Geometric and Hydrodynamic Characteristics of Three-dimensional Saturated Prefractal Porous Media Determined with Lattice Boltzmann Modeling

Kim, Jung-Woo; Sukop, Michael C.; Perfect, Edmund; Pachepsky, Yakov; Choi, Heechul

doi:10.1007/s11242-011-9818-6

Cited by 13 publications

(4 citation statements)

References 45 publications

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“…Therefore, a system of non-linear equations comprising 2N unknowns and 2N equations is obtained by combining Eqs. (21) and (32). As is shown in Eq.…”

Section: The Productivity Equation Ofmentioning

confidence: 96%

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A Fractal Analysis for Net Present Value of Multi-Stage Hydraulic Fractured Horizontal Well

Zhang

Tan

et al. 2017

Fractals

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Because of the low permeability, multi-stage hydraulic fractured horizontal wells (MHFHWs) occupy a dominant position among production wells in tight gas reservoir. However, net present value (NPV) estimation method for MHFHW in tight gas reservoirs often ignores the effect of heterogeneity in microscopic pore structure. Apart from that, a new fractal model is presented for NPV of MHFHW, based on the fractal expressions of formation parameters. First, with the aid of apparent permeability model, a pseudo pressure expression considering both reservoir fractal features and slippage effect is derived, contributing to establish the productivity model. Secondly, economic assessment method is built based on the fractal productivity model, in order to obtain the NPV of MHFHW. Thirdly, the type curves are illustrated and the influences of different fractal parameters are discussed. The pore fractal dimensions D f and the capillary tortuosity fractal dimensions D T have significant effects on the NPV of an MHFHW. Finally, the proposed model in this paper provides a new methodology for analyzing and predicting the NPV of an MHFHW and may be conducive to a better understanding of the optimal design of MHFHW.

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“…Therefore, a system of non-linear equations comprising 2N unknowns and 2N equations is obtained by combining Eqs. (21) and (32). As is shown in Eq.…”

Section: The Productivity Equation Ofmentioning

confidence: 96%

“…Fractal theory has been used to describe kinds of physical phenomenon in porous media, [16][17][18][19][20][21][22][23][24][25] such as the seepage characters of transient flow, [26][27][28] capillary imbibition, 29,30 non-Darcy flow, 31-33 thermal conductivity. 34 and multiphase flow.…”

Section: Introductionmentioning

confidence: 99%

A Fractal Analysis for Net Present Value of Multi-Stage Hydraulic Fractured Horizontal Well

Zhang

Tan

et al. 2017

Fractals

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“…Compared with fractal dimension widely used for pore structure characterization, lacunarity and succolarity are rarely used for porous media. In previous work, Roy et al [33] adopted lacunarity to characterize the clustering of fracture networks and other research described the heterogeneity of porous media as lacunarity and investigated the relationship between lacunarity and permeability [34,35]. Xia et al [25,30] analyzed pore space microstructures of reservoir rocks in terms of fractal parameters by using 3D images and demonstrated that lacunarity can quantitatively characterize the heterogeneity of the overall pore structure in core samples.…”

Section: Introductionmentioning

confidence: 99%

Characterization of Two-Phase Flow from Pore-Scale Imaging Using Fractal Geometry under Water-Wet and Mixed-Wet Conditions

Zou

Xie

et al. 2022

Energies

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High resolution micro-computed tomography images for multiphase flow provide us an effective tool to understand the mechanism of fluid flow in porous media, which is not only fundamental to the understanding of macroscopic measurements but also for providing benchmark datasets to validate pore-scale modeling. In this study, we start from two datasets of pore scale imaging of two-phase flow obtained experimentally under in situ imaging conditions at different water fractional flows under water-wet and mixed-wet conditions. Then, fractal dimension, lacunarity and succolarity are used to quantify the complexity, clustering and flow capacity of water and oil phases. The results show that with the wettability of rock surface altered from water-wet to mixed-wet, the fractal dimension for the water phase increases while for the oil phase, it decreases obviously at low water saturation. Lacunarity largely depends on the degree of wettability alteration. The more uniform wetting surfaces are distributed, the more homogeneous the fluid configuration is, which indicates smaller values for lacunarity. Moreover, succolarity is shown to well characterize the wettability effect on flow capacity. The succolarity of the oil phase in the water-wet case is larger than that in the mixed-wet case while for the water phase, the succolarity value in the water-wet is small compared with that in the mixed-wet, which show a similar trend with relative permeability curves for water-wet and mixed-wet. Our study provides a perspective into the influence that phase geometry has on relative permeability under controlled wettability and the resulting phase fractal changes under different saturations that occur during multiphase flow, which allows a means to understand phase geometric changes that occur during fluid flow.

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“…These constraints limit the numerical methods' ability to describe power-law°uid°o w in porous media. Fractal theory has been used to describe kinds of physical phenomenon in porous media, [14][15][16][17][18][19][20][21][22][23] such as the seepage characters of transient°ow, 24-26 capillary imbibition, [27][28][29] non-Darcy°ow, 30-32 thermal conductivity 33 and multiphase°ow. 26 It has been experimentally observed that a starting pressure gradient exists in power-law°u id displacement experiments.…”

Section: Introductionmentioning

confidence: 99%

Analysis of transient flow and starting pressure gradient of power-law fluid in fractal porous media

Tan

Zhang

et al. 2015

Int. J. Mod. Phys. C

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A transient°ow model for power-law°uid in fractal porous media is derived by combining transient°ow theory with the fractal properties of tortuous capillaries. Pressure changes of transient°ow for power-law°uid in fractal porous media are related to pore fractal dimension, tortuosity fractal dimension and the power-law index. Additionally, the starting pressure gradient model of power-law°uid in fractal porous media is established. Good agreement between the predictions of the present model and that of the traditional empirical model is obtained, the sensitive parameters that in°uence the starting pressure gradient are speci¯ed and their e®ects on the starting pressure gradient are discussed.

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Geometric and Hydrodynamic Characteristics of Three-dimensional Saturated Prefractal Porous Media Determined with Lattice Boltzmann Modeling

Cited by 13 publications

References 45 publications

A Fractal Analysis for Net Present Value of Multi-Stage Hydraulic Fractured Horizontal Well

A Fractal Analysis for Net Present Value of Multi-Stage Hydraulic Fractured Horizontal Well

Characterization of Two-Phase Flow from Pore-Scale Imaging Using Fractal Geometry under Water-Wet and Mixed-Wet Conditions

Analysis of transient flow and starting pressure gradient of power-law fluid in fractal porous media

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