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Impact of exposure to brine/CO₂ on the mechanical and transport properties of the Mt. Simon sandstone

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Impact of exposure to brine/CO₂ on the mechanical and transport properties of the Mt. Simon sandstone

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IMPACT OF EXPOSURE TO BRINE/CO2 ON THE MECHANICAL AND TRANSPORT
PROPERTIES OF THE MT. SIMON SANDSTONE

by

Lin Sun

A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(CHEMICAL ENGINEERING)

December 2021

Copyright 2021 Lin Sun
ii

Dedication

This thesis is dedicated to my father Mr. Linji Bai and my mother Mrs. Daoxiang Sun for their
unlimited love and support in every stage of my life. I’m very proud to have them as my parents.

iii

Acknowledgements

First and foremost, I would like to express my sincerest gratitude towards my academic
advisors Professor Kristian Jessen and Professor Theodore Tsotsis for their invaluable guidance,
heartfelt inspiration and generous support throughout my PhD studies. Without their
commitment and encouragement, it would have been impossible for me to accomplish this goal.
They serve as an example of outstanding scientists, supervisors and mentors. Their spirit will
encourage me to explore, discover and achieve in my next stage of life and beyond.
I feel grateful to Dr. Doug Hammond, Dr. Iraj Ershaghi, and Dr. Katherine Shing, who served
on my qualifying exam committee. My special thanks go to Dr. Doug Hammond, who also
served on my PhD defense committee. His invaluable suggestions and guidance are gratefully
appreciated.
Also, I am thankful to Tina Silva and Shokry Bastorous for keeping me safe from laboratory
safety violations. I want to thank Monina Letargo and Annie Lee-Houang for handling
reimbursements and orders. The help and advice from Karen Woo, Anthony Tritto and Andy
Chen are also greatly appreciated. In addition, I would like to thank Marcus Walker and
Yunpeng Zhang for their kindness help. I feel lucky to have worked with all the staff in the
Mork Family Department of Chemical Engineering and Materials Science, who have made my
PhD study a pleasant and unforgettable experience.
My special thanks also go to my fellow PhD colleagues: Dr. Zhuofan Shi, Dr. Zhongtang Li,
Dr. Alireza Divsalar, Dr. Yu Wang, Dr. Mingyuan Cao, Dr. Devang Dasani, Dr. Pooya
Khodaparast, Jiyue Wu, Ye Lyu, Linghao Zhao and Sheng Hu. They all gave me a lot of
iv

help and support along the course of my PhD studies. It was a great pleasure to have worked
with them in a friendly learning environment. Their precious friendship will be embedded in
my heart forever. Last but not least, I want to convey my deepest gratitude to my parents, Linji
Bai and Daoxiang Sun for their endless love, encouragement and support for every single day
of my life so I can live with love and responsibility for the rest of life.

v

Contents

Dedication…………………………………………………………………………………………ii
Acknowledgment…………………………………………………………………………………iii
List of Tables……………………………………………………………………………………viii
List of Figures……………………………………………………………………………………ix
Abstract…………………………………………………………………………………………xiv
Chapter 1. Introduction……………………………………………………………………………1
1.1. Radiative forcing, global warming and carbon dioxide emissions…………………………1
1.2. Carbon capture and storage (CCS) ………………………………………………………4
1.3. CCS in deep saline aquifers………………………………………………………………6
1.4. Deformation caused by CO2 injection……………………………………………………8
1.5. Knowledge gaps and objectives of this study……………………………………………12
1.6. References………………………………………………………………………………13
Chapter 2. Mt. Simon sandstone been exposed to Brine/CO2 for 500 hours……………………17
2.1. Introduction………………………………………………………………………………17
2.2. Materials and experimental approach……………………………………………………22
2.2.1. Materials and basic characterization…………………………………………………22
vi

2.2.2. Mechanical properties………………………………………………………………23
2.3. Experimental results and discussion………………………………………………………29
2.3.1. Mechanical properties………………………………………………………………29
2.3.2. Porosity and permeability measurements……………………………………………35
2.3.3. Ion chromatography analysis…………………………………………………………36
2.4. Discussion and conclusions………………………………………………………………39
2.5. References………………………………………………………………………………40
Chapter 3. Gas loading/unloading experiments on Mt. Simon sandstone………………………46
3.1. Introduction………………………………………………………………………………46
3.2. Materials and experimental approach……………………………………………………49
3.2.1. Materials and basic characterization…………………………………………………49
3.2.2. Mechanical properties………………………………………………………………50
3.3. Experimental results and discussion………………………………………………………53
3.3.1. Helium loading and unloading experiments…………………………………………53
3.3.2. Argon loading and unloading experiments…………………………………………62
3.3.3. CO2 loading and unloading experiments……………………………………………70
3.4. Different gases loading experiment comparison…………………………………………78
3.5. Modeling of experimental observations…………………………………………………81
vii

3.6. References………………………………………………………………………………86
Chapter 4. Future work…………………………………………………………………………89
References………………………………………………………………………………………91
Appendix. Supplementary information……………………………………………………….101

viii

List of Tables
Table 2.1. Composition of the synthetic brine ………...………………………………...………23
Table 2.2. Experimental protocol ………………………………………………………………...27
Table 2.3. Porosity and permeability before and after exposure to CO2/brine ………………….36
Table 2.4. Cation and anion concentration in the brine before/after the incubation …………….37
Table 2.5. Mineral composition analysis (XRD) of the Mt. Simon core at 6927 ft ………………38
Table 3.1. Experimental protocol ………………………………………………………………...53
Table 3.2. Calculated pore volume and corresponding porosity …………………………………57
Table 3.3. Calculated moles of helium expanded to the core for each loading cycle ……...…….79
Table 3.4. Calculated moles of argon expanded to the core for each loading cycle ……...……….79
Table 3.5. Calculated moles of CO2 expanded to the core for each loading cycle ……...……….79

ix

List of Figures
Figure 1.1. U.S. greenhouse gas emissions by gas, 1990–2019 …………………………………...1
Figure 1.2. Radiative forcing of climate drivers from 1750-2011…………………………………2
Figure 1.3. Climate forcing scenario predicted from 2000-2050…………………………………3
Figure 1.4. CO2’s ultra-long atmospheric residence time …………………………………………4
Figure 1.5. Schematic view of the CCS technology ………………………………………………5
Figure 1.6. Operational CCUS Sites Worldwide at the end of 2020 ………………………………6
Figure 1.7. Overview of a conceptual storage site and different trapping mechanisms ……………7
Figure 1.8. Schematic of how geomechanical deformation can influence CO2 storage sites ………9
Figure 1.9. The schematic of Cam-Clay Cap model ……………………………………………10
Figure 2.1. Photograph of the 1” × 2” core sample ………………………………………………22
Figure 2.2. Positioning of the strain gauges ……………………………………………………24
Figure 2.3. The schematic of the experimental set-up ……………………………………………26
Figure 2.4. Relative CO2 concentration at the midpoint of the core (z=0.5L) during step 7;
the insert shows the relative CO2 concentration along the length of the core at the beginning
(t=0 hr) and the end (t=500 hr) of the incubation period ………………………………………28
Figure 2.5. Axial strain during the various experimental steps, see Table 2.2……………………30
Figure 2.6. Axial strain ΔH/H0 versus time during sample incubation (step 7) …………………31
x

Figure 2.7. Young’s modulus for the various experimental steps (the orange line indicates
the average Young’s modulus calculated before and after the 500 hr incubation
experiment) ……………………… ……………………………………………………………33
Figure 2.8. Radial strain during the various experimental steps …………………………………34
Figure 2.9. Radial strain Δr/r0 versus time during sample incubation (step 7) ……………………35
Figure 3.1. Positioning of the strain gauges ……………………………………………………50
Figure 3.2. The schematic of the experimental set-up ……………………………………………52
Figure 3.3. Chamber pressure recorded as a function of time ……………………………………54
Figure 3.4. Chamber pressure as a function of time for the 1
st
step of the loading experiment …54
Figure 3.5. Chamber pressure as a function of time for the 2
nd
step of the loading experiment …55
Figure 3.6. Chamber pressure as a function of time for the 3
rd
step of the loading experiment …55
Figure 3.7. Chamber pressure as a function of time for the 4
th
step of the loading experiment …56
Figure 3.8. Chamber pressure as a function of time for the 5
th
step of the loading experiment…56
Figure 3.9. Axial strain measured by gauge 1 (attached on the top of the sample) ………………58
Figure 3.10. Axial strain measured by gauge 2 (attached on the middle of the sample) …………58
Figure 3.11. Axial strain measured by gauge 3 (attached on the bottom of the sample) …………59
Figure 3.12. Upstream chamber pressure recorded as a function of time ………………………60
Figure 3.13. Downstream flow rate recorded as a function of time ………………………………61
xi

Figure 3.14. Axial strain measured by gauge 1 (attached on the top of the sample) ………………61
Figure 3.15. Axial strain measured by gauge 2 (attached on the middle of the sample) …………62
Figure 3.16. Axial strain measured by gauge 3 (attached on the bottom of the sample) …………62
Figure 3.17. Chamber pressure recorded as a function of time …………………………………63
Figure 3.18. Chamber pressure recorded as a function of time for the 1
st
loading step ………63
Figure 3.19. Chamber pressure recorded as a function of time for the 2
nd
loading step ……64
Figure 3.20. Chamber pressure recorded as a function of time for the 3
rd
loading step ………64
Figure 3.21. Chamber pressure recorded as a function of time for the 4
th
loading step ………65
Figure 3.22. Chamber pressure recorded as a function of time for the 5
th
loading step ………65
Figure 3.23. Axial strain measured by gauge 1 (attached on the top of the sample) ………………66
Figure 3.24. Axial strain measured by gauge 2 (attached on the middle of the sample) …………66
Figure 3.25. Axial strain measured by gauge 3 (attached on the bottom of the sample) …………67
Figure 3.26. Upstream chamber pressure recorded as a function of time ………………………67
Figure 3.27. Downstream flow rate recorded as a function of time ………………………………68
Figure 3.28. Axial strain measured by gauge 1 (attached on the top of the sample) ………………69
Figure 3.29. Axial strain measured by gauge 2 (attached on the middle of the sample) …………69
Figure 3.30. Axial strain measured by gauge 3 (attached on the bottom of the sample) …………70
Figure 3.31. Chamber pressure recorded as a function of time …………………………………71
xii

Figure 3.32. Chamber pressure recorded as a function of time for the1
st
loading step ………71
Figure 3.33. Chamber pressure recorded as a function of time for the 2
nd
loading step ……72
Figure 3.34. Chamber pressure recorded as a function of time for the 3
rd
loading step ………72
Figure 3.35. Chamber pressure recorded as a function of time for the 4
th
loading step ………73
Figure 3.36. Chamber pressure recorded as a function of time for the 5
th
loading step ………73
Figure 3.37. Axial strain measured by gauge 1 (attached on the top of the sample) ………………74
Figure 3.38. Axial strain measured by gauge 2 (attached on the middle of the sample) …………74
Figure 3.39. Axial strain measured by gauge 3 (attached on the bottom of the sample) …………75
Figure 3.40. Upstream chamber pressure recorded as a function of time ………………………75
Figure 3.41. Downstream flow rate recorded as a function of time ………………………………76
Figure 3.42. Axial strain measured by gauge 1 (attached on the top of the sample) ………………77
Figure 3.43. Axial strain measured by gauge 2 (attached on the middle of the sample) …………77
Figure 3.44. Axial strain measured by gauge 3 (attached on the bottom of the sample) …………78
Figure 3.45. Gases amount in the core sample as a function of final pressure ……………80
Figure 3.46. Comparisons of pressure drop for three gases loading experiment ……………80
Figure 3.47. Illustration of the BPM for the cylindrical sandstone for modeling purposes…81
Figure A1. Schematic view (right) and photograph (left) of the porosity measurement setup ……91
Figure A2. Schematic of the experimental apparatus for permeability measurements …………93
xiii

Figure A3. Schematic of Wheatstone bridge ……………………………………………………94
Figure A4. Schematic of the IC set-up …………………………………………………………96
Figure A5. Model of the shale core sample …………………………………………………97

xiv

Abstract
When sandstone rocks are exposed to CO2-saturated brine, their transport and mechanical
properties can, potentially, change due to chemical reactions as a result of such exposure. This
work investigates changes in the flow-through characteristics, porosity, and the mechanical
properties of Mt. Simon Sandstone samples caused by such exposure to brine/CO2. A core,
extracted from the Mt. Simon formation, was first characterized for its porosity and relevant
transport properties, and it was then aged for over 500 hours in CO2-saturated brine at formation-
relevant pressure, temperature, and confining stress conditions. The deformation of the sample was
measured in situ during aging via strain gauges attached to the core’s surface. Following the aging
experiment, the sample’s porosity and transport properties were again analyzed. Our experiments
show that both the porosity and permeability of the Mt. Simon sandstone sample increase due to
exposure to brine/CO2, with the impact on permeability being more significant. The deformation
measurements, employing strain gauges, indicate a weakening of the core material. Analysis of
the composition of the brine at the conclusion of the testing reveals changes, specifically, an
increase in the concentration of several of the cations. These changes are indicative of mineral/clay
dissolution, consistent with the porosity, permeability, and strain gauge measurements.
In a tandem study, the mass transfer properties (porosity, permeability) and mechanical behavior
(deformation) of the same sandstone sample were measured, in situ, under various gas atmospheres
(Helium, Argon, and CO2) during loading/unloading experiments. The goal of these experiments
was to understand how gas adsorption and confining pressure will affect the mass transfer
characteristics and mechanical properties of the porous rock, and how such changes impact gas
storage of particular interest was to understand how CO2-induced deformation affects the bulk
geomechanical properties of the sample.
1

Chapter 1. Introduction
1.1. Radiative forcing, global warming and carbon dioxide emissions
Radiative forcing or climate forcing is defined as the difference between the amount of sunlight
absorbed by the earth and the energy radiated back into space [1]. When the radiative forcing is
positive, which means that the earth receives more energy than it radiates back into space, the net
gain of energy absorbed by the earth will cause global warming. Nowadays, radiative forcing of
the earth's atmosphere is increasing at an unprecedented rate, largely because of the increase in the
concentration of greenhouse gases (GHG) such as carbon dioxide (CO2), methane (CH4), and
nitrous oxide (N2O) in the atmosphere [2].

Figure 1.1. U.S. greenhouse gas emissions by gas, 1990–2019 [3]
2

Figure 1.1 shows the emissions of carbon dioxide, methane, nitrous oxide, and several
fluorinated gases in the United States from 1990 to 2018. The emissions of all the gases involved
are expressed as million metric tons of equivalent carbon dioxide for consistency purposes. From
Figure 1.1, one can see that around 80% of the greenhouse gases emitted in the United States from
1990 to 2018 is carbon dioxide, which makes carbon dioxide the primary greenhouse gas involved
in anthropogenic climate forcing in the US.

Figure 1.2. Radiative forcing of climate drivers from 1750-2011
The Intergovernmental Panel on Climate Change (IPCC) issued a global climate assessment in
2013 in which they calculated the radiative forcing (RF) of each climate driver [4]. Radiative
forcing units are expressed as the power (watts) per square meter surface area of earth. According
to Figure 1.2, IPCC calculated that carbon dioxide has the highest positive RF compared with all
other human-influenced climate drivers, which means that CO2 has contributed more than any
driver to the change of climate between 1750 and 2011. Further, Hansen et al. [5] estimated the
radiative forcing between 2000 and 2050 (see Figure 1.3). The vertical bars represent the
estimation calculated from data predicted from IPCC and the colored bars represent the alternative
3

scenario if there are cooperative international actions regarding emissions of greenhouse gases. In
both scenarios, we can see that carbon dioxide still has the highest positive RF compared with
other climate drivers till the middle of the 21st century.

