Diffusion Flow Research Articles

Impact of liquid nitrogen freeze–thaw on multistage gas flow: differences between shallow and deep coal in Qinshui Basin

Liquid nitrogen freeze–thaw (LNFT) is an environmentally-friendly permeability enhancement technology. There are significant differences between shallow and deep coal in their composition and stress history. Therefore, it is necessary to reveal the difference in the impact of LNFT on the multistage gas flow between shallow and deep coal. In this paper, the differences in multistage gas flow were revealed from the perspective of a multiscale structure evolution, and the differences in the multiscale structure evolution were analyzed from the coal compositions and stress history. Nuclear magnetic resonance method was used in the multiscale structure evolution characterization. As for the multistage gas flow evolution, gas ad/de-sorption, diffusion, and seepage evolution characterization were investigated. There is a quadratic relationship between the total porosity and LNFT cycles in both shallow and deep coal. The fracture expansion is dominant in deep coal, while pores connectivity enhancement is dominant in shallow coal. The permeability of both shallow and deep coal increases during the LNFT cycling, presenting a logarithmic correlation between permeability and the number of cycles. With the same porosity, shallow coal has a higher permeability. LNFT cycling can improve the Langmuir volume. Langmuir volume and gas diffusion coefficients of deep coal is smaller both pre- and post-LNFT cycling. Except for CH4 in deep coal, the Langmuir pressure and gas diffusion coefficients in both coals are improved by LNFT cycling.

Transient study of thermal stratification of full-scale chilled water storage tank during optimum discharge condition

Thermal stratification of full-scale Chilled Water Storage Tanks (5855 m3) with 18 m tank diameter, and 23 m water depth during discharge mode and optimum condition was studied. The experimental and numerical analyse of stratified thermal storage tank in full-scale dimension and discharge mode has been studied. A 3D and 2D numerical model was performed. The case simplified to divide into two parts, the first part was to simulate flow in pipes and radial diffuser, and the second part included simulation in the tank according to the part one results. The optimum operation condition which found from many tests of tank operation conditions according to high thermal stratification and low thermal mixing inside the tank. Validation test with experimental data obtained from the present work and literature. The results included to analyse the thermal stratification and the flow characteristics during the discharging mode. Also, thermal performance parameters such as discharge efficiency, Richardson number, stratification efficiency, thermocline thickness, the average temperature in the tank, and discharge temperature were presented. The important result of the above analysis was the optimum stratification phenomena in the tank with low thermal mixing. The contribution of this study was the numerical modelling and simulation setting to capture the experimental results of these phenomena in the full-scale thermal storage tank, moreover to specify the optimum condition of thermal stratification of this tank dimension, diffuser type, and flow rate.

“Eddy” Saturation of the Antarctic Circumpolar Current by Standing Waves

Abstract It is now well established that changes in the zonal wind stress over the Antarctic Circumpolar Current (ACC) do not lead to changes in its baroclinicity nor baroclinic transport, a phenomenon referred to as “eddy saturation.” Previous studies provide contrasting dynamical mechanisms for this phenomenon: on one extreme, changes in the winds lead to changes in the efficiency with which transient eddies transfer momentum to the sea floor; on the other extreme, structural adjustments of the ACC’s standing meanders increase the efficiency of momentum transfer. In this study the authors investigate the relative importance of these mechanisms using an idealized, isopycnal channel model of the ACC. Via separate diagnoses of the model’s time-mean flow and eddy diffusivity, the authors decompose the model’s response to changes in wind stress into contributions from transient eddies and the mean flow. A key result is that holding the transient eddy diffusivity constant while varying the mean flow very closely compensates for changes in the wind stress, whereas holding the mean flow constant and varying the eddy diffusivity does not. This implies that eddy saturation primarily occurs due to adjustments in the ACC’s standing waves/meanders, rather than due to adjustments of transient eddy behavior. The authors derive a quasigeostrophic theory for ACC transport saturation by standing waves, in which the transient eddy diffusivity is held fixed, and thus provides dynamical insights into standing wave adjustment to wind changes. These findings imply that representing eddy saturation in global models requires adequate resolution of the ACC’s standing meanders, with wind-responsive parameterizations of the transient eddies being of secondary importance.

