On the flow regime model for fast estimation of tight sandstone gas apparent permeability in high-pressure reservoirs

ABSTRACT

A flow regime-based gas apparent permeability model in high-pressure tight sandstone reservoirs is established by bridging molecular kinetics, gas transport mechanisms, and apparent permeability. This model is well validated against simulation and experimental data. Results indicate that an equal-flow point tends to move to a low-pressure region with an increase in a pore diameter. As an equal-flow line is close to an isoline of a Knudsen number of 1, a flow regime is divided into three Knudsen number-based regions. Both the equal-flow line and the isoline of a Knudsen number indicate that an increasing temperature expands a Knudsen diffusion-dominated region, which further enhances the gas transport permeability. A typical curve of flow-regime gas apparent permeability provides a fast estimation of gas apparent permeability based on a Knudsen number and a pore diameter. The minimum Knudsen number line constrained by a packing fraction in a typical curve also indicates a minimum gas apparent permeability when a pore diameter is less than 100 nm.

KEYWORDS:

• Tight sandstone gas
• flow regime
• gas apparent permeability
• Knudsen number
• Knudsen diffusion

Acknowledgments

The authors would like to acknowledge the NSERC/Energi Simulation and Alberta Innovates Chairs for providing research funding. Keliu Wu would like to acknowledge the Science Foundation of China University of Petroleum, Beijing (No.2462018YJRC033) for providing research funding. Xiong Liu would like to acknowledge the Chinese National Natural Science Foundation (No. 51804257) for providing research funding.

Nomenclature

$A$ parameter in the Carnahan-Starling equation of state;

$B$ parameter in the Carnahan-Starling equation of state;

$D_k$ Knudsen diffusion coefficient, $m^2/s$;

$d_p$ pore diameter, $m$;

$d_m$ is the molecular diameter, $m$;

$J_k$ Knudsen diffusion flux, $mol/\left(m^2\cdot s\right)$;

$J_t$ total flow flux, $mol/\left(m^2\cdot s\right)$;

$J_v$ viscous flow flux, $mol/\left(m^2\cdot s\right)$;

$Kn$ Knudsen number, dimensionless;

$K_A$ apparent permeability, $m^2$.

$k$ Boltzmann constant, $=1.380658\times {10}^{-23}J/K$;

$m$ molecular weight, $kg$;

$n$ molecular number density, $1/m^3$;

$P$ pressure, $kPa$;

$R$ gas constant, $=8.314J/\left(K\cdot mol\right)$;

$T$ temperature, $K$;

$\bar{v}$ average molecular speed, $m/s$;

$z$ gas compressibility, dimensionless.

${\theta }_v$ ratio of viscous flow flux to total flux, dimensionless;

${\theta }_k$ ratio of Knudsen diffusion flux to total flux, dimensionless;

$\eta$ packing fraction, dimensionless;

$\rho$ gas density, $kg/m^3$;

${\tau }_{M-M}$ intermolecular collision frequency, $1/s$;

${\tau }_{M-W}$ molecule-wall collision frequency, $1/s$;

$\lambda$ mean free path, $m$;

$\mu$ gas viscosity, $Pa\cdot s$;

$\varphi$ porosity, dimensionless;

$\iota$ tortuosity, dimensionless;

${\mathrm{\Delta }}_0$ parameter in the Carnahan-Starling equation of state;

${\mathrm{\Delta }}_1$ parameter in the Carnahan-Starling equation of state.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [51804257]; Science Foundation of China University of Petroleum, Beijing [2462018YJRC033].

Notes on contributors

Jinze Xu

Jinze Xu holds a PhD degree in Petroleum Engineering from the University of Calgary. He has reservoir engineering experience in both industry and academia.

Zhangxin Chen

Zhangxin Chen is a professor in the Department of Chemical and Petroleum Engineering and the Director of the Foundation CMG/Frank and Sarah Meyer Collaboration Centre at the University of Calgary. His research specialty is in reservoir modeling and simulation and scientific computing. Chen has the distinction of holding two chairs: the Natural Sciences and Engineering Research Council of Canada/Energi Simulation Senior Research Chair in Reservoir Simulation and the Alberta Innovates Technology Futures (Alberta Innovates Technology Futures, formerly iCORE) Industrial Chair in Reservoir Modeling. He holds a PhD degree from Purdue University.

Keliu Wu

Keliu Wu is currently an associate professor at China University of Petroleum, Beijing. Previously, he was a post-doctoral-degree fellow and a research associate at the University of Calgary. Wu’s research interests are microscale and nanoscale fluid transport, scaling up of fluid transport in heterogeneous porous media, and numerical modeling and simulation of coupled flow and geomechanics processes. He also focuses on carbon dioxide sequestration in shale-oil/gas reservoirs and tight oil/gas reservoirs. Wu holds a PhD degree in petroleum engineering from China University of Petroleum, Beijing.

Ran Li

Ran Li is currently a Postdoctoral Associate at the University of Calgary. Her research interests include modeling production of heavy oil and shale gas.

Xiong Liu

Xiong Liu is currently a lecturer at Xi'an Shiyou University. He is mainly focused on the reservoir engineering work of field development.

Jie Zhan

Jie Zhan is currently a lecturer at Xi'an Shiyou University. He holds a Ph.D degree from the University of Calgary.