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Low Pressure Gas Percolation Characteristic in Ultra-low Permeability Porous Media

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Abstract

Low pressure gas percolation characteristic in ultra-low permeability porous media is investigated in this article through core flow experiments. The results show that the wall-slip layer covers more than 10% of the average porous channel radius on account of minimum pore size when the permeability is below 0.1 × 10−3μ m 2 order, and seepage behavior is contrasted to that in mid-high permeability pore media. When the gas pressure is not high enough, the flow regime turns into transitional flow instead of slip flow, and nonlinear relationship between the measured gas permeability and the reciprocal of average pressure exists. The gas measuring permeability experiment would be influenced by the non-linear relationship. If Klinkenberg-corrected method is applied to speculate the equivalent liquid permeability, the extrapolated value will become less or minus. Simultaneously, actual gas flow velocity at the outlet is beyond the calculated value with Klinkenberg formula. A new gas seepage model based on the general slip boundary condition is derived from the homogenization technique in this article. At last the flow model is examined to be suitable for representing the gas flow behavior in ultra-low permeability media and estimating the absolute permeability from single-point, steady-states measurements.

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Abbreviations

b :

General slip coefficient

b K :

Gas slip factor

B :

Function of the gas molecule diameter and the absolute temperature

C :

Function of the diffuse reflectance fraction

D :

Molecular diameter

G :

Macroscopic pressure gradient

H :

Slip tensor

I :

Unit tensor

k :

Boltzmann constant

Kg, K∞, K:

Gas, equivalent liquid, tensorial permeability

Kn :

Knudsen number

l :

Microscopic flow field characteristic scale or microscopic length scale of the pores

L :

Macroscopic characteristic length scale of the porous media

n :

Unit normal vector to Γ

p :

Pressure

p m :

Mean pressure

r :

Mean pore-throat radius

Re :

Reynolds number

t :

Unit tangential vector to Γ

T :

Absolute temperature

v :

Gas velocity vector in the unit cell

V m :

Measured flow velocity at the outlet of the core

V th :

Theoretical flow rate by the Klinkenberg model

\({V^{\prime}_{\rm th}}\) :

Theoretical flow rate by the new model

V :

One-dimensional flow rate in the core

x :

Dimensionless macroscopic space variables

y :

Dimensionless microscopic space variables

\({\varepsilon }\) :

Small fundamental perturbation parameter

\({\varphi}\) :

Porosity of the sandstone

η :

Viscosity

Γ:

Internal surface of the unit cell

λ:

Gas molecules average free path

μ :

Viscosity

Ω:

Unit periodic cell

Ω p :

Pore volume in the unit cell

ρ :

Density

σ v :

Diffuse reflectance fraction

ψ:

Physical quantity of gas flow

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Authors and Affiliations

  1. MOE Key Laboratory of Petroleum Engineering, China University of Petroleum, Beijing, 102249, China

    Yue Xiang’an, Wei Haoguang, Zhang Lijuan, Zhao Renbao & Zhao Yongpan

  2. Enhanced Oil Recovery Research Center, China University of Petroleum, Changping district, Beijing, 102249, People’s Republic of China

    Yue Xiang’an, Wei Haoguang, Zhang Lijuan, Zhao Renbao & Zhao Yongpan

Authors
  1. Yue Xiang’an
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  2. Wei Haoguang
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  3. Zhang Lijuan
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  4. Zhao Renbao
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  5. Zhao Yongpan
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Corresponding author

Correspondence to Yue Xiang’an.

Additional information

Fund project: National science and technology key special project “Development of large oil and gas fields and coal bed gas” (2008ZX05009).

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Xiang’an, Y., Haoguang, W., Lijuan, Z. et al. Low Pressure Gas Percolation Characteristic in Ultra-low Permeability Porous Media. Transp Porous Med 85, 333–345 (2010). https://doi.org/10.1007/s11242-010-9565-0

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