Figure 1.3. Climate forcing scenario predicted from 2000–2050

The other reason we should be paying more attention to CO2 emissions, is because its lifetime
in the atmosphere is much longer than any of the other climate drivers [6]. For example, methane
is mostly removed from the atmosphere after about 12 years by chemical reaction [6]. And nitrous
oxide is consumed in the stratosphere and thus removed from the atmosphere after about 114 years.
However, as Figure 1.4 shows even after 1000 years more than 15% of emitted CO2 still remains
intact in the atmosphere [1]. This means, once CO2 is in the atmosphere, it can continue to have
impacts on climate for thousands of years.
4

Figure 1.4. CO 2’s ultra-long atmospheric residence time
In conclusion, it is critical to reduce the emissions of CO2 to mitigate further global warming.
1.2. Carbon capture and storage (CCS)
Carbon capture and storage (CCS) refers to any technology that can be used to capture the CO2
and reduce its emissions [7]. CCS aims today to capture about 90% of the CO2 generated and, thus,
prevent it from being released into the atmosphere where it can stay intact for long time periods,
as indicated in Figure 1.4. Figure 1.5 is a schematic of one possible CCS technology.
5

Figure 1.5. Schematic view of the CCS technology [8]
This CCS technology consists of three steps: capturing and compressing the carbon
dioxide, transporting it to the storage location, and then storing it underground. The first step
involves using capture technologies that separate the carbon dioxide from flue gases produced
during electricity generation and various other industrial processes. CO2 capture systems may be
classified into three categories: pre-combustion capture, post-combustion capture, and oxyfuel
combustion [8]. After the capture step, carbon dioxide is transported via a pipeline to a pre-selected
location for safe storage. In the last step, carbon dioxide is injected into carefully selected
geological rock formations that are, typically, located several kilometers below the earth's surface.
Currently, CCS is one of the promising solutions to mitigate climate change [9]. Figure 1.6 shows
the sites of operational international CCUS(carbon capture, utilization and storage )[10].
6

Figure 1.6. Operational CCUS Sites Worldwide at the end of 2020
Note that the U refers to Utilization as the majority of injected CO2 in USA is for Enhanced Oil
Recovery (EOR). It is also important to mention that not all the ‘dots’ in Figure 1.6 correspond to
injection or storage sites; some of them refer to tests of capture equipment.
1.3 CCS in deep saline aquifers
Storage of CO2 in deep saline aquifers is of particular current interest as it offers the potential of
storing billions of tons of injected CO2 (see Figure 1.7) [11]. In this approach, CO2 is injected into
a reservoir and trapped there by four main mechanisms: (1) physical or static trapping, (2) residual
trapping, (3) solution trapping and (4) mineral precipitation [12].
7

Figure 1.7. Overview of a conceptual storage site and different trapping mechanisms [11]
Physical or static trapping is the most dominant of the trapping mechanisms. Once CO2 is
injected, the supercritical CO2 will percolate upwards through the porous rocks because it is more
buoyant than any of the other liquids being present. Eventually, the CO2 will reach the top of the
formation and it will meet the impermeable layer (caprock). However, physical trapping is the
least secure mechanism because CO2 is in a gaseous state and it can easily leak to the atmosphere
through cracks in the caprock. Residual trapping takes place when CO2 after its injection into the
formation, displacing the resident fluid in the porous rocks, but in so doing gets trapped itself in
the pore structure of these rocks. Residual trapping is thought to be controlled by capillary forces.
Solubility trapping happens when CO2 dissolves into the salty water (brine) already present in the
porous rocks. This CO2-containing brine is denser than the surrounding fluids and tends to sink to
the bottom of the formation, which makes it among the more secure ways for trapping the CO2.
8

Finally mineral trapping occurs carbonic acid that is generated when CO2 dissolves in water reacts
with the minerals in the surrounding rock to form solid carbonate minerals, which constitutes a
very effective way to bind CO2 to the rock.
1.4 Deformation caused by CO2 injection
A suitable CO2 storage formation should consist of rock formations with sufficient porosity,
permeability and connectivity to provide for an adequate storage volume [13]. For the safe storage
of CO2, a significant issue is the geomechanical response of the formation. Concerns have been
raised that geomechanical deformation induced by CO2 injection will either create new or
reactivate existing fracture networks [13]. To achieve broad acceptance of CO2 storage in the
subsurface, understanding faults and their associated deformation structures (such as deformation
bands and fractures) are accordingly of vital importance.
During the injection of CO2, elevated injection pressures may induce hydraulic fractures or may
stimulate fault reactivation [13]. In addition, the pore pressure of the porous sandstones will
increase, which in turn may lead to expansion of the formation. The effective stress, 𝜎 𝑖𝑗
′
, acting on
porous rocks is defined by Terzaghi [14] as follows:
𝜎 𝑖𝑗
′
= 𝜎 𝑖𝑗
− β
𝑊 δ
𝑖𝑗
P (1.1)

where 𝜎 𝑖𝑗
(psi) is the stress applied by regional tectonic stresses and the overburden weight, βW
(unitless) is the Biot-Willis coefficient which represents the proportion of fluid pressure that
counteracts the confining stress, δ
𝑖𝑗
is the Kroenecker δ (a function of two variables, usually just
positive integers. The function is 1 if the variables are equal, and 0 otherwise), and P (psi) is the
9

pore pressure. 𝜎 𝑖𝑗
and δ
𝑖𝑗
are second order tensors. According to equation 1.1, an increase in pore
pressure will reduce the effective stress, which may cause the expansion of the rock as mentioned
above. Expansion of the rocks may, in turn, cause changes in the applied stress both in and around
the formation. Small deformations are common in many settings and will not pose any risks to
storage safety. However, if deformations become more substantial, they can affect storage
operations in many ways. Figure 1.8 shows a schematic that explains how geomechanical
deformation can influence CO2 storage sites [15].

Figure 1.8. Schematic of how geomechanical deformation can influence CO 2 storage sites
10

Deformation bands and fractures can have a wide range of effects on fluid flow, either improving
or suppressing fluid communication. From a kinematic point of view, deformation bands can be
classified as one of three types [16]: dilation bands, compaction bands, and shear bands. There are
a number of models that have been developed to describe the failure criteria. The modified Cam-
Clay Cap model is one such model to describe the failure criteria [17] and is explained in a
schematic shown in Figure 1.9. In this figure, the y-axis represents the shear stress while the x-
axis represents the effective mean stress intended to describe two yield surfaces: a shear surface
and a compaction surface (Cap). The Cam-Clay Cap model allows for a complete analysis of
various deformation modes in porous rocks, ranging from dilation to shear and compaction. The
condition for faulting happens when at the critical state. Due to the injection of CO2 the pore
pressure of rocks will increase, and this will further reduce the effective mean stress, which then
causes the stress state to move closer to the critical line (Figure 1.9). Thus, it is crucial to be able
to predict the deformation behavior of sandstones.
Figure 1.9. Schematic explaining the Cam-Clay Cap model
11

Further, the fluid-mineral interactions may convert CO2 into carbonate minerals, which is a
process thought to be beneficial for the long-term CO2 storage. However, those reactions may also
impact the reservoir’s transport and mechanical properties by corroding mineral surfaces or by
precipitating carbonates and other salts into the pores. To accurately assess the CO2 storage
capacity and safety of capture, studying the transport and mechanical properties of sandstone
during CO2 injection under reservoir conditions is critical to understand the behavior of CO2 in the
deep reservoirs. A number of studies to date have been devoted to this topic and are briefly
discussed below.
Mouzakis et al. and Miller et al. [18,19] investigated how the porosity of caprocks can be altered
by geochemical reactions induced by dissolution of CO2 into the pore fluids. Tutolo et al. [20]
performed flow-through experiments on K-feldspar-rich cores (Eau Claire caprock, overlying the
Mount Simon sandstone formation). Their results confirm the view that increased acidity caused
by supercritical carbon dioxide (scCO2) injection into feldspar-rich sandstone will dissolve
primary feldspars and precipitate secondary aluminum minerals (with corresponding changes in
permeability). Huq et al. [21] studied, via flow-through experiments, the water/rock interactions
during CO2 injection in sandstones from the Altmark natural gas reservoir (major components
include quartz, feldspars, clay minerals, cements of carbonates and anhydrite) under simulated
reservoir conditions (125 ℃ and 50 bar CO2 pressure). Fluid analysis suggested the dissolution of
both calcite and anhydrite happen simultaneously. Dissolution of feldspar and minor amounts of
clay (chlorite) was also found in their experiments. In addition, the permeability of the sample
increased by a factor of two, mostly due to the dissolution of rock cements during brine injection.
As part of the evaluation of saline aquifers in Hungary for GCS (Global Carbon Dioxide
sequestration), Kirá ly et al. [22] studied three core samples from the Pannonian Basin. These
12

samples were exposed to various CO2 environments in laboratory batch experiments for one month.
After the aging process, the brine composition and the mineral content of the reacted rock samples
were analyzed. Dissolution of the carbonate minerals was observed, and evidence was also found
for feldspar dissolution, both processes leading to secondary carbonate and clay mineral formation.
The presence of CO2 increases the mineral dissolution rates. Liu et al. [23] carried out batch
laboratory experiments of Eau Claire shale dissolution in brine at 200 ℃ and 300 bar. Results from
scanning electron microscopy (SEM) and X-ray diffraction (XRD) analysis show the minor
dissolution of K-feldspar and anhydrite, and the precipitation of pore-filling and pore-bridging
illite and/or smectite, and siderite in the vicinity of pyrite.
To study mechanical properties of sandstones under reservoir conditions. De Jong et al. [24]
studied smectite-bearing caprocks sealing carbon sequestration reservoirs. They conclude that
CO2 penetration can cause swelling of a few percent in the affected zone and can potentially close
small fractures or joints, thus reducing bulk permeability.
1.5 Knowledge gaps and objectives of this study
Even though a number of studies have been carried out to date to address the alteration of
petrophysical, mineralogical and mechanical properties of rock samples due to exposure to
CO2/brine environments, the understanding of the impact of such exposure on the pore structural
(e.g., porosity and pore size distribution), transport (permeability) and mechanical properties is
still quite limited. To close these knowledge gaps, we propose here a systematic study involving
measuring the changes in the pore structural, transport and mechanical properties of a sandstone
from the Mt. Simon formation upon its exposure to CO2/brine. Specifically, we plan to carry out
the following research plan:
13

• Study the pore structural and transport characteristics of a fresh Mt. Simon rock sample.
• Expose the Mt. Simon rock sample to CO2-saturated brine at reservoir conditions for 500
hrs while the geomechanical properties of the sample will be measured via strain gauges.
Following that, tests will be carried out to measure the change in the pore structure and
transport properties of the rock.
• Carry out gas loading/unloading experiments on the sandstone sample while
geomechanical properties of sample are measured via strain gauges.
In what follows, we first describe the experimental systems that have been constructed, then we
present the experimental data generated and describe methods to analyze the data. Finally, we
summarize our results.
1.6 References
[1] Myhre G, Shindell D, Bré on FM, Collins W, Fuglestvedt J and Huang J et al., Anthropogenic
and Natural Radiative Forcing. In: Climate Change 2013: The Physical Science Basis.
Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental
Panel on Climate Change [Stocker, T.F., D. Qin, G.-K. Plattner, M. Tignor, S.K. Allen, J.
Boschung, A. Nauels, Y. Xia, V. Bex and P.M. Midgley (eds.)]. Cambridge University Press.,
Cambridge and New York, pp. 659-720(2013).
[2] Robertson GP, Paul EA and Harwood RR, Greenhouse gases in intensive agriculture:
contributions of individual gases to the radiative forcing of the atmosphere. Science 289(5486):
1922-1925(2000).
[3] U.S. EPA (https://www.epa.gov/ghgemissions/inventory-us-greenhouse-gas-emissions-and-
sinks).
14

[4] Boucher O, Randall D, Artaxo P, Bretherton C, Feingold G, and Forster P et al., Clouds and
Aerosols. In: Climate Change 2013: The Physical Science Basis. Contribution of Working
Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change
[Stocker, T.F., D. Qin, G.-K. Plattner, M. Tignor, S.K. Allen, J. Boschung, A. Nauels, Y. Xia,
V. Bex and P.M. Midgley (eds.)]. Cambridge University Press., Cambridge and New York, pp.
571-657(2013).
[5] Hansen JE and Sato M, Trends of measured climate forcing agents. PNAS 98(26): 14778-
14783(2001).
[6] The Guardian (https://www.theguardian.com/environment/2012/jan/16/greenhouse-gases-
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[7] Fanchi JR and Fanchi CJ, Energy in the 21st Century. World Scientific Publishing Co Inc., pp.
350(2016).
[8] Smit B, Reimer JR, Oldenburg CM, and Bourg IC, Introduction to Carbon Capture and
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[9] Pires JCM, Martins FG, Alvim-Ferraz MCM and Simõ es M, Recent developments on carbon
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[11] Nordiccs (https://data.geus.dk/nordiccs/terminology.xhtml).
[12] CCP (https://www.co2captureproject.org/what_is_co2_capture_storage.html).
[13] Rutqvist J, The geomechanics of CO2 storage in deep sedimentary formations. Geotech Geol
Eng 30: 525–551(2012).
15

[14] Terzaghi K, Theoretical Soil Mechanics. J. Wiley and Sons, Inc., New York; Chapman and
Hall, Limited., London, (1943).
[15] Herwanger JV and Horne SA, Linking reservoir geomechanics and time-lapse seismics:
predicting anisotropic velocity changes and seismic attributes. Geophysics 74(4): W13-
W33(2009).
[16] Aydin A, Borja RI and Eichhubl P, Geological and mathematical framework for failure modes
in granular rock. J. Struct. Geol 28(1): 83-98(2006).
[17] Torabi A, Gabrielsen RH, Fossen H, Ringrose P, Skurtveit E, Ando E et al., Strain localization
in sandstone and its implications for CO2 storage. First Break 33: 81-92(2015).
[18] Mouzakis KM, Navarre-Sitchler AK, Rother G, Bañ uelos JL, Wang XY, Kaszuba JP et al.,
Experimental study of porosity changes in shale caprocks exposed to CO2-saturated brines I:
evolution of mineralogy, pore connectivity, pore size distribution, and surface area. Environ.
Eng. Sci 33(10): 725-735(2016).
[19] Miller QRS, Wang, XY, Kaszuba, JP, Mouzakis, KM, Navarre-Sitchler, AK, Alvarado, V et
al., Experimental study of porosity changes in shale caprocks exposed to carbon dioxide-
saturated brine II: insights from aqueous geochemistry. Environ. Eng. Sci 33(10): 736-
744(2016).
[20] Tutolo BM, Luhmann AJ, Kong XZ, Saar MO and Seyfried Jr WE, CO2 sequestration in
feldspar-rich sandstone: coupled evolution of fluid chemistry, mineral reaction rates, and
hydrogeochemical properties. Geochim. Cosmochim. Acta 160: 132-154(2015).
16

[21] Huq F, Haderlein SB, Cirpka OA, Nowak M, Blum P and Grathwohl P, Flow-through
experiments on water-rock interactions in a sandstone caused by CO2 injection at pressures
and temperatures mimicking reservoir conditions. Appl. Geochemistry 58: 136-146(2015).
[22] Kirá ly C, Szamosfalvi Á, Zilahi-Sebess L, Kó nya P, Ková cs IJ and Sendula E et al., Caprock
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[23] Liu FY, Lu P, Griffith C, W. Hedges S, Soong Y and Hellevang H et al., CO2-brine-caprock
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[24] De Jong SM, Spiers CJ, and Busch A, Development of swelling strain in smectite clays
through exposure to carbon dioxide. Int. J. Greenh. Gases Control 24: 149-161 (2012).

