**1. Introduction**

Due to their huge geological reserves and wide distributions, tight sandstone gas greatly alleviates the contradiction between the world's increasing demand on energy and the depletion of conventional resources [1]. In China, tight sandstone gas reservoirs are characterized as one with the porosity and permeability less than 10% and 0.1 mD, respectively [2], and these tight reservoirs require extensive hydraulic fracture or special gas extraction techniques to achieve commercial production [3]. In comparison with conventional sandstones, the pore structures of tight sandstones are usually more complex and heterogeneous, because of their various pore size (nano-scale to micro-scale), poor connectivity and irregular pore geometry [4–7]. The pore structure replaces porosity and permeability as the critical parameter for the evaluation of reservoir properties, as it not only controls

gas storage and transport mechanisms, but also determines the displacement efficiency and recovery rate of hydrocarbon in the tight sandstone reservoirs [6–9]. Consequently, detailed characterizations of pore structure are necessary procedures for understanding the producibility of tight sandstone gas reservoirs.

A variety of analytical methods have been geared to qualitatively and quantitatively characterize the pore structure of tight sandstone, such as casting thin sections (CAT), scanning electron microscopy (SEM), mercury injection porosimetry (MIP), gas absorption [10,11], X-ray computed tomography (XCT) [12] and nuclear magnetic resonance (NMR). Among them, NMR is a convenient and non-damaging method for characterizing the pore structure and pore fluids in the rock. In NMR experiments, proton 1H (abundant in water and hydrocarbon) can generate a dipole moment in the presence of an external magnetic field. The signal amplitude of dipole moment is in proportion to the number of protons within pore fluids [13,14]. Thus, NMR is able to characterize petrophysical properties, the saturation of different types of pore fluids (movable fluids, bound fluids and hydrocarbons) and pore size distributions (PSD) of the reservoir rocks [15].

In the past few decades, numerous studies demonstrated that fractal theory is another robust tool for the characterization of pore structure in the porous media, including sedimentary rock, soil, concrete and other materials [16–21]. Fractal geometry successfully builds a bridge between petrophysical properties and microstructures of reservoir rocks, and a single fractal dimension, D, have been introduced to describe the fractal behavior and geometric irregularity of pore structure [22–24]. As a complex geological material, the PSD curves of tight sandstones often show "fluctuations" and "jumps" at different pore size intervals, and fractal characteristics vary greatly among different pore size intervals, which cannot be explained by a single fractal dimension [25]. The reason is that the single fractal dimension can only describe the irregularity and complexity within the specific pore size intervals. Multifractal theory is an extension of single fractal theory, which can offer more precise information about pore structure by resolving multifractal structure into a set of intertwined fractal subsets [26]. Nowadays, multifractal analysis has become a widely used mean to analyze the pore structure of coal, shale, and carbonate reservoirs [25,27–31]. Nevertheless, only a little attention has been given to the pore structure of tight sandstone [32,33]. Hence, multifractal analysis based on NMR experiment provides a brand-new perspective on the nature of pore structure and heterogeneity in tight sandstone reservoirs.

In this work, a case study from the Lower Permian Taiyuan Formation (P1t) tight sandstones in the southern North China Basin was conducted to investigate pore structure features by various methods. Multifractal analysis was implemented to quantify the heterogeneity of pore structure in different probability density areas, based on NMR T2 distributions. Additionally, the relationships between multifractal parameters of different probability density areas and mineralogical compositions, pore structure parameters and petrophysical properties of tight sandstone samples were investigated. This study provides new insights into the microscopic pore structure and heterogeneity of tight sandstone with similar geological conditions.
