Nanopores and Apparent Permeability of Gas Flow in Mudrocks (Shales and Siltstone)

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.

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Macroscopic Model for Passive Mass Dispersion in Porous Media Including Knudsen and Diffusive Slip Effects

Frontiers in Water ◽

10.3389/frwa.2021.666279 ◽

2021 ◽

Vol 3 ◽

Author(s):

Francisco J. Valdés-Parada ◽

Didier Lasseux

Keyword(s):

Boundary Condition ◽

Porous Media ◽

Mass Transport ◽

Gas Flow ◽

Macroscopic Model ◽

Type Model ◽

Pore Scale ◽

Advective Transport ◽

Apparent Permeability ◽

Slip Effects

In this work, a macroscopic model for incompressible and Newtonian gas flow coupled to Fickian and advective transport of a passive solute in rigid and homogeneous porous media is derived. At the pore-scale, both momentum and mass transport phenomena are coupled, not only by the convective mechanism in the mass transport equation, but also in the solid-fluid interfacial boundary condition. This boundary condition is a generalization of the Kramers-Kistemaker slip condition that includes the Knudsen effects. The resulting upscaled model, applicable in the bulk of the porous medium, corresponds to: 1) A Darcy-type model that involves an apparent permeability tensor, complemented by a dispersive term and 2) A macroscopic convection-dispersion equation for the solute, in which both the macroscopic velocity and the total dispersion tensor are influenced by the slip effects taking place at the pore-scale. The use of the model is restricted by the starting assumptions imposed in the governing equations at the pore scale and by the (spatial and temporal) constraints involved in the upscaling process. The different regimes of application of the model, in terms of the Péclet number values, are discussed as well as its extents and limitations. This new model generalizes previous attempts that only include either Knudsen or diffusive slip effects in porous media.

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LATTICE BOLTZMANN SIMULATION OF APPARENT PERMEABILITY FOR GAS FLOW IN NANOCHANNELS

Journal of Porous Media ◽

10.1615/jpormedia.v20.i12.10 ◽

2017 ◽

Vol 20 (12) ◽

pp. 1059-1070 ◽

Cited By ~ 1

Author(s):

Kingsley I. Madiebo ◽

Hadi Nasrabadi ◽

Eduardo Gildin

Keyword(s):

Lattice Boltzmann ◽

Gas Flow ◽

Apparent Permeability ◽

Lattice Boltzmann Simulation

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Determining Shale Permeability to Gas by Simultaneous Analysis of Various Pressure Tests

SPE Journal ◽

10.2118/144253-pa ◽

2012 ◽

Vol 17 (03) ◽

pp. 717-726 ◽

Cited By ~ 56

Author(s):

F.. Civan ◽

C.S.. S. Rai ◽

C.H.. H. Sondergeld

Keyword(s):

Gas Flow ◽

Pressure Pulse ◽

Reference Conditions ◽

Transient State ◽

Data Interpretation ◽

Model Parameters ◽

Apparent Permeability ◽

Core Samples ◽

Pulse Transmission ◽

Pressure Tests

Summary A model-assisted analysis is presented of pressure-pulse-transmission data obtained under different pressure conditions with core plugs of shale-gas formations. Applications and validations for steady-state and transient-state laboratory tests are provided. Best-estimate values of the intrinsic permeability and tortuosity at a reference condition and the Langmuir volume and pressure are determined by matching the solution of a modified Darcy model to several pressure-pulse-transmission flow tests with core samples simultaneously. The data-interpretation model considers the prevailing characteristics of the apparent permeability under the various flow regimes involving gas flow through extremely low-permeability core samples. Further, the present fully pressure-dependent shale-and gas-property formulation allows for model-assisted extrapolation from the reference conditions to field conditions once the unknown model parameters have been estimated under laboratory conditions. The improved method provides a better match to the measurements of the pressure tests than previous models, which assume only Darcy flow.

