The development of the adjoint state method for the system of partial differential equations (PDEs) describing radionuclide transport in heterogeneous discrete fractured porous media in steady-state regime is presented in this study for both continuous and discrete adjoint approaches. The continuous adjoint approach has its own advantage in the sense that the adjoint system can be derived in terms of PDEs which can be solved analytically for specific performance measures. These PDEs can then be used to obtain a physical interpretation of the adjoint state functions. The discrete adjoint approach permits a simpler mathematical treatment based on the use of the same matrix (or its transpose) of the linear system of the discretized transport equations referring to from hereon as the forward problem. Analytical solutions for both the forward problem and its associated adjoint problem have been derived for radionuclide transport in layered formations including a fracture using an analytical inversion of tridiagonal matrices. A set of 14 formulas of sensitivity coefficients with respect to pertinent system parameters has been derived and presented in integral forms. Analytical results have been compared with numerical results and have shown excellent agreements. The discrete adjoint approach has been coupled with the differential sensitivity analysis 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. The results show that when a fracture is present in the vicinity of waste repository, the state parameter controlling flow through the fracture, referred to herein as fracture transmissivity, is among the important parameters which should be considered in sensitivity analysis studies.

中文翻译：

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稳态条件下非均质离散裂缝性多孔地层中放射性核素输运的伴随敏感性模型

本研究针对连续和离散伴随方法，介绍了描述稳态条件下异质离散裂缝多孔介质中放射性核素输运的偏微分方程 (PDE) 系统的伴随状态方法的发展。连续伴随方法有其自身的优势，因为伴随系统可以根据偏微分方程导出，可以针对特定的性能度量进行解析求解。然后可以使用这些偏微分方程来获得伴随状态函数的物理解释。离散伴随方法允许基于使用相同矩阵（或其转置）的离散化传输方程的线性系统的更简单的数学处理，从这里被称为前向问题。使用三对角矩阵的解析反演，已经为包括裂缝在内的层状地层中的放射性核素传输导出了正向问题及其相关伴随问题的解析解。已经导出并以积分形式呈现了一组 14 个关于相关系统参数的灵敏度系数公式。分析结果与数值结果进行了比较，并显示出极好的一致性。离散伴随方法与差分灵敏度分析方法相结合，并应用于实际现场案例，涉及目前正在考虑用于瑞士北部 Zürich Nordost 地下核储存场址的性能评估。结果表明，当废物库附近存在裂缝时，