Study on the micro-scale effect in the micro–nano organic pores of a shale reservoir

Abstract

The micro-scale effect occurs because of the gas flows in shale reservoirs containing small organic pores. In this study, based on a lattice Boltzmann model incorporating the bounce-back and specular-reflection boundary conditions, the gas flow through two parallel plates driven by differential pressures is simulated, which in turn verifies the model. Considering the effects of the slippage, surface diffusion, and adsorption, the gas flow in the organic channels is simulated based on the proposed lattice Boltzmann model. It is shown that the micro-scale effect is significant in the gas flows in the micro-scale channels. The compression effect leads to a nonlinear distribution of pressures along the centreline of the flow channels, and the nonlinearity increases with an increase in the pressure difference between the two sides of the flow channel. In case of gas flows in organic pores, the adsorption effect decreases the free-gas velocities, and with a decrease in pore sizes, the average free-gas velocity is reduced owing to the increased adsorption effect. The slippage effect and surface diffusion have a significant impact on the free-gas velocity of the mass flow. Compared to the slippage effect, surface diffusion contributes more to the mass flow of gas in organic pores. An increase in the Knudsen number intensifies the slippage effect and surface diffusion and enhances the mass flow.

Keywords

Shale reservoirs micro-scale effect lattice Boltzmann method Knudsen number mass flow

Get full access to this article

View all access options for this article.

References

Roy

Raju

Chuang

et al.

Modeling gas flow through micochannels and nanopores. J Appl Phys 2003; 93: 4870–4879.

Arkilic

Schmidt

Breuer

. Gaseous slip flow in long microchannels. J Microelectromech Syst 1997; 6: 167–178.

Bird

. Molecular gas dynamics and the direct simulation of gas flows, 2nd ed. New York: Clarendon, 2003, pp. 39–39.

Fan

Shen

. Statistical simulation of low-speed rarefied gas flows. J Comput Phys 2001; 20: 393–412.

Shen

Fan

Xie

. Statistical simulation of rarefied gas flows in micro-channels. J Comput Phys 2003; 189: 512–526.

Zhang

Qin

Emerson

. Lattice Boltzmann simulation of rarefied gas flows in microchannels. Phys Rev E Stat Nonlin Soft Matter Phys 2005; 71: 47702–47702.

Zhang

Barber

et al.

Capturing Knudsen layer phenomena using a lattice Boltzmann model. Phys Rev E 2006; 74: 406704–406704.

Guo

Zheng

Shi

. Lattice Boltzmann equation with multiple effective relaxation times for gaseous microscale flow. Phys Rev E Stat Nonlin Soft Matter Phys 2008; 77: 036707–036707.

Succi

. Mesoscopic modeling of slip motion at fluid-solid interfaces with heterogeneous catalysis. Phys Rev Lett 2002; 89: 064502–064502.

10.

Toschi

Succi

. Lattice Boltzmann method at finite-Knudsen numbers. Europhys Lett 2004; 69: 549–555.

11.

Tang

et al.

Lattice Boltzmann modeling of microchannel flows in the transition flow regime. Microfluid Nanofluid 2011; 10: 607–618.

12.

Kang

Fathi

Ambrose

et al.

Carbon dioxide storage capacity of organic-rich shales. SPE J 2013; 16: 842–855.

13.

Yang

Ning

et al.

Characterization of microscopic pore structures in shale reservoirs. Acta Petrol Sin 2013; 34: 301–311.

14.

Zhang

Yao

Sun

et al.

Permeability calculation in shale using lattice Boltzmann method. J China Univ Petrol 2014; 38: 87–91.

15.

Ren

Guo

et al.

A lattice Boltzmann model for simulating gas flow in kerogen pores. Transp Porous Media 2015; 106: 285–301.

16.

Chen

Zhang

Kang

et al.

Nanoscale simulation of shale transport properties using the lattice Boltzmann method: permeability and diffusivity. Sci Rep 2015; 5: 8089–8089.

17.

Landry

Prodanović

Eichhubl

. Direct simulation of supercritical gas flow in complex nanoporous media and prediction of apparent permeability. Int J Coal Geol 2016; 159: 120–134.

18.

Zhao

Yao

Zhang

et al.

Study of gas flow characteristics in tight porous media with a microscale lattice Boltzmann model. Sci Rep 2016; 6: 32393–32393.

19.

Germanou

et al.

On the apparent permeability of porous media in rarefied gas flows. J Fluid Mech 2017; 822: 389–417.

20.

Wang

Kang

et al.

The lattice Boltzmann method for isothermal micro-gaseous flow and its application in shale gas flow: a review. Int J Heat Mass Tran 2016; 95: 94–108.

21.

Wang

The basic theory and basic model of lattice Boltzmann method. In: Liu

(ed). Lattice Boltzmann method: theory and applications, 4th ed. Beijing: Science, 2009, pp. 57–80.

22.

Liu

Kang

Leonardi

et al.

Multiphase lattice Boltzmann simulations for porous media applications. Comput Geosc 2016; 20: 777–805.

23.

Qian

Dhumieres

Lallemand

. Lattice BGK models for Navier-Stokes equation. Europhys Lett 1992; 17: 479–484.

24.

Stops

. The mean free path of gas molecules in the transition regime. J Phy D: Appl Phys 2002; 3: 685–696.

25.

Guo

Zhao

Shi

. Physical symmetry, spatial accuracy, and relaxation time of the lattice Boltzmann equation for micro gas flows. J Appl Phys 2006; 99: 074903–074903.

26.

Tang

Tao

. Lattive Boltzmann method for simulating gas flow in microchannel. Int J Mod Phys C 2004; 15: 335–347.

27.

Ansumali

Karlin

. Kinetic boundary conditions in the lattice Boltzmann method. Phys Rev E Stat Nonlin Soft Matter Phys 2002; 66: 026311–026311.

28.

Tang

Tao

. Lattice Boltzmann method for gaseous microflows using kinetic theory boundary conditions. Phys. Fluids A 2005; 17: 058101–058101.

29.

Guo

Shi

Zhao

et al.

Discrete effects on boundary conditions for the lattice Boltzmann equation in simulating microscale gas flows. Phys Rev E Stat Nonlin Soft Matter Phys 2007; 76: 056704–056704.

30.

Shen

Tian

Xie

et al.

Examination of the LBM in simulation of microchannel flow in transitional regime. Microscale Thermophys Eng 2003; 8: 423–432.

31.

Ambrose

Hartman

Diaz-Campos

et al.

Shale gas-in-place calculations part I: new pore-scale considerations. SPE J 2012; 17: 219–229.