gcep-funded sccs project report
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GCEP-funded SCCS Project Report
Investigators
Anthony R. Kovscek, Professor, Energy Resources Engineering
Mark Zoback, Professor, Geophysics
Louis J. Durlofsky, Professor, Energy Resources Engineering
Hamdi Tchelepi, Professor, Energy Resources Engineering
Jennifer Wilcox, Assistant Professor, Energy Resources Engineering
Cathy Zhang, Graduate Student, Energy Resources Engineering
Yves Gensterblum, Post-doctoral researcher, Geophysics
Avinoam Rabinovich, Post-doctoral researcher, Energy Resources Engineering
Sara F. Farshidi, Graduate Student, Energy Resources Engineering
Beibei Wang, Graduate Student, Energy Resources Engineering
Introduction
Stanford Center for Carbon Storage (SCCS) investigates questions related to enhanced
recovery of oil and gas combined with CO2 storage, the development of monitoring
technologies for all classes of geological storage, the characterization of both near-well and
distal geochemical processes during CO2 injection, and computational optimization of the
design and operation of large projects. SCCS is a multidisciplinary research program within
the School of Earth, Energy & Environmental Sciences at Stanford University.
SCCS supports research activities across the Departments of Energy Resources
Engineering, Geophysics, and Geological Sciences within the School of Earth, Energy &
Environmental Sciences. We are a research group comprised of 13 faculty members and
about 18 graduate students and researchers involved directly or indirectly with SCCS
funds. We are funded by GCEP, as well as other industrial sponsors. In the attached report,
we provide a summary of 5 projects directly funded by GCEP.
Project 1: Experimental Investigation of Oil Recovery from Bakken Shale by Miscible
CO2 Injection, Ke (Cathy) Zhang and Anthony R. Kovscek.
Project 2: GCEP Progress Report: Upscaling of CO2-Brine Flow with Capillary
Heterogeneity Effects, Avinoam Rabinovich and Louis J. Durlofsky.
Project 3: Reactive Transport Modeling of CO2 Storage in Ultramafic Rocks, Sara F.
Farshidi.
Project 4: The Role of Kerogen versus Clay in the Adsorption Mechanisms of CO2 and
CH4 in Gas Shales, Beibei Wang and Jennifer Wilcox.
Project 5: Permeability evolution of simulated fractures in caprocks with shear
displacement and related CO2 sequestration, Yves Gensterblum and Mark Zoback.
Project 1: Experimental Investigation of Oil Recovery from Bakken Shale by Miscible
CO2 Injection, Ke (Cathy) Zhang and Anthony R. Kovscek.
Abstract
This study aims to investigate the feasibility of CO2 as an enhanced oil recovery agent
in shale oil reservoirs. Above minimum miscibility pressure (MMP), CO2 and oil are
miscible leading to reduction in capillary forces and therefore high local displacement
efficiency. The miscibility pressure of CO2 is also significantly lower than the pressure
required for other gases, which makes CO2 miscible injection attainable under a broad
spectrum of reservoir pressures.
A detailed description of the experimental set-up and procedures were presented, and
experimental conditions were determined at which CO2 and oil were miscible. Porosity
was also calculated based on a set of “dry” and “wet” images and their corresponding CT
numbers. Work is ongoing and initial efforts are reported here. The final objective is to
understand the governing mechanisms, develop better imaging techniques to capture CO2
saturation front at miscible condition with oil, and to quantify the recovery potential of low
permeability reservoir rock as a result of miscible gas injection.
Introduction
Unconventional liquid reservoirs are characterized by low porosity and matrix
permeability several orders of magnitude lower than conventional oil reservoirs. The
combination of multi-stage hydraulic fracturing and horizontal drilling has improved the
overall profitability of these tight-oil reservoirs by enhancing the wellbore - matrix
connectivity. Under primary production, however, the recovery factor remains in the range
of only 5% to 10%. Considering such a large resource base, even small improvements in
productivity could lead to billions of barrels of additional oil. Therefore, the need to
develop a viable enhanced oil recovery technique for unconventional oil reservoirs is
evident.
Figure 1 gives an overview of current range of reservoir depth and oil viscosity where main
EOR technologies have been applied. Literature review shows that a typical Bakken
reservoir is at least 9000 feet deep and produces a light crude oil with viscosity less than 1
cP at reservoir condition. The combination of these two properties makes gas injection the
most optimum choice for Bakken. Of all the gases being considered, CO2 appears as a
promising candidate because it dissolves in oil easily, swell the oil to reduce its mixture
viscosity, and has a lower miscibility pressure with Bakken crude compared to any other
gases, e.g. nitrogen and hydrocarbon gases.
Figure 1: Screening criteria for main EOR technologies (Source: Poellitzer, et al., 2009)
Background
Miscible CO2 injection has been widely applied in conventional oil reservoirs, and
reported to be successful under unfavorable condition such as naturally fractured
reservoirs. However, its use in unconventional tight oil reservoir such as Bakken is still a
new concept.
Hoffman (2012) and Mohanty et al. (2013) studied miscible CO2 injection for tight oil
reservoirs using a numerical flow simulator. Porosity is in the range of 6% to 8%, and
permeability is in the range of millidarcy to microdarcy. Both of their work shows that CO2
injection can outperform primary production and improve oil recovery. Not a lot of work
has been done on the laboratory scale due to a variety of challenges with equipment and
low injectivity of fluids within rock matrix. Vega et al. (2010) investigated miscible CO2
injection for siliceous shale with a relatively high porosity of 34% and 1.5 mD
permeability. Experimental and simulation results show that CO2 can penetrate from
fracture to matrix and recover almost all the oil when pressure is above MMP. Tovar et al.
(2014) made additional contribution by using a core sample of ultra-low permeability in
the nanodarcy range. Porosity is unknown because the core has such low permeability that
volumetric methods to calculate pore volume are dismissed. Without any information on
porosity, they cannot properly account for OOIP and recovery factor. Instead, they based
their calculations on a series of assumptions and recovery factor was estimated to be 18%
to 55%.
Results
Determination of Miscibility Pressure of CO2 in Bakken Crude
An aluminum tube was charged with dead oil and CO2, and scanned at different
pressures and a fixed temperature at 38°C. Disappearance of two phases and the formation
of a single phase is indicative of miscibility. In theory, the miscibility pressure increases
with increasing temperature. Because the coreholder had a pressure rating of only 2000 psi,
test temperature was lowered to 38°C (slightly above critical temperature of CO2) in order
to achieve miscibility at pressures attainable within the experimental apparatus. As shown
in Fig. 2, miscibility pressure is determined to be 1300 psi at a temperature of 38°C.
