Suitability of 2D modelling to evaluate flow properties in 3D porous media

The employment of 2D models to investigate the properties of 3D flows in porous media is ubiquitous in the literature. The limitations of such approaches are often overlooked. Here, we assess to which extent 2D flows in porous media are suitable representations of 3D flows. To this purpose, we compare representative elementary volume (REV) scales obtained by 2D and 3D numerical simulations of flow in porous media. The stationarity of several quantities, namely porosity, permeability, mean and variance of velocity, is evaluated in terms of both classical and innovative statistics. The variance of velocity, strictly connected to the hydrodynamic dispersion, is included in the analysis in order to extend conclusions to transport phenomena. Pore scale flow is simulated by means of a Lattice Boltzmann model. The results from pore scale simulations point out that the 2D approach often leads to inconsistent results, due to the profound difference between 2D and 3D flows through porous media. We employ the error in the evaluation of REV as a quantitative measure for the reliability of a 2D approach. Moreover, we show that the acceptance threshold for a 2D representation to be valid strongly depends on which flow/transport quantity is sought.