Simulations of Nanoscale Gas Flow with Knudsen Diffusion and Slip Flow

2021 ◽  
Vol 13 (6) ◽  
pp. 971-978
Author(s):  
I. S. Nesterova ◽  
K. M. Gerke
Keyword(s):  
Gas Flow ◽  
Knudsen Diffusion ◽  
Slip Flow

scholarly journals Multiscale Apparent Permeability Model of Shale Nanopores Based on Fractal Theory

Energies ◽  
2019 ◽  
Vol 12 (17) ◽  
pp. 3381 ◽  
Author(s):  
Qiang Wang ◽  
Yongquan Hu ◽  
Jinzhou Zhao ◽  
Lan Ren ◽  
Chaoneng Zhao ◽  
...  
Keyword(s):  
Shale Gas ◽  
Gas Flow ◽  
Gas Transport ◽  
Fractal Theory ◽  
Knudsen Diffusion ◽  
Slip Flow ◽  
Clear Understanding ◽  
Apparent Permeability ◽  
Permeability Model ◽  
Shale Gas Transport

Based on fractal geometry theory, the Hagen–Poiseuille law, and the Langmuir adsorption law, this paper established a mathematical model of gas flow in nano-pores of shale, and deduced a new shale apparent permeability model. This model considers such flow mechanisms as pore size distribution, tortuosity, slippage effect, Knudsen diffusion, and surface extension of shale matrix. This model is closely related to the pore structure and size parameters of shale, and can better reflect the distribution characteristics of nano-pores in shale. The correctness of the model is verified by comparison with the classical experimental data. Finally, the influences of pressure, temperature, integral shape dimension of pore surface and tortuous fractal dimension on apparent permeability, slip flow, Knudsen diffusion and surface diffusion of shale gas transport mechanism on shale gas transport capacity are analyzed, and gas transport behaviors and rules in multi-scale shale pores are revealed. The proposed model is conducive to a more profound and clear understanding of the flow mechanism of shale gas nanopores.

scholarly journals A non-empirical model for gas transfer through circular nanopores in unconventional gas reservoirs

2021 ◽  
Vol 11 (5) ◽  
pp. 2217-2232
Author(s):  
Jiangtao Li ◽  
Jianguang Wei ◽  
Liang Ji ◽  
Anlun Wang ◽  
Gen Rong ◽  
...  
Keyword(s):  
Gas Flow ◽  
Gas Transport ◽  
Transport Model ◽  
Knudsen Diffusion ◽  
Slip Flow ◽  
Gas Reservoirs ◽  
Permeability Model ◽  
Proposed Model ◽  
Unconventional Gas Reservoirs ◽  
Empirical Coefficients

AbstractIt is difficult to predict the flow performance in the nanopore networks since traditional assumptions of Navier–Stokes equation break down. At present, lots of attempts have been employed to address the proposition. In this work, the advantages and disadvantages of previous analytical models are seriously analyzed. The first type is modifying a mature equation which is proposed for a specified flow regime and adapted to wider application scope. Thus, the first-type models inevitably require empirical coefficients. The second type is weight superposition based on two different flow mechanisms, which is considered as the reasonable establishment method for universal non-empirical gas-transport model. Subsequently, in terms of slip flow and Knudsen diffusion, the novel gas-transport model is established in this work. Notably, the weight factors of slip flow and Knudsen diffusion are determined through Wu’s model and Knudsen’s model respectively, with the capacity to capture key transport mechanism through nanopores. Capturing gas flow physics at nanoscale allows the proposed model free of any empirical coefficients, which is also the main distinction between our work and previous research. Reliability of proposed model is verified by published molecular simulation results as well. Furthermore, a novel permeability model for coal/shale matrix is developed based on the non-empirical gas-transport model. Results show that (a) nanoconfined gas-transport capacity will be strengthened with the decline of pressure and the decrease in the pressure is supportive for the increasing amplitude; (b) the greater pore size the nanopores is, the stronger the transport capacity the nanotube is; (c) after field application with an actual well in Fuling shale gas field, China, it is demonstrated that numerical simulation coupled with the proposed permeability model can achieve better historical match with the actual production performance. The investigation will contribute to the understanding of nanoconfined gas flow behavior and lay the theoretical foundation for next-generation numerical simulation of unconventional gas reservoirs.

