非均質多孔性介質中交互式注入對混合效率之模擬

Simulations of Mixing Efficiency via Alternating Injection in a Heterogeneous Porous Medium

李政昕(Jheng-Sin Li)

指導教授 ： 陳慶耀

國立交通大學/工學院/機械工程系所/碩士(2018年)

摘要

本研究利用數值模擬探討在非均質性介質中的交互性注入對於混合效率的影響及規律性。在此模擬中，我們對注入流體使用的控制參數有: ( 1 )交互注入的時間間隔time interval ( Δt )，( 2 )兩注入流體間之黏度比值Atwood number ( A )，( 3 )對流效果以及擴散效果的比值Péclet number ( Pe )，以及對滲透率分布的控制參數 ( 4 ) 變異特徵variance ( s )，( 5 ) 特徵長度correlation length ( l )。

Atwood number數值越高表示兩注入流體的黏滯度差異越大，同時也會引發越劇烈的指狀物生成現象。Péclet number越高即代表在流體的混合中，對流作用會主導其進行，也就是指狀物的穿透及混合會變得更加的強烈，理論上有助於混合效率的提升。在此模擬中，我們將模擬的總時間t設置為1，所以Δt代表每次流體的注入間隔時間。

變異特徵s主要分為等於零(均質介質)、大於零(非均質介質)兩種情形，而當其值越大，會影響使得滲透率的極值差異越大；特徵長度l會影響單位面積內單一區塊的滲透率影響強烈與否，當l的值越大，單一區塊所占面積越廣，相對也會較劇烈的影響流體的流動情形，然而當l趨向於無限大或無限小時，也會近似於均質介質的狀態。
在均質介質中，交互注入後會使得流體層間產生隨機的混亂指狀物交互作用(randomly chaotic fingering interaction)，此現象會促使混合效率的提升，而本研究之模擬顯示黏性指狀物的生成軌跡會被滲透率之分布，亦即多孔性介質之不均勻分布劇烈地影響，這會導致在每層注入流體之介面都產生相似的指狀物，我們將此現象稱為渠道現象(channeling interaction)，有趣的是，非均質性介質所導致的渠道現象對於混合效率的趨勢影響與控制參數的高低有關，並沒有對某個控制參數有著單一的趨勢。

模擬的結果顯示在非均質介質中，較高的Péclet number會導致較差的混合效率，而這個趨勢是與均質介質中的趨勢相衝突的。我們還發現在均質介質中，交互注入產生的隨機混亂指狀物交互作用較強烈的環境下，例如:足夠短的交互注入時間間隔( Δt )、高Atwood number (A)、高Péclet number (Pe)，滲透率不一(非均質介質)的情況會導致這些隨機產生的指狀物被其限制在渠道中，使得隨機混亂指狀物交互作用降低，產生渠道現象，而在此現象主導的情況下，我們可以得知混合效率會因此較均質情況下來的差；反之，如果是在均質介質中，幾乎沒有或是極少的指狀物生成的流體條件下，因為滲透率不一產生的渠道現象反而會成為使混合效率變得更好的因素。

關鍵字

黏性指狀物 ； 交互注入 ； 強化混合效果 ； 非均質多孔性介質

並列摘要

In the study, we numerically verify how mixing efficiency is affected by alternating injection scheme in a heterogeneous porous medium. Permeability heterogeneity is characterized by two controlled parameters, i.e., the variance s and the correlation length l, and three controlled parameters correlated with injected fluid, i.e., injection time interval(Δt), viscosity difference between two fluids (Atwood number), relative measure of advection and diffusion effects (Péclet number) in the simulation. Higher Atwood number represents viscosity difference between two injected fluids is larger, and it generally leads to strong phenomenon of viscous fingering. Higher Péclet number means advection effects dominate mixing between fluids, and it results in more penetration and mixing between fingers, which usually enhances mixing efficiency.

In homogeneous condition, alternating injection cause randomly chaotic fingering interaction between fluid annuluses. However, since the fingering pattern is strongly affected by permeability distribution in heterogeneous condition, it result in similar fingering interface on each of injected layer of less viscous fluids. More orderly channeling interaction occurs in a heterogeneous medium instead of randomly chaotic fingering interaction.

As a result, higher Péclet number generally leads worse mixing efficiency in a heterogeneous medium, which might contradict the result found in a homogeneous case. In the cases which low or almost no fingering interaction occurs in homogeneous conditions, the presence of permeability heterogeneity causes the irregular fluid annuluses which promotes mixing efficiency. It results in better mixing efficiency in heterogeneous condition compared with the corresponding homogeneous cases. Nevertheless, in the cases which strong chaotic fingering interaction already exists in homogeneous conditions, e.g., sufficiently short alternating injection interval Δt, large viscosity contrast A and high Pe, the presence of permeability heterogeneity would constrain the randomly chaotic fingering interaction and favors the more orderly channeling interaction, so that mixing efficiency is deteriorated compared with the corresponding homogeneous cases.

並列關鍵字

viscous fingering ； alternating injection ； mixing enhancement ； heterogeneous porous medium

參考文獻

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[5] C.-Y. Chen, et al., “Controlling radialfingering patterns in miscible confined flows,” Physical Review E, 82, 56308, 2010.