Determination of Porosity
The calculation of sample properties such as porosity depends on establishing clear end
points for the spectrum of CT numbers ranging from a “dry” sample (air-saturated) to “wet”
sample (oil-saturated). The dry images were obtained at ambient pressure after the core
was subject to a cleaning and drying process that included decane injection, CO2 flushing,
vacuum oven drying and vacuuming. Then, the wet images were taken by saturating the
core sample with oil. The resulting set of images and their corresponding CT numbers were
used to calculate porosity. An average porosity of 7.5% was obtained, given that air CT
number is -1000 and oil CT number is -177.4. A set of cross-sectional CT images can be
interpolated to reconstruct a 3-D porosity and density profile, as shown in Fig. 3 (a) and
(b) respectively. The core is observed to be generally homogeneous with some localized
heterogeneities. It is also noted that the core has alternating layer of high density and low
density material and it is not cut quite parallel to these alterations.
Figure 2: CT scans (#30) of CO2 and Bakken crude in an aluminum tube at 38ºC and varying pressures at
0.625 mm spacing, 140 keV/120 mA. (a) Ambient Pressure, (b) 1000 psi, (c) 1100 psi, (d) 1300 psi
(a) (b)
Figure 3: 3-D reconstruction of cross-sectional CT images. (a) Porosity profile, (b) Density profile
Determination of Permeability
Absolute permeability of oil-saturated core sample can be calculated based on Darcy’s
law, since oil is the only phase present at the moment. Permeability is 1.8 microdarcy, with
essential parameters summarized in Table I.
Table 1: Summary of parameters for absolute permeability calculation
Average Flow Rate, mL/s 0.0000093
Diameter, inch 1
Length, inch 2
Dead Oil Viscosity @ 38°C, cP 6.56
∆𝑃, psi 500
Absolute Permeability (to oil), µD 1.8
Future Plans
Quantify Recovery Potentials of Miscible CO2 Injection
The oil-saturated core sample is brought to the pressure and temperature at which CO2
is miscible in oil. First, the core is exposed to CO2 in a miscible, countercurrent mode.
After countercurrent injection is completed, cocurrent CO2 flow is performed at the same
injection pressure. Sketches of countercurrent and cocurrent CO2 injection set-up is shown
in Fig. 4 and 5. In the countercurrent injection mode, the inlet face of the core is exposed
to CO2 at constant pressure while the outlet remains closed. The end cap has one port that
allows injection at one side of the core face and a second on the opposite side of the face
such that fluid is circulated perpendicular to the face of the core. Cocurrent flow, or forced
injection allows injection of CO2 at the bottom port but production at the top port.
Improve on Visualization of Phase Saturation by CT Scanning
CT monitoring will be used along the duration of the experimental stages to visualize
fluid saturations within the core. However, the challenge here is that at the energy level
currently selected, CO2 and oil are almost indistinguishable on the CT scans. This is
because at miscible condition, CO2 and oil have similar density and form a single
homogeneous phase. Therefore, we propose a dual-energy scan at 140 keV and 80 keV so
that the X-ray will interact with the sample through both Compton scattering and
photoelectric absorption, which depends on density and effective atomic number,
respectively. We expect that a comparison of images from a high and low energy level will
be sufficient to differentiate the two components, considering that CO2 and oil have very
different atomic numbers. Another alternative is to dope the oil phase to have a stronger
photoelectric effect.
Figure 4: Schematic of countercurrent injection mode (Source: Vega et al., 2010)
Figure 5: Schematic of cocurrent injection mode (Source: Vega et al., 2010)
References 1. Nordeng, S.H. et al., 2008. “State of North Dakota - Bakken Formation Resource Study Project”, North Dakota
Department of Mineral Resources, April 2008.
2. Gaswirth, S.B., Marra, K.R., Cook, T.A., Charpentier, R.R., Gautier, D.L., Higley, D.K., Klett, T.R., Lewan,
M.D., Lillis, P.G., Schenk, C.J., Tennyson, M.E., and Whidden, K.J., 2013. “Assessment of Undiscovered Oil
Resources in the Bakken and Three Forks Formations, Williston Basin Province, Montana, North Dakota, and
South Dakota, 2013 U.S. Geological Survey Fact Sheet 2013-3013. U.S. Geological Survey: Denver, CO.
3. Liu, G., Sorensen, J.A., Braunberger, J.R., Klenner, R., Ge, J., Gorecki, C.D., Steadman, E.N., Harju, J.A., 2014.
“CO2-Base Enhanced Oil Recovery from Unconventional Reservoirs: A Case Study of the Bakken
Formation”, paper SPE 168979 presented at the SPE Unconventional Resources Conference – USA held in the
Woodlands, Texas, USA, April 1-3.
4. Kurtoglu, B., Sorensen, J.A., Braunberger, J., Smith, S., Kazemi, H., 2013. “Geological Characterization of a
Bakken Reservoir for Potential CO2 EOR”, paper SPE 168915 presented at the Unconventional Resources
Technology Conference held in Denver, Colorado, USA, August 12-14.
5. Harju, J., 2012. ‘Bakken and CO2”, presentation at North Dakota Petroleum Council Annual Meeting held in
Medora, North Dakota, USA, September.
6. Tovar, F.D. et al., 2014. “Experimental Investigation of Enhanced Recovery in Unconventional Liquid
Reservoir using CO2: A Look Ahead to the Future of Unconventional EOR”, paper 169022 presented at the
SPE Unconventional Resources Conference held in the Woodlands, Texas, April 1-3.
7. Anonymous, 2012. “Survey: Miscible CO2 now eclipses steam in US EOR production”, Oil & Gas Journal,
110, 56-57.
8. Beliveau, D.A., 1987. “Midale CO2 Flood Pilot”, Journal of Canadian Petroleum Technology, 26(6). Doi:
10.2118/87-06-05.
9. Hoffman, B. Todd, 2012. “Comparison of Various Gases for Enhanced Recovery from Shale Oil Reservoirs”,
paper SPE 154329 presented at the SPE Improved Oil Recovery Symposium, Tulsa, OK.
10. Shoaib, S., Hoffman, B. Todd, 2009. “CO2 Flooding the Elm Coulee Field”, paper SPE 123176 presented at the
SPE Rocky Mountain Petroleum Technology Conference held in Denver, CO, April 14-16.
