為求解半無限長度地下水系統的耦合一階衰變反應的三維移流-延散方程組的解析解，首先藉由Laplace轉換與雙重有限Fourier cosine轉換將耦合的三維移流-延散方程式組轉化為常微分方程組，然後藉由標準的方法依序逐一求解常微分方程組獲得各子核種的解，新的解析解將表示成有較高計算效率的補誤差函數與指數函數數學型式。為方便解析解的使用計畫中將發展圖形使用者介面以方便解析解的執行，解析解將與健康風險評估模式結合以計算劑量與風險。所發展的工具不管就評估放射性廢棄物的深層地質處理功能，或者福島核災中許多核種從反應爐外洩然後污染核電廠周遭地下水與海洋所造成意外核種釋放都是非常有效工具。 ;During the transport process, radionuclides can form mobile, toxic and harmful daughter products due to a series of decay reactions. None of the existing analytical models for single-species radionuclide transport are capable of accurately evaluating plume development of the daughter species of radionuclides because they do not account for mass accumulation from the parent species. Analytical models for multiple nuclides transport equations coupled with first-order sequential decay reactions can serve as fast and cost-effective tools for the predictions of the transport of the predecessor and successor species of radionuclide decay chain. In this project, we target to develop a rapid tool for rapidly predicting the plume behavior of an arbitrary length radionuclide transport decay chain. This fast tool is achieved based on generalized analytical solutions derived for a set of three-dimensional transient advection-dispersion equations (ADEs) coupled with sequential first-order decay reactions in a sem-infinite groundwater system. First, the coupled three-dimensional transient ADEs are converted to a set of ordinary differential equations (ODEs) via the Laplace transform and double finite Fourier cosine transforms. Subsequently, the solutions for each species are sequentially obtained by solving the resulting ODEs. The novel solutions will be expressed in terms of complementary error functions and exponential functions that are computationally efficient. Moreover, a graphical user interface (GUI) will be developed to facilitate the manipulation of the derived analytical model. Ultimately, we combine the derived analytical model with the health risk assessment model to evaluate the dose and risk. The model developed in this project will be a rapid tool for assessing the performance of deep geological disposal of radioactive waste or environmental impact of the accidental radionuclide releases such as the Fukushima nuclear disaster where multiple radionuclides leaked through the reactor, subsequently contaminating the local groundwater and ocean seawater in the vicinity of the nuclear plant.