Abstract
In view of the problem of statistical regression constant in the model of capillary tube bundles in the porous media, a capillary bundle percolation model with fractal geometry was reconstructed. The function expressions of the fractal coefficient and Kozeny constant were deduced. The relationship between the macroscopic fractal properties of porous media and the fractal dimension and the micro pore parameters were obtained. Results show: Fractal coefficient is a function of fractal dimension, maximum pore radius and minimum pore radius; The macroscopic physical properties of porous media are a function of the fractal dimension and the radius of the capillary (the maximum capillary radius and the minimum capillary radius). The expression does not contain any empirical or experimental constants. In the fractal capillary percolation model, the relationship between the three kinds of surface volume, skeleton volume and pore volume are the same as the traditional equal diameter straight capillary bundle model. The Kozeny constant can be accurately described by the function expression of the z-h coefficient, which is used for correcting the difference between real and ideal porous media model.
Highlights
Since French mathematician B.B.Mandlbrot founded fractal geometry theory, scholars at home and abroad have confirmed that the microscopic pore structure of porous media has obvious fractal geometry characteristics [1,2,3,4,5,6,7,8,9]
The fractal coefficient was given a physical meaning in the model, the expression of its definition is not given and was a constant obtained by parameter fitting
This paper addresses the problems existing in the fractal capillary tube bundle model of porous media on the basis of fractal geometry theory
Summary
Since French mathematician B.B.Mandlbrot founded fractal geometry theory, scholars at home and abroad have confirmed that the microscopic pore structure of porous media (such as rock and metal materials) has obvious fractal geometry characteristics [1,2,3,4,5,6,7,8,9]. The fractal coefficient was given a physical meaning in the model (the physical meaning of the fractal coefficient is that it reflects the development degree of pores [10]), the expression of its definition is not given and was a constant obtained by parameter fitting. This paper addresses the problems existing in the fractal capillary tube bundle model of porous media on the basis of fractal geometry theory. Permeability and specific surface are established according to Poseuille's law and darcy’s formula.
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