Heterogeneous hydraulic conductivity and porosity fields reconstruction through steady-state flow and transient solute transport data using the continuous adjoint state.

Highlights • The continuous adjoint state associated with the transport equation is derived. • Hydraulic conductivity and porosity fields are estimated by inverse modeling. • Concentration data complementing heads slightly improve inverse solutions to flow. Abstract A parameter estimation methodology has been developed on the basis of model inversion using a Quasi–Newton method and adaptive parameterization. The continuous adjoint state equations for both flow and transport in porous media are employed as the tool calculating the gradient components of the objective function with respect to parameters. Solving the continuous form of the adjoint equations can be implemented independently of the code used to solve the forward problem, which renders the technique non-intrusive. The developed methodology is applied to the identification of hydraulic conductivity and porosity fields conditioned by piezometric head data associated with steady-state flow and transient solute concentrations. Synthetic numerical experiments have been undertaken for test cases of increasing complexity, from an almost uniform flow sweeping the modeled domain with a prescribed uniform continuous injection of solute at the inflow boundary, to spatially highly variable flow conditions obtained through source/sink terms within the flow domain and a local stepwise solute injection. The results of inversions are analyzed using criteria based on the comparisons between estimated concentration and reference concentration values as well as comparisons between estimated hydraulic conductivity (and porosity for one test case) and reference hydraulic conductivity fields. The results show that employing a continuous adjoint state technique computed independently of the direct problem is an efficient option for parameter estimation relying jointly upon flow and transport data. In the reported numerical examples that are characterized by the identifiability of the flow problem on the basis of hydraulic head observations, concentration data from solute transport scenarios bring few added value to sought solutions of hydraulic conductivities. The spatial structure of the conductivity fields is slightly improved compared with the reference, but the overall system in terms of head distribution, identification of main flow paths, and solute transit times, only inherits cosmetics. [ABSTRACT FROM AUTHOR]