, particle size (jamming ratio) and particle concentration on RIC using the NN
model. The results show that the most influential factor, by far, is jamming ratio
followed by brine salinity. This result can be explained by the substantial increase in
permeability reduction due to pore plugging as the jamming ratio increases.
Additionally, a significant growth of salt precipitation to reduce the pore spaces appears
to have brought an increase in brine salinity. This also accords with our experimental
observations, which showed that a steady rise in CO2 injectivity reduction when brine
salinity increases from zero to 100,000 ppm changes particle size between 0 to 0.06
μm.
Figure 4.45 Weightage of experimental parameters on RIC response evaluated using
the NN model.
4.4.3 Evaluation of the RSM model
4.4.3.1 Training and validation of the RSM model
This section presents the development of an empirical model based on the RSM
approach. The RIC results from all core -flooding experiments were statistically
evaluated to identify the influence of experimental parameters on the final CO2
injectivity changes represented by RIC. The ANOVA fitted the experimental results
into the mathematical model that could be used to predict the desired response to the
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identified parameters. Table 4.8 shows the fit summary of the available models
evaluated by ANOVA to obtain the model that best describes the desired RIC response
efficiently and satisfactorily.
Table 4.8 Evaluated models for responses on RIC by Design Expert software.
Evaluated
Sequential
Lack of fit
Std.
Adj.
Pred.
models
p-value
p-value
dev.
R2
R2
Linear
<0.0001
0.1111
7.05
0.913
0.901
0.885
2FI
<0.0001
0.251
4.48
0.972
0.960
0.922
Quadratic
<0.0001
0.7525
2.09
0.994
0.994
0.981 Suggested
Cubic
0.1268
0.9772
1.51
0.999
0.995
R2
0
Remarks
Aliased
According to the results obtained, a quadratic model is suggested to best fit the
results of the RIC changes. This is because the quadratic model gives the best
combination of R2, adjusted R2, and predicted R2. As criteria for the model suggestion
by the analysis, the second order (quadratic) polynomial equation of RSM can be
expressed as the general form:
𝑛
𝑛
𝑛
𝑛
𝑌 = 𝛽0 + ∑ 𝛽𝑖 𝑥𝑖 + ∑ 𝛽𝑖𝑖 𝑥𝑖2 + ∑ ∑ 𝛽𝑖𝑗 𝑥𝑖𝑗 + 𝑒
𝑖=1
𝑖=1
𝑖=1 𝑗=1
(4.16)
where 𝑌 is the modelled response, 𝛽 is the regression coefficient, 𝑥 is the
independent variable, and 𝑒 is the error. 𝛽0 is a constant value while 𝛽𝑖 𝑥𝑖 and
𝛽𝑖𝑖 𝑥𝑖2 represent linear terms (first-order effects of variables) and quadratic terms
(second-order effects of variables), respectively, and 𝛽𝑖𝑗 𝑥𝑖𝑗 is a two-factor interaction
term. This equation does not take the interaction between three or more factors into
account. The equation may also be simplified to a linear equation by setting 𝛽𝑖 and 𝛽𝑖𝑖
as zero. On top of that, a two-factor interaction (2FI) model can be derived from the
model by setting 𝛽𝑖𝑖 as zero.
The equation for RIC as a function of brine salinity, injection flow rate, jamming
ratio, and particle concentration is expressed as:
154
RIC = -5.65819 + 0.000221A + 6.36012B + 1530.876C - 7.16972D + (4.17)
0.005932AC + 0.00042AD+ 48.20917BC - 4.14148BD 0.45311B2 - 28133.6C2
where 𝐴, 𝐵, 𝐶 and 𝐷 represent brine salinity, injection flow rate, jamming ratio and
particle concentration respectively. The results of ANOVA are presented in Table 4.9.
The integration between model suggestion and adequacy check of the model needs to
be carried out properly to Figure 4.46 which shows the diagnostic plot of the predicted
versus the actual experimental values for the RIC changes. The results points’ position
determines the "goodness of fit". The points lying above the diagonal line indicate that
the value is overestimated whereas the points below the diagonal line indicate an
underestimated value. As can be seen, all points are distributed along the diagonal line.
This suggests that the obtained equation can make a satisfactory estimate of the
predicted value and can be used in predicting the RIC change after the CO2 exposure.
Table 4.9 ANOVA results of quadratic model for RIC response.
Source
Sum of
squares
df
Mean
square
F-Value
p-value
Prob > F
Model
17021.68
14
1215.83
279.60
<0.0001
A-Brine salinity
2803.58
1
2803.58
644.72
<0.0001
B-Injection flow
rate
92.50
1
92.50
21.27
0.0002
C-Jamming ratio
1691.50
1
1691.50
388.98
<0.0001
D-Particle
concentration
44.84
1
44.84
10.31
0.0044
AC
276.22
1
276.22
63.52
<0.0001
AD
201.46
1
201.46
46.33
<0.0001
BC
83.91
1
83.91
19.30
0.0003
BD
36.42
1
36.42
8.37
0.0090
B2
249.22
1
249.22
57.31
<0.0001
C2
88.05
1
88.05
20.25
0.0002
155
significant
Residual
86.97
20
4.35
Lack of fit
74.47
18
4.14
Pure error
12.50
2
6.25
Cor total
17108.65
34
0.66
0.7525
Not
significant
Figure 4.46 Predicted RIC versus experimental data.
