A stochastic model for air injection into saturated porous media

Air injection into porous media is investigated by laboratory experiments and numerical modelling. Typical applications of air injection into a granular bed are aerated bio-filters and air sparging of aquifers. The first stage of the dynamic process consists of air injection into a fixed or a quasi-fixed water-saturated granular bed. Later stages could include stages of movable beds as well, but are not further investigated here. A series of laboratory experiments were conducted in a two-dimensional box of the size 60 cm × 38 cm × 0.55 cm consisting of glass walls and using glass beads of diameter 0.4–0.6 mm as granular material. The development of the air flow pattern was optically observed and registered using a digital video camera. The resulting transient air flow pattern can be characterized as channelled flow in a fixed porous medium with dynamic tree-like evolution behaviour. Attempts are undertaken to model the air injection process. Multiphase pore-scale modelling is currently disregarded since it is restricted to very small scales. Invasion percolation models taking into account gravity effects are usually restricted to slow processes. On the other hand a continuum-type two-phase flow modelling approach is not able to simulate the observed air flow pattern. Instead a stochastic continuum-type approach is discussed here, which incorporates pore-scale features on a subscale, relevant for the immiscible processes involved. Consequently, the physical process can be modelled in a stochastic manner only, where the single experiment represents one of many possible realizations. However, the present procedure retains realistic water and air saturation patterns and therefore produces similar finger lengths and widths as observed in the experiments. Monte Carlo type modelling leads to ensemble mean water saturation and the related variance.