求解系列一階序列降解反應耦合移流-延散方程組所得的多物種傳輸解析解模式為同時決定如放射性核種、溶解的含氯有機化合物、農藥及氨氮衰減性污染物的母物種及子物種污染團移動不可或缺的且有效的工具。儘管前人提出一些多物種傳輸解析解模式，這些文獻可獲得之多物種傳輸解析解模式大部分是考慮常係數延散係數推導而得。近幾十年來，許多研究指出延散度會隨著溶質傳輸移動距離而隨之增加，延散度隨溶質傳輸距離而增加主要由孔隙介質中的水力特性變化造成，文獻中目前並無考慮尺度延散之多物種傳輸解析解模式。本研究發展一個考慮尺度延散的多物種傳輸解析解模式。此解析解模式應用 Laplace轉換消除時間項及廣義型積分轉換消除二階空間微分項求解，發展的解析解模式將和使用Laplace轉換有限差分之數值解模式比較確認解的正確性。結果指出，解析解與數值解兩者非常吻合。最後再將考慮尺度延散之解析解模式與已發表之常係數延散度解析解模式作比較以釐清尺度延散係數對多物種傳輸的影響。結果顯示，當延散主導傳輸行為或考慮衰變常數時，前人所提出尺度延散之解析解模式與常係數延散解析解模式之間的傳輸參數的關係式是無效的。

It is essential to develop multispecies transport analytical models based on a set of advection-dispersion equations (ADEs) coupled with sequential first-order decay reactions for the synchronous prediction of plume migrations of both parent and daughter species of decaying contaminants such as radionuclides, dissolved chlorinated organic compounds, pesticides and nitrogen. Although several multispecies transport analytical models have already been reported, those currently available have primarily been derived based on ADEs with constant dispersion coefficients. Over the past three or four decades, however, there have been a number of studies demonstrating that the dispersion coefficients are scale-dependent. In other words, the dispersion coefficient increases with the solute travel distance as a consequence of variation in the hydraulic properties of the porous media. To the best of our knowledge, multispecies transport analytical models associated with distance-dependent coefficients have not been discussed in the published literature. This study presents a novel multispecies transport analytical model with a distance-dependent dispersion coefficient. The analytical model is developed using the Laplace transform with respect to time and the generalized integral transform technique with respect to the spatial coordinate.The correctness of the derived analytical solutions is confirmed by comparing them against the numerical solutions obtained using the Laplace transform finite difference (LTFD) technique. Results show perfect agreement between the analytical and numerical solutions. Comparison of our new distance-dependent dispersion multispecies transport analytical model to an analytical model with constant dispersion is made to illustrate the effects of the dispersion coefficients on the multispecies transport of decaying contaminants. Results show that the relationship of the transport parameters between the scale-dependent dispersivity model (SDM) and constant dispersivity model (CDM) is not valid when the dispersion process dominates the transport, or when the decay constants are considered.

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