טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentDavid Nezlobin
SubjectPercolation Clusters in Fracture Network Models in Two
Dimensions
DepartmentDepartment of Agricultural Engineering
Supervisor Mr. Sinai Gideon (Deceased)


Abstract

The development of a macroscopic transport of fluids and contaminants in fractured geological formations strongly depends on the fracture network interconnectivity. According to their interconnectivity, fracture networks may belong to one of the following two major classes - those above and those below the percolation threshold. Fracture networks above the percolation threshold contain the percolation cluster, namely, a connected group of fractures which spans the entire region of interest. In the present study, the existence and basic properties of the percolation clusters in two-dimensional fracture networks have been investigated. The probability of fractures in a network to intersect and form a percolation cluster depends on the statistical distributions of the fractures’ geometrical parameters, and especially on their spatial frequencies, lengths, and orientations. The numerical model of line-segments has been elaborated with the purpose of analyzing such dependence more thoroughly. Regarding the large range of statistical distributions of the geometrical parameters mentioned above, the numerical model calculates many of the quantities that describe fracture network interconnectivity. In addition, the numerical model allows the detailed description of the inner morphological structure of the percolation (or axial percolation) cluster. Furthermore, the important conductive subset of the percolation cluster, called the descending backbone, was first introduced and investigated. The descending backbone is defined as a union of all the descending pathways. In this research the efficient algorithm for isolating the descending backbone is presented. The probability of the descending backbone to exist, its cumulative length and average tortuosity are particularly evaluated. The distributions of lengths and orientations inside the descending backbone are characterized in great detail.