![Page 1: Multiscale Modeling of Gas Transport and Storage in Shale ...2- Azom, P. N. and Javadpour, F. (2012, January 1). Dual-Continuum Modeling of Shale and Tight Gas Reservoirs. Society](https://reader033.vdocuments.us/reader033/viewer/2022042114/5e9089be8f79850e9c7d22f1/html5/thumbnails/1.jpg)
MULTISCALE MODELING OF GAS TRANSPORT AND STORAGE IN
SHALE RESOURCES
Ali Takbiri-Borujeni
12/02/2014
![Page 2: Multiscale Modeling of Gas Transport and Storage in Shale ...2- Azom, P. N. and Javadpour, F. (2012, January 1). Dual-Continuum Modeling of Shale and Tight Gas Reservoirs. Society](https://reader033.vdocuments.us/reader033/viewer/2022042114/5e9089be8f79850e9c7d22f1/html5/thumbnails/2.jpg)
WHAT TO EXPECT
An introduction to gas transport modeling techniques and their complexities at different scales.
2
http://geologycafe.com/stories/frackin.html
![Page 3: Multiscale Modeling of Gas Transport and Storage in Shale ...2- Azom, P. N. and Javadpour, F. (2012, January 1). Dual-Continuum Modeling of Shale and Tight Gas Reservoirs. Society](https://reader033.vdocuments.us/reader033/viewer/2022042114/5e9089be8f79850e9c7d22f1/html5/thumbnails/3.jpg)
DIFFERENT SCALES IN SHALE GAS RECOVERY
3 1- Ruppel and Loucks (2008)
1
![Page 4: Multiscale Modeling of Gas Transport and Storage in Shale ...2- Azom, P. N. and Javadpour, F. (2012, January 1). Dual-Continuum Modeling of Shale and Tight Gas Reservoirs. Society](https://reader033.vdocuments.us/reader033/viewer/2022042114/5e9089be8f79850e9c7d22f1/html5/thumbnails/4.jpg)
FLOW REGIME CHARACTERIZATION
Gas flow regimes are characterized by the Knudsen number (Kn). Flow regimes are1:
continuum flow (0 < Kn < 10−3)
slip flow (10−3 < Kn < 10−1)
transition flow (10−1 < Kn < 10)
free molecular flow (10 < Kn < ∞)
4 1- Roy, S., R. Raju, H. F. Chuang, B. A. Cruden, and M. Meyyappan (2003). Modeling gas flow through microchannels and nanopores. Journal of applied physics 93 (8) 2- Kang, S. M., E. Fathi, R. J. Ambrose, I. Y. Akkutlu, R. F. Sigal, et al. (2011). Carbon dioxide storage capacity of organic-rich shales. Spe Journal 16 (4), 842-855
In organic nanopores in shale, Knudsen number is larger than 0.1 2.
