10.4122/1.1000000391
Jenny, Patrick
Patrick
Jenny
jenny@ifd.mavt.ethz.ch
Tyagi, Manav
Manav
Tyagi
tyagi@ifd.mavt.ethz.ch
Tchelepi, Hamdi
Hamdi
Tchelepi
tchelepi@stanford.edu
Lunati, Evan
Evan
Lunati
lunati@ifd.mavt.ethz.ch
Jenny, Patrick
Patrick
Jenny
jenny@ifd.mavt.ethz.ch
Multi-Scale Approach for Multi-Phase Flow in Porous Media Using Stochastic Particles
XVI International Conference on Computational Methods in Water Resources
2006
2006
Particle methods have been investigated extensively for single-phase tracer
transport in porous media. However, these conventional particle methods are unable
to describe the correct non-linear macroscopic flux observed in immiscible multi-
phase flow. Here we present an alternative particle approach. The methodology is
based on transporting the particles according to statistical rules consistent with
the small-scale physics in pores and throats. The input to the model describing the
fluid particle dynamics includes the distribution functions of velocity and
capillary pressure gradient in the throats. Moreover, the multi-point statistics of
the particles in the pore network are characterized by correlation time and length
scales. As a result, the macroscopic transport equations are non local. We
demonstrate that in the limiting case of zero correlation time and length scales,
these macroscopic equations derived from the microscopic model reduce to the
standard fractional flow Darcy scale equations. We show that for more general
cases, additional terms and macroscopic closure models are required. There are no
inherent limitations in the methodology, provided the required Lagrangian
statistics are available from experiments or pore network simulations. While this
particle method may not be perfectly suited for practical macroscopic simulations
directly, its main advantage is in providing a consistent link between small and
large scales. Such a consistent multi-scale multi-physics framework allows for more
insight into multi-phase physics; moreover it can also serve to better interpret
the effective coefficients and to derive modified macroscopic models.