As shown in Table 4.8, the R2 of the suggested quadratic model is 0.9939. The value
of R2 states that 99.39% of the total RIC variation is ascribed to the studied variables
(i.e. not due to noise or unattended variables) and verified by the adopted model. In
other words, the suggested model can provide a satisfactory fit when correlating the
response and the independent variables.
156
Moreover, the efficacy of the model can be explained by using the adjusted R2 and
the predicted R2. Generally, the value of R2 tends to be higher when a new term is
introduced, whereas a slight effect can be seen on the adjusted R2. The adjusted R2 is
normally compared to the predicted R2 by calculating the difference between both
values. The value of the adjusted R2 and the predicted R2 is accepted if the difference
is less than 0.2. Based on Table 4.8, the adjusted R2 value of 0.9937 is in reasonable
agreement with the predicted R2 of 0.9814. The calculated standard deviation of the
model is 2.15, which implies that the experimental values of RIC are close enough to
the predicted RIC values.
Other statistical parameters used to evaluate the model are adequate precision, pvalue and F-value. The adequate precision compares the range of the predicted value at
the design points, and the ratio of more than 4 is anticipated for an adequate signal. The
calculated value is 73.602, which implies that the predicted model has an excellent
ability to navigate the design space designed by RSM. The overall p-value and the Fvalue of the new model are less than 0.0001 and 279.6 respectively, pointing out that
the new model is significant. The p-value and the F-value also determine the relevancy
of the factor to be included in the model. Any factor with a p-value higher than 0.05 is
considered as not significant and can be removed from the model. In Table 4.9, all
factors are at the 95% confidence interval because their p-values are less than 0.05.
Those factors with high p-values of above 0.05 (AB, CD, A2 and D2) have been
excluded from the model.
Furthermore, the lack of a fit test is used to determine the reliability of the model to
predict the response. By using this test, one can verify if the systematic or the random
error is responsible for the deviation of the expected values from the measured ones.
The significant lack of fit means that the variation of the replicates about their mean
values is less than the variation of the design points about their predicted values. A
small F-value and a high p-value (greater than 0.1) are good in this type of test. As
shown in Table 4.6, the lack of fit of the F-value is 0.66 and the lack of fit of the pvalue can be calculated by dividing the lack of the fit mean square (4.14) by the pure
error mean square (6.25) to yield 0.7525. These values imply that the lack of fit is
157
insignificant for this new equation, which means that the model can be used to represent
the RIC prediction. Therefore, as indicated by the statistical parameters and the
graphical analysis, the newly developed RSM model is able to capture the precise
correlation between four input variables and RIC changes.
Lastly, the new model was then validated using 20% of the unseen data from the
experiment. The scattered plot of the actual data against the predicted data is shown in
Figure 4.47 and the statistical parameters between both data are presented in Table 4.10.
The obtained model gives high R2 and adjusted R2 values of 0.985 and 0.983
respectively. Moreover, the calculated errors of AAPE, SSE and RMSE are
considerably low at 0.116, 80.798 and 8.157 respectively. From these statistical values,
the high value of R2 and adjusted R2 together with low errors validate the quadratic
model as appropriate and satisfactorily fit to the variability of the response produced by
the experimental data.
100
Prediction data (RIC %)
80
60
40
R2 = 0.985
AAPE = 0.116
20
0
0
20
40
60
Actual data (RIC%)
80
100
Figure 4.47 Validation of the RSM model using 20% excess experimental data showing
high accuracy of the model with R–square of 0.985.
158
Table 4.10 Goodness of fitting for the RSM model to predict the 20% excess
experimental data
Goodness of fit
Values
AAPE
0.116
SSE
80.798
R2
0.985
Adjusted R2
0.983
RMSE
8.157
4.4.3.2 Evaluation of effects of CO2-brine-rock parameters on CO2 injectivity
changes, using the RSM model
Looking into the statistical results for each CO2 (injection flow rate), brine
(salinity), rock and fines migration (jamming ratio and particle concentration)
parameters, the RSM model could predict the RIC of the changing parameters
accurately. The deviations between the experimental data and the predicted values
using the RSM model for different experimental parameters are shown in Figure 4.48,
Figure 4.49, Figure 4.50, and Figure 4.51. It is apparent that in most cases, the
percentage error is at a relatively low range, which is less than 20%. However, higher
percentage errors were found when the RSM model tried to predict the lower value of
the actual RIC. This is anticipated for small values (typically less than 10) because a
slight deviation of either a negative or a positive value would give to 10% of the
maximum of 50% in error percentages.
