The accelerated method in solving optimization problems has always been an absorbing topic.Based on the fixedtime(FxT)stability of nonlinear dynamical systems,we provide a unified approach for designing FxT gradient f...The accelerated method in solving optimization problems has always been an absorbing topic.Based on the fixedtime(FxT)stability of nonlinear dynamical systems,we provide a unified approach for designing FxT gradient flows(FxTGFs).First,a general class of nonlinear functions in designing FxTGFs is provided.A unified method for designing first-order FxTGFs is shown under Polyak-Łjasiewicz inequality assumption,a weaker condition than strong convexity.When there exist both bounded and vanishing disturbances in the gradient flow,a specific class of nonsmooth robust FxTGFs with disturbance rejection is presented.Under the strict convexity assumption,Newton-based FxTGFs is given and further extended to solve time-varying optimization.Besides,the proposed FxTGFs are further used for solving equation-constrained optimization.Moreover,an FxT proximal gradient flow with a wide range of parameters is provided for solving nonsmooth composite optimization.To show the effectiveness of various FxTGFs,the static regret analyses for several typical FxTGFs are also provided in detail.Finally,the proposed FxTGFs are applied to solve two network problems,i.e.,the network consensus problem and solving a system linear equations,respectively,from the perspective of optimization.Particularly,by choosing component-wisely sign-preserving functions,these problems can be solved in a distributed way,which extends the existing results.The accelerated convergence and robustness of the proposed FxTGFs are validated in several numerical examples stemming from practical applications.展开更多
A new numerical model for low-permeability reservoirs is developed.The model incorporates the nonlinear characteristics of oil-water two-phase flows while taking into account the initiation pressure gradient.Related n...A new numerical model for low-permeability reservoirs is developed.The model incorporates the nonlinear characteristics of oil-water two-phase flows while taking into account the initiation pressure gradient.Related numerical solutions are obtained using a finite difference method.The correctness of the method is demonstrated using a two-dimensional inhomogeneous low permeability example.Then,the differences in the cumulative oil and water production are investigated for different starting water saturations.It is shown that when the initial water saturation grows,the water content of the block continues to rise and the cumulative oil production gradually decreases.展开更多
This paper aims to propose correlations to predict pressure gradient,friction factor and fluid phase hold-up in liquid-liquid horizontal pipe flow.To develop the correlations,experiments are conducted using high visco...This paper aims to propose correlations to predict pressure gradient,friction factor and fluid phase hold-up in liquid-liquid horizontal pipe flow.To develop the correlations,experiments are conducted using high viscous oils(202 and 630 mPa⋅s)in a steel pipe of length 11.25 m and length-to-diameter ratio of 708.In addition,the experimental data from the literature comprising wide range of flow and fluid properties is analyzed.For the analysis,the liquid-liquid pipe flow data is categorized into two as:stratified and dispersed.The existing friction factor correlations are modified to incorporate the effects of viscosity of the oil phase,interfacial curvature(contact/wetting angle-in lieu of material of the pipe)and fluid phase fraction.In the two-fluid model of stratified flow,the wall stress and interfacial stress correlations are substituted with superficial velocities of fluids and superficial Reynolds numbers of fluid phases replacing fluid phase velocities and fluid Reynolds numbers.Similarly,for dispersed flow,an effective Reynolds number is described as the sum of superficial Reynolds number of oil and water phases.Substituting the generally employed mean or mixture Reynolds number with the effective Reynolds number into the existing single-phase turbulent flow friction factor correlation,an effective friction factor for oil-water flow is proposed.Employing the proposed correlations,the pressure gradient across the oil-water flow and hold-up volume fraction are predicted with significant reduction in error compared with that of conventionally employed correlations.The average error and standard deviation values of−7.06%,20.72%and 0.31%,18.79%are found for stratified flow and dispersed flow respectively.展开更多
Water seepage in soil is a fundamental problem involving various scientific and engineering fields.According to the literature,low-velocity water seepage in low-permeability porous media,such as clay,does not follow D...Water seepage in soil is a fundamental problem involving various scientific and engineering fields.According to the literature,low-velocity water seepage in low-permeability porous media,such as clay,does not follow Darcy's law,also known as pre-Darcy flow.The formation of immovable water due to water adsorption on the pore wall is believed to be responsible for the formation of pre-Darcy flow.However,this view lacks direct solid evidence.To investigate the pre-Darcy water flow in clay,head permeability experiments are conducted on six clay samples with different densities.The results indicate that water seepage in clay at low hydraulic gradients does not follow Darcy's law.A clear nonlinear relationship between flow velocity and hydraulic gradient is observed.Water flow in clay can be divided into the pre-Darcy flow and Darcy flow regions by the critical hydraulic gradient,which is 10-12 for the Albic soil with dry density between 1.3 g/cm^(3)and 1.8 g/cm^(3).According to the disjoining pressure theory,immovable water due to water adsorption on the pore wall is the primary reason for water flow deviating from Darcy's law in clay.The results indicate that the percentage of movable water ranges from 39.7%to 59.3%for the six samples at a hydraulic gradient of 1.As the hydraulic gradient increases,the percentage of moveable water also increases.Additionally,there is a strong correlation between the percentage of movable water and the variation in hydraulic conductivity with the hydraulic gradient.Furthermore,a quantitative relationship between the percentage of movable water and the hydraulic conductivity has been established.The results of this study suggest that water adsorption on the pore wall not only affects the water movability,but is also closely related to the pre-Darcy flow phenomenon in clay.展开更多
A model is proposed for liquid film profile prediction in gas-liquid two-phase flow,which is able to provide the film thickness along the circumferential direction and the pressure gradient in the flow direction.A two...A model is proposed for liquid film profile prediction in gas-liquid two-phase flow,which is able to provide the film thickness along the circumferential direction and the pressure gradient in the flow direction.A two-fluid model is used to calculate both gas and liquid phases’flow characteristics.The secondary flow occurring in the gas phase is taken into account and a sailing boat mechanism is introduced.Moreover,energy conservation is applied for obtaining the liquid film thickness distribution along the circumference.Liquid film thickness distribution is calculated accordingly for different cases;its values are compared with other models and available experimental data.As a result,the newly proposed model is tested and good performances are demonstrated.The liquid film thickness distribution in small pipes and inclined pipes is also studied,and regime transition is revealed by liquid film profile evolution.The observed inflection point demonstrates that the liquid film thickness decreases steeply along the circumference,when the circle angle ranges between 30°and 50°for gas-liquid stratified flow with small superficial velocities.展开更多
