Smoothed Particle Hydrodynamics Model of Non-Aqueous Phase Liquid Flow and Dissolution

A smoothed particle hydrodynamics model was developed to simulate the flow of mixtures of aqueous and non-aqueous phase liquids in porous media and the dissolution of the non-aqueous phase in the aqueous phase. The model was used to study the effects of pore-scale heterogeneity and anisotropy on the steady state dense non-aqueous phase liquid (DNAPL) saturation when gravity driven DNAPL displaces water from initially water saturated porous media. Pore-scale anisotropy was created by using co-oriented non-overlapping elliptically shaped grains to represent the porous media. After a steady state DNAPL saturation was reached, water was injected until a new steady state DNAPL saturation was reached. The amount of trapped DNAPL was found to be greater when DNAPL is displaced in the direction of the major axes of the soil grains than when it is displaced in the direction of the minor axes of the soil grains. The amount of trapped DNAPL was also found to increase with decreasing initial saturation of the continuous DNAPL phase. For the conditions used in our simulations, the saturation of the trapped DNAPL with a smaller initial DNAPL saturation was more than 3 times larger than the amount of trapped DNAPL with a larger initial saturation. These simulations were carried out assuming that the DNAPL did not dissolve in water. Simulations including the effect of dissolution of DNAPL in the aqueous phase were also performed, and effective (macroscopic) mass transfer coefficients were determined. The U.S. Government’s right to retain a non-exclusive, royalty-free license in and to any copyright is acknowledged.     

The interaction of background ocean air bubbles with a surface ship

A two-fluid model suitable for the calculation of the two-phase flow field around a naval surface ship is presented. This model couples the Reynolds-averaged Navier–Stokes (RANS) equations with equations for the evolution of the gas-phase momentum, volume fraction and bubble number density, thereby allowing the multidimensional calculation of the two-phase flow for monodisperse variable size bubbles. The bubble field modifies the liquid solution through changes in the liquid mass and momentum conservation equations. The model is applied to the case of the scavenging of wind-induced sea-background bubbles by an unpropelled US Navy frigate under non-zero Froude number boundary conditions at the free surface. This is an important test case, because it can be simulated experimentally with a model-scale ship in a towing tank. A significant modification of the background bubble field is predicted in the wake of the ship, where bubble depletion occurs along with a reduction in the bubble size due to dissolution. This effect is due to lateral phase distribution phenomena and the generation of an upwelling plume in the near wake that brings smaller bubbles up to the surface. © 1998 John Wiley & Sons, Ltd.     

Density-driven Transport of Volatile Organic Compounds and its Impact on Contaminated Groundwater Plume Evolution

Density-driven advection of gas phase due to vaporization of chlorinated volatile organic compounds (VOCs) has a significant effect on fate and transport of contaminants. In this study, we investigated the effects of density-driven advection, infiltration, and permeability on contaminant plume evolution and natural attenuation of VOCs in the subsurface system. To analyze these effects, multiphase flow and contaminant transport processes were simulated using a three-dimensional Galerkin-finite-element-based model. Trichloroethylene (TCE) is selected as a target contaminant. Density-driven advection of gas phase elevated the potential of groundwater pollution in the saturated zone by accelerating downward migration of vaporized contaminant in the unsaturated zone. The advection contributed to increased removal rates of non-aqueous phase liquid (NAPL) TCE source and reduced dissolved TCE plume development in the downstream area. Infiltration reduced the velocity of the density-driven advection and its influence zone, but raised TCE transfer from the unsaturated to the saturated zone. The variation in soil permeability showed greater impact on contaminant migration within water phase in the saturated zone than within gas phase in the unsaturated zone. Temporal variations of TCE mass within two-dimensional (2D) and three-dimensional (3D) domains under several modeling conditions were compared. These results are important in evaluation of natural attenuation processes, and should be considered to effectively design monitored natural attenuation as a remedial option.     

