二相流在破裂介質中的宏觀模式(I)

Abstract

這是一個三年期的計劃。我們建議探討在破裂介質中的二相流的宏觀模式。一個 已知的事實是二相流在獨立的區塊中的流動雖然很緩慢，但它對流體在整體上的表現 卻佔了十分重要的角色，它具有所謂的調節功能。表現在外的一種形式是在不同區塊 會有不同的time scale 的現象。此現象在宏觀模式下的單孔模式(single-porosity model)中無法看出，但期望在宏觀模式下的雙孔模式(dual-porosity model)可看出 來。在之前的研究中，我們考慮了區塊為小尺寸及中尺寸的情形，並證明了它們會收 歛到某種的雙孔介質模式。且這些模式在區塊與整體之間確有不同的time scale 的現 象。我們希望繼續先前的工作討論柱形區塊及混和型區塊所構成的破裂介質的情形。 目的就是想找出各種不同區塊的微觀模式所對應的宏觀模式。

for two-phase flows in fractured media. It is known that although flow moves slow in matrix blocks, it has profound influence on global flow behaviors. Usually, different time scales in different regions can be observed. This phenomenon does not show in single-porosity models, but it is expected to be captured in dual-porosity models. In previous study, we consider small-sized block case and medium-sized block case, and prove they converge to some dual-porosity models. They do show different time-scales in matrix blocks and fracture system. We plan to continue this effort to study column-block type fracture media and mixed-block fracture media. The purpose is to find the relations between microscopic models and macroscopic models for two-phase flows in fractured media.