The mathematical modelling and numerical simulation of flow and transport in porous media is traditionally approached from a macroscopic point of view, by using macro-scale averaged equations such as the Darcy law and the Advection-Dispersion-Reaction (ADR) equation with macroscopic parameters that are the results of the averaging procedure on the microscopic structures of the medium (e.g., permeability, porosity) or of the flow (e.g., tortuosity, dispersivity). This classical description however cannot be rigorously applied when dealing with problems that involve high heterogeneity, sharp transitions and discontinuities in the physical parameters, two-phase flows, non-linearities due to high flow velocities. Furthermore the estimation of the macroscopic parameters is often impossible or can be affected by large uncertainties. Moreover the non-linear dependence of these parameters on medium and flow properties is not completely understood. Therefore the simulation of micro-scale flows (i.e., pore-scale simulations) in porous media is becoming an important topic for a better understanding of complex problems arising in different fields including contaminant transport, reservoir simulation, CO\$_2\$ storage, colloidal transport. The present work, that is motivated by an important application in the field of porous media modelling, namely the remediation of contaminated aquifers by means of nanoscopic zerovalent iron particles (NZVI) injections, deals with the development of multi-scale simulation tools and numerical methods to derive adequate macroscopic models and estimate accurately their macroscopic parameters. This is achieved by solving the full Navier-Stokes equations in a realistic pore-scale sample of a three-dimensional porous media together with a transport equation for passive tracer particles. Transport coefficients and parameters of the macro-scale equations are then extracted from the micro-scale results by using non-linear fitting and method of moments for a simple one-dimensional model.

Pore-scale simulation and hydrodynamic dispersion estimation in realistic porous media / Icardi, Matteo; Marchisio, Daniele; Sethi, Rajandrea. - (2013). (Intervento presentato al convegno 5th International Conference on Porous Media tenutosi a Prague nel May 2013).

### Pore-scale simulation and hydrodynamic dispersion estimation in realistic porous media

#### Abstract

The mathematical modelling and numerical simulation of flow and transport in porous media is traditionally approached from a macroscopic point of view, by using macro-scale averaged equations such as the Darcy law and the Advection-Dispersion-Reaction (ADR) equation with macroscopic parameters that are the results of the averaging procedure on the microscopic structures of the medium (e.g., permeability, porosity) or of the flow (e.g., tortuosity, dispersivity). This classical description however cannot be rigorously applied when dealing with problems that involve high heterogeneity, sharp transitions and discontinuities in the physical parameters, two-phase flows, non-linearities due to high flow velocities. Furthermore the estimation of the macroscopic parameters is often impossible or can be affected by large uncertainties. Moreover the non-linear dependence of these parameters on medium and flow properties is not completely understood. Therefore the simulation of micro-scale flows (i.e., pore-scale simulations) in porous media is becoming an important topic for a better understanding of complex problems arising in different fields including contaminant transport, reservoir simulation, CO\$_2\$ storage, colloidal transport. The present work, that is motivated by an important application in the field of porous media modelling, namely the remediation of contaminated aquifers by means of nanoscopic zerovalent iron particles (NZVI) injections, deals with the development of multi-scale simulation tools and numerical methods to derive adequate macroscopic models and estimate accurately their macroscopic parameters. This is achieved by solving the full Navier-Stokes equations in a realistic pore-scale sample of a three-dimensional porous media together with a transport equation for passive tracer particles. Transport coefficients and parameters of the macro-scale equations are then extracted from the micro-scale results by using non-linear fitting and method of moments for a simple one-dimensional model.
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2013
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11583/2509897`
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