Simulation of Spring Management with Quasi-Aggregated Model

This technical note presents a method for calculating the flow from springs and may be useful in the management of aquifers where the spring flow is a critical factor. The note examines the conjunctive operation of a groundwater-fed spring with pumping and artificial recharge directly from and to the same aquifer. Rorabaugh's (1963) solution for a one-dimensional homogeneous aquifer of a finite length is used, so a simple solution for the aquifer outflow due to a series of instantaneous discrete recharges or to pumping uniformily distributed along the aquifer is obtained. Only a few components of the infinite terms of the analytical solution are used; these are the first Fourier components of the sinusoidal eigenfunctions that solve the problem. As the eigenvalues of the solution are (2n + 1)²α, the factor to be applied to each component is exp[−(2n + 1)²αt], which decays very fast with time for high values of n. Thus, the structure of the solution can be perceived as an extension, with several cells, of the simple approach of the unicellular model.