![Page 5: Multiscale Modeling of Gas Transport and Storage in Shale ...2- Azom, P. N. and Javadpour, F. (2012, January 1). Dual-Continuum Modeling of Shale and Tight Gas Reservoirs. Society](https://reader033.vdocuments.us/reader033/viewer/2022042114/5e9089be8f79850e9c7d22f1/html5/thumbnails/5.jpg)
ORGANIC MATTER (KEROGEN)
5
Knudsen number is larger than 0.1. Slip or transition flow regimes
Organic-rich shale are suitable for gas adsorption due to their large surface areas. Cause new transport effects, such as
pore-diffusion and surface-diffusion effects
Ruppel and Loucks (2008)
![Page 6: Multiscale Modeling of Gas Transport and Storage in Shale ...2- Azom, P. N. and Javadpour, F. (2012, January 1). Dual-Continuum Modeling of Shale and Tight Gas Reservoirs. Society](https://reader033.vdocuments.us/reader033/viewer/2022042114/5e9089be8f79850e9c7d22f1/html5/thumbnails/6.jpg)
EXAMPLE: REDUCED-ORDER BOLTZMANN EQUATION
Regularized 13-moment (R13) method: a set of 13 differential equations are
derived from the moments of Boltzmann equation
solutions to these equations provide fluid flow equations for Kn 1
6
![Page 7: Multiscale Modeling of Gas Transport and Storage in Shale ...2- Azom, P. N. and Javadpour, F. (2012, January 1). Dual-Continuum Modeling of Shale and Tight Gas Reservoirs. Society](https://reader033.vdocuments.us/reader033/viewer/2022042114/5e9089be8f79850e9c7d22f1/html5/thumbnails/7.jpg)
BOUNDARY CONDITIONS
Three types of gas-surface interactions1: Specular reflection tangential velocity of the molecule remains constant
normal velocity component changes its sign
Trapping molecules lose their translational energy as they
collide with the surface
molecules will stay on the surface (few picoseconds)
Sticking molecules hit the surface, lose their energy
they stay on the surface for a reasonable amount of time (few nanoseconds)
7 1- Masel, R. I. (1996). Principles of adsorption and reaction on solid surfaces, Volume 3. John Wiley & Sons.
![Page 8: Multiscale Modeling of Gas Transport and Storage in Shale ...2- Azom, P. N. and Javadpour, F. (2012, January 1). Dual-Continuum Modeling of Shale and Tight Gas Reservoirs. Society](https://reader033.vdocuments.us/reader033/viewer/2022042114/5e9089be8f79850e9c7d22f1/html5/thumbnails/8.jpg)
SORPTION MODELING
8
Langmuir isotherm
Myong, R. S. (2004). Gaseous slip models based on the Langmuir adsorption isotherm. Physics of Fluids, 16(1), 104.
Gas sorption capacity is defined by volume and pressure isotherms.
Langmuir model suggests the development of a single molecular layer of adsorption.
![Page 9: Multiscale Modeling of Gas Transport and Storage in Shale ...2- Azom, P. N. and Javadpour, F. (2012, January 1). Dual-Continuum Modeling of Shale and Tight Gas Reservoirs. Society](https://reader033.vdocuments.us/reader033/viewer/2022042114/5e9089be8f79850e9c7d22f1/html5/thumbnails/9.jpg)
VELOCITY PROFILES FOR DIFFERENT KNUDSEN NUMBERS
9
Assumptions: Specular and diffusive
reflections
Slip velocity increases as Knudsen number increases
![Page 10: Multiscale Modeling of Gas Transport and Storage in Shale ...2- Azom, P. N. and Javadpour, F. (2012, January 1). Dual-Continuum Modeling of Shale and Tight Gas Reservoirs. Society](https://reader033.vdocuments.us/reader033/viewer/2022042114/5e9089be8f79850e9c7d22f1/html5/thumbnails/10.jpg)
MODEL RESULTS FOR PERMEABILITY
10
![Page 11: Multiscale Modeling of Gas Transport and Storage in Shale ...2- Azom, P. N. and Javadpour, F. (2012, January 1). Dual-Continuum Modeling of Shale and Tight Gas Reservoirs. Society](https://reader033.vdocuments.us/reader033/viewer/2022042114/5e9089be8f79850e9c7d22f1/html5/thumbnails/11.jpg)
PERMEABILITY IN SLIP REGIME
11
Kd vs. inverse of mean pressure for Argon at T = 338K for different channel widths
Kd vs. inverse of the mean pressure for Argon and Helium at T= 338K for channel widths of 10 and 100 nm
![Page 12: Multiscale Modeling of Gas Transport and Storage in Shale ...2- Azom, P. N. and Javadpour, F. (2012, January 1). Dual-Continuum Modeling of Shale and Tight Gas Reservoirs. Society](https://reader033.vdocuments.us/reader033/viewer/2022042114/5e9089be8f79850e9c7d22f1/html5/thumbnails/12.jpg)
IMPACT OF TEMPERATURE ON APPARENT PERMEABILITY
12
Kd vs. channel width for different temperatures at constant pressure of 0.28 MPa for Argon.
