Many of the complex physical processes relevant for compositional
multi-phase flow in porous media are well understood at the pore-scale
level. In order to study CO2 storage in sub-surface formations,
however, it is not feasible to perform simulations at these small
scales directly and effective models for multi-phase flow description
at Darcy scale are needed. Unfortunately, in many cases it is not clear
how the micro-scale knowledge can rigorously be translated into
consistent macroscopic equations. Here, we present a new methodology,
which provides a link between Lagrangian statistics of phase particle
evolution and Darcy scale dynamics. Unlike in finite-volume methods,
the evolution of Lagrangian particles representing small fluid phase
volumes is modeled. Each particle has a state vector consisting of its
position, velocity, fluid phase information and possibly other
properties like phase composition. While the particles are transported
through the computational domain according to their individual
velocities, the properties are modeled via stochastic processes
honoring specified Lagrangian statistics. Note that the conditional
expectations of the particle velocities are different for different
fluid phases. The goal of this paper is to present the general
framework for this alternative modeling approach. Various one and
two-dimensional numerical experiments demonstrate that with appropriate
stochastic rules the particle solutions are consistent with a standard
two-phase Darcy flow formulation. In the end, we demonstrate how to
model non-equilibrium phenomena within the stochastic particle
framework, which will be the main focus of the future work. (C) 2008
Elsevier Inc. All rights reserved.