Sequential sphere packing by trilateration equations

To, Peter; Galindo‐Torres, S. A.; Scheuermann, Alexander

doi:10.1007/s10035-016-0666-5

Cited by 10 publications

(6 citation statements)

References 31 publications

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“…Then, a sequential sphere packing method was applied to establish the pore-scale domain. This packing method employs trilateration equations to pack spheres with a predefined grain size distribution (GSD of hydrogel beads) and a given porosity (To et al, 2016). In addition, the boundary conditions are specified, as shown in Figure 2.…”

Section: Numerical Simulation Setup and Settingsmentioning

confidence: 99%

Discrete Bubble Flow in Granular Porous Media via Multiphase Computational Fluid Dynamic Simulation

Yan

Scheuermann

2022

Front. Earth Sci.

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The coal seam gas industry has raised public concerns about the potential risk of groundwater contamination, where gases leaked from coal seams are thought to pollute groundwater. However, the basic principles and controlling parameters for gas seepage from deep ground formations to the ground surface have not been fully understood. As a possible mechanism for gas transport in the subsurface environment, discrete bubble flow was previously investigated using laboratory experiments by Ma et al. (Water Resour. Res, 2015, 51 (6), 4359–4373). This study developed a multiphase computational fluid dynamic (CFD) model to simulate discrete bubbly flow in a two-dimensional granular porous media at the pore scale. Following the experimental setup from Ma et al. (Water Resour. Res, 2015, 51 (6), 4359–4373), a “point source” with preset bubble fluxes was specified in a simulating domain representing the flume size in the earlier experiments. There were around 7,000 granular particles within this domain to model the porous media. This numerical model was validated by conserving the gas mass in the simulating domain. The simulation results provide more physical insights into complex bubble transport behaviour in porous media through specific plume parameters. The breakthrough time of the bubble plume and the cross-sectional averaged velocity of ambient pore water flow were manifested to be proportional to the gas release rates in the logarithmic scales. Also, the bubble plume width was also observed to be proportional to the gas release rates. Moreover, the gas distribution on the top boundary could be observed. The outcomes were further tested against the scaling solutions proposed by Ma et al. (Water Resour. Res, 2015, 51 (6), 4359–4373) with disagreements. The limitations of this multiphase computational fluid dynamic model were finally discussed.

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Section: Numerical Simulation Setup and Settingsmentioning

confidence: 99%

Discrete Bubble Flow in Granular Porous Media via Multiphase Computational Fluid Dynamic Simulation

Yan

Scheuermann

2022

Front. Earth Sci.

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“…The DEM proposed by Cundall and Strack [63] was used to simulate the packing process of particles under the action of gravity. Although there are some new packaging algorithms which are more efficient and flexible [64], DEM is still the closest algorithm to the real gravity packing process. In this study, the DEM was implemented by the software of PFC3D.…”

Section: Porositymentioning

confidence: 99%

Pore Structure of Grain-Size Fractal Granular Material

Liu

Jeng

2019

Materials

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Numerous studies have proven that natural particle-packed granular materials, such as soil and rock, are consistent with the grain-size fractal rule. The majority of existing studies have regarded these materials as ideal fractal structures, while few have viewed them as particle-packed materials to study the pore structure. In this study, theoretical analysis, the discrete element method, and digital image processing were used to explore the general rules of the pore structures of grain-size fractal granular materials. The relationship between the porosity and grain-size fractal dimension was determined based on bi-dispersed packing and the geometric packing theory. The pore structure of the grain-size fractal granular material was proven to differ from the ideal fractal structure, such as the Menger sponge. The empirical relationships among the box-counting dimension, lacunarity, succolarity, grain-size fractal dimension, and porosity were provided. A new segmentation method for the pore structure was proposed. Moreover, a general function of the pore size distribution was developed based on the segmentation results, which was verified by the soil-water characteristic curves from the experimental database.

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“…In order to obtain the free and skeleton particles in the soil, the first step is to create a soil model considering the particle distribution. In DEM modelling, there are several techniques to prepare soil samples: (1) random filling method [12,9]; (2) expansion method [3,15]; (3) meshbased method [9,19]; (4) compaction method [20]; (5) constructional method [3,11,40]; (6) gravity settlement method [11,39]. The first three methods have difficulties in generating a particle distribution with a specified gradation.…”

Section: Introductionmentioning

confidence: 99%

Size distribution of free particles in soils: a geometric modelling approach

Zhang

Luo

et al. 2021

Acta Geotech.

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Suffusion is a typical form of internal erosion for gravel soils in which fine particles are detached by seepage and transport by water through pores. The prediction of erodible particles can improve the assessment of the development of suffusion. The current research on the composition of erodible particles is not sufficiently detailed. The content of erodible particles cannot be accurately determined for a particular gradation. In this paper, a geometric method of generating a particle packing model is proposed. The particles are classified as free or skeleton particles depending on their coordination numbers; thus, their particle size distributions are obtained. Soils with different gradations were analysed using the proposed method. The results indicated that if the grading curve of a soil can be expressed using a fractal relationship, the gradation of free particles also satisfies an exponential function. This is useful in promoting the research on establishing accurate internal erosion criteria, evaluating the performance of filter layers, and predicting the degree of seepage failure caused by internal erosion.

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Sequential sphere packing by trilateration equations

Cited by 10 publications

References 31 publications

Discrete Bubble Flow in Granular Porous Media via Multiphase Computational Fluid Dynamic Simulation

Discrete Bubble Flow in Granular Porous Media via Multiphase Computational Fluid Dynamic Simulation

Pore Structure of Grain-Size Fractal Granular Material

Size distribution of free particles in soils: a geometric modelling approach

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