Global-in-time mean-field convergence for singular Riesz-type diffusive flows

We consider the mean-field limit of systems of particles with singular interactions of the type −log|x| or |x|−s, with 0<s<d−2, and with an additive noise in dimensions d≥3. We use a modulated-energy approach to prove a quantitative convergence rate to the solution of the corresponding limiting PDE. When s>0, the convergence is global in time, and it is the first such result valid for both conservative and gradient flows in a singular setting on Rd. The proof relies on an adaptation of an argument of Carlen–Loss (Duke Math. J. 81 (1995) 135–157) to show a decay rate of the solution to the limiting equation, and on an improvement of the modulated-energy method developed in (SIAM J. Math. Anal. 48 (2016) 2269–2300; Duke Math. J. 169 (2020) 2887–2935; Nguyen, Rosenzweig and Serfaty (2021)), making it so that all prefactors in the time derivative of the modulated energy are controlled by a decaying bound on the limiting solution.

Effect of Double-Diffusive Stagnation point flow of Eyring– Powell Nanofluid on a Slender Stretching Sheet with Non-uniform heat Source Sink and Inclined Magnetic Field

In the present paper, the effects of an inclined magnetic field and a non-uniform heat source sink on a double diffusive convective stagnation point flow in a slender stretching sheet are studied. The suitable similarity transformation is utilized for the conversion of nonlinear differential equations. These converted equations are solved by means of Differential Transformation method (DTM) with the support of symbolic software Mathematica. Further, the effects of appropriate parameters on velocity profile, solute, nanoparticle concentration and temperature profiles are shown graphically with some suitable discussions. It is found that velocity decreases with a rise of magnetic parameter. Because applying the uniform magnetic field normal to the flow direction gives rise to Lorentz force. This force has the tendency to slow down the velocity of the fluid in the boundary layer. Also non-uniform heat source sink parameters enhance the thermal profile of the system. But, opposite behavior can be seen in solute and nanoparticle concentration profiles. Such results can be useful in design and structure of materials, where implementation of variable thickness decreases the weight of stretched element and boosts the usage of materials.

The nonlocal thermo‐hydro‐mechanical model for cracking behaviors of quasi‐brittle materials in the framework of advanced general particle dynamics

AbstractA novel nonlocal thermo‐hydro‐mechanical coupling model is proposed to investigate cracking behaviors of quasi‐brittle materials in the framework of advanced general particle dynamics (GPD). The nonlocal thermal conduction equation and the nonlocal flow diffusion equation are derived based on nonlocal vector calculus and the microscopic constitutive equation. Moreover, the coupling influences are considered based on the nonlocal equation and the coupling principle. The governing equation of the coupling system is established in the framework of GPD. The correctness of the proposed model is verified through comparing with the corresponding experimental data, and the numerical results are in good agreement with experimental results. Finally, the proposed model is applied to analyze the deformation and cracking behaviors of rock mass around tunnels, and the stress redistribution is revealed under thermo‐hydro‐mechanical coupling condition.

Establishing highly efficient absorptive and catalytic network for depolarized high-stability lithium-sulfur batteries

Practical operation of lithium-sulfur (Li-S) batteries with high sulfur loading and efficient/stable sulfur conversion requires the suppression of the lithium polysulfides (LiPSs) shuttling and the facilitation of ion and electron transfer on the electrode material surface. Herein, a multifunctional current collector, composed of Ag@polypyrrole (PPy) coated electrospun carbon nanofibers (CNF) framework, was rationally designed to construct a highly efficient catalytic/absorptive/conductive network to improve the performance of Li-S batteries under practical operation condition. At the molecular scale, the Ag@PPy molecular not only effectively inhibits LiPSs shuttle effect, but also achieves the fast sulfur catalysis and depolarization during charge transfer due to the high conductivity of Ag nanoparticles. At the electrode scale, the three-dimensional (3D) robust fibrous nanostructure provides abundant physical space to realize high sulfur loading, maintains electrode integrity during large volume change of active sulfur and under mechanical abuse condition, as well as enables the high-flux Li+ diffusion and electrolyte flow. Consequently, Li-S batteries with the CNF/Ag@PPy current collector delivered excellent cycling stability (capacity fading of 0.048% per cycle over 500cycles at 1.0C) and high energy density (234.2 Wh kgcell-1 under high sulfur loading of 9.77 mg cm−2). Flexible Li-S batteries are also fabricated indicating the feasibility of the CNF/Ag@PPy current collector in flexible devices.

