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Register a new userEntropy-based inhomogeneity detection in porous media
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Added by
Patricia Alonso Ruiz
Publication date
2016
fields
Mathematical Statistics
and research's language is
English
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We study a change-point problem for random fields based on a univariate detection of outliers via the $3sigma$-rule in order to recognize inhomogeneities in porous media. In particular, we focus on fibre reinforced polymers modeled by stochastic fibre processes with high fibre intensity and search for abrupt changes in the direction of the fibres. As a measure of change, the entropy of the directional distribution is locally estimated within a window that scans the region to be analyzed.
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Microseismicity in subsurface geologic environments, such as sandstone gas reservoirs, is expected in the presence of liquid or gas injection. Although difficult to predict, the potential for microseismic events is important to field-scale projects, such as geologic storage of CO2 whereby the gas is injected into natural sandstone formations. We conjecture that a primary factor causing microseismicity is the existence of metastable states in granular porous medium and provide experimental evidence for its validity. External perturbation trigger abrupt relaxation events, which, with a certain probability, can grow into macroscopic microseismic events. Here the triggering perturbation is produced by cooling to a cryogenic temperature. As the sensor for the abrupt relaxation events we use thin Al films deposited on the sandstone surface. We show that as the temperature is varied, the films resistance exhibits sharp jumps, which we attribute to mechanical restructuring or microfractures in the fabric of the sandstone. We checked the superconducting characteristics of the Al thin films on the sandstone and found microwave-induced Shapiro steps on the voltage-current diagrams. Such quantized steps provide indicates that the film is made of a network of nanobridges, which makes it ever more sensitive to abrupt relaxation events occurring in the substrate, i.e., in the underlying sandstone.
We investigate the elastoviscoplastic flow through porous media by numerical simulations. We solve the Navier-Stokes equations combined with the elastoviscoplastic model proposed by Saramito for the stress tensor evolution. In this model, the material behaves as a viscoelastic solid when unyielded, and as a viscoelastic Oldroyd-B fluid for stresses higher than the yield stress. The porous media is made of a symmetric array of cylinders, and we solve the flow in one periodic cell. We find that the solution is time-dependent even at low Reynolds numbers as we observe oscillations in time of the unyielded region especially at high Bingham numbers. The volume of the unyielded region slightly decreases with the Reynolds number and strongly increases with the Bingham number; up to 70% of the total volume is unyielded for the highest Bingham numbers considered here. The flow is mainly shear dominated in the yielded region, while shear and elongational flow are equally distributed in the unyielded region. We compute the relation between the pressure drop and the flow rate in the porous medium and present an empirical closure as function of the Bingham and Reynolds numbers. The apparent permeability, normalized with the case of Newtonian fluids, is shown to be greater than 1 at low Bingham numbers, corresponding to lower pressure drops due to the flow elasticity, and smaller than 1 for high Bingham numbers, indicating larger dissipation in the flow owing to the presence of the yielded regions. Finally we investigate the effect of the Weissenberg number on the distribution of the unyielded regions and on the pressure gradient.
The tendency of irreversible processes to generate entropy is the ultimate driving force for the evolution of nature. In engineering, entropy production is often used as a measure of usable energy losses. In this study we show that the analysis of the entropy production patterns can help understand the vastly diversified experimental observations of water-rock interactions in natural porous media. We first present a numerical scheme for the analysis of entropy production in dissolving porous media. Our scheme uses a greyscale digital model of natural chalk obtained by X-ray nanotomography. Greyscale models preserve structural heterogeneities with very high fidelity, which is essential for simulating a system dominated by infiltration instability. We focus on the coupling between two types of entropy production: the percolative entropy generated by dissipating the kinetic energy of fluid flow and the reactive entropy that originates from the consumption of chemical free energy. Their temporal patterns pinpoint three stages of microstructural evolution. We then show that the regional mixing deteriorates infiltration instability by reducing local variations in reactant distribution. In addition, we show that the microstructural evolution can be particularly sensitive to the initially present transport heterogeneities when the global flowrate is small. This dependence on flowrate indicates that the need to resolve the structural features of a porous system is greater when the residence time of the fluid is long.
Porous media with hierarchical structures are commonly encountered in both natural and synthetic materials, e.g., fractured rock formations, porous electrodes and fibrous materials, which generally consist of two or more distinguishable levels of pore structure with different characteristic lengths. The multiphase flow behaviours in hierarchical porous media have remained elusive. In this study, we investigate the influences of hierarchical structures in porous media on the dynamics of immiscible fingering during fluid-fluid displacement. By conducting a series of numerical simulations, we found that the immiscible fingering can be suppressed due to the existence of secondary porous structures. To characterise the fingering dynamics in hierarchical porous media, a phase diagram is constructed by introducing a scaling parameter, i.e., the ratio of time scales considering the combined effect of characteristic pore sizes and wettability. The findings present in this work provide a basis for further research on the application of hierarchical porous media for controlling immiscible fingerings.
Transport of viscous fluid through porous media is a direct consequence of the pore structure. Here we investigate transport through a specific class of two-dimensional porous geometries, namely those formed by fluid-mechanical erosion. We investigate the tortuosity and dispersion by analyzing the first two statistical moments of tracer trajectories. For most initial configurations, tortuosity decreases in time as a result of erosion increasing the porosity. However, we find that tortuosity can also increase transiently in certain cases. The porosity-tortuosity relationships that result from our simulations are compared with models available in the literature. Asymptotic dispersion rates are also strongly affected by the erosion process, as well as by the number and distribution of the eroding bodies. Finally, we analyze the pore size distribution of an eroding geometry. The simulations are performed by combining a high-fidelity boundary integral equation solver for the fluid equations, a second-order stable time stepping method to simulate erosion, and new numerical methods to stably and accurately resolve nearly-touching eroded bodies and particle trajectories near the eroding bodies.
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