Finite-Difference Approximation for Fluid-Flow Simulation and Calculation of Permeability in Porous Media

Shabro, Vahid; Torres‐Verdín, Carlos; Javadpour, Farzam; Sepehrnoori, Kamy

doi:10.1007/s11242-012-0024-y

Cited by 78 publications

(29 citation statements)

References 28 publications

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“…Due to the ultra-low permeability of mudstones, it is difficult to experimentally investigate the transport processes inside shales as well as to accurately measure the transport properties. Alternatively, advanced pore-scale numerical methods, such as the lattice Boltzmann method (LBM) 16 17 , have been shown to be an efficient alternative 18 19 20 21 22 23 . In the present study, the LBM is employed to simulate fluid flow and Knudsen diffusion processes in shales as well as to predict the transport properties.…”

mentioning

confidence: 99%

Nanoscale simulation of shale transport properties using the lattice Boltzmann method: permeability and diffusivity

Chen

Zhang

Kang

et al. 2015

Sci Rep

241

188

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Porous structures of shales are reconstructed using the markov chain monte carlo (MCMC) method based on scanning electron microscopy (SEM) images of shale samples from Sichuan Basin, China. Characterization analysis of the reconstructed shales is performed, including porosity, pore size distribution, specific surface area and pore connectivity. The lattice Boltzmann method (LBM) is adopted to simulate fluid flow and Knudsen diffusion within the reconstructed shales. Simulation results reveal that the tortuosity of the shales is much higher than that commonly employed in the Bruggeman equation, and such high tortuosity leads to extremely low intrinsic permeability. Correction of the intrinsic permeability is performed based on the dusty gas model (DGM) by considering the contribution of Knudsen diffusion to the total flow flux, resulting in apparent permeability. The correction factor over a range of Knudsen number and pressure is estimated and compared with empirical correlations in the literature. For the wide pressure range investigated, the correction factor is always greater than 1, indicating Knudsen diffusion always plays a role on shale gas transport mechanisms in the reconstructed shales. Specifically, we found that most of the values of correction factor fall in the slip and transition regime, with no Darcy flow regime observed.

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mentioning

confidence: 99%

Nanoscale simulation of shale transport properties using the lattice Boltzmann method: permeability and diffusivity

Chen

Zhang

Kang

et al. 2015

Sci Rep

241

188

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“…The Euler characteristic ( χ ) for a digital image ( X ) is expressed as

χ ((), X) = I - L +

where I is the number of isolated objects, L is the number of redundant loops, and O is the number of cavities (Armstrong et al, 2019). Pore size distribution is estimated by a local distance maximum method (Chung et al, 2020; Shabro et al, 2012; Y. D. Wang, Chung, et al, 2020), which is similar to a watershed‐distance transform (Strahler, 1957) or the maximum inscribed spheres method (Silin & Patzek, 2006). Lastly, the corresponding absolute permeability is calculated based on the single phase Lattice‐Boltzmann method (McClure et al, 2014; Y. D. Wang, Chung, et al, 2020).…”

Section: Image Processing and Petrophysical Analysismentioning

confidence: 99%

“…where I is the number of isolated objects, L is the number of redundant loops, and O is the number of cavities (Armstrong et al, 2019). Pore size distribution is estimated by a local distance maximum method (Chung et al, 2020;Shabro et al, 2012;Y. D. Wang, Chung, et al, 2020), which is similar to a watershed-distance transform (Strahler, 1957) or the maximum inscribed spheres method (Silin & Patzek, 2006).…”

Section: Image Processing and Petrophysical Analysismentioning

confidence: 99%

An Innovative Application of Generative Adversarial Networks for Physically Accurate Rock Images With an Unprecedented Field of View