It has not been a simple matter to obtain a sound extension of the classical J2 flow theory of plasticity that incorporates a dependence on plastic strain gradients and that is capable of capturing size-dependent beha...It has not been a simple matter to obtain a sound extension of the classical J2 flow theory of plasticity that incorporates a dependence on plastic strain gradients and that is capable of capturing size-dependent behaviour of metals at the micron scale. Two classes of basic extensions of classical J2 theory have been proposed： one with increments in higher order stresses related to increments of strain gradients and the other characterized by the higher order stresses themselves expressed in terms of increments of strain gradients. The theories proposed by Muhlhans and Aifantis in 1991 and Fleck and Hutchinson in 2001 are in the first class, and, as formulated, these do not always satisfy thermodynamic requirements on plastic dissipation. On the other hand, theories of the second class proposed by Gudmundson in 2004 and Gurtin and Anand in 2009 have the physical deficiency that the higher order stress quantities can change discontinuously for bodies subject to arbitrarily small load changes. The present paper lays out this background to the quest for a sound phenomenological extension of the rateindependent J2 flow theory of plasticity to include a de- pendence on gradients of plastic strain. A modification of the Fleck-Hutchinson formulation that ensures its thermo- dynamic integrity is presented and contrasted with a comparable formulation of the second class where in the higher or- der stresses are expressed in terms of the plastic strain rate. Both versions are constructed to reduce to the classical J2 flow theory of plasticity when the gradients can be neglected and to coincide with the simpler and more readily formulated J2 deformation theory of gradient plasticity for deformation histories characterized by proportional straining.展开更多
Subsurface water flow velocity influences the hydrodynamic characteristics of soil seepage and the interaction between subsurface water flow and surface runoff during soil erosion and sediment transport.A visualized m...Subsurface water flow velocity influences the hydrodynamic characteristics of soil seepage and the interaction between subsurface water flow and surface runoff during soil erosion and sediment transport.A visualized method and equipment was adopted in this study to observe the subsurface water flow.Quartz sand was used as the test material of subsurface water flow and fluorescent dye was used as the indicator for tracing subsurface water flow.Water was supplied at the same flow discharge to the three parts at the bottom of the test flume,and the subsurface water flow were determined with four slope gradients(4°,8°,10°,and 12°).The results showed that the seepage velocity gradually increased with increasing slope gradient.The pore water velocity at different depths of sand layer profile increased with increasing slope gradient,whereas the thickness of the flow front gradually decreased.For the same slope gradient,the pore water velocity in the lower layer was the largest,whereas the thickness of the flow front was the smallest.Comparative analysis of the relationship between seepage velocity and pore water velocity at different depths of sand layer profile showed that the maximum relative difference between the measured pore water velocity and the computational pore water velocity at different depths of sand profile in the experiment was 4.38%.Thus,the test method for measuring the subsurface water flow velocity of sand layer profile adopted in this study was effective and feasible.The development of this experiment and the exploration of research methods would lay a good test foundation for future studies on the variation law of subsurface water flow velocity and the determination of flow velocity in purple soils,thus contributing to the improvement of the hydrodynamic mechanism of purple soils.展开更多
Gradient vector flow （GVF） is an effective external force for active contours, but its iso- tropic nature handicaps its performance. The recently proposed gradient vector flow in the normal direction （NGVF） is ani...Gradient vector flow （GVF） is an effective external force for active contours, but its iso- tropic nature handicaps its performance. The recently proposed gradient vector flow in the normal direction （NGVF） is anisotropic since it only keeps the diffusion along the normal direction of the isophotes; however, it has difficulties forcing a snake into long, thin boundary indentations. In this paper, a novel external force for active contours called normally generalized gradient vector flow （NGGVF） is proposed, which generalizes the NGVF formulation to include two spatially varying weighting functions. Consequently, the proposed NGGVF snake is anisotropic and would improve ac- tive contour convergence into long, thin boundary indentations while maintaining other desirable properties of the NGVF snake, such as enlarged capture range, initialization insensitivity and good convergence at concavities. The advantages on synthetic and real images are demonstrated.展开更多
This paper uses the Oseen transformation to solve the differential equations governing motion of the vertical linear gradient flow distribution close to a wall surface. The Navier-Stokes equations are used to consider...This paper uses the Oseen transformation to solve the differential equations governing motion of the vertical linear gradient flow distribution close to a wall surface. The Navier-Stokes equations are used to consider the inertia term along the flow direction. A novel contour integral method is used to solve the complex Airy function. The boundary conditions of linear gradient flow distribution for finite problems are determined. The vorticity function, the pressure function, and the turbulent velocity profiles are provided, and the stability of particle trajectories is studied. An Lx-function form of the third derivative circulation is used to to simplify the solution. Theoretical results are compared with the experimental measurements with satisfactory agreement.展开更多
The flow behavior in porous media with threshold pressure gradient(TPG) is more complex than Darcy flow and the equations of motion, and outer boundary and inner boundary with TPG are also different from Darcy flow fo...The flow behavior in porous media with threshold pressure gradient(TPG) is more complex than Darcy flow and the equations of motion, and outer boundary and inner boundary with TPG are also different from Darcy flow for unsteady flow of a producing well in a reservoir. An analytic method to solve this kind of problem is in a need of reestablishment. The classical method of Green's function and Newman product principle in a new way are used to solve the unsteady state flow problems of various shapes of well and reservoir while considering the TPG. Four Green's functions of point, line, band and circle while considering the TPG are achieved. Then, two well models of vertical well and horizontal well are built and simultaneously the function to calculate the moving boundary of each well model is provided. The results show that when considering TPG the pressure field is much different, which has a sudden pressure change, with a moving boundary in it. And the moving boundary of each well model increases with time but slows down rapidly, especially when the TGP is large.展开更多
