孔隙-孔喉分形多孔介质复杂类型组构模式表征

Quantitative characterization of complex assembly in fractal pore-throat porous media

自然储层孔隙结构复杂,孔隙和孔喉共存且往往会表现出分形特征。经典的数量-尺度关系Rns及其衍生模型虽然能有效获取分形维数D,然而它们之间多对一的关系无法保证反演建模的惟一性。与此同时,分形对象中复杂类型的种类及其组构模式尚不明了,这导致储层复杂孔隙结构等效表征的困难。因此,厘清孔隙和孔喉多类型共存、多尺度分布的孔隙结构中的复杂类型,进而定量表征其组构模式对评估油气的赋存和运移规律至关重要。新近出现的分形拓扑理论表明分形对象是耦合原始复杂性与行为复杂性的双复杂系统。这两类复杂类型表现出相互独立的组构模式,其中原始复杂性确定单尺度与多尺度、单相与多相、单类型与多类型等缩放类型,而行为复杂性则决定自相似、自仿射、多重分形等尺度不变特征。基于此,本文有效标定了孔隙-孔喉耦合分形结构中的复杂类型种类,查明了孔隙、孔喉以及其连通性的原始复杂性归属,利用泰森多边形算法实现了孔隙-孔喉耦合行为的定量描述,依据分形拓扑理论给出了行为复杂性的尺度不变定义,结合原始复杂性与行为复杂性组构模式发展了一种精细表征孔隙-孔喉耦合分形孔隙结构的算法。基于新算法,模拟了不同复杂组构模式下的分形多孔介质,分析了原始复杂性与行为复杂性对孔隙结构的影响,推演了孔隙度及比表面积计算公式并验证了其有效性。

The pore structure of natural reservoirs is complex,where the coexistence of pores and throats and their scale-invariance distribution have been widely observed.Although the fractal dimension D is easy to obtain by the classical number-size model Rns or its variants,it is hard to guarantee that the many-to-one relationship between Rns and D is unique for reverse modeling.Meanwhile,the unclear nature in complexity types and their assembly patterns of fractal objects causes the effective characterization of the complex pore structure in natural reservoir very difficult.Therefore,it is of fundamental importance for a clear understanding of the complexity types to quantitatively represent their assembly pattern in fractal pore-throat porous media,because all these would affect the occurrence and migration of oil and gas significantly.The newly emerged fractal topography points out that a fractal set is a dual-complexity system,in which the original complexity and behavioral complexity are coexisting but independent to each other.In other words,the former determines the scaling type of single or multi scale,phase,and type,while the latter decides the scale-invariant properties of self-similarity,self-affinity,and multifractality.In this study,the authors identify the complexity types in fractal pore-throat porous media,and clarify the original complexity composed of pore,throat and its connectivity.In addition,the authors propose an approach to effectively represent the original complexity of pore-throat coupling geometries by Voronoi model,define the scale-invariance behavioral complexity as per the fractal topography theory,and develop an algorithm for the quantitative representation of fractal pore-that porous media.Thereafter,the authors model the fractal pore-throat porous media with diverse complexity assembly,investigate the effects of original and behavioral complexities of the total complexity of pore structure,analytically derive the estimation models of porosity and specific surface area,and verify the validity of the novel algorithm.