Modeling multiphase flow in porous media with an application to permafrost soil

3 Abstract This thesis contains the derivation of two-scale models for multi phase and multi con- stituent flow in porous media. It will be achieved by using phase field models for the porespace together with formal asymptotic expansion. The equations describing the processes in the porespace are ob...

Full description

Bibliographic Details
Main Author: Heida, Martin
Other Authors: Málek, Josef, Jäger, Willi
Format: Thesis
Language:English
Published: Univerzita Karlova, Matematicko-fyzikální fakulta 2011
Subjects:
Online Access:https://hdl.handle.net/20.500.11956/35294
id ftunivpraha:oai:https://dspace.cuni.cz:20.500.11956/35294
record_format openpolar
spelling ftunivpraha:oai:https://dspace.cuni.cz:20.500.11956/35294 2023-08-20T04:09:15+02:00 Modeling multiphase flow in porous media with an application to permafrost soil Modelování vícefázového proudění v porózním prostředí zaměřené na trvale zmrzlou půdu Heida, Martin Málek, Josef Jäger, Willi 2011 application/pdf https://hdl.handle.net/20.500.11956/35294 English en_US eng Univerzita Karlova, Matematicko-fyzikální fakulta http://hdl.handle.net/20.500.11956/35294 110103 001489545 dizertační práce 2011 ftunivpraha https://doi.org/20.500.11956/35294 2023-08-01T20:27:47Z 3 Abstract This thesis contains the derivation of two-scale models for multi phase and multi con- stituent flow in porous media. It will be achieved by using phase field models for the porespace together with formal asymptotic expansion. The equations describing the processes in the porespace are obtained by using the assumption of maximal entropy production rate, which was first developed and used by Rajagopal and Srinivasa. This method is able to yield thermodynamically consitent models in the bulk starting from constitutive assumptions on energy and on the rate of entropy production. In partic- ular, the method will lead to a new point of view on phase field models and it will be possible to derive well known models like the Cahn-Hilliard-Navier-Stokes system, Korteweg's equation or the Allen-Cahn model of phase transition. In order to derive suitable boundary coditions, the assumption of maximum rate of entropy production is generalized to processes on the surface of a bounded domain and applied to phase field models. Finally, the same method is used to derive a thermodynamically consistent scaling of such multi phase and multi constituent systems. The resulting equations are homogenized via formal asymptotic expansion. This method will be applied to the air/water system in soil as well as to the active. V práci je odvozen dvouškálový model pro vícefázové a vícesložkové proudění tekutin porózním prostředím. Odvození vychází z nového modelu pro proudění pórovitým prostředím a je provedeno standardním formálním asymptotickým rozvojem a porovná- ním člen u stejného řádu. Rovnice popisující chování tekutiny v pórech jsou získány po- mocí principu maximalizace rychlosti produkce entropie, navrženého a poprvé použitého Rajagopalem a Srinivasou. Metoda, která vychází z konstitutivních rovnic pro vnitřní energii a rychlost produkce entropie, vede k termodynamicky konsistentním model um platných uvnitř daného tělesa. Metoda tak dává nový pohled na fázové modely a umožňuje odvodit známé ... Thesis permafrost Charles University CU Digital repository Ular ENVELOPE(140.951,140.951,72.498,72.498)
institution Open Polar
collection Charles University CU Digital repository
op_collection_id ftunivpraha
language English
description 3 Abstract This thesis contains the derivation of two-scale models for multi phase and multi con- stituent flow in porous media. It will be achieved by using phase field models for the porespace together with formal asymptotic expansion. The equations describing the processes in the porespace are obtained by using the assumption of maximal entropy production rate, which was first developed and used by Rajagopal and Srinivasa. This method is able to yield thermodynamically consitent models in the bulk starting from constitutive assumptions on energy and on the rate of entropy production. In partic- ular, the method will lead to a new point of view on phase field models and it will be possible to derive well known models like the Cahn-Hilliard-Navier-Stokes system, Korteweg's equation or the Allen-Cahn model of phase transition. In order to derive suitable boundary coditions, the assumption of maximum rate of entropy production is generalized to processes on the surface of a bounded domain and applied to phase field models. Finally, the same method is used to derive a thermodynamically consistent scaling of such multi phase and multi constituent systems. The resulting equations are homogenized via formal asymptotic expansion. This method will be applied to the air/water system in soil as well as to the active. V práci je odvozen dvouškálový model pro vícefázové a vícesložkové proudění tekutin porózním prostředím. Odvození vychází z nového modelu pro proudění pórovitým prostředím a je provedeno standardním formálním asymptotickým rozvojem a porovná- ním člen u stejného řádu. Rovnice popisující chování tekutiny v pórech jsou získány po- mocí principu maximalizace rychlosti produkce entropie, navrženého a poprvé použitého Rajagopalem a Srinivasou. Metoda, která vychází z konstitutivních rovnic pro vnitřní energii a rychlost produkce entropie, vede k termodynamicky konsistentním model um platných uvnitř daného tělesa. Metoda tak dává nový pohled na fázové modely a umožňuje odvodit známé ...
author2 Málek, Josef
Jäger, Willi
format Thesis
author Heida, Martin
spellingShingle Heida, Martin
Modeling multiphase flow in porous media with an application to permafrost soil
author_facet Heida, Martin
author_sort Heida, Martin
title Modeling multiphase flow in porous media with an application to permafrost soil
title_short Modeling multiphase flow in porous media with an application to permafrost soil
title_full Modeling multiphase flow in porous media with an application to permafrost soil
title_fullStr Modeling multiphase flow in porous media with an application to permafrost soil
title_full_unstemmed Modeling multiphase flow in porous media with an application to permafrost soil
title_sort modeling multiphase flow in porous media with an application to permafrost soil
publisher Univerzita Karlova, Matematicko-fyzikální fakulta
publishDate 2011
url https://hdl.handle.net/20.500.11956/35294
long_lat ENVELOPE(140.951,140.951,72.498,72.498)
geographic Ular
geographic_facet Ular
genre permafrost
genre_facet permafrost
op_relation http://hdl.handle.net/20.500.11956/35294
110103
001489545
op_doi https://doi.org/20.500.11956/35294
_version_ 1774722075076853760