近年來，大多數的多物種解析模式都假設溶解相和吸附相之間的溶質交換是瞬間平衡吸附的。然而在過去的研究當中，所發展出的限制速率吸附的解析模式已證明限制速率吸附的過程會影響地下環境中污染物濃度的預測。而多維度、多物種傳輸模式在預測某些污染物，如放射性核種、氨氮轉化物和含氯有機溶劑等化學混合物的傳輸方面將具有更實際的應用，主要原因為這些污染物會涉及一階的衰變或降解反應。
本研究發展了考慮限速吸附作用下的二維多物種與其降解相關副產物的半解析解模式。對由偏微分方程描述的多污染物的耦合移流-延散方程 (ADE), 依序透過積分轉換的應用求得線性代數方程。每個物種的污染物濃度是通過求解線性代數方程並將其解重新轉換回原始時空域來計算的。首先將所推得的解析模式與數值模式結果進行驗證，其高度的吻合證明了所發展模式計算的準確性和可靠性。接著探討不同吸附速率對於污染團遷移的影響，對於平衡吸附和限制速率吸附模式的比較，當吸附速率常數達到 50 year-1 時，其遷移的範圍幾乎相同。隨著吸附速率常數的減小，限制速率吸附模式將會計算較寬和較高濃度的污染團，也說明了當考慮平衡吸附模式無效時，應使用本研究新導出的解析模式。

In recent years, most studies using an analytical multispecies model have assumed the mass transfer between the dissolved and the sorbed phases to be equilibrium-controlled. However, in some previous studies analytical models incorporating rate-limited sorption process have been developed which demonstrate that the rate-limited sorption process can affect the accurate prediction of the contaminant concentration in the subsurface environment. However, a multidimensional, multispecies transport model would have more practical applications for predicting the transport of chemical mixture of some contaminants such as radionuclides, nitrogen and dissolved chlorinated solvents which generally involve a series of first-order or pseudo first-order decay/degradation chain reactions.
This study introduces a semi-analytical model for the two-dimensional multispecies transport of contaminants and their degradation-related by products under the action of rate-limited sorption. Coupled advection-dispersion equations (ADEs) for multiple contaminants as described by a system of partial differential equations are reduced to obtain linear algebraic equations through sequential application of integral transforms. The contaminant concentration of each species is calculated by solving the linear algebraic equations and retransforming the solutions back to the original time-space domain. Comparison of the results of the derived analytical model with those obtained with the numerical model show, high similarity proving the accuracy and reliability of the new model. Investigation on how the sorption rate affects contaminant plume migration indicates the identical plumes for equilibrium-controlled and rate-limited sorption models and when the sorption rate constant reaches 50 year-1. A wider plume and the high concentration level rate-limited model as the sorption rate constant decreases, implying the newly derived solutions should be used when the equilibrium-controlled model is invalid.

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