200 research outputs found
Self-organization of network dynamics into local quantized states
Self-organization and pattern formation in network-organized systems emerges
from the collective activation and interaction of many interconnected units. A
striking feature of these non-equilibrium structures is that they are often
localized and robust: only a small subset of the nodes, or cell assembly, is
activated. Understanding the role of cell assemblies as basic functional units
in neural networks and socio-technical systems emerges as a fundamental
challenge in network theory. A key open question is how these elementary
building blocks emerge, and how they operate, linking structure and function in
complex networks. Here we show that a network analogue of the Swift-Hohenberg
continuum model---a minimal-ingredients model of nodal activation and
interaction within a complex network---is able to produce a complex suite of
localized patterns. Hence, the spontaneous formation of robust operational cell
assemblies in complex networks can be explained as the result of
self-organization, even in the absence of synaptic reinforcements. Our results
show that these self-organized, local structures can provide robust functional
units to understand natural and socio-technical network-organized processes.Comment: 11 pages, 4 figure
A locally conservative variational multiscale method for the simulation of porous media flow with multiscale source term
We present a variational multiscale mixed
finite element method for the solution of Darcy flow
in porous media, in which both the permeability field
and the source term display a multiscale character.
The formulation is based on a multiscale split of the
solution into coarse and subgrid scales. This decomposition
is invoked in a variational setting that leads
to a rigorous definition of a (global) coarse problem
and a set of (local) subgrid problems. One of the key
issues for the success of the method is the proper
definition of the boundary conditions for the localization
of the subgrid problems. We identify a weak
compatibility condition that allows for subgrid communication
across element interfaces, a feature that
turns out to be essential for obtaining high-quality
solutions. We also remove the singularities due to
concentrated sources from the coarse-scale problem
by introducing additional multiscale basis functions,
based on a decomposition of fine-scale source terms
into coarse and deviatoric components. The method
is locally conservative and employs a low-order approximation
of pressure and velocity at both scales.
We illustrate the performance of the method on several
synthetic cases and conclude that the method
is able to capture the global and local flow patterns
accurately
Morphodynamics of Fluid-Fluid Displacement in Three-Dimensional Deformable Granular Media
We study experimentally the displacement of one fluid by another in a granular pack to uncover relationships between fluid invasion and medium deformation. We develop an experimental setup that allows us to reconstruct the coupled invasion-deformation dynamics in 3D. We simultaneously characterize the fluid invasion pattern and document a transition from fluid-fluid displacement in pores to the formation of conduits by grain motion. We rationalize the findings in terms of a simple poromechanics model that indeed captures this transition as a result of the balance between viscous and frictional forces. These results contribute to elucidating the role of three dimensionality in the timing, mode, and morphology of fluid-fluid displacement and injection-induced deformation in porous media.United States. Department of Energy (Grant DE-SC0018357
Inverse modeling of nonisothermal multiphase poromechanics using physics-informed neural networks
We propose a solution strategy for parameter identification in multiphase
thermo-hydro-mechanical (THM) processes in porous media using physics-informed
neural networks (PINNs). We employ a dimensionless form of the THM governing
equations that is particularly well suited for the inverse problem, and we
leverage the sequential multiphysics PINN solver we developed in previous work.
We validate the proposed inverse-modeling approach on multiple benchmark
problems, including Terzaghi's isothermal consolidation problem, Barry-Mercer's
isothermal injection-production problem, and nonisothermal consolidation of an
unsaturated soil layer. We report the excellent performance of the proposed
sequential PINN-THM inverse solver, thus paving the way for the application of
PINNs to inverse modeling of complex nonlinear multiphysics problems
Viscous fingering with partially miscible fluids
Viscous fingering—the fluid-mechanical instability that takes place when a low-viscosity fluid displaces a high-viscosity fluid—has traditionally been studied under either fully miscible or fully immiscible fluid systems. Here we study the impact of partial miscibility (a common occurrence in practice) on the fingering dynamics. Through a careful design of the thermodynamic free energy of a binary mixture, we develop a phase-field model of fluid-fluid displacements in a Hele-Shaw cell for the general case in which the two fluids have limited (but nonzero) solubility into one another. We show, by means of high-resolution numerical simulations, that partial miscibility exerts a powerful control on the degree of fingering: fluid dissolution hinders fingering while fluid exsolution enhances fingering. We also show that, as a result of the interplay between compositional exchange and the hydrodynamic pattern-forming process, stronger fingering promotes the system to approach thermodynamic equilibrium more quickly
Wettability control on multiphase flow in patterned microfluidics
Multiphase flow in porous media is important in many natural and industrial processes, including geologic CO₂ sequestration, enhanced oil recovery, and water infiltration into soil. Although it is well known that the wetting properties of porous media can vary drastically depending on the type of media and pore fluids, the effect of wettability on multiphase flow continues to challenge our microscopic and macroscopic descriptions. Here, we study the impact of wettability on viscously unfavorable fluid–fluid displacement in disordered media by means of high-resolution imaging in microfluidic flow cells patterned with vertical posts. By systematically varying the wettability of the flow cell over a wide range of contact angles, we find that increasing the substrate’s affinity to the invading fluid results in more efficient displacement of the defending fluid up to a critical wetting transition, beyond which the trend is reversed. We identify the pore-scale mechanisms—cooperative pore filling (increasing displacement efficiency) and corner flow (decreasing displacement efficiency)—responsible for this macroscale behavior, and show that they rely on the inherent 3D nature of interfacial flows, even in quasi-2D media. Our results demonstrate the powerful control of wettability on multiphase flow in porous media, and show that the markedly different invasion protocols that emerge—from pore filling to postbridging—are determined by physical mechanisms that are missing from current pore-scale and continuum-scale descriptions.United States. Department of Energy (DE-SC0003907)United States. Department of Energy (DE-FE0009738
