Flow Intermittency, Dispersion, and Correlated Continuous Time Random Walks in Porous Media

Anna, Pietro de; Borgne, Tanguy Le; Dentz, Marco; Tartakovsky, Alexandre M.; Bolster, Diogo; Davy, Philippe

doi:10.1103/physrevlett.110.184502

Cited by 208 publications

(266 citation statements)

References 35 publications

Supporting

Mentioning

258

Contrasting

Order By: Relevance

“…Avalanches and non-Gaussian intermittent velocity fluctuations [8][9][10][11][12][13][14][15][16][17] can arise from the medium heterogeneous structure, which may involve a very wide range of spatial scales, from nanometer pore size to kilometer field scales. A common theoretical approach to study those flows consists in a volume-averaging or homogenization procedure in order to obtain effective behavior at large scale from the up-scaling of microscopic phenomena [18].…”

Section: Introductionmentioning

confidence: 99%

Experimental study of stable imbibition displacements in a model open fracture. II. Scale-dependent avalanche dynamics

2016

View full text Add to dashboard Cite

We report the results of an experimental investigation of the spatiotemporal dynamics of stable imbibition fronts in a disordered medium, in the regime of capillary disorder, for a wide range of experimental conditions. We have used silicone oils of various viscosities μ and nearly identical oil-air surface tension, and forced them to slowly invade a model open fracture at very different flow rates v. In this second part of the study we have carried out a scale-dependent statistical analysis of the front dynamics. We have specifically analyzed the influence of μ and v on the statistical properties of the velocity V , the spatial average of the local front velocities over a window of lateral size . We have varied from the local scale defined by our spatial resolution up to the lateral system size L. Even though the imposed flow rate is constant, the signals V (t) present very strong fluctuations which evolve systematically with the parameters μ, v, and . We have verified that the non-Gaussian fluctuations of the global velocity V (t) are very well described by a generalized Gumbel statistics. The asymmetric shape and the exponential tail of those distributions are controlled by the number of effective degrees of freedom of the imbibition fronts, given by N eff = / c (the ratio of the lateral size of the measuring window to the correlation length c ∼ 1/ √ μv). The large correlated excursions of V (t) correspond to global avalanches, which reflect extra displacements of the imbibition fronts. We show that global avalanches are power-law distributed, both in sizes and durations, with robustly defined exponents-independent of μ, v, and . Nevertheless, the exponential upper cutoffs of the distributions evolve systematically with those parameters. We have found, moreover, that maximum sizes ξ S and maximum durations ξ T of global avalanches are not controlled by the same mechanism. While ξ S are also determined by / c , like the amplitude fluctuations of V (t), ξ T and the temporal correlations of V (t) evolve much more strongly with imposed flow rate v than with fluid viscosity μ.

show abstract

Section: Introductionmentioning

confidence: 99%

Experimental study of stable imbibition displacements in a model open fracture. II. Scale-dependent avalanche dynamics

2016

View full text Add to dashboard Cite

show abstract

“…Using CTRW to model diffusion in confined geometries, such as porous media formed by either sintered or unconsolidated granular materials, is very attractive [8][9][10][11] because it alleviates the need to simulate directly the dynamics of particles within the pore space, reducing significantly the computational burden. In addition, it alleviates finite-size errors due to finite samples.…”

Section: Introductionmentioning

confidence: 99%

Modifying continuous-time random walks to model finite-size particle diffusion in granular porous media

Amitai

Blumenfeld

2017

Granular Matter

View full text Add to dashboard Cite

The continuous-time random walk (CTRW) model is useful for alleviating the computational burden of simulating diffusion in actual media. In principle, isotropic CTRW only requires knowledge of the step-size, P l , and waiting-time, P t , distributions of the random walk in the medium and it then generates presumably equivalent walks in free space, which are much faster. Here we test the usefulness of CTRW to modelling diffusion of finite-size particles in porous medium generated by loose granular packs. This is done by first simulating the diffusion process in a model porous medium of mean coordination number, which corresponds to marginal rigidity (the loosest possible structure), computing the resulting distributions P l and P t as functions of the particle size, and then using these as input for a free space CTRW. The CTRW walks are then compared to the ones simulated in the actual media. In particular, we study the normal-to-anomalous transition of the diffusion as a function of increasing particle size. We find that, given the same P l and P t for the simulation and the CTRW, the latter predicts incorrectly the size at which the transition occurs. We show that the discrepancy is related to the dependence of the effective connectivity of the porous media on the diffusing particle size, which is not captured simply by these distributions. We propose a correcting modification to the CTRW model-adding anisotropy-and show that it yields good agreement with the simulated diffusion process. We also present a method to obtain P l and P t directly from the porous sample, without having to simulate an actual diffusion process. This extends the use of CTRW, with all its advantages, to modelling diffusion processes of finite-size particles in such confined geometries.

show abstract

“…This phenomenon has been observed in several physical topics such as Lorenz system, Rayleigh-Benard convection, forced nonlinear oscillators, plasma physics, turbulence, porous media, combustion, reaction diffusion systems, etc. [4][5][6][7][8][9][10][11]. Some examples of control parameters for these physical systems are the Rayleigh number, the excitation frequency, the damping coefficient, etc.…”

Section: Introductionmentioning

confidence: 99%

Type-I intermittency with discontinuous reinjection probability density in a truncation model of the derivative nonlinear Schrödinger equation

2014

View full text Add to dashboard Cite

In previous papers, the type-I intermittent phenomenon with continuous reinjection probability density (RPD) has been extensively studied. However, in this paper type-I intermittency considering discontinuous RPD function in one-dimensional maps is analyzed. To carry out the present study the analytic approximation presented by del Rio and Elaskar (Int. J. Bifurc. Chaos 20:1185-1191, 2010) and Elaskar et al. (Physica A. 390:2759(Physica A. 390: -2768(Physica A. 390: , 2011) is extended to consider discontinuous RPD functions. The results of this analysis show that the characteristic relation only depends on the position of the lower bound of reinjection (LBR), therefore for the LBR below the tangent point the relation (/) a £ -1 / 2 , where s is the control parameter, remains robust regardless the form of the RPD, although the average of the laminar phases (/) can change. Finally, the study of discontinuous RPD for type-I intermittency which occurs in a three-wave truncation model for the derivative nonlinear Schrodinger equation is presented. In all tests the theoretical results properly verify the numerical data.

show abstract

Flow Intermittency, Dispersion, and Correlated Continuous Time Random Walks in Porous Media

Cited by 208 publications

References 35 publications

Experimental study of stable imbibition displacements in a model open fracture. II. Scale-dependent avalanche dynamics

Experimental study of stable imbibition displacements in a model open fracture. II. Scale-dependent avalanche dynamics

Modifying continuous-time random walks to model finite-size particle diffusion in granular porous media

Type-I intermittency with discontinuous reinjection probability density in a truncation model of the derivative nonlinear Schrödinger equation

Contact Info

Product

Resources

About