The present article deals with the study of the hydrodynamics of a porous sphere in an oscillatory viscous flow of an incompressible Newtonian fluid. Unsteady Stokes equations are used for the flow outside the porous sphere and Darcy’s equation is used for the flow inside the porous sphere. Corresponding Faxén’s law for drag and torque acting on the surface of the porous sphere is derived. Also the results are compared with few existing special cases. Examples like uniform flow, oscillating Stokeslet, oscillatory shear flow and quadratic shear flow are discussed.
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An analytical solution of the flow of a hydromagnetic fluid through a porous medium between permeable beds is obtained and studied. The fluid is under an exponential decaying pressure gradient and the uniform magnetic field in a direction normal to the flow saturated porous medium is considered. Two governing equations, namely Navier-Stokes equations and Darcy's law, are employed for the flow between and through the permeable beds, respectively. Injection and suction of the fluid through lower and upper permeable beds, respectively, with same velocity are allowed in the presence of porous medium and the uniform magnetic field. The velocity field and the volume flux are calculated analytically and presented graphically for different choices of the parameters exhibiting their phenomenal nature. Additionally if we replace the exponentially decaying pressure gradient by the pulsatile one and porousity of medium tends to zero, the results match excellently with those of Malathy and Srinivas [T. Malathy and S. Srinivas, Pulsatile flow of a hydromagnetic fluid between permeable beds, Int. Comm. In Heat and Mass Transfer 35, 681-688 (2008)].
In the "new age" oil and gas industry came more and more into focus term of unconventional hydrocarbons. Gained experience and success in the United States tight gas sand reservoirs Piceance, Anadarko, Greater Green, Lobo fields confirmed the hidden potential of unconventional hydrocarbon resources. In some production and development areas called coal bed seam, shale gas and tight sand reservoirs without intensifying operations isn't possible to produce commercial gas volumes. Used practises and gained large experiences in the crude oil fields are commonly used in the shale and tight gas fields across the United States. Application of these technologies of stimulation methods like fracturing in Europe is at the very beginning. Pioneer investors are waiting in all Europe for the well testing results from the first dozen fractured shale gas and tight sand reservoirs. Test results could have significant influence on the future planned massive drilling campaign of exploration of the unconventional hydrocarbon resources
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Prawo Darcy. Badania Pane'a i Schiffmana, Tavenasa, Olsena. Zakres stosowalności prawa Darcy. Badania własne iłów w standardowym aparacie trójosiowym. Badania własne w prototypowym aparacie do badania przepuszczalności gruntów słabo przepuszczalnych. Liniowa zależność prędkości przepływu od spadku hydraulicznego.
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Darcy's law. Pane's, Schiffman's Tavenas'es and Olsen's investigations. Darcy's law application range. Own investigations on clays in standard triaxial apparatus. The experiments in prototype apparatus for testing the permeability of semi pervious soils. Linear dependence of flow velocity with hydraulic gradient.
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In this paper, a simple generalization of Darcy’s law is proposed for the description of hydraulic properties of anisotropic porous materials. The coefficient of permeability is defined as a scalar valued function of orientation. The principal directions of permeability are determined from a fabric descriptor specifying the distribution of average pore size. An example is provided for identification of material parameters, which is based on an idealized “pipe network model”. A procedure for defining the anisotropy in strength properties, which incorporates a conceptually similar approach, is also reviewed and an illustrative example is provided.
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