砂岩孔隙结构分维及其应用

分形几何学特别适合于解决复杂环境中的许多问题。本文把砂岩孔隙结构置于分形几何学框架内，推导了小于孔隙半径ｒ的孔隙度与孔隙半径之间幂函数关系，表明其指数与孔隙结构分维（Ｄ）有关，用压汞曲线证实这种幂函数关系是客观存在的，提供了一种测量孔隙结构分维的方法。作者研究认为，孔隙结构分维（Ｄ）能定量表征砂岩的储集性能，并能反映砂岩孔隙结构的成因特征。Ｄ接近于２，砂岩储集性能极好；Ｄ接近于３，砂岩储集性能极差。不同成因的孔隙结构具有不同的分维，但相同或相似成因的孔隙结构的分维具有固定的范围。因此可用分维对砂岩孔隙结构进行分类和评价。实际应用效果较好。

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

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.