Laminar Forced Convection in Annular Microchannels With Slip Flow Regime

2009 ◽  
Author(s):  
Arman Sadeghi ◽  
Abolhassan Asgarshamsi ◽  
Mohammad Hassan Saidi
Keyword(s):  
Nusselt Number ◽  
Fluid Flow ◽  
Aspect Ratio ◽  
Boundary Conditions ◽  
Knudsen Number ◽  
Gas Flow ◽  
Slip Flow ◽  
Outer Wall ◽  
Graphical Form ◽  
Uniform Temperature

Fluid flow and heat transfer at microscale have attracted an important research interest in recent years due to the rapid development of microelectromechanical systems (MEMS). Fluid flow in microdevices has some characteristics which one of them is rarefaction effect related with gas flow. In this research, hydrodynamically and thermally fully developed laminar rarefied gas flow in annular microducts is studied using slip flow boundary conditions. Two different cases of the thermal boundary conditions are considered, namely: uniform temperature at the outer wall and adiabatic inner wall (Case A) and uniform temperature at the inner wall and adiabatic outer wall (Case B). Using the previously obtained velocity distribution, energy conservation equation subjected to relevant boundary conditions is numerically solved using fourth order Runge-Kutta method. The Nusselt number values are presented in graphical form as well as tabular form. It is realized that for the case A increasing aspect ratio results in increasing the Nusselt number, while the opposite is true for the case B. The effect of aspect ratio on Nusselt number is more notable at smaller values of Knudsen number, while its effect becomes slighter at large Knudsen numbers. Also increasing Knudsen number leads to smaller values of Nusselt number for the both cases.

scholarly journals NMR Analysis Method of Gas Flow Pattern in the Process of Shale Gas Depletion Development

Geofluids ◽  
2022 ◽  
Vol 2022 ◽  
pp. 1-7
Author(s):  
Rui Shen ◽  
Zhiming Hu ◽  
Xianggang Duan ◽  
Wei Sun ◽  
Wei Xiong ◽  
...  
Keyword(s):  
Flow Pattern ◽  
Pore Pressure ◽  
Shale Gas ◽  
Gas Flow ◽  
Continuous Medium ◽  
Slip Flow ◽  
Flow Patterns ◽  
Transitional Flow ◽  
Analysis Method ◽  
Adsorbed Gas

Shale gas reservoirs have pores of various sizes, in which gas flows in different patterns. The coexistence of multiple gas flow patterns is common. In order to quantitatively characterize the flow pattern in the process of shale gas depletion development, a physical simulation experiment of shale gas depletion development was designed, and a high-pressure on-line NMR analysis method of gas flow pattern in this process was proposed. The signal amplitudes of methane in pores of various sizes at different pressure levels were calculated according to the conversion relationship between the NMR T 2 relaxation time and pore radius, and then, the flow patterns of methane in pores of various sizes under different pore pressure conditions were analyzed as per the flow pattern determination criteria. It is found that there are three flow patterns in the process of shale gas depletion development, i.e., continuous medium flow, slip flow, and transitional flow, which account for 73.5%, 25.8%, and 0.7% of total gas flow, respectively. When the pore pressure is high, the continuous medium flow is dominant. With the gas production in shale reservoir, the pore pressure decreases, the Knudsen number increases, and the pore size range of slip flow zone and transitional flow zone expands. When the reservoir pressure is higher than the critical desorption pressure, the adsorbed gas is not desorbed intensively, and the produced gas is mainly free gas. When the reservoir pressure is lower than the critical desorption pressure, the adsorbed gas is gradually desorbed, and the proportion of desorbed gas in the produced gas gradually increases.

