Probability density function of steady state concentration in two-dimensional heterogeneous porous media

Cirpka OA, De Barros FP, Chiogna G, Nowak W (2011)

Publication Type: Journal article

Publication year: 2011

Journal

Water Resources Research American Geophysical Union (AGU)

Book Volume: 47

Article Number: W11523

Journal Issue: 11

DOI: 10.1029/2011WR010750

Abstract

Spatial variability of hydraulic aquifer parameters causes meandering, squeezing, stretching, and enhanced mixing of steady state plumes in concentrated hot-spots of mixing. Because the exact spatial distribution of hydraulic parameters is uncertain, the spatial distribution of enhanced mixing rates is also uncertain. We discuss how relevant the resulting uncertainty of mixing rates is for predicting concentrations. We develop analytical solutions for the full statistical distribution of steady state concentration in two-dimensional, statistically uniform domains with log-hydraulic conductivity following an isotropic exponential model. In particular, we analyze concentration statistics at the fringes of wide plumes, conceptually represented by a solute introduced over half the width of the domain. Our framework explicitly accounts for uncertainty of streamline meandering and uncertainty of effective transverse mixing (defined at the Darcy scale). We make use of existing low-order closed-form expressions that lead to analytical expressions for the statistical distribution of local concentration values. Along the expected position of the plume fringe, the concentration distribution strongly clusters at its extreme values. This behavior extends over travel distances of up to tens of integral scales for the parameters tested in our study. In this regime, the uncertainty of effective transverse mixing is substantial enough to have noticeable effects on the concentration probability density function. At significantly larger travel distances, intermediate concentration values become most likely, and uncertainty of effective transverse mixing becomes negligible. A comparison to numerical Monte Carlo simulations of flow and solute transport show excellent agreement with the theoretically derived expressions. Copyright 2011 by the American Geophysical Union.

Involved external institutions

Eberhard Karls Universität Tübingen DE Germany (DE) Universitat Politècnica de Catalunya · BarcelonaTech (UPC) ES Spain (ES) Università degli Studi di Trento IT Italy (IT) Universität Stuttgart DE Germany (DE)

How to cite

APA:

Cirpka, O.A., De Barros, F.P., Chiogna, G., & Nowak, W. (2011). Probability density function of steady state concentration in two-dimensional heterogeneous porous media. Water Resources Research, 47(11). https://doi.org/10.1029/2011WR010750

MLA:

Cirpka, Olaf A., et al. "Probability density function of steady state concentration in two-dimensional heterogeneous porous media." Water Resources Research 47.11 (2011).

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