模擬飽和孔隙介質中化學溶解反應波前之型態發展

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賴庚辛(Keng-Hsin Lai) 查詢紙本館藏

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論文名稱

模擬飽和孔隙介質中化學溶解反應波前之型態發展
(Simulated Morphological Evolution of Chemical Dissolution Fronts in a Fluid-Saturated Porous Medium)

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摘要(中)

孔隙介質礦物內之反應化學傳輸造成地下流體流動型態改變與化學溶解反應波前的發展，對地球科學、石油工業與環境工程等都是一個重要的研究領域。數值模式為研究相關現象常用的工具，在這些模式中分別使用不同滲透係數-孔隙率模式描述孔隙率與滲透係數兩者間的關係，然而並無實驗數據證明何者較為合適；過去模式發展多考慮孔隙介質礦物之滲透係數為等向性，然而在自然孔隙介質礦物中滲透係數多存在異向性與異質性。本研究分別探討：(1)滲透係數-孔隙率模式；(2)滲透係數異向性對化學溶解反應波前型態發展之影響。第一部分結果顯示使用修正型Fair-Hatch模式與Kozeny-Carman模式預測到相似的孔隙率反應波前型態發展，而使用Verma-Pruess模式獲得較低的第一與第二臨界地下水上游壓力梯度。第二部份結果顯示在地下水上游壓力梯度較低時，滲透係數異向性主導側向流體捕捉進而影響流體集中機制，顯著改變形成單指狀波前的第一臨界地下水上游壓力梯度，然而滲透係數異向性對反應波前的影響隨著地下水上游壓力梯度增加而降低，形成雙指狀波前的第二臨界地下水上游壓力梯度未受到顯著的影響。

摘要(英)

The formation of dissolution-induced finger patterns in geological media is an important issue in a varity of geological settings and industrial applications. Numerical models have been developed to investigate the morphological evolution of chemical dissolution fronts within a fluid-saturated porous medium. In these numerical models, the properties that govern fluid flow through the geological medium are porosity and permeability, which may change in time and space due to mineral dissolution. To describe simultaneous changes in permeability and porosity induced by mineral dissolution, the permeability-porosity model has been incorporated into the numerical model. Several permeability-porosity models have been proposed but experimental data that justify one is superior from the others are limited. Furthermore, the permeability of geological medium has been considered to be isotropic, even though the permeability anisotropy is more likely to occur in naturally geological medium. Until recently the effect of permeability anisotropy has received little attention. Accordingly, this study attempts to investigate the effects of permeability-porosity models and permeability anisotropy on morphological evolution of a chemical dissolution front. A series of numerical simulation are performed to evaluate the relevant effects on the morphological evolution of a chemical dissolution front. Results show that the morphological evolution is similar in both the modified Fair-Hatch and Kozeny-Carman model. The Verma-Pruess model yields a relatively low primary and secondary critical upstream pressure gradient value owing to the flow-focusing effect enhanced by the stronger dependence of permeability on porosity. Our simulations demonstrate that the choice of the permeability-porosity function plays an important roles on the evolution patterns of the dissolution front. A adequate description of the permeability-porosity relationship may lead to a more realistic simulation of field problems. Capture of lateral flow is significantly influenced by permeability anisotropy ratios, thereby affecting the flow-focusing mechanism. Permeability anisotropy significantly modify the primary upstream pressure gradient. The effects of the permeability anisotropy on the evolution of a chemical dissolution front decrease with an increasing upstream pressure gradient. The difference between chemical dissolution fronts of the two media with permeability anisotropy ratio equal and smaller than unity diminishes when the upstream pressure gradient is large.

關鍵字(中)

★ 孔隙率反應波前
★ 滲透係數
★ 異向性

關鍵字(英)

論文目次

LIST OF FIGURES……………………………………....…………………………..……….v
LIST OF ABBREVIATIONS....................................vii
LIST OF SYMBOLS………………………………………….………………...…………..viii
1. Introduction…………………………………………………………………………..…1
1.1 Background…………………..……………………………….…..……………………1
1.2 Literature review……………………………………………….…..…………………..3
1.3 Permeability-porosity models…………………………………….…..…..6
1.4 Permeability anisotropy…………………………………………….…..………………8
1.5 Objectives…………………………………………………………….….………...….9
2. Mathematical model…………………………………..………………….……………...12
2.1 Governing equations of the coupled nonlinear system………..................………….....12
2.2 Non-dimensional governing equations………………………………….…………….16
2.3 Solution methods………………………………………………………….…………..17
3. Results and discussions………………………………………………………………..25
3.1 Effect of permeability-porosity models…………………………28
3.1.1 Case I Homogeneous media with single local non-uniformity……….28
3.1.2 Case II Homogeneous media with two local non-uniformities…………..…….30
3.2 Effect of permeability anisotropy……………………………………….31
4. Conclusions………………………………………………………………………………48
References……………………………………………………………………………………50
Appendix……………………………………………………………………………………..55

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指導教授

陳瑞昇

審核日期

2014-7-29

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