Poiseuille Number Correlations of Gas Flow in Concentric Micro Annular Tubes

2008 ◽  
Author(s):  
Chungpyo Hong ◽  
Yutaka Asako ◽  
Koichi Suzuki
Keyword(s):  
Boundary Conditions ◽  
Gas Flow ◽  
Slip Flow ◽  
Tube Length ◽  
Slip Boundary Conditions ◽  
Slip Boundary ◽  
Rarefaction Effect ◽  
Wide Range ◽  
Poiseuille Number ◽  
Fast Flow

Poiseuille number, the product of friction factor and Reynolds number (f · Re) for quasi-fully developed concentric micro annular tube flow was obtained for both no-slip and slip boundary conditions. The numerical methodology is based on the Arbitrary-Lagrangian-Eulerian (ALE) method. The compressible momentum and energy equations were solved for a wide range of Reynolds and Mach numbers for both isothermal flow and no heat conduction flow conditions. The detail of the incompressible slip Poiseuille number is kindly documented and its value defined as a function of r* and Kn is represented. The outer tube radius ranges from 50 to 150μm with the radius ratios of 0.2, 0.5 and 0.8 and selected tube length is 0.02m. The stagnation pressure, pstg is chosen in such away that the exit Mach number ranges from 0.1 to 0.7. The outlet pressure is fixed at the atmospheric pressure. In the case of fast flow, the value of f · Re is higher than that of incompressible slip flow theory due to the compressibility effect. However in the case of slow flow the value of f · Re is slightly lower than that of incompressible slip flow due to the rarefaction effect, even the flow is accelerated. The value of f · Re obtained for no-slip boundary conditions is compared with that of obtained for slip boundary conditions. The values of f · Re obtained for slip boundary conditions are predicted by f · Re correlations obtained for no-slip boundary conditions since rarefaction effect is relatively small for the fast flow.

scholarly journals Prediction of Production Performance of Refractured Shale Gas Well considering Coupled Multiscale Gas Flow and Geomechanics

Geofluids ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-21 ◽  
Author(s):  
Zhiqiang Li ◽  
Zhilin Qi ◽  
Wende Yan ◽  
Zuping Xiang ◽  
Xiang Ao ◽  
...  
Keyword(s):  
Shale Gas ◽  
Gas Flow ◽  
Knudsen Diffusion ◽  
Stress Sensitivity ◽  
Production Performance ◽  
Design Parameters ◽  
Production Loss ◽  
Apparent Permeability ◽  
Gas Well ◽  
The Matrix

Production simulation is an important method to evaluate the stimulation effect of refracturing. Therefore, a production simulation model based on coupled fluid flow and geomechanics in triple continuum including kerogen, an inorganic matrix, and a fracture network is proposed considering the multiscale flow characteristics of shale gas, the induced stress of fracture opening, and the pore elastic effect. The complex transport mechanisms due to multiple physics, including gas adsorption/desorption, slip flow, Knudsen diffusion, surface diffusion, stress sensitivity, and adsorption layer are fully considered in this model. The apparent permeability is used to describe the multiple physics occurring in the matrix. The model is validated using actual production data of a horizontal shale gas well and applied to predict the production and production increase percentage (PIP) after refracturing. A sensitivity analysis is performed to study the effects of the refracturing pattern, fracture conductivity, width of stimulated reservoir volume (SRV), SRV length of new and initial fractures, and refracturing time on production and the PIP. In addition, the effects of multiple physics on the matrix permeability and production, and the geomechanical effects of matrix and fracture on production are also studied. The research shows that the refracturing design parameters have an important influence on the PIP. The geomechanical effect is an important cause of production loss, while slippage and diffusion effects in matrix can offset the production loss.

scholarly journals A Stochastic Two-Scale Model for Rarefied Gas Flow in Highly Heterogeneous Porous Media

