Transport, Dilution, and Dispersion of Contaminant in a Leaky Karst Conduit

Step-like rising and falling of a breakthrough curve observed at a karst spring

Spring breakthrough curves induced by conventional advection and dispersion often present a gentle (smooth) change of concentration with time. We investigated an electrical-conductivity breakthrough curve which originated from a chemical release into the aquifer matrix and was measured in June 2007 at Qinglondong Spring, southwest China. The curve presented abrupt rising and falling limbs. Modeling efforts were focused on the migration of the contaminants from the conduit wall to the spring. The conduit production segment was defined to be the conduit section where the chemical plume entered the conduit from aquifer fractures. The first model assumed that the time variance of the plume front reaching the conduit wall was much shorter than transport time over the conduit production segment. The model yielded a decrease of spring discharge which was inconsistent with the observed increase with time. In the second model, the above assumption was relaxed, and wall contaminant flux was inverted as function of downstream distance and time. The observed abrupt rising and falling in the breakthrough curve were interpreted as: (1) Taylor dispersion was too small to identify for a short conduit; (2) seepage from the fractures to the conduit was monodirectional and diluting.

Solute Migration from the Aquifer Matrix into a Solution Conduit and the Reverse

A solution conduit has a permeable wall allowing for water exchange and solute transfer between the conduit and its surrounding aquifer matrix. In this paper, we use Laplace Transform to solve a one-dimensional equation constructed using the Euler approach to describe advective transport of solute in a conduit, a production-value problem. Both nonuniform cross-section of the conduit and nonuniform seepage at the conduit wall are considered in the solution. Physical analysis using the Lagrangian approach and a lumping method is performed to verify the solution. Two-way transfer between conduit water and matrix water is also investigated by using the solution for the production-value problem as a first-order approximation. The approximate solution agrees well with the exact solution if dimensionless travel time in the conduit is an order of magnitude smaller than unity. Our analytical solution is based on the assumption that the spatial and/or temporal heterogeneity in the wall solute flux is the dominant factor in the spreading of spring-breakthrough curves, and conduit dispersion is only a secondary mechanism. Such an approach can lead to the better understanding of water exchange and solute transfer between conduits and aquifer matrix.

HIGHLIGHTS

Euler and Lagrangian approaches are used to solve transport in conduit. Two-way transfer between conduit and matrix is investigated. The solution is applicable to transport in conduit of persisting solute from matrix.