Linear Stability Analysis of Two-phase, Two-Component Flow in Porous Media

Physics > Fluid Dynamics [Submitted on 18 Jun 2026] Title:Linear Stability Analysis of Two-phase, Two-Component Flow in Porous Media View PDF HTML (experimental)Abstract:Viscous fingering instabilities during fluid displacement in porous media can compromise the efficiency of applications such as enhanced oil recovery, CO2 sequestration, and groundwater remediation. While extensive research exists on linear stability analysis for fully immiscible and fully miscible displacements, the intermediate case of partially miscible flow with limited mass transfer between phases remains largely unexplored. This study extends linear stability analysis to a two-phase, two-component system that accounts for gravity effects, fractional flow, capillary forces, mechanical dispersion, and interphase mass transfer, focusing on the case where a partially miscible gaseous fluid displaces a liquid. We formulate an eigenvalue problem to characterize instability growth rates and cutoff wavenumbers. The resulting ordinary differential equations have discontinuous coefficients at the transition from two-phase to pure-liquid flow, resulting in discontinuous eigenfunction derivatives. We derive jump conditions for the derivatives at this transition, and solve the eigenvalue problem using the matched initial value problem method. Results demonstrate that mass transfer has a pre-dominantly stabilizing effect by reducing viscosity contrast and altering shock properties at the displacement front. This stabilizing influence is particularly pronounced for high viscosity contrasts and dampens gravity-induced instability in upward displacements. Mass transfer most significantly affects the perturbation growth rate, while its effect on the cutoff wavenumber is less pronounced. We identify a critical value for the dimensionless longitudinal dispersion coefficient where both growth rate and cutoff wavenumber are maximized, suggesting complex interactions between capillary forces and mechanical dispersion. Current browse context: physics.flu-dyn References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer (What is the Explorer?) Connected Papers (What is Connected Papers?) Litmaps (What is Litmaps?) scite Smart Citations (What are Smart Citations?) Code, Data and Media Associated with this Article alphaXiv (What is alphaXiv?) CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub (What is DagsHub?) Gotit.pub (What is GotitPub?) Hugging Face (What is Huggingface?) ScienceCast (What is ScienceCast?) Demos Recommenders and Search Tools Influence Flower (What are Influence Flowers?) CORE Recommender (What is CORE?) arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.