11. Mohanty, K., Chen, C., Balhoff, M., 2013. “Effect of Reservoir Heterogeneity on Improved Shale Oil Recovery
by CO2 Huff-n-Puff”, paper SPE 164553 presented at the SPE Unconventional Resources Conference held in
the Woodlands, TX.
12. U.S. Energy Information Administration, 2013. “Annual Energy Outlook 2013”, Washington, DC.
13. Sahin, Secaeddin, Kalfa, Ulker, and Celebioglu, Demet, 2008. “Bati Rman Field Immiscible CO2 Application –
Status Quo and Future Plans”, SPE Reservoir Evaluation & Engineering, 11(4), pp. 778-791. Doi:
10.2118/106575-pa.
14. Vega, B., O’Brien, W.J., Kovscek, A.R., 2010. “Experimental Investigation of Oil Recovery from Siliceous
Shale by Miscible CO2 Injection”, paper SPE 135627 presented at the SPE Annual Technical Conference and
Exhibition, Florence, Italy.
15. Vinegar, H.J., Wellington, S.L., 1987. “Tomographic Imaging of Three-Phase Flow Experiments”, Review of
Scientific Instruments, 58(1), 96.
16. Akin, S. and Kovscek, A.R., 2003. “Computed Tomography in Petroleum Engineering Research”, Applications
of X-ray Computed Tomography in the Geosciences, Geological Society, London, Special Publications, 215,
23-28.
17. MHRA Evaluation Report, 2003. “GE Lightspeed Ultra Advantage: CT Scanner Technical Evaluation”,
MHRA 03066.
Contacts
Cathy Zhang: kez@stanford.edu
Anthony R. Kovscek: kovscek@stanford.edu
Project 2: GCEP Progress Report: Upscaling of CO2-Brine Flow with Capillary
Heterogeneity Effects, Avinoam Rabinovich and Louis J. Durlofsky.
Abstract
The large-scale simulation of CO2 storage operations can be expensive
computationally, particularly when the effects of fine-scale capillary pressure
heterogeneity are included. The application of upscaling techniques could lead to
substantial reductions in computational cost. In this work, we develop and apply a new
upscaling technique for two-phase flow in heterogeneous formations with capillary
heterogeneity effects. The procedure entails first upscaling capillary pressure in the
capillary limit, and then computing coarse-scale relative permeability functions using a
global dynamic upscaling procedure. An iterative method is applied to enhance the
accuracy of the upscaled capillary pressure. The new dynamic upscaling approach is
applied to a synthetic heterogeneous two-dimensional aquifer model that involves injection
of CO2 into brine. Fine-scale simulation results are compared with coarse-scale results
generated using both the dynamic upscaling approach and a simpler method that entails the
use of upscaled capillary pressure in conjunction with rock relative permeability curves. It
is shown that the dynamic upscaling procedure provides results that are close to those from
the fine-scale simulation and are consistently more accurate than results from the simpler
method. The upscaling procedure is tested over a range of injection rates spanning three
orders of magnitude. We show that, although the upscaled functions are in general rate
dependent, accurate coarse-scale results can be obtained using upscaled relative
permeability functions computed at only two different flow rates. We also observe that the
model constructed using our method retains reasonable accuracy even when the flow
problem differs from that used to compute the upscaled functions.
Introduction
Simulations of CO2 storage operations are computationally expensive due to the
complex multiscale flow phenomena involved as well as the large spatial and temporal
scales that must be considered. Upscaling represents a means for reducing computational
costs while approximately maintaining key aspects of the fine-scale flow solution. In CO2-
brine flows capillary pressure effects can be much more important, largely because of the
low flow rates that characterize these processes. The fine-scale variations of capillary
pressure with permeability, referred to as capillary heterogeneity, provide an essential
mechanism for CO2 trapping. Thus, upscaling techniques intended for CO2 storage
simulation must capture these fine-scale capillary heterogeneity effects.
In this work we present a dynamic upscaling method that is applicable to two-phase
flow in highly heterogeneous media with capillary heterogeneity. The procedure includes
accurate single-phase and near-well upscaling, capillary pressure upscaling (assuming the
capillary limit), and dynamic relative permeability upscaling. An iteration procedure that
improves the accuracy of the upscaled capillary pressure is also applied. In contrast to
existing procedures, our technique is able to capture rate-dependency effects, and is thus
applicable away from the viscous/capillary limits. In fact, our analysis allows us to
determine regions where the conventional viscous limit (VL) and capillary limit (CL)
upscaling methods are not valid. We also explore the robustness of the upscaled model
with respect to injection rate and well location. A high level of robustness will enable the
model to be used for a range of flow rates, thus avoiding the need to recompute the upscaled
functions.
The systems considered here are intended to be representative of the injection and early
post-injection stages of a CO2 storage operation. In our upscaling calculations, we thus
neglect some of the physical effects that are important in later stages, such as gravity,
hysteresis, dissolution and mineralization. These need to be addressed in the future for
considering applications in realistic operations.
Background
Most previous work on two-phase dynamic upscaling does not consider capillary
heterogeneity effects. An exception is an example given in [4], though this case involves
fairly simple heterogeneity and does not focus on capillary heterogeneity effects or the
impact of flow rate on upscaling.
There have been a few studies focusing specifically on upscaling for CO2 storage
simulations. A discussion of some of this work is given by [2]. In [3], an upscaling model
for vertical migration of a CO2 plume through a vertical column with periodically layered
porous medium assuming the capillary limit is presented. Upscaling procedures, such as
that of [1] are based on the assumption of vertical equilibrium. This approach is
fundamentally different than that presented here as it does not consider detailed capillary
heterogeneity effects, or the impact of rate on the upscaled model.
Results
To demonstrate the capabilities of the proposed upscaling technique we present an
example case. We consider a two-dimensional system containing 200x100 grid blocks with
each block of size 2x1 ft. The rock is taken to be incompressible and of uniform porosity
throughout the aquifer. The permeability field is anisotropic and Gaussian. The coarse
model is generated by upscaling uniformly by a factor of 10 in both directions. This gives
a coarse model comprised of 20x10 grid blocks. The system is initially saturated with water
and then injected with CO2 by a horizontal well at the bottom of the aquifer.
Results for fractional flow are presented in Fig. 1. It can be seen that simulations of the
coarse model with the properties obtained using the new dynamic upscaling method are in
agreement with the fine-scale simulations. Furthermore, the simpler “rock curves”
upscaling method, which entails only single phase and CL capillary pressure upscaling
does not perform as well.
