非均質多孔介質中之徑向Hele-Shaw流場

Abstract

本研究根據Darcy-Cahn-Hilliard模型的擴散界面法發展出一套高精準度的數值方法，以此模擬將可互溶液體與不可互溶液體定量注入及線性注入各種多孔介質中，藉此模擬來分析將二氧化碳注入到石油油場之過程，並研究各種控制指狀物的方法，希望能減緩界面不穩定的程度，提高採油效率，並達到注入不同多孔隙油層之最佳化。多孔隙油層有不同的滲透率非均質性，假設variance及spatial correlation scale可分別控制多孔介質滲透率在數值大小及空間上的分布，即控制非均質性。本研究發現variance越大或spatial correlation scale越小時，亦即多孔介質之滲透率數值差異越大或空間上分布越分散時，不穩定現象如分裂、分枝、融合、擴展及界面互相競爭等會越劇烈，這符合直觀上認為的非均質性越高界面的不穩定現象越顯著的想法。此外亦發現variance越大時通道效應越顯著。另外在近期可互溶液體注入均質介質的實驗結果中界面周長L~t1/2的這項性質，可在本研究中擴大應用到可互溶液體定量注入非均質介質的結果。除此之外，可互溶液體定量注入的界面周長會比較小，所以就整體界面不穩定程度的分析而言，用定量注入所提升採油效率的效果比較好，而不可互溶液體則是線性注入的效果較好，由此我們可成功地做到多孔介質的注入最佳化。

In this study, we successfully use high-order numerical scheme and diffuse-interface method based on Darcy-Cahn-Hilliard model to simulate miscible and immiscible injection flows with constant and linear injection rate in various heterogeneous porous media. It can be applied to analyze the process whereby carbon dioxide is injected into an oil reservoir. We optimize the injection process by reducing the extent of fingering instability and hence increase oil recovery efficiency. Direct qualitative and quantitative comparisons regarding the pattern formations in different fluid miscibility conditions are presented in details. With the presences of heterogeneity, active secondary phenomena such as finger competition, side-branching, and tip-splitting are triggered. Prominences of fingering instability are quantitatively evaluated by the channeling and interfacial lengths. The channeling lengths show strong and monotonic dependences on the heterogeneous variances. In addition, the regime of slower growth of interfacial length at later times which was experimentally observed in homogeneous miscible injection is universally verified in heterogeneous porous media. Furthermore, we can successfully optimize the injection process by analyzing the channeling effects and fingering instabilities.