An inverse analysis of fluid flow through granular media using differentiable lattice Boltzmann method

This study presents a method for the inverse analysis of fluid flow problems.The focus is put on accurately determining boundary conditions and characterizing the physical properties of granular media,such as permeability,and fluid components,like viscosity.The primary aim is to deduce either constant pressure head or pressure profiles,given the known velocity field at a steady-state flow through a conduit containing obstacles,including walls,spheres,and grains.The lattice Boltzmann method(LBM)combined with automatic differentiation(AD)(AD-LBM)is employed,with the help of the GPU-capable Taichi programming language.A lightweight tape is used to generate gradients for the entire LBM simulation,enabling end-to-end backpropagation.Our AD-LBM approach accurately estimates the boundary conditions for complex flow paths in porous media,leading to observed steady-state velocity fields and deriving macro-scale permeability and fluid viscosity.The method demonstrates significant advantages in terms of prediction accuracy and computational efficiency,making it a powerful tool for solving inverse fluid flow problems in various applications.

Numerical Solutions of the Classical and Modified Buckley-Leverett Equations Applied to Two-Phase Fluid Flow

Climate change is a reality. The burning of fossil fuels from oil, natural gas and coal is responsible for much of the pollution and the increase in the planet’s average temperature, which has raised discussions on the subject, given the emergencies related to climate. An energy transition to clean and renewable sources is necessary and urgent, but it will not be quick. In this sense, increasing the efficiency of oil extraction from existing sources is crucial, to avoid waste and the drilling of new wells. The purpose of this work was to add diffusive and dispersive terms to the Buckley-Leverett equation in order to incorporate extra phenomena in the temporal evolution between the water-oil and oil-water transitions in the pipeline. For this, the modified Buckley-Leverett equation was discretized via essentially weighted non-oscillatory schemes, coupled with a three-stage Runge-Kutta and a fourth-order centered finite difference methods. Then, computational simulations were performed and the results showed that new features emerge in the transitions, when compared to classical simulations. For instance, the dispersive term inhibits the diffusive term, adding oscillations, which indicates that the absorption of the fluid by the porous medium occurs in a non-homogeneous manner. Therefore, based on research such as this, decisions can be made regarding the replacement of the porous medium or the insertion of new components to delay the replacement.

Non-invasive assessment for intratumoural distribution of interstitial fluid flow

Interstitial fluid plays a vital role in drug delivery and tumour treatment.However,few non-invasive measurement methods are available for measuring low-velocity biological fluid flow.Therefore,this study aimed to develop a novel technology called interstitial flow velocity-MRI.The interstitial flow velocity-MRI sequence consists of a dual inversion recovery preparation and an improved stimulated echo sequence(ISTE)combined with phase-contrast MRI.A homemade flow phantom was used to assess the feasibility and sensitivity of interstitial flow velocity-MRI.In addition,xenografts of female BALB/c mouse models of 4T1 breast cancer administered losartan(40 mg/kg)or saline(n?6)were subjected to imaging on a 7.0 T scanner to assess the in vivo interstitial fluid flow velocity.The results showed a significant correlation(P<0.001)between the theoretical velocities and velocities measured using the flow phantom.Interstitial flow velocity-MRI could detect a velocity as low as 10.21±2.65 mm/s with a spatial resolution of 0.313 mm.The losartan group had a lower mean interstitial fluid velocity than the control group(85±16 vs 113±24 mm/s).In addition,compared to the saline treatment,losartan treatment reduced the proportion of collagen fibres by 10%and 12%in the Masson and Sirius red staining groups,respectively.Interstitial flow velocity-MRI has the potential to determine interstitial fluid flow velocity non-invasively and exhibits an intuitive velocity map.

Three-dimensional simulation of pore scale fluid flow in granular ore media with realistic geometry

The images of granular ore media were captured by X-ray CT scanner. Combined with digital image processing and finite element techniques, the three-dimensional geometrical model, which represents the realistic pore structure of the media, was constructed. With this model, three dimensional pore scale fluid flow among particles was simulated. Then the distributions of fluid flow velocity and pressure were analyzed and the hydraulic conductivity was calculated. The simulation results indicate the fluid flow behaviors are mainly dominated by the volume and topological structure of pore space. There exist obvious preferential flow and leaching blind zones simultaneously in the medium. The highest velocities generally occur in those narrow pores with high pressure drops. The hydraulic conductivity obtained by simulation is the same order of magnitude as the laboratory test result, which denotes the validity of the model. The pore-scale and macro-scale are combined and the established geometrical model can be used for the simulations of other phenomena during heap leaching process.

