One-dimensional uniform and time varying solute dispersion along transient groundwater flow in a semi-infinite aquifer |
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| Authors: | Mritunjay K Singh Shafique Ahamad Vijay P Singh |
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| Institution: | 1. Department of Applied Mathematics, Indian School of Mines, Dhanbad, Jharkhand, India
2. Department of Biological and Agricultural Engineering, Zachry Department of Civil Engineering, Texas A&M University, College Station, USA
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| Abstract: | An analytical solution for the space-time variation of contaminant concentration in one-dimensional transient groundwater flow in a homogenous semi-infinite aquifer, subjected to time-dependent source contamination, is derived. The uniform and time varying dispersion along transient groundwater flow is investigated under two conditions. First, the flow velocity distribution in the aquifer is considered as a sinusoidally varying function, and second, the flow velocity distribution is treated as an exponentially increasing function of time. It is assumed that initially the aquifer is not solute free, so the initial background concentration is considered as an exponentially decreasing function of the space variable which is tending to zero at infinity. It is assumed that dispersion is directly proportional to the square of the velocity, noting that experimental observations indicate that dispersion is directly proportional to the velocity with a power ranging from 1 to 2. The analytical solution is illustrated using an example and may help benchmark numerical codes and solutions. |
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