# Effects of Velocity and Permeability on Tracer Dispersion in Porous Media
###### Abstract  
During micro-scale tracer flow in porous media, the permeability and fluid velocity significantly affect the fluid dispersion properties of the media. However, the relationships between the dispersion coefficient, permeability, and fluid velocity in core samples are still not clearly understood. Two sets of experiments were designed to study the effects of tracer fluid flow velocity and porous medium permeability on the dispersion phenomenon in a core environment, using natural and sand-filled cores, respectively. From experimental data-fitting by a mathematical model, the relationship between the dispersion coefficient, flow velocity, and permeability was identified, allowing the analysis of the underlying mechanism behind this phenomenon. The results show that a higher volumetric flow rate and lower permeability cause a delay in the tracer breakthrough time and an increase in the dispersion coefficient. The core experimental results show that the dispersion coefficient is negatively correlated with the permeability and positively correlated with the superficial velocity. The corresponding regression equations indicate linear relations between the dispersion coefficient, core permeability, and fluid velocity, resulting from the micron scale of grain diameters in cores. The combination of high velocity and low permeability yields a large dispersion coefficient. The effects of latitudinal dispersion in porous media cannot be ignored in low-permeability cores or formations. These findings can help to improve the understanding of tracer flow in porous media, the design of injection parameters, and the interpretation of tracer concentration distribution in inter-well tracer tests. t  
[1] 2021  
Hydrodynamic dispersion is one of the mixing effects that occur in laminar flow through a porous medium [5; 6]. It is a macroscopic phenomenon determined by the interaction of molecular diffusion and advection processes, resulting in the development of a transition zone between miscible fluids with two different components [7]. This phenomenon, which was first discovered in groundwater, is now widely encountered in many fields, such as chemical engineering, materials science, hydrology, and petroleum engineering. Hydrodynamic dispersion can be regarded as an attribute of the porous system, or as the spreading behavior of a solute during its transportation [8]. The dispersion process may be described with reference to a model system consisting of a cylindrical tube filled with homogeneous sand grains initially saturated with fresh water. At the start of the experiment--i.e., \(t=0\)--water containing a type of tracer was injected into the porous medium. The produced tracer concentration was measured as a function of time \(t\) at a point located at a distance \(L\) downstream of the injection point, yielding the so-called breakthrough curve. Assuming that no dispersion occurs, the breakthrough curve should show a step change--i.e., a sharp front moving at the average velocity--which is determined by [PERSON]'s law. However, due to the existence of hydrodynamic dispersion, the observed breakthrough curve is actually S-shaped, with a part of the tracer-containing water being ahead of the position where the average flow velocity is reached and a transition zone occurring between the tracer concentrations due to hydrodynamic dispersion. Since the 1950s, many scholars have observed, analyzed, and summarized a large number of tracer dispersion experiments in the laboratory and proposed various models to describe the solute dispersion process in porous media. By the 1960s, a more systematic description of dispersion in porous media had been formulated. In theory, the hydrodynamic dispersion approximation follows [PERSON]'s law of material diffusion in free solutions. An advection-dispersion equation was established for solute transport based on this theory [3].