The competition between gravity and flow focusing in two-layered porous media
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Abstract The gravitationally driven flow of a dense fluid within a two-layered porous media is examined experimentally and theoretically. We find that in systems with two horizontal layers of differing permeability a competition between gravity driven flow and flow focusing along high-permeability routes can lead to two distinct flow regimes. When the lower layer is more permeable than the upper layer, gravity acts along high-permeability pathways and the flow is enhanced in the lower layer. Alternatively, when the upper layer is more permeable than the lower layer, we find that for a sufficiently small input flux the flow is confined to the lower layer. However, above a critical flux fluid preferentially spreads horizontally within the upper layer before ultimately draining back down into the lower layer. This later regime, in which the fluid overrides the low-permeability lower layer, is important because it enhances the mixing of the two fluids. We show that the critical flux which separates these two regimes can be characterized by a simple power law. Finally, we briefly discuss the relevance of this work to the geological sequestration of carbon dioxide and other industrial and natural flows in porous media.In previous studies, it is found that the frame and pore in porous media both possess the fractal geometric character. So the permeability and porosity models of bi-fractal porous media are derived based on the assumption that a porous media consists of fractal solid clusters and capillary bundles. The expressions of presented models are constituted by the fractal parameters of solid cluster and those of capillary bundle. Good agreement between model predictions and experimental data is obtained. This verifies the validity of the permeability and porosity models for bi-fractal porous media. The sensitive parameters that influence the permeability and porosity are specified, and their effects on the relationship between permeability and porosity are discussed.
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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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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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Several results of lattice-gas and lattice-Boltzmann simulations of single-fluid flow in 2D and 3D porous media are discussed. Simulation results for the tortuosity, effective porosity and permeability of a 2D random porous medium are reported. A modified Kozeny–Carman law is suggested, which includes the concept of effective porosity. This law is found to fit well the simulated 2D permeabilities. The results for fluid flow through large 3D random fibre webs are also presented. The simulated permeabilities of these webs are found to be in good agreement with experimental data. The simulations also confirm that, for this kind of materials, permeability depends exponentially on porosity over a large porosity range.
Tortuosity
Lattice Boltzmann methods
Darcy's law
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The porosity is often regarded as a linear function of fluid pressure in porous media and permeability is approximately looked as constants. However, for some scenarios such as unconsolidated sand beds, abnormal high pressured oil formation or large deformation of porous media for pore pressure dropped greatly, the change in porosity is not a linear function of fluid pressure in porous media, and permeability can't keep a constant yet. This paper mainly deals with the relationship between the damage variable and permeability properties of a deforming media, which can be considered as an exploratory attempt in this field.
Poromechanics
Fluid pressure
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AbstractKozeny-Carman permeability equation is an important relation for the determination of permeability in porous media. In this study, the permeabilities of porous media that contains rectangular rods are determined, numerically. The applicability of Kozeny-Carman equation for the periodic porous media is investigated and the effects of porosity and pore to throat size ratio on Kozeny constant are studied. The continuity and Navier-Stokes equations are solved to determine the velocity and pressure fields in the voids between the rods. Based on the obtained flow field, the permeability values for different porosities from 0.2 to 0.9 and pore to throat size ratio values from 1.63 to 7.46 are computed. Then Kozeny constants for different porous media with various porosity and pore to throat size ratios are obtained and a relationship between Kozeny constant, porosity and pore to throat size ratio is constructed. The study reveals that the pore to throat size ratio is an important geometrical parameter that should be taken into account for deriving a correlation for permeability. The suggestion of a fixed value for Kozeny constant makes the application of Kozeny-Carman permeability equation too narrow for a very specific porous medium. However, it is possible to apply the Kozeny-Carman permeability equation for wide ranges of porous media with different geometrical parameters (various porosity, hydraulic diameter, particle size and aspect ratio) if Kozeny constant is a function of two parameters as porosity and pore to throat size ratios.Keywords: porous medianumerical simulationpermeabilityKozeny constantKozeny-Carman equation
Constant (computer programming)
Rod
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The concept of permeability of porous media is discussed, and a modification of Kozeny's permeability equation to include the effect of effective porosity is introduced. An analytical expression for the specific surface area of a system constructed of randomly placed identical obstacles with unrestricted overlap is derived, and a lattice-gas cellular automaton method is then used to simulate the dependence on porosity of permeability, tortuosity, and effective porosity for a flow of Newtonian uncompressible fluid in this two-dimensional porous substance. The simulated permeabilities can well be explained by the concept of effective porosity, and the exact form of the specific surface area. The critical exponent of the permeability near the percolation threshold is also determined from the simulations.
Tortuosity
Exponent
Percolation Theory
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The existing of voids is the nature characteristic of the porous media,which not only alters the mechanical character of the rock masses,but also affects their permeabilities.Most of the porous media models in the past regard the porosity and permeability coefficient as the constant which were irrelevant to the time constant.In fact,they varied with time and coordinates due to erosion,and other reasons.At the same time,the porosity and permeability coefficient were relevant to the pore pressure and velocity of the porosity water.From the continuum damage mechanics point of view,the mechanical permeability properties of the porous media were studied based on the quantitative relationship between the porosity rate and the damage variables.First of all,the traditional Darcy law was modified,and the complete effective Darcy law(model) inside the complete and effective seepage field in porous media was derived.Then,the model’s properties of permeability parameters were discussed and analyzed.Finally,some useful and valuable conclusions are drawn.
Darcy's law
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