1.1 The Continuum Approach
The solid matrix of the subsurface (rocks and other solid geological material) contains interstices or open spaces (pores or fissures) in which air, water or other fluids (such as hydrocarbons) are present. When water infiltrates, it moves through a network of interconnected pores or fissures downwards. A fraction of the infiltrating water remains in the unsaturated soil zone, attracted by soil matrix suction forces and available for subsequent evapotranspiration, while the remainder moves further down, reaches the fully saturated zone and joins in the local groundwater flow.
At the micro-scale, say at the scale of drops of water and grains of sand, it is extremely difficult (or even impossible) to observe and describe the presence and movement of groundwater inside the labyrinth of pores or fissures. In addition, it would not serve any practical purpose. Therefore, groundwater hydrodynamics and groundwater hydraulics have adopted the macroscopic continuum approach as common practice. In this approach, the very complex physical reality is replaced by simple homogeneous elementary volumes, characterized only by location, geometry and hydraulic parameters (e.g., effective porosity, hydraulic conductivity); these elementary volumes reproduce in a macroscopic modeling approach (e.g., using Darcy’s equation) the overall behavior of the replaced physical system (e.g., aggregated flow rate). Although the porosity and other properties of very small neighboring volumetric units (containing no more than a few pores and grains of sand) can be very different, they tend to converge to a meaningful statistical average as the control volume is gradually increased in size (Figure 1). A certain minimum size of the elementary volume – the Representative Elementary Volume – is required to filter out the effect of micro-scale variations and to ensure that the adopted hydraulic parameters are meaningful and spatially continuous (Bear, 1972; Bear, 1979; Freeze and Cherry, 1979).
Figure 1 – Demonstration of the concept of ‘Representative Elementary Volume (REV)’ of a porous medium (here shown in 2D projection). Explanation: With increasing size, the observed porosity (or void ratio) of a control volume changes from meaningless for macroscopic analysis (red boxes or smaller) to meaningful and representative (large blue box). Intermediate sizes may yield poorly (green boxes) to nearly representative porosity values (yellow box) for the medium considered.