Fracture Network Modeling: Minkowski Functionals, Spatial Derivatives, and Gravitational Optimization

Effective modeling of fracture networks is essential for accurately simulating fluid dynamics and mass transfer processes in the subsurface environment. In this paper, we define an objective function that incorporates various constraints to replicate the fracture network effectively. These constraints include Minkowski functionals (MFs), and the first (Gradient) and second (Laplacian) spatial derivatives, which are applied to a 2-dimensional fracture network. The methodology involves utilizing gravitational search optimization to solve these objective functions. We examine the statistical parameters and spatial criteria to validate our approach in reproducing fracture network modeling. Our results show that the first spatial derivative yields the most accurate fracture network model, with a classification accuracy of 82.5% for fracture cells and 83.3% for non-fracture cells. This indicates an accurate categorization and simulation of fracture and non-fracture cells, thus offering a promising method for fracture network modeling.