Three-dimensional turbulent model of heat transfer and fluid flow in GTAW process

A two-equation K-ε turbulent fluid flow model is built to model the heat transfer and fluid flow in gas tungsten arc welding （GTAW） process of stainless steel S US310 and S US316. This model combines the buoyancy force, lorentz force and marangni force as the driving forces of thefluidflow in the weld pool. The material properties are functions of temperature in this model. The simulated results show that the molten metal flowing outward is mainly caused by the marangoni convection, which makes the weld pool become wider and shallower. The comparison of the weld pool shape of SUS310 and SUS316 shows that the slight differences of the value of thermal conductivity mainly attributes to the difference of the weld pool shape and the distinction of heat transport in laminar and turbulent model makes large diversity in the simulated results.

3D topographic correction of the BSR heat flow and detection of focused fluid flow

The bottom-simulating reflector（BSR） is a seismic indicator of the bottom of a gas hydrate stability zone. Its depth can be used to calculate the seafloor surface heat flow. The calculated BSR heat flow variations include disturbances from two important factors：（1） seafloor topography, which focuses the heat flow over regions of concave topography and defocuses it over regions of convex topography, and（2） the focused warm fluid flow within the accretionary prism coming from depths deeper than BSR. The focused fluid flow can be detected if the contribution of the topography to the BSR heat flow is removed. However, the analytical equation cannot solve the topographic effect at complex seafloor regions. We prove that 3D finite element method can model the topographic effect on the regional background heat flow with high accuracy, which can then be used to correct the topographic effect and obtain the BSR heat flow under the condition of perfectly flat topography. By comparing the corrected BSR heat flow with the regional background heat flow, focused fluid flow regions can be detected that are originally too small and cannot be detected using present-day equipment. This method was successfully applied to the midslope region of northern Cascadia subducting margin. The results suggest that the Cucumber Ridge and its neighboring area are positive heat flow anomalies, about 10%–20% higher than the background heat flow after 3D topographic correction. Moreover, the seismic imaging associated the positive heat flow anomaly areas with seabed fracture–cavity systems. This suggests flow of warm gas-carrying fluids along these high-permeability pathways, which could result in higher gas hydrate concentrations.

Application of Stochastic Fracture Network with Numerical Fluid Flow Simulations to Groundwater Flow Modeling in Fractured Rocks

The continuum approach in fluid flow modeling is generally applied to porous geological media, but has limited applicability to fractured rocks. With the presence of a discrete fracture network relatively sparsely distributed in the matrix, it may be difficult or erroneous to use a porous medium fluid flow model with continuum assumptions to describe the fluid flow in fractured rocks at small or even large field scales. A discrete fracture fluid flow approach incorporating a stochastic fracture network with numerical fluid flow simulations could have the capability of capturing fluid flow behaviors such as inhomogeneity and anisotropy while reflecting the changes of hydraulic features at different scales. Moreover, this approach can be implemented to estimate the size of the representative elementary volume (REV) in order to find out the scales at which a porous medium flow model could be applied, and then to determine the hydraulic conductivity tensor for fractured rocks. The following topics are focused on in this study: (a) conceptual discrete fracture fluid flow modeling incorporating a stochastic fracture network with numerical flow simulations; (b) estimation of REV and hydraulic conductivity tensor for fractured rocks utilizing a stochastic fracture network with numerical fluid flow simulations; (c) investigation of the effect of fracture orientation and density on the hydraulic conductivity and REV by implementing a stochastic fracture network with numerical fluid flow simulations, and (d) fluid flow conceptual models accounting for major and minor fractures in the 2 D or 3 D flow fields incorporating a stochastic fracture network with numerical fluid flow simulations.

Relationship between the transition frequency of local fluid flow and the peak frequency of attenuation

Local fluid flow（LFF） at the mesoscopic scale is the main dissipation mechanism of seismic waves in heterogeneous porous media within the seismic frequency band.LFF is easily influenced by the structure and boundary conditions of the porous media,which leads to different behaviors of the peak frequency of attenuation.The associated transition frequency can provide detailed information about the trend of LFF;therefore,research on the transition frequency of LFF and its relationship with the peak frequency of the corresponding attenuation（i.e.,inverse of quality factor） facilitates the detailed understanding of the effect of inner structures and boundary conditions in porous media.In this study,we firstly obtain the transition frequency of fluid flux based on Biot＇s theory of poroelasticity and the fast Fourier transform algorithm in a sample containing one repeating unit cell（RUC）.We then analyze changes of these two frequencies in porous media with different porous properties.Finally,we extend our analysis to the influence of the undrained boundary condition on the transition frequency and peak frequency in porous media with multiple RUCs.This setup can facilitate the understanding of the effect from the undrained boundary condition.Results demonstrate that these two frequencies have the same trend at low water saturation,but amplitude variations differ between the frequencies as the amount of saturation increases.However,for cases of high water saturation,both the trend and the amplitude variation of these two frequencies fit well with each other.

