arXiv subjects

Morten Vassvik

Publications and source records attributed to Morten Vassvik.

7 recordsLinked to original sources

arXiv2019

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

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.

physics.flu-dyn↗

arXiv2018

Stable and efficient time integration of a dynamic pore network model for two-phase flow in porous media

We study three different time integration methods for a dynamic pore network model for immiscible two-phase flow in porous media. Considered are two explicit methods, the forward Euler and midpoint methods, and a new semi-implicit method developed herein. The explicit methods are known to suffer from numerical instabilities at low capillary numbers. A new time-step criterion is suggested in order to stabilize them. Numerical experiments, including a Haines jump case, are performed and these demonstrate that stabilization is achieved. Further, the results from the Haines jump case are consistent with experimental observations. A performance analysis reveals that the semi-implicit method is able to perform stable simulations with much less computational effort than the explicit methods at low capillary numbers. The relative benefit of using the semi-implicit method increases with decreasing capillary number $\mathrm{Ca}$, and at $\mathrm{Ca} \sim 10^{-8}$ the computational time needed is reduced by three orders of magnitude. This increased efficiency enables simulations in the low-capillary number regime that are unfeasible with explicit methods and the range of capillary numbers for which the pore network model is a tractable modeling alternative is thus greatly extended by the semi-implicit method.

physics.comp-ph↗

arXiv2017

Relations between Seepage Velocities in Immiscible, Incompressible Two-Phase Flow in Porous Media

Based on thermodynamic considerations we derive a set of equations relating the seepage velocities of the fluid components in immiscible and incompressible two-phase flow in porous media. They necessitate the introduction of a new velocity function, the co-moving velocity. This velocity function is a characteristic of the porous medium. Together with a constitutive relation between the velocities and the driving forces, such as the pressure gradient, these equations form a closed set. We solve four versions of the capillary tube model analytically using this theory. We test the theory numerically on a network model.

physics.flu-dyn↗

arXiv2017

Rheology of High-Capillary Number Flow in Porous Media

Immiscible fluids flowing at high capillary numbers in porous media may be characterized by an effective viscosity. We demonstrate that the effective viscosity is well described by the Lichtenecker-Rother equation. The exponent $α$ in this equation takes either the value 1 or 0.6 in two- and 0.5 in three-dimensional systems depending on the pore geometry. Our arguments are based on analytical and numerical methods.

physics.flu-dyn↗

arXiv2016

A new set of equations describing immiscible two-phase flow in isotropic porous media

Based on non-equilibrium thermodynamics we derive a set of general equations relating the partial volumetric flow rates to each other and to the total volumetric flow rate in immiscible two-phase flow in porous media. These equations together with the conservation of saturation reduces the immiscible two-phase flow problem to a single-phase flow problem of a complex fluid. We discuss the new equation in terms of the relative permeability equations. We test the equations on model systems, both analytically and numerically.

physics.flu-dyn↗

arXiv2016

A Monte Carlo Algorithm for Immiscible Two-Phase Flow in Porous Media

We present a Markov Chain Monte Carlo algorithm based on the Metropolis algorithm for simulation of the flow of two immiscible fluids in a porous medium under macroscopic steady-state conditions using a dynamical pore network model that tracks the motion of the fluid interfaces. The Monte Carlo algorithm is based on the configuration probability, where a configuration is defined by the positions of all fluid interfaces. We show that the configuration probability is proportional to the inverse of the flow rate. Using a two-dimensional network, advancing the interfaces using time integration the computational time scales as the linear system size to the fourth power, whereas the Monte Carlo computational time scales as the linear size to the second power. We discuss the strengths and the weaknesses of the algorithm.

physics.flu-dyn↗

arXiv2016

Ensemble Distribution for Immiscible Two-Phase Flow in Porous Media

We construct an ensemble distribution to describe steady immiscible two-phase flow of two incompressible fluids in a porous medium. The system is found to be ergodic. The distribution is used to compute macroscopic flow parameters. In particular, we find an expression for the overall mobility of the system from the ensemble distribution. The entropy production at the scale of the porous medium is shown to give the expected product of the average flow and its driving force, obtained from a black-box description. We test numerically some of the central theoretical results.

physics.flu-dyn↗