Fractal Geometry Based Mathematical Model and Simulation of Permeability of Dehulled Rapeseed Cake


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In view of the fact that dehulled rapeseed cake formed under cold pressing condition is a fractal structure, the relation between the permeability and the pore fractal dimension of dehulled rapeseed cake has been investigated using fractal geometry. The microstructures of dehulled rapeseed cake under six pressing pressures are measured by using scanning electronic microscope and Image-pro image analyzer. The fractal dimensions of pore size distributions are measured by the box-counting method. Combining Hagen-Poiseulle equation with Darcy’s law for flow of fluid through porous media, the relational expression of fractal dimension and permeability has been developed to predicate the permeability of compressed dehulled rapeseed cake under cold condition. The permeability experiments of dehulled rapeseed cake are also carried out in order to validate the predication model proposed in this study. The value of mean relative error is 15.5%. A fairly good agreement is obtained in the case of high pressing pressures.



Edited by:

Honghua Tan




X. Zheng et al., "Fractal Geometry Based Mathematical Model and Simulation of Permeability of Dehulled Rapeseed Cake", Applied Mechanics and Materials, Vols. 29-32, pp. 269-274, 2010

Online since:

August 2010




[1] Wang Jinzhou, Zheng Xiao, Wang Nong, Lin Guoxiang, Fractal character of the pore structure of dehulled rapeseed cake based on scanning electron microscopy image analysis, Transactions of the Chinese Society of Agricultural Engineering, vol 24, 2008, pp.16-20.


[2] B.B. Mandelbrot: The Fractal Geometry of Nature, San Francisco: Freeman, (1982).

[3] A. Majumdar, B. Bhushan, Role of fractal geometry in roughness characterization and contact mechanics of surfaces, J of Tribology, vol 112, 1990, pp.205-216.


[4] S.W. Wheatcraft, S.W. Tyler, An explanation of scale dependent dispersivity in heterogeneous aquifers using concepts of fractal geometry, Water Res Researches, vol 24, 1988, pp.566-578.


[5] B.M. Yu, L.J. Lee, H.Q. Cao, A fractal in-plane permeability model for fabrics, Polymer Composites, vol 22, 2002, pp.201-221.

[6] Wang Jingzhou, Research on Pore Structure and Permeability of Oil Cake Based on Fractal Geometry, Ph.M. Thesis, Wuhan Polytechnic University, (2008).