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Fractal Simulation of Three-Dimensional Pore Architectures

FAUCETTE, R. CHRIS, and LEON E. BORGMAN, University of Wyoming, Laramie, WY

A Fortran program has been developed that uses the Hausdorf-Besicovitch fractal number to model sedimentary pore systems in three dimensions. A high-resolution grid of points is established in a parallelopiped, and solid particles are randomly inserted into the grid until a predetermined porosity value is reached. The particle shapes used are spheres, ellipsoids, and randomly generated shapes with a fixed Hausdorf-Besicovitch number. The size, location, and orientation of each particle is determined by random numbers. Particle size is only allowed to fall within predetermined limits and is further constrained in that the final distribution of particle sizes must have

a predetermined mean and variance. The resulting systems are graphically displayed and compared to actual pore systems with particle size distributions of the same mean and variance.

Pore interconnectedness and tortuosity are then estimated using repeated random walks. The permeability of the system is estimated by solving pipe-flow equations for each system. These values are then compared with empirical values for corresponding actual pore systems and a relationship with the Hausdorf-Besicovitch number established.

The program is then modified so that pores are inserted into a solid grid. This gives a more geologically realistic system. The resulting pore interconnectedness and tortuosity and system permeability are compared to empirical values for corresponding actual pore systems.

 

AAPG Search and Discovery Article #91004 © 1991 AAPG Annual Convention Dallas, Texas, April 7-10, 1991 (2009)