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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Transport in porous media 2 (1987), S. 521-531 
    ISSN: 1573-1634
    Keywords: Porous media ; high velocity flow ; non-Darcy flow ; Forchheimer equation ; inertial effects ; constitutive equations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract Experimental observations have established that the proportionality between pressure head gradient and fluid velocity does not hold for high rates of fluid flow in porous media. Empirical relations such as Forchheimer equation have been proposed to account for nonlinear effects. The purpose of this work is to derive such nonlinear relationships based on fundamental laws of continuum mechanics and to identify the source of nonlinearity in equations. Adopting the continuum approach to the description of thermodynamic processes in porous media, a general equation of motion of fluid at the macroscopic level is proposed. Using a standard order-of-magnitude argument, it is shown that at the onset of nonlinearities (which happens at Reynolds numbers around 10), macroscopic viscous and inertial forces are negligible compared to microscopic viscous forces. Therefore, it is concluded that growth of microscopic viscous forces (drag forces) at high flow velocities give rise to nonlinear effects. Then, employing the constitutive theory, a nonlinear relationship is developed for drag forces and finally a generalized form of Forchheimer equation is derived.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Transport in porous media 3 (1988), S. 319-321 
    ISSN: 1573-1634
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Transport in porous media 3 (1988), S. 299-318 
    ISSN: 1573-1634
    Keywords: Brine transport ; species transport ; radionuclides ; aggregated porous media ; micropores ; macropores ; structured porous media ; Darcy's law ; Fick's law
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract Basic equations governing the transport of species by concentrated brine flowing through an aggregated porous medium are developed. Some simple examples are solved numerically. The medium is considered to be composed of porous rock aggregates separated by ‘macropores’ through which the brine flows and transport of salt and low-concentration species takes place. The aggregates contain dead-end pores, cracks, and stationary pockets collectively called ‘micropores’. The micropore space does not contribute to the flow, but it serves as a storage for salt and species. Adsorption of fluid species takes place at internal surface of aggregates where it is assumed that a linear equilibrium isotherm describes the process. The effects of high salt concentrations are accounted for in the brine density relation, the viscosity relation, Darcy's and Fick's laws, and the rate of mass transfer between macropores and micropores. Mass balance equations, supplemented by extended forms of Darcy's and Fick's laws, are employed to arrive at two sets of equations. One set consists of seven coupled equations for the salt mass fraction and fluid density in macropores, salt mass fraction in micropores, fluid velocity vector, and the fluid pressure. The other set consists of two coupled equations to be solved for the mass fractions of low-concentration species in micropores and macropores. Based on these equations, a mathematical model called TORISM is developed. Using this model, the potential significance of modifications to Darcy's Law are demonstrated.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 21 (1985), S. 671-681 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The theorems of structural variation for rigidly jointed frames are extended to cover the nonlinear elastic-plastic analysis of frames to collapse. Strain hardening and other material changes are included in the analysis. It is shown that the entire load-deflection history of a frame, following the successive formation of plastic hinges up to and including collapse, is obtained from a single initial elastic analysis.The manner in which these theorems are used to insert real (or plastic) hinges to a frame is presented and details of the manual calculations involved in the elastic-plastic analysis of a portal is given to demonstrate the simplicity of the method. This is followed by a comparison of the results with those obtained experimentaly by Baker and Charlton. The versatility of the method is then demonstrated by altering the shape of a frame before its elastic-plastic analysis.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
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