Immiscible front evolution in randomly heterogeneous porous media

Alexandre M. Tartakovsky, Shlomo P Neuman, Robert J. Lenhard

Research output: Contribution to journalArticle

18 Citations (Scopus)

Abstract

The evolution of a sharp interface between two immiscible fluids in a randomly heterogeneous porous medium is investigated analytically using a stochastic moment approach. The displacing fluid is taken to be at constant saturation and to have a much larger viscosity than does the displaced fluid, which is therefore effectively static. Capillary pressure at the interface is related to porosity and permeability via the Leverett J-function. Whereas porosity is spatially uniform, permeability forms a spatially correlated random field. Displacement is governed by stochastic integro-differential equations defined over a three-dimensional domain bounded by a random interface. The equations are expanded and averaged in probability space to yield leading order recursive equations governing the ensemble mean and variance of interface position, rate of propagation and pressure gradient within the displacing fluid. Solutions are obtained for one-dimensional head- and flux-driven displacements in statistically homogeneous media and found to compare well with numerical Monte Carlo simulations. The manner in which medium heterogeneity affects the mean pressure gradient is indicative of how it impacts the stability of the mean interface. Capillary pressure at the interface is found to have a potentially important effect on its mean dynamics and stability.

Original languageEnglish (US)
Pages (from-to)3331-3341
Number of pages11
JournalPhysics of Fluids
Volume15
Issue number11
DOIs
StatePublished - Nov 2003

Fingerprint

Porous materials
Fluids
Capillarity
Pressure gradient
Porosity
fluids
pressure gradients
Integrodifferential equations
permeability
porosity
Viscosity
Fluxes
differential equations
viscosity
moments
saturation
gradients
propagation
simulation

ASJC Scopus subject areas

  • Mechanics of Materials
  • Computational Mechanics
  • Physics and Astronomy(all)
  • Fluid Flow and Transfer Processes
  • Condensed Matter Physics

Cite this

Immiscible front evolution in randomly heterogeneous porous media. / Tartakovsky, Alexandre M.; Neuman, Shlomo P; Lenhard, Robert J.

In: Physics of Fluids, Vol. 15, No. 11, 11.2003, p. 3331-3341.

Research output: Contribution to journalArticle

Tartakovsky, Alexandre M. ; Neuman, Shlomo P ; Lenhard, Robert J. / Immiscible front evolution in randomly heterogeneous porous media. In: Physics of Fluids. 2003 ; Vol. 15, No. 11. pp. 3331-3341.
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