Interestingly, the percentage error strongly suggests that the RSM model is more
accurate in predicting the RIC when there is salt precipitation and fines particles in the
system. It can be seen the percentage errors for all samples saturated with NaCl brine
are lower than 15% with an average of about 5.6%. The prediction values were found
to be more accurate as the value of the experimental parameters increased. On the other
hand, as shown in Figures 4.48 - 4.51, the percentage error of above 20% is only
159
observed for sandstone samples saturated with fresh water. Hence, salt precipitation is
not likely to occur because of no salt content in the fluid system.
Furthermore, ANOVA results for the response (RIC) in Table 4.9 highlight that all
four parameters are affecting the injectivity change of the sandstone after being injected
with CO2. Moreover, two individual parameters (brine salinity and jamming ratio) and
two two-factor interactions (brine salinity-jamming ratio and brine salinity-particle
concentration) are found to be significant variables for injectivity change. All these
terms have positive (synergistic) signs in the adopted model. In other words, all these
terms have a favorable influence on contributing to permeability impairment.
Absolute Percentage Error (%)
30
20
10
0
0
25000
50000
Brine salinity (ppm)
No particle
0.005
0.015
75000
100000
0.06
Figure 4.48 Absolute percentage error between the measured and calculated RIC at
increasing brine salinity using RSM model.
160
Absolute Percentage Error (%)
30
20
10
0
0
2
Fresh water
4
6
Injection flow rates (cm3/min)
30,000 ppm NaCl
8
10
30,000 ppm NaCl + 0.3 wt% 0.015 μm
Figure 4.49 Absolute percentage error between the measured and calculated RIC at
injection flow rate from 2 cm3/min to 10 cm3/min using the RSM model.
Absolute Percentage Error (%)
30
20
10
0
0.00
0.01
No particle
0.02
0.03
Particle size (μm)
6,000 ppm NaCl
0.04
30,000 ppm NaCl
0.05
0.06
100,000 ppm NaCl
Figure 4.50 Absolute percentage error between the measured and calculated RIC at
various particle sizes using the RSM model.
161
60
Absolute Percentage Error (%)
50
40
30
20
10
0
0
0.1
0.2
0.3
Particle concentration (wt%)
Freash water + 0.3 wt% 0.015 μm
0.4
0.5
30,000 ppm NaCl + 0.3 wt% 0.015 μm
Figure 4.51 Absolute percentage error between the measured and calculated RIC by the
RSM model using 0.015 μm at different particle concentrations.
A review of the F-values of the model terms, which are shown in Table 4.9,
indicates that brine salinity and jamming ratio (with F-values of 644.72 and 388.98
respectively) have the highest effects on injectivity impairment. The injection flow rate
and particle concentration are less dominant compared to brine salinity and the jamming
ratio, but their effects are still considerable and almost equivalent to the two-factor
interactions and squared parameters. Furthermore, the brine salinity-jamming ratio, the
brine salinity-particle concentration, and the jamming flow rate-jamming ratio
interactions, and squared parameters of injection flow rate and jamming ratio have
moderate effects while others give fewer effects on RIC response.
Figure 4.52 which shows the contour response plots, indicates the relationship of
RIC as a function of four experimental parameters. The calculated RIC value is crucial
because a lower RIC is desired to allow a large and lasting injection of CO2 for
sequestration over a long period of time [194]. It is apparent from Figure 4.52a that RIC
decreases with the decrease in brine salinity and the jamming ratio so that the lowest
RIC value is related to the lowest examined point for both variables. For example, when
162
the brine salinity and jamming ratio were less than 40,000 ppm and 0.00056
respectively, a low RIC value was achieved. In accordance with the present results, our
experimental findings and previous studies demonstrate that higher brine salinity
would give rise to a higher amount of salt precipitate, which reduces the pore spaces
[125, 145].
Figure 4.52 3D response surface plot of RIC: a) effects of brine salinity and jamming
ratio; b) effects of brine salinity and particle concentration; c) effects of injection flow
rate and jamming ratio; d) effects of particle concentration and injection flow rate.
Moreover, at a high jamming ratio, the moving particles are highly susceptible to
get trapped while moving through narrow pore throat [37, 195]. Thus, a dramatic
reduction in the final permeability is expected due to the plugging of the flow path by
a higher amount of salt precipitation and fines particle migration. Moreover, a closer
163
inspection of Figure 4.52a and Figure 4.52b shows that the brine salinity of 70,000 ppm
is a critical boundary before significant permeability damage occurs due to the high
RIC value (above 70).
Furthermore, as shown in Figure 4.52c, the RIC was found to be very low (less than
25) when the jamming ratio was almost zero and the injection flow rate increased from
2 to 4 cm3/min and decreased from 8 to 10 cm3/min. This also accords with our earlier
observations, which showed that there was a critical zone that exists as the turning point
of permeability reduction from an increasing trend to a lower permeability reduction.
