發展一同時適用於可互溶與不可互溶界面之擴散界面數值方法及其於二氧化碳封存之應用與模擬

Abstract

多相流流場是比一般流體力學相對複雜許多的物理現象，其包含流體與流體間的分子 力學運動。在多相流流場中不考慮化學反應情況下，大致上可依照流體間界面的情況分 為兩種：可互溶與不可互溶之流體。在研究多相流流場中，流體界面應力均僅考慮於不 可互溶間產生之表面張力，而若二流體為可互溶，則視為無應力存在。而不可互溶之流 體研究中，流體界面為狹小的界面(sharp interface)，這種物理現象在數值模擬上會造 成流體分布在某個區間產生如步階函數一樣的變化而造成數值發散。1958 年Cahn and Hilliard 兩位學者由分子凡得瓦力理論，提出兩種流體界面能量(表面自由能)之觀點， 並發展成一套利用相場(phase field)分佈而形成之[擴散界面](diffuse-interface)， 同時並可來描述流體間界面運動之方程式。若應用此一概念，並擇取適合之界面能量函 數，則將可同時適用於可互溶與不可互溶之流體之界面分析。 同時為因應大氣中溫室氣體(二氧化碳、甲烷及氫氟碳化物等)的濃度急遽上升，二氧 化碳封存技術亦為現今研究之重要課題。二氧化碳封存技術可大致區分為注入與封存兩 個部分。在整個注入過程中可視為流體流過一多孔隙材質之不可互溶流場。而當封存在 地下鹽水層後，二氧化碳會開始由超臨界狀態回復到一般狀態時而開始滲透(溶解)於地 下鹽水層中。故而分析注入之不可互溶流場與封存後二氧化碳溶解之可互溶流場情況， 便成了能源研究的重點之一。 本計畫為全期三年之計畫，重點在於完成一套可模擬在可互溶與不可互溶之流體的兩 相流流場之擴散界面數值方法，並應用此數值方法於多孔隙流場之二氧化碳封存技術。 其主要執行內容如下：第一年期計畫之研究重點首先為發展針對多相流流場在多孔性材 質(或Hele-Shaw cell)之界面擴散法流場數值模擬程式，並分別在流體為可互溶與不可 互溶的情況下與先前或同時進行之實驗研究成果進行比對，充分驗證數值模擬程式之正 確性。第二年期計畫則針對二氧化碳在注入與封存兩個不同過程中的物理現象進行模 擬，並分析在各種不同的流場環境下(包含不可互溶之超臨界二氧化碳注入過程及與鹽水 互溶之二氧化碳穩定性分析)於不同擴散效應、黏滯效應與孔隙滲透率下，對封存過程與 後續二氧化碳穩定性之影響。第三年期計畫將利用平行運算技術來提高程式計算效率， 試圖將物理模型拓展至三維流場，以比較二維與三維流場現象差異。

The mixing phenomena of fluids are generally classified as being miscible or immiscible. An immiscible system is characterized by a strict interface, whose boundary cannot be crossed by the molecules of adjoining liquids. This high potential barrier can be explained by different intermolecular interactions within the mixture components on molecular scale. A surface tension is commonly introduced to define the macroscopic effects of the interfacial potential barrier. On the other hand, the intermolecular forces between miscible fluids are much smaller. The molecules of initially separated components are assumed to freely codiffuse, so that there is no surface tension on the fluids’ boundary. Based on the above arguments, the two systems of miscible/immiscible are usually modeled differently into the governing equations. For instance, an additional term of surface tension acting at a moving boundary is included into the momentum equations for an immiscible system, while the miscible system is solved associated with a conventional advection-diffusion equation of concentration followed by the Fick’s Law. Nevertheless, there are cases of the miscible liquids, for which the intermolecular forces cannot be neglected, and apparent interfaces are visible for a long period time. As a result, it is also necessary to describe the concept of interfacial tension of a slowly miscible system. On the other hand, CO2 capture and storage are important issues due to the greenhouse effects. In general, the complete procedure of CO2 storage consists of two major steps, eg. injection and storage. In the injecting process, the super-critical CO2 is injected into a porous reservoir, whose condition is immiscible. Afterward, CO2 would resume to normal state, in which is miscible to the environmental brine. As a result, both immiscible/miscible interfaces occur through entire CO2 storages. In this proposal, the diffuse-interface model in a porous medium (or Hele-Shaw cell) will be established in the 1st year. By considering the free surface energy within the diffuse interface, the approach is capable to catch the interfacial phenomena for both a miscible system. Afterward, the numerical programs developed will be applied to simulate the CO2 storages in the 2nd year. Both the immiscible flow fields within injecting processes and the dissolution of CO2 to the underground brine will be studied numerically. In the 3rd year, the simulations will be extended to full three dimensions implemented by parallel computing techniques.