Adjoint sensitivity analysis of steady-state groundwater flow and solute transport

The analysis and understanding of groundwater flow and solute transport in the neighbourhood of a site for a radioactive waste repository play important roles in a performance assessment. Generally, numerical models of flow and transport must be employed in order first to study the behaviour of the system over the very long times that have to be considered, and secondly to evaluate quantities (''performance measures'') of interest and relevance to the evaluation of repository performance. For flow, performance measures of interest include specific discharge at the repository, groundwater travel time from the repository to the surface environment, and calculated heads (for comparison with observations). For transport, radionuclide concentrations, radionuclide fluxes from the repository and in the surrounding geological formations, and radionuclide fluxes to the surface environment are of interest. Often it is important to estimate the uncertainties in the performance measures that are implied by the uncertainties in the model parameters. In this study, the usefulness of adjoint sensitivity theory as a method for estimating the uncertainties in these performance measures due to parameter uncertainty is investigated. The adjoint equations and sensitivity coefficients for steady-state groundwater flow and solute transport in a porous medium are derived for both standard finite-element and mixed-element formulations. The flow, transport and adjoint equations are solved using the Galerkin finite-element method and a direct frontal solver. The new code developed was verified using one-dimensional flow and solute transport test cases, together with two- and three-dimensional models which included three different strata. (UK)