Role of NAPL Thermal Properties in the Effectiveness of Hot Water Flooding

Hot water flooding is a thermal nonaqueous phase liquid (NAPL) recovery technology originally developed in the petroleum industry that has recently been proposed for enhanced recovery of NAPLs in the contaminated subsurface. This technology, however, has received relatively little laboratory or numerical modeling investigation in the contaminant hydrology community. In this study the utility of flooding NAPL contaminated source zones at elevated water temperatures was investigated. Simulations were conducted using 16 different geostatistical representations of an actual field site. Two NAPLs were selected for this study—a light NAPL with hydraulic properties that have moderate temperature dependencies and a dense NAPL with significant viscosity temperature dependency. For these two NAPLs, flooding the source zone with water at elevated temperatures resulted in enhanced NAPL recovery. However, injection of hot water also resulted in accelerated downward movement of coal tar DNAPL due to the reduced viscosity at elevated temperatures. NAPL recovery was also dependent on the source zone architecture with greater NAPL mass recovery when the NAPL was localized in a small volume at high saturations. These results suggest that hot water flooding can significantly speed up the recovery of viscous NAPLs and, as such, is a powerful technique for the remediation of viscous NAPLs.     

Comparison of light transmission and reflection techniques to determine concentrations in flow tank experiments

Transmissive and reflective intensity measurements for visual concentration determinations in 2D flow tank experiments were compared and evaluated for their applicability in the study of flow and transport phenomena. A density-dependent heterogeneous flow experiment was conducted and transmission and reflection images of the dyed saltwater plume were analyzed. A single light source and dark curtains forced the light to pass through the porous media only, thus facilitating the transmission measurements. The reflection images delivered a more homogeneous spatial illumination than the transmission images. Major perturbations of the transmission images were lens flare effects and light dispersion within the bead–water–Plexiglas system which smear the front of the plume. Based on the conducted evaluation of transmissive and reflective intensity measurements, the reflection data delivered more reliable intensity values to derive solute concentrations in intermediate scale flow tank experiments.     

A Fickian diffusion model for the spreading of liquid plumes infiltrating in heterogeneous media

Infiltration of water and non-aqueous phase liquids (NAPLs) in the vadose zone gives rise to complex two- and three-phase immiscible displacement processes. Physical and numerical experiments have shown that ever-present small-scale heterogeneities will cause a lateral broadening of the descending liquid plumes. This behavior of liquid plumes infiltrating in the vadose zone may be similar to the familiar transversal dispersion of solute plumes in single-phase flow. Noting this analogy we introduce a mathematical model for ‘phase dispersion’ in multiphase flow as a Fickian diffusion process. It is shown that the driving force for phase dispersion is the gradient of relative permeability, and that addition of a phase-dispersive term to the governing equations for multiphase flow is equivalent to an effective capillary pressure which is proportional to the logarithm of the relative permeability of the infiltrating liquid phase. The relationship between heterogeneity-induced phase dispersion and capillary and numerical dispersion effects is established. High-resolution numerical simulation experiments in heterogeneous media show that plume spreading tends to be diffusive, supporting the proposed convection-dispersion model. Finite difference discretization of the phase-dispersive flux is discussed, and an illustrative application to NAPL infiltration from a localized source is presented. It is found that a small amount of phase dispersion can completely alter the behavior of an infiltrating NAPL plume, and that neglect of phase-dispersive processes may lead to unrealistic predictions of NAPL behavior in the vadose zone.     

Scalar transport from a point source in flows over wavy walls

Simultaneous measurements of the velocity and concentration field in fully developed turbulent flows over a wavy wall are described. The concentration field originates from a low-momentum plume of a passive tracer. PLIF and digital particle image velocimetry are used to make spatially resolved measurements of the structure of the scalar distribution and the velocity. The measurements are performed at three different Reynolds numbers of Re _b = 5,600, Re _b = 11,200 and Re _b = 22,400, respectively, based on the bulk velocity u _b and the total channel height 2h. The velocity field and the scalar field are investigated in a water channel with an aspect ratio of 12:1, where the bottom wall of the test section consists of a train of sinusoidal waves. The wavy wall is characterized by the amplitude to wavelength ratio α = 0.05 and the ratio β between the wave amplitude and the half channel height where β = 0.1. The scalar is released from a point source at the wave crest. For the concentration measurements, Rhodamine B is used as tracer dye. At low to moderate Reynolds number, the flow field is characterized through a recirculation zone which develops after the wave crest. The recirculation zone induces high intensities of the fluctuations of the streamwise velocity and wall-normal velocity. Furthermore, large-scale structures are apparent in the flow field. In previous investigations it has been shown that these large-scale structures meander laterally in flows over wavy bottom walls. The investigations show a strong effect of the wavy bottom wall on the scalar mixing. In the vicinity of the source, the scalar is transported by packets of fluid with a high scalar concentration. As they move downstream, these packets disintegrate into filament-like structures which are subject to strong gradients between the filaments and the surrounding fluid. The lateral scale of the turbulent plume is smaller than the lateral scale of the large-scale structures in the flow field and the plume dispersion is dominated by the structures in the flow field. Due to the lateral meandering of the large-scale structures of the flow field, also the scalar plume meanders laterally. Compared to turbulent plumes in plane channel flows, the wavy bottom wall enhances the mixing effect of the turbulent flow and the spreading rate of the scalar plume is increased.     

