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Pore Network Modeling of Shale Gas Reservoirs: Gas Desorption and Slip Flow Effects

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Abstract

Shale reservoirs are characterized by very low permeability in the scale of nano-Darcy. This is due to the nanometer scale of pores and throats in shale reservoirs, which causes a difference in flow behavior from conventional reservoirs. Slip flow is considered to be one of the main flow regimes affecting the flow behavior in shale gas reservoirs and has been widely studied in the literature. However, the important mechanism of gas desorption or adsorption that happens in shale reservoirs has not been investigated thoroughly in the literature. This paper aims to study slip flow together with gas desorption in shale gas reservoirs using pore network modeling. To do so, the compressible Stokes equation with proper boundary conditions was applied to model gas flow in a pore network that properly represents the pore size distribution of typical shale reservoirs. A pore network model was created using the digitized image of a thin section of a Berea sandstone and scaled down to represent the pore size range of shale reservoirs. Based on the size of pores in the network and the pore pressure applied, the Knudsen number which controls the flow regimes was within the slip flow regime range. Compressible Stokes equation with proper boundary conditions at the pore’s walls was applied to model the gas flow. The desorption mechanism was also included through a boundary condition by deriving a velocity term using Langmuir-type isotherm. It was observed that when the slip flow was activated together with desorption in the model, their contributions were not summative. That, is the slippage effect limited the desorption mechanism through a reduction of pressure drop. Eagle Ford and Barnett shale samples were investigated in this study when the measured adsorption isotherm data from the literature were used. Barnett sample showed larger contribution of gas desorption toward gas recovery as compared to Eagle Ford sample. This paper has produced a pore network model to further understand the gas desorption and the slip flow effects in recovery of shale gas reservoirs.

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Abbreviations

N :

Coordination normal to the wall

\( L_{\text{s}} \) :

Slip length (m)

\( u_{\text{T}} \) :

Thermal motion velocity

\( u_{\text{s}} \) :

Slip velocity (m/s)

u w :

Wall velocity (m/s)

u d :

Velocity term for desorption boundary condition

C 1 :

First-order slip coefficient

u :

Fluid velocity

K :

Permeability (m2)

M :

Gas molecular mass (kg/mol)

L :

Length (m)

p :

Pore pressure (Pa)

D :

Diffusion coefficient

D n :

Knudsen diffusion coefficient

d p :

Pore diameter

A :

Cross-sectional area (m2)

T :

Temperature (K)

vl :

Langmuir volume (m3/kg)

\( R = 8.31445 \times 10^{3} \) :

Gas constant (g/m2/s2/mol/K)

λ :

Mean free path of flowing gas

μ :

Gas viscosity (Pa s)

σ v :

Tangential accommodation coefficient

ρ :

Gas density (kg/m3)

ρ r :

Rock density (kg/m3)

s :

Slip

K n :

Knudsen number

\( {\text{Re}} \) :

Reynold number

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Acknowledgements

This research has been carried out in Petroleum Engineering Department at Universiti Teknologi PETRONAS (UTP). UTP has fully supported this research which is greatly acknowledged.

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Authors and Affiliations

  1. Petroleum Engineering Department, Universiti Teknologi PETRONAS, Perak, Malaysia

    Jalal Foroozesh & Amr Ibrahim Mohamed Abdalla

  2. School of Chemistry and Chemical Engineering, Chongqing University of Technology, Chongqing, 400054, China

    Zhien Zhang

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  1. Jalal Foroozesh
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Correspondence to Jalal Foroozesh.

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Foroozesh, J., Abdalla, A.I.M. & Zhang, Z. Pore Network Modeling of Shale Gas Reservoirs: Gas Desorption and Slip Flow Effects. Transp Porous Med 126, 633–653 (2019). https://doi.org/10.1007/s11242-018-1147-6

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