Development of a Darcy- Brinkman model to simulate water flow and tracer transport in a heterogeneous karstic aquifer (Val d'Orléans, France)

Abstract : Modelling karstic aquifers is problematic because the equation of references (i.e. Darcy) is adapted to describe hydrodynamics of flow in a rock where porosity is low. The modelling of the karstic drains requires to use a macroscopic equation representative of the physics of flows occurring in rock where pores are important in size. To answer this question, our study presents an example of the hydrodynamic model adapted to the karstic aquifer of the Val d'Orléans starting from two equations characterizing the dynamics of the fluids: i) the Darcy law used to describe the hydraulic behaviour of massive limestone, and ii) the equation of Brinkman models the flows in vacuums of big sizes within the karstic drain. In the second objective, the flow equations are coupled with the transport equation to predict the karst properties. The results are tested by using six tracer tests carried out in the Val d'Orléans. The simulations show that the draining permeability ranges from 5 10-6 to 5.5 10-5 m2, the limestone permeability ranges from 8 10-11 to 6 10-10 m2. The dispersivity coefficients in the drains range from 23 to 43 m and in the fractured zone from 1 to 5 m.