# Effects of Velocity and Permeability on Tracer Dispersion in Porous Media
## 3 Experimental Results and Discussion
### Discussion
#### 3.3.2 Mechanisms of the Relations  
To find the mechanisms of the relationships between the dispersion coefficient, permeability, and fluid velocity, two types of porous media were constructed as shown in Figure 9, which represent lower permeability (small pore sizes, Figure 9a) and higher permeability (large pore sizes, Figure 9b), respectively.  
When tracers flow through the porous media, as shown in Figure 9, there are two main controlling factors, namely longitudinal and latitudinal dispersion [14; 19]. Due to hydrodynamic retention, some of the tracers stay in the first layer while the rest continue on to the second layer, which is referred to as longitudinal dispersion. Additionally, due to the pore structure of the porous medium, the width of tracer liquid becomes twice that of the grain size in the second layer, resulting in dispersion in the latitudinal direction.  
The relationship between dispersion coefficient and permeability can be explained using Figure 9. In the five-layer example illustrated here, at a given injection velocity, the width of tracer liquid becomes five times the grain size in the medium with small  
Figure 8: Dispersion coefficient versus injection (superficial) velocity in sand-filled cores.  
Figure 7: Dispersion coefficient versus injection (superficial) velocity in natural cores.  
pore size (Figure 9a) but three times the grain size in the medium with a large pore size (Figure 9b) along the same flow distance. The difference in width is due to the difference in the average pore sizes at different permeabilities. Meanwhile, the pore structure of the lower-permeability core is more heterogeneous and small-scale breakthrough will occur, which results in an earlier breakthrough, slower rise in concentration, and larger dispersion coefficient.  
The relationship between the dispersion coefficient and injection velocity can also be explained using Figure 9. When the permeability is fixed, the higher the superficial velocity, the greater the pressure gradient, and the smaller the fluid-activated pores--i.e., the fluid flows preferentially into the low-permeability pores. Along a given flow distance, the width of the tracer liquid becomes five times the grain size at high velocity (i.e., small pore size medium, Figure 9a) but three times the grain size at low velocity (i.e., large pore size medium, Figure 9b) due to the difference in the average size of flow pores at different velocities. Therefore, when a small volume of displacement fluid is injected, a tracer will be produced at the outlet, corresponding to the so-called \"channeling effect\" in the pore network. Meanwhile, as the injection rate increases, it may strengthen some of the microscopic heterogeneous features that actually exist inside the core, resulting in a small amount of intrusion and hence an earlier breakthrough, a slower concentration increase, and a larger dispersion coefficient. Therefore, in the core displacement experiments, the small sizes of flow pores at high velocities result in more complex flow paths within porous media and thereby experience stronger dispersion.  
The work in this paper demonstrates that there are different dispersion coefficients resulting from different porous media size and tracer interstitial velocity. It can improve inter-well tracer test not only in injection parameters design, but also in tracer concentration interpretation. Firstly, the injection velocity in a project should be optimized, because the economic benefit can be reduced if the velocity is too low; on the other hand, the mixing effect can be amplified if the velocity is too high. Secondly, it is more suitable to use the dispersion coefficient of the high permeability layer, rather than that corresponding to the average reservoir permeability.