用於生產多種工業產品所使用的化學溶劑在不當處理的情況下會滲入地下水造成污染，其中四氯乙烯(Tetrachloroethylene，PCE)及其降解的子物種等含氯有機溶劑為工業場址中常見的污染物。現地污染場址內常見多個污染源釋出的情況，然而在過去發展污染傳輸模式的諸多研究中，大部分研究所考慮的邊界源傳輸模式在模擬場址內污染源的污染傳輸問題時會受到限制且難以廣泛應用。考慮場址內污染源（後稱內部污染源）的污染傳輸模式可以模擬污染場址中多個污染源的釋出情形，且模式中所考量的限制速率吸附可以避免低估可降解污染物之濃度和線性平衡吸附不適用的情況。本研究欲發展考量多個內部污染源的多物種污染物傳輸半解析解模式，且模式考慮移流、延散、限制速率吸附和一階降解反應等前人研究中所納入的重要傳輸機制。此半解析解推導依序應用Laplace轉換、finite Fourier cosine轉換及廣義型積分轉換消去時間及空間微分項，將偏微分方程式轉換為代數方程式進行求解，再利用一系列逆轉換求得半解析解。本模式的最大特點在於可以模擬多個內部污染源釋出的情況，並可以在任意地下水流速度下進行模擬，其不僅能提供更精確的污染團分布情形，亦能替代過去僅考慮邊界污染源的模式作為初步評估污染整治的基礎。

Chemical solvents used in the production of many industrial products can seep into groundwater and cause pollution if improperly executed. For example, PCE (tetrachloroethylene) and the daughter species of it are the common chlorinated solvents in industrial sites. The release of multiple internal pollution sources is common to observe at the in-situ contaminated sites. However, in many previous studies on the development of contaminant transport models in the past, the models considered boundary sources in most studies would be limited and difficult to be widely used when simulating the contaminant transport problems of multiple internal pollution sources. Contaminant transport model considering internal sources can simulate the release of multiple pollution sources inside the contaminated site, and the rate-limited sorption is considered in the model to avoid underestimating the concentration of degradable pollutants and the situation where linear equilibrium sorption is not applicable. This study develops a semi-analytical model of multi-species contaminant transport subject to multiple internal pollution sources, which also considers important transport mechanisms included in previous studies, such as advection, dispersion, rate-limited sorption and first-order decay. The derivation of this semi-analytical model applies Laplace transform, finite Fourier cosine transform, generalized integral transform and a series of inverse transform. The greatest contribution of this model is that it can simulate the release of multiple internal pollution sources at the contaminated sites, and can be simulated at any groundwater flow velocity. It can not only provide a more accurate prediction for the distribution of the pollution plume, but also replace the previous models that only considered boundary source as the basis for preliminary assessment of pollution remediation.

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