Numerical simulation of fracturing and imbibition in shale oil horizontal wells

The shale oil reservoir is characterized by tight lithology and ultra-low permeability, and its efficient exploitation requires the technology of multi-stage and multi-cluster hydraulic fracturing in horizontal wells and shut-in imbibition. After multi-stage and multi-cluster hydraulic fracturing, a complex fracture network is formed, and a large volume of frac fluid is stored within the fracture network. During shut-in, imbibition and exchange between oil and water occurs under the action of the capillary force and osmotic pressure, and the formation pressure builds up in the shale reservoir. On basis of the characteristics of shale oil reservoir, we establish a model of imbibition during fracturing injection and shut-in by coupling oil–water two-phase flow and saline ion diffusion in the hydraulic fractures (HFs) network, natural fractures (NFs) and matrix system under the action of capillary force and osmotic pressure. The DFN method and the multiple continuum method are introduced to characterize fluid flow between the HF and the NF and that between the NF and the matrix respectively, which avoids the problem of a large amount of computation of seepage within the complex fracture. Then, the discrete fracture network (DFN) model and the multiple continuum model are solved with the finite element method, and it is verified in flow field, saturation field and concentration field that the models are accurate and reliable. We propose the imbibition exchange volume for quantitative evaluation of the imbibition degree and a method of calculating the imbibition exchange volume. Simulation of oil and water flow in the fracturing and shut-in stages is performed based on these models. It is found that imbibition in the shale reservoir is driven by mechanisms of pressure difference, capillary force and osmotic pressure. The osmotic pressure and capillary force only cause an increase in the imbibition rate and a reduction in the imbibition equilibrium time and do not lead to variation in the peak of imbibition exchange volume. The imbibition equilibrium time under the action of the capillary force and osmotic pressure is reduced from 150 to 45 d compared with that under the action of the pressure difference. If imbibition equilibrium is reached, low initial water saturation, strong rock compressibility, high formation water salinity and high matrix permeability enhance imbibition and exchange of oil and water in the reservoir. The leakoff volume of frac fluid is generally larger than the imbibition exchanged volume. Leakoff equilibrium occurs slightly earlier than imbibition equilibrium. The imbibition equilibrium time is mainly affected by reservoir permeability and NF density. The number of interconnected fractures mainly affects the frac fluid volume within the hydraulic fracture in the fracturing process. The stimulated reservoir volume (SRV) mainly affects frac fluid imbibition exchange in the shut-in process.

Permeability evolution and gas flow in wet coal under non-equilibrium state: Considering both water swelling and process-based gas swelling

Accurate knowledge of gas flow within the reservoir and related controlling factors will be important for enhancing the production of coal bed methane. At present, most studies focused on the permeability evolution of dry coal under gas adsorption equilibrium, gas flow and gas diffusion within wet coal under the generally non-equilibrium state are often ignored in the process of gas recovery. In this study, an improved apparent permeability model is proposed which accommodates the water and gas adsorption, stress dependence, water film thickness and gas flow regimes. In the process of modeling, the water adsorption is only affected by water content while the gas adsorption is time and water content dependent; based on poroelastic mechanics, the effective fracture aperture and effective pore radius are derived; and then the variation in water film thickness for different pore types under the effect of water content, stress and adsorption swelling are modeled; the flow regimes are considered based on Beskok’s model. Further, after validation with experimental data, the proposed model was applied to numerical simulations to investigate the evolution of permeability-related factors under the effect of different water contents. The gas flow in wet coal under the non-equilibrium state is explicitly revealed.

