Simple approximate closed-form expressions for tracer injection in aquifer with a radially converging or diverging flow field

Dominique Thiéry (1)

1 BRGM - Bureau de Recherches Géologiques et Minières (BRGM)

The exact solution for the concentration breakthrough curves resulting from a solute injection in radially converging flow in an aquifer obtained using Laplace transforms has a complex form difficult to compute, and cannot be given in closed-form expression. This makes it difficult to use for tracer tests analysis in radial flow. To overcome this difficulty new simple approximate but accurate closed-form expressions are derived in the present paper for slug and continuous injections. The improvement of accuracy of these new closed-form expressions is demonstrated. The paper establishes also that the breakthrough curves resulting from slug injections into a radially diverging or radially converging flow are exactly identical at the sampling well in domains having the same spatial extension. Solutions were also derived for tracers or solutes subject to degradation. The new closed-form expressions were used for the analysis of 12 field tracer tests to highlight the difference in transport parameters determination compared to previous approximate expressions.

Mots clés: Radial flow tracer tests; Closed-form approximation; Dimensional expression; Field test applications

Domaines: Hydrologie; Géologie appliquée

Dominique Thiéry. Simple approximate closed-form expressions for tracer injection in aquifer with a radially converging or diverging flow field. Journal of Hydrology, 2022, 608, pp.127661. ⟨10.1016/j.jhydrol.2022.127661⟩. ⟨hal-03640158⟩