17

Chapter 2. The Impacts of Exposure of Mt. Simon Sandstone to
Brine/CO2
2.1. Introduction
The injection of supercritical CO2 (scCO2) into a formation can, potentially, have serious
impacts on the rock’s mechanical properties [1]. Presently, the effects that scCO2 injection in rocks
can have on their physical properties are not fully understood and they may vary significantly
among different formations [2]. There are three trapping mechanisms that are known to take place
when CO2 is injected into saline formations: (i) CO2 can be trapped in the formation as a gas or
supercritical fluid by structural barriers and/or by capillarity, a mechanism known as
hydrodynamic trapping; (ii) CO2 can also be dissolved into the formation water, a trapping
mechanism known as solubility trapping, resulting in an increase in the formation water’s acidity
and the potential dissolution of the rock minerals; (iii) and in the third trapping mechanism, CO 2
reacts directly or indirectly with minerals in the rock formation, which may then cause the
formation of secondary carbonates [3].
Such CO2-brine-rock interaction processes may result in changes in permeability, porosity, pore
geometry and grain size distribution, and may influence the mechanical properties of reservoir
rocks [4-8]. For the study of CO2-brine-rock interactions impacting the mechanical properties of
rocks, both direct measurements via strain gauges (as in this study) and linear variable
displacement transducers (LVDT), and indirect measurements via monitoring of ultrasonic wave
propagation through laboratory rock samples have been utilized.
Hangx et al. [9]

performed conventional triaxial creep experiments in combination with biaxial
flow-through (brine and CO2-rich brine) experiments with sandstone samples from the Goldeneye
field. They studied the effect of carbonate cement dissolution on the mechanical properties of the
18

material. Their laboratory flow-through experiments mimicking CO2 injection were performed
under reservoir-relevant conditions. Calcite dissolution was observed during their experiments, but
the mechanical parameters measured did not differ significantly from those measured prior to the
CO2-saturated brine flow-through experiments.
Kitamura et al. [10] conducted strain measurements on a high-permeability (105 mD) Mt. Simon
sandstone (saturated with distilled water) during CO2 flow-through experiments. For the strain
measurements, they utilized two strain gauges attached at the center of the core measuring the
vertical and horizontal strain. Their measurements indicated a substantial expansion in both
directions during CO2 injection into the core. The Mt. Simon sandstone formation, studied by
Kitamura et al. [10] is among the best-known sites selected by the US Department of Energy (DOE)
for field-testing at large scale of geologic CO2 storage, based on its favorable depth location,
thickness, permeability, hydraulic properties and brine salinity [11]. At the end of 2014, one million
metric tons of CO2 were injected into the Mt. Simon Formation by the Midwest Geologic
Sequestration Consortium (MGSC), one of the seven Regional Carbon Sequestration Partnerships
(RCSPs) funded by the US DOE [12]. Micro-seismic events were observed both during and soon
after CO2 injection in and around the injection sites [13,14]. This has then motivated a number of
studies (the key of which are reviewed in this section) by several groups, including ours, on this
interesting and concerning behavior.
Zhang et al. [15] studied the mechanical properties of a Xujiahe sandstone pressurized with
supercritical CO2 and water under various confining pressure conditions. A triaxial mechanical
testing system was applied to perform compression tests of rocks exposed to scCO2 and water, and
LVDTs were used to measure the axial and radial strains. They found that the CO2/H2O mixture
significantly deteriorated the deformation modulus and stiffness of the sandstone sample.
19

Akono et al. [16] studied the impact of CO2-induced geochemical reactions on the creep
response of Mt. Simon sandstone samples after they had undergone both static incubation and
dynamic flow-through experiments at geologically relevant conditions. Scanning electron
microscopy (SEM)/energy dispersive X-ray analysis (EDX)analyses were performed to probe the
microstructure, and grid nanoindentation was used to measure the mechanical response of the Mt.
Simon sandstone after exposure to CO2; changes both in the microstructure and in the mechanical
properties of the cores were detected. Akono et al. [16] also observed increases in both the
mesoporosity and microporosity of the sandstone samples after aging, as well as CO2-induced clay
and K-feldspar dissolution. In a later study they presented a model to describe the geomechanical
changes of the Mt. Simon sandstone due to its exposure to CO2-saturated brine [17]. The model
predicts the observed decrease in the macroscopic creep modulus. Their study concludes that the
CO2-induced geochemical reactions influence the geomechanical properties of the rock by altering
the local packing density as well as by affecting the coefficient of intergranular friction.
Marbler et al. [18] and Rathnaweera et al. [19] studied both the mineralogical and the
mechanical properties of sandstone samples (from the North German Basin and the Sydney
Australia basin, respectively) before and after exposure to CO2 and brine to examine how such
exposure would affect their mechanical behavior. They measured the mechanical properties of the
sandstone samples both under confined and unconfined conditions. In their experiments, ultrasonic
wave velocity and acoustic emission measurements were applied to measure the mechanical
properties of the samples. They reported mineralogical alteration of the samples and a decrease in
strength. Rimmele et al. [20] performed a similar study but they found that the mechanical and
mineralogical properties of their sandstone sample from the Paris basin were maintained after
exposure to CO2-saturated water for one month. They reported, however, an increase in the
20

porosity and permeability of the sandstone sample after exposure.
Da´vila et al. [21] performed a series of acidified-brine flow-through experiments designed to
quantify the alteration of geochemical, structural and fluid transport properties of a Mt. Simon
sandstone core extracted from a depth of 2110.5 m (same depth as the sandstone used in this study)
as part of the Illinois Basin Decatur Project (IBDP). The synthetic brine used in their experiments
is the same as the one previously used by our team [22]. To simulate the solute transport during
the CO2-saturated brine flow-through experiments through the core, they used in their simulations
the open-source CrunchTope software. They reported clear evidence for dissolution of carbonates
at the inlet and along the core length over a relatively short time scale of 120 hr.
This team studied the transport and mechanical properties of the Mt. Simon sandstone upon
exposure to brine and CO2 [22]. We measured the change in the flow-through characteristics,
porosity, and the mechanical behavior of Mt. Simon sandstone samples before and after their
exposure to brine/CO2 for one to two weeks. Mechanical properties such as the Young's Modulus,
Poisson's Ratio and Bulk Modulus were calculated from the wave velocity data measured with the
samples, using a NER Autolab 1500 system, both before and after incubation. The studies showed
a slight increase of the sandstone’s porosity, while a substantial increase of the sample’s
permeability was observed. Comparing mechanical properties before and after exposure to
CO2/brine indicated a weakening of the materials.
In a follow-up study, Harbert et al. [23] studied the CO2-induced changes of two additional Mt.
Simon sandstone samples, extracted from depths of 6919.3 ft (2109 m) and 6926.1 ft (2111 m),
that were incubated in scCO2/brine at reservoir-relevant conditions for a longer period of one
month. The porosity and permeability of each sample were again measured before and after the
incubation. The permeability of both samples increased after incubation. The porosity
21

measurements indicated that the porosity of one sample increased while that of the other sample
decreased. For the geomechanical analysis of samples before and after incubation, we again
utilized the NER Autolab 1500 apparatus to monitor ultrasonic wave propagation through the
samples to measure the ultrasonic velocities, Vp (compression-wave velocities), and Vs (shear-
wave velocities) to calculate the dynamic modulus. The measurement of geomechanical properties
again indicated weakening for both samples after exposure to the scCO2/brine.
In summary, to date there have been a number of studies by this team and others focusing on the
impact on the pore structure, transport, petrophysical, mineralogical and geomechanical properties
of the, mostly, short-time exposure of rock samples to CO2/brine. In general, after exposure
changes in porosity and permeability were found. Companion measurements of mechanical
properties before and after exposure, mostly, via monitoring of ultrasonic wave propagation,
indicate a weakening of the materials due to the exposure, but the impact on the transport properties
is far from clear.
In this study, we present results of our continued efforts to study the impact of exposure to
CO2/brine on the Mt. Simon sandstone material [22]. The focus is again on changes in transport
and mechanical properties, but unlike our past efforts where these changes were measured ex-situ
before and after exposure [22], in this study relevant properties are measured in-situ while the Mt.
Simon sandstone is being continuously exposed to CO2/brine for over 500 hours. We investigate
the impact on mechanical properties at various pore and confining pressures. The study of
geomechanical properties in-situ is then combined with measurements of changes in porosity,
permeability, and brine composition due to exposure.
The key significance of this paper is in providing direct experimental evidence that relatively
short-term exposure of the Mt. Simon sandstone to a CO2/brine environment may cause rock
22

alterations, which could ultimately result in weakening of its mechanical strength and potentially
explain the micro-seismic events observed at the formation during and after CO2 injection [13,14].

2.2. Materials and experimental approach
2.2.1. Materials and basic characterization
The rock sample studied in this work is from the Mt. Simon sandstone that constitutes a ∼1500
ft (∼460 m) thick storage zone in the Illinois Basin - Decatur Project (IBDP) [24]. In that project,
a verification well (VW1) was drilled in 2010 located 305 m (1000 ft) north of the CO2 injection
well [24]. The rock sample studied here was extracted from VW1 from a depth of 2111.4 m (6927
ft). It is a cylindrical core sample, with a size of 1” × 2”, see Figure 2.1 for a photograph, which
was prepared via liquid nitrogen drilling in the horizontal direction (along the bedding plane) from
the main core extracted (depth range between 2110.4 and 2111.4 m (6924 – 6927 ft)).

Figure 2.1. Photograph of the 1” × 2” core sample

The permeability of the sample was measured before and after exposure to CO2/brine via N2 gas
flow-through experiments employing a TKA-209 gas permeameter. Its porosity was measured via
23

He pycnometry (schematics of the experimental apparatuses and further experimental details can
be found in the Supplementary Information section).
A synthetic brine with composition, shown in Table 2.1, simulating one of the resident brines
found in the Mt. Simon formation [24], was used in the experiments. The brine was prepared using
deionized (DI) water to dissolve the various salts, all of which were american chemical society
(ACS) grade or better. The concentrations of the cations and anions in the fresh brine, as well as
in the used brine after the core incubation experiment, were determined via ion chromatography
(IC) analysis, employing an ICS-2100 IC system (Dionex). We used laboratory DI water (Fluka)
to prepare all diluted solutions for the IC tests. Standard solutions from Dionex were used to
calibrate the instrument using the absolute calibration method for three anions (Cl
−
and Br
−
) and
six cations (Ca
2+
, Mg
2+
, K
+
, Sr
2+
, Na
+
and Li
+
). Additional information related to the IC analysis
can be found in the Supplementary Information section.
Table 2.1. Composition of the synthetic brine
Reagent Concentration (g/L)
NaCl 114.16
CaCl2 73.37
MgCl2·6H2O 16.73
KCl 40.30
KBr 1.12
LiCl 0.12
SrCl2·6H2O 2.43
Na2B4O7 0.77

2.2.2 Mechanical properties
Direct strain measurement techniques for rock specimens involve the use of either linear
variable displacement transducers or direct-contact extensometers, commonly known as strain
gauges. A major drawback for the LVDT method includes bedding measurement error, which is
24

caused by the initial lack of fit between the sample surface and the platen or sleeve of the transducer
[25]. Strain gauges, in contrast, are free from bedding errors, and they can be also affixed to any
location on the core selected to measure localized deformation. In our experiments, two strain
gauges were attached at the middle section of the sandstone sample, as shown in Figure 2.2, to
measure the potential deformation (radial and axial) due to its exposure to CO2/brine mixture.

Figure 2.2. Positioning of the strain gauges

Figure 2.3 shows a schematic of the overall experimental set-up. It consists of a biaxial core-
holder, a hydraulic pump, a syringe pump, an ISCO pump with an accumulator, two pressure
transducers and assorted data acquisition devices. The hydraulic pump, employing oil as the
working fluid, is used to apply the confining pressure on the sample. The syringe pump is used to
inject brine, if so desired, into the core from the bottom side up. The ISCO pump, fitted with an
accumulator, is used to pressurize CO2 gas from a cylinder to the desired pressure and to inject it
into the top chamber of the core-holder in contact with the brine-saturated core. Data acquisition
devices (NI USB 6210 from National Instruments, USA) are used to record the signals of the
pressure transducers (PX 409 series from Omega Engineering, USA) and the strain gauges (KFH
series from Omega Engineering, USA). The sandstone core sample is first saturated with brine and
is then fitted with the strain gauges. It is then placed into the core-holder. The wires of the strain
25

gauges attached to the core sample, once inside the core-holder, are connected to the data
acquisition system via 3-pin feedthroughs. To avoid corrosion of the strain gauge wires as well as
of the feedthrough pins because of exposure to CO2/brine, and to prevent short-circuiting, all wires
are painted with insulation varnish.
Once the sample was installed in the core-holder, and the strain gauges were connected to the
data acquisition system, to initiate the experiments the confining pressure was raised to 500 psig
(34.5 bar) via the hydraulic pump (this and all the subsequent steps raising the confining pressure
were completed within 30 sec). Then, the state of the core was monitored for several hours via the
strain gauges to establish the experimental baseline. The confining pressure was then raised to
1000 psig (68.9 bar) and the state of the system was recorded for 20 min via the strain gauges.
With the aid of the ISCO pump, the CO2 pressure in the core-holder top chamber in contact with
the brine-saturated core (the bottom chamber is filled with brine) was then raised to 500 psig (this
and all the subsequent steps raising the CO2 pressure were completed within 2 min) and the
confining pressure was then raised to 1500 psig (103.4 bar).

26

Figure 2.3. The schematic of the experimental set-up

The state of the core was then again monitored via the strain gauges for another 20 min. This
procedure was then repeated three more times: The CO2 pressure was raised to 1000 psig and the
confining pressure was raised 2000 psig (137.9 bar), followed by 20 min of monitoring; the gas
pressure was then raised to 1500 psig and the confining pressure to 2500 psig (172.4 bar), followed
again by 20 min monitoring of the core behavior; the gas pressure was then raised to 2000 psig
and the confining pressure to 3000 psig (206.8 bar) and the state of the core was again monitored
for 20 min. As a final step, the CO2 pressure was raised to 2500 psig and the core was allowed to
stay incubated at this condition for 500 hr with continuous monitoring via the strain gauges. At the
end of this 500 hr incubation period, the gas pressure was decreased to 2000 psig (within 2 min),
and the state of the core was recorded via the strain gauges for 20 min. Then, the confining pressure
was decreased to 2500 psig (within 30 sec), followed by a decrease in the pore pressure to 1500
Syringe pump
Pressure
gauge 2
Relief
Valve 1
Valve 2
Valve 4
Sample
Chamber
CO2
(He)
Valve 5
Valve 6
DAQ
Data
Acquisition
Valve 3
Isco pump
Accumulator
Pressure
gauge 1
Heating tape
Hydraulic
pump
Two gauges
27

psig and recording of the state of the sample via the strain gauges for an additional 20 min.
Subsequently, the confining pressure was reduced to 2000 psig and the gas pressure to 1000 psig,
with the state of the core recorded for an additional 20 min. The confining pressure was then
decreased to 1500 psig. After that, the experiment was stopped, and the brine was collected from
the bottom of the core-holder system. Table 2.2 summarizes the above experimental procedure, for
convenient reference.
Table 2.2. Experimental protocol

Since in these experiments the CO2 pressure on the top of the core is kept constant, we cannot
measure the CO2 mass diffusing into the brine-saturated core. We have previously measured via in
situ ATR-FTIR the diffusion of CO2 into a Mt. Simon sandstone sample from the same depth of
6927 ft, saturated with a brine of similar composition [26]. The experimental diffusivity value is
then used here to model the CO2 concentration profiles in the core during the series of experimental
steps described above and summarized in Table 2.2. In Figure 2.4 we plot the ratio of the calculated
CO2 concentration, C, at the midpoint point of the core divided by the CO2 concentration in the
brine in equilibrium with the gas on the top of the core (note, that the assumption that the gas and
liquid phases equilibrate with each other does not, in any way, imply that equilibrium is also
Step # Pore pressure/psig Confining
pressure/psig
Time duration
Initial State 0 0
1 0 500 several hours
2 0 1000 20 min
3 500 1500 20 min
4 1000 2000 20 min
5 1500 2500 20 min
6 2000 3000 20 min
7 2500 3000 500 hr
8 2000 3000 20 min
9 1500 2500 20 min
10 1000 2000 20 min
28

established between the solid core material and the liquid phase imbibed in its pore structure), Ceq,
during step 7 (the 500 hr incubation period). Shown on an insert in the same Figure are the relative
concentration (C/Ceq) profile at the start (t=0) and the end (t=500 hr) of step 7. It is clear from
Figure 2.4, that very little, if any, CO2 has diffused inside the core prior to the start of the incubation
period (steps 3 – 6, see Table 2.2).
As noted above, throughout the whole experiment the mechanical state of the core was
monitored and recorded via two strain gauges: Gauge 1, recording the axial strain,

