Solute transport in a semi-infinite homogeneous aquifer with a fixed point source concentration

  • Mritunjay Kumar Singh
  • Sultana Begam
  • Chandan Kumar Thakur
  • Vijay P. Singh
Original Article


This study derives an analytical solution of the advection–dispersion (AD) equation commonly used to describe the transport of pollutants in a semi-infinite homogeneous aquifer. When an extra constant source term is added to the AD equation, it changes the solution of the equation. The AD equation is solved analytically using Laplace transform. Also, the equation is solved numerically using an explicit finite difference method and its stability condition is presented with the aid of matrix method. For the solution of the AD equation the following considerations are made: (1) The dispersion and velocity are considered as time-dependent; (2) dispersion is expressed as directly proportional to the square of velocity; (3) there is also diffusion; (4) there is some initial concentration and the aquifer domain is, therefore, not pollutant-free; (5) There is a time-dependent exponentially decreasing input source; and (6) the concentration gradient is assumed to be zero at the exit boundary. It is found that the contaminant concentration decreases with time contrary to what happens when the extra term is not included.


Solute Aquifer Groundwater-recharge Advection–dispersion Analytical and numerical solutions 



The authors are thankful to Indian Institute of Technology (Indian School of Mines), Dhanbad for providing financial support to Ph.D. candidate under the JRF scheme. This work is also partially supported by CSIR New Delhi under the project No. 25(0251)/16/EMR-II.


Funding was provided by Council of Scientific and Industrial Research (Grant No. 25(0251)/16/EMR-II).


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Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  • Mritunjay Kumar Singh
    • 1
  • Sultana Begam
    • 1
  • Chandan Kumar Thakur
    • 1
  • Vijay P. Singh
    • 2
  1. 1.Department of Applied MathematicsIndian Institute of Technology (Indian School of Mines)DhanbadIndia
  2. 2.Department of Biological and Agricultural Engineering and Zachry Department of Civil EngineeringTexas A&M UniversityCollege StationUSA

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