利用理論模型和動態蒙地卡羅模擬探討客體分子在水合物中藉由躍遷的擴散行為

Abstract

客體分子在籠形水合物晶格中的擴散被認為是一系列的客體分子躍遷，從一個水籠子到另一個相鄰的空水籠子，其由自然形成之水洞促進並且在躍遷的過程中沒有顯著的晶格重構。在這項工作中，我們提出了一個解析模型，可以根據客體分子躍遷的速率決定sI籠形水合物籠中氣體分子的平衡分布和擴散係數，不須藉由實驗得到之數據。此外，我們利用動力學蒙特卡羅模擬以驗證此解析模型。我們由解析模型得到之客體分子平衡分布、輸送（transport）和跳躍（Maxwell-Stefan）擴散係數以及熱力學校正因子皆與模擬結果非常一致。除此之外我們還可以知道影響輸送性質的主要躍遷路徑。我們將利用平衡路徑採樣計算之客體分子躍遷的速率常數代入此解析模型，可以得到在溫度為275 K時甲烷之輸送擴散係數為5.06×10-14 m2/s，這與最近在相同溫度下的實驗測量值4.00×10-14 m2/s非常接近。此外，此解析模型可用於描述龍形水和物中客體分子和外界交換以及在晶體內擴散的過程，可以用於計算二氧化碳置換天然氣水合物儲集層中甲烷的速率。

Guest migration in clathrate hydrates is a slow but important process for reaching thermodynamic equilibrium. The transport of guest molecules in a hydrate lattice is considered as a series of hopping events from an occupied cage to an empty neighboring cage facilitated by water vacancies and without significant lattice restructuring in the bulk. In this work, we developed an analytical model for determining the equilibrium distribution and the diffusivity of gas molecules in the cages of sI clathrate hydrate based on their hopping rate. Furthermore, kinetic Monte Carlo simulations were performed to verify the analytical model. The equilibrium occupancies, transport (Fickian) and jump (Maxwell-Stefan) diffusion coefficients, and the thermodynamic correction factors determined from the analytical model are in good agreement with the simulation results. The predominant hopping pathway for the transport properties can also be obtained. Using the hopping rate constants determined based on equilibrium path sampling calculations, we obtain methane transport-diffusion coefficient at 275 K to be 5.06×10-14 m2/s, which is in good agreement with the recent experimental measurements (4.00×10-14 m2/s at 275 K). In addition, the analytical model is useful for modeling the solid-state guest exchange process, which is of great importance in the replacement of methane with CO2 in natural gas hydrate reservoirs.