Figure 2.4. Relative CO 2 concentration at the midpoint of the core (z=0.5L) during step 7; the insert shows the
relative CO 2 concentration along the length of the core at the beginning (t=0 hr) and the end (t=500 hr) of the
incubation period
and Gauge 2, recording the radial strain. The principle of operation allowing the measurement of
the strain is simple, in that each strain gauge functions as one of the resistances of a Wheatstone
bridge (see supplementary material for additional details). During operation, one records, via the
LabView software, the voltage output of the strain gauge, 𝑢 𝑜 , which relates to the resistance
29

characteristics of the bridge according to the following equation:

𝑢 𝑜 =𝑢 𝑖𝑛
∗{
𝑅 𝑆 +𝛥𝑅𝑠 𝑅 𝑆 +𝛥𝑅 𝑠 +𝑅 3
−
𝑅 2
𝑅 1
+𝑅 2
} , (1)

In Eqn. 1, 𝑢 𝑖𝑛 is the excitation voltage of the Wheatstone bridge (in this experiment, 𝑢 𝑖𝑛
= 0.908
V), Ri is the resistance of individual resistors in the Wheatstone bridge (here R1=R2=R3=120 Ohm),
Rs is the initial resistance of the strain gauge itself (Rs = 120 Ohm), and ΔRs the change in the
strain gauge’s resistance caused by its deformation.
The strain 𝜀 , either in the axial or the radial direction, relates to the ∆R s of the corresponding
gauge via the following equation:
𝜀 =(
𝛥𝑅𝑠 𝑅 𝑆 ) 𝐺𝐹 , (2) ⁄
where GF is the so-called gauge factor (GF=1.51 for the strain gauges employed here). The average
axial strain is given by εa=ΔH/H0, where H0 = 5.08 cm is the initial height of the sample, and ΔH
=H - H0, where H is the height at any point during the experiment, is the change in height. This
definition assumes that the sample has uniform mechanical properties in the axial direction,
otherwise the strain should be interpreted as the quantity at the location to which the gauge is
affixed to. The average radial strain is given by εr=Δr/r0, where r0 = 1.27 cm is the initial radius of
the sample and Δr is the change in radius at any point during the experiment.
2.3. Experimental results and discussion
2.3.1 Mechanical properties
Figure 2.5 reports the axial strain measured at the end of each step change reported in Table 2.2.
At the end of steps 1 and 2 the sample height has decreased (the axial strain is negative), as
30

expected, as the sandstone is subjected first to a net stress of 500 psi (step 1) and then to a net
stress of 1000 psi at the end of step 2 (the same is also true for the radial strain, see further
discussion below). In steps 3-6, as the CO2 pressure above the sample is raised from 500 psig (step
3) to 2000 psig (step 6), while the net stress stays the same (1000 psi), the sample height begins to
increase (as can be seen in Figure 2.4, during this period very little, if any, CO2 has infiltered the
core). After the CO2 gas pressure was raised to 2500 psig (while maintaining the confining pressure
constant at 3000 psig) at the end of Step 6, the sample height decreased from 5.0485 cm to 5.0456
cm (the strain decreased from -0.0062 to ~-0.0068).

Figure 2.5. Axial strain during the various experimental steps, see Table 2.2

Figure 2.6 shows the axial strain during the 500 hr incubation test (step 7). For the first 170 hr
of testing, the strain remained largely constant. At that time, however, the strain suddenly
decreased, signifying an abrupt change in the mechanical state of the sandstone sample (the delay
in change may be explained by the gradual build-up in CO2 concentration in the core, see Figure
2.4). For the remainder of the incubation test period, small changes in the mechanical state of the
-8.0E-03
-6.0E-03
-4.0E-03
-2.0E-03
0.0E+00
1 2 3 4 5 6 7 8 9 10
Axial strain ΔH/H
0
Step number#
31

sample (as manifested by the value of the measured strain) continued to happen, potentially,
signifying the rearrangement of the sample’s quartz grains as chemical changes take place in the
clay components that serve as a cement gluing such grains together (for further experimental
evidence that such phenomena are, indeed, occurring, see further discussion in the ion
chromatography analysis section). That such changes take place over relatively short times of
incubation, is consistent with the study by Da´vila et al. [21] who also reported noticeable
alterations in the transmissivity and structure of a Mt. Simon sandstone core during CO 2/brine
flow-through experiments over a time scale of 120 hr.
At the end of the incubation period (step 7), the CO2 pressure on the top of the sample was
decreased to 2000 psig (step 8, see Table 2.2). As a result of this change in CO2 gas pressure, the
strain decreased from a value of -0.0069 at the end of the step 7 to a value of -0.0070 at the end of
step 8. Similar but larger in absolute magnitude decreases were also observed at the end steps 9
and 10, as shown in Figure 2.5.

Figure 2.6. Axial strain ΔH/H0 versus time during sample incubation (step 7)
-7.2E-03
-7.0E-03
-6.8E-03
-6.6E-03
-6.4E-03
0 100 200 300 400 500 600
axial strain ΔH/H
0
time/hr
32

If one was to interpret the change in the axial strain as being due to a change in the net stress,
ΔP in the same direction, one can then calculate the Young’s modulus, Y , for the core sample
according to the Equation 3 below:
𝑌 =−
𝛥𝜎
𝜀 𝑖 , (3)
where, Δσ is the change of net stress and εi (𝜀 𝑖 =
𝐻 𝑖 −𝐻 𝑖 −1
𝐻 𝑖 −1
, where Hi is the sample height at the end
of step i and Hi-1 the corresponding height at the step i-1) is the axial strain calculated based on the
previous step. The sandstone sample (see Figure 2.1) consists mostly of quartz grains interspersed
in a matrix of K-feldspar and various clays and smaller quantities of assorted other minerals (see
Table 2.5), and it is fairly brittle in nature. During the initial phase, i.e., steps 1 and 2 with no CO2
being present, from Equation 3 we estimate a value of Y=0.97 GPa, which indicates a mechanically
weak material.
For the subsequent steps 3-6, after step 2, both the CO2 pressure and confining pressure were
ramped upwards in a stagewise manner, as discussed previously: First the CO2 pressure was
increased by 500 psi (over a 2 min period), followed by an increase of 500 psi in the confining
pressure (over a 20 sec period). After the incubation period (step 7) and the initial CO2
depressurization step (step 8), the CO2 pressure and confining pressure were ramped downwards
(steps 9 and 10) again in a stagewise manner: In this case, the confining pressure was decreased
by 500 psi, followed by a 500 psi decrease in the CO2 pressure. During these steps, all the change
in the strain happens during the CO2 pressure increase (steps 3-6) or decrease (steps 9 and 10) part
of the step. One can then use Equation 3 to calculate an average value of Y, and these values are
shown in Figure 2.7. These values are similar to those previously measured for the same sandstone
by our team using the NER Autolab 1500 apparatus [22]. The Y values after incubation (steps 9
and 10) are, on the average (indicated in Figure 2.7 by the orange line) a bit lower than those
33

measured prior to it (steps 3-6), signifying a potential weakening of the pore structure.

Figure 2.7. Young’s modulus for the various experimental steps (the orange line indicates the average Young’s
modulus calculated before and after the 500 hr incubation experiment)
Akono et al. [17] also found in their experiments a weakening of the Mt. Simon sandstone, as
manifested by a decrease of the Young’s modulus, after incubation in CO2-saturated brine after
one week. Marbler et al. [14] and Rathnaweera et al. [15] also reported a decrease of the sandstone
elastic modulus after the sample was exposed to CO2/brine.
For the radial strain, the corresponding behavior is shown in Figure 2.8. The behavior is different
from that shown in Figure 2.4, in that after the initial changes in radial strain occurring in steps 1
and 2, the radial strain remains invariant for steps 3 - 6, signifying perhaps an anisotropy in
mechanical properties between the radial and axial directions.

34

Figure 2.8. Radial strain during the various experimental steps

Figure 2.9 shows the radial strain during the 500 hr incubation test (step 7). Again, for the first
170 hr the radial strain remains constant and equal to -0.0010. At that time, however, the radial
strain, as was the case with the axial strain in Figure 2.6, suddenly changes to -0.0013, signifying
once more an abrupt change in the mechanical state of the sandstone sample. Once more, the
incubation times involved over which these changes radial strain take place are consistent with the
time scales for geochemical alterations to take place with the same materials during flow-through
experiments reported by Da´vila et al [21].
-1.5E-03
-1.2E-03
-9.0E-04
-6.0E-04
-3.0E-04
0.0E+00
1 2 3 4 5 6 7 8 9 10
Radial strain Δr/r
0
Step number#
35

Figure 2.9. Radial strain Δr/r0 versus time during sample incubation (step 7)

For the remainder of the incubation period the radial strain, similarly to the axial strain,
undergoes additional changes which are, however, more significant in the relative magnitude of
change than those experienced by the axial strain. Post-incubation (i.e., steps 8, 9, 10) the radial
strain remains invariant (see Figure 2.8) in contrast with the axial strain behavior, again likely
signifying the presence of anisotropy in mechanical behavior between these two directions.
2.3.2. Porosity and permeability measurements
After the CO2/brine incubation test was completed, valve 6 was opened (see Figure 2.3) to
collect the brine inside the core-holder for further analysis via the IC technique, as described in
the materials and basic characterization section, see also the ion chromatography analysis section
below for further discussion of the experimental results. After completely draining the brine, the
core-holder was opened and the sandstone sample was removed and placed in a vacuum oven for
24 hr at 50 ℃. The porosity of the sample was then measured via the He pycnometry technique -
for further details about the technique, see our team’s previous work [22]. The sandstone
-1.7E-03
-1.5E-03
-1.3E-03
-1.1E-03
-9.0E-04
0 100 200 300 400 500 600
radial strain Δr/r
0
time/hr
36

permeability was measured, as described in the materials and basic characterization section. Table
2.3 reports the values for the sample porosity and permeability both before and after the sample
had been exposed to the CO2/brine. As Table 2.3 shows, the porosity and permeability of the Mt.
Simon sample both increase after exposure to CO 2/brine, but the increase in permeability is more
substantial than that for the porosity. The increase in porosity and permeability of the sandstone
sample is consistent with dissolution of the core material taking place, and is in line with the
observations of changes in the mechanical properties of the sample discussed above. However, the
relative change of porosity is larger than our previous work with a sample from the same location
[22]. This is likely due to the longer exposure time in this work compared to the study of Shi et al.
[22] resulting in greater mineral dissolution. That such dissolution causes a larger impact on
permeability rather than on the porosity can be explained by the fact that it may result in the
connection of previously disconnected pores, and in the opening of new paths that were previously
inaccessible to the N2 flow in the permeation apparatus. Furthermore, dissolution of minerals near
or in the pore throats has a larger impact on permeability than on porosity.

Table 2.3. Porosity and permeability before and after exposure to CO 2/brine
Fresh Aged
Porosity 16.0/15.8
a
22.2
Permeability/mD 9.0 30.3
a
Repeated measurement (after 2 months) to validate repeatability of the porosity measurement
method

2.3.3. Ion chromatography analysis
After the core incubation experiment, the brine that was left in the core-holder was collected
and analyzed via IC to determine the concentrations of cations and anions it contains. The analysis
37

results are shown in Table 2.4 where they are compared with the corresponding results of the fresh
brine.
Table 2.4. Cation and anion concentration in the brine before/after the incubation
Before (mg/L) After (mg/L) Change (%)
Na 45083± 69 41131± 69 -8.8
K 21501± 161 23246± 161 8.1
Mg 2000± 16 2115± 16 5.7
Ca 26491± 152 29792± 152 12.5
Sr 800± 9 862± 9 7.7
Li 20± 1 30± 1 51.4
Cl 141406± 312 125266± 312 -11.4
Br 750± 6 688± 6 -8.2

For the cations, namely K, Mg, Ca, Sr and Li, we found that their concentration had increased
upon exposure to CO2/brine, while the concentration of Na decreased. For the concentration
changes of K, Mg, Ca and Sr, our results are in accordance with our previous findings [22].
However, for the Li concentration, our results are inconsistent with our previous findings [22],
which for three different core samples from varying locations (6924 ft, 6925 ft, and 6827 ft) show
a slight decrease in Li concentration rather than the large increase we observe here. It should be
noted though that the brine used in the study of Shi et al. [22] was of a different composition
containing ~1232 ppm of Li.
The mineral composition of the Mt. Simon formation in a range of depths from 2082.7 m to
2131.5 m (6833ft to 6993 ft) was previously determined by X-ray dispersive spectroscopy (XRD)
and energy dispersive spectroscopy (EDS) [27].

In the formation, quartz and feldspar contents were
reported ranging from 40% to 80% and 13% to 22%, respectively, with clays content ranging from
5% to 29% for different samples between depths of 2082.7m to 2131.5 m (6833 ft to 6993 ft) [27].

For the depth closest to the sample studied here, at 2118.4 m (6950 ft) the study reports the core
38

composition to consist of quartz (79%), K-feldspar (15%), sericite (1%), illite-smectite (4%), iron
oxide-illite (1%), together with other trace minerals [27]. Most recently, Fuchs et al. [28]

reported
XRD analysis on a Mt. Simon core from VW1 which was extracted at exactly the same depth
(6927 ft) as the one used in our experiment. The mineral composition of the core sample, as
reported by Fuchs et al. [28] is shown in Table 2.5.

Table 2.5. Mineral composition analysis (XRD) of the Mt. Simon core at 6927 ft
Minerals Wt%
Quartz 75.7
K-feldspar 17.0
Calcite 0.8
Ankerite/Fe-dolomite Tr
Illite 2.8
Illite-smectite 3.1
Hematite 0.6
Halite Tr

The Mt. Simon sandstone at this depth consists primarily of quartz and K-feldspar, but also
contains a variety of other minerals and clays, as Table 2.5 indicates. The experimental data from
the cation analysis (other than for Li) of the used brine is, indeed, consistent with the potential
dissolution of such minerals. For example, the observed increase of the concentration of K is
consistent with the dissolution of K-feldspar and illite. The increase of Mg concentration is
consistent with dissolution of illite and illite-smectite. The increase of Ca concentration may be
caused by the dissolution of calcite, Fe-dolomite and illite-smectite. The increase of Sr
concentration is consistent with dissolution of Fe-dolomite [29]. The presence of minor quantities
of Li (compared to the other cations) in both the fresh and the used brine is not consistent with the
compositional analysis of the core in Table 2.5. It could be due to a trace amount either naturally
39

occurring or introduced during the extraction and processing of the core. For anions, we observed
a decrease for both the concentrations of Cl and Br. For the concentration change of Cl, our
previous results with the 6927 ft core indicated no change, and for the other two cores extracted
from different depths it showed an increase in one case (the 6925 ft core) and a decrease in the
other after incubation. The concentration change of Br is consistent with our previous results,
however [22].

