A mathematical model for co-current spontaneous water imbibition into oil-saturated tight sandstone: Upscaling from pore-scale to core-scale with fractal approach

Wang, Fuyong; Zhao, Jiuyu

doi:10.1016/j.petrol.2019.03.055

Cited by 51 publications

(24 citation statements)

References 43 publications

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“…The topology of porous media is tortuous. Therefore, simulated results of linear capillary model may be not accurate for spontaneous imbibition (Li et al, 2018;Wang and Zhao, 2019). Cai and Yu (2011) reported that the tortuosity is an important factor affecting on fluid flow features such as permeability and flow resistance in porous media.…”

Section: Capillary Model Of Spontaneous Imbibition With Different Boumentioning

confidence: 99%

Recent advances in spontaneous imbibition with different boundary conditions

Meng¹,

Cai²

2018

Capillarity

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Spontaneous imbibition plays an important role in many practical processes, such as oil recovery, hydrology, and environmental engineering. The past few years have witnessed a rapid development in the mechanism analysis and industry applications of spontaneous imbibition. In this paper, we focus on boundary conditions of spontaneous imbibition, which has important effects on the imbibition rate and efficiency. Various boundary conditions are first generated using different capillary model and introduced focusing on the fundamental physical mechanisms. Then, the studies of spontaneous imbibition in core scale are reviewed. The feature is discussed and the relative permeability for coand counter-current imbibition is analyzed. The scaling of imbibition data with different boundary conditions is also presented by combination of experimental and numerical methods. An analytical model to describe spontaneous imbibition is provided at the end.

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Section: Capillary Model Of Spontaneous Imbibition With Different Boumentioning

confidence: 99%

Recent advances in spontaneous imbibition with different boundary conditions

Meng¹,

Cai²

2018

Capillarity

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“…Ignoring the second differential term, the flow velocity v can be expressed as:

v ((), r, t) = \frac{dx}{dt} = \frac{2 italicrσ \cos θ + r^{2} ((), 2 ρ_{w} - ρ_{o}) ((), l - x) g \sin α}{8 ([], μ_{w} x + μ_{o} ((), l - x))}

Equation () is the imbibition flow rate in a capillary tube under gravity and buoyancy, which is expressed with the r 2 (2 ρ w − ρ o )( l − x ) g sin α term. When this term is neglected, Equation () can be simplified into the equation for the concurrent spontaneous water imbibition process into an oil‐saturated capillary tube without gravity 11 …”

Section: Spontaneous Imbibition In a Capillary Tube With Gravity And Buoyancymentioning

confidence: 99%

“…Reservoir simulations based on the continuum model can investigate the gravity effect at the field scale but cannot intuitively reveal the fluid flow in micro/nanopores. The capillary tube model effectively describes the spontaneous imbibition process and upscales the pore‐scale flow behavior to the core‐scale flow behavior based on the pore size distribution 11,32 . The fractal characteristics of the pore size distribution in tight sandstones have been demonstrated with mercury intrusion porosimetry, nuclear magnetic resonance, 33 and N 2 adsorption 34 .…”

Section: Introductionmentioning

confidence: 99%

Mathematical modeling of gravity and buoyancy effect on low interfacial tension spontaneous imbibition in tight oil reservoirs

Wang

Zhao

2021

AIChE Journal

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Considering capillary force, viscous force, and gravity and buoyancy effects due to the oil–water density difference during the imbibition process, a new mathematical model for core‐scale spontaneous imbibition considering gravity and buoyancy is established. The imbibition rates with and without gravity and buoyancy in high‐, low‐, and ultralow‐interfacial tension (IFT) solutions are compared. The study shows that oil buoyancy can accelerate the imbibition rate, and with increasing core permeability and decreasing IFT, the differences in imbibition rate with and without gravity and buoyancy become more significant. At a high IFT of dozens of mN/m, the gravity and buoyancy effects are nonsignificant and can be ignored, but at a low IFT such as at 0.355 mN/m and a core permeability above 1 mD, gravity and buoyancy must be considered in spontaneous imbibition simulations. In low‐IFT solutions, the critical inverse Bond number when gravity and buoyancy must be considered is approximately 1 × 10−2.

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“…The pore radius of shale is distributed at 0.3-300 nm [32], while the complex structure of matrix pores can be described by fractal geometry theory within a certain scale. Therefore, based on the fractal geometry theory, the tortuous bundle model with uneven pore radius distribution is adopted to characterize shale [19,33,34]. The physical model is shown in Figure 1.…”

Section: Fractal Porous Media Modelmentioning

confidence: 99%

Multiscale Apparent Permeability Model of Shale Nanopores Based on Fractal Theory

Wang

Zhao

et al. 2019

Energies

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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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A mathematical model for co-current spontaneous water imbibition into oil-saturated tight sandstone: Upscaling from pore-scale to core-scale with fractal approach

Cited by 51 publications

References 43 publications

Recent advances in spontaneous imbibition with different boundary conditions

Recent advances in spontaneous imbibition with different boundary conditions

Mathematical modeling of gravity and buoyancy effect on low interfacial tension spontaneous imbibition in tight oil reservoirs

Multiscale Apparent Permeability Model of Shale Nanopores Based on Fractal Theory

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