Interface dynamics in randomly heterogeneous porous media

We consider the dynamics of a fluid interface in heterogeneous porous media, whose hydraulic properties are uncertain. Modeling hydraulic conductivity as a random field of given statistics allows us to predict the interface dynamics and to estimate the corresponding predictive uncertainty by means o...

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Bibliographic Details
Published in:Advances in water resources 2005-04, Vol.28 (4), p.393-403
Main Authors: Lazarev, Yu.N., Petrov, P.V., Tartakovsky, Daniel M.
Format: Article
Language:English
Subjects:
Conductivity tensor
equations
fluid mechanics
Free surface
groundwater flow
hydrogeology
hydrologic models
mathematical models
Moment equations
porous media
Random fluctuations
saturated hydraulic conductivity
Stochastic
stochastic closures
stochastic processes
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Summary:We consider the dynamics of a fluid interface in heterogeneous porous media, whose hydraulic properties are uncertain. Modeling hydraulic conductivity as a random field of given statistics allows us to predict the interface dynamics and to estimate the corresponding predictive uncertainty by means of statistical moments. The novelty of our approach to obtaining the interface statistics consists of dynamically mapping the Cartesian coordinate system onto a coordinate system associated with the moving front. This transforms a difficult problem of deriving closure relationships for highly nonlinear stochastic flows with free surfaces into a relatively simple problem of deriving stochastic closures for linear flows in domains with fixed boundaries. We derive a set of deterministic equations for the statistical moments of the interfacial dynamics, which hold in one and two spatial dimensions, and analyze their solutions for one-dimensional flow.
ISSN:0309-1708
1872-9657
DOI:10.1016/j.advwatres.2004.11.003