2.4. Discussion and conclusions
The experimental findings in this paper indicate changes in the transport, pore structural
characteristics and mechanical properties of the Mt. Simon sandstone during its extended-period
exposure to CO2/brine. Specifically, the porosity of the sandstone sample increased after such an
exposure to CO2/brine, which is likely due to the dissolution of mineral phases originally found in
the sandstone. The permeability of the sandstone sample also increased, likely due to the same
cause. Such observations are in accordance with our team’s previous results [22],

and also with
results reported by a number of other Groups (e.g., Xie et al [30].). The analysis of the brine
composition before and after exposure to brine/CO2 shows an increase in the concentration of K,
Mg, Ca and Sr, which provides evidence of dissolution occurring of minerals/clays, similar to those
comprising the Mt. Simon sandstone, which supports the hypothesis that the increases in porosity
and permeability are due to such dissolution phenomena.
The mechanical properties of the sandstone during exposure to CO2/brine, were studied in situ via
strain gauges affixed to the sample. They indicate the presence of mechanical changes occurring
in the core during its incubation in the CO2/brine mixture. Estimates of the Young’s modulus before
and after exposure indicate a potential weakening of the structure. These findings are in agreement
with prior reports by our group that reported [22], in ex situ tests, a decrease of the Bulk modulus
40

and Young’s modulus (a measure of the ability of a material to withstand changes in length when
under tension or compression) of the Mt Simon sandstone samples before and after exposure to
CO2/brine. Our observations are also in line with past studies by other Groups most of which have
been reviewed in the Introduction. For example, Dimadis et al. [31] measured the tensile strength
of sandstone samples and reported a reduction of the strength of sandstone after exposure to a CO2-
water solution. Alam et al. [32] studied the effect of scCO2 injection on both the static and dynamic
modulus of a chalk core from the South Arne field via strain gauges and LVDTs. They concluded
that CO2 injection had a negative effect on the elastic stiffness properties of the rock. Rathnaweera
et al. [15] studied the microstructural changes that occur in reservoir rocks during the injection of
CO2 in deep saline aquifers. Specifically, the deformation of cylindrical sandstone specimens from
the Gosford basin were measured via an acoustic emission technique. Their results, as previously
noted, also showed a decrease in the rock’s strength upon CO2 exposure. From these past studies
and the results reported here, one may conclude, therefore, that long-term exposure of the Mt.
Simon sandstone to a CO2/brine environment may cause rock alterations, which could ultimately
result in weakening of its mechanical strength.
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[2] Evans B, Predicting CO2 injectivity properties for application at CCS sites.
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[3] Zhang W, Li YL, Xu TF, Cheng HL, Zheng Y and Xiong P, Long-term variations of CO2
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[8] Aminu MD, Nabavi SA and Manovic V, CO2-brine-rock interactions: The effect of impurities
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[10] Kitamura K, Nishizawa O, Christensen KT, Ito T and Finley RJ, Seismic and strain detection
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sequestration in the Mt. Simon sandstone formation, Midwest U.S.A. Int. J. Greenh. Gases
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[12] Gollakota S and McDonald S, Commercial-scale CCS project in Decatur, Illinois –
construction status and operational plans for demonstration. Enrgy. Proced 63:5986–5993
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[13] Bauer RA, Carney M, Finley RJ, Overview of microseismic response to CO2 injection into
the Mt. Simon saline reservoir at the Illinois Basin-Decatur Project. Int. J. Greenh. Gas Control
54: 378–388 (2016).
[14] Will R, Smith V, Leetaru HE, Freiburg JT and Lee DW, Microseismic monitoring, event
occurrence, and the relationship to subsurface geology. Enrgy. Proced 63: 4424–4436 (2014).
[15] Zhang Q, Ye W, Chen YH, Li XC and Hu SB, Mechanical behavior of sandstone pressurized
with supercritical CO2 and water under different confining pressure conditions. Int. J. Geomech
21(7): 04021100 (2021).
[16] Akono AT, Davila G, Druhan J, Shi ZF, Jessen K and Tsotsis TT, Influence of geochemical
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[17] Akono AT, Werth C, Shi ZF, Jessen K and Tsotsis TT, Advanced geomechanical model to
predict the impact of CO2-induced microstructural alterations on the cohesive-frictional
behavior of Mt. Simon sandstone. Minerals 11(1): 38 (2021).
[18] Marbler H, Erickson KP, Schmidt M, Lempp C and Pö llmann H, Geomechanical and
geochemical effects on sandstones caused by the reaction with supercritical CO2: An
experimental approach to in situ conditions in deep geological reservoirs. Environ. Earth Sci
69 (6): 1981–1998 (2013).
[19] Rathnaweera TD, Ranjith PG, Perera MSA, Haque A, Lashin A, Al-Arifi A et al., CO2-
induced mechanical behaviour of Hawkesbury sandstone in the Gosford basin: An
experimental study. Mater. Sci. Eng. A 641: 123–137 (2015).
[20] Rimmelé G, Barlet-Goué dard V and Renard F, Evolution of the petrophysical and
mineralogical properties of two reservoir rocks under thermodynamic conditions relevant for
CO2 geological storage at 3 km depth. Oil Gas Sci. Technol. – Rev. IFP 65(4): 565–580 (2010).
[21] Da´ vila G, Dalton L, Crandall DM, Garing C, Werth CJ and Druhan JL, Reactive alteration
of a Mt. Simon Sandstone due to CO2-rich brine displacement. Geochim. Cosmochim. Acta
271: 227–247 (2019).
[22] Shi ZF, Sun L, Haljasmaa I, Harbert W, Sanguinito S, Tkach M et al., Impact of Brine/CO 2
exposure on the transport and mechanical properties of the Mt. Simon sandstone. J. Petrol. Sci.
Eng 177: 295-305 (2019).
[23] Harbert W, Goodman A, Spaulding R, Haljasmaa I, Crandall D, Sanguinito S et al., CO2-
induced changes in Mt. Simon sandstone: Understanding links to post-CO2 injection
44

monitoring, seismicity, and reservoir integrity. Int. J. Greenh. Gases Control 100:103109
(2020).
[24] Labotka DM, Panno SV, Locke RA and Freiburg JT, Isotopic and geochemical
characterization of fossil brines of the Cambrian Mt. Simon sandstone and Ironton–Galesville
formation from the Illinois basin, USA. Geochim. Cosmochim. Acta 165: 342–360 (2015).
[25] Taheri A and Tani K, Use of down-hole triaxial apparatus to estimate the mechanical
properties of heterogeneous mudstone. Int. J. Rock Mech. Min. Sci 45(8): 1390-1402 (2008).
[26] Shi ZF, Sanguinito S, Goodman A, Jessen K and Tsotsis TT, Investigation of mass transfer
and sorption in CO2/Brine/Rock systems via in-situ FT-IR. Ind. Eng. Chem. Res 59(45):
20181–20189 (2020).
[27] Freiburg JT, Morse DG, Leetaru HE, Hoss RP, Yan Q, A depositional and diagenetic
characterization of the Mt. Simon Sandstone at the Illinois Basin – Decatur project carbon
capture and storage site. http://hdl.handle.net/2142/55338/[October 2014]
[28] Fuchs SJ, Espinoza DN, Lopano CL, Akono AT and Werth CJ, Geochemical and
geomechanical alteration of siliciclastic reservoir rock by supercritical CO2-saturated brine
formed during geological carbon sequestration. Int. J. Greenh. Gas Control 88: 251–260
(2019).
[29] Shearman D and Shirmohammadi N, Distribution of strontium in dedolomites from the
French Jura. Nature 223: 606–608 (1969).
[30] Xie SY, Shao JF and Xu WY, Influences of chemical degradation on mechanical behaviour
of a limestone. Int. J. Rock Mech. Min. Sci 48 (5): 741–747 (2011).
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[31] 10th International Conference on Energy and Climate Change, Impact of CO2 on mechanical
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[32] 74th EAGE Conference and Exhibition incorporating EUROPEC, Change of static and
dynamic elastic properties due to CO2 injection in North Sea chalk. Paper presented at 74th
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https://doi.org/10.3997/2214-4609.20148230/ (2012).

46

Chapter 3. Gas Loading/Unloading Experiments with the Mt. Simon
Sandstone
3.1. Introduction
Gas loading and unloading is commonly used to perform laboratory tests for measurement of
the permeability and porosity of porous rocks [1]. It also takes place during gas storage [2]. The
deformation response of a rock subjected to cyclic gas loading and unloading varies from rock to
rock due to the complex microstructures of natural materials. It can typically cause a rock to
deform, and can result the in substantial changes to rock porosity and permeability [3].
Brace et al. [4]. measured the permeability of Westerly granite via a transient method, in which
a small change of pressure was recorded. They presented measurements of permeability for a
typical crystalline rock sample as a function of the effective net stress and found that the
permeability varies markedly with the effective net stress. Hoholick et al. [5] studied the porosity
of more than 230 thin sections of cuttings, cores, and outcrop samples from St. Peter Sandstone
formation and Mt. Simon Sandstone formation in the Illinois basin. They found that porosity
decreases along the depth in both sandstones. For the Mt. Simon Sandstone, the porosity decrease
is continuous downward which may be due to increasing confining stress. David et al. [6]
investigated experimentally the dependence of permeability on confining pressure and porosity for
five sandstones with porosities ranging from 14% to 35%. From their experimental results, they
concludeded that the impacts of pressure and porosity differ significantly depending on the type
of compaction mechanism (crack closure, grain rearrangement, or pore collapse). However, the
data can often be approximated by the empirical relations: The relationship between permeability
and effective mean stress is often shown to be exponential, and for permeability vs. porosity, it is
assumed to be a power law relationship). Dana et al. [7] applied a modified version of the pulse-
47

decay method to measure the gas relative-permeability for three different typess of sandstone and
two fluids (argon and water/ethanol) when they are simultaneously injected into sandstone samples
at constant and known flow rates. Their test results show that the gas permeability is closely
dependent on pore structure parameters including pore size distribution and pore-throat to pore-
body diameter. Dong et al. [8] used an integrated permeability and porosity measurement system
to measure the stress dependent permeability and porosity of sedimentary rocks. They found that
porosity of samples studied was reduced by about 10–20% when the confining pressure was
increased from 3 to 120 MPa. For the permeability measurement, they also found that when the
confining pressure was 10 MPa, it was one to two orders of magnitude smaller than when confining
pressure was 3 MPa. Wang et al. [9] studied the effect of confining pressure on the permeability
of a granitic gneiss rock via a fluid flow triaxial test system. They found that the impact of
confining pressure on gas permeability is not significant, which is different from what is observed
with rocks with large porosity. They concluded that it may be due to the dense structure and small
porosity of the granitic gneiss sample.
In addition, one of the long-standing problems in adsorption science is to understand the
adsorption-induced deformation of microporous solids [10]. Porous rocks are usually
heterogonous and contain pores with different pore sizes. Comparing to larger pores, the solid-
fluid interaction potential in smaller pores is very high which may cause the high compression of
guest molecules. This additional force leads to the so-called adsorption-induced deformation
particularly for carbonaceous porous rocks. When it comes to phenomena in a single pore, the
internal adsorption force may be either positive or negative, depending on the type of fluid solid
interactions and the confining stress. As a result, depending on whether the stress is positive or
negative the pore may contract or expand. Kowalczyk et al. [11] proposed a model for the observed
48

deformation of an amorphous matrix can be treated as a superposition/combination of adsorbed-
induced deformations of individual stacks of slit-shaped pores.
Understanding the mechanical properties of porous rocks is of critical importance for a number
of technological applications, one of them is the geosequestration of carbon dioxide which has
received increased research interest in recent years. There is need for further study today to
improve the understanding at the micropore level of the mechanism of adsorption-induced
deformation during the storage of carbon dioxide in geologic formations. When large quantities of
carbon dioxide are injected into a geologic formation, they will produce an internal adsorption-
induced stress which may cause the rock matrix to deform (particularly for carbonaceous rocks)
and may also change the mass transfer properties of the rock. Better understanding of adsorption-
induced rock deformation during carbon dioxide storage process is of critical importance since
fluid leakage may pose environmental risks including groundwater contamination, and damage to
local vegetation, and adverse impacts on animal life and human health.
Ravikovitch et al. [12] proposed a nonlocal density functional theory (NLDFT) model to
theoretically describe the adsorption-induced deformation phenomenon. They showed that the
changes observed in experiments in the adsorbent volume are proportional to the solvation pressure
which is caused by the adsorption stress exerted on the pore walls. Kowalczyk et al. [11] suggested
a thermodynamic model of adsorption-induced deformation of microporous carbons. The model
results indicate that the elastic deformation resulting from the adsorption stress depends strongly
on the pore size. In addition, they concluded that the deformation curve is determined by the pore
size distribution. Later, Kowalczyk et al. [10] continued to study the deformation of carbonaceous
amorphous porous materials resulting from adsorption of CO2. They found that the internal
adsorption stress induced by adsorbed CO2 is very high in the micropores, which dominates sample
49

deformation upon adsorption of CO2 at their experimental conditions. Fomkin et al. [13] studied
the adsorption-induced deformation of carbon adsorbents upon adsorption of CO2. They concluded
that the adsorption-induced deformation is positive (expansion) upon the gas adsorption on the
surface of a macroporous solid when excess adsorption is positive. Günther et al. [14] studied the
impact of pore deformation on capillary condensation in nanoconfined fluids via Monte Carlo
simulations. They found that sorption-induced strains should be capable of deforming the pore
walls from their simulation results.
To the best of our knowledge, there are few attempts to date to describe adsorption-induced
deformation for the Mt. Simon sandstone, while its mass transfer properties are measured in-situ.
The aim of our research in this Chapter is to study the mechanism of adsorption-induced
deformation of a Mt. Simon sandstone sample upon adsorption of argon and CO2 at high pressures
in order investigate how the sample’s mass transfer properties change upon gas adsorption and
while experiencing confining stress. For that purpose, the mass transfer properties (porosity,
permeability) and mechanical behavior (deformation) of porous rock (sandstone) are determined
in situ under various gas atmospheres (helium, argon, and CO2) during loading/unloading
experiments. Our goal is to understand how gas adsorption and confining pressure affect the mass
transfer characteristics and mechanical properties of the porous rock, and how such changes
impact its gas storage characteristics. Of particular interest is to better understand how CO2-
induced deformation affects the bulk geomechanical properties of the sample.
3.2. Materials and experimental approach
3.2.1. Materials and basic characterization
The rock sample studied in this work is the same sample discusseded in the previous chapter
which is from the Mt. Simon sandstone that constitutes a ∼1500 ft (∼460 m) thick storage zone in
50

the Illinois Basin - Decatur Project (IBDP) [15]. In that project, a verification well (VW1) was
drilled in 2010 located 305 m (1000 ft) north of the CO2 injection well [15]. The rock sample
studied here was extracted from VW1 from a depth of 2111.4 m (6927 ft). It is a cylindrical core
sample with a size of 1” × 2”, which was prepared via liquid nitrogen drilling in the horizontal
direction (along the bedding plane) from the main core extracted (depth range between 2110.4 and
2111.4 m (6924 – 6927 ft)). After the sample has been exposed to CO2/brine for 500 hours, it was
prepared for the gas loading/unloading experiments described below.
As mentioned in the previous chapter, at the end of the CO2/brine exposure experiment, after
completely draining the brine, the core-holder was opened and the sandstone sample was removed
and placed in a vacuum oven for 24 hr at 50 ℃. Then the permeability of the sample was measured
before gas loading/unloading experiment via N2 gas flow-through experiments employing a TKA-
209 gas permeameter. Its porosity was measured via He pycnometry (schematics of the
experimental apparatuses and further experimental details can be found in the Supplementary
Information section).
3.2.2 Mechanical properties
In our experiments, three strain gauges were attached on the sandstone sample, as shown in
Figure 3.1, to measure the potential deformation in the axial direction during the gas
loading/unloading experiments.