Lastly, the RIC trends are less sensitive when the particle concentration and the
injection flow rate change as depicted in Figure 4.52d.
4.4.4 Testing of new CO2 injectivity models
Model testing is an essential part of the model development process to know the
capability of the newly developed relationship to assess the real practical need. This
section presents the performance of the NN regression model and the RSM model after
being tested with the actual data from experimental data and published case studies.
4.4.4.1 Trend analysis of NN and RSM models
The trend analysis for all four experimental variables, brine salinity, injection flow
rate, particle size and particle concentration were performed. The trend analysis is used
to confirm the prediction model is align with the physical behavior between the input
and output variables of the model. Figure 4.53 shows the trend of brine salinity
predicted by NN model and RSM model as compared to the actual data. Both models
predicted increasing RIC values as the brine salinity increases. The results obtained
agreed with the experimental data and previous studies [125, 182].
164
50
RIC (%)
40
30
20
10
0
0
20000
40000
60000
Brine salinity (ppm)
Experiment
RSM
80000
100000
NN
Figure 4.53 Brine salinity trend analysis of the NN model and RSM model.
The effect of injection flow rate on RIC for the NN model, RSM model and actual
data is shown in Figure 4.54. From the figure, increasing the injection flow rate
increases the RIC to an optimum value. At lower injection flow rate, the electrostatic
force is more dominant which cause a stable progression of salt precipitation. However,
increasing the injection flow rate to more than its optimum value decreases the RIC.
Since the hydrodynamic force increases with injection flow rate, there should be a
critical point at which these forces are sufficient to overcome this equilibrium due to
pressure distribution and flow reversal. This is in consistent with our experimental data
in section 4.3.2.
Moreover, Figure 4.55 presents the particle size trend analysis of the NN model and
RSM model. As can be seen, the RIC value increases with increasing particle size. The
predicted values by RSM and NN models almost fitted with the actual data. Large
particle size can be easily trapped within the narrow pore channel as compared to
smaller particle size due to jamming ratio. As stated by past researchers [37], different
value of jamming ratio would cause different types of pore plugging mechanisms such
as piping, multi-particle deposition, bridging and particle exclusion.
165
40
RIC (%)
30
20
10
0
2
3
4
5
6
7
8
3
Injection flow rate (cm /min)
Experiment
RSM
NN
9
10
Figure 4.54 Injection flow rate trend analysis of the NN model and RSM model.
40
RIC (%)
30
20
10
0
0
0.01
0.02
0.03
Particle size (μm)
Experiment
RSM
0.04
0.05
NN
Figure 4.55 Particle size trend analysis of the NN model and RSM model.
166
40
RIC (%)
30
20
10
0
0
0.1
0.2
0.3
0.4
0.5
Particle concentration (wt%)
Experiment
RSM
NN
0.6
0.7
Figure 4.56 Particle concentration trend analysis of the NN model and RSM model.
Lastly, the trend for the increasing particle concentration to the RIC values is
depicted in Figure 4.56. From the graph, the RIC values increased with increase in
particle concentration and levelled off at around 0.4 wt%. The predicted values by RSM
and NN models were also shown to follow similar trend by the actual experimental
data.
To summarize the trend analysis, all the experimental variables (brine salinity,
injection flow rate, particle size and particle concentration) of the developed RSM and
NN models can follow the correct trends, indicating the models reliability.
4.4.4.2 Comparison between NN and RSM models
The comparison of the NN and the RSM for the training and validation is shown in
Table 4.11. The criteria used for measuring the model performance were the R2,
adjusted R2, AAPE, RMSE and SSE. In view of the results obtained, both models gave
excellent statistical values to be considered as good prediction models.
167
For training data set, the R2 and the adjusted-R2 were 0.994 for both the NN model
and the RSM model. Hence, it is apparent that NN gives slightly better accuracy when
predicting the training data set. This is also supported by the lower AAPE, SSE and
RMSE values for the RSM model which were 0.053, 95.371 and 1.783 respectively.
Moreover, the NN model also gives better accuracy when using the validation data set.
As can be seen, the NN model has a lower value of AAPE, SSE and RMSE than the
RSM model. The R2 and the adjusted-R2 were 0.999 for the NN model which were
higher than the RSM model when forecasting the validation data set. The high R2 values
and the low SSE and RMSE values indicate a good and satisfactory prediction. The
validation results also show that the AAPE value is very small, less than 1%, suggesting
that the predicted value is very close to the real value. Based on the statistical
calculation and the values of the statistical parameters, the NN model provides an
excellent ability to describe the CO2 injectivity changes as a function of brine salinity,
injection flow rate, particle size and particle concentration.
Table 4.11 Comparison between NN model and RSM model.
