**5.4 Dispersion of dissolved CO2 due to flow through a porous medium**

In addition to diffusion, dispersion occurs when a solute flows through a porous medium. This can essentially be understood as an unsteady irreversible mixing process of two miscible fluids which have different solute concentrations (e.g. brine saturated with CO2 = fluid 1, and brine undersaturated with CO2 = fluid 2). Dispersion can therefore influence CO2 mass transfer as it changes the CO2 concentration gradient. Dispersion is caused by several effects (Bear 1972, Özgür 2006, 2010):


Bear (1972) distinguishes between mechanical dispersion and hydrodynamic dispersion. He defined hydrodynamical dispersion as the sum of mechanical dispersion plus molecular diffusion. The dispersion described above - and all dispersion mentioned in this text – is the same as Bear's mechanical dispersion.

At reservoir scale dispersion can be described by equation (21) where Ddis is the dispersion coefficient, u is the average pore flow velocity and α the dispersivity (Bear, 1972; Özgür, 2006).

$$D\_{dis} = \mu \alpha \tag{21}$$

The dispersivity α is a property of the reservoir and it depends on the heterogeneity of the porous medium and the length of flow. Schulze-Makuch (2005) reviewed 307 datasets and suggested αL = c 0.5 L (where αL is the longitudinal dispersivity, L is flow distance and c varies between 0.01 m for sandstones and unconsolidated material and 0.8 m for carbonates). A detailed discussion of dispersion and dispersivities is given by Bear (1972).
