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TECHNICAL PAPERS

# Simulation of Contaminant Transport in a Fractured Porous Aquifer

[+] Author and Article Information
Sergei Fomin

Department of Mathematics and Statistics, California State University, Chico, CA 95928sfomin@csuchico.edu

Department of Applied Mathematics, Kazan State University, Kazan, Russia

Toshiyuki Hashida

Fracture & Reliability Research Institute, School of Engineering, Tohoku University, Sendai, Japan

J. Fluids Eng 129(9), 1157-1163 (Mar 30, 2007) (7 pages) doi:10.1115/1.2754327 History: Received August 27, 2006; Revised March 30, 2007

## Abstract

Solute transport in the fractured porous confined aquifer is modeled by the advection-dispersion equation with fractional time derivative of order $γ$, which may vary from 0 to 1. Accounting for diffusion in the surrounding rock mass leads to the introduction of an additional fractional time derivative of order $1∕2$ in the equation for solute transport. The closed-form solutions for concentrations in the aquifer and surrounding rocks are obtained for the arbitrary time-dependent source of contamination located in the inlet of the aquifer. Based on these solutions, different regimes of contamination of the aquifers with different physical properties are modeled and analyzed.

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## Figures

Figure 1

Schematic of the model

Figure 2

Variation of concentration in the aquifer C in streamwise direction for the permanent uniform source of concentration C0=1 in the inlet of the aquifer

Figure 3

Distributions of concentrations in the confining porous rocks C1 with respect to transverse coordinate Y over the period of contamination, 0<t<t* (solid lines), and after the elimination of the source of contamination, t>t* (dashed lines) at X∕Pe=0.5, b=1 and different γ: (a)γ=0.2 and (b)γ=0.8

Figure 5

Distributions of concentrations in the aquifer C along the aquifer over the period of contamination, 0<t<t* (solid lines), and after the elimination of the source of contamination, t>t* (dashed lines), for different b and γ: (a)b=1, γ=0.2; (b)b=1, γ=0.8; (c)b=0.1, γ=0.2

Figure 4

Distributions of concentrations in the confining from above porous rocks C1 with respect to transverse coordinate Y over the period of contamination, 0<t<t* (solid lines), and after the elimination of the source of contamination, t>t* (dashed lines) for γ=0.2 and different t*, X, and b

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