Probabilistic stability analysis of multiphase flow in porous media Conference Paper uri icon

abstract

  • 2018 Society of Petroleum Engineers (SPE). All Rights Reserved. The problem of viscous fingering in multi-phase fluid flow in porous media affects the understanding, design, and evaluation of both laboratory experiments and reservoir processes. Existing methods of studying fingered floods are either phenomenological, or rely heavily on high order numerical methods. In this work, a novel "random walk " analysis is described and utilized to study both miscible and immiscible floods. Simple "walking " and "trapping " rules are derived directly from the usual differential equations describing multi-phase flow. It is straight forward to include the effects of capillary pressure, heterogeneity, diffusion-dispersion, gravity, different geometries, and to study multiple (>2) phase flow. The random walk model implicitly performs a stability analysis as the flood proceeds. The solutions vary from compact to highly fingered profiles, depending upon the value of the mobility ratio, M. The entire range of displacements, from stable to unstable, may be simulated. The random walk methods are an extension of the diffusion-limited aggregation (DLA) model of Witten and Sander. The concept of trapping has been substantially generalized beyond that of DLA. The DLA rules are recovered dynamically as a special case in the extreme mobility (M ) limit.

published proceedings

  • Proceedings - SPE Annual Technical Conference and Exhibition

author list (cited authors)

  • King, M. J., & Scher, H.

complete list of authors

  • King, MJ||Scher, H

publication date

  • January 1985