多物種汙染傳輸模式為模擬降解污染物(含氯有機溶劑、殺蟲劑、核種放射性物質、肥料與農藥等)宿命傳輸過程的有效工具。為簡化數學推導的過程，前人的多物種模式大多假設瞬間平衡吸附與常係數延散。然而許多文獻指出尺度延散與限制速率吸附對於汙染物的傳輸有重大影響，尺度延散是指延散度會隨著溶質傳輸距離增加，而限制速率吸附則考慮了吸附項與溶解項在溶質質量上的交換速率。前人已發展出分別考慮限制速率吸附與尺度延散的多物種傳輸模式，但並沒有能整合兩者的多物種傳輸模式。因此本研究發展出同時考慮尺度延散與限制速率吸附之多物種污染物傳輸的解析解模式。求解過程使用廣義型積分轉換與Laplace轉換消除空間與時間的微分項，最後使用一系列逆轉換求得原值域的解析解。解析解的驗證是利用有限差分的數值方法求解相同的控制方程式，並把數值模式所得結果與本研究之解析解做對照，兩者結果相當吻合。最後新的模式將作為基準與前人模式做比較，以了解尺度延散與限制速率吸附之綜合效應對污染傳輸的影響，在比較本模式(SR)和傳統常係數延散與平衡吸附的模式(CI)後，結果顯示CI模式在模擬多物種汙染物傳輸時會高估或低估汙染物濃度的影響。

Multispecies transport models are effective tools for predicting the transport and fate of decaying or degradable contaminants such as dissolved chlorinated solvents, pesticides, radionuclides, and nitrogen chains in the subsurface environment. For simplification of solution, the existing multispecies transport analytical models are currently derived assuming instantaneous equilibrium sorption and constant dispersion. However, both experimental and theoretical research indicate that both rate-limited sorption and scale-dependent dispersion have profound effects on the movement of contaminants in the subsurface. Although models have been derived assuming instantaneous sorption or scale-dependent dispersion individually, both processes have not been integrated into the governing equations of a single analytical model. The goal of this study is to fill this gap and to develop a multispecies transport analytical model in which first-order reversible kinetic sorption reaction equation system is incorporated into two sets of simultaneous advection-dispersion equations with scale-

dependent dispersion coefficients coupled by sequential first-order decay reactions. The analytical solution to the complicated governing equation system are obtained by using the Laplace transform and the generalized integral transform technique. The correctness of the derived analytical model and of the corresponding computer code are proved by the excellent agreements between the computational results obtained from the derived model and those obtained with a numerical model where the same governing equations are solved using the advanced Laplace transform finite difference method. The new model is compared to a previous model to demonstrate the synergy of the rate-limited sorption and scale-dependent dispersion on multispecies transport. Comparison of the model developed in this study(labelled SR) and a constant dispersion model with instantaneous sorption(labbled CI), shows that solute concentration may be underestimated or overestimated in the CI model.

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