Numerical modelling of structural controls on fluid flow and mineralization

This paper presents the results of a set of numerical models focussing on structural controls on hydrothermal mineralization. We first give an overview of natural phenomena of structurally-controlled ore formation and the background theory and mechanisms for such controls. We then provide the results of a group of simple 2D numerical models validated through comparison with Cu-vein structure observed near the Shilu Copper deposit （Yangchun, Guangdong Province, China） and finally a case study of 3D numerical modelling applied to the Hodgkinson Province in North Queensland （Australia）. Two modelling approaches, discrete deformation modelling and continuum coupled deformation and fluid flow modelling, are involved. The 2D model-derived patterns are remarkably consistent with the Cu-vein structure from the Shilu Copper deposit, and show that both modelling approaches can realistically simulate the mechanical behaviours of shear and dilatant fractures. The continuum coupled deformation and fluid flow model indicates that pattern of the Cu- veins near the Shilu deposit is the result of shear strain localization, development of dilation and fluid focussing into the dilatant fracture segments. The 3D case-study models （with deformation and fluid flow coupling） on the Hodgkinson Province generated a number of potential gold mineralization

Effects of hydrocarbon generation on fluid flow in the Ordos Basin and its relationship to uranium mineralization

The Ordos Basin of North China is not only an important uranium mineralization province, but also a major producer of oil, gas and coal in China. The genetic relationship between uranium mineralization and hydrocarbons has been recognized by a number of previous studies, but it has not been well understood in terms of the hydrodynamics of basin fluid flow. We have demonstrated in a previous study that the preferential localization of Cretaceous uranium mineralization in the upper part of the Ordos Jurassic section may have been related to the interface between an upward flowing, reducing fluid and a downward flowing, oxidizing fluid. This interface may have been controlled by the interplay between fluid overpressure related to disequilibrium sediment compaction and which drove the upward flow, and topographic relief, which drove the downward flow. In this study, we carried out numerical modeling for the contribution of oil and gas generation to the development of fluid overpressure, in addition to sedi- ment compaction and heating. Our results indicate that when hydrocarbon generation is taken into account, fluid overpressure during the Cretaceous was more than doubled in comparison with the simu- lation when hydrocarbon generation was not considered. Furthermore, fluid overpressure dissipation at the end of sedimentation slowed down relative to the no-hydrocarbon generation case. These results suggest that hydrocarbon generation may have played an important role in uranium mineralization, not only in providing reducing agents required for the mineralization, but also in contributing to the driving force to maintain the upward flow.

Evaluation of gas wettability and its effects on fluid distribution and fluid flow in porous media

The special gas wettability phenomenon of reservoir rocks has been recognized by more and more researchers.It has a significant effect on efficient development of unconventional reservoirs.First,based on the preferentially gas-covered ability and surface free energy changes,definition and evaluation methods have been established.Second,a method for altering rock wettability and its mechanisms have been studied,surface oriented phenomena of functional groups with low surface energy are the fundamental reason for gas wettability alteration of rock.Third,the effect of gas wettability on the surface energy,electrical properties and dilatability are investigated.Last,the effects of gas wettability on capillary pressure,oil/gas/water distribution and flow are investigated with capillary tubes and etchedglass network models.The gas wettability theory of reservoir rocks has been initially established,which provides theoretical support for the efficient production of unconventional reservoirs and has great significance.

Multiple Dolomitization and Fluid Flow Events in the Precambrian Dengying Formation of Sichuan Basin, Southwestern China