Progress
The upscaling method has been found to be suitable for test cases similar to the one
described above, for a wide range of injection rates and for different injection schemes. For
implementation of this method in realistic CO2 storage simulations a number of
advancements, described in the next section, still need to be made. Implementation of this
upscaling procedure may significantly reduce simulation times, thus allowing to simulate
more complex CO2 storage scenarios and help in assessing the feasibility of and managing
these projects.
Figure 1: Fractional flow of 2CO at the producer for different injection rates.
Future Plans
We plan to extend the upscaling method to include physical process important in the
post-injection stage of equilibration such as gravity, dissolution and hysteresis.
Furthermore, we plan to extend the methodology to more realistic three-dimensional
systems.
Publications
1. Rabinovich, A., K. Itthisawatpan and L.J. Durlofsky, Upscaling of CO2-Brine Flow with Capillary Heterogeneity
Effects, Under review.
References
1. Gasda, S.E., J.M. Nordbotten, and M.A.Celia, Vertically averaged approaches for CO2 migration with solubility
trapping, Water Resources Research, 47, W05528, 2011.
2. Hassan, W.A.A and J. Xi, Upscaling and its application in numerical simulation of long-term CO2 storage,
Greenhouse Gases: Science and Technology, 2 (6), 408-418, 2012.
3. Mouche, E., M. Hayek and C. Mügler, Upscaling of CO2 vertical migration through a periodic layered porous
medium: The capillary-free and capillary-dominant cases, Advances in Water Resources, 33 (9), 1164-1175,
2010.
4. Pickup, G.E. and K.S. Sorbie, Scaleup of two-phase flow in porous media using phase permeability tensors, SPE
Journal 1 (4), 369-382, 1996.
Contacts
Avinoam Rabinovich: avinoamr@stanford.edu
Louis J. Durlofsky: lou@stanford.edu
Project 3: Reactive Transport Modeling of CO2 Storage in Ultramafic Rocks, Sara
F. Farshidi, Hamdi Tchelepi and Lou Durlofsky.
Abstract
The treatment of chemical reactions is required for many simulation applications. In
this work we have incorporated chemical reaction modeling into an existing EOS-based
compositional simulator, where both kinetic and equilibrium, as well as heterogeneous and
homogeneous chemical reactions are included. Furthermore, the formulations consist of
one based on the natural set of variables as well as the overall-compositions. This
implementation has been applied to the problems of shale in-situ upgrading as well as CO2
storage in saline aquifers. More recently, we have focused on modeling the interactions of
aqueous solutions with ultramafic rocks, starting with verifying our model against
published measured weathering data [2]. The data is then used to forecast the outcome of
CO2 sequestration in hydraulically fractured ultramafic rocks, focusing on engineering
reservoir management schemes to encourage faster mineralization.
Introduction
The accurate and efficient treatment of chemical reactions is essential in the simulation
of a number of subsurface flow processes. Application areas include the in-situ
conversion/upgrading of oil shale/oil sands, and the long-term geological storage of CO2.
Reactions of various types, and new treatments for some of the complex physical
phenomena that can occur, are incorporated into a general fully-implicit reservoir
simulator. Our implementation is compatible with most if not all of the capabilities that
currently exist in state-of-the-art compositional simulators. Our 3D reactive transport
simulation results regarding CO2 storage in ultramafic rocks will be briefly discussed in
this report.
Background
CO2 sequestration in ultramafic rocks has been the focus of many geology and
geochemistry research groups due to the high propensity of these rocks to react with the
CO2 resulting in mineralization, a highly secure storage mechanism. Drilling of a pilot in
Oman Samail Ophiolite peridotite is currently under investigation [1], and we have aimed
at modeling the reactive transport phenomena in such development.
Results
This work is concerned with the treatment of chemical reactions as required for many
simulation applications including geological carbon storage.
Numerical results are presented for a realistic reservoir employing our natural variable
formulation treatment. 1MT/year of CO2 is injected through a horizontal well into the
center of a three dimensional aquifer for 40 years, and the system is then simulated for
another 1960 years. A quarter of this reservoir, a 6.2 km×17.5 km×400 m system, is
modeled by dividing it into 10×5×10 (total of 500) blocks. Permeability of 10 md and
porosity of 1% are considered. The reservoir is at 2 km depth, with initial reservoir pressure
of 200 bar and temperature of 90 oC. Fig. 1 displays the mineralized CO2 at 2000 years.
We see that CO2 has migrated to the top of the aquifer due to gravity segregation, and is
then converted to carbonates. The fate of the injected CO2 as a function of time is shown
in Fig. 2. At 1600 years, more than 94% of the CO2 has mineralized, while the rest is
trapped in the form of ions, enhancing solubility trapping. It is also obvious that
mineralization rate is faster in the first 250 years.
We have conducted many sensitivity studies on various parameters such as initial
reservoir pressure, temperature, permeability, porosity, reservoir height, as well as
reservoir management. The results so far indicate a significant dependence on reservoir
temperature as a main driving force in kinetics, as expected. Moreover, the plume shape
and size have proven to play a major role in the kinetics in larger scales. Consequently,
various well management strategies have been studied as a means of enhancing early time
mineralization. Brine recycling schemes have been proposed where mineralization is
increased up to 3.5 times our base case at 10 years post injection; moreover this
enhancement is sustained through the main part of the life of the reservoir. The best
scenario in Fig. 3 entails the conversion of 80% of CO2 to minerals within 200 years,
without the need to preheat the reservoir. This case however demands a 17% pore volume
equivalent brine to be recycled during the 40 years of CO2 injection; the brine production
happens at a vertical production well across the reservoir from the injection well.
Figure 1: Magnesite concentration in kmol/m3. Magnesite, MgCO3, is the main carbonate in this system of
reactions precipitating to lock CO2 in the solid form.
Figure 2: Distribution of the injected CO2 over time
05
05
10
0
5
10
Dolomite
-6 -4 -2 0
x 10-3
05
05
10
0
5
10
Brucite
0 0.02 0.04
05
05
10
0
5
10
Magnesite
0 0.05 0.1
05
05
10
0
5
10
Calcite
2 4 6
x 10-3
Figure 3: Distribution of the injected CO2 over time for various brine recycling schemes
Progress
The incorporation of chemical reactions in our EOS-based reservoir simulator has
offered an opportunity to predict the fate CO2 sequestration in saline aquifers over the
geological time scale. Precisely, chemical reaction considerations are essential for
modeling both ionic (solubility) and mineral trapping of CO2. To date, we have considered
in our work CO2 storage in both sandstones and ultramafic rocks. Ultramafic rocks have
proven to have the capacity to convert a major fraction of the CO2 to minerals which is a
much more secure storage mechanism than the structural form generally predicted for
sandstones.