Ultra-deep carbonate basement reservoirs formed by polyphase fracture-related karstification in the Offshore Bohai Bay Basin, China

The Palaeozoic carbonate basement of the Offshore Bohai Bay Basin (OBBB) presents considerable potential for hydrocarbon exploration. However, the multistage tectonism and complex superimposed palaeo-karstification in the area are unclear, which leads to a lack of understanding on the formation mechanism and distribution of the deep carbonate basement reservoirs. In this study, the occurrence of a fracture-vug network and its fillings in carbonate reservoirs were investigated based on borehole cores, thin sections, and image logs from the southwestern slope of the OBBB's Bozhong Sag. Then the diagenetic fluid properties of the carbonate matrix and fillings were analysed via the data of carbon, oxygen, and strontium isotopes, and major, rare elements from coring intervals. The results revealed that fracture-related karst reservoirs have lithologic selectivity inclined toward dolomite strata. The intersecting relationships, widths, and strikes of the fractures and the regional tectonic background indicate three structural fracture families: NW-, NNE-, and NNW- trending, related to the Indosinian, middle Yanshanian, and late Yanshanian orogeny, respectively. The Indosinian NW- and end-Mesozoic NNE-trending fractures produced by compressional tectonic stress mainly contributed to the formation of the basement reservoirs. The geochemistry of the calcite veins filling these fractures suggests two main types of diagenetic fluids. The fluid of autogenic recharge related to the earlier fills is karstification diffuse flow dominated by internal runoff from rainfall in the highland setting of the Indosinian thrusting orogenic belt. The other fluid of allogenic recharge related to the later fills is the main lateral freshwater flow dominated by external runoff from the catchment in the setting of the horst-lowland within the rifting basin, induced by the Yanshanian destruction of the North China Craton. Finally, the relationship between the three fracture families and two kinds of related fluids is revealed. This allows us to propose a model to understand the polyphase-superimposed fracture-related karst reservoir complexes within the deep carbonate basement of tilting fault blocks that neighbour the Bozhong hydrocarbon kitchen and predict the formation of potential plays with high accuracy.

Modes of multi-mechanistic gas diffusion in shale matrix at varied effective stresses: Observations and analysis

Gas diffusion in the shale matrix has a dominant effect on late-stage production from shale gas reservoirs. However, adequate research on the mechanisms and contributions of gas diffusion for varied pore size populations in shale matrix under recreated in situ stress is lacking. We report gas-diffusion measurements under constant in situ stress but variable gas pressures for contrasting non-adsorbent (helium (He)) and adsorbed (methane (CH4)) gases to investigate the impact of effective stress on the evolution of dominant mechanisms of diffusion. An intact sample replicates true pore-network topology and diffusion paths. An integrated diffusion model is proposed that combines the effects of slip flow, Knudsen flow, and surface diffusion to constrain the evolution of these flow regimes and their respective contributions to the observational data. Finally, a probability density function (PDF) is employed to separate the gas content distributions of macropores and micropores from the total gas content and to investigate gas contributions in various pores. The results reveal that the diffusion coefficients of both He and CH4 in macropores and micropores increase with gas pressure but decrease with increasing effective stress. The diffusion coefficients of He and CH4 are different in macropores but remain nearly the same in micropores. The diffusion coefficients of slip flow and surface diffusion increase with decreasing effective stress except for CH4 diffusion in the micropores, while the evolution of Knudsen diffusion shows the opposite trend. Slip flow plays a dominant role in He and CH4 diffusion within macropores (pore size 45 nm). Knudsen diffusion gradually becomes significant for He diffusion in the micropores (pore size 4 nm), conversely, for CH4 diffusion in the micropores, surface diffusion becomes significant. Related to gas production from reservoirs, the contributions of the micropores will increase gradually with the duration of gas recovery, indicating the significant role of gas diffusion in micropores to steady supply during late-stage production.

Significance of MHD Cross nanofluid analysis near a stretched surface with double stratification and activation energy

The flow of 2-D cross fluid model with mass and heat transmission over a linearly stretched sheet is analyzed in this paper. Furthermore, we have expanded our study by considering the effects of MHD flow, stagnation point, double stratification, heat generation, radiation effect, nanofluid flow, activation energy and mass diffusion. This type of study has not being investigated previously in literature. The flow generating PDEs are altered into ODEs by deploying suitable transformations. The effects of the parameters involved, namely the Weissenberg number, magnetic field coefficient, Brownian motion coefficient, radiation parameter, Damkohler number, thermophoresis coefficient, Schmidt number, activation energy, heat generation parameter and temperature difference coefficient on the velocity, concentration and energy fields are thoroughly scrutinized. The problem is solved through numerical technique (BVP4c) on MATLAB. The outcomes reveal that the velocity curve upsurges for rising Weissenberg number and decreases due to magnetic parameter. The heat field improves for increasing behavior of the Brownian motion, thermophoresis, heat generation, thermal conductivity and radiation coefficient whereas reverse results are obtained due to Prandtl number and stratification parameter. The concentration improves due to thermophoresis parameter and diffusivity coefficient while reverse outcomes are noticed due to Schmidt number, Damkohler number, temperature difference parameter and Brownian motion parameter.