In this paper, we propose a fast centerline extraction method to be used for gradient and direction vector flow of active contours. The gradient and direction vector flow is a recently reported active contour model ca...In this paper, we propose a fast centerline extraction method to be used for gradient and direction vector flow of active contours. The gradient and direction vector flow is a recently reported active contour model capable of significantly improving the image segmentation performance especially for complex object shape, by seamlessly integrating gradient vector flow and prior directional information. Since the prior directional information is provided by manual line drawing, it can be inconvenient for inexperienced users who might have difficulty in finding the best place to draw the directional lines to achieve the best segmentation performance. This paper describes a method to overcome this problem by automatically extracting centerlines to guide the users for providing the right directional information. Experimental results on synthetic and real images demonstrate the feasibility of the proposed method.展开更多
The segregated flow pattern, which occurs in a 26.1 mm diameter, horizontal, stainless steel test section, is investigated. Pressure gradient and in situ phase distribution data were obtained for different combination...The segregated flow pattern, which occurs in a 26.1 mm diameter, horizontal, stainless steel test section, is investigated. Pressure gradient and in situ phase distribution data were obtained for different combinations of phase superficial velocities ranging from 0.05 m.s^-1 to 0,96 m.s^-1. For the current small Eoetvoes number liquid-liquid system （EOD=4.77）, the dominant effect of interfacial tension and wall-wetting properties of the liquids over the gravity is considered. The approach introduces the closure relationship for the case of turbulent flow m a rough pipe, and attempts to modify the two-fluid model to account for the curved interface. In present flow rates range, wave amplitudes were found small, while interfacial mixing was observed. An adjustable definition for hydraulic diame- ters of two fluids and interfacial friction factor is adopted. The predicted pressure gradient and in situ phase distribution data have been compared with present experimental data and those reported in the literature.展开更多
A local gradient estimate for positive solutions of porous medium equations on complete noncompact Riemannian manifolds under the Ricci flow is derived. Moreover, a global gradient estimate for such equations on compa...A local gradient estimate for positive solutions of porous medium equations on complete noncompact Riemannian manifolds under the Ricci flow is derived. Moreover, a global gradient estimate for such equations on compact Riemannian manifolds is also obtained.展开更多
Aqueous foam is broadly applicable to enhanced oil recovery(EOR).The rheology of foam as a function of foam quality,gas and liquid velocities,and surfactant concentration constitute the foundation of its application.T...Aqueous foam is broadly applicable to enhanced oil recovery(EOR).The rheology of foam as a function of foam quality,gas and liquid velocities,and surfactant concentration constitute the foundation of its application.The great variations of the above factors can affect the effectiveness of N2 foam in EOR continuously in complex formations,which is rarely involved in previous relevant studies.This paper presents an experimental study of foam flow in porous media by injecting pre-generated N2 foam into a sand pack under the conditions of considering a wide range of gas and liquid velocities and surfactant concentrations.The results show that in a wide range of gas and liquid velocities,the pressure gradient contours are L-shaped near the coordinate axes,but V-shaped in other regions.And the surfactant concentration is a strong factor influencing the trend of pressure gradient contours.Foam flow resistance is very sensitive to the surfactant concentration in both the high-and low-foam quality regime,especially when the surfactant concentration is less than CMC.The foam quality is an important variable to the flow resistance obtained.There exists a transition point from low-to high-quality regime in a particular flow system,where has the maximum flow resistance,the corresponding foam quality is called transition foam quality,which increases as the surfactant concentration increases.The results can add to our knowledge base of foam rheology in porous media,and can provide a strong basis for the field application of foams.展开更多
As has been observed by Morse [1], any generic vector field v on a compact smooth manifold X with boundary gives rise to a stratification of the boundary by compact submanifolds , where . Our main observation is that ...As has been observed by Morse [1], any generic vector field v on a compact smooth manifold X with boundary gives rise to a stratification of the boundary by compact submanifolds , where . Our main observation is that this stratification re-flects the stratified convexity/concavity of the boundary ?with respect to the ?v-flow. We study the behavior of this stratification under deformations of the vector field v. We also investigate the restrictions that the existence of a convex/concave traversing ?v-flow imposes on the topology of X. Let be the orthogonal projection of on the tangent bundle of . We link the dynamics of theon the boundary with the property of in X being convex/concave. This linkage is an instance of more general phenomenon that we call “holography of traversing fields”—a subject of a different paper to follow.展开更多
The present paper is concerned with the steady thin film flow of the Sisko fluid on a horizontal moving plate, where the surface tension gradient is a driving mechanism. The analytic solution for the resulting nonline...The present paper is concerned with the steady thin film flow of the Sisko fluid on a horizontal moving plate, where the surface tension gradient is a driving mechanism. The analytic solution for the resulting nonlinear ordinary differential equation is obtained by the Adomian decomposition method （ADM）. The physical quantities are derived including the pressure profile, the velocity profile, the maximum residue time, the stationary points, the volume flow rate, the average film velocity, the uniform film thickness, the shear stress, the surface tension profile~ and the vorticity vector. It is found that the velocity of the Sisko fluid film decreases when the fluid behavior index and the Sisko fluid parameter increase, whereas it increases with an increase in the inverse capillary number. An increase in the inverse capillary number results in an increase in the surface tension which in turn results in an increase in the surface tension gradient on the Sisko fluid film. The locations of the stationary points are shifted towards the moving plate with the increase in the inverse capillary number, and vice versa locations for the stationary points are found with the increasing Sisko fluid parameter. Furthermore, shear thinning and shear thickening characteristics of the Sisko fluid are discussed. A comparison is made between the Sisko fluid film and the Newtonian fluid film.展开更多
