Numerical Integration Methods for the Dual Porosity Model in Sorbing Porous Media

1994 ◽  
pp. 621-628 ◽  
Author(s):  
Giuseppe Gambolati ◽  
Claudio Gallo ◽  
Claudio Paniconi
Keyword(s):  
Porous Media ◽  
Numerical Integration ◽  
Dual Porosity ◽  
Integration Methods ◽  
Dual Porosity Model ◽  
Numerical Integration Methods ◽  
Porosity Model

Direct Calculation of Permeability by High-Accurate Finite Difference and Numerical Integration Methods

2016 ◽  
Vol 20 (2) ◽  
pp. 405-440 ◽  
Author(s):  
Yi Wang ◽  
Shuyu Sun
Keyword(s):  
Porous Media ◽  
Fluid Flow ◽  
Finite Difference ◽  
Numerical Integration ◽  
Finite Difference Methods ◽  
Direct Calculation ◽  
Numerical Error ◽  
Integration Methods ◽  
Numerical Integration Methods ◽  
Tensor Permeability

AbstractVelocity of fluid flow in underground porous media is 6~12 orders of magnitudes lower than that in pipelines. If numerical errors are not carefully controlled in this kind of simulations, high distortion of the final results may occur [1–4]. To fit the high accuracy demands of fluid flow simulations in porous media, traditional finite difference methods and numerical integration methods are discussed and corresponding high-accurate methods are developed. When applied to the direct calculation of full-tensor permeability for underground flow, the high-accurate finite difference method is confirmed to have numerical error as low as 10–5% while the high-accurate numerical integration method has numerical error around 0%. Thus, the approach combining the high-accurate finite difference and numerical integration methods is a reliable way to efficiently determine the characteristics of general full-tensor permeability such as maximum and minimum permeability components, principal direction and anisotropic ratio.

scholarly journals EFFECTIVE PERMEABILITY OF FRACTURED POROUS MEDIA WITH FRACTAL DUAL-POROSITY MODEL

Fractals ◽  
2017 ◽  
Vol 25 (04) ◽  
pp. 1740014 ◽  
Author(s):  
PENG XU ◽  
HAICHENG LIU ◽  
AGUS PULUNG SASMITO ◽  
SHUXIA QIU ◽  
CUIHONG LI
Keyword(s):  
Porous Media ◽  
Hydraulic Properties ◽  
Effective Permeability ◽  
Scaling Laws ◽  
Fractured Porous Media ◽  
Dual Porosity ◽  
Statistical Characteristics ◽  
Fracture Aperture ◽  
Dual Porosity Model ◽  
Porosity Model

As natural fractures show statistically fractal scaling laws, fractal geometry has been proposed and applied to model the fracture geometry and to study the hydraulic properties of fractured porous media. In this paper, a fractal dual-porosity model is developed to study the single-phase fluid flow through fractured porous media. An analytical expression for effective permeability of fractured porous media is derived, which depends on the fractal dimension and fracture aperture. The effect of fractal dimensions for fracture aperture distribution and tortuosity, the ratio of minimum to maximum fracture apertures and fracture fraction on the effective permeability have been discussed. In addition, a power law relationship between the effective permeability and fracture fraction is proposed to predict the equivalent hydraulic properties of fractured porous media. Compared with empirical formulas for effective permeability, the present fractal dual-porosity model can capture the statistical characteristics of fractures and shed light on the transport mechanism of fractured porous media.

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