Spanish National Research Council IDAeA CSIC

Barcelona, Spain

Spanish National Research Council IDAeA CSIC

Barcelona, Spain
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Aquino T.,University of Notre Dame | Aquino T.,Spanish National Research Council IDAEA CSIC | Bolster D.,University of Notre Dame
Transport in Porous Media | Year: 2017

Mixing is driven by an interplay between diffusion and flow-induced concentration gradients. Accurately describing the effect of flow heterogeneity on the mixing state of a plume is a challenging problem that has important repercussions on the modeling of plume dilution and chemical reactions. In this technical note, we propose a simple, semi-analytic measure to quantify the local mixing potential at a point based on the local properties of the flow-induced strain. Specifically, it is the trace of the local strain matrix squared, (Formula presented.), which we demonstrate controls mixing from a point source over small times. Due to its mathematically similar influence to a shear flow on mixing, we propose an ansatz to attempt to use this metric as a predictor for mixing. We test its performance via random walk particle tracking simulations in heterogeneous Darcy flow through lognormal permeability fields. The ansatz appears to work better and better the more heterogeneous the flow, unlike more traditional approaches that rely on weak heterogeneity assumptions. While we cannot rigorously demonstrate why this is, we find it sufficiently promising that it may guide future model development. © 2017 Springer Science+Business Media B.V.


Lapeyre G.J.,Spanish National Research Council IDAEA CSIC | Lapeyre G.J.,ICFO - Institute of Photonic Sciences | Dentz M.,Spanish National Research Council IDAEA CSIC
Physical Chemistry Chemical Physics | Year: 2017

Understanding anomalous transport and reaction kinetics due to microscopic physical and chemical disorder is a long-standing goal in many fields including geophysics, biology, and engineering. We consider reaction-diffusion characterized by fluctuations in both transport times and decay rates. We introduce and analyze a model framework that explicitly connects microscopic fluctuations with the mescoscopic description. For broad distributions of transport and reaction time scales we compute the particle density and derive the equations governing its evolution, finding power-law decay of the survival probability, and spatially varying decay that leads to subdiffusion and an asymptotically stationary surviving-particle density. These anomalies are clearly attributable to non-Markovian effects that couple transport and chemical properties in both reaction and diffusion terms. © the Owner Societies 2017.


Dentz M.,Spanish National Research Council IDAeA CSIC | Bolster D.,University of Notre Dame
Physical Review Letters | Year: 2010

We study mechanisms of anomalous transport in quenched random media. Broad disorder point distributions and strong disorder correlations cause anomalous transport and can lead to the same anomalous scaling laws for the mean and variance of the particle displacements. The respective mechanisms, however, are fundamentally different. This difference is reflected in the spatial particle densities and first passage time distributions, which provide an indicator to identify the origins of anomalous transport. © 2010 The American Physical Society.


De Anna P.,CNRS Geosciences Laboratory of Rennes | De Anna P.,Massachusetts Institute of Technology | Le Borgne T.,CNRS Geosciences Laboratory of Rennes | Dentz M.,Spanish National Research Council IDAEA CSIC | And 3 more authors.
Physical Review Letters | Year: 2013

We study the intermittency of fluid velocities in porous media and its relation to anomalous dispersion. Lagrangian velocities measured at equidistant points along streamlines are shown to form a spatial Markov process. As a consequence of this remarkable property, the dispersion of fluid particles can be described by a continuous time random walk with correlated temporal increments. This new dynamical picture of intermittency provides a direct link between the microscale flow, its intermittent properties, and non-Fickian dispersion. © 2013 American Physical Society.


Geiger S.,Heriot - Watt University | Dentz M.,Spanish National Research Council IDAEA CSIC | Neuweiler I.,Leibniz University of Hanover
SPE Journal | Year: 2013

A major part of the world's remaining oil reserves is in fractured carbonate reservoirs, which are dual-porosity (fracture-matrix) or multiporosity (fracture/vug/matrix) in nature. Fractured reservoirs suffer from poor recovery, high water cut, and generally low performance. They are modeled commonly by use of a dual-porosity approach, which assumes that the high-permeability fractures are mobile and low-permeability matrix is immobile. A single transfer function models the rate at which hydrocarbons migrate from the matrix into the fractures. As shown in many numerical, laboratory, and field experiments, a wide range of transfer rates occurs between the immobile matrix and mobile fractures. These arise, for example, from the different sizes of matrix blocks (yielding a distribution of shape factors), different porosity types, or the inhomogeneous distribution of saturations in the matrix blocks. Thus, accurate models are needed that capture all the transfer rates between immobile matrix and mobile fracture domains, particularly to predict late-time recovery more reliably when the water cut is already high. In this work, we propose a novel multi-rate mass-transfer (MRMT) model for two-phase flow, which accounts for viscous-dominated flow in the fracture domain and capillary flow in the matrix domain. It extends the classical (i.e., singlerate) dual-porosity model to allow us to simulate the wide range of transfer rates occurring in naturally fractured multiporosity rocks. We demonstrate, by use of numerical simulations of waterflooding in naturally fractured rock masses at the gridblock scale, that our MRMT model matches the observed recovery curves more accurately compared with the classical dual-porosity model. We further discuss how our multi-rate dual-porosity model can be parameterized in a predictive manner and how the model could be used to complement traditional commercial reservoir-simulation workflows. Copyright © 2013 Society of Petroleum Engineers.


