The terms homogeneity and heterogeneity are used to describe the uniformity and regularity in spatial distribution of geomaterial properties in natural subsurface systems. Homogeneity means spatially uniform-distributed properties. In natural systems, geological media are almost always heterogeneous. That is, their physical and (bio)geochemical properties vary spatially. Spatial heterogeneity can refer to both physical and geochemical properties. Physical properties include mineral grain size, porosity, and permeability / conductivity. Geochemical properties include, for example, mineral types, lithology, mineral surface area, and cation exchange capacity. Figure 2 shows a picture of an outcrop with layers of different types of geomaterials from the Macrodispersion site (MADE) in Columbia, Mississippi (Zheng and Gorelick, 2003).
Spatial heterogeneities can lead to significantly different chemical reactions and physical transport processes from their homogeneous counterparts. As a result, heterogeneities play an important role in determining processes and applications in subsurface systems. Examples include contaminant reactive transport (Li et al., 2011), oil and gas production (Chen et al., 2014; Hewett, 1986), and environmental bioremediation (Murphy et al., 1997; Song et al., 2014). For example, as shown in Figure 3, the different geomaterials in Figure 2 leads to orders of magnitude in the spatial variation of hydraulic conductivity (Figure 3A), and abnormal solute transport (Figure 3B) (Zheng et al., 2011).