A permeability model for power-law fluids in fractal porous media composed of arbitrary cross-section capillaries

Wang, Shifang; Wu, Tao; Qi, Hongyan; Zheng, Qiusha; Zheng, Qiang

doi:10.1016/j.physa.2015.05.089

Cited by 24 publications

(9 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This fractal distribution has been found to be useful to describe groundwater flow in the literature (e.g. Tyler and Wheatcraft [50], Yu et al [57], Yu and Li [56], Guarracino et al [20], Wang et al [52]). The fractal dimension can be related to the pore size distribution index λ proposed in the Brooks and Corey model (see Sec.…”

Section: Discussionmentioning

confidence: 99%

A Simple Hysteretic Constitutive Model for Unsaturated Flow

2017

View full text Add to dashboard Cite

In this paper we present a constitutive model to describe unsaturated flow that considers the hysteresis phenomena. This constitutive model provides simple mathematical expressions for both saturation and hydraulic conductivity curves, and a relationship between permeability and porosity. The model is based on the assumption that the porous media can be represented by a bundle of capillary tubes with throats or "ink-bottles" and a fractal pore size distribution. Under these hypotheses, hysteretic curves are obtained for saturation and relative hydraulic conductivity in terms of pressure head. However, a non-hysteretic relationship is obtained when relative hydraulic conductivity is expressed as a function of saturation. The proposed relationship between permeability and porosity is similar to the well-known Kozeny-Carman equation but depends on the fractal dimension. The performance of the constitutive model is tested against different sets of experimental data and previous models. In all of the cases the proposed expressions fit fairly well the experimental data and predicts values of permeability and hydraulic conductivity better than others models.

show abstract

Section: Discussionmentioning

confidence: 99%

A Simple Hysteretic Constitutive Model for Unsaturated Flow

2017

View full text Add to dashboard Cite

show abstract

“…In order to describe the water flow at the representative elementary volume (REV) scale, capillary tube models have proven to be useful for characterizing the porous media by considering different shapes and pore size distributions (e.g., Jerauld and Salter, 1990;Xu and Torres-Verdín, 2013;Wang et al, 2015). Recently, these models have provided valuable insight in the study of, for example, mineral dissolution (e.g., Guarracino et al, 2014), electrical conductivity (e.g., Thanh et al, 2019), saturation hysteretic effects on seismic signatures (e.g., Solazzi et al, 2019) and streaming potential phenomenon (e.g., Jackson, 2008Jackson, , 2010Linde, 2009;Jougnot et al, 2012Jougnot et al, , 2015Thanh et al, 2018;Guarracino and Jougnot, 2018).…”

Section: Introductionmentioning

confidence: 99%

An effective excess charge model to describe hysteresis effects on streaming potential

Soldi

Guarracino

Jougnot

2020

Journal of Hydrology

View full text Add to dashboard Cite

Streaming potentials are produced by the coupling between the water flow and the electrical current generated by the drag of electrical charges within the pore water of the media. This electrokinetic coupling is strongly influenced by the hydraulic properties that control groundwater flow (permeability, saturation and pressure head). Under unsaturated conditions, hydrogeologic studies have widely established that the relationships of permeability and saturation with pressure head are different for drainage and imbibition experiments. The hysteresis phenomenon present on these properties produces a hysteretic behaviour on the streaming potential which has been recently observed in experimental data. Hysteresis can be explained by the presence of irregularities in the pore geometry of the media which affects the water flow and, therefore, the excess charge density that is effectively dragged by the flow. In this study, we present a physically-based analytical model to describe the hysteresis phenomenon in the estimates of the effective excess charge density. Under the assumptions of a porous medium represented by a bundle of tortuous capillary tubes with throats and a fractal pore size distribution, hysteretic curves are obtained for the effective excess charge density as a function of pressure head using a flux averaging technique. These analytical expressions are closed-form and depend on the medium petrophysical and chemical properties. The predictions of the proposed model are consistent with laboratory data from drainage-imbibition experiments. These results open up exciting possibilities for studies involving water movement and processes in the vadose zone.

show abstract

“…It is noted that the tortuosity in Singh et al model can be determined by τ = 1 + 0.63 ln 1 φ [48]. Figure 3 shows a comparison of existing model with the predicted values based on fractal apparent permeability model given by Equation ( 25) with the parameter d t = 1.1 (the same value as that in available references [38,49]), and other parameters are illustrated on Table 2. As we can observe from Figure 3, our apparent gas permeability model (Equation ( 25)) for fractured porous media based on the fractal theory at the relative roughness ε = 0 matches well with Singh et al model [8].…”

Section: The Results and Discussionmentioning

confidence: 97%

An Apparent Gas Permeability Model for Real Gas Flow in Fractured Porous Media with Roughened Surfaces

Wang

2021

Polymers

Self Cite

View full text Add to dashboard Cite

The investigation of gas transport in fractured porous media is essential in most petroleum and chemical engineering. In this paper, an apparent gas permeability model for real gas flow in fractured porous media is derived with adequate consideration of real gas effect, the roughness of fracture surface, and Knudsen diffusion based on the fractal theory. The fractal apparent gas permeability model is obtained to be a function of micro-structural parameters of fractured porous media, relative roughness, the pressure, the temperature, and the properties of gas. The predictions from the apparent gas permeability model based on the fractal theory match well with the published permeability model and experimental data, which verifies the rationality of the present fractal apparent gas permeability model.

show abstract

A permeability model for power-law fluids in fractal porous media composed of arbitrary cross-section capillaries

Cited by 24 publications

References 31 publications

A Simple Hysteretic Constitutive Model for Unsaturated Flow

A Simple Hysteretic Constitutive Model for Unsaturated Flow

An effective excess charge model to describe hysteresis effects on streaming potential

An Apparent Gas Permeability Model for Real Gas Flow in Fractured Porous Media with Roughened Surfaces

Contact Info

Product

Resources

About