## 1 Introduction  
In recent years, with the increasing global demand for energy, natural gas, as a clean, environmentally friendly, stable, and economical low-carbon fossil fuel, has been playing an irreplaceable role in economic development and energy transition [1, 2]. Currently, the growth rate of proven reserves of conventional oil and gas resources is decreasing year by year [3]. Tight sandstone oil and gas, as a very important resource to replace conventional energy, has become the strategic focus of exploration and development in China. Since the discovery of unconventional natural gas in the tight sandstone of the Appalachian Basin in the United States in 1921, more than 70 basins or deep structural areas worldwide have been continuously discovered as natural gas reservoirs with tight sandstone as the reservoir. The development of tight gas in China started relatively late. The distinctive nature of these gas reservoirs compared with conventional hydrocarbon accumulations became scientifically recognized following the 1971 identification of the Zhongba Gas Field within the Sichuan Basin's western sector. Since the 1990s, multiple tight gas reservoirshave been discovered successively in the Ordos Basin and Turpan-Hami Basin in China, effectively alleviating the supply-demand contradiction of natural gas in China [4; 5; 6]. Tight sandstone gas and tight gas refer to natural gas reservoirs located within tight sandstone reservoirs [7]. Typically, these reservoirs have a porosity of less than 10% and a matrix permeability under overburden pressure of less than 0.1 \(\times\) 10\({}^{-3}\)\(\upmu\)m\({}^{2}\). Compared with conventional natural gas resources, these reservoirs exhibit high heterogeneity and poor lateral continuity [8]. The micropore structure of the reservoir primarily includes pore size, throat size, and the connectivity of pores and throats (such as pore-throat coordination number and pore-throat ratio), which affect the reservoir's storage space, porosity, permeability, and other macroscopic physical properties [9]. Pore structure is a critical factor in determining the physical properties of the reservoir and its oil and gas production potential. Therefore, accurately characterizing the micropore structure of tight gas reservoirs is crucial [10; 11]. Originating to quantify irregular geometries, dynamic instabilities, and structural complexities, fractal analysis has evolved into a fundamental methodology for deciphering systems governed by scale-invariant patterns [12; 13; 14]. In geological applications, the integration of fractal theory with seismic data facilitates the more precise first-arrival picking of seismic waves, while its extension to geochemical element distribution analysis demonstrates universal applicability [15]. Fractal dimension serves as a vital parameter for quantifying pore-throat heterogeneity, establishing critical connections between macroscopic reservoir properties and microscopic architectural features [16; 17; 18; 19]. Substantive progress has been achieved through experimental investigations employing high-pressure mercury intrusion (HPMI) and low-temperature nitrogen adsorption (LTNA) techniques, where fractal dimensions effectively quantify the structural complexity of shale pore networks [20]. Comparative HPMI studies of tight sandstone reservoirs across multiple basins reveal distinct fractal signatures within their pore architectures, enabling quantitative heterogeneity assessments [21; 22; 23]. This advancement informed the development of permeability prediction models specifically calibrated for tight sandstone systems [25; 26]. However, the universality of such permeability models remains limited, necessitating region-specific model formulations tailored to geological particularities. Overall, previous studies have conducted detailed research on the lithology, storage space types, and physical properties of the Denglouku Formation reservoir in the Xuijaweizi area of the northern Songliao Basin [27; 28].