Figure 3.1. Positioning of the strain gauges
51

Figure 3.1 shows a schematic of the overall experimental set-up. It consists of a biaxial core-
holder, a hydraulic pump, a pressure transducer, a temperature recorder and a bubble flow meter.
The hydraulic pump, employing oil as the working fluid, is used to apply the confining pressure
on the sample. Data acquisition devices (NI USB 6210 from National Instruments, USA) are used
to record the signals of the pressure transducer (PX 409 series from Omega Engineering, USA)
and the strain gauges (KFH series from Omega Engineering, USA). The sandstone core sample
was fitted with the strain gauges and then placed into the core-holder. The wires of the strain gauges
attached to the core sample, once inside the core-holder, are connected to the data acquisition
system via 3-pin feedthroughs. To avoid corrosion of the strain gauge wires as well as of the
feedthrough pins because of exposure to oil, and to prevent short-circuiting, all wires are painted
with insulation varnish.
Once the sample was installed in the core-holder, and the strain gauges were connected to the
data acquisition system, to initiate the experiments the confining pressure was raised to 500 psig
(34.5 bar) via the hydraulic pump (this and all the subsequent steps raising the confining pressure
were completed within 30 secs). Then, the state of the core was monitored for several hours via
the strain gauges to establish the experimental baseline. The confining pressure was then raised to
1000 psig (68.9 bar) within 30 secs. After that, the confining pressure was then raised to 1500 psig
(103.4 bar) within 30 secs. The helium pressure on both sides of the core was raised to 1060 psig
(this step of raising the helium pressure was completed within 2 secs), then valve 2 was closed to
run the gas (helium was tested first) loading experiment. Regarding the loading experiment, when
calculating sample’s porosity (see section 3.3 for detail), the volume between valve 2 and the core
holder system is measured as 4.28 cc with the upstream volume (volume between valve 2 and
upper side of the core holder) and downstream volume (volume between valve 2 and lower side of
52

the core holder) being 0.95 cc and 3.33 cc, respectively.
Gas (He or Argon)
Valve 1 Valve 2
Valve 5
Core
Holder
Valve 4
Valve 6
Hydraulic Pump
for confinement
Pressure
transducer
Valve 3
MFM/Bubble Flow Meter
Temperature
Reader
3-Pin Feed-through

Figure 3.2. The schematic of the experimental set-up
The state of the core was monitored via the strain gauges until the pressure on both sides of the
core reached a constant value, which in this case means a change of <0.2 psi over a 10 minutes
period. This procedure was then repeated several times: The helium pressure was raised to 1060
psig while monitoring the core behavior until the core pore pressure reaches a constant value. The
loading experiment ended when the pressure of the core reached a constant value of 1000 psig and
the core was allowed to stay in this state (under a confining pressure is 1500 psig), with the pressure
being continuously monitored via the strain gauges for an additional 20 min.
Following the above loading experiment, we then initiated the gas unloading experiment.
During this experiment, the flow rate of the gas exiting the core is measured via three mass flow
meters with different measuring ranges, see Figure 3.2, by appropriately adjusting the 3-way valve
3. During the unloading experiment, the pressure upstream of the core was measured by a gauge
while the mechanical state of the system was continuously monitored via the strain gauges. The
53

unloading experiment was stopped when the upstream pressure reached ambient conditions. After
that, the sample was evacuated for 24 hours connecting valve 1 with a vacuum pump (SCS type
from Marathon Electric, USA). Table 3.1 summarizes the above experimental procedure for the
loading/unloading experiments, for convenient reference.
Table 3.1. Experimental protocol

For the argon and CO2 loading/unloading experiment, we followed the same experimental
procedure as described above.
As noted above, throughout the whole experiment the mechanical state of the core was
monitored and recorded via three strain gauges: all of which were recording the axial strain. The
principle of operation allowing the measurement of the strain is simple, in that each strain gauge
functions as one of the resistances of a Wheatstone bridge (see supplementary material for
additional details). Further experimental details about the strain gauge measurements have been
presented in chapter 2.
3.3. Experimental results and discussion
3.3.1 Helium loading and unloading experiments
During the loading process, the chamber pressure as a function of time is shown in Figure 3.3:
Step Pore pressure/psig Confining pressure/psig Time duration
Initial State 0 0
raising confining 0 500 several hours
raising confining 0 1000 less than 30 secs
raising confining 0 1500 less than 30 secs
gas loading variable 1500 depends on the gas
gas unloading variable 1500 depends on the gas
54

Figure 3.3. Chamber pressure as a function of time for the loading experiment
Figures 3.4 to 3.8 show the pressure vs. time for each of the individual loading steps in Figure
3.3.

Figure 3.4. Chamber pressure as a function of time for the 1
st
step of the loading experiment

55

Figure 3.5. Chamber pressure as a function of time for the 2
nd
step of the loading experiment

Figure 3.6. Chamber pressure as a function of time for the 3
rd
step of the loading experiment

56

Figure 3.7. Chamber pressure as a function of time for the 4
th
step of the loading experiment

Figure 3.8. Chamber pressure as a function of time for the 5
th
step of the loading experiment
To calculate the pore volume measured by helium loading experiment, the following equation
is used:
𝑃 𝑐 𝑉 𝑐 +𝑃 𝑝 𝑉 𝑝 =(𝑉 𝑐 +𝑉 𝑝 )𝑃 𝑒𝑞
, (1)

57

where 𝑉 𝑐 is the chamber volume, which is 4.28 cc, 𝑃 𝑐 is the initial chamber pressure (psi), 𝑃 𝑝 is the
initial pore pressure (psi), 𝑃 𝑒𝑞
is the pressure (psi) at the end of the step and 𝑉 𝑝 is the pore volume.
The results are summarized in Table 3.2 shown below. The bulk volume of the sample was
measured as 25.73 cc previously. The porosity of sample measured by helium pycnometry was
measured as 22.2%
Table 3.2. Calculated pore volume and corresponding porosity
Loading cycle Calculated pore volume/cc Porosity
1 5.37 20.9%
2 5.35 20.8%
3 5.30 20.6%
4 5.32 20.7%
5 5.41 21.0%

From Table 3.2 we can see that the measured pore volumes and porosities are consistent among
the various loading steps. These values are, however, lower than the value measured by helium
pycnometry which likely signifies the impact of confining stress.
The axial strain measured by the three strain gauges during the whole He loading experiment
are shown in Figures 3.9 to 3.11.

58

Figure 3.9. Axial strain measured by gauge 1 (attached on the top of the sample)

Figure 3.10. Axial strain measured by gauge 2 (attached on the middle of the sample)

59

Figure 3.11. Axial strain measured by gauge 3 (attached on the bottom of the sample)

From Figure 3.9 and Figure 3.10, one can see that the strain increases as the pore pressure inside
the sample increases, as expected, since the confining pressure stays constant and thus the net
stress decreases. However, strain gauge 3 did not record similar increase in strain, which may
indicate localized or heterogeneous mechanical properties of sandstones.
For the helium unloading experiment, the upstream pressure as a function of time is shown in
Figure 3.12.

60

Figure 3.12. Upstream chamber pressure recorded as a function of time

The flow rate measured at the downstream of the core holder via a series of three MFM’s is
shown in Figure 3.13. The behavior for both the upstream pressure and the discharge flow rate are
consistent with what we would expect for a non-adsorbing gas like He.
The strain gauge results recorded during the unloading experiment are shown in Figures 3.14
to 3.16. From Figure 3.14, one can see that after an initial drop in the strain, which is consistent
with the pressure drop decrease at the same location (and thus an increase in the net stress), see
Figure 3.12, the strain first increased and then remained constant for the duration of the whole
experiment. For gauge 2, which is located in the middle of the core sample, one can see that the
strain decreased initially up to a certain time and then remained invariant for the remainder of the
unloading experiment. Gauge 3, on the other hand, did not detect much of any strain change.
which again may indicate localized or heterogeneous mechanical properties of sandstones.

61

Figure 3.13. Downstream flow rate recorded as a function of time

Figure 3.14. Axial strain measured by gauge 1 (attached on the top of the sample)
62

Figure 3.15. Axial strain measured by gauge 2 (attached on the middle of the sample)

Figure 3.16. Axial strain measured by gauge 3 (attached on the bottom of the sample)
3.3.2 Argon loading and unloading experiments
For the argon loading experiment, the chamber pressure as a function of time for the whole
loading process is shown in Figure 3.17. The pressure as a function of time for each step of the
loading process is shown in Figure 3.18 to 3.22 (Note that due to experimental limitations the
63

initial and final pressures for each step are somewhat different than those for the He experiment,
shown in Figure 3.3).

Figure 3.17. Chamber pressure recorded as a function of time

Figure 3.18. Chamber pressure recorded as a function of time for the 1
st
loading step
64

Figure 3.19. Chamber pressure recorded as a function of time for the 2
nd
loading step

Figure 3.20. Chamber pressure recorded as a function of time for the 3
rd
loading step

65

Figure 3.21. Chamber pressure recorded as a function of time for the 4
th
loading step

Figure 3.22. Chamber pressure recorded as a function of time for the 5
th
loading step
The axial strains measured are shown in Figures 3.23 to 3.25. All three gauges show an initial
increase in strain consistent with the decrease in the net stress (due to the increase in the pore
66

pressure under constant confining pressure) up to a certain time, and remain fairly constant after
that time.

Figure 3.23. Axial strain measured by gauge 1 (attached on the top of the sample)

Figure 3.24. Axial strain measured by gauge 2 (attached on the middle of the sample)

67

Figure 3.25. Axial strain measured by gauge 3 (attached on the bottom of the sample)
For the argon unloading experiment, the upstream pressure as a function of time is shown in
Figure 3.26 and the flow rate measured downstream of the core holder is shown in Figure 3.27.

Figure 3.26. Upstream chamber pressure recorded as a function of time

68

Figure 3.27. Downstream flow rate recorded as a function of time
Compared to the helium unloading experiment, it is clear that it takes longer time for the argon
to deplete from the sandstone sample which is, likely, be due to the stronger adsorption affinity of
argon but also its slower mass transfer rate out of the core. Consistent with the pressure data, the
flow rate of argon out of the core is also slower than that of helium.
The strain gauge results recorded during the unloading experiment are shown in Figures 3.28 to
Figure 3.30. Gauge 1 and 3, following some initial perturbation, which are likely due to plastic
rearrangements of the quartz grains, exhibit a continuous decrease in strain which is consistent
with the fact that the pore pressure at these two locations also monotonically decreases as a
function of time resulting an increasing net strain. Strain gauge 2 in the middle of the core increases
with time, which may indicate localized or heterogeneous mechanical properties of the core.
69

Figure 3.28. Axial strain measured by gauge 1 (attached on the top of the sample)

Figure 3.29. Axial strain measured by gauge 2 (attached on the middle of the sample)

70

Figure 3.30. Axial strain measured by gauge 3 (attached on the bottom of the sample)
3.3.3 CO2 loading and unloading experiments
For the CO2 loading experiment, the chamber pressure as a function of time for the whole
loading process is shown in Figure 3.31. The chamber pressure as a function of time for each
loading step is shown in Figures 3.32 to 3.36. It is clear from these figures, that the criterion of
waiting for 10 min with a pressure change of <0.2 psi to terminate the loading step is not sufficient
to establish a steady state pressure condition during loading of CO2, as it was previously the case
for the He loading experiment.
The axial strain measurements are shown in Figures 3.37 to 3.39. The strain gauges 1 and 2
show an initial increase in strain, consistent with the increase in pore pressure (and accompanying
decrease in net stress) until a certain time, and stay fairly constant after that until around 12 hours,
when there is a dramatic change of strain which may be due to adsorption-induced sudden
deformation of the sample. For gauge 3, there is again initially a small increase in strain, but a slow
71

downward trend after until again around 12 hours when a similar abrupt change takes place
signifying a sudden potentially sorption-induced sample deformation.

Figure 3.31. Chamber pressure recorded as a function of time

Figure 3.32. Chamber pressure recorded as a function of time for the1
st
loading step

72

Figure 3.33. Chamber pressure recorded as a function of time for the 2
nd
loading step

Figure 3.34. Chamber pressure recorded as a function of time for the 3
rd
loading step

73

Figure 3.35. Chamber pressure recorded as a function of time for the 4
th
loading step

Figure 3.36. Chamber pressure recorded as a function of time for the 5
th
loading step
74

Figure 3.37. Axial strain measured by gauge 1 (attached on the top of the sample)

Figure 3.38. Axial strain measured by gauge 2 (attached on the middle of the sample)

75

Figure 3.39. Axial strain measured by gauge 3 (attached on the bottom of the sample)
For the CO2 unloading experiment, the upstream pressure recorded as a function of time is
shown in Figure 3.40:

Figure 3.40. Upstream chamber pressure recorded as a function of time
The flow rate measured at the downstream of the core holder is shown in Figure 3.41:
76

Figure 3.41. Downstream flow rate recorded as a function of time
Compared to argon unloading experiment, it is clear that it takes longer time for CO2 to deplete
from the sandstone sample potentially signifying a stronger adsorption affinity of CO2. The CO2
flow rate during depletion during the initial phase (the first 0.4 hr or so) is higher than that of Ar,
which is also consistent with the larger quantity of CO2 stored in the pores.
The strain gauge results recorded during the unloading experiment are shown in Figures 3.42 to
3.44. In the initial stage of unloading up to ~ 3 hr, the strain indicated by all gauges stays fairly
constant. Beginning at the 3 hr, all gauges indicate a significant change in axial strain potentially
due to desorption-induced core deformation.
77

Figure 3.42. Axial strain measured by gauge 1 (attached on the top of the sample)

Figure 3.43. Axial strain measured by gauge 2 (attached on the middle of the sample)

78

Figure 3.44. Axial strain measured by gauge 3 (attached on the bottom of the sample)
3.4. Different gases loading experiment comparison
To compare the results of the loading experiments with the different gases (He, Ar, and CO2),
we calculated the moles of gas loaded into the core sample during each loading cycle. To calculate
the number of moles of gas loaded in the core sample during each step, we used the following
equation:
𝜌 𝑖𝑐
𝑉 𝑐 =𝜌 𝑓𝑐
𝑉 𝑐 +𝑛 𝑖 , (2)

where, 𝑉 𝑐 (L)is the chamber volume, 𝜌 𝑖𝑐
(mol/L) is the initial gas density (from NIST) with
respect to the initial chamber pressure (psi), 𝜌 𝑓𝑐
(mol/L) is the final gas density (from NIST) with
respect to the final chamber pressure (psi) and 𝑛 𝑖 (mol) is the amount of gas loaded into the core
during each step. Tables 3.3 to 3.5 summarize the findings.

79

Table 3.3. Cumulative number of moles of He expanded into the core during each loading cycle
Loading cycle Initial pressure/psi Final pressure/psi Moles of gases in the core/mol
1
1078.8 486.8 0.0062
2
1055.6 739.7 0.0095
3
1063.3 884.2 0.0114
4
1071.6 967.8 0.0124
5
1084.8 1019.5 0.0131

Table 3.4. Cumulative number of moles of Ar expanded into the core during each loading cycle
Loading cycle Initial pressure/psi Final pressure/psi Moles of gases in the core/mol
1
1035.0 559.8 0.0054
2
1021.6 771.6 0.0082
3
1009.9 873.8 0.0098
4
999.4 926.7 0.0106
5
1003.6 964.9 0.0111

Table 3.5. Cumulative number of moles of CO 2 expanded into the core during each loading cycle
Loading cycle Initial pressure/psi Final pressure/psi Moles of gases in the core/mol
1
998.5 705.7 0.0064
2
983.7 820.3 0.0102
3
983.5 878.0 0.0128
4
981.7 913.8 0.0145
5
983.5 934.9 0.0157

Figure 3.45 compares the quantities of gas loaded in the pore space as a function of the final
pressure at the completion of each step. When comparing the quantities of He loaded into the core
they are higher than the corresponding quantities of Ar at the same pressure. This likely reflects
the slower rates of mass transfer (uptake) into the core. It is also possible, that when each step was
stopped (based on the initial criterion of terminating the step after 10 min if the pressure changed
less than 0.2 psi) the loading into the core had not been completed. As discussed previously, this
is clearly the case for CO2, as indicated from the dynamic loading curves. Despite this fact, at the
end of the complete loading experiment, the quantity of CO2 loaded into the core is higher than
that of both He and Ar, reflecting the higher adsorption rates of CO2 into the material.
80

Figure 3.45. Gases amount in the core sample as a function of final pressure
To highlight the importance of the role that mass transfer plays during the loading phase we plot
in Figure 3.46 the pressure profiles during the 1
st
loading cycle for the three different gases. The
difference in mass transfer rates is clear form this Figure with the larger molecules transported at
much slower rates.

