Applied Mathematics and Plasma Physics

A. M. Tartakovsky, S. P. Neuman and D. M. Tartakovsky, "Mean and variance of DNAPL finger development in a
saturated, randomly heterogeneous porous medium", in *Proceedings of the XIV International
Conference
"Computational Methods
in Water Resources
(CMWR 2002)"*, (Delft, the Netherlands, June 23-28), pp. 1307-1314, Jun 2002

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Chlorinated organic solvents such as TCE and PCE are among the most ubiquitous and problematic groundwater contaminants at many sites. They usually enter the subsurface in the form of organic liquids which exhibit low miscibility with water and thus form a separate dense non-aqueous phase liquid (DNAPL). Here we analyze the horizontal movement of DNAPL in a two-dimensional randomly heterogeneous porous medium saturated with water. We consider the fluid interface between DNAPL and water to form a sharp boundary at which the capillary pressure head, assumed equal to the entry pressure head of DNAPL, is prescribed either deterministically or randomly. We treat log hydraulic conductivity as a statistically homogeneous random field with given mean, variance and covariance. We then recast the governing stochastic differential equations in integro-differential form and average them in probability space to obtain leading-order ensemble moment equations for the mean and variance of front evolution with time. We solve these integro-differential equations numerically for flow perpendicular to random layers.

@inproceedings{tartakovsky-2002-mean,

author = {A. M. Tartakovsky and S. P. Neuman and D. M. Tartakovsky},

title = {Mean and variance of {DNAPL} finger development in a
saturated, randomly heterogeneous porous medium},

year = {2002},

month = Jun,

booktitle = {Proceedings of the XIV {I}nternational
{C}onference
"{C}omputational {M}ethods
in {W}ater {R}esources
({CMWR} 2002)"},

address = {Delft, the Netherlands, June 23-28},

pages = {1307-1314}

}