Significance of Mass–Concentration Relation on the Contaminant Source Depletion in the Nonaqueous Phase Liquid (NAPL) Contaminated Zone

This study develops a new numerical model adopting a generic relation between the nonaqueous phase liquid (NAPL) mass and aqueous-phase NAPL concentration to simulate the relationship between NAPL contaminant mass discharge and contaminant mass reduction in the source zone, which plays a critical role to assist with site management decisions on contaminated zone remediation. The model can accommodate any contaminant mass and concentration relations and applicable to the situations when groundwater flowrate in the NAPL source zone varies in any form temporally. Therefore, the combined effects of mass–concentration relation and groundwater flowrate variations can be examined. It is hypothesized that the NAPL mass–concentration relations reflect the spatial variability of porous media in the subsurface. The developed model is compared with results from field monitoring sites and found to exhibit high flexibility and capability in capturing the observed complex NAPL source zone dynamics. Using six contaminant mass and concentration functions of varying shapes, we show that contaminant mass and concentration relation has pronounced effects on contaminant mass discharge dynamics in addition to the groundwater flowrate temporal variations. In general, the coupled mass–concentration relation and groundwater flowrate variations demonstrate stronger capability in capturing the NAPL source zone dynamics under a wide range of field porous medium conditions reported in the literature than the models that only consider groundwater flux variations. In particular, the concave mass–concentration models can be used in less heterogeneous porous media, while the convex mass–concentration models are more appropriate in more heterogeneous site conditions.

     

Mass and heat transfer during solid sphere dissolution in a non-uniform fluid flow

We studied a nonisothermal dissolution of a solvable solid spherical particle in an axisymmetric non-uniform fluid flow when the concentration level of the solute in the solvent is finite (finite dilution of solute approximation). It is shown that simultaneous heat and mass transfer during solid sphere dissolution in a uniform fluid flow, axisymmetric shear flow, shear-translational flow and flow with a parabolic velocity profile can be described by a system of generalized equations of convective diffusion and energy. Solutions of diffusion and energy equations are obtained in an exact analytical form. Using a general solution the asymptotic solutions for heat and mass transfer problem during spherical solid particle dissolution in a uniform fluid flow, axisymmetric shear flow, shear-translational flow and flow with parabolic velocity profile are derived. Theoretical results are in compliance with the available experimental data on falling urea particles dissolution in water and for solid sphere dissolution in a shear flow.     

Stability of a melt/solid interface with reference to a plume channel

The structure of free-convection flow in a plume channel formed as a result of melting above a local heat source placed on the basement of a solid mass is experimentally investigated. The channel shape and the flow pattern in it are functions of the relative power Ka = N/N ₁, where N is the plume source power and N ₁ is the heat removed to the surrounding mass. When the heat is withdrawn from the plume channel by heat conduction, the channel represents a system of convective cells on whose boundaries there are channel constrictions. The temperature fields and the cell flow patterns are investigated. For mantle plumes, such as the Hawaiian, Iceland, and Bouvet plumes and extended igneous provinces, the basement diameter and the values of the criterion Ka are determined.     

A Study of Microscale Gas Trapping Using Etched Silicon Micromodels

Immobilization and trapping of carbon dioxide (CO₂) enhances the security of geological storage. Trapping mechanisms have been characterized in four groups: structural, residual, dissolution, and mineralization. While structural trapping acts immediately when injection starts and is well investigated, the contribution of residual and dissolution trapping increases over storage time and these contributions need to be better understood for better predictions. This paper focuses on an experimental pore-scale investigation of residual and capillary trapping. CO₂?Cwater imbibition experiments were conducted in micromodels whose homogenous pore space is geometrically and topologically similar to Berea sandstone. Microvisual data, photographs and video footage, describes the trapping mechanism and, especially, the disconnection and shrinkage of the CO₂ phase. Results show that depending on the flow rate of the imbibing water different trapping mechanisms are observed. Lower flow rates, comparable to the trailing edge of a CO₂ plume, lead to more snap-off events and greater trapped residual saturation, whereas rates comparable to the near wellbore area during enhanced sequestration showed displacement of gas bubbles and greater dissolution that ultimately leads to very low or zero gas saturations. Furthermore, complete dissolution events showed that homogenous as well as heterogeneous dissolution occurs. Whereas the latter is subdivided into microbubble formation and dissolution on crevices or pore roughness, the former occurs without the influence of pore walls. Based on the observations we suggest that the type of rock and its roughness as well as the fines present at the CO₂ brine interface are important factors determining the dissolution mechanism.     

