本研究以數值模擬的方式，分析多膜管系統設計對於氫氣滲透之影響及運用最佳化計算尋找多膜管間最佳的相對角度。藉由數值結果，了解薄膜管間的排列方式及相對角度對於流場改變伴隨氫氣滲透之影響，並提供膜管操作參數之建議，作為實驗之參考依據，本文主要分為兩大部分，如下所述。
在本研究的第一部分為研究單膜管和串列式雙膜管系統對氫氣分離及二氧化碳富集之影響，在單管系統中測試了四種不同的富氫氣體，且在雙管系統中考慮雷諾數（Re）、兩膜管之間的距離以及壓力差三個參數，同時，通過檢查當地的捨伍德數量來強調界面運輸現象。模擬結果顯示，無論是哪種進料氣體混合物，當雷諾數從1增加到100時，氫氣回收率和二氧化碳富集皆顯著降低，這表明雷諾數在氫氣滲透和二氧化碳富集中起著重要作用，且應控制在Re≤10。在低雷諾數和短間距時，兩膜管之間的相互作用產生，使得雙膜管系統中的單一膜管回收率明顯低於單膜管系統，且因前管的流動阻力和濃度極化現象而導致後管的的氫氣滲透效果降低。然而，當雷諾數高達100時，相互作用和濃度極化幾乎可以忽略不計。
第二部分中，考慮了單膜管、雙膜管、三膜管和四膜管系統在雷諾數1-50範圍內的現象。為了最大限度地提高系統中的氫氣回收和二氧化碳的濃度，採用兩階段優化設計膜管位置的配置。在第一階段，應用參數掃描先尋找膜管間可行的角度組合；在第二階段，採用Nelder-Mead單純形法的演化計算來找出膜管最佳的排列位置，其中選擇出口氫氣濃度作為目標函數，而優化的目標則是減小前管對後管的濃度極化影響。結果顯示，管數量的增加提高了優化效率。與串列式膜管系統相比，在Re = 10時的最佳化排列可將氫氣回收率提高12.2％，而二氧化碳富集可提高7％

In this study, numerical simulation was conducted to analyze the effects of multi-membrane tube system design on hydrogen permeation and optimization was carried out to determine the best relative angles between multi-membrane tubes. The study was divided into two parts.
In the first part of this research, H2 separation and CO2 enrichment in a duct using a single membrane tube and two membrane tubes in tandem are investigated numerically. Four different hydrogen-rich gases are tested in the single tube system, while three parameters of Reynolds number (Re), the distance between the two membrane tubes, and pressure difference are considered in the dual tube system. Meanwhile, the interfacial transport phenomena are underlined via examining the local Sherwood number. The results suggest that the H2 recovery and CO2 enrichment decrease dramatically when the Reynolds number increases from 1 to 100, regardless of which gas mixture is fed. This reveals that the Reynolds number plays a prominent role in H2 permeation and CO2 enrichment, and should be controlled at Re ≤ 10. The interaction between the two tubes are evidently exhibited at low Reynolds numbers and short distances, so the H2 recoveries by the two individual tubes are significantly lower than that by the single tube. The flow retardation and H2 concentration polarization from the leading tube upon the trailing tube deteriorate the H2 permeation of the latter. However, when the Reynolds number is as high as 100, the interaction and concentration polarization are almost ignorable.
In the second part of this research, single-, double-, triple-, and quadruple-tube systems with palladium (Pd) membranes are considered, while the Reynolds number (Re) is in the range of 1-50. To maximize H2 recovery and CO2 enrichment in the systems, their configurations are designed using a two-stage optimization. In the first stage, the parametric sweep technology is applied to find the feasible angle combination of the membrane tubes. In the second stage, the evolutionary computation of the Nelder-Mead simplex method is adopted to refine the locations of the tubes, where the exit H2 concentration is chosen as the objective function. On account of the scavenging waves stemming from the upstream tubes, the goals of the optimization is to diminish the concentration polarization of the upstream tubes on the downstream ones. The predictions indicate that an increase in the number of tubes raises the optimization efficiency. Compared to the tubes in tandem, the optimized configuration at Re=10 can improve the hydrogen recovery up to 12.2%, while the CO2 enrichment can be intensified by up to 7%.

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