arXiv subjects

Alex Hansen

Publications and source records attributed to Alex Hansen.

At least 73 records · Page 4Linked to original sources

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

Effective Rheology of Two-phase Flow in Three-Dimensional Porous Media: Experiment and Simulation

We present an experimental and numerical study of immiscible two-phase flow in 3-dimensional (3D) porous media to find the relationship between the volumetric flow rate ($Q$) and the total pressure difference ($ΔP$) in the steady state. We show that in the regime where capillary forces compete with the viscous forces, the distribution of capillary barriers at the interfaces effectively creates a yield threshold, making the fluids reminiscent of a Bingham viscoplastic fluid in the porous medium, introducing a threshold pressure $P_t$. In this regime, $Q$ depends quadratically on an excess pressure drop ($ΔP-P_t$). While increasing the flow-rate, there is a transition, beyond which the flow is Newtonian and the relationship is linear. In our experiments, we build a model porous medium using a column of glass beads transporting two fluids -- de-ionized water and air. For the numerical study, reconstructed 3D pore-networks from real core samples are considered and the transport of wetting and non-wetting fluids through the network are modeled by tracking the fluid interfaces with time. We find agreement between our numerical and experimental results. Our results match the mean-field results reported earlier.

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↗

arXiv2015

Cracks in random brittle solids: From fiber bundles to continuum mechanics

Statistical models are essential to get a better understanding of the role of disorder in brittle disordered solids. Fiber bundle models play a special role as a paradigm, with a very good balance of simplicity and non-trivial effects. We introduce here a variant of the fiber bundle model where the load is transferred among the fibers through a very compliant membrane. This Soft Membrane fiber bundle mode reduces to the classical Local Load Sharing fiber bundle model in 1D. Highlighting the continuum limit of the model allows to compute an equivalent toughness for the fiber bundle and hence discuss nucleation of a critical defect. The computation of the toughness allows for drawing a simple connection with crack front propagation (depinning) models.

cond-mat.dis-nn↗

arXiv2015

Dynamic wettability alteration in immiscible two-phase flow in porous media: Effect on transport properties and critical slowing down

The change in contact angles due to the injection of low salinity water or any other wettability altering agent in an oil-rich porous medium is modeled by a network model of disordered pores transporting two immiscible fluids. We introduce a dynamic wettability altering mechanism, where the time dependent wetting property of each pore is determined by the cumulative flow of water through it. Simulations are performed to reach steady-state for different possible alterations in the wetting angle ($θ$). We find that deviation from oil-wet conditions re-mobilizes the stuck clusters and increases the oil fractional flow. However, the rate of increase in the fractional flow depends strongly on $θ$ and as $θ\to 90^\circ$, a critical angle, the system shows critical slowing down which is characterized by two dynamic critical exponents.

physics.flu-dyn↗

arXiv2015

The Local load sharing fiber bundle model in higher dimensions

We consider the local load sharing fiber bundle model in one to five dimensions. Depending on the breaking threshold distribution of the fibers, there is a transition where the fracture process becomes localized. In the localized phase, the model behaves as the invasion percolation model. The difference between the local load sharing fiber bundle model and the equal load sharing fiber bundle model decreases with increasing dimensionality as a power law.

cond-mat.dis-nn↗

arXiv2013

Local dynamics of a randomly pinned crack front: A numerical study

We investigate numerically the dynamics of crack propagation along a weak plane using a model consisting of fibers connecting a soft and a hard clamp. This bottom-up model has previously been shown to contain the competition of two crack propagation mechanisms: coalescence of damage with the front on small scales and pinned elastic line motion on large scales. We investigate the dynamical scaling properties of the model, both on small and large scale. The model results compare favorable with experimental results.

cond-mat.dis-nn↗

arXiv2013

History-independence of steady-state in simultaneous two-phase flow through porous media

It is well known that the transient behavior during drainage or imbibition in multiphase flow in porous media strongly depends on the history and initial condition of the system. However, when the steady-state regime is reached and both drainage and imbibition take place at the pore level, the influence of the evolution history and initial preparation is an open question. Here, we present an extensive experimental and numerical work investigating the history dependence of simultaneous steady-state two-phase flow through porous media. Our experimental system consists of a Hele-Shaw cell filled with glass beads which we model numerically by a network of disordered pores transporting two immiscible fluids. From the measurements of global pressure evolution, histogram of saturation and cluster-size distributions, we find that when both phases are flowing through the porous medium, the steady state does not depend on the initial preparation of the system or on the way it has been reached.

