FRACTAL ANALYSIS OF 2-D FRACTURE NETWORKS OF NATURALLY FRACTURED RESERVOIRS ANALOG IN SOUTH ALGERIA

Three main formations, Ajjers, In-Tahouite, and Tamadjert compose the Cambro-Ordovician in the Saharan platform. These formations are characterized by stiff tectonic style, showing a dense net of faults and folds affected the Paleozoic series. The fractal approach is based on the estimation of the global fractal dimension for the basement formation and Cambro-Ordovician units, and determine the fractal dimension for each fracture set. The fractal dimensions for the whole fracture networks affecting the Cambro-Ordovician units and the different fracture sets are estimated using two fractal methods. The first method is named the center distance algorithm, considers that only the fault centers distribution is fractal. The dimension suited for random sets of points is the correlation dimension deduced from the two-points correlation function. If the centers population is fractal, this function is proportional to a power law. The dimension correlation gives an indicator of faults centers spatial distribution. The second method is named the box-counting algorithm, is one of the methods used to evaluate the fractal dimension of a set of points or a set of lineaments like fault traces. It considers that the whole network is fractal. The box-counting algorithm consists in discretizing a 2D fault trace map with different grids, successively. For these two methods, the fractal dimension is determined on a log-log cross-plot. If the points are on the same straight line, the set of lineaments is said to be fractal, and the steepness of this straight line is the fractal dimension. The fractal dimension of a 2D set of lineaments is in the range [1, 2]. A fractal dimension of 1, means that all the lineaments are superimposed; a fractal dimension of 2, means that the lineaments are randomly located, with no clustering. However, few fracture sets show no fractal dimension due to the insufficient number of fractures.