A Simple Model for Anomalous Relaxation in Porous Media

1995 ◽  
Vol 407 ◽  
Author(s):  
Mariela Araujo ◽  
Orlando Gonzalez
Keyword(s):  
Porous Media ◽  
Simple Model ◽  
Disordered Systems ◽  
Particle Density ◽  
Numerical Data ◽  
Random Variable ◽  
Porous Rocks ◽  
Power Law Distribution ◽  
Numerical Predictions ◽  
Anomalous Relaxation

ABSTRACTWe present a simple model to explain anomalous relaxation in random porous media. The model, based on the properties of random walks on a disordered structure, is able to describe essential features of the relaxation process in terms of a one body picture, in which the many body effects are approximated by geometrical restrictions on the particles diffusion. Disorder is considered as a random variable (quenched and annealed) taken from a power-law distribution |μ|ξμ−1. Quantities relevant to relaxation phenomena, such as the characteristic function and the particle density are calculated. Different regimes are observed as a function of the disorder parameter μ. For μ > 1 the relaxation is of exponential or Debye type, and turns into a stretched exponential as μ decreases. We compare numerical predictions (based on Monte Carlo simulations) with experimental data from porous rocks obtained by Nuclear Magnetic Resonance, and numerical data from other disordered systems.

Testing a simple model of gas bubble dynamics in porous media

2015 ◽  
Vol 51 (2) ◽  
pp. 1036-1049 ◽  
Author(s):  
Jorge A. Ramirez ◽  
Andy J. Baird ◽  
Tom J. Coulthard ◽  
J. Michael Waddington
Keyword(s):  
Porous Media ◽  
Simple Model ◽  
Bubble Dynamics ◽  
Gas Bubble

scholarly journals Phenotyping Women Based on Dietary Macronutrients, Physical Activity, and Body Weight Using Machine Learning Tools

Nutrients ◽  
2019 ◽  
Vol 11 (7) ◽  
pp. 1681 ◽  
Author(s):  
Ramyaa Ramyaa ◽  
Omid Hosseini ◽  
Giri P. Krishnan ◽  
Sridevi Krishnan
Keyword(s):  
Physical Activity ◽  
Machine Learning ◽  
Cluster Analysis ◽  
Body Weight ◽  
Energy Balance ◽  
Numerical Data ◽  
Support Vector ◽  
Learning Tools ◽  
K Nearest Neighbor ◽  
Numerical Predictions

Nutritional phenotyping can help achieve personalized nutrition, and machine learning tools may offer novel means to achieve phenotyping. The primary aim of this study was to use energy balance components, namely input (dietary energy intake and macronutrient composition) and output (physical activity) to predict energy stores (body weight) as a way to evaluate their ability to identify potential phenotypes based on these parameters. From the Women’s Health Initiative Observational Study (WHI OS), carbohydrates, proteins, fats, fibers, sugars, and physical activity variables, namely energy expended from mild, moderate, and vigorous intensity activity, were used to predict current body weight (both as body weight in kilograms and as a body mass index (BMI) category). Several machine learning tools were used for this prediction. Finally, cluster analysis was used to identify putative phenotypes. For the numerical predictions, the support vector machine (SVM), neural network, and k-nearest neighbor (kNN) algorithms performed modestly, with mean approximate errors (MAEs) of 6.70 kg, 6.98 kg, and 6.90 kg, respectively. For categorical prediction, SVM performed the best (54.5% accuracy), followed closely by the bagged tree ensemble and kNN algorithms. K-means cluster analysis improved prediction using numerical data, identified 10 clusters suggestive of phenotypes, with a minimum MAE of ~1.1 kg. A classifier was used to phenotype subjects into the identified clusters, with MAEs <5 kg for 15% of the test set (n = ~2000). This study highlights the challenges, limitations, and successes in using machine learning tools on self-reported data to identify determinants of energy balance.