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Leakage Predictions for Static Gasket Based on the Porous Media Theory

Journal of Pressure Vessel Technology ◽

10.1115/1.3008031 ◽

2008 ◽

Vol 131 (2) ◽

Cited By ~ 11

Author(s):

Pascal Jolly ◽

Luc Marchand

Keyword(s):

Porous Media ◽

Gas Flow ◽

Molecular Flow ◽

Intrinsic Permeability ◽

Slip Boundary Conditions ◽

Apparent Permeability ◽

Slip Boundary ◽

Porous Media Theory ◽

Porous Media Model ◽

Different Gases

In the present work, the annular static gaskets are considered as porous media and Darcy’s law is written for a steady radial flow of a compressible gas with a first order slip boundary conditions. From this, a simple equation is obtained that includes Klinkenberg’s intrinsic permeability factor kv of the gasket and the Knudsen number Kn′o defined with a characteristic length ℓ. The parameters kv and ℓ of the porous gasket are calculated from experimental results obtained with a reference gas at several gasket stress levels. Then, with kv and ℓ, the inverse procedure is performed to predict the leakage rate for three different gases. It is shown that the porous media model predicts leak rates with the same accuracy as the laminar-molecular flow (LMF) model of Marchand et al. However, the new model has the advantage of furnishing phenomenological information on the evolution of the intrinsic permeability and the gas flow regimes with the gasket compressive stress. It also enables quick identification of the part of leakage that occurs at the flange-gasket interface at low gasket stresses. At low gas pressure, the behavior of the apparent permeability diverges from that of Klinkenberg’s, indicating that the rarefaction effect becomes preponderant on the leak.

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Analytical and Experimental Investigations of Gas-Flow Regimes in Shales Considering the Influence of Mean Effective Stress

SPE Journal ◽

10.2118/178429-pa ◽

2016 ◽

Vol 21 (02) ◽

pp. 557-572 ◽

Cited By ~ 20

Author(s):

Alireza A. Moghadam ◽

Rick Chalaturnyk

Keyword(s):

Flow Regime ◽

Effective Stress ◽

Gas Flow ◽

Gas Permeability ◽

Slip Flow ◽

Flow Regimes ◽

Absolute Permeability ◽

Apparent Permeability ◽

Reservoir Conditions ◽

Slip Flow Regime

Summary Flow conditions determine the flow regimes governing gas flow in porous media. Slip-flow regime commonly occurs in laboratory gas-permeability measurements, and one must consider the physics of that when finding the absolute permeability of a sample. Accurate permeability estimates are paramount for production forecasts, financial planning, and recovery estimation. Slip flow is present in low-permeability rocks, both in the laboratory environment and at reservoir conditions. Gas flow through the matrix lies under the slip-flow regime for the majority of low-permeability-reservoir production scenarios, and accurate prediction of pressure and production rate requires a good understanding of the flow regime. In this paper, an analytical study is conducted on the dominant flow regimes under typical shale-gas reservoir conditions. A flow-regime map is produced with respect to gas pressure and matrix permeability. Steady-state gas-permeability experiments are conducted on three shale samples. An analytical model is used to match the experimental results that could explain the order-of-magnitude difference between the permeabilities of gas and liquid in shales. Experimental results are combined with further tests available in the literature to inform a discussion of the model's parameters. The results improve the accuracy of gas-flow modeling and of absolute-permeability estimates from laboratory tests. Similar tests performed at various mean effective stresses investigate the influence of mean effective stress on flow regime and apparent permeability. The results indicate that flow regime is a function of mean effective stress, and that the apparent permeability of shale rocks is a function of both flow regime and mean effective stress.

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A New Dynamic Apparent Permeability Model for Gas Flow in Microfractures of Shale

Proceedings of the SPE/AAPG/SEG Asia Pacific Unconventional Resources Technology Conference ◽

10.15530/ap-urtec-2019-198302 ◽

2019 ◽

Author(s):

Yudan Li ◽

Pingchuan Dong ◽

Dawei Zhou

Keyword(s):

Gas Flow ◽

Apparent Permeability ◽

Permeability Model

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Multiscale Apparent Permeability Model of Shale Nanopores Based on Fractal Theory

Energies ◽

10.3390/en12173381 ◽

2019 ◽

Vol 12 (17) ◽

pp. 3381 ◽

Cited By ~ 10

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.

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