Abstract
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.
Highlights
Upscaling procedures are based on a bottom-up approach, where the analysis of flow and transport features at the pore scale is conducted through both physical (Narsilio et al 2009; Tallakstad et al 2009) and numerical models (Raeini et al 2014b; Blunt 2001; Spanne et al 1994; Porta et al 2013)
The structure of the paper is as follows: in Sect. 2 we briefly introduce the Lattice Boltzmann Method (LBM), the algorithms adopted for the generation of the porous media and the scaling employed in the simulations; in Sect. 3 we present results and discussion of the 2D and 3D simulations; Sect. 4 is dedicated to conclusions, perspectives and recommendations, which are drawn based on the outcome of the study
The estimation of the representative elementary volume (REV) is carried out using the values of Convergence Criterion (CC) and Relative Error (RE) for porosity, permeability, mean velocity and velocity variance
Summary
Upscaling procedures are based on a bottom-up approach, where the analysis of flow and transport features at the pore scale is conducted through both physical (Narsilio et al 2009; Tallakstad et al 2009) and numerical models (Raeini et al 2014b; Blunt 2001; Spanne et al 1994; Porta et al 2013). Large-scale modelling of flow and transport in porous media is drawing a considerable amount of attention. These models employ various levels of upscaling of the dynamics acting at pore (and subpore) scale (Raeini et al 2014a; Ling et al 2018)
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