The origin of a large apparent tortuosity factor for the Knudsen diffusion inside monoliths of a samaria–alumina aerogel catalyst: a diffusion NMR study

2015 ◽  
Vol 17 (41) ◽  
pp. 27481-27487 ◽  
Author(s):  
R. Mueller ◽  
S. Zhang ◽  
M. Klink ◽  
M. Bäumer ◽  
S. Vasenkov
Keyword(s):  
Surface Diffusion ◽  
Knudsen Diffusion ◽  
Porous Catalyst ◽  
Tortuosity Factor ◽  
Diffusion Nmr ◽  
Alumina Aerogel ◽  
Nmr Study

The contribution from surface diffusion into the apparent tortuosity factor can be separated for light gases in a porous catalyst.

Diffusion-Based Modeling of Gas Transport in Organic-Rich Ultratight Reservoirs

SPE Journal ◽  
2021 ◽  
pp. 1-26
Author(s):  
Zizhong Liu ◽  
Hamid Emami-Meybodi
Keyword(s):  
Diffusion Coefficient ◽  
Adsorption Capacity ◽  
Surface Diffusion ◽  
Diffusion Coefficients ◽  
Gas Transport ◽  
Knudsen Diffusion ◽  
Gas Production ◽  
Hydrocarbon Transport ◽  
The Impact ◽  
And Storage

Summary The complex pore structure and storage mechanism of organic-rich ultratight reservoirs make the hydrocarbon transport within these reservoirs complicated and significantly different from conventional oil and gas reservoirs. A substantial fraction of pore volume in the ultratight matrix consists of nanopores in which the notion of viscous flow may become irrelevant. Instead, multiple transport and storage mechanisms should be considered to model fluid transport within the shale matrix, including molecular diffusion, Knudsen diffusion, surface diffusion, and sorption. This paper presents a diffusion-based semianalytical model for a single-component gas transport within an infinite-actingorganic-rich ultratight matrix. The model treats free and sorbed gas as two phases coexisting in nanopores. The overall mass conservation equation for both phases is transformed into one governing equation solely on the basis of the concentration (density) of the free phase. As a result, the partial differential equation (PDE) governing the overall mass transport carries two newly defined nonlinear terms; namely, effective diffusion coefficient, De, and capacity factor, Φ. The De term accounts for the molecular, Knudsen, and surface diffusion coefficients, and the Φ term considers the mass exchange between free and sorbed phases under sorption equilibrium condition. Furthermore, the ratio of De/Φ is recognized as an apparent diffusion coefficient Da, which is a function of free phase concentration. The nonlinear PDE is solved by applying a piecewise-constant-coefficient technique that divides the domain under consideration into an arbitrary number of subdomains. Each subdomain is assigned with a constant Da. The diffusion-based model is validated against numerical simulation. The model is then used to investigate the impact of surface and Knudsen diffusion coefficients, porosity, and adsorption capacity on gas transport within the ultratight formation. Further, the model is used to study gas transport and production from the Barnett, Marcellus, and New Albany shales. The results show that surface diffusion significantly contributes to gas production in shales with large values of surface diffusion coefficient and adsorption capacity and small values of Knudsen diffusion coefficient and total porosity. Thus, neglecting surface diffusion in organic-rich shales may result in the underestimation of gas production.

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.

Single-File Diffusion of Gas Mixtures in Nanochannels of the Dipeptide l-Ala-l-Val: High-Field Diffusion NMR Study

2016 ◽  
Vol 120 (18) ◽  
pp. 9914-9919 ◽  
Author(s):  
Akshita R. Dutta ◽  
Poorvajan Sekar ◽  
Muslim Dvoyashkin ◽  
Clifford R. Bowers ◽  
Kirk J. Ziegler ◽  
...  
Keyword(s):  
High Field ◽  
Gas Mixtures ◽  
Diffusion Nmr ◽  
Single File ◽  
Nmr Study ◽  
Field Diffusion ◽  
Single File Diffusion

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.

Continuum-Scale Gas Transport Modeling in Organic Nanoporous Media Based on Pore-Scale Density Distributions

2021 ◽  
Author(s):  
Zizhong Liu ◽  
Hamid Emami-Meybodi
Keyword(s):  
Surface Diffusion ◽  
Gas Transport ◽  
Local Density ◽  
Knudsen Diffusion ◽  
Effective Diffusion ◽  
Pore Scale ◽  
Multilayer Adsorption ◽  
Nanoporous Media ◽  
Continuum Scale ◽  
Sorbed Phase

