擬譜法於多孔隙介質之最佳化控制分析

Abstract

在一油滴抽取的過程中，在多孔隙介質內的油滴因為毛細作用的抗力而被困在毛細管中不能輕易被抽出，因此在抽取過程中會額外施加一振動頻率，使油滴產生共振抵抗毛細作用的抗力，因此提升油滴抽取的效率。而本研究即以在抽取過程中最低能量消耗為目標建構一最佳化控制問題，並調整額外施加之振動頻率與外力以達使油滴可抽出之最小距離。 為解決此一最佳化控制問題，本研究使用擬譜法最佳化控制解決。擬譜法最佳化控制為一數值分析方法，其過程首先為離散化原函數簡化原函數的複雜度，並選取適當之節點逼近，其後在加入微分轉換與積分轉換處理函數中的微分積分項，最後再加入可容許誤差值彌補離散化過程後的微小偏差，再經過一連串的轉換後，便能使原問題轉變為一非線性問題，再利用GAMS、MATLAB等軟體便能得到此一問題之解答。

In the process of extracting oil, it is common that there is still a large amount of oil remaining in the crust because of the tension force and resistance caused by the capillary in the porous media. To eliminate the trapped oil in the porous media, a excitation frequency is applied and causes oil blobs resonance. Because of the resonance, oil blobs can easily cancel out the resistance of capillarity and tension force. In this research, an optimal control problem is constructed in order to minimize the energy consumption by adjusting the excitation frequency and extracting force. Pseudospectral method, which is a numerical method specializing in solving partial differential equation, is applied to simplify the origin function and transforms the origin optimal control problem into a nonlinear program. Therefore, this problem can eventually be solved by GAMS.