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MULTISCALE MODELING OF GAS TRANSPORT AND STORAGE IN
SHALE RESOURCES
Ali Takbiri-Borujeni
12/02/2014
WHAT TO EXPECT
An introduction to gas transport modeling techniques and their complexities at different scales.
2
http://geologycafe.com/stories/frackin.html
DIFFERENT SCALES IN SHALE GAS RECOVERY
3 1- Ruppel and Loucks (2008)
1
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.
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)
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
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.
SORPTION MODELING
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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.
VELOCITY PROFILES FOR DIFFERENT KNUDSEN NUMBERS
9
Assumptions: Specular and diffusive
reflections
Slip velocity increases as Knudsen number increases
MODEL RESULTS FOR PERMEABILITY
10
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
IMPACT OF TEMPERATURE ON APPARENT PERMEABILITY
12
Kd vs. channel width for different temperatures at constant pressure of 0.28 MPa for Argon.
CORE PLUG SCALE
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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.
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
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.
PERMEABILITY MEASUREMENT
16
laboratory measured apparent permeability, if conducted in low pressure and temperatures, need to be extrapolated to reservoir conditions.
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
CYLINDRICAL BUNDLE
For a known pore size distribution, permeability of the core can be calculated from:
φ/T: porosity-tortuosity ratio
18
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
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
FLOW IN FRACTURED POROUS MEDIA
21
Fluid transport is governed by Darcy equation. Different measurement techniques exist: Flow experiments Correlations Numerical techniques
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
FLOW IN PROPPED FRACTURES
23 Takbiri Borujeni, A. (2013). Multi-scale modeling of inertial flows through propped fractures. PhD dissertation, Louisiana State University.
RESERVOIR SIMULATION
24
INERTIAL FLOWS AT PROPPANT-RESERVOIR INTERFACE
25
Inertial flows can not be upscaled
DISCRETE MODELS
In discrete models, fractures are discretely within the reservoir
26
http://en.wikipedia.org/wiki/User:Jpvandijk/TaskForceMajella#CITEREFvan_Dijk2002.2C_b
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.
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
APPENDIX
29
MOLECULAR DYNAMICS
30
Lennard-Jones Plot of Carbon, Methane, and CO21
1- Wilcox, Jennifer, Carbon Capture, Springer New York Dordrecht Heidelberg London, 2012
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.
32
33
The International Union of Pure and Applied Chemistry (IUPAC) pore size classifications
BOLTZMANN EQUATION
34
35
36
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)