Abstract This paper presents a continuum-scale diffusion-based model informed by pore-scale data for gas transport in organic nanoporous media. A mass transfer and adsorption model is developed by considering multiple transport and storage mechanisms, including bulk diffusion and Knudsen diffusion for free phase, surface diffusion for sorbed phase, and multilayer adsorption. The continuum-scale diffusion-based governing equation is developed solely based on free phase concentration for the overall mass conservation of free and sorbed phases, carrying a newly-defined effective diffusion coefficient and a capacity factor to account for multilayer adsorption. Diffusion of free and sorbed phases is coupled through the pore-scale simplified local density method based on the modified Peng-Robinson equation of state for confinement effects. The model is first utilized to analyze pore-scale adsorption data from the krypton (Kr) gas adsorption experiment on graphite. Then we implement the model to conduct sensitivity analysis for the effects of pore size on gas transport for Kr-graphite and methane-coal systems. The model is finally used to study Kr diffusion profiles through a coal matrix obtained through X-ray micro-CT imaging. The results show that the sorbed phase occupies most of the pore space in organic nanoporous media due to multilayer adsorption, and surface diffusion contributes significantly to the total mass flux. Therefore, neglecting the volume of sorbed phase and surface diffusion in organic nanoporous rocks may result in considerable errors. Furthermore, the results reveal that implementing a Langmuir-based model may be erroneous for an organic-rich reservoir with nanopores during the early depletion period when the reservoir pressure is high.

scholarly journals Structure, Diffusion, and Permeability of Protein-Stabilized Monodispersed Oil in Water Emulsions and Their Gels: A Self-Diffusion NMR Study

Langmuir ◽  
2010 ◽  
Vol 26 (9) ◽  
pp. 6184-6192 ◽  
Author(s):  
Alexandre I. Romoscanu ◽  
Annia Fenollosa ◽  
Simone Acquistapace ◽  
Deniz Gunes ◽  
Teresa Martins-Deuchande ◽  
...  
Keyword(s):  
Self Diffusion ◽  
Diffusion Nmr ◽  
Nmr Study ◽  
Oil In Water

A Unified Model for Gas Transfer in Nanopores of Shale-Gas Reservoirs: Coupling Pore Diffusion and Surface Diffusion

SPE Journal ◽  
2016 ◽  
Vol 21 (05) ◽  
pp. 1583-1611 ◽  
Author(s):  
Keliu Wu ◽  
Xiangfang Li ◽  
Chaohua Guo ◽  
Chenchen Wang ◽  
Zhangxin Chen
Keyword(s):  
High Pressure ◽  
Diffusion Coefficient ◽  
Surface Diffusion ◽  
Shale Gas ◽  
Pore Radius ◽  
Knudsen Diffusion ◽  
Slip Flow ◽  
Transfer Mechanism ◽  
Gas Transfer ◽  
Gas Reservoirs

Summary A model for gas transfer in nanopores is the basis for accurate numerical simulation, which has important implications for economic development of shale-gas reservoirs (SGRs). The gas-transfer mechanism in SGRs is significantly different from that of conventional gas reservoirs, which is mainly caused by the nanoscale phenomena and organic matter as a medium of gas sourcing and storage. The gas-transfer mechanism includes bulk-gas transfer and adsorption-gas surface diffusion in nanopores of SGRs, where the bulk-gas-transfer mechanism includes continuous flow, slip flow, and Knudsen diffusion. First, a model for bulk-gas transfer in nanopores was established, which was dependent on slip flow and Knudsen diffusion. The total gas flux in the bulk phase is not a simple sum of slip-flow flux and Knudsen-diffusion flux but a weighted sum on the basis of corresponding contributions. The weighted factors are primarily controlled by the mutual interaction between slip flow and Knudsen diffusion, which is determined by probabilities between gas molecules colliding with each other and colliding with nanopore surface in this newly proposed model. Second, a model for adsorbed-gas surface diffusion in nanopores was established, which was modeled after the Hwang and Kammermeyer (1966) model and considered the effect of gas coverage under a high-pressure condition. Finally, with the combination of these two models, a unified model for gas transport in nanopores of SGRs was established, and this model was validated through molecular simulation and experimental data. Results show that: Slip flow makes a great contribution to gas transfer under the condition of meso/macropores (pore radius greater than 2 nm) and high pressure. Knudsen diffusion makes an important contribution to gas transfer under the condition of macropores (pore radius greater than 50 nm) and less than 1 MPa in pressure, whereas it can be ignored in other cases. A surface-diffusion coefficient is comparable with a pore-diffusion coefficient, and gas transfer is always dominated by surface diffusion over all the ranges of pressure in micropores (pore radius ≤ 2 nm). Surface-diffusion contribution decreases with an increase in pore size, isosteric sorption heat, pressure, and temperature in SGRs.

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.

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