A FRACTAL PERMEABILITY MODEL FOR REAL GAS IN SHALE RESERVOIRS COUPLED WITH KNUDSEN DIFFUSION AND SURFACE DIFFUSION EFFECTS

Fractals ◽  
2020 ◽  
Vol 28 (01) ◽  
pp. 2050017 ◽  
Author(s):  
TAO WU ◽  
SHIFANG WANG
Keyword(s):  
Fractal Dimension ◽  
Surface Diffusion ◽  
Shale Gas ◽  
Gas Transport ◽  
Fractal Theory ◽  
Knudsen Diffusion ◽  
Apparent Permeability ◽  
Permeability Model ◽  
Real Gas ◽  
Shale Reservoirs

A better comprehension of the behavior of shale gas transport in shale gas reservoirs will aid in predicting shale gas production rates. In this paper, an analytical apparent permeability expression for real gas is derived on the basis of the fractal theory and Fick’s law, with adequate consideration of the effects of Knudsen diffusion, surface diffusion and flexible pore shape. The gas apparent permeability model is found to be a function of microstructural parameters of shale reservoirs, gas property, Langmuir pressure, shale reservoir temperature and pressure. The results show that the apparent permeability increases with the increase of pore area fractal dimension and the maximum effective pore radius and decreases with an increase of the tortuosity fractal dimension; the effects of Knudsen diffusion and surface diffusion on the total apparent permeability cannot be ignored under high-temperature and low-pressure circumstances. These findings can contribute to a better understanding of the mechanism of gas transport in shale reservoirs.

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 Analysis of gas transport behavior in organic and inorganic nanopores based on a unified apparent gas permeability model

2019 ◽  
Vol 17 (1) ◽  
pp. 168-181 ◽  
Author(s):  
Qi Zhang ◽  
Wen-Dong Wang ◽  
Yilihamu Kade ◽  
Bo-Tao Wang ◽  
Lei Xiong
Keyword(s):  
Pore Pressure ◽  
Surface Diffusion ◽  
Pore Radius ◽  
Gas Transport ◽  
Gas Permeability ◽  
Knudsen Diffusion ◽  
Permeability Model ◽  
Real Gas ◽  
Apparent Gas Permeability ◽  
Transport Behavior

Abstract Different from the conventional gas reservoirs, gas transport in nanoporous shales is complicated due to multiple transport mechanisms and reservoir characteristics. In this work, we presented a unified apparent gas permeability model for real gas transport in organic and inorganic nanopores, considering real gas effect, organic matter (OM) porosity, Knudsen diffusion, surface diffusion, and stress dependence. Meanwhile, the effects of monolayer and multilayer adsorption on gas transport are included. Then, we validated the model by experimental results. The influences of pore radius, pore pressure, OM porosity, temperature, and stress dependence on gas transport behavior and their contributions to the total apparent gas permeability (AGP) were analyzed. The results show that the adsorption effect causes Kn(OM) > Kn(IM) when the pore pressure is larger than 1 MPa and the pore radius is less than 100 nm. The ratio of the AGP over the intrinsic permeability decreases with an increase in pore radius or pore pressure. For nanopores with a radius of less than 10 nm, the effects of the OM porosity, surface diffusion coefficient, and temperature on gas transport cannot be negligible. Moreover, the surface diffusion almost dominates in nanopores with a radius less than 2 nm under high OM porosity conditions. For the small-radius and low-pressure conditions, gas transport is governed by the Knudsen diffusion in nanopores. This study focuses on revealing gas transport behavior in nanoporous shales.

EVOLUTION OF FRACTAL DIMENSIONS AND GAS TRANSPORT MODELS DURING THE GAS RECOVERY PROCESS FROM A FRACTURED SHALE RESERVOIR

Fractals ◽  
2019 ◽  
Vol 27 (08) ◽  
pp. 1950129 ◽  
Author(s):  
BOWEN HU ◽  
J. G. WANG ◽  
ZHONGQIAN LI ◽  
HUIMIN WANG
Keyword(s):  
Fractal Dimension ◽  
Surface Diffusion ◽  
Gas Transport ◽  
Knudsen Diffusion ◽  
Fractal Dimensions ◽  
Gas Extraction ◽  
Multilayer Adsorption ◽  
Permeability Model ◽  
Dimension Formula ◽  
Shale Reservoir

Previous studies ignore the evolutions of pore microstructure parameters (pore diameter fractal dimension [Formula: see text] and tortuosity fractal dimension [Formula: see text]) but these evolutions may significantly impact the gas transport during gas extraction. In order to investigate these evolutions of fractal dimension properties during gas extraction, following four aspects are studied. Firstly, surface diffusion in adsorbed multilayer is modeled for fractal shale matrix. Our new matrix permeability model considers the slip flow, Knudsen diffusion and surface diffusion. This model is verified by experimental data. Secondly, a new fracture permeability model is proposed based on fractal theory and the coupling of viscous flow and Knudsen diffusion. Thirdly, the multilayer adsorption and these permeability models are introduced into the equations of gas flow and reservoir deformation. Finally, sensitivity analysis is performed to determine the key factors on fractal dimension evolution. The results show that the multilayer adsorption can accurately describe the adsorption properties of real shale reservoir. Shale reservoir deformation and gas desorption govern the evolutions of fractal dimensions. The multilayer adsorption and adsorbed gas porosity [Formula: see text] play an important role in the evolutions of fractal dimensions during gas extraction. The monolayer saturated adsorption volume [Formula: see text] is the most sensitive parameter affecting the evolution of fractal dimensions. Therefore, the effects of gas adsorption on the evolution of fractal dimensions cannot be neglected in shale reservoirs.

