MULTISCALE MODELING OF GAS TRANSPORT AND STORAGE IN SHALE RESOURCES

Transcription

1 MULTISCALE MODELING OF GAS TRANSPORT AND STORAGE IN SHALE RESOURCES Ali Takbiri-Borujeni 12/02/2014

2 WHAT TO EXPECT An introduction to gas transport modeling techniques and their complexities at different scales. 2

3 DIFFERENT SCALES IN SHALE GAS RECOVERY 1 1- Ruppel and Loucks (2008) 3

4 FLOW REGIME CHARACTERIZATION Gas flow regimes are characterized by the Knudsen number (Kn). Flow regimes are 1 : continuum flow (0 < Kn < 10 3 ) slip flow (10 3 < Kn < 10 1 ) transition flow (10 1 < Kn < 10) free molecular flow (10 < Kn < ) In organic nanopores in shale, Knudsen number is larger than 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),

5 ORGANIC MATTER (KEROGEN) 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) 5

6 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

7 BOUNDARY CONDITIONS Three types of gas-surface interactions 1 : 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) 1- Masel, R. I. (1996). Principles of adsorption and reaction on solid surfaces, Volume 3. John Wiley & Sons. 7

8 SORPTION MODELING Gas sorption capacity is defined by volume and pressure isotherms. Langmuir model suggests the development of a single molecular layer of adsorption. Langmuir isotherm Myong, R. S. (2004). Gaseous slip models based on the Langmuir adsorption isotherm. Physics of Fluids, 16(1),

9 VELOCITY PROFILES FOR DIFFERENT KNUDSEN NUMBERS Assumptions: Specular and diffusive reflections Slip velocity increases as Knudsen number increases 9

10 MODEL RESULTS FOR PERMEABILITY 10

11 PERMEABILITY IN SLIP REGIME K d vs. inverse of mean pressure for Argon at T = 338 K for different channel widths K d vs. inverse of the mean pressure for Argon and Helium at T= 338 K for channel widths of 10 and 100 nm 11

12 IMPACT OF TEMPERATURE ON APPARENT PERMEABILITY K d vs. channel width for different temperatures at constant pressure of 0.28 MPa for Argon. 12

13 CORE PLUG SCALE 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. 13

14 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

15 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 Comparison of crushed rock permeability from different laboratories 1 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. 15

16 PERMEABILITY MEASUREMENT laboratory measured apparent permeability, if conducted in low pressure and temperatures, need to be extrapolated to reservoir conditions. 16

17 EXPERIMENTAL RESULTS-STEADY STATE A new steady-state permeability measurement technique Permeability measurement using steady-state method 1 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: / ms 17

18 CYLINDRICAL BUNDLE For a known pore size distribution, permeability of the core can be calculated from: φ/t: porosity-tortuosity ratio 18

19 EXAMPLE Pore-size distribution obtained by Nitrogen adsorption method at 77 K 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: / ms 19

20 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. Organic pores inorganic pores fractures Multicontinuum approach for shale gas transport 1 1- Akkutlu, I.Y., and Fathi, E. (2012). Multiscale gas transport in shales with local Kerogen heterogeneities. SPE Journal, Volume 17, Number Azom, P. N. and Javadpour, F. (2012, January 1). Dual-Continuum Modeling of Shale and Tight Gas Reservoirs. Society of Petroleum Engineers. doi: / ms 20

21 FLOW IN FRACTURED POROUS MEDIA Fluid transport is governed by Darcy equation. Different measurement techniques exist: Flow experiments Correlations Numerical techniques 21

22 IMAGE-BASED NUMERICAL MODELING SEM image of the rock Constructed 3D gray scale image Flow simulation results 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;

23 FLOW IN PROPPED FRACTURES Takbiri Borujeni, A. (2013). Multi-scale modeling of inertial flows through propped fractures. PhD dissertation, Louisiana State University. 23

24 RESERVOIR SIMULATION 24

25 INERTIAL FLOWS AT PROPPANT-RESERVOIR INTERFACE Inertial flows can not be upscaled 25

26 DISCRETE MODELS In discrete models, fractures are discretely within the reservoir 26

27 MULTICONTINUUM APPROACH FOR FRACTURED FORMATIONS Principle of multicontinuum approach for fractured formations 1 1- Dietrich, P., R. Helmig, M. Sauter, H. Htzl, J. Kngeter, and G. Teutsch (2005). Flow and Transport in Fractured Porous Media. Springer. 27

28 CONCLUSION Continuum assumptions are valid Inertial flows come to the picture Two modeling approaches: discrete and multicontinuum 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. 28

29 APPENDIX 29

30 MOLECULAR DYNAMICS Lennard-Jones Plot of Carbon, Methane, and CO Wilcox, Jennifer, Carbon Capture, Springer New York Dordrecht Heidelberg London,

31 MODELING OF FLUID FLOW IN KEROGEN Classical continuum-based gas flow equations cannot be used 1. Modeling approaches: Molecular Dynamics Direct Simulation Monte Carlo Burnett equation Reduced-order Boltzmann equations Configuration of molecules and channel in molecular dynamic simulator. Javadpour, F Nanopores and Apparent Permeability of Gas Flow in Mudrocks (Shales and Siltstone). J. Cdn. Pet. Tech. 48 (8):

32 32

33 The International Union of Pure and Applied Chemistry (IUPAC) pore size classifications 33

34 BOLTZMANN EQUATION 34

35 35

36 36

37 IMAGE-BASED PORE-SCALE MODELING Berea Core Sample (Petroleum Cores) Image from XCT Segmented Image Pore-scale Flow Simulation (Lattice Boltzmann)(Sukop et al., 2007) Proppants (CARBO Ceramics) Impacts on productivity indices Reservoir Simulation Velocity field at the pore space