Inversion of a set of well-test interferences in a fractured limestone aquifer by using an automatic downscaling parameterization technique

Abstract : This work inverts interference hydraulic tests from a karstic aquifer modeled as a single continuum with heterogeneous hydraulic properties (hydraulic conductivity K and specific storage capacity Ss). An automatic technique of parameterization is proposed to solve the inverse problem. Sought parameters are located at the nodes of a parameter grid made of triangular elements and independently superimposed onto the calculation grid of the flow problem. The parameter grid can be refined within the process of inversion so that the solution is improved locally because increasing the number of parameters better depicts spatial heterogeneity. Applied to hydraulic tests carried out at the Hydrogeological Experimental Site (HES) of Poitiers–France, this Adaptative Multi-scale Triangulation (AMT) method of parameterization reveals that hydraulic conductivity K and hydraulic diffusion K/Ss are structured in space as correlated stochastic continuums. This structure is not imposed a priori but is found as the mere consequence of inverting drawdown data. The sought stochastic continuums are discussed and compared to previous results obtained by processing the same data with various techniques. Even though interference data show evidences of local karstic features, the hydraulic bulk behavior of the aquifer is that of a diffusive continuous medium. This reinforces the idea that at mid to large scales, flow in fractured rocks can also be handled with relevance by means of a continuous heterogeneous approach. This result would extend to fractured aquifers with local draining in open conduits as is the case in this study.