A Monte Carlo Algorithm for Immiscible Two-Phase Flow in Porous Media

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• 作者：Isha Savani ; Santanu Sinha ; Alex Hansen ; Dick Bedeaux…
• 关键词：Dynamical pore network models ; Markov Chain Monte Carlo ; Metropolis Monte Carlo ; Immiscible two ; phase flow ; Ergodicity
• 刊名：Transport in Porous Media
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：116
• 期：2
• 页码：869-888
• 全文大小：1295KB
• 刊物类别：Earth and Environmental Science
• 刊物主题：Geotechnical Engineering & Applied Earth Sciences; Industrial Chemistry/Chemical Engineering; Hydrology/Water Resources; Civil Engineering; Hydrogeology; Classical and Continuum Physics;
• 出版者：Springer Netherlands
• ISSN：1573-1634
• 卷排序：116

文摘

We present a Markov Chain Monte Carlo algorithm based on the Metropolis algorithm for simulation of the flow of two immiscible fluids in a porous medium under macroscopic steady-state conditions using a dynamical pore network model that tracks the motion of the fluid interfaces. The Monte Carlo algorithm is based on the configuration probability, where a configuration is defined by the positions of all fluid interfaces. We show that the configuration probability is proportional to the inverse of the flow rate. Using a two-dimensional network, advancing the interfaces using time integration, the computational time scales as the linear system size to the fourth power, whereas the Monte Carlo computational time scales as the linear size to the second power. We discuss the strengths and the weaknesses of the algorithm.