Improved thermal conductivity of hydrodynamic third‐grade ferrofluid using nanolayer concept: A PTSC application

AbstractThe current study numerically investigates the heat diffusion in the cylindrical film flow of third‐grade ferroliquid. The nanolayer concept is used to analyze the effective thermal conductivity of ferrofluid in different shapes of nanoparticles. Ethylene glycol (EG)‐based cobalt (Co) nano‐sized particles are measured. Using hydrodynamics, Darcy‐Forchheimer, Ohmic heating, and nonlinear radiation effects, an exact model was developed and resolved through the bvp5c Matlab scheme. The computational outcomes are elucidated through pictorial and tabular results. The cylindrical‐shaped nanoparticles are reported to have more advanced heat relocation than the spherical‐shaped nanoparticles. This proved that the nanolayer formed with the cylindrical‐shaped nanoparticles' effectivity boosts the base liquid thermal conductivity. So, to enlarge the PTSC heat spread rate, suspension of Co‐cylindrical nanoparticles in base liquid with third‐grade rheological behavior is very helpful.

Dynamics of recombination in viscous electron–hole plasma in a mesoscopic GaAs channel

The recombination dynamics are studied in viscous electron–hole plasma, consisting of electrons and photo-generated heavy and light holes, formed in the high-mobility mesoscopic GaAs channel. It is shown that an increase in the pump power reduces the concentration and mobility of background electrons, which, in turn, slows down their recombination with photogenerated holes. At a critical pump power, the recombination time begins to decrease, which is a consequence of the transition of a viscous electron–hole plasma from the hydrodynamic regime to the Drude diffusive regime. The observed transition occurs when the scattering of electrons with disorder begins to dominate over electron–electron scattering, which leads to the transformation of an inhomogeneous Poiseuille charge flow into a homogeneous diffusion flow. As a result, an optical analogue of the Gurzhi effect has been found.

Rates of Convergence to Non-degenerate Asymptotic Profiles for Fast Diffusion via Energy Methods

This paper is concerned with a quantitative analysis of asymptotic behaviors of (possibly sign-changing) solutions to the Cauchy–Dirichlet problem for the fast diffusion equation posed on bounded domains with Sobolev subcritical exponents. More precisely, rates of convergence to non-degenerate asymptotic profiles are revealed via an energy method. The sharp rate of convergence to positive ones was recently discussed by Bonforte and Figalli (Commun Pure Appl Math 74:744-789, 2021) based on an entropy method. An alternative proof for their result is also provided. Furthermore, the dynamics of fast diffusion flows with changing signs is discussed more specifically under concrete settings; in particular, exponential stability of some sign-changing asymptotic profiles is proved in dumbbell domains for initial data with certain symmetry.

Theory and numerics for Chen's flow of curves

In this article we study Chen's flow of curves from theoretical and numerical perspectives. We investigate two settings: that of closed immersed ω-circles, and immersed lines satisfying a cocompactness condition. In each of the settings our goal is to find geometric conditions that allow us to understand the global behaviour of the flow: for the cocompact case, the condition is straightforward and the argument is largely standard. For the closed case however, the argument is quite complex. The flow shrinks every initial curve to a point if it does not become singular beforehand, and we must identify a condition to ensure this behaviour as well as identify the point in order to perform the requisite rescaling. We are able to successfully conduct a full analysis of the rescaling under a curvature condition. The analysis resembles the case of the mean curvature flow more than other fourth-order curvature flow such as the elastic flow or the curve diffusion flow, despite the lack of maximum and comparison principles. Our work is informed by a numerical study of the flow, and we include a section that explains the algorithms used.