The Precambrian Dengying Formation is a set of large-scale, extensively dolomitized, carbonate reservoirs occurring within the Sichuan Basin. Petrographic and geochemical studies reveal dolomitization was a direct result of precipitation by chemically distinct fluids occurring at different times and at different intensities. Based on this evidence, dolomitization and multiple fluid flow events are analyzed, and three types of fluid evolution models are proposed. Results of analysis show that Precambrian Dengying Formation carbonates were deposited in a restricted peritidal environment （630- 542 Ma）. A high temperature and high Mg2＋ concentration seawater was a direct result of dolomitization for the micrite matrix, and for fibrous aragonite in primary pores. Geochemical evidence shows low δ18O values of micritic dolomite varying from -1.29%o to -4.52%o PDB, abundant light rare earth elements （REEs）, and low dolomite order degrees. Microbes and meteoric water significantly altered dolomite original chemical signatures, resulting in algal micritic dolomite and the fine-grained, granular, dolosparite dolomite having very negative δ18O values. Finely crystalline cement dolomite （536.3-280 Ma） and coarsely crystalline cement dolomite have a higher crystallization degree and higher order degree. The diagenetic sequence and fluid inclusion evidence imply a linear correlation between their burial depth and homogenization temperatures, which closely resemble the temperature of generated hydrocarbon. Compared with finely crystalline dolomite, precipitation of coarsely crystalline dolomite was more affected by restricted basinal fluids. In addition, there is a trend toward a more negative δ18O value, higher salinity, higher Fe and Mn concentrations, REE-rich. Two periods of hydrothermal fluids are identified, as the exceptionally high temperatures as opposed to the temperatures of burial history, in addition to the presence of high salinity fluid inclusions. The early hydrothermal fluid flow event was characterized by hot magnesium- and silicon-rich fluids, as demonstrated by the recrystallized matrix dolomite that is intimately associated with flint, opal, and microcrystalline quartz in intergranular or intercrystalline pores. This event was likely the result of a seafloor hydrothermal chimney eruption during Episode I of the Tongwan Movement （536.3-5.5 Ma）. In contrast, later hydrothermal fluids, which caused precipitation of saddle dolomite, were characterized by high salinity （15-16.05wt% NaCI equivalent） and homogenization temperatures （250 to 265℃）, δ18O values that were more enriched, and REE signatures. Geochemical data and the paragenetic sequence indicate that this hydrothermal fluid was related to extensive Permian large igneous province activity （360-280 Ma）. This study demonstrates the presence of complicated dolomitization processes occurring during various paleoclimates, tectonic cycles, and basinal fluids flow; results are a useful reference for these dolomitized Precambrian carbonates reservoirs.

Focused fluid flow in the Baiyun Sag, northern South China Sea: implications for the source of gas in hydrate reservoirs

The origin and migration of natural gas and the accumulation of gas hydrates within the Pearl River Mouth Basin of the northern South China Sea are poorly understood. Based on high-resolution 2D/3D seismic data, three environments of focused fluid flow： gas chimneys, mud diapirs and active faults have been identified. Widespread gas chimneys that act as important conduits for fluid flow are located below bottom simulating reflections and above basal uplifts. The occurrence and evolution of gas chimneys can be divided into a violent eruptive stage and a quiet seepage stage. For most gas chimneys, the strong eruptions are deduced to have happened during the Dongsha Movement in the latest Miocene, which are observed below Pliocene strata and few active faults develop above the top of the Miocene. The formation pressures of the Baiyun Sag currently are considered to be normal, based on these terms： 1） Borehole pressure tests with pressure coefficients of 1.043-l.047; 2） The distribution of gas chimneys is limited to strata older than the Pliocene; 3） Disseminated methane hydrates, rather than fractured hydrates, are found in the hydrate samples; 4） The gas hydrate is mainly charged with biogenic gas rather than thermogenic gas based on the chemical tests from gas hydrates cores. However, periods of quiet focused fluid flow also enable the establishment of good conduits for the migration of abundant biogenic gas and lesser volumes ofthermogenic gas. A geological model goveming fluid flow has been proposed to interpret the release of overpressure, the migration of fluids and the formation of gas hydrates, in an integrated manner. This model suggests that gas chimneys positioned above basal uplifts were caused by the Dongsha Movement at about 5.5 Ma. Biogenic gas occupies the strata above the base of the middle Miocene and migrates slowly into the gas chimney columns. Some of the biogenic gas and small volumes ofthermogenic gas eventually contribute to the formation of the gas hydrates.

Effect of Thermal Buoyancy on Fluid Flow and Inclusion Motion in Tundish without Flow Control Devices——Part II :Inclusion Motion

Following up the fluid flow simulation in a 60 t tundish, the trajectories of inclusions in the 60 t tundish without flow control are simulated by considering the force balance between the drag force and the inertial buoyancy force. The Stochastic model yields more accurate inclusion motion than the non-Stochastic model due to including the effect of the turbulent fluctuation. The average residence time of inclusions decreases with increasing size. The thermal buoyancy favors inclusions removal especially the small inclusions. Using solute transport like the dye injection in water model and copper addition in the real steel tundish cannot accurately study the motion of the inclusions. In the simulation, more than 68% inclusions bigger than 10μm are removed to the top, and less than 32% enters the mold. The thermal buoyancy has little effect on the fraction of inclusions moved to the top of the inlet zone, and it mainly favors the removal of inclusions smaller than 100μm to the top surface of the outlet zone. For inclusions bigger than 100μm, the effect of thermal buoyancy on their motion can be ignored compared to the inertial buoyancy effect.