A New Unified Gas-Transport Model for Gas Flow in Nanoscale Porous Media

SPE Journal ◽  
2019 ◽  
Vol 24 (02) ◽  
pp. 698-719 ◽  
Author(s):  
Di Chai ◽  
Zhaoqi Fan ◽  
Xiaoli Li
Keyword(s):  
Viscous Flow ◽  
Pore Size ◽  
Surface Diffusion ◽  
Gas Flow ◽  
Gas Transport ◽  
Transport Model ◽  
Knudsen Diffusion ◽  
Apparent Permeability ◽  
Real Gas ◽  
Reservoir Conditions

Summary A new unified gas-transport model has been developed to characterize single-component real-gas flow in nanoscale organic and inorganic porous media by modifying the Bravo (2007) model. More specifically, a straight capillary tube is characterized by a conceptual layered model consisting of a viscous-flow zone, a Knudsen-diffusion zone, and a surface-diffusion zone. To specify the contributions of the viscous flow and the Knudsen diffusion to the gas transport, the virtual boundary between the viscous-flow and Knudsen-diffusion zones is first determined using an analytical molecular-kinetics approach. As such, the new unified gas-transport model is derived by integrating the weighted viscous flow and Knudsen diffusion, and coupling surface diffusion. The model is also comprehensively scaled up to the bundles-of-tubes model considering the roughness, rarefaction, and real-gas effect. Nonlinear programming methods have been used to optimize the empirical parameters in the newly proposed gas-transport model. Consequently, the newly proposed gas-transport model yields the most accurate molar fluxes compared with the Bravo (2007) model and four other analytical models. One of the advantages of the new unified gas-transport model is its great flexibility, because the Knudsen number is included as an independent variable, which also endows the newly proposed model with the capability to cover the full-flow regimes. In addition, the apparent permeability has been mathematically derived from the new unified gas-transport model. A series of simulations has been implemented using methane gas. It is found through sensitivity analysis that apparent permeability is strongly dependent on pore size, porosity, and tortuosity, and weakly dependent on the surface-diffusivity coefficient and pore-surface roughness. The increased viscosity can reduce the total molar flux in the inorganic pores up to 66.0% under the typical shale-gas-reservoir conditions. The viscous-flow mechanism cannot be neglected at any pore sizes under reservoir conditions, whereas the Knudsen diffusion is found to be important when pore size is smaller than 2 nm and pressure is less than 35.0 MPa. The contribution of surface diffusion cannot be ignored when the pore size is smaller than 10 nm and the pressure is less than 15.0 MPa.

Apparent permeability model for gas transport in shale reservoirs with nano-scale porous media

2018 ◽  
Vol 55 ◽  
pp. 508-519 ◽  
Author(s):  
Shan Wang ◽  
Juntai Shi ◽  
Ke Wang ◽  
Zheng Sun ◽  
Yanan Miao ◽  
...  
Keyword(s):  
Porous Media ◽  
Gas Transport ◽  
Apparent Permeability ◽  
Permeability Model ◽  
Nano Scale ◽  
Shale Reservoirs

Analytical Model for Real Gas Transport in Shale Reservoirs with Surface Diffusion of Adsorbed Gas

2019 ◽  
Vol 58 (51) ◽  
pp. 23481-23489 ◽  
Author(s):  
Tianyu Wang ◽  
Shouceng Tian ◽  
Gensheng Li ◽  
Panpan Zhang
Keyword(s):  
Surface Diffusion ◽  
Analytical Model ◽  
Gas Transport ◽  
Real Gas ◽  
Adsorbed Gas ◽  
Shale Reservoirs

The Calculation of Apparent Permeability for Shale Gas Considering Adsorption and Flow Patterns

2014 ◽  
Vol 1073-1076 ◽  
pp. 2305-2309
Author(s):  
Wen Xu She ◽  
Jun Bin Chen ◽  
Jie Zhang ◽  
Bo Wei ◽  
Han Qing Wang ◽  
...  
Keyword(s):  
Pore Size ◽  
Flow Pattern ◽  
Shale Gas ◽  
Knudsen Diffusion ◽  
Slip Flow ◽  
Great Influence ◽  
Flow Patterns ◽  
Apparent Permeability ◽  
Longmaxi Formation ◽  
Shale Reservoirs

The flow pattern is unique in a certain range of pore size divided by the Knudsen number. In order to characterize permeability of nanopore in shale gas reservoir more accurately, the formulas of nanopore permeability are put forward considering the influence of adsorption gas and flow patterns. After the calculated results were compared and analyzed, the conclusions are obtained as follows: (1) Pore size is the main factor to determine the flow pattern; (2) There are three main flow pattern in the nanopore of Longmaxi formation shale reservoirs, slip flow, Fick diffusion and transition diffusion, meanwhile Darcy percolation and Knudsen diffusion do not exist; (3) Flow pattern has great influence on apparent permeability and adsorption has a greater impact in a high pressure condition (greater than 20MPa).

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