An Adjoint Sensitivity Model for Steady-State Sequentially Coupled Radionuclide Transport in Porous Media

This work presents an efficient mathematical/numerical model to compute the sensitivity coefficients of a predefined performance measure to model parameters for one-dimensional steady-state sequentially coupled radionuclide transport in a finite heterogeneous porous medium. The model is based on the adjoint sensitivity approach that offers an elegant and computationally efficient alternative way to compute the sensitivity coefficients. The transport parameters include the radionuclide retardation factors due to sorption, the Darcy velocity, and the effective diffusion/dispersion coefficients. Both continuous and discrete adjoint approaches are considered. The partial differential equations associated with the adjoint system are derived based on the adjoint state theory for coupled problems. Physical interpretations of the adjoint states are given in analogy to results obtained in the theory of groundwater flow. For the homogeneous case, analytical solutions for primary and adjoint systems are derived and presented in closed forms. Numerically calculated solutions are compared to the analytical results and show excellent agreements. Insights from sensitivity analysis are discussed to get a better understanding of the values of sensitivity coefficients. The sensitivity coefficients are also computed numerically by finite differences. The numerical sensitivity coefficients successfully reproduce the analytically derived sensitivities based on adjoint states. A derivative-based global sensitivity method coupled with the adjoint state method is presented and applied to a real field case represented by a site currently being considered for underground nuclear storage in Northern Switzerland, "Zurich Nordost", to demonstrate the proposed method. The results show the advantage of the adjoint state method compared to other methods in term of computational effort.