Future Plans
We plan on investigating fracture models to more accurately predict CO2 storage
mechanisms in hydraulically fractured ultramafic rocks.
Publications and Patents 1. Farshidi, S., Fan, Y., Durlofsky, L., and Tchelepi, H. Chemical Reaction Modeling in a
Compositional Reservoir Simulation Framework. SPE Reservoir Simulation Symposium, The
Woodlands, TX, February 2013
References 1. Kelemen P.B., Matter, J.M., Streit, E.E., Rudge, J.F., Curry, W.B., and Blusztajn, J. Rates and
Mechanisms of Mineral Carbonation in Peridotite: Natural Processes and Recipes for Enhanced, in
situ CO2 Capture and Storage. Annu. Rev. Earth Planet. Sci. 39, 545-576 (2011)
2. Paukert, A.N., Matter, J.M., Kelemen P.B., Shock, E.L., and Haig, J.R., Reaction path modeling of
enhanced in situ CO2 mineralization in the peridotite of the Samail Ophiolite, Sultanate of Oman.
Chemical Geology, 330-331, 86-100 (2012)
Contacts
Sara F. Farshidi: farshidi @stanford.edu
Project 4: The Role of Kerogen versus Clay in the Adsorption Mechanisms of CO2
and CH4 in Gas Shales, Beibei Wang and Jennifer Wilcox.
Abstract
The global atmospheric carbon dioxide concentration, primarily related to fossil fuel
combustion, has increased significantly compared to pre-industrial levels, resulting in a
rise in the global average temperature. To stabilize the atmospheric CO2 concentration, one
possible approach is to inject and store CO2 into gas shale, where significant amounts of
methane are present and can be exploited and recovered. Experimental studies indicate that
CO2 has a stronger likelihood of being adsorbed over CH4, thus the injected CO2 may
displace the adsorbed methane inside the gas shale, thereby potentially enhancing methane
recovery efficiency. However, the adsorption properties of CO2 and methane on gas shale
are not fully understood.
In our recent work, the excess adsorption isotherms of CO2 and CH4 on gas shale samples
have been measured under subsurface temperature condition, using a Rubotherm magnetic
suspension balance. The sample used in this study is from Barnett formations. Because
kerogen and clay are the major constituents that contribute to the adsorption behavior in
gas shale, adsorption isotherm measurements for isolated kerogen and illite (used as
reference clay) are performed to determine the roles that each component plays in the
overall shale adsorption mechanism and capacity estimates.
Introduction
As a possible underground geological location for carbon sequestration, depleted gas
shale reservoirs contain a considerable amount of pore space in their matrices. [Kang,
2010] Sorption is the main mechanism for gas storage within shale due to its surface
chemistry and microporous structure. After primary shale gas recovery methods are
employed, there still remains some natural gas left in the matrix due to gas adsorption.
Ideally, most of the CH4 molecules will be recovered while CO2 will be stored in the shale
matrix permanently separated from the atmosphere. Since the generated CH4 can be served
as fuel or technical gas, this process is able to make CO2 storage economically viable.
Shale is composed of organic matter, clay, and a variety of other minerals, some of which
include quarts and pyrite. Kerogen and clay are the major constituents that contribute to
the adsorption behavior in gas shales. In this work, adsorption isotherm measurements for
isolated kerogen and illite are performed to determine the relative roles that each
component plays in the overall adsorption mechanism and capacity estimates.
Background
Previous research has shown that organic material matter, also termed kerogen, is one
of the important factors responsible for adsorbed gas storage due to the abundance of
micropores. [Lu et al., 1995, Rexer, Thomas F., et al., 2014] In 1995, Lu et al. from Texas
A&M University observed a linear relationship between the total organic content (TOC)
and gas capacity for some Devonian shales. However, a significant amount of gas
adsorption has been observed for some shale samples with very low TOC content (less than
1%) as well, indicating some other compositions may also be responsible for adsorbed gas
storage. In a recent study, Rexer et al. tested samples from the Lower Toarcian Posidonia
shale formation. Methane sorption results from shales and isolated kerogen indicated that
half of the sorption in these dry shales is in the organic matter, with the rest likely coming
from the clay minerals and the organic-inorganic interface.
Results
Figure 1: Excess CO2 isotherm on shale, isolated kerogen, and illite at 80 ˚C.
Figure 1 shows the CO2 adsorption isotherm at 80 ̊ C for pressures up to 140 bar. Compared
with shale, the kerogen and illite samples have a higher adsorption capacity for CO2 since
they are the two major constituents that contribute to the adsorption behavior of gas shale.
Kerogen adsorbs the most, likely due to its highly heterogeneous and porous structure as
well as its high affinity to CO2. [Zhang et al., 2012] In all cases, the powder forms have a
higher gas capacity compared to the particulate forms. This discrepancy is even more
obvious in shale and kerogen measurements, a feature attributed to the reduced mass
transfer resistance and larger pore space introduced in the powder sample. The illite
particulate sample also shows a higher adsorption capacity for CO2 compared to the powder
form, but the discrepancy in adsorption between the two forms is far more subtle than that
observed for kerogen. It may be due to the layered structure of illite, which makes its
sorption sites accessible in both particulate and powdered forms, resulting in less
discrepancy between their adsorption gas capacities.
CH4 adsorption isotherm measurements have been performed and compared with CO2 for
implications of CO2 storage in depleted gas shale reservoirs. All of the samples were in
particulate form.
As shown in Figure 2, all samples exhibited a greater adsorption capacity for CO2. This
may be due to the fact that the quadrupole moment within the CO2 molecule has a stronger
associated charge compared to the octupole moment of CH4, leading to its stronger fluid-
wall and fluid-fluid interaction. At 140 bar, relative to CH4, CO2 demonstrates about 5
times greater capacity in shale, 4 times greater capacity in kerogen and 27 times greater
capacity in illite.
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0 20 40 60 80 100 120 140
q*[gCO
2/gsorb]
Pressure[bar]
Shalepar cle
ShalePowder
KerogenPar cle
KerogenPowder
IllitePar cle
IllitePowder
Figure 2: Comparison of excess CO2 and CH4 adsorption isotherms on shale, isolated kerogen, and illite at
80°C as a function of pressure.
