A Dynamic Network Simulator for Immiscible Two-Phase Flow in Porous Media

Abstract

We present in detail a set of algorithms to carry out fluid displacements in a dynamic pore-network model of immiscible two-phase flow in porous media. The algorithms are general and applicable to regular and irregular pore networks in two and three dimensions with different boundary conditions. Implementing these sets of algorithms, we describe a dynamic pore-network model and reproduce some of the fundamental properties of both the transient and steady-state two-phase flow. During drainage displacements, we show that the model can reproduce the flow patterns corresponding to viscous fingering, capillary fingering and stable displacement by altering the capillary number and the viscosity ratio. In steady-state flow, the model verifies the linear to non-linear transition of the effective rheological properties and satisfy the relations between the seepage velocities of two-phase flow in porous media.

Immiscible two-phase flow in porous media: Effective rheology in the continuum limit

“…We base our simulations on the dynamic network simulator described in [34][35][36]. It consists of interfaces that span the pores and move according to the pressure gradient they experience.…”

“…Our conclusion, based on numerical evidence from the dynamic network model [34][35][36] and on analytic calculation using the capillary fiber bundle model [39], is that the non-linear regime shrinks away with increasing system size.…”

“…Sinha et al [27] report for their experiments β = 1/0.46 = 2.2, based on there being a threshold. Sinha and Hansen [26] in numerical work also assuming a threshold pressure based on a dynamic network simulator [33] where fluid interfaces are moved according to the forces they experience [34][35][36][37], found β = 1/0.51 = 2.0. The network representing the porous medium was here a disordered square lattice.…”

Flow-Area Relations in Immiscible Two-Phase Flow in Porous Media

“…Then follows Section V which then moves beyond the results of the pseudo-thermodynamics by focusing on fluctuations. In Section VI we use the dynamic network simulator [24] first introduced by Aker et al [25] and then later refined [26][27][28] to verify the relations derived in the earlier sections. There is also a second goal behind this numerical work: the dynamic network model is a model at pore level and by its use, we show how the formalism developed here connect to the flow patterns at the pore level.…”

Onsager-Symmetry Obeyed in Athermal Mesoscopic Systems: Two-Phase Flow in Porous Media

“…The transport of the two immiscible fluids through a two-dimensional porous medium is represented by a dynamical pore network model [18,19]. This model has been in development over two decades and has a record of explaining experimental and theoretical results in steady and transient two-phase flow in porous media [11][12][13][18][19][20][21][22][23]. In this model the two fluids are separated by interfaces and are flowing in a network of links which are connected at nodes.…”