Niu

Wang

Mostaghimi

et al. 2020

Geophysical Research Letters

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High-resolution X-ray microcomputed tomography (micro-CT) data are used for the accurate determination of rock petrophysical properties. High-resolution data, however, result in a small field of view, and thus, the representativeness of a simulation domain can be brought into question when dealing with geophysical applications. This paper applies a cycle-in-cycle generative adversarial network (CinCGAN) to improve the resolution of 3-D micro-CT data and create a super-resolution image using unpaired training images. Effective porosity, Euler characteristic, pore size distribution, and absolute permeability are measured on super-resolution and high-resolution ground-truth images to evaluate the physical accuracy of the proposed CinCGAN. The results demonstrate that CinCGAN provides physically accurate images with an order of magnitude larger field of view when compared to typical micro-CT methods. This unlocks new pathways for the geophysical characterization of subsurface rocks with broad implications for flow modeling in highly heterogeneous rocks or fundamental studies on nonlocal forces that extend beyond domain sizes typically used for pore-scale simulation. Plain Language Summary Digital rock analysis aims to characterize the physical structure of porous rocks with the aid of X-ray computed microtomography for the simulation of effective properties. The accuracy of these simulations to actual physical rock properties is highly dependent on how well the rock pores are resolved in addition to the particular setup and solvers used. We expect to obtain accurate results from high-resolution images with a large enough field of view to fully characterize microstructural heterogeneities given an appropriate numerical scheme. However, high-resolution data are obtained at the cost of a smaller field of view due to technological limitations. To circumvent this issue, super-resolution methods based on deep learning algorithms can be applied to improve image resolution by learning the mappings between low-and high-resolution data. The training data, however, often require the pairing of low-/high-resolution images, which is obtained by a time-consuming process of image registration. We apply a novel deep learning algorithm to achieve 3-D super-resolution images using unpaired training data. We demonstrate that super-resolution data can provide physically accurate rock images compared to high-resolution ground-truth images. The presented method provides new opportunities to study core-scale properties, such as heterogeneity and flow dynamics, at a resolution high enough to resolve the microscopic rock structure.

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“…Mostaghimi et al (2012) applied an algebraic multigrid method to study the permeability anisotropy at the pore scale and opined that rock pores are mainly unidirectionally connected. Shabro et al (2012) applied a finite difference method in which a weighting factor is defined and a Laplace equation is solved to study the flow characteristics of the fluid in the core. Moreover, they considered limestone and dolomite as examples for the practical application of their method and simulated the permeability distribution of rocks well.…”

Section: Introductionmentioning

confidence: 99%

Construction of pore structure and lithology of digital rock physics based on laboratory experiments

Huang¹,

Zhang²,

Liu³

et al. 2021

J Petrol Explor Prod Technol

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The development and stimulation of oil and gas fields are inseparable from the experimental analysis of reservoir rocks. Large number of experiments, poor reservoir properties and thin reservoir thickness will lead to insufficient number of cores, which restricts the experimental evaluation effect of cores. Digital rock physics (DRP) can solve these problems well. This paper presents a rapid, simple, and practical method to establish the pore structure and lithology of DRP based on laboratory experiments. First, a core is scanned by computed tomography (CT) scanning technology, and filtering back-projection reconstruction method is used to test the core visualization. Subsequently, three-dimensional median filtering technology is used to eliminate noise signals after scanning, and the maximum interclass variance method is used to segment the rock skeleton and pore. Based on X-ray diffraction technology, the distribution of minerals in the rock core is studied by combining the processed CT scan data. The core pore size distribution is analyzed by the mercury intrusion method, and the core pore size distribution with spatial correlation is constructed by the kriging interpolation method. Based on the analysis of the core particle-size distribution by the screening method, the shape of the rock particle is assumed to be a more practical irregular polyhedron; considering this shape and the mineral distribution, the DRP pore structure and lithology are finally established. The DRP porosity calculated by MATLAB software is 32.4%, and the core porosity measured in a nuclear magnetic resonance experiment is 29.9%; thus, the accuracy of the model is validated. Further, the method of simulating the process of physical and chemical changes by using the digital core is proposed for further study.

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Finite-Difference Approximation for Fluid-Flow Simulation and Calculation of Permeability in Porous Media

Cited by 78 publications

References 28 publications

Nanoscale simulation of shale transport properties using the lattice Boltzmann method: permeability and diffusivity

Nanoscale simulation of shale transport properties using the lattice Boltzmann method: permeability and diffusivity

An Innovative Application of Generative Adversarial Networks for Physically Accurate Rock Images With an Unprecedented Field of View

Construction of pore structure and lithology of digital rock physics based on laboratory experiments

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