scholarly journals Unsteady Stokes flow near boundaries: the point-particle approximation and the method of reflections

2018 ◽  
Vol 841 ◽  
pp. 883-924 ◽  
Author(s):  
A. Simha ◽  
J. Mo ◽  
P. J. Morrison
Keyword(s):  
Brownian Motion ◽  
Slip Plane ◽  
Metallic Nanoparticles ◽  
Particle Density ◽  
Point Particle ◽  
Plane Boundary ◽  
Short Time Scale ◽  
Approximation Techniques ◽  
Numerical Predictions ◽  
Particle Approximation

Problems of particle dynamics involving unsteady Stokes flows in confined geometries are typically harder to solve than their steady counterparts. Approximation techniques are often the only resort. Felderhof (see e.g. J. Phys. Chem. B, vol. 109 (45), 2005, pp. 21406–21412; J. Fluid Mech., vol. 637, 2009, pp. 285–303) has developed a point-particle approximation framework to solve such problems, especially in the context of Brownian motion. Despite excellent agreement with past experiments, this framework produces unsteady drag coefficients that depend on particle density. This is inconsistent, since the problem can be formulated mathematically without any reference to the particle’s density. We address this inconsistency in our work. Upon implementing our modifications, the framework passes consistency checks that it previously failed. Further, it is not obvious that such an approximation should work for short-time-scale motion. We investigate its validity by deriving it from a general formalism based on integral equations through a series of systematic approximations. We also compare results from the point-particle framework against a calculation performed using the method of reflections, for the specific case of a sphere near a full-slip plane boundary. We find from our analysis that the reasons for the success of the point-particle approximation are subtle and have to do with the nature of the unsteady Oseen tensor. Finally, we provide numerical predictions for Brownian motion near a full-slip and a no-slip plane wall based on the point-particle approximation as used by Felderhof, our modified point-particle approximation and the method of reflections. We show that our modifications to Felderhof’s framework would become significant for systems of metallic nanoparticles in liquids.

Chemotaxis under flow disorder shapes microbial dispersion in porous media 

2021 ◽  
Author(s):  
Pietro de Anna ◽  
Amir A. Pahlavan ◽  
Yutaka Yawata ◽  
Roman Stocker ◽  
Ruben Juanes
Keyword(s):  
Porous Media ◽  
Dispersion Coefficient ◽  
Pore Space ◽  
Low Flow ◽  
Pore Scale ◽  
Porous Rocks ◽  
Chemical Gradients ◽  
Deep Earth ◽  
Bacterium Bacillus Subtilis ◽  
Bacterium Bacillus

&lt;div&gt; &lt;div&gt; &lt;div&gt; &lt;p&gt;Natural soils are host to a high density and diversity of microorganisms, and even deep-earth porous rocks provide a habitat for active microbial communities. In these environ- ments, microbial transport by disordered flows is relevant for a broad range of natural and engineered processes, from biochemical cycling to remineralization and bioremediation. Yet, how bacteria are transported and distributed in the sub- surface as a result of the disordered flow and the associ- ated chemical gradients characteristic of porous media has remained poorly understood, in part because studies have so far focused on steady, macroscale chemical gradients. Here, we use a microfluidic model system that captures flow disorder and chemical gradients at the pore scale to quantify the transport and dispersion of the soil-dwelling bacterium Bacillus subtilis in porous media. We observe that chemotaxis strongly modulates the persistence of bacteria in low-flow regions of the pore space, resulting in a 100% increase in their dispersion coefficient. This effect stems directly from the strong pore-scale gradients created by flow disorder and demonstrates that the microscale interplay between bacterial behaviour and pore-scale disorder can impact the macroscale dynamics of biota in the subsurface.&lt;/p&gt; &lt;/div&gt; &lt;/div&gt; &lt;/div&gt;

Porous Medium Interconnector Effects on the Thermohydraulics of Near-Compact Heat Exchangers Treated as Porous Media