2020 ◽  
Vol 135 (1) ◽  
pp. 219-242
Author(s):  
Francesc Pérez-Ràfols ◽  
Fredrik Forsberg ◽  
Gunnar Hellström ◽  
Andreas Almqvist
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Gas Flow ◽  
Present Model ◽  
Rarefied Gas ◽  
Slip Flow ◽  
Local Scale ◽  
Heterogeneous Porous Media ◽  
Scale Model ◽  
Rarefied Gas Flow

Abstract This paper presents the development of a model enabling the analysis of rarefied gas flow through highly heterogeneous porous media. To capture the characteristics associated with the global- and the local-scale topology of the permeable phase in a typical porous medium, the heterogeneous multi-scale method, which is a flexible framework for constructing two-scale models, was employed. The rapid spatial variations associated with the local-scale topology are accounted for stochastically, by treating the permeability of different local-scale domains as a random variable. The results obtained with the present model show that an increase in the spatial variability in the heterogeneous topology of the porous medium significantly reduces the relevance of rarefaction effects. This clearly shows the necessity of considering a realistic description of the pore topology and questions the applicability of the results obtained for topologies exhibiting regular pore patterns. Although the present model is developed to study low Knudsen number flows, i.e. the slip-flow regime, the same development procedure could be readily adapted for other regimes as well.

Experimental Study on Single-Phase Gas Flow in Microtubes

2011 ◽  
Vol 133 (11) ◽  
Author(s):  
T. T. Zhang ◽  
L. Jia ◽  
C. W. Li ◽  
L. X. Yang ◽  
Y. Jaluria
Keyword(s):  
Heat Transfer ◽  
Gas Flow ◽  
Single Phase ◽  
Slip Flow ◽  
Experimental System ◽  
Flow Region ◽  
Flow And Heat Transfer ◽  
Wide Range ◽  
Physical Insight ◽  
Insight Into

An experimental system for single-phase gas flow in microtubes has been developed. The effects of viscous heating and compressibility on the flow and temperature field were studied for a wide range of governing parameters. Also, an analytical/numerical model of the flow was developed. Numerical results for the flow and heat transfer in the slip flow region were found to agree quite well with the experimental data, lending support to the model. The study provides greater physical insight into and understanding the effects of viscous dissipation and compressibility in microtube flow and the associated heat transfer. In addition, the combined experimental and numerical simulation approaches of the process can be used for control and optimization of systems based on microtube heat transfer.

Estimation of Leak Flow Rates Through Narrow Cracks

2009 ◽  
Vol 131 (5) ◽  
Author(s):  
Chungpyo Hong ◽  
Yutaka Asako ◽  
Jae-Heon Lee
Keyword(s):  
Friction Factor ◽  
Gas Flow ◽  
Slip Flow ◽  
Nonlinear Ordinary Differential Equation ◽  
Opening Displacement ◽  
Flow Rates ◽  
Choked Flow ◽  
Runge Kutta Method ◽  
Wide Range ◽  
Leak Before Break

The estimation of the gaseous leak flow rates through a narrow crack is important for a leak-before-break analysis as a method of nondestructive testing. Therefore, the methodology to estimate the gaseous leak flow rates in a narrow crack for a wide range of flow conditions, from no-slip to slip flow and from unchoked to choked flow, by using f⋅Re (the product of friction factor and Reynolds number) correlations obtained for a microchannel, was developed and presented. The correlations applied here were proposed by the previous study (Hong, et al., 2007, “Friction Factor Correlations for Gas Flow in Slip Flow Regime,” ASME J. Fluids Eng., 129, pp. 1268–1276). The detail of the calculation procedure was appropriately documented. The fourth-order Runge–Kutta method was employed to integrate the nonlinear ordinary differential equation for the pressure, and the regular-Falsi method was employed to find the inlet Mach number. An idealized crack, whose opening displacement ranges from 2 μm to 50 μm, with the crack aspect ratio of 200, 1000, and 2000, was chosen for sample estimation. The present results were compared with both numerical simulations and available experimental measurements. The results were in excellent agreement. Therefore, the gaseous leak flow rates can be correctly predicted by using the proposed methodology.

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