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Relative Permeability of Gas for Unconventional Reservoirs

Abstract

Relative permeability of gas gains great significance in exploring unconventional gas. This paper developed a universal relative permeability model of gas, which is applicable for unconventional gas reservoirs such as coal, tight sandstone and shale. The model consists of the absolute relative permeability of gas and the gas slippage permeability. In the proposed model, the effects of water saturation and mean pore pressure on gas slippage permeability are taken into account. Subsequently, the evaluation of the model with existing model is done and then the validation of the model is made with data of tight sandstones, coals and shales from published literatures. The modeling results illustrate that a strong power-law relationship between relative permeability of gas and water saturation and the contribution of gas slippage permeability to relative permeability is determined by water saturation and mean pore pressure simultaneously. Furthermore, a sensitivity analysis of the impact of the parameters in the model is conducted and their effects are discussed.

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Abbreviations

K eg :

Effective permeability of gas (μm2)

K a :

Absolute permeability of unconventional gas reservoirs (μm2)

K rg :

Relative permeability of gas (μm2)

K rgw :

Relative permeability of gas at Sw (μm2)

K rgw∞ :

Absolute relative permeability of gas at Sw (μm2)

K egw :

Effective permeability of gas at Sw (μm2)

K gw∞ :

Absolute permeability of gas at Sw (μm2)

K g0∞ :

Absolute permeability of gas at water saturation of 0 (μm2)

S w :

Water saturation (percentage)

V w :

Volume of water (m3)

V :

Pore volume in unconventional gas reservoirs (m3)

b :

Gas slippage factor (MPa)

b w :

Gas slippage factor at Sw (MPa)

b 0 :

Gas slippage factor at water saturation of 0 (MPa)

R 0 :

Radius of capillary tube before wetting (m)

R w :

Radius of capillary tube after wetting (m)

W 0 :

Width of fracture before wetting (m)

W w :

Width of fracture after wetting (m)

H 0 :

Height of fracture before wetting (m)

H w :

Height of fracture after wetting (m)

P m :

Mean pore pressure (MPa)

L :

Length of capillary tube/fracture (m)

τ:

Tortuosity of capillary tube/fracture (fraction)

ϕ 0 :

Porosity of unconventional gas reservoirs before wetting (percentage)

ϕ w :

Porosity of unconventional gas reservoirs after wetting (percentage)

c :

A constant factor with a value less than 1

r:

Average pore radius in unconventional gas reservoirs (m)

r 0 :

Average pores radius in unconventional gas reservoirs before wetting (m)

r w :

Average pores radius in unconventional gas reservoirs after wetting (m)

λ :

Gas mean free path (m)

K :

Boltzmann constant

T :

Temperature (°C)

d :

Diameter of gas molecules (m)

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Acknowledgements

The authors gratefully acknowledge the funding support of the State Key Research Development Program of China (2016YFC0600708, 2016YFC0801402), and the National Natural Science Foundation of China (Grant Nos. 51774292, 51474219, 51604278).

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Correspondence to Kai Wang.

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Liu, A., Wang, K., Zang, J. et al. Relative Permeability of Gas for Unconventional Reservoirs. Transp Porous Med 124, 289–307 (2018). https://doi.org/10.1007/s11242-018-1064-8

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Keywords

  • Unconventional gas reservoirs
  • Gas slippage
  • Water saturation
  • Relative permeability