2006 ◽  
Vol 129 (3) ◽  
pp. 273-281 ◽  
Author(s):  
K. Sumithra Raju ◽  
Arunn Narasimhan
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Heat Exchangers ◽  
Fluid Transport ◽  
Energy Transport ◽  
Metal Foam ◽  
Volume Ratio ◽  
Numerical Data ◽  
Darcy Number ◽  
Compact Heat Exchangers

A novel approach of treating near-compact heat exchangers (NCHX) (surface to volume ratio, α=100-300m2∕m3 with hydraulic diameter DM∼6mm) as a “global” porous media, whose thermohydraulic performance is being influenced by the presence of “local” tube-to-tube porous medium interconnectors, connecting the in-line arrangement of tubes (D=2mm) having square pitch of XT=XL=2.25, is investigated in this study using numerical methods. The thermohydraulics of the global porous media (NCHX) are characterized by studying the effect of transverse thickness (δ) and permeability (represented by Dai) of the local metal foam type porous medium interconnectors on the global heat transfer coefficient (Nu) and nondimensional pressure drop (ξ). The fluid transport in the porous medium interconnectors is governed by the Brinkman–Darcy flow model while the volume averaged energy equation is used to model energy transport, with the tube walls kept at constant temperature and exchanging heat with the cooling fluid having Pr=0.7 under laminar flow (10<Re<100). For the chosen NCHX configuration, ξ and Nu increases for an increase in Re and also with an increase in the thickness (δ) of the interconnecting porous medium. However, as the local Darcy number (Dai) of the interconnecting porous medium increases, the ξ decreases but the Nu increases. Treating the heat exchanger as a global porous media this result translates to an increase in the ξ and Nu as the global permeability (represented by Dag) decreases, where the decrease in Dag is because of either an increase in δ or a decrease in Dai. Separate correlations predicting ξ and Nu as a function of Re and Dag (which in turn is correlated to δ and Dai) have been developed for the chosen NCHX configuration, both of which predict the numerical data with ±20% accuracy.

Foams as Blocking Agents in Porous Media

1970 ◽  
Vol 10 (01) ◽  
pp. 51-55 ◽  
Author(s):  
Robert A. Albrecht ◽  
Sullivan S. Marsden
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Natural Gas ◽  
Gas Flow ◽  
Gas Storage ◽  
Flow In Porous Media ◽  
Porous Rocks ◽  
Experimental Conditions ◽  
Storage Reservoirs

Abstract Although foam usually will flow in porous media, under certain controllable conditions it can also be used to block the flow of gas, both in unconsolidated sand packs and in sandstones. After steady gas or foam flow has been established at a certain injection pressure pi, the pressure is decreased until flow pressure pi, the pressure is decreased until flow ceases at a certain blocking pressure pb. When flow is then reestablished at a second, higher pi, blocking can again occur at another pb that will usually be greater than the first pi. The relationship between pi and Pb depends on the type of porous medium and the foamer solution saturation in the porous medium. A process is suggested whereby porous medium. A process is suggested whereby this phenomenon might be used to impede or block leakage in natural gas storage projects. Introduction The practice of storing natural gas in underground porous rocks has developed rapidly, and it now is porous rocks has developed rapidly, and it now is the major way of meeting peak demands in urban areas of the U. S. Many of these storage projects have been plagued with gas leakage problems that have, in some cases, presented safety hazards and resulted in sizeable economic losses. Usually these leaks are due to such natural factors as faults and fractures, or to such engineering factors as poor cement jobs and wells that were improperly abandoned. For the latter, various remedies such as spot cementing have been tried but not always with great success. In recent years several research groups have been studying the flow properties of aqueous foams and their application to various petroleum engineering problems. Most of this work has been done under problems. Most of this work has been done under experimental conditions such that the foam would flow in either tubes or porous media. However, under some extreme or unusual experimental conditions, flow in porous media becomes very difficult or even impossible. This factor also has suggested m us as well as to others that foam can be used as a gas flow impeder or as a sealant for leaks in gas storage reservoirs. In such a process, the natural ability of porous media to process, the natural ability of porous media to generate foam would be utilized by injecting a slug of foamer solution and following this with gas to form the foam in situ. This paper presents preliminary results of a sandy on the blockage of gas flow by foam in porous media. It also describes how this approach might be applied to a field process for sealing leaks in natural gas storage reservoirs. Throughout this report, we use the term "foam" to describe any dispersed gas-liquid system in which the liquid is the continuous phase, and the gas is the discontinuous phase. APPARATUS AND PROCEDURE A schematic drawing of the apparatus is shown in Fig. 1. At least 50 PV of filtered, deaerated foamer solution were forced through the porous medium to achieve liquid saturation greater than 80 percent. Afterwards air at controlled pressures was passed into the porous medium in order to generate foam in situ. Table 1 shows the properties and dimensions of the several porous media that were used. The beach sands were washed, graded and packed into a vibrating lucite tube containing a constant liquid level to avoid Stoke's law segregation over most of the porous medium. JPT P. 51

