Mathematical algorithm development and parametric studies with the GEOFRAC three-dimensional stochastic model of natural rock fracture systems

• The GEOFRAC 3D model applies sequential stochastic processes to represent rock fracture systems.
• We propose new algorithms for modeling fracture intensity, size, aperture, and connectivity.
• Poisson-Voronoi Tessellation of planes into polygons optimizes fracture intensity modeling.
• A statistical parametric study shows how fracture intensity and size might affect connectivity.

This paper presents results from research conducted at MIT during 2010–2012 on modeling of natural rock fracture systems with the GEOFRAC three-dimensional stochastic model. Following a background summary of discrete fracture network models and a brief introduction of GEOFRAC, the paper provides a thorough description of the newly developed mathematical and computer algorithms for fracture intensity, aperture, and intersection representation, which have been implemented in MATLAB. The new methods optimize, in particular, the representation of fracture intensity in terms of cumulative fracture area per unit volume, P32, via the Poisson-Voronoi Tessellation of planes into polygonal fracture shapes. In addition, fracture apertures now can be represented probabilistically or deterministically whereas the newly implemented intersection algorithms allow for computing discrete pathways of interconnected fractures. In conclusion, results from a statistical parametric study, which was conducted with the enhanced GEOFRAC model and the new MATLAB-based Monte Carlo simulation program FRACSIM, demonstrate how fracture intensity, size, and orientations influence fracture connectivity.

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