Abstract
We present in detail a set of algorithms for a dynamic pore-network model of immiscible two-phase flow in porous media to carry out fluid displacements in pores. The algorithms are universal for regular and irregular pore networks in two or three dimensions and can be applied to simulate both drainage displacements and steady-state flow. They execute the mixing of incoming fluids at the network nodes, then distribute them to the outgoing links and perform the coalescence of bubbles. Implementing these algorithms in a dynamic pore-network model, we reproduce some of the fundamental results of transient and steady-state two-phase flow in porous media. For drainage displacements, we show that the model can reproduce the flow patterns corresponding to viscous fingering, capillary fingering and stable displacement by varying the capillary number and viscosity ratio. For steady-state flow, we verify non-linear rheological properties and transition to linear Darcy behavior while increasing the flow rate. Finally we verify the relations between seepage velocities of two-phase flow in porous media considering both disordered regular networks and irregular networks reconstructed from real samples.
Highlights
Flow of multiple immiscible fluids inside a porous medium shows a range of complex characteristics during transient as well as in steady state [1, 2]
We present in detail a set of algorithms for a dynamic pore-network model of immiscible two-phase flow in porous media to carry out fluid displacements in pores
The capillary fingering patterns appear during slow displacement process and are well described by invasion percolation [7, 8], whereas the viscous fingering patterns appear during fast displacement and can be modeled by diffusion limited aggregation (DLA) model [9, 10]
Summary
Flow of multiple immiscible fluids inside a porous medium shows a range of complex characteristics during transient as well as in steady state [1, 2]. This provides straightforward calculation of capillary pressures from the meniscus positions and resolves different dynamical events such as the retraction of invasion fronts after a Haines jump [44,45,46,47] This meniscus-tracking approach to model the fluid transport in pore-network model was first introduced by Aker et al in the late nineties [43] to study transient two-phase flow – i.e. drainage – in a pore network. All the previous studies were performed for specific flow types or boundary conditions, and description of any universal set of meniscus algorithms were lacking in those works This is the first time we present a complete model with a general set of meniscus algorithms which can be applied to simulate both the drainage displacements and the steady-state flow in different network geometries and driving conditions.
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