Fluid Flow Modeling of Arc Plasma and Bath Circulation in DC Electric Arc Furnace

A mathematical model describing the flow field, heat transfer and the electromagnetic phenomenon in a DC electric arc furnace has been developed. First the governing equations in the arc plasma region are solved and the calculated results of heat transfer, current density and shear stresses on the anode surface are used as boundary conditions in a model of molten bath. Then a two-dimensional time-dependent model is used to describe the flow field and electromagnetic phenomenon in the molten bath. Moreover, the effect of bottom electrode diameter on the circulation of molten bath is studied.

Effect of Thermal Buoyancy on Fluid Flow and Inclusion Motion in Tundish without Flow Control Devices——Part Ⅰ: Fluid Flow

The κ-ε two-equation model is used to simulate the fluid flow in the continuous casting tundish coupling with the effect of thermal buoyancy. The natural convection induced by the thermal buoyancy generates an upward flow pattern especially at the outlet zone, and has little effect on the fluid flow in the inlet zone. The maximum viscosity is 700 times larger than the laminar viscosity, which indicates the strong turbulent flow in the tundish. The maximum temperature difference in the whole tundish is 82 K. The temperature near the stopper rod and the short wall is obviously lower than that in the inlet zone. The existence of the stopper rod has a big effect on the fluid flow entering the SEN and the mold. All the characteristics of the tundish geometry should be considered to accurately simulate the fluid flow in the tundish.

NUMERICAL ANALYSIS OF THREE-DIMENSIONAL FLUID FLOW AND HEAT TRANSFER IN TIG WELD POOL WITH FULL PENETRATION

A model is established to analyze three-dimensional fluid flow and heat transfer in TICweld pools with full penetration.It considers the deformation of the molten pool surfaceat the condition of full penetrated workpieees,takes the are pressure as the drivingforce of the pool surface deformation,and determines the surface configuration of weldpool based on the dynamic balance of arc pressure,pool gravity and surface tension atdeformed weld pool surface. The SIMPLER algorithm is used to calculate the fluid flowfield and temperature distribution in TIG weld pools of stainless steel workpieces.TIGwelding experiments are made to verify the validity of the model.It shows the calculatedresults by the model are in good agreement with experimental measurements. professor,Dept of Welding Engineering,Harbin Institute of Technology,Harbin 150006,China

Bifurcation and stability of an improved time-delayed fluid flow model in internet congestion control

Based on the fluid flow time-delayed model proposed by Misra et al in internet congestion control, one modified time-delayed model is presented, where the influence of the communication delay on the router queue length is investigated in detail. The main advantage of the new model is that its stability domain is larger even without an extra controller. By linear stability analysis and numerical simulation, tbe effectiveness and feasibility of the novel model in internet congestion control are verified.

Fluid Flow in Tundish Due to Different Type Arrangement of Weir and Dam

Tundish is an important metallurgical reactor in the continuous castingprocess. In order to control the fluid flow in tundish and thus take full advantage of the residencetime available for the removal of inclusions from molten steel, the effect of weir and dam on thefluid flow has been studied in a water model based on the characteristic number Froude and Reynoldnumber similarity criteria. The residence time distribution curves of the flow were measured bySG800. The optimum arrangement of darn and weir and the nonstationary flow in tundish werediscussed. The results show that the combination of weir and dam is benefit for the flow pattern intundish, weir can prevent the upper recirculating flow, dam can cut off the bottom flow and turn toupwards, it is advantageous to separate the nonmetallic inclusions. Furthermore, it is important toexceed the critical depth of bath during exchange ladles, not only for the inclusion floatation butalso for avoiding tundish slag drainage earlier.

Hierarchical model for strain generalized streaming potential induced by the canalicular fluid flow of an osteon

A hierarchical model is developed to predict the streaming potential （SP） in the canaliculi of a loaded os teon. Canaliculi are assumed to run straight across the os teon annular cylinder wall, while disregarding the effect of lacuna. SP is generalized by the canalicular fluid flow. Ana lytical solutions are obtained for the canalicular fluid veloc ity, pressure, and SP. Results demonstrate that SP amplitude （SPA） is proportional to the pressure difference, strain am plitude, frequency, and strain rate amplitude. However, the key loading factor governing SP is the strain rate, which is a representative loading parameter under the specific phys iological state. Moreover, SPA is independent of canalicu lar length. This model links external loads to the canalicu lar fluid pressure, velocity, and SP, which can facilitate fur ther understanding of the mechanotransduction and electro mechanotransduction mechanisms of bones.