Gas Transport Model in Organic Shale Nanopores Considering Langmuir Slip Conditions and Diffusion: Pore Confinement, Real Gas, and Geomechanical Effects

Zhang, Liehui; Shan, Baochao; Zhao, Yulong; Du, Jia Yao; Tao, Xiaoping

doi:10.3390/en11010223

Cited by 26 publications

(17 citation statements)

References 68 publications

(88 reference statements)

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“…An important example of these structures are micro-and nano-electro-mechanical systems (MEMS/NEMS) devices such as micromotors, comb microdrives, blood flow analysers and particle separators [1,2]. Other areas of interest include transport in aquaporin water channels in biological cell membranes [3] and gas flow through shale rock formations [4]. A key feature of fluid flow in these confined spaces is a significant departure from predictions of the classical Navier-Stokes equations.…”

Section: Introductionmentioning

confidence: 99%

Investigating enhanced mass flow rates in pressure-driven liquid flows in nanotubes

2019

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Over the past two decades, several researchers have presented experimental data from pressure-driven liquid flows through nanotubes. They quote flow velocities which are four to five orders of magnitude higher than those predicted by the classical theory. Thus far, attempts to explain these enhanced mass flow rates at the nanoscale have focused mainly on introducing wall-slip boundary conditions on the fluid mass velocity. In this paper, we present a different theory. A change of variable on the velocity field within the classical Navier-Stokes equations is adopted to transform the equations into physically different equations. The resulting equations, termed re-casted Navier-Stokes equations, contain additional diffusion terms whose expressions depend upon the driving mechanism. The new equations are then solved for the pressure driven flow in a long nano-channel. Analogous to previous studies of gas flows in micro-and nano-channels, a perturbation expansion in the aspect ratio allows for the construction of a 2D analytical solution. In contrast to slip-flow models, this solution is specified by a no-slip boundary condition at the channel walls. The mass flow rate can be calculated explicitly and compared to available data. We conclude that the new re-casting methodology may provide an alternative theoretical physical explanation of the enhanced mass flow phenomena.

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Section: Introductionmentioning

confidence: 99%

Investigating enhanced mass flow rates in pressure-driven liquid flows in nanotubes

2019

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“…The influence of solid surface roughness on Knudsen diffusion cannot be negligible, because the Knudsen diffusion decreased due to the long gas retention in the vicinity of a pore wall under severe wall roughness. Combined with Equation (27), the Knudsen diffusion flux with considering solid surface roughness in shale nanopores can be written as:

J_{normalK} = - δ^{D_{normalf} - 2} \frac{D_{normalK} M}{ZRT} \nabla p .

…”

Section: Gas Transport Models In Shale Nanoporesmentioning

confidence: 99%

“…The Maxwell slip model is a first‐order approximation from kinetic theory, and second‐order slip models have been successively proposed to improve calculation precision. In summary, slip velocity models can uniformly be expressed as:

u_{normalslip} = C_{1} λ {()(, \frac{\partial u}{\partial n})}_{normalS} + C_{2} λ^{2} {()(, \frac{\partial^{2} u}{\partial n^{2}})}_{normalS} .

…”

Section: Introductionmentioning

confidence: 99%

“…The Maxwell slip model 13 is a first-order approximation from kinetic theory, and second-order [14][15][16][17][18] slip models have been successively proposed to improve calculation precision. In summary, slip velocity models can uniformly be expressed as 19 : Table 1 shows the different slip velocity models and the disadvantages when these models are applied in shale system. To avoid these disadvantages and their impact on the permeability models developed based on Maxwell slip model and other second-order slip models, a Langmuir slip boundary condition more accurately describes the real slip phenomenon from the perspective of a physical meaning.…”

Section: Introductionmentioning

confidence: 99%

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A novel numerical model of gas transport in multiscale shale gas reservoirs with considering surface diffusion and Langmuir slip conditions

Huang

Cao

Yuan

et al. 2019

Energy Science & Engineering

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Multiflow mechanisms coexist in shale gas reservoirs (SGRs) due to the abundant nanopores and the organic matter as a medium of gas souring and storage. The gas transport mechanisms in nanopores including bulk gas transfer and adsorption‐gas surface diffusion were already investigated in pore‐scale models, but their effects on actual gas production of multistage fractured horizontal wells in SGRs are not clearly understood, which are crucial for the economic development of unconventional resources. Therefore, a comprehensive apparent permeability (AP) model which couples the surface diffusion of adsorbed gas, slippage flow considering the additional flux generated by surface diffusion based on Langmuir's theory, and Knudsen diffusion is established. The presented model is validated with the experimental data and lattice Boltzmann method (LBM) simulation results. Then, we propose a numerical model which combines multiflow mechanisms in microscale pores and a multistage fractured horizontal well (MSFHW) in macroscale shale gas reservoirs together. The effects of different transport mechanisms on both AP of nanopores and gas production are analyzed thoroughly. The results show that the effect of surface diffusion on the apparent permeability of nanopores is much greater than that on the actual gas production of MSFHW, and the influence of high‐pressure condition must be considered when calculating the surface diffusion coefficient. The presented numerical model has important implications for accurate numerical simulation and efficient development of shale gas reservoirs.

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“…Many previous works have been performed to understand the characteristics of gas flow and stress sensitivity in shale gas [1][2][3]. Huang et al [1] shows that gas transportation in shale cannot be simply characterized by the Darcy law, and a method by calculating the Knudsen number was proposed to analyze the shale gas flow regime.…”

Section: Introductionmentioning

confidence: 99%

Numerical Simulation of Shale Gas Multiscale Seepage Mechanism-Coupled Stress Sensitivity

Yan

Sun

Liu

2019

Journal of Chemistry

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The complexity of the gas transport mechanism in microfractures and nanopores is caused by the feature of multiscale and multiphysics. Figuring out the flow mechanism is of great significance for the efficient development of shale gas. In this paper, an apparent permeability model which covers continue, slip, transition, and molecular flow and geomechanical effect was presented. Additionally, a mathematical model comprising multiscale, geomechanics, and adsorption phenomenon was proposed to characterize gas flow in the shale reservoir. The aim of this paper is to investigate some important impacts in the process of gas transportation, which includes the shale stress sensitivity, adsorption phenomenon, and reservoir porosity. The results reveal that the performance of the multistage fractured horizontal well is strongly influenced by stress sensitivity coefficient. The cumulative gas production will decrease sharply when the shale gas reservoir stress sensitivity coefficient increases. In addition, the adsorption phenomenon has an influence on shale gas seepage and sorption capacity; however, the effect of adsorption is very weak in the early gas transport period, and the impact of later will increase. Moreover, shale porosity also greatly affects the shale gas transportation.

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Gas Transport Model in Organic Shale Nanopores Considering Langmuir Slip Conditions and Diffusion: Pore Confinement, Real Gas, and Geomechanical Effects

Cited by 26 publications

References 68 publications

Investigating enhanced mass flow rates in pressure-driven liquid flows in nanotubes

Investigating enhanced mass flow rates in pressure-driven liquid flows in nanotubes

A novel numerical model of gas transport in multiscale shale gas reservoirs with considering surface diffusion and Langmuir slip conditions

Numerical Simulation of Shale Gas Multiscale Seepage Mechanism-Coupled Stress Sensitivity

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