# A Critical Review of the Modelling Tools for the Reactive Transport of Organic Contaminants
## 2 Processes
### Dispersion  
The elimination of pollutants in soil and groundwater is the result of several processes in which dispersion plays an important role. In groundwater, two processes are associated with dispersion: molecular diffusion, and mechanical dispersion. Mechanical dispersion is defined as the spreading of a plume of contaminants as dissolved substances move through porous media. This process has long been recognised as a component of monitored natural attenuation (MNA) of contaminant plumes [151; 152]. Mechanical dispersion, as defined by Domenico and Schwartz (1990) [153], is the mixing/spreading (depending on scale) of solutes caused by local displacements about the mean velocity. The differences in flow directions and velocities are naturally caused by the heterogeneity of a porous aquifer and the pore-scale bifurcation of groundwater flow lines consisting of clean and contaminated groundwater. This phenomenon occurs at all scales, from the microscopic (pore to pore) to the megascopic (aquifer, catchment). On the small scale, three factors can influence the flow velocity: different pore sizes, tortuosity, and friction. On the large scale, the flow velocity is influenced by stratification, folds, faults, etc. Dispersion is therefore scale-dependent, but even at a given scale, the data published by Gelhar [154, 155] show considerable differences with scale length (more than three orders of magnitude) (Figure 5). Dispersion reduces the concentration of the pollutant in groundwater, but not the total mass of the pollutant in the aquifer. The process in which molecular diffusion and mechanical dispersion come together is referred to as hydrodynamic dispersion [156, 157, 158]. The hydrodynamic dispersion coefficient, a key parameter in solute transport, characterizes this process and is known to vary with the Peclet number. The Peclet number compares the timescales of diffusion and advection over an average pore length. Despite its significance, the hydrodynamic dispersion coefficient remains incompletely known and understood, yet it is indispensable for numerous solute transport investigations. The hydrodynamic dispersion coefficient is a parameter that is not yet fully known and understood, but is crucial for many solute transport studies. In general, there are two basic approaches to hydrodynamic dispersion: the Eulerian, and the Lagrangian [159]. The first method may not be entirely efficient, since hydrodynamic dispersion is also a parameter at the pore scale, and Euler's approach is tied to the macroscale and an advection-diffusion equation [160, 161, 162]. The curve obtained is fitted to the analytical solution of Ogata-Banks [163] to obtain the dispersion value [164, 165, 166, 167]. The Lagrangian approach adjusts the conservation of mass as the movement of the deformable fluid volume along the streamline according to the local velocity so that only the local dispersion and reaction are responsible for the instantaneous change in concentration [169]. In this way, global conservation of mass is guaranteed, while local conservation depends on the accuracy of the velocity estimation method. The most common Lagrangian methods are Random Walk Particle Tracking (RWPT) and Smoothed Particle Hydrodynamics (SPH). The first group of algorithms captures the motion and dispersion of a large set of particles representing a plume of fluid in an advancing flow field, while the element of Brownian motion is added to reproduce the effect of local dispersion [170, 171, 172]. Smoothed particle hydrodynamics is a mesh-free method that uses interpolation to obtain smooth field variables. The fluid is represented by particles, which in turn carry all the physical properties associated with the forces (gravity, rotation, and pressure) of the system to be reproduced. By interpolation, these properties are estimated  
Figure 5: Relation between longitudinal dispersivity and scale after [155]. from all neighbouring particles within the range of this function, the so-called smoothing kernel.