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)

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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)

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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

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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

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Assumptions: Specular and diffusive

reflections

Slip velocity increases as Knudsen number increases

MODEL RESULTS FOR PERMEABILITY

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PERMEABILITY IN SLIP REGIME

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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

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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.

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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

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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

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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

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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

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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

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Fluid transport is governed by Darcy equation. Different measurement techniques exist: Flow experiments Correlations Numerical techniques

IMAGE-BASED NUMERICAL MODELING

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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

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INERTIAL FLOWS AT PROPPANT-RESERVOIR INTERFACE

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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

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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

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APPENDIX

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MOLECULAR DYNAMICS

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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

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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.

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The International Union of Pure and Applied Chemistry (IUPAC) pore size classifications

BOLTZMANN EQUATION

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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)