![Page 13: Multiscale Modeling of Gas Transport and Storage in Shale ...2- Azom, P. N. and Javadpour, F. (2012, January 1). Dual-Continuum Modeling of Shale and Tight Gas Reservoirs. Society](https://reader033.vdocuments.us/reader033/viewer/2022042114/5e9089be8f79850e9c7d22f1/html5/thumbnails/13.jpg)
CORE PLUG SCALE
13
A multiscale medium consisting of inorganic matrix and organic matter (kerogen).
Inorganic pores are dominantly slit-like in shape or microfracture and therefore they are stress-sensitive.
![Page 14: Multiscale Modeling of Gas Transport and Storage in Shale ...2- Azom, P. N. and Javadpour, F. (2012, January 1). Dual-Continuum Modeling of Shale and Tight Gas Reservoirs. Society](https://reader033.vdocuments.us/reader033/viewer/2022042114/5e9089be8f79850e9c7d22f1/html5/thumbnails/14.jpg)
CORE PLUG SCALE
Intrinsic permeability for conventional reservoir simulators: a property of porous media
independent of the fluid type
Due to existence of nanoscale pores in Shale, permeability is: sensitive to effective stress, pore pressure,
temperature, and the fluid type.
14
![Page 15: Multiscale Modeling of Gas Transport and Storage in Shale ...2- Azom, P. N. and Javadpour, F. (2012, January 1). Dual-Continuum Modeling of Shale and Tight Gas Reservoirs. Society](https://reader033.vdocuments.us/reader033/viewer/2022042114/5e9089be8f79850e9c7d22f1/html5/thumbnails/15.jpg)
EXPERIMENTAL MEASUREMENT
•Unsteady state methods such as GRI and pressure pulse decay are faster and can measure permeability as low as 1 nD
•Steady-state permeability measurements
15
Comparison of crushed rock permeability from different laboratories1
1- Passey, Q. R., Bohacs, K., Esch, W. L., Klimentidis, R., & Sinha, S. (2010, January 1). From Oil-Prone Source Rock to Gas-Producing Shale Reservoir - Geologic and Petrophysical Characterization of Unconventional Shale Gas Reservoirs. Society of Petroleum Engineers.
![Page 16: Multiscale Modeling of Gas Transport and Storage in Shale ...2- Azom, P. N. and Javadpour, F. (2012, January 1). Dual-Continuum Modeling of Shale and Tight Gas Reservoirs. Society](https://reader033.vdocuments.us/reader033/viewer/2022042114/5e9089be8f79850e9c7d22f1/html5/thumbnails/16.jpg)
PERMEABILITY MEASUREMENT
16
laboratory measured apparent permeability, if conducted in low pressure and temperatures, need to be extrapolated to reservoir conditions.
![Page 17: Multiscale Modeling of Gas Transport and Storage in Shale ...2- Azom, P. N. and Javadpour, F. (2012, January 1). Dual-Continuum Modeling of Shale and Tight Gas Reservoirs. Society](https://reader033.vdocuments.us/reader033/viewer/2022042114/5e9089be8f79850e9c7d22f1/html5/thumbnails/17.jpg)
EXPERIMENTAL RESULTS-STEADY STATE
A new steady-state permeability measurement technique
17
Permeability measurement using steady-state method1
1- Zamirian, M., Aminian, K. K., Fathi, E., & Ameri, S. (2014, October 21). A Fast and Robust Technique for Accurate Measurement of the Organic-rich Shales Characteristics under Steady-State Conditions. Society of Petroleum Engineers. doi:10.2118/171018-MS
![Page 18: Multiscale Modeling of Gas Transport and Storage in Shale ...2- Azom, P. N. and Javadpour, F. (2012, January 1). Dual-Continuum Modeling of Shale and Tight Gas Reservoirs. Society](https://reader033.vdocuments.us/reader033/viewer/2022042114/5e9089be8f79850e9c7d22f1/html5/thumbnails/18.jpg)
CYLINDRICAL BUNDLE
For a known pore size distribution, permeability of the core can be calculated from:
φ/T: porosity-tortuosity ratio
18
![Page 19: Multiscale Modeling of Gas Transport and Storage in Shale ...2- Azom, P. N. and Javadpour, F. (2012, January 1). Dual-Continuum Modeling of Shale and Tight Gas Reservoirs. Society](https://reader033.vdocuments.us/reader033/viewer/2022042114/5e9089be8f79850e9c7d22f1/html5/thumbnails/19.jpg)
EXAMPLE
Pore-size distribution obtained by Nitrogen adsorption method at 77K1.
