An Adjoint Sensitivity Model for Transient Sequentially Coupled Radionuclide Transport in Porous Media

Abstract

We present an efficient mathematical/numerical adjoint sensitivity analysis model for transient radionuclide transport through heterogeneous porous media. This work extends our previous research on radionuclide transport in a steady‐state regime. Both continuous and discrete adjoint approaches have been developed in this current research. The mathematical equations associated with the adjoint system and required for the continuous approach have been derived. The methodology for deriving the discrete adjoint solution is also presented. For the homogeneous case, the adjoint system for radionuclide decay chain is solved analytically. The four‐member decay chain (238Pu → 234U → 230Th → 226Ra) is considered for validation. The validity of the analytical adjoint sensitivity model has been shown using two illustrative examples associated with two performance measures. The analytical adjoint states are compared with calculated numerical results and show excellent agreements. The sensitivity coefficients are also computed numerically using the perturbation method. The numerical sensitivity coefficients successfully reproduce the analytically derived sensitivities based on adjoint states. The adjoint model has been coupled with a derivative‐based global sensitivity method and applied to a real field case involving the performance assessment of a site currently being considered for underground nuclear storage in northern Switzerland, Zürich Nordost. An illustrative case study of spent fuel and high‐level waste (SF/HLW) repository involving 6 radionuclides and 48 parameters has been considered for identifying the most important parameters with respect to the maximum radionuclide dose at the interface geosphere/biosphere. Based on the results of sensitivity analysis, the uncertainty of the maximum radionuclide dose has been performed using Monte Carlo simulations.

An Adjoint Sensitivity Model for Radionuclide Transport in Heterogeneous Discrete Fractured Porous Formation in Steady‐State Regime

“…The Zürich Nordost model is described in detail in Hayek et al. (2019, 2020). In brief, the model consists of six geological layered formations denoted from bottom to top by TL (Toniger Lias formation), OPA (Opalinus clay host rock), BD‐SKA (Sandkalkabfolgen formation), BD‐TA‐STA (Tonige Abfolgen and Sandig‐tonige Abfolgen formations), EFF‐KBA (Kalkbankabfolgen formation), and EFF‐KMA (Kalkmergelabfolgen formation), respectively.…”

“…However, the method provides exact sensitivities in contrast to other numerical approaches (i.e., the influence coefficient method). Recently, the adjoint state method has been applied and used successfully in problems related to flow and transport processes in porous media (see for instance Delay et al, 2017Delay et al, , 2019Hayek et al, 2019Hayek et al, , 2020Lu & Vesselinov, 2015).…”

Monte Carlo Simulations of Shear‐Thinning Flow in Geological Fractures

“…The pioneering work of Bellin et al (1992) investigated the conditions for the validity of first-order flow and transport theories in random porous media; Berkowitz and Scher (1998) adopted a Monte Carlo approach to determine velocity distributions in fracture networks, as a function of the fracture orientations, to study anomalous transport at the network scale; Gómez-Hernández and Wen (1998) analyzed the applicability of multi-Gaussian random function models in hydrogeology. More recently this methodology has been applied to study transient sequentially coupled radionuclide transport (Hayek et al, 2020), to investigate flow in two dimensional (2-D) conductivity fields and derive a large-scale transport model (Comolli et al, 2019), to simulate CO 2 plume migration (Zhong et al, 2019), and to perform uncertainty quantification (Yang et al, 2020).…”