Natural Convection from a Vertical Plate in a Porous Medium Using Brinkman's Model

A regular perturbation analysis is presented for the following laminar natural convection flows of Newtonian fluids with temperature-dependent effective viscosity: a freely-rising plane plume, the flow above a horizontal line source on an adiabatic surface (a plane wall plume) and the flow adjacent to a vertical uniform flux surface for porous medium. The temperature-dependent effective viscosity introduces nonsimilarity into the governing equations. Numerical results are presented for the flow and heat transfer characteristics.     

Stochastic Simulations of NAPL Mass Transport in Variably Saturated Heterogeneous Porous Media

A multiphase flow and transport numerical model is developed to study the effects of porous media heterogeneities on residual NAPL mass partitioning and transport of dissolved and/or volatilized NAPL mass in variably saturated media. The results indicate the significance of porous media heterogeneity in influencing the mass transfer processes and NAPL transport in the subsurface. Among the parameters investigated in this study, the heterogeneity of the permeability field has the most significant influence on the NAPL mass partitioning and transport. In general, the heterogeneity of the porous media properties enhances the NAPL mass plume spreading in both the water phase and the gas phase while the influence on the water phase is much more significant. Overall, the porous media property heterogeneities tend to increase the accumulation of NAPL mass in the water phase. The nonequilibrium mass transfer processes result in the expected trend of decreasing the NAPL mass dissipation rate and causing long-term groundwater contamination.     

材料表面润湿性调控及减阻性能研究

设计合成不同结构的自组装分子,使其可以在不改变表面粗糙度的情况下改变表面的润湿性能;利用低表面能涂层修饰粗糙表面得到超疏水表面.采用流变仪和水洞试验分别在层流和湍流流动状态下测试了具有不同润湿行为的亲、疏水材料的减阻性能.结果表明:在层流流动状态,随着不同表面的接触角从13°增加到45°、113°和161°,减阻率随之从1.8%增大到7.2%、7.9%和14.9%;在湍流流动状态下,自组装涂层接触角为13°、45°和113°的三组模型的平均减阻率为0.8%、1.9%和6.8%,最大减阻率分别可达3.6%、9.2%和18.0%.两种流体流动中均存在材料表面水接触角增加减阻效率增大的行为.     

Analysis of a turbulent buoyant confined jet modeled using realizable k–ɛ model

Through this paper, analyses of components of the unheated/heated turbulent confined jet are introduced and some models to describe them are developed. Turbulence realizable k–? model is used to model the turbulence of this problem. Numerical simulations of 2D axisymmetric vertical hot water confined jet into a cylindrical tank have been done. Solutions are obtained for unsteady flow while velocity, pressure, temperature and turbulence distributions inside the water tank are analyzed. For seeking verification, an experiment was conducted for measuring of the temperature of the same system, and comparison between the measured and simulated temperature shows a good agreement. Using the simulated results, some models are developed to describe axial velocity, centerline velocity, radial velocity, dynamic pressure, mass flux, momentum flux and buoyancy flux for both unheated (non-buoyant) and heated (buoyant) jet. Finally, the dynamics of the heated jet in terms of the plume function which is a universal quantity and the source parameter are studied and therefore the maximum velocity can be predicted theoretically.     

