# Effects of Velocity and Permeability on Tracer Dispersion in Porous Media
###### Abstract
With increased research on miscible and chemical flooding, the effects of adsorption and other factors on solute transport have been incorporated, allowing the establishment of equations describing the dispersion phenomenon under different conditions [9; 10], which can be solved using numerical techniques [11]. The main cause of the dispersion phenomenon is purely mechanical and is therefore different from that of molecular diffusion caused by concentration differences. The primary mechanism is the resistance caused by the friction between the fluid and the complex microstructure of the porous medium, which causes the fluid to pass through different pores at different velocities [12]. The dispersion coefficient is a parameter that characterizes the ability of a fluid to disperse in a porous medium at a certain flow rate [13]. It is significantly correlated with the parameters that describe the structure of a porous medium (such as porosity [14], pore size [15; 16], pore uniformity [17], and tortuosity [18]) and the characteristics of particles (such as particle uniformity [19], shape (curvature) [20; 21], and size [22; 23]). Generally, dispersion is a phenomenon caused by differences in velocity due to the different structures in porous media, and the dispersion coefficient is considered to have a close relationship with the structures of the porous medium and the velocity of the fluid. To further elucidate the relationship between the porous medium and the dispersion coefficient, [PERSON] et al. (1984) [24] proposed a correlation for a single solid phase considering the dispersion coefficient as a sole function of liquid superficial velocity. [PERSON] et al. (2006) [25] investigated the steady-state segregation and dispersion of a binary system of particles in a liquid-fluidized bed, illustrating that the dispersion coefficient exhibits a positive linear relationship with interstitial fluid velocity. [PERSON] (2007) [26] conducted core displacement experiments on sandstone, using a light volatile oil to displace crude oil. The results showed that the calculated dispersion coefficient was positively correlated with the core permeability on a semi-logarithmic scale. In 2010, [PERSON] [27] conducted experiments on the relationship between the dispersion and flow conductivity in a horizontal fracture. The results showed that the dispersion in the Darcy flow was negatively correlated with the permeability coefficient. [PERSON] et al. (2017) [28] used a particle tracking method based on a capillary network model, as well as the method of moments in conjunction with percolation theory to establish a three-dimensional percolation network model to determine the relationship between the dispersion coefficient and the permeability. The results showed that the dispersion coefficient was negatively correlated with the permeability if the hydraulic radii were constant and vice versa if they were variable. [PERSON] et al. (2017) [29] utilized different dispersion correlations to describe the intermixing and segregation behavior for the binary particle species differing in density in terms of axial particle concentration profile. Moreover, [PERSON] et al. (2020) [30] reported a model for dispersion coefficient along the line of definition for diffusion coefficient incorporating the mean free path of collision and interstitial fluid velocity as the characteristic velocity of collision. A summary of some of the main findings since the 1950s regarding the relationship between the dispersion coefficient and velocity is shown in Table 1.  
The aforementioned research on the mechanism of dispersion phenomenon shows that there are different relationships between the dispersion coefficient, the structure of the particles (grains), and the fluid velocity. Moreover, there are few studies on the permeability-dispersion relationship, and they are all focused on soil or packed bed rather than porous