Neural Network model
RSM model
Training
Validation
Training
Validation
AAPE
0.053
0.005
0.059
0.030
SSE
95.371
2.535
104.504
80.797
RMSE
1.783
0.281
1.730
1.799
R2
0.995
0.999
0.994
0.985
Adjusted R2
0.994
0.999
0.994
0.983
4.4.4.3 Testing the models using actual data from published works
Experimental data from five different case studies were used to evaluate the
effectiveness of the newly developed regression model. A summary of the case studies
is presented in Table 4.11. The case studies were selected because of a similar type of
CO2 injection scheme, rock sample (sandstone), brine properties, availability of the
jamming ratio, and permeability change values.
168
Table 4.12 Summary of data used for model testing.
Reference
Edem, et
al. [125]
Othman, et
al. [18]
SokamaNeuyam et
al. (2017)
SokamaNeuyam,
et al. [17]
Rock type
Grey Berea
sandstone
K = 294 mD
Φ = 19-20 %
D = 1 in
L = 3 in
Berea
sandstone
K = 67 mD
Φ = 20 %
D = 0.98 in
L = 1.97 in
Kipton Berea
sandstone
K = 90-120
mD
Φ = 17-19 %
D = 1.5 in
L = 7.87 in
Berea
sandstone
K = 209-219
mD
Φ = 18-20 %
D = 1.5 in
L = 7.87 in
Brine
Particle properties
Injection
Pressure/
type
flow rate
Temperature
5000,
15000,
250000
ppm
NaCl
Not used
1, 1.5, 2,
2.5, 3
cm3/min
6.9 Mpa
45°C
60000
ppm
NaCl
Not used
2.5
cm3/min
10 Mpa
50°C
105500
ppm
NaCl
with
other
salts
Fumed alumina
latex
− 0.08 μm
− 0.04, 0.07
jamming ratio
− 0.3, 0.5, 1wt%
0.25, 0.5,
1.0
cm3/min
8 Mpa
50°C
105500
ppm
NaCl
with
other
salts
Fumed alumina
latex
− 0.08, 0.14 μm
− 0.04, 0.07
jamming ratio
− 0.3, 0.5, 1wt%
2, 5, 10
cm3/min
8 Mpa
50°C
The NN and the RSM models were used to predict the CO2 injectivity change of
the sandstone rock at different experimental conditions which was reported by previous
researchers. The input parameters, brine salinity, CO2 injection flow rate, jamming
ratio, and particle concentration of these experiments were used to calculate the RIC
value. The results were compared with the reported permeability change value
(converted to RIC), and the differences were analyzed statistically. The accuracy of the
model can be checked statistically using R2, adjusted-R2, AAPE, RMSE, SSE and the
169
regression line between the RIC values from published works and the predicted RIC by
both models.
The actual data from published works which were fitted into the NN model and the
RSM model are shown in Figure 4.57. The statistical parameters of the regression line,
which are the AAPE, SSE, RMSE, R2 and adjusted R-square, are given in Table 4.13.
Figure 4.57 Predicted RIC versus reported data from the literature for the NN model
and the RSM model.
As can be seen, most of the points are located on the midline, which indicates that
there is good agreement between model prediction and the actual data. The obtained R2
was 0.969 with the AAPE 0.099% for the NN model, while for the RSM model the R2
was 0.965 with the AAPE value of 0.098%. The adjusted R2 for the NN model and the
RSM model were found to be 0.969 and 0.965 respectively. The R2 and the adjusted R2
values are approximately close to 1, which indicate the fittings are extremely accurate.
Moreover, the low AAPE values imply that the model predicted values co-relate well
with the actual data. The NN model reported SSE of 490.658, below the threshold of
170
500 which indicates the predicted value using the NN model is consistent with the actual
value. The calculated RMSE values for both models are far lower than 100. Therefore,
these values denote good and satisfactory predictions.
Table 4.13 Statistical data of the NN Model and the RSM Model to predict the
reported data from published literature
Neural Network model
RSM model
AAPE
0.099
0.098
SSE
490.658
599.190
RMSE
5.856
5.730
R2
0.971
0.967
Adjusted R2
0.969
0.965
The predicted RIC using the NN and the RSM models versus all training, validation
and testing samples are also plotted in Figure 4.58 to help highlight the efficiency of
the models. As can be seen, the NN model tried to avoid overfitting when predicting
the lower RIC values (less than 20%) and high RIC values of above 80%. This
apparently reflects the slightly higher prediction accuracy by the NN model, for all data
sets, because it allows the NN model to adapt the introduction of new data without
depending too much on the range of training data parameters. In monitoring the testing
data set, both the RSM and NN models failed to predict the higher RIC values of above
80%. This can be explained by the heavier salt precipitation due the existence of KCl
and other salt types in the brine composition used to saturate their sandstone core
samples. This is consistent with our earlier findings on the effect of KCl brine types on
CO2 injectivity changes in Sections 4.1.3.3 and 4.2.6.