Many in vitro studies focus on effects of wall shear stress (WSS) and wall shear stress gradient (WSSG) on endothelial cells, which are linked to the initiation and progression of atherosclerosis in the arterial syste...Many in vitro studies focus on effects of wall shear stress (WSS) and wall shear stress gradient (WSSG) on endothelial cells, which are linked to the initiation and progression of atherosclerosis in the arterial system. Limitation in available flow chambers with a constant WSSG in the testing region makes it difficult to quantify cellular responses to WSSG. The current study proposes and characterizes a type of converging parallel plate flow chamber (PPFC) featuring a constant gradient of WSS. A simple formula was derived for the curvature of side walls, which relates WSSG to flow rate (Q), height of the PPFC (h), length of the convergent section (L), its widths at the entrance (w0) and exit (w1). CFD simulation of flow in the chamber is carried out. Constant WSSG is observed in most regions of the top and bottom plates except those in close proximity of side walls. A change in Q or h induces equally proportional changes in WSS and WSSG whereas an alteration in the ratio between w0 and w1 results in a more significant change in WSSG than that in WSS. The current design makes possible an easy quantification of WSSG on endothelial cells in the flow chamber.展开更多
Analysis of high resolution of aeromagnetic data was carried out over Lamurde, Adamawa state north-eastern Nigeria to determine the Curie point depth (CPD), heat flow and geothermal gradient. The aeromagnetic data use...Analysis of high resolution of aeromagnetic data was carried out over Lamurde, Adamawa state north-eastern Nigeria to determine the Curie point depth (CPD), heat flow and geothermal gradient. The aeromagnetic data used for this work was obtained at Nigerian geological survey agency, the total magnetic intensity was processed to produce the residual magnetic map which was divided into 4 overlapping blocks, each block was subjected to spectral analyses to obtain depths to the top boundary and centroid, while depth to bottom of the magnetic sources was calculated using empirical formula. The depths values obtained were then used to assess the CPD, heat flow and geothermal gradient in the area. The result shows that the CPD varies between 9.62 and 10.92 km with an average of 10.45 k, the heat flow varies between 150.73 and 132.78 mWm−20⋅°C−1 with an average of 139.12 mWm−20⋅°C−1 and the geothermal gradient in the study area varies between 12.16 and 15.67 °C/km with an average of 13.39 °C/km. In view of the above results, the high heat flow may be responsible for maturation of hydrocarbon in Benue Trough as well as responsible for the lead Zinc Mineralization. Again by implication, Lamurde area can be a good area for geothermal reservoir exploration for an alternative source for power generation.展开更多
Information on geothermal gradient and heat flow within the subsurface is critical in the quest for geothermal energy exploration. In a bid to ascertain the thermal potential of Nigeria sector of the Chad Basin for en...Information on geothermal gradient and heat flow within the subsurface is critical in the quest for geothermal energy exploration. In a bid to ascertain the thermal potential of Nigeria sector of the Chad Basin for energy generation, subsurface temperature information from 19 oil wells, 24 water boreholes drilled to depths beyond 100 metres and atmospheric temperature from the Chad basin were utilized in calculating geothermal gradient of the area. Selected ditch cuttings from the wells were subjected to thermal conductivity test using Thermal Conductivity Scanner (TCS) at the Polish Geological Institute Laboratory in Warsaw. The terrestrial heat flow was calculated according to the Fourier’s law as a simple product of the geothermal gradient and the mean thermal conductivity. Results obtained indicated geothermal gradient range of 2.81<sup> °</sup>C/100 m to 5.88<sup> °</sup>C/100 m with an average of 3.71<sup> °</sup>C/100 m. The thermal conductivity values from the different representative samples range from 0.58 W/m*K to 4.207 W/m*K with an average of 1.626 W/m*K. The work presented a heat flow value ranging from 45 mW/m<sup>2</sup> to about 90 mW/m<sup>2</sup> in the Nigerian sector of the Chad Basin.展开更多
Some patients with severe aortic stenosis (AS), due to restrictive cardiac physiology, paradoxically have relatively low flow and low gradients across stenotic aortic valves despite preserved left ventricular (LV) sys...Some patients with severe aortic stenosis (AS), due to restrictive cardiac physiology, paradoxically have relatively low flow and low gradients across stenotic aortic valves despite preserved left ventricular (LV) systolic function. It results in symptoms and reduced quality of life and carries a high mortality. Whilst this form of severe AS, termed paradoxical low flow low gradient (pLFLG), is well reported, patients with this diagnosis experience inappropriate barriers to aortic valve replacement (AVR), the only efficacious treatment. We present the case of an 88-year-old female with 12 months of exertional dyspnoea on a background of hypothyroidism and hypercholesterolemia. Transthoracic echocardiogram (TTE) revealed LV hypertrophy, with a small LV cavity size and reduced stroke volume, yet normal systolic function. A heavily calcified aortic valve was identified with severe aortic stenosis, based on valve area, yet with incongruous mean transvalvular gradient of 25 mmHg (severe ≥ 50 mmHg). Following exclusion of other differential diagnoses, her symptoms were attributed to paradoxical LFLG severe AS. She was however declined definitive transcatheter aortic valve implantation (TAVI) due to her paradoxically low mean aortic gradient. Following further deterioration in her symptoms and supportive quantification of poor exercise performance, she was ultimately re-referred, accepted, and underwent TAVI. Following her AVR, the patient experiences significant improvement in both symptoms and quality of life after only one month. Paradoxical LFLG severe AS remains a well-documented yet under recognized disease. It carries high morbidity and mortality if untreated, yet is significantly less likely to be referred and accepted for intervention. With its prevalence expected to rise with an ageing population, this case serves as a timely reminder for clinicians to address the under recognition of important pathology.展开更多
基金supported by the National Key Research and Development Program of China(2020YFA0714300)the National Natural Science Foundation of China(62003084,62203108,62073079)+3 种基金the Natural Science Foundation of Jiangsu Province of China(BK20200355)the General Joint Fund of the Equipment Advance Research Program of Ministry of Education(8091B022114)Jiangsu Province Excellent Postdoctoral Program(2022ZB131)China Postdoctoral Science Foundation(2022M720720,2023T160105).