19 1- Zamirian, M., Aminian, K. K., Fathi, E., & Ameri, S. (2014, October 21). A Fast and Robust Technique for Accurate Measurement of the Organic-rich Shales Characteristics under Steady-State Conditions. Society of Petroleum Engineers. doi:10.2118/171018-MS
![Page 20: Multiscale Modeling of Gas Transport and Storage in Shale ...2- Azom, P. N. and Javadpour, F. (2012, January 1). Dual-Continuum Modeling of Shale and Tight Gas Reservoirs. Society](https://reader033.vdocuments.us/reader033/viewer/2022042114/5e9089be8f79850e9c7d22f1/html5/thumbnails/20.jpg)
MULTICONTINUUM APPROACH
•The governing equations are based on the principle of conservation of mass.
•Fluid transport and storage of each continuum can be governed by different physics.
•Spatial coordinates of each continuum are not explicitly defined.
20 1- Akkutlu, I.Y., and Fathi, E. (2012). Multiscale gas transport in shales with local Kerogen heterogeneities. SPE Journal, Volume 17, Number 4. 2- Azom, P. N. and Javadpour, F. (2012, January 1). Dual-Continuum Modeling of Shale and Tight Gas Reservoirs. Society of Petroleum Engineers. doi:10.2118/159584-MS
Multicontinuum approach for shale gas transport1 Organic pores inorganic pores fractures
![Page 21: Multiscale Modeling of Gas Transport and Storage in Shale ...2- Azom, P. N. and Javadpour, F. (2012, January 1). Dual-Continuum Modeling of Shale and Tight Gas Reservoirs. Society](https://reader033.vdocuments.us/reader033/viewer/2022042114/5e9089be8f79850e9c7d22f1/html5/thumbnails/21.jpg)
FLOW IN FRACTURED POROUS MEDIA
21
Fluid transport is governed by Darcy equation. Different measurement techniques exist: Flow experiments Correlations Numerical techniques
![Page 22: Multiscale Modeling of Gas Transport and Storage in Shale ...2- Azom, P. N. and Javadpour, F. (2012, January 1). Dual-Continuum Modeling of Shale and Tight Gas Reservoirs. Society](https://reader033.vdocuments.us/reader033/viewer/2022042114/5e9089be8f79850e9c7d22f1/html5/thumbnails/22.jpg)
IMAGE-BASED NUMERICAL MODELING
22
Chukwudozie C. Pore-scale lattice Boltzmann simulations of inertial flows in realistic porous media: a first principle analysis of the Forchheimer relationship. Master’s thesis, Louisiana State University; 2011.
SEM image of the rock Constructed 3D gray scale image Flow simulation results
![Page 23: Multiscale Modeling of Gas Transport and Storage in Shale ...2- Azom, P. N. and Javadpour, F. (2012, January 1). Dual-Continuum Modeling of Shale and Tight Gas Reservoirs. Society](https://reader033.vdocuments.us/reader033/viewer/2022042114/5e9089be8f79850e9c7d22f1/html5/thumbnails/23.jpg)
FLOW IN PROPPED FRACTURES
23 Takbiri Borujeni, A. (2013). Multi-scale modeling of inertial flows through propped fractures. PhD dissertation, Louisiana State University.