Flow separation control and performance evaluation of an asymmetric diffuser using vortex generators

Results are presented from a RANS study of an asymmetric diffuser with mild separation incorporating a vortex generator (VG) at the entrance. Three types of VGs in the form of a pyramidal ramp, and a pair of vanes that produces an upwash or a downwash respectively in the channel between them. In total, twelve VG configurations were included in this study. The flowfield downstream of the VG was analyzed using limiting streamlines. It was found that the VGs disrupted the two-dimensionality of the undisturbed flow, generally reducing the separation zone. In some cases, the separation bubble was split into two. The preliminary examination of the flow structures downstream of the VGs will help to improve the understanding of the underlying flow physics of VGs. The overall drag of the diffuser was analyzed using a non-dimensional parameter ΔCD obtained from a control volume analysis. None of the VGs caused the overall drag of the diffuser to decrease, with the best performance being no decrease. In the best case involving vanes that produce a downwash, an improvement was obtained in the distortion index. This study shows that there is promise in improving diffuser flows through placing vanes at the entrance.

Apparent permeability in tight gas reservoirs combining rarefied gas flow in a microtube

In tight gas reservoirs, the major flow channels are composed of micro/nanopores in which the rarefaction effect is prominent and the traditional Darcy law is not appropriate for gas flow. By combining the Maxwell first-order slip boundary condition and Navier–Stokes equations, a three-dimensional (3D) analysis of compressible gas slip flow in a microtube was presented, and the flux rate and pressure variation in the flow direction were discussed. Subsequently, by superimposing the Knudsen diffusion, a gas flux formula applicable to a larger Knudsen number was further proposed and satisfactorily verified by two groups of published experimental data in microtubes or microchannels in the membrane. The results indicate that slip flow and Knudsen diffusion make an important contribution to the total gas flow in the microtube, and their weight increases with an increase in the Knudsen number. By substituting the gas flux formula into Darcy’s law for compressible gas, a new apparent permeability model for tight gas reservoirs was proposed, in which the slippage effect and Knudsen diffusion were synthetically considered. The results indicate that the apparent permeability of tight reservoirs strongly depends on the reservoir pressure and pore-throat radius, and an underestimation value may be predicted by the previously published models. This study provides a case study for evaluating these apparent permeability models, which remains a challenging task in the laboratory.

Smoke dispersion test and emergency control plan of fire in mine roadway during downward ventilation

To explore the wind flow turbulence and smoke flow diffusion law during the mine downward ventilation fire, two similar experimental platforms of a inclined single pipe test device and a loop system multiple pipe test device were built. The change data of the air flow in the pipeline during the fire period under different air volumes were measured. The evolution process of downward ventilation fire in the whole roadway network domain in Dayan Mine was simulated, and the emergency plan was put forward. The results show that in the experiment, the combustion intensity of the fire source is positively correlated with the ventilation power, and the fire wind pressure increases with the increase of the inclination angle of the pipeline. The throttling effect of the fire area and the combustion of the fire source together make the air volume in the pipeline change rapidly. The critical wind speed that makes the downward ventilation flow fire wind pressure equal to the fan power is 1.8 m s−1. The stronger the fan capacity, the stronger the ability of the main air path to overcome the resistance of the fire zone and maintain the original state. In the simulation, the most dangerous place when the downward ventilation fire smoke is reversed is the area (weak flow area) in the mine tunnel network where the ventilation power is weaker than the fire wind power. This study can provide a theoretical basis for the formulation of emergency plans for mine fire accidents.

Hot Vents Beneath an Icy Ocean: The Aurora Vent Field, Gakkel Ridge, Revealed

Evidence of hydrothermal venting on the ultra-slow spreading Gakkel Ridge in the Central Arctic Ocean has been available since 2001, with first visual evidence of black smokers on the Aurora Vent Field obtained in 2014. But it was not until 2021 that the first ever remotely operated vehicle (ROV) dives to hydrothermal vents under permanent ice cover in the Arctic were conducted, enabling the collection of vent fluids, rocks, microbes, and fauna. In this paper, we present the methods employed for deep-sea ROV operations under drifting ice. We also provide the first description of the Aurora Vent Field, which includes three actively venting black smokers and diffuse flow on the Aurora mound at ~3,888 m depth on the southern part of the Gakkel Ridge (82.5°N). The biological communities are dominated by a new species of cocculinid limpet, two small gastropods, and a melitid amphipod. The ongoing analyses of Aurora Vent Field samples will contribute to positioning the Gakkel Ridge hydrothermal vents in the global biogeographic puzzle of hydrothermal vents.