文摘The accelerated method in solving optimization problems has always been an absorbing topic.Based on the fixedtime(FxT)stability of nonlinear dynamical systems,we provide a unified approach for designing FxT gradient flows(FxTGFs).First,a general class of nonlinear functions in designing FxTGFs is provided.A unified method for designing first-order FxTGFs is shown under Polyak-Łjasiewicz inequality assumption,a weaker condition than strong convexity.When there exist both bounded and vanishing disturbances in the gradient flow,a specific class of nonsmooth robust FxTGFs with disturbance rejection is presented.Under the strict convexity assumption,Newton-based FxTGFs is given and further extended to solve time-varying optimization.Besides,the proposed FxTGFs are further used for solving equation-constrained optimization.Moreover,an FxT proximal gradient flow with a wide range of parameters is provided for solving nonsmooth composite optimization.To show the effectiveness of various FxTGFs,the static regret analyses for several typical FxTGFs are also provided in detail.Finally,the proposed FxTGFs are applied to solve two network problems,i.e.,the network consensus problem and solving a system linear equations,respectively,from the perspective of optimization.Particularly,by choosing component-wisely sign-preserving functions,these problems can be solved in a distributed way,which extends the existing results.The accelerated convergence and robustness of the proposed FxTGFs are validated in several numerical examples stemming from practical applications.
文摘A new numerical model for low-permeability reservoirs is developed.The model incorporates the nonlinear characteristics of oil-water two-phase flows while taking into account the initiation pressure gradient.Related numerical solutions are obtained using a finite difference method.The correctness of the method is demonstrated using a two-dimensional inhomogeneous low permeability example.Then,the differences in the cumulative oil and water production are investigated for different starting water saturations.It is shown that when the initial water saturation grows,the water content of the block continues to rise and the cumulative oil production gradually decreases.
文摘This paper aims to propose correlations to predict pressure gradient,friction factor and fluid phase hold-up in liquid-liquid horizontal pipe flow.To develop the correlations,experiments are conducted using high viscous oils(202 and 630 mPa⋅s)in a steel pipe of length 11.25 m and length-to-diameter ratio of 708.In addition,the experimental data from the literature comprising wide range of flow and fluid properties is analyzed.For the analysis,the liquid-liquid pipe flow data is categorized into two as:stratified and dispersed.The existing friction factor correlations are modified to incorporate the effects of viscosity of the oil phase,interfacial curvature(contact/wetting angle-in lieu of material of the pipe)and fluid phase fraction.In the two-fluid model of stratified flow,the wall stress and interfacial stress correlations are substituted with superficial velocities of fluids and superficial Reynolds numbers of fluid phases replacing fluid phase velocities and fluid Reynolds numbers.Similarly,for dispersed flow,an effective Reynolds number is described as the sum of superficial Reynolds number of oil and water phases.Substituting the generally employed mean or mixture Reynolds number with the effective Reynolds number into the existing single-phase turbulent flow friction factor correlation,an effective friction factor for oil-water flow is proposed.Employing the proposed correlations,the pressure gradient across the oil-water flow and hold-up volume fraction are predicted with significant reduction in error compared with that of conventionally employed correlations.The average error and standard deviation values of−7.06%,20.72%and 0.31%,18.79%are found for stratified flow and dispersed flow respectively.
基金funding support from the China National Science Foundation(Grant Nos.42072280,U2244215,41172205).
文摘Water seepage in soil is a fundamental problem involving various scientific and engineering fields.According to the literature,low-velocity water seepage in low-permeability porous media,such as clay,does not follow Darcy's law,also known as pre-Darcy flow.The formation of immovable water due to water adsorption on the pore wall is believed to be responsible for the formation of pre-Darcy flow.However,this view lacks direct solid evidence.To investigate the pre-Darcy water flow in clay,head permeability experiments are conducted on six clay samples with different densities.The results indicate that water seepage in clay at low hydraulic gradients does not follow Darcy's law.A clear nonlinear relationship between flow velocity and hydraulic gradient is observed.Water flow in clay can be divided into the pre-Darcy flow and Darcy flow regions by the critical hydraulic gradient,which is 10-12 for the Albic soil with dry density between 1.3 g/cm^(3)and 1.8 g/cm^(3).According to the disjoining pressure theory,immovable water due to water adsorption on the pore wall is the primary reason for water flow deviating from Darcy's law in clay.The results indicate that the percentage of movable water ranges from 39.7%to 59.3%for the six samples at a hydraulic gradient of 1.As the hydraulic gradient increases,the percentage of moveable water also increases.Additionally,there is a strong correlation between the percentage of movable water and the variation in hydraulic conductivity with the hydraulic gradient.Furthermore,a quantitative relationship between the percentage of movable water and the hydraulic conductivity has been established.The results of this study suggest that water adsorption on the pore wall not only affects the water movability,but is also closely related to the pre-Darcy flow phenomenon in clay.
