Evaluation of aquifer thickness by analysing recession hydrographs. Application to the Oman ophiolite hard-rock aquifer

Abstract

For more than a century, hydrologists and hydrogeologists have been investigating the processes of stream and spring baseflow recession, for obtaining data on aquifer characteristics. The Maillet Formula [Librairie Sci., A. Hermann, Paris (1905) 218], an exponential equation widely used for recession curve analysis, is an approximate analytical solution for the diffusion equation in porous media whereas the equation proposed by Boussinesq [C. R. Acad. Sci. 137 (1903) 5; J. Math. Pure Appl. 10 (1904) 5], that depicts baseflow recession as a quadratic form, is an exact analytical solution. Other formulas currently used involve mathematical functions with no basis on groundwater theory. Only the exact analytical solutions can provide quantitative data on aquifer characteristics. The efficiency of the two methods was compared on the basis of recession curves obtained with a 2D cross-sectional finite differences model that simulates natural aquifers. Simulations of shallow aquifers with an impermeable floor at the level of the outlet show that their recession curves have a quadratic form. Thus, the approximate Maillet solution largely overestimates the duration of the ‘influenced’ stage and underestimates the dynamic volume of the aquifer. Moreover, only the Boussinesq equations enable correct estimates of the aquifer parameters. Numerical simulations of more realistic aquifers, with an impermeable floor much deeper than the outlet, proves the robustness of the Boussinesq formula even under conditions far from the simplifying assumptions that were used to integrate the diffusion equation. The quadratic form of recession is valid regardless of the thickness of the aquifer under the outlet, and provides good estimates of the aquifer's hydrodynamic parameters. Nevertheless, the same numerical simulations show that aquifers with a very deep floor provide an exponential recession. Thus, in that configuration, the Maillet formula also provides a good fit of recession curves, even if parameter estimation remains poor. In fact, the recession curve appears to be closer to exponential when flow has a very important vertical component, and closer to quadratic when horizontal flow is dominant. As a consequence, aquifer permeability anisotropy also changes the recession form. The combined use of the two fitting methods allows one to quantify the thickness of the aquifer under the outlet.