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Multiscale, Multiphysics Network Modeling of Shale Matrix Gas Flows

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Abstract

We present a pore network model to determine the permeability of shale gas matrix. Contrary to the conventional reservoirs, where permeability is only a function of topology and morphology of the pores, the permeability in shale depends on pressure as well. In addition to traditional viscous flow of Hagen–Poiseuille or Darcy type, we included slip flow and Knudsen diffusion in our network model to simulate gas flow in shale systems that contain pores on both micrometer and nanometer scales. This is the first network model in 3D that combines pores with nanometer and micrometer sizes with different flow physics mechanisms on both scales. Our results showed that estimated apparent permeability is significantly higher when the additional physical phenomena are considered, especially at lower pressures and in networks where nanopores dominate. We performed sensitivity analyses on three different network models with equal porosity; constant cross-section model (CCM), enlarged cross-section model (ECM) and shrunk length model (SLM). For the porous systems with variable pore sizes, the apparent permeability is highly dependent on the fraction of nanopores and the pores’ connectivity. The overall permeability in each model decreased as the fraction of nanopores increased.

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Abbreviations

\(A\) :

Cross-sectional area, \(\text{ m }^{2}\)

\(f\) :

Nanopore fraction, dimensionless

\(F\) :

Theoretical dimensionless coefficient

\(J\) :

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

\(K\) :

Permeability, \(\text{ m }^{2}\)

\(L\) :

Pore length, m

\(M\) :

Molar mass, kg/kmol

\(p\) :

Pressure, Pa

\(q\) :

Flow rate, m\(^{3}\)/s

\(r\) :

Pore radius, m

\(R\) :

Gas constant, J/mol/K

\(t\) :

Time, s

\(T\) :

Temperature, K

\(u\) :

Velocity, m/s

\(w\) :

Relaxation factor

\(\alpha \) :

Tangential momentum accommodation coefficient, dimensionless

\(\mu \) :

Viscosity, Pa.s

\(\rho \) :

Density, kg/m\(^{3}\)

\(\varphi \) :

Porosity, fraction

app :

Apparent

avg :

Average

\(i,j\) :

Pore identity number

\(ij\) :

Throat identity number (throat connecting pore \(i\) and pore \(j\))

D :

Darcy (referring to Darcy permeability)

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Authors and Affiliations

  1. Department of Petroleum and Geosystems Engineering, The University of Texas at Austin, Austin, TX, USA

    Ayaz Mehmani & Maša Prodanović

  2. Bureau of Economic Geology, Jackson School of Geosciences, The University of Texas at Austin, Austin, TX, USA

    Farzam Javadpour

Authors
  1. Ayaz Mehmani
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  2. Maša Prodanović
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  3. Farzam Javadpour
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Correspondence to Maša Prodanović.

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Mehmani, A., Prodanović, M. & Javadpour, F. Multiscale, Multiphysics Network Modeling of Shale Matrix Gas Flows. Transp Porous Med 99, 377–390 (2013). https://doi.org/10.1007/s11242-013-0191-5

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