Experiment and Mathematical Model of Gas Flow in Low Permeability Porous Media

Various flow regimes including Knudsen, transition, slip and viscous flows (Darcy's law), as applied to flow of natural gas through porous conventional rocks, tight formations and shale systems, are investigated. Data from the Mesaverde formation in the United States are used to demonstrate that the permeability correction factors range generally between 1 and 10. However, there are instances where the corrections can be between 10 and 100 for gas flow with high Knudsen number in the transition flow regime, and especially in the Knudsen's flow regime. The results are of practical interest as gas permeability in porous media can be more complex than that of liquid. The gas permeability is influenced by slippage of gas, which is a pressure-dependent parameter, commonly referred to as Klinkenberg's effect. This phenomenon plays a substantial role in gas flow through porous media, especially in unconventional reservoirs with low permeability, such as tight sands, coal seams, and shale formations. A higher-order permeability correlation for gas flow called Knudsen's permeability is studied. As opposed to Klinkenberg's correlation, which is a first-order equation, Knudsen's correlation is a second-order approximation. Even higher-order equations can be derived based on the concept used in developing this model. A plot of permeability correction factor versus Knudsen number gives a typecurve. This typecurve can be used to generalize the permeability correction in tight porous media. We conclude that Knudsen's permeability correlation is more accurate than Klinkenberg's model especially for extremely tight porous media with transition and free molecular flow regimes. The results from this study indicate that Klinkenberg's model and various extensions developed throughout the past years underestimate the permeability correction especially for the case of fluid flow with the high Knudsen number.

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“…Zhu et al (2007) proposed the following nonlinear equation for the gas permeability with slippage effects:…”

Section: Higher-order Equationmentioning

confidence: 99%

“…Zhu et al (2007) reported that gas permeability in their low permeability cores did not follow Klinkenberg's first-order equation, and they recommended using a higher-order equation. A more general second-order equation can be written as (Tang et al 2005):…”

Section: Introductionmentioning

confidence: 97%

Knudsen’s Permeability Correction for Tight Porous Media

2011

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“…Several numerical and experimental models for apparent permeability have also been proposed (Zhu et al, 2009;Tang et al, 2005;Akkutlu and Fathi, 2012;Sakhaee-Pour and Bryant, 2011;Jones et al, 1980;Civan, 2010;Florence et al, 2007;Sampath and Keighin, 1982). The contribution of the surface roughness added to the Javadpour (2009) model by Darabi et al (2012).…”

Section: Introductionmentioning

confidence: 97%

An analytical model for shale gas permeability

Kazemi

Takbiri-Borujeni

2015

International Journal of Coal Geology

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“…In tight and shale gas reservoirs, it has been investigated that the gas permeability has higher-order dependency with the mean pressure (Moghadam and Chalaturnyk, 2014;Ziarami and Aguilera, 2012;Tang et al, 2005b;Zhu et al, 2007). The general higher-order form or the Klinkenberg-corrected permeability can be written as:…”

Section: Investigation Of Effective Gas Permeability On Complex Poroumentioning

confidence: 99%

“…Each approach has its limitations and gives very different values, sometimes several orders of magnitude (Ghanizadeh et al, 2015). Many theoretical works based on Klinkenberg equation have been proposed in order to effectively describe gas permeability in low-permeability porous media (Moghadam and Chalaturnyk, 2014;Ziarami and Aguilera, 2012;Zhu et al, 2007). According to the Klinkenberg theory (Klinkenberg, 1941), gas permeability follows:…”

Section: Investigation Of Effective Gas Permeability On Complex Poroumentioning

confidence: 99%

Numerical modeling of slippage and adsorption effects on gas transport in shale formations using the lattice Boltzmann method

Yang

Jiang

Liu

et al. 2015

Journal of Natural Gas Science and Engineering

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a b s t r a c tShale formations consist of numerous nanoscale pores within a range of 2 nme50 nm; the shale gas flow within this size range under typical shale reservoir pressure and temperature will fall into the slip flow or the transitional flow regime 0.001 < K n < 10. Besides nano-pores in shale, there exist a number of mesoscopic and macroscopic pores with size larger than 50 nm, and many micrometer fractures. Natural gas, mainly methane, flows through nanoscale pores, mesoscale, and macroscopic pores or fractures during the production period. Gas slippage described by the Klinkenberg effect reduces viscous drag near the pore walls and influences permeability. In shale, the majority of gas molecules are adsorbed in kerogen that is considered to be organic source rocks. Within nano-pores and meso-pores, Darcy's law cannot effectively describe this type of transport phenomena due to its continuum assumption. Alternatively, the kinetic-based lattice Boltzmann method (LBM) becomes a strong candidate for simulating an organic-rich shale reservoir that contains a large number of nano-pores. In this paper, we present a multiple-relaxation-time (generalized) LBM, which is considered to be one of the most efficient LBM models. For gas flow in a confined system, its molecular mean free path is corrected depending on the size of the confined system and the distance of the gas molecules from the pore walls. Gas slippage on pore walls is captured with a combined bounce-back specular reflection boundary condition. In addition, adsorbed gas in shale has a significant influence on gas transport in shale gas production. Here, we propose to incorporate inter-molecular and adsorptive forces into the generalized LBM algorithm to capture gas adsorptions in organic nano-pores. Therefore, this approach is able to simulate gas flow with adsorption effect. Many factors are believed to control the flow mechanisms in these types of pores, including the pore size distribution, the specific surface area, and the adsorptive feature of the pore walls. The simulation results agree well with the existing data for high Knudsen flows between 2D parallel plates. Accounting for the adsorption and slippage effects, flow phenomena are investigated by varying different controlling factors in both simple and complex structures. The permeability of methane is also determined for complex porous geometries.

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Experiment and Mathematical Model of Gas Flow in Low Permeability Porous Media

Cited by 20 publications

References 4 publications

Knudsen’s Permeability Correction for Tight Porous Media

Knudsen’s Permeability Correction for Tight Porous Media

An analytical model for shale gas permeability

Numerical modeling of slippage and adsorption effects on gas transport in shale formations using the lattice Boltzmann method

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