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)

References 1. Ghanizadeh, A., et al., Experimental study of fluid transport processes in the matrix system of the

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

exposure to carbon dioxide. International Journal of Greenhouse gas Control, 2014. 24: p. 149-161.

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.

International Journal of Rock Mechanics and Mining Science & Geomechanics Abstracts, 1968.

5(5): p. 415-426.

17. Garg, S.K. and A. Nur, Effective stress laws for fluid-saturated porous rocks. Journal of Geophysical

Research, 1973. 78(26): p. 5911-5921.

18. Warpinski, N.R. and L.W. Teufel, Laboratory measurements of the effective-stress law for

carbonate rocks under deformation. International Journal of Rock Mechanics and Mining Sciences

& Geomechanics Abstracts, 1993. 30(7): p. 1169-1172.

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.

23. Hol, S., Y. Gensterblum, and P. Massarotto, Sorption and changes in bulk modulus of coal —

experimental evidence and governing mechanisms for CBM and ECBM applications. International

Journal of Coal Geology, 2014. 128–129(0): p. 119-133.

24. Gutierrez, M., L.E. Øino, and R. Nygård, Stress-dependent permeability of a de-mineralised fracture

in shale. Marine and Petroleum Geology, 2000. 17(8): p. 895-907.

Contact

Yves Gensterblum: gensterblum@stanford.edu

Mark Zoback: zoback@stanford.edu