## 1 Introduction  
In recent years, unconventional reservoirs, such as tight sandstone oil and gas, have become increasingly popular in the petroleum industry due to their wide distribution and abundance of subsurface reserves [1; 2; 3; 4]. Tight sandstone reservoirs contain oil and gas with low connectivity between pores, ranging in size from nano-scale to micro-scale, resulting in low porosity and permeability [5; 6]. Horizontal drilling and hydraulic fracturing technology have become essential due to the complexity of the naturally formed micro-fractures and the artificial fractures created by stimulating the reservoir volume [7]. These fractures significantly impact the fluid flow patterns and the capacity of extraction [8]. For this reason, geologists and engineers must study the micro-fracture's effect on petrophysical properties [9]. The presence of micro-fractures can enhance the porosity and permeability of rock by altering the connection of tight sandstone reservoirs. However, whether micro-fractures cause pore structure changes in tight sandstone reservoirs is unclear. The petrophysical properties include permeability, capillary pressure, and relative permeability which are functions of pore structure [10] and are the most important parameters to describe fluid flow within micro-fractures. Furthermore, it is common to apply the cubic law to describe fluid flow within micro-fractures which are viewed as parallel plates with impermeable and smooth walls [11]. On the other hand, the oil and gas flow between micro-fractures and matrix pores are not considered [12]. In reality, due to filling with mineral cement or proppant, complicated micro-fractures tend to be coarse and curved [13]. Hence, to accurately describe the oil and gas flow within micro-fractures, the impact of surface roughness, aperture distribution, length, and matrix-fractures transfer must be accounted for. Recently, many researchers have conducted experiments [13] and developed numerical models [14; 15] to investigate the oil and gas flow in micro-fractures at the pore scale which was initially simplified by reducing the parallel plates to single fractures and deriving the well-known cubic law. However, experiments have revealed the micro-fractures' complexity, ranging from the distribution of aperture and roughness to length and inclination. This stresses the significance of quantifying the roughness in order to accurately capture the effect of the fractures' structure on the capacity to transport fluids. Several experiments have been conducted to explore the fluid flow in rough-walled micro-fractures which have reported favored flow channels and convoluted pathways [16]. The majority of such studies use single flows and artificial samples, though pore-scale experimental measurements are often challenging, costly, and time-consuming. Beyond experiment technology, a numerical model can also provide a tool to measure and describe the oil and gas flow in micro-fracture with the microstructure of fracture. More recently, with the development of visualization and computer techniques, pore-scale modeling, as a recent approach, has been used to investigate the petrophysical properties of porous media. According to the numerical approaches used to simulate oil and gas flow processes, these can be divided into two classes: pore-scale modeling with image-based data and pore network modeling [17; 18]. Pore-scale modeling with image-based methods includes particle-based methods, such as the lattice Boltzmann method (LBM) [19; 20], and mesh-based approaches, such as finite difference [21], finite volume [22], and finite element method [23]. Additionally, for multi-phase flow, the level set [24], phase field [25], and smoothed-particle hydrodynamic (SPH) methods [26] can be used to define an interface between fluids and track their movement.