Random walk–percolation-based modeling of two-phase flow in porous media: Breakthrough time and net to gross ratio estimation

Ganjeh-Ghazvini, Mostafa; Masihi, Mohsen; Ghaedi, Mojtaba

doi:10.1016/j.physa.2014.03.051

Cited by 8 publications

(8 citation statements)

References 35 publications

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“…The number of groups (k) should be known before the k-means method is applied. Whereas binary system including just permeable and impermeable regions is very common in percolation [47], 5-11 groups are often used in facies modeling [48]. From a mathematical viewpoint, the silhouette plots can offer an appropriate choice of k [46].…”

Section: Methodology: the Heterogeneity Quantification By Clustering mentioning

confidence: 99%

“…Although the solution to multiphase flow problem is computationally demanding, the pressure field can be easily found under incompressible single phase flow assumptions. In this case, the governing equations imply the net volume entering to (or exiting from) a cell is zero [47]. If the mass balance equation is combined with Darcy's law, one obtains…”

Section: Modification Of Permeability For Cells Hosting a Wellborementioning

confidence: 99%

“…(17) and (19) for all blocks results in a set of linear algebraic equations. The pressure distribution is found after these equations are solved [47]. The problem of permeability modification for well blocks is to minimize the objective function defined as follows.…”

Section: Modification Of Permeability For Cells Hosting a Wellborementioning

confidence: 99%

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Study of heterogeneity loss in upscaling of geological maps by introducing a cluster-based heterogeneity number

Ganjeh-Ghazvini

Masihi

Baghalha

2015

Physica A: Statistical Mechanics and its Applications

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Section: Methodology: the Heterogeneity Quantification By Clustering mentioning

confidence: 99%

Section: Modification Of Permeability For Cells Hosting a Wellborementioning

confidence: 99%

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Study of heterogeneity loss in upscaling of geological maps by introducing a cluster-based heterogeneity number

Ganjeh-Ghazvini

Masihi

Baghalha

2015

Physica A: Statistical Mechanics and its Applications

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“…For detection purposes, there is no need for multi‐phase simulation as it seems too difficult in the fine grid model. Under incompressible single phase flow, Ganjeh‐Ghazvini et al . wrote the governing equation as

is the harmonic average permeability and L is the distance between the cell and its adjacent blocks.…”

Section: Connectivity Misrepresentation In Upscaling Processmentioning

confidence: 99%

Effect of connectivity misrepresentation on accuracy of upscaled models in oil recovery by CO₂ injection

2015

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An upscaling method such as renormalization converts a detailed geological model to a coarse one. Although flow equations can be solved faster on a coarse model, its results have more errors. Numerical dispersion, heterogeneity loss, and connectivity misrepresentation are the factors responsible for errors. Connectivity has a great effect on the fluid distribution and leakage pathways in EOR processes or CO2 storage. This paper deals with the description and quantification of connectivity misrepresentation in the upscaling process. For detection of high‐flow regions, the flow equations are solved under simplified single‐phase conditions. These regions are recognized as the cells whose fluxes are greater than a cut‐off. The connectivity is investigated by checking whether the high‐flux region forms a spanning cluster across the model. An indicator called the flux connectivity distortion is defined to measure the connectivity misrepresentation of coarse grids. This indicator is shown to have a strong correlation with the oil saturation error. For renormalization method, this relation helps to propose an upper limit of coarsening beyond which the coarse model results are not reliable. Once the proper sizes of coarse blocks are determined, flow behavior can be simulated accurately in a project of CO2‐EOR or CO2 sequestration. © 2015 Society of Chemical Industry and John Wiley & Sons, Ltd

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“…Therefore, the development of reliable mathematical models of this transport process is very important. Several previous studies have sought to describe crowded transport processes using either random walk simulation models [8][9][10][11][12][13][14][15][16][17][18] or fractional order diffusion equation (FDE) models [19][20][21][22][23][24][25][26][27][28][29]. a b Fig.…”

Section: Introductionmentioning

confidence: 99%

Modeling transport through an environment crowded by a mixture of obstacles of different shapes and sizes

Ellery

Baker

McCue

et al. 2016

Physica A: Statistical Mechanics and its Applications

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h i g h l i g h t s• Stochastic simulations of individual and collective motion through a crowded environment. • Crowded environments populated by mixtures of obstacles of different shapes and sizes.• Transport properties depend on the obstacle volume fraction and details of the obstacle shape and size distribution. • Standard fractional diffusion equation descriptions ought to be used with care. a b s t r a c tMany biological environments are crowded by macromolecules, organelles and cells which can impede the transport of other cells and molecules. Previous studies have sought to describe these effects using either random walk models or fractional order diffusion equations. Here we examine the transport of both a single agent and a population of agents through an environment containing obstacles of varying size and shape, whose relative densities are drawn from a specified distribution. Our simulation results for a single agent indicate that smaller obstacles are more effective at retarding transport than larger obstacles; these findings are consistent with our simulations of the collective motion of populations of agents. In an attempt to explore whether these kinds of stochastic random walk simulations can be described using a fractional order diffusion equation framework, we calibrate the solution of such a differential equation to our averaged agent density information. Our approach suggests that these kinds of commonly used differential equation models ought to be used with care since we are unable to match the solution of a fractional order diffusion equation to our data in a consistent fashion over a finite time period.

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Random walk–percolation-based modeling of two-phase flow in porous media: Breakthrough time and net to gross ratio estimation

Cited by 8 publications

References 35 publications

Study of heterogeneity loss in upscaling of geological maps by introducing a cluster-based heterogeneity number

Study of heterogeneity loss in upscaling of geological maps by introducing a cluster-based heterogeneity number

Effect of connectivity misrepresentation on accuracy of upscaled models in oil recovery by CO₂ injection

Modeling transport through an environment crowded by a mixture of obstacles of different shapes and sizes

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Random walk–percolation-based modeling of two-phase flow in porous media: Breakthrough time and net to gross ratio estimation

Cited by 8 publications

References 35 publications

Study of heterogeneity loss in upscaling of geological maps by introducing a cluster-based heterogeneity number

Study of heterogeneity loss in upscaling of geological maps by introducing a cluster-based heterogeneity number

Effect of connectivity misrepresentation on accuracy of upscaled models in oil recovery by CO2 injection

Modeling transport through an environment crowded by a mixture of obstacles of different shapes and sizes

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Effect of connectivity misrepresentation on accuracy of upscaled models in oil recovery by CO₂ injection