基金support provided by Shandong Provincial Science and Technology Plan Project(No.2023TSGC0625)Natural Resources Defense Council(NRDC,K94).
文摘A model is proposed for liquid film profile prediction in gas-liquid two-phase flow,which is able to provide the film thickness along the circumferential direction and the pressure gradient in the flow direction.A two-fluid model is used to calculate both gas and liquid phases’flow characteristics.The secondary flow occurring in the gas phase is taken into account and a sailing boat mechanism is introduced.Moreover,energy conservation is applied for obtaining the liquid film thickness distribution along the circumference.Liquid film thickness distribution is calculated accordingly for different cases;its values are compared with other models and available experimental data.As a result,the newly proposed model is tested and good performances are demonstrated.The liquid film thickness distribution in small pipes and inclined pipes is also studied,and regime transition is revealed by liquid film profile evolution.The observed inflection point demonstrates that the liquid film thickness decreases steeply along the circumference,when the circle angle ranges between 30°and 50°for gas-liquid stratified flow with small superficial velocities.
文摘It has not been a simple matter to obtain a sound extension of the classical J2 flow theory of plasticity that incorporates a dependence on plastic strain gradients and that is capable of capturing size-dependent behaviour of metals at the micron scale. Two classes of basic extensions of classical J2 theory have been proposed： one with increments in higher order stresses related to increments of strain gradients and the other characterized by the higher order stresses themselves expressed in terms of increments of strain gradients. The theories proposed by Muhlhans and Aifantis in 1991 and Fleck and Hutchinson in 2001 are in the first class, and, as formulated, these do not always satisfy thermodynamic requirements on plastic dissipation. On the other hand, theories of the second class proposed by Gudmundson in 2004 and Gurtin and Anand in 2009 have the physical deficiency that the higher order stress quantities can change discontinuously for bodies subject to arbitrarily small load changes. The present paper lays out this background to the quest for a sound phenomenological extension of the rateindependent J2 flow theory of plasticity to include a de- pendence on gradients of plastic strain. A modification of the Fleck-Hutchinson formulation that ensures its thermo- dynamic integrity is presented and contrasted with a comparable formulation of the second class where in the higher or- der stresses are expressed in terms of the plastic strain rate. Both versions are constructed to reduce to the classical J2 flow theory of plasticity when the gradients can be neglected and to coincide with the simpler and more readily formulated J2 deformation theory of gradient plasticity for deformation histories characterized by proportional straining.
基金This work was supported by the Fundamental Research Funds for the National Natural Science Foundation of China(No.41571265,41971244)the Key Research and Development Project of Social Livelihood in Chongqing(cstc2018jscxmszdX0061)the Foundation of Graduate Research and Innovation in Chongqing under project CYB18089.
文摘Subsurface water flow velocity influences the hydrodynamic characteristics of soil seepage and the interaction between subsurface water flow and surface runoff during soil erosion and sediment transport.A visualized method and equipment was adopted in this study to observe the subsurface water flow.Quartz sand was used as the test material of subsurface water flow and fluorescent dye was used as the indicator for tracing subsurface water flow.Water was supplied at the same flow discharge to the three parts at the bottom of the test flume,and the subsurface water flow were determined with four slope gradients(4°,8°,10°,and 12°).The results showed that the seepage velocity gradually increased with increasing slope gradient.The pore water velocity at different depths of sand layer profile increased with increasing slope gradient,whereas the thickness of the flow front gradually decreased.For the same slope gradient,the pore water velocity in the lower layer was the largest,whereas the thickness of the flow front was the smallest.Comparative analysis of the relationship between seepage velocity and pore water velocity at different depths of sand layer profile showed that the maximum relative difference between the measured pore water velocity and the computational pore water velocity at different depths of sand profile in the experiment was 4.38%.Thus,the test method for measuring the subsurface water flow velocity of sand layer profile adopted in this study was effective and feasible.The development of this experiment and the exploration of research methods would lay a good test foundation for future studies on the variation law of subsurface water flow velocity and the determination of flow velocity in purple soils,thus contributing to the improvement of the hydrodynamic mechanism of purple soils.
基金Supported by the National Natural Science Foundation of China(60805004)the State Key Lab of Space Medicine Fundamen-tals and Application(SMFA09A16)
文摘Gradient vector flow （GVF） is an effective external force for active contours, but its iso- tropic nature handicaps its performance. The recently proposed gradient vector flow in the normal direction （NGVF） is anisotropic since it only keeps the diffusion along the normal direction of the isophotes; however, it has difficulties forcing a snake into long, thin boundary indentations. In this paper, a novel external force for active contours called normally generalized gradient vector flow （NGGVF） is proposed, which generalizes the NGVF formulation to include two spatially varying weighting functions. Consequently, the proposed NGGVF snake is anisotropic and would improve ac- tive contour convergence into long, thin boundary indentations while maintaining other desirable properties of the NGVF snake, such as enlarged capture range, initialization insensitivity and good convergence at concavities. The advantages on synthetic and real images are demonstrated.