physics.flu-dyn↗

arXiv2013

Universality Classes in Constrained Crack Growth

Based on an extension of the fiber bundle model we investigate numerically the motion of the crack front through a weak plane separating a soft and an infinitely stiff block. We find that there are two regimes. At large scales the motion is consistent with the pinned elastic line model and we find a roughness exponent equal to 0.39 +/- 0.04 characterizing it. At smaller scales, coalescence of holes dominates the motion rather than pinning of the crack front. We find a roughness exponent consistent with 2/3, which is the gradient percolation value. The length of the crack front is fractal on these smaller scales. We determine its fractal dimension to be 1.77 +/- 0.02, consistent with the hull of percolation clusters, 7/4. This suggests that the crack front is described by two universality classes: on large scales, the pinned elastic line one and on small scales, the percolation universality class.

cond-mat.dis-nn↗

arXiv2012

Topology of Fracture Networks

We propose a mapping from fracture systems consisting of intersecting fracture sheets in three dimensions to an abstract network consisting of nodes and links. This makes it possible to analyze fracture systems with the methods developed within modern network theory. We test the mapping for two-dimensional geological fracture outcrops and find that the equivalent networks are small-world and dissasortative. By anlayzing the Discrete Fracture Network model, which is used to generate artifical fracture networks, we also find small world networks. However, the networks turn out to be assortative.

physics.data-an↗

arXiv2012

Effective Rheology of Bubbles Moving in a Capillary Tube

We calculate the average volumetric flux versus pressure drop of bubbles moving in a single capillary tube with varying diameter, finding a square-root relation from mapping the flow equations onto that of a driven overdamped pendulum. The calculation is based on a derivation of the equation of motion of a bubble train from considering the capillary forces and the entropy production associated with the viscous flow. We also calculate the configurational probability of the positions of the bubbles.

physics.flu-dyn↗

arXiv2012

Effective Rheology of Immiscible Two-Phase Flow in Porous Media

We demonstrate through numerical simulations and a mean field calculation that immiscible two-phase flow in a porous medium behaves effectively as a Bingham viscoplastic fluid. This leads to a generalized Darcy equation where the volumetric flow rate depends quadratically on an excess pressure difference in the range of flow rates where the capillary forces compete with the viscous forces. At higher rates, the flow is Newtonian.

physics.flu-dyn↗

arXiv2012

A model for stable interfacial crack growth

We present a model for stable crack growth in a constrained geometry. The morphology of such cracks show scaling properties consistent with self affinity. Recent experiments show that there are two distinct self-affine regimes, one on small scales whereas the other at large scales. It is believed that two different physical mechanisms are responsible for this. The model we introduce aims to investigate the two mechanisms in a single system. We do find two distinct scaling regimes in the model.

physics.comp-ph↗

arXiv2012

Onset of Localization in Heterogeneous Interfacial Failure

We study numerically the failure of an interface joining two elastic materials under load using a fiber bundle model connected to an elastic half space. We find that the breakdown process follows the equal load sharing fiber bundle model without any detectable spatial correlations between the positions of the failing fibers until localization sets in. The onset of localization is an instability, not a phase transition. Depending on the elastic constant describing the elastic half space, localization sets in before or after the critical load causing the interface to fail completely, is reached. There is a crossover between failure due to localization or failure without spatial correlations when tuning the elastic constant, not a phase transition. Contrary to earlier claims based on models different from ours, we find that a finite fraction of fibers must fail before the critical load is attained, even in the extreme localization regime, i.e.\ for very small elastic constant. We furthermore find that the critical load remains finite for all values of the elastic constant in the limit of an infinitely large system.

physics.comp-ph↗

arXiv2012

Relation Between First Arrival Time and Permeability in Self-Affine Fractures with Areas in Contact

We demonstrate that the first arrival time in dispersive processes in self-affine fractures are governed by the same length scale characterizing the fractures as that which controls their permeability. In one-dimensional channel flow this length scale is the aperture of the bottle neck, i.e., the region having the smallest aperture. In two dimensions, the concept of a bottle neck is generalized to that of a minimal path normal to the flow. The length scale is then the average aperture along this path. There is a linear relationship between the first arrival time and this length scale, even when there is strong overlap between the fracture surfaces creating areas with zero permeability. We express the first arrival time directly in terms of the permeability.

physics.flu-dyn↗