延散效應對水岩交互作用反應波前的影響

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賴庚辛(Geng-Xin Lai) 查詢紙本館藏

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論文名稱

延散效應對水岩交互作用反應波前的影響
(Effect of Dispersion on Reactive Fronts of Water－Rock Interaction)

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摘要(中)

當地下流體因水頭差而流動，其流動過程常會帶動化學物種之遷移，使得地下流動流體、多孔隙介質與化學物種之間產生溶解反應，使得多孔隙介質之孔隙率改變，進而改變多孔隙介質之水力傳導係數等水文地質物理特性參數。當反應流體優先進入孔隙率較高地區，將會造成反應波前的不穩定現象，反應波前的型態將會受到地下水上游壓力梯度及孔隙率較高地區分佈影響，其中擴散/延散效應可壓制反應波前的不穩定現象。
過去的研究多為探討地下流體流動緩慢下之現象，只考慮化學物種之擴散傳輸，在模式上多忽略了延散傳輸之影響，然而在許多情況下地下水流速不見得會緩慢，此條件下化學物種延散傳輸顯得比擴散傳輸更為重要，因此本研究在數值模式中加入延散傳輸，並比較擴散傳輸及延散傳輸對反應波前的影響。本研究之數值方法耦合地下流體流動、化學物種傳輸、地球化學反應之非線性偏微分方程組，利用逐步迭代法結合隱式有限差分法求解。
經數值模式分析結果發現，延散度將影響反應波前形態的發展，延散度增加將造成單波鋒反應波前縮短、雙波鋒反應波前合併。當上游地下水壓力梯度在2到5之間、初始雙擾動之間距在1.25至2.25之間，雙波鋒反應波前之型態將會發展為單波鋒。

摘要(英)

While flowing through a porous medium, migration of solute causes mineral dissolution thereby increasing its porosity and ultimately permeability. The reactive fluid flows preferentially into highly permeable zones, which are therefore dissolved most rapidly, producing a further preferential permeability enhancement. Thus, the reactive front may be unstable. A reactive front will be affected by upstream pressure gradient and initial local non-uniformities. Previous studies neglected dispersion process and considered that solute is only transported by diffusion. This study takes dispersion into consideration and investigates the effect of dispersion process on evolution of reactive front. An implicit sequential iteration approach method is used to solve a set of nonlinear equations coupled with fluid flow, species transport, and fluid-rock reaction. Results show that the dispersion have significant effects on shape of reactive front. Increasing dispersion will cause that double fingers develop into single finger in cases that upstream pressure gradient is between 2 and 5, initial local non-uniformities spacing is between 1.25 and 2.25.

關鍵字(中)

★ 延散效應
★ 反應波前
★ 傳輸
★ 波鋒行為圖

關鍵字(英)

★ dispersion
★ reactive front
★ front behavior diagr

論文目次

目錄
中文摘要.................................................i
英文摘要................................................ii
目錄.....................................................iii
圖目錄...................................................v
表目錄..................................................xi
符號說明...............................................xii
一、緒論...............................................1
1-1 前言.............................................1
1-2 文獻回顧.........................................2
1-3 研究目的.........................................4
二、模式推導與求解.....................................5
2-1 多孔隙介質溶解反應...............................5
2-2 地下水流動.......................................6
2-3 溶質傳輸.........................................8
2-4 無因次化........................................12
2-5 初始條件........................................14
2-6 邊界條件........................................16
2-6-1壓力邊界條件.................................16
2-6-2濃度邊界條件.................................17
2-7 方程式離散......................................17
2-7-1無因次化孔隙率變化方程式離散化...............17
2-7-1無因次化地下水流方程式離散化.................18
2-7-3無因次化溶質傳輸方程式.......................20
2-8 聯立微分方程式求解..............................24
三、結果與討論........................................26
3-1 初始擾動為單一擾動之模擬結果....................28
3-2 初始擾動為等強度雙擾動之模擬結果................33
3-3 延散效應對反應波前之影響........................51
3-3-1初始擾動為單一擾動...........................51
3-3-2初始雙擾動為等強度雙擾動.....................53
3-4 波鋒行為圖......................................62
3-5 無因次水力傳導係數空間分佈......................65
3-6 無因次壓力空間分佈..............................70
四、結論與建議........................................75
4-1 結論............................................75
4-2 建議............................................75
參考文獻................................................76

參考文獻

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指導教授

陳瑞昇、倪春發
(Jui-sheng Chen、Chuen-fa Ni)

審核日期

2008-7-22

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