基金Project supported by the National Natural Science foundation of China(No.51079095)the Science Fund for Creative Research Groups of the National Natural Science Foundation of China(No.51021004)
文摘This paper uses the Oseen transformation to solve the differential equations governing motion of the vertical linear gradient flow distribution close to a wall surface. The Navier-Stokes equations are used to consider the inertia term along the flow direction. A novel contour integral method is used to solve the complex Airy function. The boundary conditions of linear gradient flow distribution for finite problems are determined. The vorticity function, the pressure function, and the turbulent velocity profiles are provided, and the stability of particle trajectories is studied. An Lx-function form of the third derivative circulation is used to to simplify the solution. Theoretical results are compared with the experimental measurements with satisfactory agreement.
基金Project(51304220) supported by the National Natural Science Foundation of ChinaProject(3144033) supported by the Beijing Natural Science Foundation,ChinaProject(20130007120014) supported by the Specialized Research Fund for the Doctoral Program of Higher Education of China
文摘The flow behavior in porous media with threshold pressure gradient(TPG) is more complex than Darcy flow and the equations of motion, and outer boundary and inner boundary with TPG are also different from Darcy flow for unsteady flow of a producing well in a reservoir. An analytic method to solve this kind of problem is in a need of reestablishment. The classical method of Green's function and Newman product principle in a new way are used to solve the unsteady state flow problems of various shapes of well and reservoir while considering the TPG. Four Green's functions of point, line, band and circle while considering the TPG are achieved. Then, two well models of vertical well and horizontal well are built and simultaneously the function to calculate the moving boundary of each well model is provided. The results show that when considering TPG the pressure field is much different, which has a sudden pressure change, with a moving boundary in it. And the moving boundary of each well model increases with time but slows down rapidly, especially when the TGP is large.
文摘In this paper, we propose a fast centerline extraction method to be used for gradient and direction vector flow of active contours. The gradient and direction vector flow is a recently reported active contour model capable of significantly improving the image segmentation performance especially for complex object shape, by seamlessly integrating gradient vector flow and prior directional information. Since the prior directional information is provided by manual line drawing, it can be inconvenient for inexperienced users who might have difficulty in finding the best place to draw the directional lines to achieve the best segmentation performance. This paper describes a method to overcome this problem by automatically extracting centerlines to guide the users for providing the right directional information. Experimental results on synthetic and real images demonstrate the feasibility of the proposed method.
基金the National High Technology Research and Development Program of China (2006AA09Z333)
文摘The segregated flow pattern, which occurs in a 26.1 mm diameter, horizontal, stainless steel test section, is investigated. Pressure gradient and in situ phase distribution data were obtained for different combinations of phase superficial velocities ranging from 0.05 m.s^-1 to 0,96 m.s^-1. For the current small Eoetvoes number liquid-liquid system （EOD=4.77）, the dominant effect of interfacial tension and wall-wetting properties of the liquids over the gravity is considered. The approach introduces the closure relationship for the case of turbulent flow m a rough pipe, and attempts to modify the two-fluid model to account for the curved interface. In present flow rates range, wave amplitudes were found small, while interfacial mixing was observed. An adjustable definition for hydraulic diame- ters of two fluids and interfacial friction factor is adopted. The predicted pressure gradient and in situ phase distribution data have been compared with present experimental data and those reported in the literature.
基金Supported by the National Natural Science Foundation of China(11571361)China Scholarship Council
文摘A local gradient estimate for positive solutions of porous medium equations on complete noncompact Riemannian manifolds under the Ricci flow is derived. Moreover, a global gradient estimate for such equations on compact Riemannian manifolds is also obtained.
基金financially supported by National Natural Science Foundation of China(No.U20B6003).
文摘Aqueous foam is broadly applicable to enhanced oil recovery(EOR).The rheology of foam as a function of foam quality,gas and liquid velocities,and surfactant concentration constitute the foundation of its application.The great variations of the above factors can affect the effectiveness of N2 foam in EOR continuously in complex formations,which is rarely involved in previous relevant studies.This paper presents an experimental study of foam flow in porous media by injecting pre-generated N2 foam into a sand pack under the conditions of considering a wide range of gas and liquid velocities and surfactant concentrations.The results show that in a wide range of gas and liquid velocities,the pressure gradient contours are L-shaped near the coordinate axes,but V-shaped in other regions.And the surfactant concentration is a strong factor influencing the trend of pressure gradient contours.Foam flow resistance is very sensitive to the surfactant concentration in both the high-and low-foam quality regime,especially when the surfactant concentration is less than CMC.The foam quality is an important variable to the flow resistance obtained.There exists a transition point from low-to high-quality regime in a particular flow system,where has the maximum flow resistance,the corresponding foam quality is called transition foam quality,which increases as the surfactant concentration increases.The results can add to our knowledge base of foam rheology in porous media,and can provide a strong basis for the field application of foams.
文摘As has been observed by Morse [1], any generic vector field v on a compact smooth manifold X with boundary gives rise to a stratification of the boundary by compact submanifolds , where . Our main observation is that this stratification re-flects the stratified convexity/concavity of the boundary ?with respect to the ?v-flow. We study the behavior of this stratification under deformations of the vector field v. We also investigate the restrictions that the existence of a convex/concave traversing ?v-flow imposes on the topology of X. Let be the orthogonal projection of on the tangent bundle of . We link the dynamics of theon the boundary with the property of in X being convex/concave. This linkage is an instance of more general phenomenon that we call “holography of traversing fields”—a subject of a different paper to follow.
