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Multi-scale Analysis of Gas Transport Mechanisms in Kerogen

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Abstract

Quantification of natural gas transport in organic-rich shale is important in predicting natural gas production. However, laboratory measurements are challenging due to tight nature of the rock and include large uncertainties. The emphasis of this work is to understand mass transport mechanisms inside the organic nanoporous material known as kerogen under subsurface conditions and describe its permeability. This requires a multi-scale theoretical approach that includes flow measurements in model nanocapillaries and within their network. Molecular dynamics simulation results of steady-state supercritical methane flow in single-wall carbon nanotube are presented in this article. A transition from convection to molecular diffusion is observed. The simulation results show that the adsorbed methane molecules are mobile and contribute a significant portion to the total mass flux in nanocapillaries with diameter \({<}\)10 nm. They experience cluster diffusion that is dependent on the applied pressure drop across the capillary. A modified Hagen–Poiseuille equation is proposed considering the convective–diffusive nature of the overall transport in nanocapillary. The molecular-level study of steady-state transport is extended to a simple network of interconnected nanocapillaries representing kerogen. The modified Hagen–Poiseuille equation leads to a representative elementary volume of the model kerogen. The estimated permeability of the volume is sensitive to compressed and adsorbed fluids density ratio and to surface properties of the nanocapillary walls, indicating that fluid–wall interactions driven by molecular forces could be significant during the large-scale transport within shale. A modified Kozeny–Carman correlation is proposed, relating kerogen porosity and tortuosity to the permeability.

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Abbreviations

\(A_{\text {ads}} \) :

Cross section area for adsorbed-phase transport, m\(^{2}\)

\(A_{\text {diff}} \) :

Cross section area for diffusion transport, m\(^{2}\)

C :

Molar density, or concentration, mol/m\(^{3}\)

\(D_s\) :

Adsorbed-phase mobility, nm\(^{2}\)/(psi  ps)

D :

Diffusion coefficient, m\(^{2}\)/s

\(J_{\text {vis}}\) :

Mass flux of viscous flow, kg/m\(^{2}\)/s

\(J_{\text {total}}\) :

Total mass flux, kg/m\(^{2}\)/s

\(J_{\text {diff}}\) :

Mass flux by diffusion, kg/m\(^{2}\)/s

k :

Intrinsic permeability, m\(^{2}\)

\(k_\text {a}\) :

Apparent permeability, m\(^{2}\)

\(k_{\text {app}}\) :

Apparent pore network permeability, m\(^{2}\)

\(K_n\) :

Knudsen number, dimensionless

\(M_{\text {CH4}}\) :

Molecular weight of methane, kg/mol

\(m_{\text {total}}\) :

Total mass transfer rate, kg/s

\(m_{\text {ads}}\) :

Cluster diffusion mass transfer rate, kg/s

\(m_{\text {diff}}\) :

Pore diffusion mass transfer rate, kg/s

\(m_{\text {vis}}\) :

Viscous flow mass transfer rate, kg/s

\(m_{\text {HP}}\) :

Mass transfer rate based on HP equation, kg/s

\(N_{\text {Pe}}\) :

Péclet number, dimensionless

\(N_{\text {Bi}}\) :

Biot number, dimensionless

P :

Pressure, psi

\(Q_{\text {ads}}\) :

Volume transfer rate of adsorbed phase, m\(^{3}\)/s

\(Q_{\text {vis}}\) :

Volume transfer rate of viscous flow, m\(^{3}\)/s

\(r_{\text {tube}}\) :

Radius of capillary, m

\(r_{\text {ads}}\) :

Radius of capillary excluding adsorbed layer, m

\(r_{\text {avg}}\) :

Average radius of capillary network, m

\(R_{\text {mf}}\) :

Mass flux ratio, dimensionless

t :

Time, femtosecond

\(V_{\text {ads}}\) :

Adsorbed-phase velocity, nm/ps

x :

Distance in x-direction, nm

Z :

Network coordination number, dimensionless

\(\rho _s\) :

Adsorbed-phase density, kg/m\(^{3}\)

\(\rho \) :

Bulk phase density, kg/m\(^{3}\)

\(\mu \) :

Viscosity, Pa\(\cdot \)s

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Acknowledgements

RK has been funded by the Crisman Institute for Petroleum Engineering Research at Texas A&M University; SFKA has been funded by the King Fahad University of Petroleum and Minerals and by the Saudi Arabian Cultural Mission. The authors gratefully acknowledge their supports. RK and IYA acknowledge fruitful discussions with Dr. Khoa Bui and Sansarng Riewchotisakul on the MD flow simulations. The simulations have been performed using EOS cluster of the Supercomputing Facilities at Texas A&M University.

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  1. Texas A&M University, College Station, TX, USA

    Rui Kou, Saad F. K. Alafnan & I. Yucel Akkutlu

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  1. Rui Kou
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Correspondence to I. Yucel Akkutlu.

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Kou, R., Alafnan, S.F.K. & Akkutlu, I.Y. Multi-scale Analysis of Gas Transport Mechanisms in Kerogen. Transp Porous Med 116, 493–519 (2017). https://doi.org/10.1007/s11242-016-0787-7

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