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Lattice Boltzmann simulation of shale gas transport in organic nano-pores.

Zhang X, Xiao L, Shan X, Guo L - Sci Rep (2014)

Bottom Line: Simulation results show that at small Knudsen number, LBM results agree well with Poiseuille's law, and flow rate (flow capacity) is proportional to the square of the pore scale.In addition, velocity increases as the slip effect causes non negligible velocities on the pore wall, thereby enhancing the flow rate inside the pore, i.e., the permeability.Therefore, the LBM simulation of gas flow characteristics in organic nano-pores provides an effective way of evaluating the permeability of gas-bearing shale.

View Article: PubMed Central - PubMed

Affiliation: State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum, Beijing 102249, People's Republic of China.

ABSTRACT
Permeability is a key parameter for investigating the flow ability of sedimentary rocks. The conventional model for calculating permeability is derived from Darcy's law, which is valid only for continuum flow in porous rocks. We discussed the feasibility of simulating methane transport characteristics in the organic nano-pores of shale through the Lattice Boltzmann method (LBM). As a first attempt, the effects of high Knudsen number and the associated slip flow are considered, whereas the effect of adsorption in the capillary tube is left for future work. Simulation results show that at small Knudsen number, LBM results agree well with Poiseuille's law, and flow rate (flow capacity) is proportional to the square of the pore scale. At higher Knudsen numbers, the relaxation time needs to be corrected. In addition, velocity increases as the slip effect causes non negligible velocities on the pore wall, thereby enhancing the flow rate inside the pore, i.e., the permeability. Therefore, the LBM simulation of gas flow characteristics in organic nano-pores provides an effective way of evaluating the permeability of gas-bearing shale.

No MeSH data available.


Relationship between relaxation time and Knudsen number.
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f2: Relationship between relaxation time and Knudsen number.

Mentions: Reynolds number, Re, which is related to fluid shear viscosity η, is the basic characteristic quantity of fluid flow in macroscopic flow. Relaxation time τ can be uniquely determined by the Reynolds number according to the relationship between τ and viscosity when LBM simulation is used for macroscopic flow. With continuum flows (Kn<10−3), τ can be assumed to be constant. In the LBM model, the second-order error due to spatial discretization can be absorbed into the hydrodynamic equation, yielding a kinematic viscosity18 as follows: where υ is the kinematic viscosity, R is the ideal gas constant, T is the temperature. In D2Q9 model, RT is usually taken as 1/3. The Knudsen number Kn is the characteristic parameter for nano-scale shale gas flow in porous media, i.e., in the case of slip flow (10−3<Kn<10−1). Thus, one key issue of the LBM simulation of micro-scale flow is to give the right relaxation time for a specified Kn. According to kinetic theory, the molecular mean-free-path of a gas and the Knudsen number19 can be calculated according to Eq. (2) and (3)20. where λ is the molecular mean-free-path; kB is the Boltzmann constant; d is the molecular diameter; p is the fluid pressure; T is the ambient temperature; υ is the kinematic viscosity; H is characteristic length of flow. Relaxation time τ should be corrected according to the Knudsen number Kn. Correction is calculated by Eq. (4) and Eq. (5)13: where the modified relaxation time τ* introduces the effect of the pore walls. In the continuum flow region, relaxation time remains substantially constant. However, in the slip flow regime, relaxation time decreases when the Knudsen number increases as shown in Fig. 2, indicating that the collision portion of the actual particles has a short relaxation time, and slip velocity exists on pore walls in the macro-level.


Lattice Boltzmann simulation of shale gas transport in organic nano-pores.

Zhang X, Xiao L, Shan X, Guo L - Sci Rep (2014)

Relationship between relaxation time and Knudsen number.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4007072&req=5

f2: Relationship between relaxation time and Knudsen number.
Mentions: Reynolds number, Re, which is related to fluid shear viscosity η, is the basic characteristic quantity of fluid flow in macroscopic flow. Relaxation time τ can be uniquely determined by the Reynolds number according to the relationship between τ and viscosity when LBM simulation is used for macroscopic flow. With continuum flows (Kn<10−3), τ can be assumed to be constant. In the LBM model, the second-order error due to spatial discretization can be absorbed into the hydrodynamic equation, yielding a kinematic viscosity18 as follows: where υ is the kinematic viscosity, R is the ideal gas constant, T is the temperature. In D2Q9 model, RT is usually taken as 1/3. The Knudsen number Kn is the characteristic parameter for nano-scale shale gas flow in porous media, i.e., in the case of slip flow (10−3<Kn<10−1). Thus, one key issue of the LBM simulation of micro-scale flow is to give the right relaxation time for a specified Kn. According to kinetic theory, the molecular mean-free-path of a gas and the Knudsen number19 can be calculated according to Eq. (2) and (3)20. where λ is the molecular mean-free-path; kB is the Boltzmann constant; d is the molecular diameter; p is the fluid pressure; T is the ambient temperature; υ is the kinematic viscosity; H is characteristic length of flow. Relaxation time τ should be corrected according to the Knudsen number Kn. Correction is calculated by Eq. (4) and Eq. (5)13: where the modified relaxation time τ* introduces the effect of the pore walls. In the continuum flow region, relaxation time remains substantially constant. However, in the slip flow regime, relaxation time decreases when the Knudsen number increases as shown in Fig. 2, indicating that the collision portion of the actual particles has a short relaxation time, and slip velocity exists on pore walls in the macro-level.

Bottom Line: Simulation results show that at small Knudsen number, LBM results agree well with Poiseuille's law, and flow rate (flow capacity) is proportional to the square of the pore scale.In addition, velocity increases as the slip effect causes non negligible velocities on the pore wall, thereby enhancing the flow rate inside the pore, i.e., the permeability.Therefore, the LBM simulation of gas flow characteristics in organic nano-pores provides an effective way of evaluating the permeability of gas-bearing shale.

View Article: PubMed Central - PubMed

Affiliation: State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum, Beijing 102249, People's Republic of China.

ABSTRACT
Permeability is a key parameter for investigating the flow ability of sedimentary rocks. The conventional model for calculating permeability is derived from Darcy's law, which is valid only for continuum flow in porous rocks. We discussed the feasibility of simulating methane transport characteristics in the organic nano-pores of shale through the Lattice Boltzmann method (LBM). As a first attempt, the effects of high Knudsen number and the associated slip flow are considered, whereas the effect of adsorption in the capillary tube is left for future work. Simulation results show that at small Knudsen number, LBM results agree well with Poiseuille's law, and flow rate (flow capacity) is proportional to the square of the pore scale. At higher Knudsen numbers, the relaxation time needs to be corrected. In addition, velocity increases as the slip effect causes non negligible velocities on the pore wall, thereby enhancing the flow rate inside the pore, i.e., the permeability. Therefore, the LBM simulation of gas flow characteristics in organic nano-pores provides an effective way of evaluating the permeability of gas-bearing shale.

No MeSH data available.