Progress
Due to the higher adsorption for CO2 in gas shale, conditions for CO2 storage and
potential enhanced methane recovery in gas shales has promise, with a mechanism similar
to that of enhanced coalbed methane recovery.
Future Plans
Simulation methods will be developed to understand the the adsorption properties of CO2
and methane on gas shale.
References 1. Kang, S.M., Fathi, E., Ambrose, R.J., Akkutlu, I.Y., and Sigal R.F., MPGE. (2010). CO2 Storage
Capacity of Organic-rich Shales. SPE 134583. SPE Annual Technical Conference and Exhibition,
19-22 September 2010, Florence, Italy.
2. Lu, X. C., Li, F. C., & Watson, A. T. (1995). Adsorption measurements in Devonian shales. Fuel,
74(4), 599-603.
3. Rexer, Thomas F., et al. (2014). High-pressure methane adsorption and characterization of pores in
Posidonia shales and isolated kerogens. Energy & Fuels, 28.5, 2886-2901.
4. Zhang, T., Ellis, G. S., Ruppel, S. C., Milliken, K., & Yang, R. (2012). Effect of organic-matter type
and thermal maturity on methane adsorption in shale-gas systems. Organic Geochemistry, 47, 120-
131.
Contacts
Beibei Wang: beibeiw@stanford.edu
Jennifer Wilcox: jen.wilcox@stanford.edu
Project 5: Permeability evolution of simulated fractures in caprocks with shear
displacement and related CO2 sequestration, Yves Gensterblum and Mark Zoback.
Abstract
The fundamental understanding of the processes when sorbing and non-sorbing gases
are permeating shale fractures and the response of transport properties on changing stress
conditions is of multiple benefits such as caprock integrity for CO2 storage applications or
using CO2 for enhanced gas recovery from unconventional gas or liquid-rich reservoirs.
This experimental study examines the effect of shear-deformation on fracture permeability
in carbonate-rich and clay-lean shales under varying stress conditions. Furthermore we are
investigating how sorbing and non-sorbing gases affect the transport and poroelastic
properties of the shale fractures.
Our results shows that clay-rich caprocks provides very favorable properties for carbon
sequestration, because firstly, critically stressed fractures shear aseismically. Secondly, the
apparent fracture permeability is not enhanced by sliding. It is more likely that the apparent
permeability decreases. Furthermore, this can already be observed in laboratory tests on a
sample containing roughly 20% clay. Whereas, for a carbonate-rich sample with 11% clay
we have observed a permeability increase after shear displacement. Thirdly, the poroelastic
properties are almost identical for CO2 (sorbing) and argon (approximation for non-sorbing
and inert gas types). Therefore, CO2 has no effect on the poroelastic properties. Fourthly,
the poroelastic properties are not or only marginally affected by shear displacement.
Therefore our results suggest that the clay content is determining the fracture transport
properties of critical stressed fractures and is one of several key factor for the assessment
of sequestration strategies.
Introduction
Underground storage of carbon dioxide (CO2) into permeable aquifers such as deep
saline aquifers or depleted oil and gas reservoirs is considered to be a potential method to
reduce the greenhouse gas emissions. Supercritical CO2 has a lower fluid density than
water typically at depth greater than 800m. Therefore, a potential storage reservoir requires
an impermeable caprock. Because of their low permeability [1-3], shales can serve as
barrier for repositories of CO2 and waste material. Such a caprock is naturally
discontinuous and contains imperfections such as fractures. An increase in pore pressure
in the reservoir resulting from injection of CO2 can potentially lead to the creation or
reactivation of fractures [4-6] in otherwise sealing caprocks, which may cause CO2 leakage
or even worse casing damage. As slip on fractures is expected to be unstable (stick-slip)
for low clay content and stable (aseismic) for high clay content [7], the size, style, and
location of the damage zone within the fracture may differ between both slip mechanisms
and has an effect on fracture permeability [8]. It is shown through laboratory experiments
that permeability of fractures and joints increases with shear deformation for ultra-low
(<1%) porosity granite samples [9, 10] and decreases for moderate porosity (11%)
Coconino sandstone [11]. However, the influence of shear slip on fracture permeability of
clay rich and lean shales with respect to CO2 interaction has not been studied yet.
The nature of the fracture damage zone is controlled by two processes that are governed
by the grain size and composition, and ultimately, control the fracture permeability: 1)
formation of smear, a membrane seal where clay particles preferentially align with the
shear direction; and 2) formation of a gouge zone where other grains and grain fragments
are plucked off of the sliding surfaces and crushed.
The interaction of CO2 and different types of clay, such as smectites, illites and kaolinites,
has been investigated in great detail in last decades. CO2 is able to induce swelling on
specific clay types. CO2-induced mechanical swelling of montmorillonite (SWy-1) is a
function of the clay’s initial hydration state and corresponding interlayer d-spacing [12]. It
has been shown by the group of Chris Spiers that partially hydrated Na-rich Wyoming
smectite (Na-SWy-2) clay is able to reach several MPa of swelling pressure [13], but is not
able to weaken the friction process [14].
To understand and reduce the likelihood of occurrence of damage and leakage is an
incentive for researchers. However, we still do not know the degree to which slip along
fractures in the caprock would create potentially permeable pathways along which fluids
could leak. Further, we want to learn whether certain caprock compositions are more
vulnerable to leakage than others, probably such as clay-lean, if triggered fracture slip
occurred. Additionally, we do not know, how and to what extent pre-adsorbed water and
CO2 affect the reactivation and flow through fractures.
This experimental study examines the effect of shear-deformation on fracture permeability
in carbonate-rich shales under varying stress conditions. Furthermore we are investigating
how sorbing and non-sorbing gases affect the transport and poro-elastic properties of the
shale fractures.
We will present results of coupled shear-flow-stress experiments in a conventional triaxial
apparatus on shale core samples with a saw cut at 30° to the cylindrical core axis. A non-
sorbing gases such as argon and furthermore carbon dioxide are used as permeating fluid
to test its effect on fracture permeability and further, the shale-fracture elastic properties.
The experimental study is examining the effect of shear deformation on fracture
permeability in organic-rich shales with varying clay contents and under varying stress
conditions. Furthermore we will investigate how sorbing and non-sorbing gases affect the
transport and poro-elastic properties of the shale fractures.