![Page 24: Multiscale Modeling of Gas Transport and Storage in Shale ...2- Azom, P. N. and Javadpour, F. (2012, January 1). Dual-Continuum Modeling of Shale and Tight Gas Reservoirs. Society](https://reader033.vdocuments.us/reader033/viewer/2022042114/5e9089be8f79850e9c7d22f1/html5/thumbnails/24.jpg)
RESERVOIR SIMULATION
24
![Page 25: Multiscale Modeling of Gas Transport and Storage in Shale ...2- Azom, P. N. and Javadpour, F. (2012, January 1). Dual-Continuum Modeling of Shale and Tight Gas Reservoirs. Society](https://reader033.vdocuments.us/reader033/viewer/2022042114/5e9089be8f79850e9c7d22f1/html5/thumbnails/25.jpg)
INERTIAL FLOWS AT PROPPANT-RESERVOIR INTERFACE
25
Inertial flows can not be upscaled
![Page 26: Multiscale Modeling of Gas Transport and Storage in Shale ...2- Azom, P. N. and Javadpour, F. (2012, January 1). Dual-Continuum Modeling of Shale and Tight Gas Reservoirs. Society](https://reader033.vdocuments.us/reader033/viewer/2022042114/5e9089be8f79850e9c7d22f1/html5/thumbnails/26.jpg)
DISCRETE MODELS
In discrete models, fractures are discretely within the reservoir
26
http://en.wikipedia.org/wiki/User:Jpvandijk/TaskForceMajella#CITEREFvan_Dijk2002.2C_b
![Page 27: Multiscale Modeling of Gas Transport and Storage in Shale ...2- Azom, P. N. and Javadpour, F. (2012, January 1). Dual-Continuum Modeling of Shale and Tight Gas Reservoirs. Society](https://reader033.vdocuments.us/reader033/viewer/2022042114/5e9089be8f79850e9c7d22f1/html5/thumbnails/27.jpg)
MULTICONTINUUM APPROACH FOR FRACTURED FORMATIONS
27
Principle of multicontinuum approach for fractured formations1
1- Dietrich, P., R. Helmig, M. Sauter, H. Htzl, J. Kngeter, and G. Teutsch (2005). Flow and Transport in Fractured Porous Media. Springer.
![Page 28: Multiscale Modeling of Gas Transport and Storage in Shale ...2- Azom, P. N. and Javadpour, F. (2012, January 1). Dual-Continuum Modeling of Shale and Tight Gas Reservoirs. Society](https://reader033.vdocuments.us/reader033/viewer/2022042114/5e9089be8f79850e9c7d22f1/html5/thumbnails/28.jpg)
CONCLUSION
• Klinkenberg equation might not be sufficient to determine permeability.
• Apparent permeability is stress-dependent.
• Multicontinuum approaches can be used.
• Knudsen number is larger than 0.1.
• Continuum assumptions are no longer valid.
• Sorption and slippage phenomena comes into the picture.
• Continuum assumptions are valid • Inertial flows come to the picture • Two modeling approaches: discrete and
multicontinuum
28
![Page 29: Multiscale Modeling of Gas Transport and Storage in Shale ...2- Azom, P. N. and Javadpour, F. (2012, January 1). Dual-Continuum Modeling of Shale and Tight Gas Reservoirs. Society](https://reader033.vdocuments.us/reader033/viewer/2022042114/5e9089be8f79850e9c7d22f1/html5/thumbnails/29.jpg)
APPENDIX
29
![Page 30: Multiscale Modeling of Gas Transport and Storage in Shale ...2- Azom, P. N. and Javadpour, F. (2012, January 1). Dual-Continuum Modeling of Shale and Tight Gas Reservoirs. Society](https://reader033.vdocuments.us/reader033/viewer/2022042114/5e9089be8f79850e9c7d22f1/html5/thumbnails/30.jpg)
MOLECULAR DYNAMICS
30
Lennard-Jones Plot of Carbon, Methane, and CO21
1- Wilcox, Jennifer, Carbon Capture, Springer New York Dordrecht Heidelberg London, 2012
![Page 31: Multiscale Modeling of Gas Transport and Storage in Shale ...2- Azom, P. N. and Javadpour, F. (2012, January 1). Dual-Continuum Modeling of Shale and Tight Gas Reservoirs. Society](https://reader033.vdocuments.us/reader033/viewer/2022042114/5e9089be8f79850e9c7d22f1/html5/thumbnails/31.jpg)
MODELING OF FLUID FLOW IN KEROGEN
Classical continuum-based gas flow equations cannot be used1.