Holzner M.,ETH Zurich | Morales V.L.,University of Abertay Dundee | Willmann M.,ETH Zurich | Dentz M.,Spanish National Research Council IDAEA CSIC
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics | Year: 2015

Intermittency of Lagrangian velocity and acceleration is a key to understanding transport in complex systems ranging from fluid turbulence to flow in porous media. High-resolution optical particle tracking in a three-dimensional (3D) porous medium provides detailed 3D information on Lagrangian velocities and accelerations. We find sharp transitions close to pore throats, and low flow variability in the pore bodies, which gives rise to stretched exponential Lagrangian velocity and acceleration distributions characterized by a sharp peak at low velocity, superlinear evolution of particle dispersion, and double-peak behavior in the propagators. The velocity distribution is quantified in terms of pore geometry and flow connectivity, which forms the basis for a continuous-time random-walk model that sheds light on the observed Lagrangian flow and transport behaviors. ©2015 American Physical Society.


Kang P.K.,Massachusetts Institute of Technology | Dentz M.,Spanish National Research Council IDAEA CSIC | Le Borgne T.,CNRS Geosciences Laboratory of Rennes | Juanes R.,Massachusetts Institute of Technology
Physical Review Letters | Year: 2011

Flow through lattice networks with quenched disorder exhibits a strong correlation in the velocity field, even if the link transmissivities are uncorrelated. This feature, which is a consequence of the divergence-free constraint, induces anomalous transport of passive particles carried by the flow. We propose a Lagrangian statistical model that takes the form of a continuous time random walk with correlated velocities derived from a genuinely multidimensional Markov process in space. The model captures the anomalous (non-Fickian) longitudinal and transverse spreading, and the tail of the mean first-passage time observed in the Monte Carlo simulations of particle transport. We show that reproducing these fundamental aspects of transport in disordered systems requires honoring the correlation in the Lagrangian velocity. © 2011 American Physical Society.


Kang P.K.,Massachusetts Institute of Technology | Dentz M.,Spanish National Research Council IDAeA CSIC | Juanes R.,Massachusetts Institute of Technology
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics | Year: 2011

We study stochastic transport through a lattice network with quenched disorder and evaluate the limits of predictability of the transport behavior across realizations of spatial heterogeneity. Within a Lagrangian framework, we perform coarse graining, noise averaging, and ensemble averaging, to obtain an effective transport model for the average particle density and its fluctuations between realizations. We show that the average particle density is described exactly by a continuous time random walk (CTRW), and the particle density variance is quantified by a novel two-particle CTRW. © 2011 American Physical Society.


Cueto-Felgueroso L.,Technical University of Madrid | Cueto-Felgueroso L.,Massachusetts Institute of Technology | Dentz M.,Spanish National Research Council IDAEA CSIC | Juanes R.,Massachusetts Institute of Technology
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics | Year: 2015

We develop a framework that casts the point water-vegetation dynamics under stochastic rainfall forcing as a continuous-time random walk (CTRW), which yields an evolution equation for the joint probability density function (PDF) of soil-moisture and biomass. We find regime shifts in the steady-state PDF as a consequence of changes in the rainfall structure, which flips the relative strengths of the system attractors, even for the same mean precipitation. Through an effective potential, we quantify the impact of rainfall variability on ecosystem resilience and conclude that amplified rainfall regimes reduce the resilience of water-stressed ecosystems, even if the mean annual precipitation remains constant. ©2015 American Physical Society.


Le Borgne T.,CNRS Geosciences Laboratory of Rennes | Dentz M.,Spanish National Research Council IDAEA CSIC | Villermaux E.,Aix - Marseille University
Physical Review Letters | Year: 2013

We study scalar mixing in heterogeneous conductivity fields, whose structural disorder varies from weak to strong. A range of stretching regimes is observed, depending on the level of structural heterogeneity, measured by the log-conductivity field variance. We propose a unified framework to quantify the overall concentration distribution predicting its shape and rate of deformation as it progresses toward uniformity in the medium. The scalar mixture is represented by a set of stretched lamellae whose rate of diffusive smoothing is locally enhanced by kinematic stretching. Overlap between the lamellae is enforced by confinement of the scalar line support within the dispersion area. Based on these elementary processes, we derive analytical expressions for the concentration distribution, resulting from the interplay between stretching, diffusion, and random overlaps, holding for all field heterogeneities, residence times, and Péclet numbers. © 2013 American Physical Society.

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