Figure 3.46. Comparisons of pressure drop for three gases loading experiment
81

3.5. Modeling of experimental observations
Figure 3.47. Illustration of the BPM for the cylindrical sandstone for modeling purposes
To model our experimental results, a dual porosity model will be applied. The figure to represent
the model is shown above. We first derive the mass balance equation for the mesopore region as
follows:
Assume the cross-sectional area of the core sample is A, and Δz is the length of the differential
slice of the core sample (AΔz represents its differential volume).
The material balance for the mesoporous region is:
𝜕 (𝐴𝛥𝑧 𝜀 𝑀 𝐶 𝑀 )
𝜕𝑡
+(1−𝜀 𝑀 )
𝜕 (𝐴𝛥𝑧 𝜀 𝜇 𝐶 𝜇 ̅̅̅̅̅̅
+𝐴𝛥𝑧 (1−𝜀 𝜇𝑜
)𝜌 𝑠 𝐶 ̅
𝑖)
𝜕𝑡
+(𝐹 𝑍 +𝛥𝑍
−𝐹 𝑍 )𝐴 𝜀 𝑀 =0 , (3)

Dividing both sides of equation (3) by 𝐴𝛥𝑧 and letting 𝛥𝑧 → 0, then equation (3) becomes:

V
Microparticle which
contains micropores
Void between microparticles
contributes to the mesopores
82

𝜕 (𝜀 𝑀 𝐶 𝑀 )
𝜕𝑡
+(1−𝜀 𝑀 )
𝜕 (𝜀 𝜇 𝐶 𝜇 ̅̅̅̅̅̅
+(1−𝜀 𝜇𝑜
)𝜌 𝑠 𝐶 ̅
𝑖)
𝜕𝑡
+𝜀 𝑀 𝜕𝐹
𝜕𝑧
=0 , (4)

In the above equation, 𝜀 𝑀 is the mesoporosity. 𝜀 𝜇𝑜
is the initial microporosity and 𝜀 𝜇 is the
microporosity (both defined with respect to the volume of the microsphere and not the total volume
of the sample), 𝜌 𝑠 is the skeletal density of the sandstone sample (kg.m
-3
) which is the value of the
mass of the sandstone sample (under vacuum) divided by the sample skeletal volume, 𝑧 is the
spatial co-ordinate (m), CM is the free gas concentration (mol.m
3
) in the mesopore region, 𝐶 𝜇 is the
free gas concentration (mol.m
3
) in the micropore region, 𝐶 𝑖 is the equilibrium gas concentration
(mol.kg
-1
) adsorbed in the micropore region. 𝐶 ̅
𝜇 and 𝐶 ̅
𝑖 are the volume-averaged concentrations at
position z and they can be calculated via equation (5) and (6) as following:
𝜀 𝜇 𝐶 𝜇 ̅̅̅̅̅̅
=
3
𝑅 𝜇 3
∫ 𝜀 𝜇 𝑟 2
𝐶 𝜇 𝑑𝑟 𝑅 𝜇 0
, (5)

𝐶 ̅
𝑖 =
3
𝑅 𝜇 3
∫ 𝑟 2
𝐶 𝑖𝑑𝑟 𝑅 𝜇 0
, (6)

where, Rμ is the radius of the microparticle (m).
In equation (4), F is the gas flux with units of mol/m
2
.s. If we apply the dusty gas model to
describe such transport, F is described by the following equation:
𝐹 =−(
𝐷 𝑀 𝑅𝑇
+
𝑃𝐵 𝜇𝑅𝑇 )
𝜕𝑝
𝜕𝑧
, (7)
Then, equation (4) becomes:
𝜕 (𝜀 𝑀 𝐶 𝑀 )
𝜕𝑡
+(1−𝜀 𝑀 )
𝜕 (𝜀 𝜇 𝐶 𝜇 ̅̅̅̅̅̅
+(1−𝜀 𝜇𝑜
)𝜌 𝑠 𝐶 ̅
𝑖)
𝜕𝑡
=𝜀 𝑀 𝜕 𝜕𝑧
((
𝐷 𝑀 𝑅𝑇
+
𝑃 𝑀 𝐵 𝜇𝑅𝑇 )
𝜕 𝑃 𝑀 𝜕𝑧
) , (8)
83

Assuming ideal gas law (a good assumption for He and Ar, but for CO2, the following equation
must be modified accordingly using an appropriate Equation of State), we have the following
equation:
𝑅 𝑔 𝑇 𝐶 𝑀 =𝑃 𝑀 , (9)

where, PM (Pa) is the gas pressure in the mesoporous region.
If we substitute PM in equation (8), then:
𝜕 (𝜀 𝑀 𝐶 𝑀 )
𝜕𝑡
+(1−𝜀 𝑀 ){
𝜕 (𝜀 𝜇 𝐶 𝜇 ̅̅̅̅̅̅
)
𝜕𝑡
+(1−𝜀 𝜇𝑜
)𝜌 𝑠 𝜕 𝐶 ̅
𝑖 𝜕𝑡
}=𝜀 𝑀 𝜕 𝜕𝑧
((𝐷 𝑀 +
𝑅 𝑔 𝑇 𝐶 𝑀 𝐵 𝜇 )
𝜕 𝐶 𝑀 𝜕𝑧
) , (10)
In the above equation, DM is the Knudsen diffusivity (m
2
.s
-1
), B is the bulk-flow parameter (m
2
),
T is the temperature of the system (K), μ is the viscosity (Pa.s), and Rg is the universal gas constant
(m
3
.Pa.K
-1
.mol
-1
). In Eqn. (10) the first term on the left describes the accumulation of gas in the
mesopore gas phase, the second and third term describe the accumulation of gas including free gas
and adsorbed gas in the microporous inclusions. The first term on the right describes the Knudsen
(slip-flow) mass transfer term, and the second term is the convective flow contribution.
The material balance in the microporous region for a gas can be written as:
𝜕 (𝐶 𝜇 𝜀 𝜇 4π𝑟 2
𝛥𝑟 )
𝜕𝑡
+
𝜕 (𝐶 𝑖(1−𝜀 𝜇𝑜
)4π𝑟 2
𝛥𝑟 𝜌 𝑠 )
𝜕𝑡
=
𝜀 𝜇 4π(𝑟 2
𝐷 𝑖 𝜕 𝐶 𝜇 𝜕𝑟
@𝑟 𝜇 −(𝑟 +𝛥𝑟 )
2
𝐷 𝑖 𝜕 𝐶 𝜇 𝜕𝑟
@(𝑟 𝜇 +𝛥𝑟 )
), (11)

If we divide both sides of equation (11) by 4π𝑟 2
and let 𝛥𝑟 → 0, then equation (11) becomes:
𝜕 (𝐶 𝜇 𝜀 𝜇 )
𝜕𝑡
+(1−𝜀 𝜇𝑜
)𝜌 𝑠 𝜕 𝐶 𝑖 𝜕𝑡
=
𝐷 𝑖 𝑟 𝜇 2
𝜕 𝜕 𝑟 𝜇 (𝜀 𝜇 𝑟 𝜇 2
𝜕 𝐶 𝜇 𝜕 𝑟 𝜇 ) , (12)
84

where, Di is the diffusivity (m
2
.s
-1
) and rμ is the spatial variable of the microparticle. If we assume
gas adsorption in the micropores follows the Langmuir adsorption model, we have:
𝐶 𝑖 =𝐶 𝑖 𝑚𝑎𝑥
𝐾 𝐴 𝐶 𝜇 1+𝐾 𝐴 𝐶 𝜇 , (13)

where, KA is the adsorption equilibrium constant and 𝐶 𝑖 𝑚𝑎𝑥
(mol/kg) is the maximum gas sorption
concentration. Then equation (8) can be written as:
𝜕 (𝐶 𝜇 𝜀 𝜇 )
𝜕𝑡
+(1−𝜀 𝜇𝑜
)𝜌 𝑠 𝐶 𝑖 𝑚𝑎𝑥
𝐾 𝐴 (1+𝐾 𝐴 𝐶 𝜇 )
2
𝜕 𝐶 𝜇 𝜕𝑡
=
𝐷 𝑖 𝑟 𝜇 2
𝜕 𝜕 𝑟 𝜇 (𝜀 𝜇 𝑟 𝜇 2
𝜕 𝐶 𝜇 𝜕 𝑟 𝜇 ) , (14)
where 𝜀 𝜇 is given by
𝜀 𝜇 =𝜀 𝜇𝑜
−
(1−𝜀 𝜇𝑜
)𝜌 𝑠 𝐶 𝑖 𝜌 𝛼 , (15)
where, 𝜌 𝛼 (can be calculated by Langmuir parameters) is the molar density of the adsorbed phase
(mol/m
3
).
The initial and boundary conditions consistent with the gas loading experiment are:
𝑡 =0: 𝐶 𝑀 =0, 𝐶 𝜇 =0 , (16)

𝑟 𝜇 =𝑅 𝜇 : 𝐶 𝜇 =𝐶 𝑀 (𝑧 ), 𝑟 𝜇 =0∶
𝜕 𝐶 𝜇 𝜕 𝑟 𝜇 =0 , (17)

𝑧 =0: 𝐶 𝑀 =𝐶 𝑜 , 𝑧 =𝐿 : 𝐶 𝑀 =𝐶 𝑜 , (18)
For the gas unloading experiment, the initial and boundary conditions are:
𝑡 =0: 𝐶 𝑀 =𝐶 𝑜𝑜
, 𝐶 𝜇 =𝐶 𝑜𝑜
, (19)

𝑟 𝜇 =𝑅 𝜇 : 𝐶 𝜇 =𝐶 𝑀 (𝑧 ), 𝑟 𝜇 =0∶
𝜕 𝐶 𝜇 𝜕 𝑟 𝜇 =0 , (20)

85

𝑧 =0: 𝐶 𝑀 =𝐶 𝑜 , 𝑧 =𝐿 : 𝐶 𝑀 =0 , (21)
In the above equations, Co denotes the bulk phase gas concentration (mol.m
-3
) (which during
the loading/unloading experiments changes as a function of time), and 𝐶 𝑜𝑜
is the bulk phase gas
concentration (mol.m
-3
) at the beginning of gas unloading experiment. L is the length of the core.
From the helium loading/unloading experiments, one can calculate the total porosity of the
sample 𝜀 described by the following equation:
𝜀 =𝜀 𝑀 +(1−𝜀 𝑀 )𝜀 𝜇𝑜
, (22)

From the BET results, we can first calculate the (1−𝜀 𝑀 )𝜀 𝜇𝑜
term, and then we can calculate
𝜀 𝑀 . Also, from the BET results for the sample, we can also calculate the average pore size of the
micropores 𝑑 𝑝 µ
(which is ~5 nm for this particular sandstone sample). From equations (10) and
(12), for helium we have two parameters we need to fit which are the average pore size of the
mesopores, 𝑑 𝑝𝑀
(𝐷 𝑀 and 𝐵 can be calculated from average pore size, see equation (23) to (25))
and the radius 𝑅 𝜇 of the microspheres. 𝑑 𝑝𝑀
can be calculated from the initial time data where
transport is primarily in the mesopores while 𝑅 𝜇 can be calculated from the longer time data when
He begins to enter the micropores.
𝐵 =0.0389
𝑑 𝑝𝑀
2
𝜏 2
𝜀 𝑀 0.1
, (23)
𝐷 𝑀 =
1
3
𝜀 𝑀 𝑑 𝑝𝑀
𝜏 √
8𝑅𝑇
𝜋𝑀
, (24)

𝜏 =
1.25
𝜀 𝑀 1.1
, (25)
86

For argon, from the analysis of the helium loading/unloading experiments, we can get the
average pore size of the mesopore region (𝑑 𝑝𝑀
) and the radius of the micropore spheres 𝑅 𝜇 . The
diffusivity 𝐷 𝑖 can be calculated from the average pore size in the micropore region 𝑑 𝑝 µ
, see
equation (26). Since Argon can adsorb in the micropores, we have then one additional parameter
to fit which is 𝐾 𝐴 (𝐶 𝑖 𝑚𝑎𝑥
can be calculated from the gas loading/unloading experiment).
𝐷 𝑖 =
1
3
𝜀 𝜇 𝑑 𝑝 µ
𝜏 √
8𝑅𝑇
𝜋𝑀
, (26)

For CO2, similar to argon, since CO2 can adsorb in the micropores, and assuming that CO2 does
not swell the microspheres, we have one additional parameter to fit which is 𝐾 𝐴 (again, 𝐶 𝑖 𝑚𝑎𝑥
can
be calculated from the gas loading/unloading experiment). If the CO2 causes a swelling of the
microspheres the model must be modified accordingly to account for that.
3.6 References
[1] Yang DS, Wang W, Chen, WZ, Wang SG and Wang XQ, Experimental investigation on the
coupled effect of effective stress and gas slippage on the permeability of shale. Sci Rep 7:
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[2] 45th U.S. Rock Mechanics/Geomechanics Symposium, Investigating the Effect of Fatigue On
Fracturing Resistance of Rocks Subjected to Cyclic Loading. Paper presented at the 45th U.S.
Rock Mechanics/Geomechanics Symposium, San Francisco.
https://onepetro.org/ARMAUSRMS/proceedings-abstract/ARMA11/All-ARMA11/ARMA-
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[3] 54th U.S. Rock Mechanics/Geomechanics Symposium, Stress-Dependent Permeability and
Porosity in Three Forks Carbonate Reservoir, Williston Basin. Paper presented at the 54th U.S.
87

Rock Mechanics/Geomechanics Symposium, physical event cancelled.
https://onepetro.org/ARMAUSRMS/proceedings-abstract/ARMA20/All-ARMA20/ARMA-
2020-1742/450703.
[4] Brace WF, Walsh JB and Frangos WT, Permeability of granite under high pressure. J. Geophys.
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[5] Hoholick JD, Metarko T and Potter PE, Regional Variations of Porosity and Cement: St. Peter
and Mount Simon Sandstones in Illinois Basin. Am Assoc Pet Geol Bull 68(6): 753–764(1984).
[6] David C, Wong TF, Zhu WL and Zhang JX, Laboratory measurement of compaction-induced
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[7] Dana E and Skoczylas F, Experimental study of two-phase flow in three sandstones. I.
Measuring relative permeabilities during two-phase steady-state experiments. Int. J. Multiph
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[8] Dong JJ, Hsu JY, Wu WJ, Shimamoto TS, Hung JH, Yeh EC et al., Stress-dependence of the
permeability and porosity of sandstone and shale from TCDP Hole-A. Int. J. Rock Mech. Min.
Sci 47(7): 1141-1157(2010).
[9] Wang W, Zheng Z, Wang RB, Wang H and Xu W, Experimental study of permeability
properties of granitic gneiss under different stress paths. Chin. J. Rock Mech. Eng 35(2): 260-
267(2016).
[10] Kowalczyk P, Furmaniak S, Gauden PA and Terzyk AP, Carbon dioxide adsorption-induced
deformation of microporous carbons. J. Phys. Chem. C 114(11): 5126-5133(2010).
88

[11] Kowalczyk, P, Ciach A and Neimark AV, Adsorption-induced deformation of microporous
carbons: pore size distribution effect. Langmuir 24(13): 6603-6608(2008).
[12] Ravikovitch PI and Neimark AV, Density functional theory model of adsorption on
amorphous and microporous silica materials. Langmuir 22(26): 11171–11179(2006).
[13] Fomkin AA, Shkolin AV, Pulin AL, Men’shchikov IE and Khozina EV, Adsorption-induced
deformation of adsorbents. Colloid J 80: 578–586(2018).
[14] Gü nther G, Prass J, Paris O and Schoen M, Novel insights into nanopore deformation caused
by capillary condensation. Phys. Rev. Lett 101(8): 086104-086107(2008).
[15] Labotka DM, Panno SV, Locke RA and Freiburg JT, Isotopic and geochemical
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formation from the Illinois basin, USA. Geochim. Cosmochim. Acta 165: 342–360 (2015).

