### 博碩士論文 105624013 詳細資訊

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(Analytical model for multispecies scale-dependent dispersive transport subject to rate-limited sorption)

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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.

★ 多物種模式
★ 限制速率吸附
★ 尺度延散

★ multisepcies model
★ rate-limited sorption
★ scale-dependent dispersion

ABSTRACT -------------------------------- -------------------------------- ------- ii

LIST OF FIGURES -------------------------------- ----------------------------- vi
LIST OF TABLES -------------------------------- ----------------------------- viii
Notation -------------------------------- -------------------------------- ------------ x
1 Introduction -------------------------------- -------------------------------- ----- 1
1.1 Motivation -------------------------------- -------------------------------- 1
1.2 Literature review -------------------------------- ------------------------- 3
1.3 Research objectives-------------------------------- ---------------------- 9
2 Methodology -------------------------------- -------------------------------- -- 10
2.1 Mathematical model -------------------------------- ------------------- 10
2.2 Solution derivation -------------------------------- -------------------- 15
3 Results and discussion -------------------------------- ----------------------- 22
3.1 Convergence behavior of the derived solution --------------------- 22
3.2. Verification tests -------------------------------- ---------------------- 38
3.3 Effect of rate-limited sorption and scale-dependent dispersion on solute transport -------------------------------- -------------------------- 42
3.4 Comparison of different models -------------------------------- ----- 45
4. Conclusions -------------------------------- -------------------------------- --- 51
References -------------------------------- -------------------------------- ------- 53

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