Three-dimensional simulation of unstable gravity-driven infiltration of water into a porous medium
Infiltration of water in dry porous media is subject to a powerful gravity-driven instability. Although the phenomenon of unstable infiltration is well known, its description using continuum mathematical models has posed a significant challenge for several decades. The classical model of water flow in the unsaturated flow, the Richards equation, is unable to reproduce the instability. Here, we present a computational study of a model of unsaturated flow in porous media that extends the Richards equation and is capable of predicting the instability and captures the key features of gravity fingering quantitatively. The extended model is based on a phase-field formulation and is fourth-order in space. The new model poses a set of challenges for numerical discretizations, such as resolution of evolving interfaces, stiffness in space and time, treatment of singularly perturbed equations, and discretization of higher-order spatial partial–differential operators. We develop a numerical algorithm based on Isogeometric Analysis, a generalization of the finite element method that permits the use of globally-smooth basis functions, leading to a simple and efficient discretization of higher-order spatial operators in variational form. We illustrate the accuracy, efficiency and robustness of our method with several examples in two and three dimensions in both homogeneous and strongly heterogeneous media. We simulate, for the first time, unstable gravity-driven infiltration in three dimensions, and confirm that the new theory reproduces the fundamental features of water infiltration into a porous medium. Our results are consistent with classical experimental observations that demonstrate a transition from stable to unstable fronts depending on the infiltration flux.United States. Dept. of Energy (Early Career Award Grant DE-SC0003907
Pattern formation and coarsening dynamics in three-dimensional convective mixing in porous media
Geological carbon dioxide (CO[subscript 2]) sequestration entails capturing and injecting CO[subscript 2][subscript 2]into deep saline aquifers for long-term storage. The injected CO[subscript 2] partially dissolves in groundwater to form a mixture that is denser than the initial groundwater. The local increase in density triggers a gravitational instability at the boundary layer that further develops into columnar plumes of CO[subscript 2]-rich brine, a process that greatly accelerates solubility trapping of the CO[subscript 2]. Here, we investigate the pattern-formation aspects of convective mixing during geological CO[subscript 2] sequestration by means of high-resolution three-dimensional simulation. We find that the CO[subscript 2] concentration field self-organizes as a cellular network structure in the diffusive boundary layer at the top boundary. By studying the statistics of the cellular network, we identify various regimes of finger coarsening over time, the existence of a non-equilibrium stationary state, and a universal scaling of three-dimensional convective mixing
Pore-scale modeling of phase change in porous media
The combination of high-resolution visualization techniques and pore-scale flow modeling is a powerful tool used to understand multiphase flow mechanisms in porous media and their impact on reservoir-scale processes. One of the main open challenges in pore-scale modeling is the direct simulation of flows involving multicomponent mixtures with complex phase behavior. Reservoir fluid mixtures are often described through cubic equations of state, which makes diffuse-interface, or phase-field, theories particularly appealing as a modeling framework. What is still unclear is whether equation-of-state-driven diffuse-interface models can adequately describe processes where surface tension and wetting phenomena play important roles. Here we present a diffuse-interface model of single-component two-phase flow (a van der Waals fluid) in a porous medium under different wetting conditions. We propose a simplified Darcy-Korteweg model that is appropriate to describe flow in a Hele-Shaw cell or a micromodel, with a gap-averaged velocity. We study the ability of the diffuse-interface model to capture capillary pressure and the dynamics of vaporization-condensation fronts and show that the model reproduces pressure fluctuations that emerge from abrupt interface displacements (Haines jumps) and from the breakup of wetting films
Phase field model of fluid-driven fracture in elastic media: Immersed-fracture formulation and validation with analytical solutions
Propagation of fluid-driven fractures plays an important role in natural and engineering processes, including transport of magma in the lithosphere, geologic sequestration of carbon dioxide, and oil and gas recovery from low-permeability formations, among many others. The simulation of fracture propagation poses a computational challenge as a result of the complex physics of fracture and the need to capture disparate length scales. Phase field models represent fractures as a diffuse interface and enjoy the advantage that fracture nucleation, propagation, branching, or twisting can be simulated without ad hoc computational strategies like remeshing or local enrichment of the solution space. Here we propose a new quasi-static phase field formulation for modeling fluid-driven fracturing in elastic media at small strains. The approach fully couples the fluid flow in the fracture (described via the Reynolds lubrication approximation) and the deformation of the surrounding medium. The flow is solved on a lower dimensionality mesh immersed in the elastic medium. This approach leads to accurate coupling of both physics. We assessed the performance of the model extensively by comparing results for the evolution of fracture length, aperture, and fracture fluid pressure against analytical solutions under different fracture propagation regimes. The excellent performance of the numerical model in all regimes builds confidence in the applicability of phase field approaches to simulate fluid-driven fracture.United States. Department of Energy (Grant DE-SC0009286)Spain. Ministerio de EconomĂa y Competitividad (Grant RyC-2012-11704)Spain. Ministerio de EconomĂa y Competitividad (Grant CTM2014-54312-P
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