Multidimensional self-similar analytical solutions of two-phase flow in porous media

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F16%3A00239812" target="_blank" >RIV/68407700:21340/16:00239812 - isvavai.cz</a>
Result on the web
<a href="http://www.sciencedirect.com/science/article/pii/S030917081630032X" target="_blank" >http://www.sciencedirect.com/science/article/pii/S030917081630032X</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.advwatres.2016.02.007" target="_blank" >10.1016/j.advwatres.2016.02.007</a>

Result language
angličtina
Original language name
Multidimensional self-similar analytical solutions of two-phase flow in porous media
Original language description
In general, analytical solutions serve a useful purpose to obtain better insights and to verify numerical codes. For flow of two incompressible and immiscible phases in homogeneous porous media without gravity, one such method that neglects capillary pressure in the solution was first developed by Buckley and Leverett (1942). Subsequently, McWhorter and Sunada (1990) derived an exact solution for the one and two dimensional cases that factored in capillary effects. This solution used a similarity transform that allowed to reduce the governing equations into a single ordinary differential equation (ODE) that can be further integrated into an equivalent integral equation. We present a revision to McWhorter and Sunada solution by extending the self-similar solution into a general multidimensional space. Inspired by the derivation proposed by McWhorter and Sunada (1990), we integrate the resulting ODE in the third and higher dimensions into a new integral equation that can be subsequently solved iteratively by means of numerical integration. We developed implementations of the iterative schemes for one- and higher dimensional cases that can be accessed online on the authors’ website.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BK - Liquid mechanics
OECD FORD branch
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Project
<a href="/en/project/LH14003" target="_blank" >LH14003: Development and Validation of Porous Media Fluid Dynamics and Phase Transitions Models for Subsurface Environmental Application</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>S - Specificky vyzkum na vysokych skolach

Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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