Flow in double-porosity aquifers: Parameter estimation using an adaptive multiscale method

•Adjoint state equations for a double porosity flow model are rigorously developed.•A detailed algorithm for the adaptive multiscale parameterization is presented.•Parameter spatial distributions are retrieved by solving the inverse problem.•Adjoint state and multiscale parameterizations yield a robust inversion technique.

The double porosity model (DPM) concept is a widely used approach to simulate flow in fractured aquifers. Parameter estimation methods to calibrate standard groundwater flow models have been rarely applied to the DPM. In this paper, we make use of a multiscale parameterization which defines the spatial distribution of parameter by an adaptive discretization refined within the iterative inversion procedure. The mathematical developments, including a presentation of the adjoint state equations, and the adaptive multiscale algorithm are described in detail. The parameter estimation procedure is applied to a heterogeneous synthetic case, where each type of parameter is spatially distributed according to a different variogram. Without any prior knowledge of theses variograms conditioning the adaptive multiscale method, the latter is able to retrieve with good precision the reference model for both its local parameter values and their associated spatial distribution.