Study on Fractal Characteristics of Cementation Exponent in Porous Media

This paper discussed the fractal properties of well logging curve, and according to the Hausdorff fractal dimension, defined the logging curve's fractal dimension, and as examples, resistivity and porosity fractal dimension, DR and D¦Õ, were given. Subsequently, based on the two variables, this study further presented a method to calculate cementation exponent m. The practical example proved validity of this method. Through the calculation of m, the fractal characteristics of it was discussed, which revealed the profound geological and petrophysical meanings of m. According to this research, m not only reflects the degree of cementation of intergranulars of rocks, but further depicts the heterogeneity of microstructure of pores and sedimentary environments. The more heterogeneous of the reservoir, the much higher value of m, and the calculation results shows that values of m are sound agreement with core-electrical experiments results. The advantage, of this method is that m can be calculate directly from logging curve, but not rely on laboratory measurements at high temperature and high pressure. This method allows point-by-point calculation, and can be used to identify hydrocarbon. The paper also discussed the tortuosity of path which current penetrates through in the rocks. Commonly, for a rock with certain pores and porosity, water saturated has less tortuosity than that of hydrocarbon saturated rocks. So, the proportion of hydrocarbon in the pores, that is the saturation, affects the tortuosity of current path, and the law is that the more saturated hydrocarbon in the pores, the more tortuose of the path. The measurements of cores show that the value of m is a function of porosity and hydrocarbon saturation of these rocks, while the novel algorithm of fractal dimension DR and D¦Õ, illustrates that m is also a function of tortuosity of current path. The tortuosity depends on the saturation of hydrocarbon, and the molecules of hydrocarbon and water will established a lot of micro capacitors, which is just reason of increasing of tortuosity.