Analytical Solution for One-Dimensional Solute Dispersion with Time-Dependent Source Concentration along Uniform Groundwater Flow in a Homogeneous Porous Formation
Publication: Journal of Engineering Mechanics
Volume 138, Issue 8
Abstract
An analytical solution for the space-time variation of contaminant concentration in one-dimensional uniform groundwater flow in a homogenous semi-infinite porous formation (e.g., aquifer) subjected to time-dependent source contamination is derived. The temporally dependent dispersion in the aquifer is investigated under two conditions. First, the temporally dependent dispersion distribution in the aquifer is considered as a sinusoidally varying function and, second, the temporally dependent dispersion distribution is treated as an exponentially increasing function of time. It is assumed that initially the aquifer is not solute free; i.e., the aquifer is not clean and the initial concentration is an exponentially decreasing function of the space variable and is tending to zero toward infinity. The concept that dispersion is directly proportional to the seepage velocity is employed. The analytical solution is illustrated using an example and may help benchmark a numerical code and solution.
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Acknowledgments
The writers are grateful to the University Grants Commission, New Delhi, and Government of India for their financial support of the research work. Prof. Naveen Kumar, Department of Mathematics, BHU, Varanasi, India, is also thanked for his valuable suggestions. The writers are thankful to the reviewers for their constructive comments, which have helped improve the quality of the paper.
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Published In
Journal of Engineering Mechanics
Volume 138 • Issue 8 • August 2012
Pages: 1045 - 1056
Copyright
© 2012. American Society of Civil Engineers.
History
Received: Feb 24, 2011
Accepted: Dec 13, 2011
Published online: Dec 14, 2011
Published in print: Aug 1, 2012
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