Gravity segregation during miscible displacement—re-investigation and re-interpretation

Soil Research ◽  
2007 ◽  
Vol 45 (5) ◽  
pp. 319 ◽  
Author(s):  
D. A. Rose ◽  
F. Abbas
Keyword(s):  
Cross Sections ◽  
Formal Analysis ◽  
Safety Margin ◽  
Breakthrough Curves ◽  
Hydrodynamic Dispersion ◽  
Immiscible Liquids ◽  
Saline Groundwater ◽  
Gravity Segregation ◽  
Dimensional Gravity ◽  
Miscible Liquids

When the liquid residing in a horizontal bed of porous material is displaced by another liquid of different density, the resulting hydrodynamic dispersion is modified by the formation of a tongue of denser liquid undershooting the less dense liquid, a phenomenon known as gravity segregation. An earlier account of gravity segregation contained a substantial error (that of an incorrect frame of reference for flow) and several printing mistakes. In this paper we (i) correct these errors, (ii) extend the analysis to describe the course of breakthrough in beds of rectangular and circular cross-sections, (iii) re-interpret the existing experimental evidence, and (iv) present new experimental results on the vertical and horizontal transport of ionic solutions of different concentrations and densities through inert and reactive porous materials, ballotini, and sepiolite, respectively. The behaviour of immiscible liquids is predicted by the non-dimensional gravity segregation number, β, segregation becoming more extreme as β increases. With miscible liquids, however, breakthrough starts later and ends earlier then predicted for immiscible liquids, mixing by hydrodynamic dispersion moderating the effect of segregation. Breakthrough curves are well fitted by CXTFIT 2.0; apparent coefficients of hydrodynamic dispersion vary much less with pore-water velocity in horizontal than in vertical flow, but retardation factors are not influenced by orientation. Although a formal analysis of the combined effect of gravity segregation and hydrodynamic dispersion was not possible, the statistically significant inverse relation between β and column Peclet number was explained qualitatively. Gravity segregation occurs during the intrusion of saline groundwater into coastal aquifers. The simple theory for immiscible displacement overestimates the actual intrusion that occurs with miscible liquids and so provides an effective safety margin.

scholarly journals Viscous Fingering and Gravity Segregation through Porous Media: Experimental Findings

2010 ◽  
Vol 14 (11) ◽  
pp. 1-13 ◽  
Author(s):  
Farhat Abbas ◽  
Derek A. Rose
Keyword(s):  
Porous Media ◽  
Oil Recovery ◽  
Preferential Flow ◽  
Saline Water ◽  
Viscous Fingering ◽  
Breakthrough Curves ◽  
Bulk Solution ◽  
Hydrodynamic Dispersion ◽  
Vertical Flow ◽  
Gravity Segregation

Abstract During downward vertical flow of a viscous solution, the viscous fingering (VF) phenomenon affects miscible displacement of solutes through a soil profile. On the other hand, during horizontal flow, when the liquid residing in a horizontal bed of porous materials is displaced by another liquid of different density, the resulting hydrodynamic dispersion is modified by the formation of a tongue of denser liquid undershooting the less dense liquid, a phenomenon known as gravity segregation (GS). To explore VF and GS phenomena, the authors present laboratory experimental results on the vertical and horizontal transport of bulk solution and ions of different concentrations and/or densities through inert and reactive porous media. The study showed that, with miscible liquids, breakthrough starts later and ends earlier. The authors predicted the behavior of immiscible liquids by the nondimensional gravity segregation number β: that is, with increase in β, the segregation becomes extreme. The curve fitting technique CXTFIT 2.0 fitted the experimental breakthrough curves well, showing that the apparent coefficients of hydrodynamic dispersion vary much less with pore-water velocity in horizontal than in vertical flow, but retardation factors are not influenced by the orientation of flow. This work is relevant to the preferential flow of viscous liquids such as liquid fertilizers in agricultural fields, oil recovery processes, and the intrusion of saline water into the freshwater of coastal aquifers.

Pore-scale Mixing and the Evolution from Anomalous to Normal Hydrodynamic Dispersion

2021 ◽  
Author(s):  
Marco Dentz ