FRACTAL GENERATION OF SURFACE-AREA OF POROUS-MEDIA

Many natural porous geological rock formations, as well as engineered porous structures, have fractal properties, i.e., they are self-simila r over several length scales. While there have been many experimental and theoretical studies on how to quantify a fractal porous medium and on how to determine its fractal dimension, the numerical generation o f a fractal pore structure with predefined statistical and scaling pro perties is somewhat scarcer. In the present paper a new numerical meth od for generating a three-dimensional porous medium with any desired p robability density function (PDF) and autocorrelation function (ACF) i s presented. The well-known Turning Bands Method (TBM) is modified to generate three-dimensional synthetic isotropic and anisotropic porous media with a Gaussian PDF and exponential-decay ACF. Porous media with other PDF's and ACF's are constructed with a nonlinear, iterative PDF and ACF transformation, whereby the arbitrary PDF is converted to an equivalent Gaussian PDF which is then simulated with the classical TBM . Employing a new method for the estimation of the surface area for a given porosity, the fractal dimensions of the surface area of the synt hetic porous media generated in this way are then measured by classica l fractal perimeter/area relationships. Different 3D porous media are simulated by varying the porosity and the correlation structure of the random field. The performance of the simulations is evaluated by chec king the ensemble statistics, the mean, variance and ACF of the simula ted random field. For a porous medium with Gaussian PDF, an average fr actal dimension of approximately 2.76 is obtained which is in the rang e of values of actually measured fractal dimensions of molecular surfa ces. For a porous medium with a non-Gaussian quadratic PDF the calcula ted fractal dimension appears to be consistently higher and averages 2 .82. The results also show that the fractal dimension is neither stron gly dependent of the porosity nor of the degree of anisotropy assumed.