171
Figure 4.58 Predicted RIC using the NN and the RSM models versus actual data from
training, validation, and testing data sets.
The graphical and statistical parameters show that both the NN model and the RSM
model had been successfully tested by using the data published by previous works. The
results for both models were satisfactory and reliable with acceptable proximity.
However, the NN model provides better accuracy than the RSM model when predicting
the CO2 injectivity changes value for the given experimental and published data sets
because of having higher values of R2 and adjusted R2 with a lower value of AAPE,
SSE and RMSE. Overall, the NN model can be used satisfactorily and is suggested as
a good alternative for predicting the CO2 injectivity changes due to salt precipitation
and fines migration at various brine salinity, injection flow rate, particle size and
particle concentration.
172
CHAPTER 5
CONCLUSION AND RECOMMENDATIONS
In this chapter the conclusions derived from the findings of this research on
modeling the impact of CO2, brine, rock, and particles properties on CO2 injectivity
changes are described. The conclusions were based on the objective and results of the
study. Then, several recommendations for the future research work are also listed.
5.1 Conclusion
As stated in Chapter 1, the first objective of the study is to evaluate the individual
and combined effect of salt precipitation and fines migration on CO2 injectivity at
various CO2, brine, rock, and particles parameters. A comprehensive semi-static batch
and core flooding experiments were executed to evaluate the contribution of each
parameter on the permeability changes which directly affect the CO2 injectivity. ICPAES analysis and FESEM images revealed that the pore space modifications due to
mineral dissolution, salt precipitation and fines migration took place on the sandstone
core samples after injected with CO2. Results from the individual analysis confirmed
that brine salinity has a greater influence on permeability reduction than that of the
influence of particle (jamming ratio and particle concentration). The permeability
reduction contributed by salt precipitation is about two-times higher than the damage
by particles when considering each mechanism alone. The combined effect of salt
precipitation and fines migration led to a threefold increase of permeability reduction
compared to salt precipitation alone. A critical flow rate around 5-6 cm3/min, which
was equivalent to 2.19 cm/min was also observed. This critical flow rate acts as a
turning point of permeability reduction from increasing trend to lower permeability
reduction.
With regard to the second objective in assessing the applicability of the existing
CO2 injectivity models, data from the experimental work, which was based on different
brine salinity, injection flow rate, jamming ratio and particle concentration had been
fitted into the existing theoretical models. It was found that Kozeny-Carman based
models, Hagen-Poiseuille based models and Power law model were able to give good
prediction of CO2 injectivity change values, but only in the condition where changing
flow rate and fines particles were absent.
In addressing the last objective, results from the core flooding experiments were
used to develop alternative model for predicting CO2 injectivity change. New models
were developed by using NN model and RSM model to predict CO2 injectivity in the
presence of fines particles. It was both statistically and graphically found that the NN
model gives better CO2 injectivity change prediction than RSM model for training,
validation and testing data sets. The testing of the models using data from five case
studies have shown that the R2 and adjusted R2 values are approximately close to 1,
which indicates the fittings are reasonably accurate. The reported SSE is lower than 500
and the calculated RMSE and AAPE values for NN model is very low which implies
values predicted by the model co-relate well with the actual data. NN model as overall
is considered as efficient statistical tools in predicting the CO2 injectivity change of the
sandstone rock after exposed with dynamic injection of scCO2 at different brine salinity,
injection flow rate, particle size and particle concentration.
5.2 Recommendations
The following areas where additional scientific research works are recommended
for further studies on the evaluating the CO2-brine-rock interactions on CO2 injectivity.
•
Evaluating the effect of particle’s wettability on CO2 injectivity changes.
The wettability of particles has been regarded as one of the controlling
factors to determine the particulate process in fines migration. Therefore,
the details understanding of effect of minerals wettability and its relations
174
on fines migration during reactive CO2 injection could be interesting to be
investigated.
•
Assessing the effect of temperature and pressure on CO2 injectivity changes.
The particulate processed in the porous media were subjected to the physical
properties of fine particles, porous media, and carrier fluid. The viscosity of
scCO2 is changing at different pressure and temperature.
•
Exploring on the effect of brine type and its different compositions and
salinity on petro physical changes.
•
Microscopic study during the scCO2 injection with presence of particles. To
get dynamic images of particulate process in the porous media during the
scCO2 injection.
•
Comparison of the developed models with a wide range of data from field
case studies.
