Homogenization of a stochastic model of a single phase flow in partially fissured media

2021 ◽  
pp. 1-38
Author(s):  
Chigoziem Emereuwa ◽  
Mogtaba Mohammed
Keyword(s):  
Stochastic Model ◽  
Stochastic Partial Differential Equations ◽  
Single Phase ◽  
Double Porosity ◽  
Perforated Domain ◽  
Probability Measures ◽  
Porous System ◽  
Single Phase Flow ◽  
Phase Fluid ◽  
Porosity Model

In this paper, we present new homogenization results of a stochastic model for flow of a single-phase fluid through a partially fissured porous medium. The model is a double-porosity model with two flow fields, one associated with the system of fissures and the other associated with the porous system. This model is mathematically described by a system of nonlinear stochastic partial differential equations defined on perforated domain. The main tools to derive the homogenized stochastic model are the Nguetseng’s two-scale convergence, tightness of constructed probability measures, Prokhorov and Skorokhod compactness process and Minty’s monotonicity method.

scholarly journals Analysis of a multiple-porosity model for single-phase flow through naturally fractured porous media

2003 ◽  
Vol 2003 (7) ◽  
pp. 327-364 ◽  
Author(s):  
Anna Maria Spagnuolo ◽  
Steve Wright
Keyword(s):  
Single Phase ◽  
Flow System ◽  
Double Porosity ◽  
Phase Flow ◽  
Fractured Reservoir ◽  
Single Phase Flow ◽  
Naturally Fractured ◽  
Flow Through ◽  
Multiple Porosity ◽  
Porosity Model

A derivation of a multiple-porosity model for the flow of a single phase, slightly compressible fluid in a multiscale, naturally fractured reservoir is presented by means of recursive use of homagnetization theory. We obtain a model which generalizes the double-porosity model of Arbogast et al. (1990) to a flow system with an arbitrary finite number of scales.

scholarly journals Effects of coupled hydro-mechanical model considering two-phase fluid flow on potential for shallow landslides: a case study in Halmidang Mountain, Yongin, South Korea

2019 ◽  
Author(s):  
Sinhang Kang ◽  
Byungmin Kim
Keyword(s):  
Fluid Flow ◽  
Slope Stability ◽  
Single Phase ◽  
Flow Model ◽  
Coupled Model ◽  
Shallow Landslides ◽  
Single Phase Flow ◽  
Two Phase ◽  
Fully Coupled ◽  
Phase Fluid

Abstract. More than 30 shallow landslides were caused by heavy rainfall that occurred on July 26 and 27, 2011, in Halmidang Mountain, Yongin-si, Gyeonggi Province, South Korea. To precisely analyze shallow landslides and to reflect the mechanism of fluid flow in void spaces of soils, we apply a fully coupled hydro-mechanical model considering two-phase fluid flow of water and air. The available GIS-based topographic data, geotechnical and hydrological properties, and historical rainfall data are used for infiltration and slope stability analyses. Changes in pore air and water pressures and saturations of air and water are obtained from the infiltration analysis, which were used to calculate the safety factor for slope stability assessment. By comparing the results from numerical models by applying a single-phase flow model and a fully coupled model, we investigate the effects of air flow and variations in hydraulic conductivity affected by stress–strain behavior of soil on slope stability. Our results suggest that air flow and hydro-mechanical coupling affects the rate of increase in pore water pressure, thus influencing the safety factor on slopes when ponding is more likely to occur during heavy rainfall. Finally, we conduct slope failure assessments using the fully coupled model, slightly more consistent with actual landslide events than the single-phase flow model.

scholarly journals Linear estimation of flux sensitivity to uncertainty in porous media

2015 ◽  
Vol 768 ◽  
pp. 600-622
Author(s):  
A. J. Evans ◽  
C. P. Caulfield ◽  
Andrew W. Woods
Keyword(s):  
Porous Medium ◽  
Layered Structure ◽  
Single Phase ◽  
Pressure Field ◽  
Porous System ◽  
Integral Expression ◽  
Permeability Model ◽  
Fully Nonlinear ◽  
Phase Fluid ◽  
Good Agreement

We derive an integral expression for the flux of a single-phase fluid through a porous medium with prescribed boundary conditions. Taking variations with respect to the parameters of a given permeability model yields an integral expression for the sensitivity of the flux. We then extend the method to consider linear changes in permeability. This yields a linearised flux expression which is independent of changes in the pressure field that result from the changes in the permeability. For demonstration purposes, we first consider an idealised layered porous medium with a point source and point sink. We show how the effects of changes in permeability are affected by the position of the source and sink relative to the layered structure as well as the layer height and orientation of the layered structure. The results demonstrate that, even in a simple porous system, flux estimates are sensitive to the way in which the permeability is represented. We derive relationships between the statistical moments of the flux and of the permeability parameters which are modelled as random variables. This allows us to estimate the number of permeability parameters that should be varied in a fully nonlinear calculation to determine the variance of the flux. We demonstrate application of the methods to permeability fields generated through fast Fourier transform and kriging methods. We show that the linear estimates for the variability in flux show good agreement with fully nonlinear calculations for sufficiently small standard deviations in the underlying permeability.

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