Two-Dimensional Multifractional Brownian Motion- Based Investigation of Heterogeneities from a Core Image - Advances in Data, Methods, Models and Their Applications in Geoscience - page 109

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Two-Dimensional Multifractional Brownian
Motion- Based Investigation of
Heterogeneities from a Core Image
Saïd Gaci and Naïma Zaourar
University of Sciences and Technology Houari Boumediene, Algiers,
Algeria
1. Introduction
A core sample is a cylindrical section obtained by driving a hollow tube into the
undisturbed medium and withdrawing it with its content. In practice, the sample is pushed
more or less unbroken into the tube. Once removed from the tube in the laboratory, it is
analyzed by different techniques and equipment depending on the desired type of data. The
hole made for the core sample is called the "core hole". A variety of core samplers exist to
sample different media under diverse conditions. For instance, sediments or rocks are
sampled with a hollow steel tube called a core drill.
A scientific coring has been used in the first time for sampling the ocean floor. Then, it is
soon exploited to analyze lakes, ice, mud, soil and wood. Cores provide precious
information about the evolution of climate, species and sedimentary composition during
geologic history.
In petroleum engineering, core analysis presents a way of measuring well conditions
downhole by studying samples of reservoir rocks. It gives the most accurate estimations of
porosity, permeability, fluid saturation and grain density. These measurements help to
understand the conditions of the well and its potential productivity.
In addition to the basic petrophysical properties estimated from the core, a special core
analysis can be undertaken in order to determine permeability, wettability, capillary
pressure, and electrical properties. Petrographic studies and sieve analysis can also be
carried out in such analysis.
In recent years, numerical analysis has been widely used for the investigation of images,
since it yields results more objective and reliable than those obtained by conventional
methods based on human observations. Fractal analysis has been introduced to examine
images texture (Bourissou et al. , 1994; Lévy-Véhel and Mignot, 1994; Liu and Li, 1997; Lévy-
Véhél, 1995, 1997, 1998; Pesquet-Popescu and Lévy-Véhel, 2002; Malladi et al. , 2003; Tahiri et
al. , 2005).
In this study, we suggest to go beyond the conventional core analysis, and to perform a new
approach to extract the maximum features from a core image using a fractal analysis. The
conventional fractal model used previously in image processing, the two-dimensional
fractional Brownian motion (2D- fBm), presents a constant Hölder function H , thus does not
allow to explore the spatial evolution of the local regularity. To do so, we suggest to