175
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186
APPENDIX A
CORE FLOOD EXPERIMENTAL DATA
Summary of Experimental Conditions
Core type
Brine salinity
(ppm)
Flow rate
(cm3/min)
Jamming
ratio
Particle concentration
(wt%)
Berea
30000
2
0
0
Berea
30000
2
0
0
Berea
Berea
30000
30000
2
5
0
0
0
0
Berea
30000
7
0
0
Berea
30000
10
0
0
Berea
Berea
6000
100000
2
2
0
0
0
0
Berea
30000
2
0
0
Berea
30000
2
0
0
Kirby
30000
2
0
0
Berea
30000
2
0
0
Berea
Berea
0
0
2
5
0
0
0
0
Berea
0
7
0
0
Berea
0
10
0
0
Berea
Berea
0
0
2
2
0.004
0.011
0.3
0.3
Berea
0
2
0.043
0.3
Berea
0
2
0.011
0.1
Berea
0
2
0.011
0.3
Berea
0
2
0.011
0.5
Berea
6000
2
0.011
0.3
Berea
Berea
6000
6000
2
2
0.004
0.043
0.3
0.3
Berea
30000
2
0.004
0.3
Berea
30000
2
0.011
0.3
Berea
Berea
30000
100000
2
2
0.043
0.004
0.3
0.3
Berea
100000
2
0.011
0.3
187
Berea
100000
2
0.043
0.3
Berea
30000
2
0.011
0.1
Berea
30000
2
0.011
0.5
Berea
30000
2
0.011
0.7
Berea
30000
5
0.011
0.3
Berea
Berea
30000
30000
7
10
0.011
0.011
0.3
0.3
Berea
30000
7
0.043
0.5
Berea
0
10
0.043
0.3
Berea
Berea
6000
100000
5
10
0.011
0.043
0.5
0.1
Berea
100000
2
0.043
0.3
Berea
6000
7
0.011
0.1
Berea
Berea
100000
100000
2
7
0.011
0.011
0.5
0.5
Berea
30000
0.5
0.011
0.3
Berea
30000
7
0.011
0.3
Berea
Berea
50000
100000
2
0
2
0
0.043
0.3
Berea
50000
2
0.011
0.1
Berea
100000
Berea
Berea
50000
100000
7
7
0
0.043
0.3
0.1
10
0.3
Berea
50000
10
0
0.011
Berea
100000
5
0.043
0.3
Berea
Berea
50000
100000
5
0.1
2
0.011
0.011
Berea
50000
7
0.043
0.1
Berea
100000
0.011
Berea
Berea
50000
0
10
7
2
0.011
0.011
0.3
0.1
0.5
Berea
0
2
0.043
0.5
Berea
0
5
0.011
0.1
Berea
0
2
0.043
0.1
Berea
50000
6
0.011
0.1
Berea
80000
3
0
0.1
Berea
80000
6
0
0.1
Berea
80000
7
0
0.1
188
0.1
0.5
Berea
60000
7
0
0.1
Berea
80000
6
0
0.1
Berea
60000
7
0
0.1
Berea
60000
3
0
0.1
Berea
60000
6
0
0.1
Berea
80000
0
Berea
30000
3
2
0.011
0.1
0.2
Berea
30000
2
0.011
0.4
Berea
6000
2
0.021
0.3
Berea
Berea
6000
30000
2
2
0.032
0.021
0.3
0.3
Berea
30000
2
0.032
0.3
Berea
100000
2
0.021
0.3
Berea
100000
2
0.032
0.3
Berea
0
2
0.011
0.2
Berea
0
2
0.011
0.4
Berea
0
2
0.011
0.7
Berea
0
7
0.043
0.5
Berea
6000
7
0.011
0.3
Berea
50000
10
0.043
0.5
Berea
50000
7
0.011
0.3
189
APPENDIX B
GOOGLE COLAB CODE
Import Libraries & Data Cleaning
[]
# Import libraries
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import matplotlib
import joblib
from matplotlib import rcParams
from cycler import cycler
import seaborn as sns
from google.colab import files
uploaded = files.upload()
from sklearn.datasets import make_hastie_10_2
# from sklearn.ensemble import GradientBoostingClassifier
# from sklearn.ensemble import BaggingClassifier
# from sklearn.neighbors import KNeighborsClassifier
from datetime import datetime, timedelta
from sklearn.neural_network import MLPRegressor
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import MinMaxScaler
from sklearn import metrics
from scipy.optimize import minimize, rosen, rosen_der, fmin_slsqp
, differential_evolution
190
[]
# %matplotlib notebook
Exploratory Data Analysis
[]
import io
data = pd.read_csv(io.BytesIO(uploaded['lab_data.csv']))
df = data.copy()
df.head()
# data cleaning: missing & outlier treatment
# data preparation: merge/integrate
[]
191
# Splitting dataset into train and test.
def split_data(df):
x_train, x_test, y_train, y_test = train_test_split(df.drop('
Measured RIC', axis=1), df['Measured RIC'], train_size=.69, rando
m_state=123)
return x_train, x_test, y_train, y_test
Neural Network Training
[]
def neural_network_regression(x_train, x_test, y_train, y_test):
# Scaling
scaler = MinMaxScaler()
x_train = scaler.fit_transform(x_train)
x_test = scaler.transform(x_test)
start_time = datetime.now()
# Neural network model
regr = MLPRegressor(hidden_layer_sizes=(1000, 1000, 100),
activation='relu',
solver='sgd',
alpha=1e-5,
learning_rate='adaptive',
random_state=123,
max_iter=3000,
learning_rate_init=0.001,
192
shuffle=False,
momentum=0)
regr.fit(x_train, y_train)
y_pred = regr.predict(x_test)
print('ANN score:[125].'.format(regr.score(x_test, y_test)))
print("ANN Training done in [67].".format(datetime.now() - start_
time))
return y_pred, regr, scaler
[]
def regression_evaluation_metrics(model, detail, y_test, y_pred, X_test):
'''Calculate regression evaluation metric score as follow
ed.
