Fractional Dimension of The Pore-Texture in Sandstones and Its Application

Key words: 
• sandstone pore /
• texture fractional /
• dimension /
• classification and evaluation

Abstract: Recently, studies on the pore-texture have made significant progress. Many researchers consider that the pore-texture is a fractional texture with the self-similarity in sandstone. In this study, the authors inferred the power relationship between Φ(r) and r with fractional geometric principles, i.e. Φ(r)=K·r 3-0 (1) Where Φ(r)-porosity whose pore radius is less than r, r-pore radius, k-proportional constant, and D-fractional dimension of the pore-texture. The relationship between Φ(r) and r obtained from the mercury injection curve usually follows a straight line in the log-log plot. Thus, it was proved that the power relationship between Φ(r) and r inferred theoretically is correct and could dprovide a method for measuring fractional dimension of the pore-texture. The experimental results showed that fractional dimension of the pore-texture is a fraction between 2 and 3 in the three dimensions and that its size indicates a complex degree of the pore-texture which has a close relationship with the reservoir property in sandstones. Surface shape and size distribution of pores are either relatively simple if D is close to 2, so the reservoir property is extremely good; or relatively complex if D close to 3, so the reservoir property extremely poor in sandstones. Comparing Eq.(1) with Φ(r)'s expression which is transformed from Milligan and Adams' formula of the accumulational pore volume, the authers considered that types of the pore-texture with different origin have different fractional dimensions, and fractional dimensions of the pore-texture with either the same or similar origin are usually within a certain range. It is seen that fractional dmension not only discribes mathmatical characters of complex degree of the pore-texture, but also indicates its original characters. In this paper, this is theoretical basis to classify and evaluate the pore-texture in sandstones. In the study on the Xia Ermen oilfield, although the fractional dimension value of the pore-texture has a closer relatinship with permeability, no clear relationship exists with porosity in sandstones. The pore-textures could be divided into four types clearly according to distribution characters of samples on the fractional dimension's axis. Among these, the reservoir property of type Ⅰ is good, type Ⅱ moderate, type Ⅲ poor and type Ⅳ worst. The results are consistent with those observed with microscope and scanning electric microscope, showing that fractional dimension is of importance in classification and evaluation of the pore-texture in sandstones.