Modeling approaches: Molecular Dynamics Direct Simulation Monte Carlo Burnett equation Reduced-order Boltzmann equations
31
Configuration of molecules and channel in molecular dynamic simulator.
Javadpour, F. 2009. Nanopores and Apparent Permeability of Gas Flow in Mudrocks (Shales and Siltstone). J. Cdn. Pet. Tech. 48 (8): 16–21.
![Page 32: Multiscale Modeling of Gas Transport and Storage in Shale ...2- Azom, P. N. and Javadpour, F. (2012, January 1). Dual-Continuum Modeling of Shale and Tight Gas Reservoirs. Society](https://reader033.vdocuments.us/reader033/viewer/2022042114/5e9089be8f79850e9c7d22f1/html5/thumbnails/32.jpg)
32
![Page 33: Multiscale Modeling of Gas Transport and Storage in Shale ...2- Azom, P. N. and Javadpour, F. (2012, January 1). Dual-Continuum Modeling of Shale and Tight Gas Reservoirs. Society](https://reader033.vdocuments.us/reader033/viewer/2022042114/5e9089be8f79850e9c7d22f1/html5/thumbnails/33.jpg)
33
The International Union of Pure and Applied Chemistry (IUPAC) pore size classifications
![Page 34: Multiscale Modeling of Gas Transport and Storage in Shale ...2- Azom, P. N. and Javadpour, F. (2012, January 1). Dual-Continuum Modeling of Shale and Tight Gas Reservoirs. Society](https://reader033.vdocuments.us/reader033/viewer/2022042114/5e9089be8f79850e9c7d22f1/html5/thumbnails/34.jpg)
BOLTZMANN EQUATION
34
![Page 35: Multiscale Modeling of Gas Transport and Storage in Shale ...2- Azom, P. N. and Javadpour, F. (2012, January 1). Dual-Continuum Modeling of Shale and Tight Gas Reservoirs. Society](https://reader033.vdocuments.us/reader033/viewer/2022042114/5e9089be8f79850e9c7d22f1/html5/thumbnails/35.jpg)
35
![Page 36: Multiscale Modeling of Gas Transport and Storage in Shale ...2- Azom, P. N. and Javadpour, F. (2012, January 1). Dual-Continuum Modeling of Shale and Tight Gas Reservoirs. Society](https://reader033.vdocuments.us/reader033/viewer/2022042114/5e9089be8f79850e9c7d22f1/html5/thumbnails/36.jpg)
36
![Page 37: Multiscale Modeling of Gas Transport and Storage in Shale ...2- Azom, P. N. and Javadpour, F. (2012, January 1). Dual-Continuum Modeling of Shale and Tight Gas Reservoirs. Society](https://reader033.vdocuments.us/reader033/viewer/2022042114/5e9089be8f79850e9c7d22f1/html5/thumbnails/37.jpg)
IMAGE-BASED PORE-SCALE MODELING
Velocity field at the pore space
Image from
XCT
Segmented Image Pore-scale Flow Simulation
(Lattice Boltzmann)(Sukop et al., 2007)
Reservoir Simulation Impacts on productivity indices
Berea Core Sample (Petroleum Cores)
Proppants (CARBO Ceramics)