1. Mean Absolute Percentage error (MAPE)
2. Root Mean Squared Error (RMSE)
3. R2 score
4. R2 score adjusted '''
summary_dict = {'model': [model], 'detail': [detail],
'mean_absolute_percentage_error': [np.mea
n(np.abs((y_test - y_pred) / y_test)) * 100],
'mean_absolute_error': [metrics.mean_abso
lute_error(y_test, y_pred)],
'root_mean_squared_error': [np.sqrt(metri
cs.mean_squared_error(y_test, y_pred))],
'r2_score': [metrics.r2_score(y_test, y_p
red)],
193
'r2_adjusted': [1 - (1 - metrics.r2_score
(y_test, y_pred)) * (y_test.shape[0] - 1) / (
y_test.shape[0] - X_test.shape[1] - 1
)],
}
training_metrics = pd.DataFrame.from_dict(summary_dict)
return training_metrics
[]
# function to save model
# def save_model(model, scaler, file_name):
#
d = {
#
'model': model,
#
'scaler': scaler,
#
}
#
joblib.dump(d, file_name)
[]
x_train, x_test, y_train, y_test = split_data(df)
y_pred, regr, scaler = neural_network_regression(x_train, x_test,
y_train, y_test)
# save_model(regr, scaler, "Exp.pkl")
194
regression_evaluation_metrics('Neural Network Regression', 'Exper
iment Model', y_test, y_pred, x_test)
Prediction
[]
# input data frame table
input_data = pd.DataFrame([[5000, 2, 0, 0],
[5000, 2.5, 0, 0],
[5000, 3, 0, 0],
[100000, 2, 0.004, 0.3],
[5000, 1.5, 0, 0]], # insert input valu
e here, follow columns sequence
columns=['Brine Salinity (ppm)',
'Flow rate (ml/min)',
'Jamming ratio',
'Particle Concentration (wt%
)'])
# scale input
input_scaled = scaler.transform(input_data.values)
# call prediction model
RIC_predict = regr.predict(input_scaled)
# output
RIC_predict
# Measured RIC
195
# 22.19, 47.6, 26.8, 94, 9.5
array([ 8.03810885,
6.83936085])
9.15221643, 10.18646637, 45.46412867,
[]
input_data.head()
196
LIST OF PUBLICATIONS
Journals publication:
1. Md Yusof, M. A., Arif Ibrahim, M., Idress, M., Idris, A. K., Saaid, I. M., Rosdi,
N. M., ... & Azhari Awangku Matali, A. A. (2020). Effects of
CO2/Rock/Formation
Brine
Parameters
on
CO2
Injectivity
for
Sequestration. SPE Journal. (ISI Q1 Indexed)
2. Yusof, M. A. M., Mohamed, M. A., Akhir, N. A. M., Ibrahim, M. A., &
Mardhatillah, M. K. (2021). Combined Impact of Salt Precipitation and Fines
Migration on CO2 Injectivity Impairment. International Journal of Greenhouse
Gas Control, 110, 103422.. (ISI Q2 indexed)
3. Md Yusof, M. A., Mohamed, M. A., Md Akhir, N. A., Ibrahim, M. A., Saaid, I.
M., Idris, A. K., ... & Awangku Matali, A. A. A. (2021). Influence of Brine–
Rock Parameters on Rock Physical Changes During CO2 Sequestration in
Saline Aquifer. Arabian Journal for Science and Engineering, 1-15. (ISI Q3
indexed)
4. Md Yusof, M. A., Zainal, M. Z., Idris, A. K., Ibrahim, M. A., Yusof, S. R. M.,
Ismail, S. N., & Mohshim, D. F. (2020). Petrophysical Changes of Sandstone
Due to Salt Precipitation and Fines Migration During Carbon Dioxide
Injection. Journal of Computational and Theoretical Nanoscience, 17(2), 12071213. (Scopus indexed)
Conference publication:
1. Md Yusof, M. A., Saaid, I. M., Mohamed, M. A., Ibrahim, M. A., Md Akhir,
N. A., Ziaudin Ahamed, M. N., Idris, A. K., Azhari Awangku Matali, A. A.
(2021). Predictive Modelling of CO2 Injectivity Impairment due to Salt
Precipitation and Fines Migration During Sequestration. In International
Petroleum Technology Conference.
197