Characterization Of Scale-invariance In Coal Reservoir:Principle,Methodology And Modeling Application

The pore structure of natural reservoir is the dominant factor in determining its reservoir quality and transport properties.An accurate description of the topological geometry of pore structure is the basic premise for the quantitative assessment of reservoir productivity,with essential theoretical value and practical significance.Ample evidence suggests that reservoir rock is a complex fractal porous media,in which the pore size distribution and the development characteristics of pore space satisfy the scale invariance.Nevertheless,the traditional number-size relationship and its derivative model are not unique in describing the fractal behavior of pore structure,hard to interpret the mechanism of the scale-invariant behavior in pore topology,leading to the impossibility of fine reservoir description.The newly proposed fractal topography gives the essential definition of fractal behavior,providing a powerful theoretical support for the quantitative characterization of the scale-invariant properties of reservoir pore structure.Therefore,this thesis develops a multifractal topological framework for the description of multifractal,as per the narrow fractal topography and general definition of multifractal.On this basis,the calculation model of fractal dimension of reservoir pore structure was deduced,and the essential explanation of the fractal topography of the classical fractal dimension calculation model was given.Meanwhile,the influence of the coal matrix compression on the fractal characteristics of the pore structure was discussed,combined with the above fractal dimension calculation methods,and the validity of the newly deduced fractal dimension calculation model was verified.For the fractal topological description of reservoir pore structure,a theoretical method for extracting the scale-invariant parameters in multifractal was proposed,rest on the mathematical definition of fractal topography of multifractal and its impact on physical parameters.Then in terms of above researches,the quantitative evaluation of different fractal topological features under the pore scale was realized,providing an important basis for the exploration of the influence of fractal topological parameters on reservoir physical properties.The result shows that coal pore structure mostly manifests multifractal characteristics,with a kind of fractal topological relations.The fractal topological parameters obtained from the experiment can explicitly demonstrate the development and heterogeneity of the pore structure.As for the reconstruction of reservoir pore structure,in the light of above researches,a new pore-fracture fractal model was proposed to characterize the porous media according to the unstructured spatial subdivision strategy of voronoi method,combined with the pore-fracture characteristics of coal reservoir.Then,the pore-fracture fractal model was constructed by the fractal topological parameters extracted from the experiment,which shows the coupling and interconnection of particle pore and capillary pore.Moreover,the simulated pore volume distribution was in good conformity with the measured pore volume distribution,indicating that the fractal topological parameters can be used to magnificently reproduce the distribution characteristics of pore structure.Therefore,this thesis focuses on the study of the influence mechanism of the fractal topography of coal reservoir on its complex pore structure,and then implements the fine description of the scale-invariance of coal reservoir and the quantitative characterization of pore structure.The equivalent characterization method based on fractal topological parameters provides an open mathematical framework for the establishment of reservoir pore-fracture structure with multi-type,multi-scale and complicated coupling features,and gives an essential explanation for the evolution and distribution of scale invariant behavior of reservoir pore-fracture,creating a new system framework for quantitative evaluation of reservoir physical properties.