Two-Phase Flows in Karstic Geometry


Multiphase flow phenomena are ubiquitous. Common examples include coupled atmosphere and ocean system (air and water), oil reservoir (water, oil, and gas), and cloud and fog (water vapor, water, and air). Multiphase flows also play an important role in many engineering and environmental science applications. In some applications such as flows in unconfined karst aquifers, karst oil reservoir, proton membrane exchange fuel cell, multiphase flows in conduits, and in porous media must be considered together. Geometric configurations that contain both conduit (or vug) and porous media are termed karstic geometry. Despite the importance of the subject, little work has been performed on multiphase flows in karstic geometry. In this paper, we present a family of phase-field (diffusive interface) models for two-phase flow in karstic geometry. These models together with the associated interface boundary conditions are derived utilizing Onsager's extremum principle. The models derived enjoy physically important energy laws. A uniquely solvable numerical scheme that preserves the associated energy law is presented as well.


Mathematics and Statistics

Keywords and Phrases

Aquifers; Fuel cells; Geometry; Hydrogeology; Multiphase flow; Petroleum reservoir engineering; Petroleum reservoirs; Phase interfaces; Porous materials; Energy law; Extremum principles; Interface model; Karstic; Phase field models; Time discretization; Unique solvability; Two phase flow; Diffusive interface model; Karstic geometry; Onsager's extremum principle; Phase-field model; Two-phase flow

International Standard Serial Number (ISSN)

0170-4214; 1099-1476

Document Type

Article - Journal

Document Version


File Type





© 2014 John Wiley & Sons, All rights reserved.

Publication Date

01 Nov 2014