Macroscale Models of Flow Through Highly Heterogeneous Porous Media

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Appearing at the scale of pores the micro scale such processes can affect the micro-scale structure of the medium. This impacts the behaviour of the system at a larger scale macro-scale , which is of primary interest.

When performing numerical simulations, one has to account for the occurrence of different scales, and with the fact that the micro-structure is changing in time in a manner that is not known a-priori. Here we consider a phase field model for precipitation and dissolution in porous media [1, 4].

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Using periodic homogenization, we derive an upscaled macro-scale model. The resulting is a system of equations coupling parabolic and elliptic equations at the macro-scale. These involve effective parameters like diffusivity, porosity and permeability, which are obtained by solving locally coupled systems again.

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Macroscale Models of Flow Through Highly Heterogeneous Porous Media - mauclutbackbe.tk

We proposed a combination of numerical techniques to solve the upscaled models. At each time step, the macro-scale system receives information from the micro-scale problems, which are updated as the phase field evolves. To deal with the nonlinearity of the model, we use an L-type linearization scheme [2, 3].

This is combined with mesh refinement at the micro-scale, improving both the accuracy and the efficiency of the simulations.

Discrete Reduced Models for Flow in Porous Media

References [1] C. Bringedal, L. List and F. Pop, F.

Chemical or Heat Convection-Diffusion Transport Through Highly Heterogeneous Porous Media

The The book book was was planned planned in in such such a a manner manner that that two two basic basic goals goals would would be be reached. On On the the one one hand, hand, the the goal goal was was to to show show some some new new results results in in the the field field of of modeling modeling transport transport through through highly highly heterogeneous heterogeneous media, media, based based on on the the homogenization homogenization theory. Multiple Multiple new new mathematical mathematical models models of of transport transport are are presented presented herein, herein, studying studying their their properties, properties, developing developing methods methods to to compute compute effective effective parameters parameters of of the the averaged averaged media, media, simulation simulation of of cell cell problems, problems, using using new new models models to to simulate simulate some some practical practical problems.

High High heterogeneity heterogeneity being being subjected subjected to to the the homogenization homogenization procedure, procedure, generates generates non-local non-local phenomena phenomena and and then then gives gives a a possibility possibility to to develop develop a a new, new, non-local non-local or or "dynamic" , "dynamic" , theory theory of of transport transport in in porous porous media.

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Macroscale models of flow through highly heterogeneous porous media

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