Toward the Detailed Simulation of the Heat Transfer Processes in Unsaturated Porous Media

2009 ◽  
Author(s):  
F. A. Jafar ◽  
G. R. Thorpe ◽  
O¨. F. Turan
Keyword(s):  
Heat Transfer ◽  
Porous Media ◽  
Unsaturated Porous Media ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients ◽  
Transfer Processes ◽  
Numerical Predictions ◽  
Three Phase ◽  
Detailed Simulation ◽  
Horizontal Cylinders

Trickle bed chemical reactors and equipment used to cool horticultural produce usually involve three phase porous media. The fluid dynamics and heat transfer processes that occur in such equipment are generally quantified by means of empirical relationships between dimensionless groups. The research reported in this paper is motivated by the possibility of using detailed numerical simulations of the phenomena that occur in beds of irrigated porous media to obviate the need for empirical correlations. Numerical predictions are obtained using a CFD code (FLUENT) for 2-D configurations of three cylinders. Local and mean heat transfer coefficients around these non-contacting horizontal cylinders are calculated numerically. The present results compare well with those available in the literature. The numerical results provide an insight into the cooling mechanisms within beds of unsaturated porous media.

Experimental and Numerical Investigation of Secondary Flow Structures in an Annular Low Pressure Turbine Cascade Under Periodic Wake Impact—Part 2: Numerical Results

2019 ◽  
Vol 141 (2) ◽  
Author(s):  
Benjamin Winhart ◽  
Martin Sinkwitz ◽  
Andreas Schramm ◽  
David Engelmann ◽  
Francesca di Mare ◽  
...  
Keyword(s):  
Secondary Flow ◽  
Direct Interaction ◽  
Numerical Data ◽  
Horseshoe Vortex ◽  
Low Pressure ◽  
Navier Stokes ◽  
Flow Structures ◽  
Pressure Loss Coefficient ◽  
Low Pressure Turbine ◽  
Numerical Predictions

In this work, we present the results of the numerical investigations of periodic wake–secondary flow interaction carried out on a low pressure turbine (LPT) equipped with modified T106-profile blades. The numerical predictions obtained by means of unsteady Reynolds-averaged Navier–Stokes (URANS) simulations using a k-ω-model have been compared with measurements conducted in the same configuration and showed a good agreement. Based on the verified numerical data, the Q-criterion has been employed to characterize the secondary flow structures and accurately identify their origin. An analysis of the fundamental wake kinematics and the unsteady vortex migration revealed dominant interaction mechanisms such as the circumferential fluctuation of the pressure side horseshoe vortex (HSV) and its direct interaction with the passage vortex (PV) and the concentrated shed vortex (CSV). Finally, a correlation with the total pressure loss coefficient is provided and a link to the incoming wake structures is given.

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