89

Chapter 4. Future work
Sorption phenomena are of key importance to most research activities related to sandstone and
shale-gas systems. The experimental and modeling efforts presented in the preceding sections have
investigated the interaction between Mt. Simon Sandstone and various gases with and without
brine present in the pore space. The workflow, including simultaneous investigation of mass
transfer and fluid/rock interactions may be extended directly to investigate shale-gas systems
where water-based fracturing fluids are commonly applied and/or connate water resides in the pore
spaces prior to development.
One of the most important unconventional resources, shale gas, has a significant potential for
wide distribution/consumption, not only as a fuel but also as a feedstock to the petrochemical
industry. Development of shale gas resources, in the US and internationally, has led to increased
interest in and demand for a solid understanding of transport/geomechanical characteristics of
shales. The Eagle Ford formation in the United States has experienced dramatic production
increases since 2010. The geomechanical/transport properties when CO2 is used as a fracturing
fluid of eagle ford shales are rarely studied. A future study could focus on investigating how gas
adsorption will affect the mass transfer properties of the Eagle Ford shales and relate sorption
behaviors to the bulk mechanical properties by measuring the sample deformation during the
experiments (as discussed in this thesis).
An outline for a further study of the transport and geomechanical properties of the Eagle Ford
shale should start with a detailed characterization of relevant samples. The characterization should
include a careful delineation of porosity and permeability, including relevant average pore sizes in
micro/mesopores. After that, the shale sample could be studies in a biaxial core holder, where the
pore volume and transport behavior can be measured via He gas expansion/loading experiment.
90

Mass transfer parameters (including viscous flow parameters, B, and Knudsen diffusivity Dm) of
the shale core sample can be interpreted by recording the upstream Helium pressure of the core
sample during the gas loading experiment. Helium flow rate measurements during a gas unloading
experiment will help to validate the parameters based on simulation of the mass transfer process.
The deformation of the sample can be measured via strain gauges during the He gas
loading/unloading processes (as discussed in this thesis). The effects of gas adsorption in a shale
sample, and the relation to mass transfer characteristics can be studied via experiments with
Ar/CO2. Most importantly, behavior of supercritical CO2 should be studied in terms of mass
transfer and mechanical properties of the shale: CO2 is a candidate to replace water-based
fracturing fluids to limit fresh-water consumption during resource developments. Accordingly, the
effects of CO2 adsorption on geomechanical property must be carefully studied. To facilitate a
better understanding of the potential volumetric swelling of shale and the impact of mass transfer
parameters, tandem experiments with e.g., a microbalance to directly measure the change in shale
sample mass associated with sorption is also recommended in the future experiments.

91

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101

Appendix. Supplementary information
The porosity of the sandstone sample was measured by the helium pycnometry method, while
its permeability was measured with the N2 gas flow-through method. The deformation of the
sandstone was measured in situ by installation of strain gauges along the core’s body and the brine
composition was analyzed by ion chromatography. Additional details for these techniques are
provided below:
A1 - Porosity
The porosity of the rock sample was measured via helium pycnometry. A schematic, as well as
a photograph, of the set-up are shown in Figure A1.

Figure A1. Schematic view (right) and photograph (left) of the porosity measurement setup
The following discussion describes the experimental procedure:
1. The volume of the reference chamber Vr, the sample chamber Vs and the rock sample volume
Vb are measured before the porosity experiments.
2. Open Valve 3 (Valve 2 is closed) and evacuate the sample chamber (with the sandstone sample
inside the sample chamber) via the vent.
102

3. Open Valve 1 and load helium into the reference chamber. Close Valve 1 and wait until the
pressure becomes constant. Record the pressure as P1.
4. Open Valve 2 and let helium expand into the sample chamber. Wait until the pressure becomes
constant. Record the pressure as P2.
The porosity of the sandstone sample is calculated by the equation below (we assume that the
helium under the experimental condition follows the ideal gas law):
𝑃𝑜𝑟𝑜𝑠𝑖𝑡𝑦 =
𝑉 𝑣 𝑉 𝑏 =1−
(1−
𝑃 1
𝑃 2
)∗𝑉 𝑟 𝑉 𝑏 +𝑉 𝑆 𝑉 ⁄ , (A1)

where Vv is the effective volume of the pores
A2 - Permeability
The permeability of a rock sample is measured with the N2 gas flow-through method. A
schematic of this set-up is shown in Figure A2.
103

Figure A2. Schematic of the experimental apparatus for permeability measurements
The following discussion describes the experiment procedure:
1. Apply the confining pressure (200 psig) to the core via the air cylinder.
2. Adjust the pressure of nitrogen via the regulator, in a stepwise manner.
3. Record the pressure with the pressure gauge and measure the flow rate with the bubble-flow
meter (or mass-flow meter).
4. For each pressure set by the pressure regulator, measure the flow rate three times and record the
average flow rate.
The permeability is calculated by the equation below:
𝐽𝐿
𝛥𝑃
=(
𝐾 0
𝑅𝑇
+
𝐵 0
𝑃 𝑎𝑣𝑔 𝜇𝑅𝑇 ) , (A2)
Pressure Gauge
Nitrogen Tank Air Tank
Pressure Regulator
Core Holder
Mass Flow Meter
104

where
J: Flux through the sample, mol/m
2
/s
μ: The viscosity, Pa*s
Pavg: Average of the upstream and downstream pressures, Pa
T: Temperature, K
R: Universal gas constant, m
3
PaK
-1
mol
-1

B0: convective factor, m
2

K0: Knudsen factor, m
2
/s
We then plot JL/△P versus Pavg and determine the value of B0 and K0 from the slope and
intercept. B0 is the liquid permeability that is reported in this paper.

A3 – Wheatstone bridge
Figure A3 illustrates the principle of the Wheatstone bridge.

Figure A3. Schematic of Wheatstone bridge
During operation, one records the voltage output of the strain gauge, 𝑢 𝑜 , which relates to the
105

resistance characteristics of the bridge according to:

𝑢 𝑜 =𝑢 𝑖𝑛
∗{
𝑅 𝑆 +𝛥𝑅𝑠 𝑅 𝑆 +𝛥𝑅 𝑠 +𝑅 3
−
𝑅 2
𝑅 1
+𝑅 2
} , (A3)

In Eqn. A3, 𝑢 𝑖𝑛
is the excitation voltage of the Wheatstone bridge (in this experiment, 𝑢 𝑖𝑛
=
0.908 V), Ri is the resistance of individual resistors in the Wheatstone bridge (here R1=R2=R3=120
Ohm), Rs is the initial resistance of the strain gauge itself (Rs = 120 Ohm), and ΔRs the change in
the strain gauge’s resistance caused by its deformation. The strain 𝜀 , either in the axial or the radial
direction, relates to the ∆Rs of the corresponding gauge via the following equation:
𝜀 =(
𝛥𝑅𝑠 𝑅 𝑆 ) 𝐺𝐹 ⁄ , (A4)
where GF is the so-called gauge factor (GF=1.51 for the strain gauges employed here).

A4 – Ion Chromatography
The concentration of cations and anions in the original brine, as well as of the various “reacted”
brine solutions was determined via Ion Chromatography (IC) by employing an ICS-2100 IC
system (Dionex). The IC analysis is performed by injecting 25 µ L of diluted sample into the IC
instrument, which is equipped with an Ion Pac CS12A column for cation analysis and an Ion Pac
AS14 column for anion analysis. 20 mM (molar concentration) methanosulfonic acid is used as
the eluent for the cations and 3.5 mM (Na2CO3 + 1 mM NaHCO3) is used as the eluent for the
anions. The effluent flow rate for cations is set to 0.8 mL/min while that for anions is 1.2 mL/min.
The suppressor voltage is adjusted to 42 mA for best peak separation for cations, and 24 mA for
anions. Fluka water is used to prepare all diluted solutions for the IC tests. Standard solutions from
106

Dionex were used to calibrate the instrument using the absolute calibration method for 3 anions
(Cl
-
, Br
-
, and SO4
2-
) and 6 cations (Li
+
, Ca
2+
, Mg
2+
, K
+
, Sr
2+
and Na
+
). From the peaks of the
standard solution, the cations and anions of brine can be determined. Figure A4 shows the
schematic of the IC set-up.
Figure A4. Schematic of the IC set-up
A5 – Simulation Method
Besides the dual porosity model, another model we may apply is described in this section. To
simulate the pressure profile (chamber and core) and downstream gas flow rate during the gas
unloading experiment, finite difference method is applied. The core sample is divided into 100
layers (see Figure A5) and for each piece, the pressure for each layer is simulated by dusty gas
model.
107

Figure A5. Model of the shale core sample
A5.1 Governing equation for the core
𝜕𝑐
𝜕𝑡
+∇⋅𝐹 =0 , (A5)
𝐹 =−(
𝐾 0
𝑅𝑇
+
𝑃𝐵 0
𝜇𝑅𝑇 )
𝜕𝑝
𝜕𝑧
, (A6)
where,
c: molar concentration of gas
F: flux through the sample
K0, Knudsen diffusivity
R: universal gas constant
P: pore pressure
B0: convective factor (liquid permeability)
µ: gas viscosity
T: temperature of the system
If assuming gas which flow through the core sample follows the ideal gas law, equation (A5)
becomes to
1
𝑅𝑇
𝜕𝑝
𝜕𝑡
+∇⋅𝐹 =0 , (A7)
n=1
n=100
108

Initial and boundary conditions of equation (A7) are:
𝑝 (𝑧 ,𝑡 =0)=𝑝 𝑖𝑛𝑖𝑡𝑖𝑎𝑙
𝐹 (𝑧 =0,𝑡 )= −
𝑑 𝑛 𝐻 ɛ𝐴𝑑𝑡
𝐹 (𝑧 =𝐿 ,𝑡 )=
𝑑 𝑛 𝐿 ɛ𝐴𝑑𝑡
where,
𝑧 : the gradient of the core from high pressure side to low pressure side
𝑝 𝑖 : the initial core pressures
𝑛 𝐻 : moles of gas at the high-pressure side
𝑛 𝐿 : moles of gas at the low-pressure side
𝐴 : cross section area of the core sample
ɛ: Porosity of the core sample
A5.2 Equations to describe the high- and low-pressure side (for gas loading experiment, both sides
of the core have the same pressure; for gas unloading experiment, high-pressure side refers to the
upstream of the core):
𝑑 𝑝 𝐿 𝑑𝑡 𝑉 𝐿 =
𝑑 𝑛 𝐿 𝑑𝑡 𝑅𝑇 , (A8)
𝑑 𝑝 𝐻 𝑑𝑡 𝑉 𝐻 =
𝑑 𝑛 𝐻 𝑑𝑡 𝑅𝑇 , (A9)
For Equation (A8) and (A9) , ideal gas law is assumed.
where,
𝑝 𝐿 : the pressure at the low-pressure side
𝑝 𝐻 : the pressure at the high-pressure side
𝑉 𝐿 : the volume of the low-pressure side, which is known
109

𝑉 𝐻 : the volume of the high-pressure side, which is known
A5.3 Get the pressure profile for the core and both the up and downstream cell
A5.3.1 Explicit Finite Difference Method
If we combine equation (A6) and (A7), we get following equation:
1
𝑅𝑇
𝜕𝑝
𝜕𝑡
−
𝜕 𝜕𝑧
((
𝐾 0
𝑅𝑇
+
𝑃𝐵 0
𝜇𝑅𝑇 )
𝜕𝑝
𝜕𝑧
)=0 , (A10)
Then, the above equation can be written as:
𝑝 𝑖 𝑗 +1
−𝑝 𝑖 𝑗 ∆𝑡 =
𝐵 0
𝜇 (𝑝 𝑖 +1
𝑗 −𝑝 𝑖 𝑗 )
2
∆𝑧 2
+
𝐾 0
+
𝑝 𝑖 𝑗 𝐵 0
𝜇 ∆𝑧 2
(𝑝 𝑖 +1
𝑗 −2𝑝 𝑖 𝑗 +𝑝 𝑖 −1
𝑗 ) , (A11)

where,
i: piece number of the core from high pressure side to low pressure side ranging from 1 to n+1(1
means the interface between high pressure side and core, n+1 means the interface between low
pressure side and core).
∆𝑧 : ∆𝑧 =
𝐿 𝑛
j: time steps, range from 1 to m.
∆𝑧 : ∆𝑡 =𝑡 /𝑚
If we rearrange equation (A11), we have:
𝑝 𝑖 𝑗 +1
=𝑝 𝑖 𝑗 +∆𝑡 (

𝐵 0
𝜇 (𝑝 𝑖 +1
𝑗 −𝑝 𝑖 𝑗 )
2
∆𝑧 2
+
𝐾 0
+
𝑝 𝑖 𝑗 𝐵 0
𝜇 ∆𝑧 2
(𝑝 𝑖 +1
𝑗 −2𝑝 𝑖 𝑗 +𝑝 𝑖 −1
𝑗 )
)

, (A12)
Equation (A8) and (A9) can be written as following after combining with equation (A6),
respectively:
110

𝑝 𝑛 +1
𝑗 +1
−𝑝 𝑛 +1
𝑗 ∆𝑡 =+
ɛ𝐴 𝑉 𝐿 (𝐾 0
+
𝑝 𝑛 𝑗 +𝑝 𝑛 +1
𝑗 2
𝐵 0
𝜇 )
𝑝 𝑛 𝑗 −𝑝 𝑛 +1
𝑗 ∆𝑧 , (A13)
𝑝 1
𝑗 +1
−𝑝 1
𝑗 ∆𝑡 =−
ɛ𝐴 𝑉 𝐻 (𝐾 0
+
𝑝 1
𝑗 +𝑝 2
𝑗 2
𝐵 0
𝜇 )
𝑝 1
𝑗 −𝑝 2
𝑗 ∆𝑧 , (A14)
A5.3.2 steps to estimate the pressure profile for the core and both the up and downstream cell
When j=1 (means t = 0), 𝑝 𝑖 2
for i=2,3,4… to n can be calculated by Equation (A12). The updated
the pressure of both high- and low-pressure side will be calculated via equation (A13) and (A14),
then we have updated boundary conditions for equation (A7).
For j=2 to m, follow the steps above to get 𝑝 𝑖 𝑗 then update the pressure for both high- and low-
pressure side as above.
If we assume B0 and K0 are functions of porosity, average pore diameter and tortuosity, and the
porous shale sample is modeled as a bundle of crooked capillary tubes (Shugard et al., 2014), the
following equations are used to determine values of B0 and K0:

𝐵 0
=0.0389
𝑑 2
𝜏 2
ɛ
0.1
, (A15)

𝐾 0
=
1
3
ɛ𝑑 𝜏 √
8𝑅𝑇
𝜋𝑀
, (A16)

𝜏 =
1.25
ɛ
1.1
, (A17)

Abstract (if available)

Abstract When sandstone rocks are exposed to CO₂-saturated brine, their transport and mechanical properties can, potentially, change due to chemical reactions as a result of such exposure. This work investigates changes in the flow-through characteristics, porosity, and the mechanical properties of Mt. Simon Sandstone samples caused by such exposure to brine/CO₂. A core, extracted from the Mt. Simon formation, was first characterized for its porosity and relevant transport properties, and it was then aged for over 500 hours in CO₂-saturated brine at formation-relevant pressure, temperature, and confining stress conditions. The deformation of the sample was measured in situ during aging via strain gauges attached to the core’s surface. Following the aging experiment, the sample’s porosity and transport properties were again analyzed. Our experiments show that both the porosity and permeability of the Mt. Simon sandstone sample increase due to exposure to brine/CO₂, with the impact on permeability being more significant. The deformation measurements, employing strain gauges, indicate a weakening of the core material. Analysis of the composition of the brine at the conclusion of the testing reveals changes, specifically, an increase in the concentration of several of the cations. These changes are indicative of mineral/clay dissolution, consistent with the porosity, permeability, and strain gauge measurements. ❧ In a tandem study, the mass transfer properties (porosity, permeability) and mechanical behavior (deformation) of the same sandstone sample were measured, in situ, under various gas atmospheres (Helium, Argon, and CO₂) during loading/unloading experiments. The goal of these experiments was to understand how gas adsorption and confining pressure will affect the mass transfer characteristics and mechanical properties of the porous rock, and how such changes impact gas storage of particular interest was to understand how CO₂-induced deformation affects the bulk geomechanical properties of the sample.

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Asset Metadata

Creator Sun, Lin (author)

Core Title Impact of exposure to brine/CO₂ on the mechanical and transport properties of the Mt. Simon sandstone

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Chemical Engineering

Publication Date 11/19/2021

Defense Date 06/16/2021

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag change of mechanical properties,CO₂-brine-rock interactions,gas loading/unloading,increase of permeability and porosity,ion analysis,OAI-PMH Harvest

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Jessen, Kristian (committee chair), Hammond, Douglas E. (committee member), Tsotsis, Theo T. (committee member)

Creator Email linsunsjtu@gmail.com,sunlin@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-oUC17138462

Unique identifier UC17138462

Legacy Identifier etd-SunLin-10243

Document Type Dissertation

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Type texts

Source 20211122-wayne-usctheses-batch-899-nissen (batch), University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

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