Multi-Scale Approach for Multi-Phase Flow in Porous ...

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XVI International Conference on Computational Methods in Water Resources (CMWR-XVI) Ingeniørhuset

Multi-Scale Approach for Multi-Phase Flow in Porous Media Using Stochastic Particles
Author:Patrick Jenny <> (ETH, Zurich)
Manav Tyagi <> (ETH, Zurich)
Hamdi Tchelepi <> (Stanford University)
Evan Lunati <> (ETH, Zurich)
Presenter:Patrick Jenny <> (ETH, Zurich)
Date: 2006-06-18     Track: Special Sessions     Session: Multiscale methods for flow in porous media

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.