Heat and mass transfer in a visco–elastic fluid flow over an accelerating surface with heat source/sink and viscous dissipation

 In this paper we present a mathematical analysis of heat and mass transfer phenomena in a visco–elastic fluid flow over an accelerating stretching sheet in the presence of heat source/sink, viscous dissipation and suction/blowing. Similarity transformations are used to convert highly non-linear partial differential equations into ordinary differential equations. Several closed form analytical solutions for non-dimensional temperature, concentration, heat flux, mass flux profiles are obtained in the form of confluent hypergeometric (Kummer's) functions for two different cases of the boundary conditions, namely, (i) wall with prescribed second order power law temperature and second order power law concentration (PST), and (ii) wall with prescribed second order power law heat flux and second order power law mass flux (PHF). The effect of various physical parameters like visco–elasticity, Eckert number, Prandtl number, heat source/sink, Schmidt number and suction/blowing parameter on temperature and concentration profiles are analysed. The effects of all these parameters on wall temperature gradient and wall concentration gradient are also discussed. Received on 23 March 2000 / Published online: 29 November 2001     

Single-Phase (Brine) and Two-Phase (DNAPL–Brine) Flows in Induced Fractures

This study reports an investigation on the characteristics of single-phase (brine) and two-phase (DNAPL–brine) flows in induced fractures. The fracture aperture and fluid phase distributions were determined using X-ray computer tomography. In the single-phase flow tests, the pressure gradient across the induced fractures increases linearly with increasing flow rate. However, models based on the measured aperture do not yield a consistent match with the experimental data because the effect of pressure losses due to aperture variation and undulation are not taken into account. In the two-phase flow tests, the measured phase distributions reveal that the flow pattern is dominated by a dispersed or mixed flow in which either DNAPL or brine phase is discontinuous. The channel flow pattern, in which DNAPL and brine phases are continuous in the fracture and well represented by the widely used Romm’s relative permeability relationship was not observed in this study. In contrast, a Lockhart–Martinelli-type correlation developed for gas–liquid flow in pipes was found to match the pressure gradient and phase saturation results obtained from the laboratory tests.     

Experiments in Turbulent Pipe Flow with Polymer Additives at Maximum Drag Reduction

In this paper we report on (two-component) LDV experiments in a fully developed turbulent pipe flow with a drag-reducing polymer (partially hydrolyzed polyacrylamide) dissolved in water. The Reynolds number based on the mean velocity, the pipe diameter and the local viscosity at the wall is approximately 10000. We have used polymer solutions with three different concentrations which have been chosen such that maximum drag reduction occurs. The amount of drag reduction found is 60–70%. Our experimental results are compared with results obtained with water and with a very dilute solution which exhibits only a small amount of drag reduction. We have focused on the observation of turbulence statistics (mean velocities and turbulence intensities) and on the various contributions to the total shear stress. The latter consists of a turbulent, a solvent (viscous) and a polymeric part. The polymers are found to contribute significantly to the total stress. With respect to the mean velocity profile we find a thickening of the buffer layer and an increase in the slope of the logarithmic profile. With respect to the turbulence statistics we find for the streamwise velocity fluctuations an increase of the root mean square at low polymer concentration but a return to values comparable to those for water at higher concentrations. The root mean square of the normal velocity fluctuations shows a strong decrease. Also the Reynolds (turbulent) shear stress and the correlation coefficient between the stream wise and the normal components are drastically reduced over the entire pipe diameter. In all cases the Reynolds stress stays definitely non-zero at maximum drag reduction. The consequence of the drop of the Reynolds stress is a large polymer stress, which can be 60% of the total stress. The kinetic-energy balance of the mean flow shows a large transfer of energy directly to the polymers instead of the route by turbulence. The kinetic energy of the turbulence suggests a possibly negative polymeric dissipation of turbulent energy. This revised version was published online in July 2006 with corrections to the Cover Date.     

Dynamics of a “collective” bubble in a magma melt flow behind the decompression wave front

Specific features of the dynamics of the wave field structure and growth of a “collective” bubble behind the decompression wave front in the “Lagrangian” section of the formed cavitation zone are numerically analyzed. Two cases are considered: with no diffusion of the dissolved gas from the melt to cavitation nuclei and with the diffusion flux providing an increase in the gas mass in the bubbles. In the first case, it is shown that an almost smooth decompression wave front approximately 100 m wide is formed, with minor perturbations that appear when the front of saturation of the cavitation zone with nuclei is passed. In the case of the diffusion process, the melt state behind the saturation front is principally different: jumps in mass velocity and viscosity are observed in the vicinity of the free surface, and the pressure in the “collective” cavitation bubble remains unchanged for a sufficiently long time interval, despite the bubble growth and intense diffusion of the gas from the melt. It is assumed that the diffusion process (and, therefore, viscosity) actually become factors determining the dynamics of growth of cavitation bubbles beginning from this time interval. A pressure jump is demonstrated to form near the free surface.