Experimental description
Coupled shear-flow-stress experiments are being carried out in a conventional triaxial
apparatus for shale core with a saw cut at 30° to the cylindrical core axis (Figure 2). A non-
sorbing gas such as argon and furthermore carbon dioxide are used as permeating fluid to
test its effect on fracture permeability and further, the shale-fracture elastic properties.
The sample preparation contains two main steps: Introducing a fracture artificially and
drilling two small holes parallel to the cylindrical axis into the shale cores to allow fracture
permeability experiments after individual shear deformation increments using the non-
steady state pressure decay method (Figure 2).
Figure 1: Sample types and experimental testing setup for a) saw-cut shale sample (taken from Reece and
Zoback, SRB 2014).
Figure 2: Illustration of the experimental setup. The pressure decay method has been applied. The required
volume calibration has be conducted by applying Boyles law.
To determine the permeability we have applied the pressure decay method. For evaluation
of the non-steady state gas permeability coefficients, we used a formulation which is based
on the interpretation of the fundamental flow equations, i.e. the mass balance equation
(continuity equation) and Darcy's law:
𝑘(𝑝𝑚) =𝑐𝜇𝐿
𝐴𝑝𝑚(1
𝑉1+
1
𝑉2) (1)
where the parameters V1, V2, L, A, Pmean and μ represent the upstream and downstream
volumes, the length of the sample, the cross-sectional area of the sample, the mean pore
pressure and gas viscosity, respectively. The parameter c in this equation is the slope of the
plot of ln(Pup(t) − Pdown(t)) versus time, which is calculated using the recorded upstream
and downstream pressure data. The required volume calibration for upstream and
downstream compartment has been performed by applying Boyles law.
Figure 3: Experimental testing strategy to investigate the poro-elastic properties as a function of fracture
shear displacement
To investigate the effective stress coefficient the permeability have to be determined at
different pore pressure and confining pressure. The confining pressure are varied at each
fracture displacement step to investigate the elastic properties of the shale-fracture (Figure
3). To achieve reliable and reproducible results at each stress level at least 3 permeability
measurements have been conducted. To investigate the influence of sorbing and non-
sorbing permeating gases we have alternated argon and carbon dioxide (CO2) to
deconvolute the influence of sorption and swelling on permeability.
Samples
We have investigated the fracture transport on a sample from the Haynesville basin. The
Haynesville sample has a moderate calcite and clay content.
Table 1: The results of the sample characterization using XRD analysis and Rietveld
refinement.
XRD Data (wt%)
Quartz Feld-spar Calcite Pyrite Clay TOC Other
Haynesville 16.3 5.3 52.3 1.7 22.3 2.3 0.2
Table 2: The sample dimensions.
Length
(mm)
Diameter
(mm)
Fracture
length
(mm)
Estimated
aperture
(mm)
Haynesville 50.8 25.4 29 0.001
Results
In this study we have conducted roughly 540 permeability measurements at different
effective stress levels by varying mean pore pressure and confining pressure separately.
The determined permeability coefficient at different effective stress levels show clearly the
exponential decrease with increasing effective stress which is predicted by the poroelastic
theory (Figure 5). The apparent permeability decreases by at least one order of magnitude
after the first shear displacement step (Figure 5). Furthermore the permeability measured
right after the shear displacement is higher than the permeability at stress equilibration after
a few days. Typically the permeability determined right after shear displacement shows a
much higher stress sensitivity then after stress equilibration. The stress equilibration is
reached when the permeability is reproducible on two subsequent days.
Figure 4: This figure is showing the apparent permeability as a function of shear displacement.
Poroelastic results
As indicated in part A of Figure 6 the permeability decrease exponentially with
increasing effective stress, as predicted by the derivation from the poroelastic theory.
Figure 5: Apparent permeability of the Haynesville sample for argon A) and carbon dioxide B) as
permeating fluid through the fracture.
Figure 6: The stress sensitivity coefficient for the fracture transport of the Haynesville sample. The fracture
permeability of the Haynesville sample does not change the stress sensitivity under stress equilibrated
conditions.
Figure 7: The intrinsic permeability k0 of the Haynesville shale as a function of shear displacement. The
dotted blue line indicates the permeability measured directly after shear displacement of the fracture. The
dotted gray line is illustrating the permeability trend after stress equilibration of the fracture.
The stress sensitivity which is the slope in Figure 5, B) and C) is obviously not effected by
the shear displacement.
Furthermore, the stress sensitivity is almost identical for Argon and CO2. Therefore we are
able to conclude that CO2 is not affecting the poro-elastic properties of the fracture
transport processes of the Haynesville sample. In comparison to the CO2 induced softening
on coal cleats [23]. This is illustrated in
Figure 6 and Table 3.
Figures 7 and 8 show the stress sensitivity coefficient and the intrinsic permeability k0
evaluation by following equation 3. The initial permeability (z=0mm) shows overall the
highest permeability coefficient (Figure 7). The permeability coefficient determined when
the fracture and its gauge is stress equilibrated shows an approximately exponential decay
however the first permeability measurements shows the biggest permeability reduction
after the second shear displacement step.
Table 3: The poroelastic parameters as a function of shear displacement of the Haynesville
shale determined on a stress equilibrated sample by using argon as permeating fluid.
Gas Shear displacement
(mm)
Fracture compressibility
(MPa-1
)
Intrinsic
permeability (mD)
Arg
on
0 0.082 0.008 162.6 32
0.29 0.03 0.072 0.023 5.8 1.5
0.87 0.03 0.103 0.008 2.8 0.5
CO
2
0 0.091 0.011 38.8 32
0.29 0.03 0.104 0.023 5.8 1.5
0.87 0.03 0.095 0.017 1.2 0.5
Discussion
We hypothesize that during stable sliding (for high clay contents, > 20%) the hydraulic
aperture of the fracture is reduced to the fracture plane because of the formation of a thin
clay-rich smear layer resulting in a decrease in fracture permeability with increasing shear
deformation [24]. Whereas during sliding of a sample with a low clay contents <20%, a
higher permeability has been observed. The produced fines which are small particles
plucked off of the sliding surfaces are increasing the hydraulic aperture. Therefore initialy
we observe a softer stress-permeability response the after stress equilibrium.
Furthermore, we hypothesize that natural fractures have a higher-permeability initially due
to a damage zone including small fractures adjacent to it. This probably results in an initial
increase in fracture permeability followed by an decrease due to the combined effects of
particle alignment associated with the smaller smear and a dominating gouge layer [8].
