Multiscale local porosity theory, weak limits, and dielectric response in composite and porous media

2018 ◽  
Vol 59 (10) ◽  
pp. 103511 ◽  
Author(s):  
R. Hilfer
Keyword(s):  
Porous Media ◽  
Dielectric Response ◽  
Weak Limits ◽  
Local Porosity

CHARACTERIZATION OF POROUS MEDIA WITH GEOMETRICAL MULTIFRACTALS

Fractals ◽  
1993 ◽  
Vol 01 (04) ◽  
pp. 894-903 ◽  
Author(s):  
ANTOINE SAUCIER ◽  
JIRI MULLER
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Spatial Distribution ◽  
Multifractal Spectrum ◽  
Spatial Variations ◽  
Local Porosity

In a porous medium the local porosity often exhibits spatial variations. These variations can be characterized by a multifractal spectrum, as long as suitable scaling characteristics are present. We derive some of the properties of such geometrical multifractals, and discuss how the spatial distribution of a set is related to its multifractal spectrum.

scholarly journals Rules for Flight Paths and Time of Flight for Flows in Porous Media with Heterogeneous Permeability and Porosity

Geofluids ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-18 ◽  
Author(s):  
Lihua Zuo ◽  
Ruud Weijermars
Keyword(s):  
Porous Media ◽  
Fluid Transport ◽  
Initial Conditions ◽  
Time Of Flight ◽  
Flight Path ◽  
Flow In Porous Media ◽  
Transport Mechanisms ◽  
Local Porosity ◽  
Fluid Properties ◽  
Porosity And Permeability

Porous media like hydrocarbon reservoirs may be composed of a wide variety of rocks with different porosity and permeability. Our study shows in algorithms and in synthetic numerical simulations that the flow pattern of any particular porous medium, assuming constant fluid properties and standardized boundary and initial conditions, is not affected by any spatial porosity changes but will vary only according to spatial permeability changes. In contrast, the time of flight along the streamline will be affected by both the permeability and porosity, albeit in opposite directions. A theoretical framework is presented with evidence from flow visualizations. A series of strategically chosen streamline simulations, including systematic spatial variations of porosity and permeability, visualizes the respective effects on the flight path and time of flight. Two practical rules are formulated. Rule  1 states that an increase in permeability decreases the time of flight, whereas an increase in porosity increases the time of flight. Rule  2 states that the permeability uniquely controls the flight path of fluid flow in porous media; local porosity variations do not affect the streamline path. The two rules are essential for understanding fluid transport mechanisms, and their rigorous validation therefore is merited.

scholarly journals Rules for Flight Paths and Time of Flight for Flows in Porous Media with Heterogeneous Permeability and Porosity

Geofluids ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-18 ◽  
Author(s):  
Lihua Zuo ◽  
Ruud Weijermars
Keyword(s):  
Porous Media ◽  
Fluid Transport ◽  
Initial Conditions ◽  
Time Of Flight ◽  
Flight Path ◽  
Flow In Porous Media ◽  
Transport Mechanisms ◽  
Local Porosity ◽  
Fluid Properties ◽  
Porosity And Permeability

Porous media like hydrocarbon reservoirs may be composed of a wide variety of rocks with different porosity and permeability. Our study shows in algorithms and in synthetic numerical simulations that the flow pattern of any particular porous medium, assuming constant fluid properties and standardized boundary and initial conditions, is not affected by any spatial porosity changes but will vary only according to spatial permeability changes. In contrast, the time of flight along the streamline will be affected by both the permeability and porosity, albeit in opposite directions. A theoretical framework is presented with evidence from flow visualizations. A series of strategically chosen streamline simulations, including systematic spatial variations of porosity and permeability, visualizes the respective effects on the flight path and time of flight. Two practical rules are formulated. Rule  1 states that an increase in permeability decreases the time of flight, whereas an increase in porosity increases the time of flight. Rule  2 states that the permeability uniquely controls the flight path of fluid flow in porous media; local porosity variations do not affect the streamline path. The two rules are essential for understanding fluid transport mechanisms, and their rigorous validation therefore is merited.

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