Abstract
<abstract> An accurate modeling of reactive flows in fractured porous media is a key ingredient to obtain reliable numerical simulations of several industrial and environmental applications. For some values of the physical parameters we can observe the formation of a narrow region or layer around the fractures where chemical reactions are focused. Here, the transported solute may precipitate and form a salt, or vice-versa. This phenomenon has been observed and reported in real outcrops. By changing its physical properties, this layer might substantially alter the global flow response of the system and thus the actual transport of solute: the problem is thus non-linear and fully coupled. The aim of this work is to propose a new mathematical model for reactive flow in fractured porous media, by approximating both the fracture and these surrounding layers via a reduced model. In particular, our main goal is to describe the layer thickness evolution with a new mathematical model, and compare it to a fully resolved equidimensional model for validation. As concerns numerical approximation we extend an operator splitting scheme in time to solve sequentially, at each time step, each physical process thus avoiding the need for a non-linear monolithic solver, which might be challenging due to the non-smoothness of the reaction rate. We consider bi- and tridimensional numerical test cases to asses the accuracy and benefit of the proposed model in realistic scenarios. </abstract>
Highlights
The study of reactive flows in porous media is a challenging problem in a large variety of applications, from geothermal energy to CO2 sequestration up to the study of flow in tissues or that of the degradation of monuments and cultural heritage sites
In a conforming method the computational grid used for the porous media is conformal to that used in the fractures, which means that the elements of the grid used to discretize the fractures coincide geometrically with facets of the mesh used for the porous medium
In this work we have introduced a mathematical model that is able to simulate in an accurate, yet affordable way simple reactive transport flow problems in the presence of a fracture
Summary
The study of reactive flows in porous media is a challenging problem in a large variety of applications, from geothermal energy to CO2 sequestration up to the study of flow in tissues or that of the degradation of monuments and cultural heritage sites. In a conforming method the computational grid used for the porous media is conformal to that used in the fractures, which means that the elements of the grid used to discretize the fractures coincide geometrically with facets of the mesh used for the porous medium In this setting, many numerical schemes have been proposed, from classical finite volume approaches, like in [40], to mimetic finite differencing [5], gradient schemes [13], discontinuous Galerkin [4] and hybrid-high order schemes [15], just to mention some recent works. The first concerns the so called geometrically non-matching discretizations, where the grid used in the fracture is completely independent to that of the porous media Among this type of techniques we mention the embedded discrete fracture network (e-DFM) [24, 41] and approaches based on the use of extended finite elements [19]. See [7, 18] for a comparison of some of these models
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