The most important issue related to the interpretation of this data set is which representative
initial fracture condition for a critical stressed fracture is representative for the in-situ
conditions? Is the fracture condition at initial state representative or more likely the fracture
conditions after the first shear displacement step?
Conclusion
This experimental study examines the effect of shear-deformation on fracture
permeability in carbonate-rich and clay-lean shales under varying stress conditions.
Furthermore we are investigating how sorbing and non-sorbing gases affect the transport
and poro-elastic properties of the shale fractures.
Our results shows that clay-rich caprocks provides very favorable properties for CCS. First
critically stress fractures with a high clay content (>40%) shear aseismically. Secondly the
apparent permeability is not enhanced by sliding. It is more likely that the apparent
permeability decreases. Furthermore, this can already be observed in laboratory tests on a
sample containing roughly 20%. However for a carbonte-rich sample with 11% clay we
have observed a permeability increase after shear displacement. Thirdly the poro-elastic
properties are almost identical for CO2 (sorbing) and argon (approximation for non-sorbing
and inert gas types). Therefore CO2 has no effect on the poroelastic properties of the
fracture transport. Fourthly, the determined effective stress coefficient is = 1.15 0.11
and therefore, follows approximately Terzaghis principle. This indicates that pore pressure
changes have a more significant influence on the state of stress in the fractures in
comparison to effective stress coefficient <1 values determined by Heller, Vermylen [21]
for shale matrix transport.
Therefore our results suggest that the clay content is determining the fracture transport
properties and is an important parameter for assessing the evolution of caprocks during
CO2 sequestration.
Notation
Terms and
symbols
Definition Unit
Apparent gas
permeability
coefficient, kgas
Gas permeability coefficient from single-phase gas
flow tests corresponding to a given mean pore
pressure – value is not corrected for the
Klinkenberg effect.
Darcy, m2
1 Darcy = 9.87
× 10−13 m2
μ Gas/water viscosity Pa s
A Cross-sectional area of the sample fracture m2
c, β, Constant dimensionless
L Length of fracture m
Pup,down Upstream/downstream pressure Pa
Q Volumetric gas flow rate m3
V1,2 Upstream/downstream volumes m3
Terms and
symbols
Definition Unit
Z Compressibility factor of gas dimensionless
kn Knudsen Number dimensionless
Pconf. Confining pressure Pa
Pm Mean pore pressure Pa
Pe Effective pressure Pa
eff Effective stress Pa
Effective stress coefficient
(‘Biot coefficient’ when it is related to volume
changes)
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European organic-rich shales: II. Posidonia Shale (Lower Toarcian, northern Germany).
International Journal of Coal Geology, 2013. 123: p. 20-33.
2. Ghanizadeh, A., et al., Experimental study of fluid transport processes in the matrix system of the
European organic-rich shales: I. Scandinavian Alum Shale. Marine and Petroleum Geology, 2014.
51: p. 79-99.
3. Ghanizadeh, A., et al., Lithological controls on matrix permeability of organic-rich shales: An
experimental study. Energy Procedia, 2013.
4. Das, I. and M. Zoback, Long-period, long-duration seismic events during hydraulic fracture
stimulation of a shale gas reservoir. The Leading Edge, 2011. 30(7): p. 778-786.
5. Das, I. and M. Zoback, Long-period, long-duration seismic events during hydraulic stimulation of
shale and tight-gas reservoirs — Part 1: Waveform characteristics. Geophysics, 2013. 78(6): p.
KS97-KS108.
6. Das, I. and M. Zoback, Long-period long-duration seismic events during hydraulic stimulation of
shale and tight-gas reservoirs — Part 2: Location and mechanisms. Geophysics, 2013. 78(6): p.
KS109-KS117.
7. Kohli, A.H. and M.D. Zoback, Frictional properties of shale reservoir rocks. Journal of Geophysical
Research: Solid Earth, 2013. 118(9): p. 5109-5125.
8. Rutqvist, J. and O. Stephansson, The role of hydromechanical coupling in fractured rock
engineering. Hydrogeology Journal, 2003. 11(1): p. 7-40.
9. Chen, Z., et al., An experimental investigation of hydraulic behaviour of fractures and joints in
granitic rock. International Journal of Rock Mechanics and Mining Sciences, 2000. 37(7): p. 1061-
1071.
10. Esaki, T., et al., Development of a shear-flow test apparatus and determination of coupled properties
for a single rock joint. International Journal of Rock Mechanics and Mining Sciences, 1999. 36(5):
p. 641-650.
11. Teufel, L.W., Permeability Changes During Shear Deformation Of Fractured Rock. 1987, American
Rock Mechanics Association.
12. Giesting, P., et al., Interaction of carbon dioxide with Na-exchanged montmorillonite at pressures
to 640 bars: Implications for CO2 sequestration. International Journal of Greenhouse Gas Control,
2012. 8(0): p. 73-81.
13. De Jong S.M., Spiers C.J., and B. A., Development of swelling strain in smectite clays through
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14. Samuelson, J. and C.J. Spiers, Fault friction and slip stability not affected by Co2 storage: Evidence
from short-term laboratory experiments on North Sea reservoir sandstones and caprocks.
International Journal of Greenhouse Gas Control 2012. 11: p. S78-S90.
15. Nur, A. and J.D. Byerlee, An exact effective stress law for elastic deformation of rock with fluids.
Journal of Geophysical Research, 1971. 76(26): p. 6414-6419.
16. Brace, W.F. and R.J. Martin, A test of the law of effective stress for crystalline rocks of low porosity.
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19. Kwon, O., et al., Permeability of Wilcox shale and its effective pressure law. Journal of Geophysical
Research: Solid Earth, 2001. 106(B9): p. 19339-19353.
20. Kwon, O., et al., Permeability of illite-bearing shale: 1. Anisotropy and effects of clay content and
loading. Journal of geophysical research, 2004. 109(10): p. B10205-B10205.19.
21. Heller, R., J. Vermylen, and M. Zoback, Experimental investigation of matrix permeability of gas
shales. AAPG Bulletin, 2014. 98(5): p. 975-995.
22. Zoback, M.D. and J.D. Byerlee, The effect of microcrack dilatancy on the permeability of westerly
granite. Journal of Geophysical Research, 1975. 80(5): p. 752-755.
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Contact
Yves Gensterblum: gensterblum@stanford.edu
Mark Zoback: zoback@stanford.edu
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