文摘The present paper is concerned with the steady thin film flow of the Sisko fluid on a horizontal moving plate, where the surface tension gradient is a driving mechanism. The analytic solution for the resulting nonlinear ordinary differential equation is obtained by the Adomian decomposition method （ADM）. The physical quantities are derived including the pressure profile, the velocity profile, the maximum residue time, the stationary points, the volume flow rate, the average film velocity, the uniform film thickness, the shear stress, the surface tension profile~ and the vorticity vector. It is found that the velocity of the Sisko fluid film decreases when the fluid behavior index and the Sisko fluid parameter increase, whereas it increases with an increase in the inverse capillary number. An increase in the inverse capillary number results in an increase in the surface tension which in turn results in an increase in the surface tension gradient on the Sisko fluid film. The locations of the stationary points are shifted towards the moving plate with the increase in the inverse capillary number, and vice versa locations for the stationary points are found with the increasing Sisko fluid parameter. Furthermore, shear thinning and shear thickening characteristics of the Sisko fluid are discussed. A comparison is made between the Sisko fluid film and the Newtonian fluid film.
文摘Many in vitro studies focus on effects of wall shear stress (WSS) and wall shear stress gradient (WSSG) on endothelial cells, which are linked to the initiation and progression of atherosclerosis in the arterial system. Limitation in available flow chambers with a constant WSSG in the testing region makes it difficult to quantify cellular responses to WSSG. The current study proposes and characterizes a type of converging parallel plate flow chamber (PPFC) featuring a constant gradient of WSS. A simple formula was derived for the curvature of side walls, which relates WSSG to flow rate (Q), height of the PPFC (h), length of the convergent section (L), its widths at the entrance (w0) and exit (w1). CFD simulation of flow in the chamber is carried out. Constant WSSG is observed in most regions of the top and bottom plates except those in close proximity of side walls. A change in Q or h induces equally proportional changes in WSS and WSSG whereas an alteration in the ratio between w0 and w1 results in a more significant change in WSSG than that in WSS. The current design makes possible an easy quantification of WSSG on endothelial cells in the flow chamber.
文摘Analysis of high resolution of aeromagnetic data was carried out over Lamurde, Adamawa state north-eastern Nigeria to determine the Curie point depth (CPD), heat flow and geothermal gradient. The aeromagnetic data used for this work was obtained at Nigerian geological survey agency, the total magnetic intensity was processed to produce the residual magnetic map which was divided into 4 overlapping blocks, each block was subjected to spectral analyses to obtain depths to the top boundary and centroid, while depth to bottom of the magnetic sources was calculated using empirical formula. The depths values obtained were then used to assess the CPD, heat flow and geothermal gradient in the area. The result shows that the CPD varies between 9.62 and 10.92 km with an average of 10.45 k, the heat flow varies between 150.73 and 132.78 mWm−20⋅°C−1 with an average of 139.12 mWm−20⋅°C−1 and the geothermal gradient in the study area varies between 12.16 and 15.67 °C/km with an average of 13.39 °C/km. In view of the above results, the high heat flow may be responsible for maturation of hydrocarbon in Benue Trough as well as responsible for the lead Zinc Mineralization. Again by implication, Lamurde area can be a good area for geothermal reservoir exploration for an alternative source for power generation.
文摘Information on geothermal gradient and heat flow within the subsurface is critical in the quest for geothermal energy exploration. In a bid to ascertain the thermal potential of Nigeria sector of the Chad Basin for energy generation, subsurface temperature information from 19 oil wells, 24 water boreholes drilled to depths beyond 100 metres and atmospheric temperature from the Chad basin were utilized in calculating geothermal gradient of the area. Selected ditch cuttings from the wells were subjected to thermal conductivity test using Thermal Conductivity Scanner (TCS) at the Polish Geological Institute Laboratory in Warsaw. The terrestrial heat flow was calculated according to the Fourier’s law as a simple product of the geothermal gradient and the mean thermal conductivity. Results obtained indicated geothermal gradient range of 2.81<sup> °</sup>C/100 m to 5.88<sup> °</sup>C/100 m with an average of 3.71<sup> °</sup>C/100 m. The thermal conductivity values from the different representative samples range from 0.58 W/m*K to 4.207 W/m*K with an average of 1.626 W/m*K. The work presented a heat flow value ranging from 45 mW/m<sup>2</sup> to about 90 mW/m<sup>2</sup> in the Nigerian sector of the Chad Basin.
文摘Some patients with severe aortic stenosis (AS), due to restrictive cardiac physiology, paradoxically have relatively low flow and low gradients across stenotic aortic valves despite preserved left ventricular (LV) systolic function. It results in symptoms and reduced quality of life and carries a high mortality. Whilst this form of severe AS, termed paradoxical low flow low gradient (pLFLG), is well reported, patients with this diagnosis experience inappropriate barriers to aortic valve replacement (AVR), the only efficacious treatment. We present the case of an 88-year-old female with 12 months of exertional dyspnoea on a background of hypothyroidism and hypercholesterolemia. Transthoracic echocardiogram (TTE) revealed LV hypertrophy, with a small LV cavity size and reduced stroke volume, yet normal systolic function. A heavily calcified aortic valve was identified with severe aortic stenosis, based on valve area, yet with incongruous mean transvalvular gradient of 25 mmHg (severe ≥ 50 mmHg). Following exclusion of other differential diagnoses, her symptoms were attributed to paradoxical LFLG severe AS. She was however declined definitive transcatheter aortic valve implantation (TAVI) due to her paradoxically low mean aortic gradient. Following further deterioration in her symptoms and supportive quantification of poor exercise performance, she was ultimately re-referred, accepted, and underwent TAVI. Following her AVR, the patient experiences significant improvement in both symptoms and quality of life after only one month. Paradoxical LFLG severe AS remains a well-documented yet under recognized disease. It carries high morbidity and mortality if untreated, yet is significantly less likely to be referred and accepted for intervention. With its prevalence expected to rise with an ageing population, this case serves as a timely reminder for clinicians to address the under recognition of important pathology.
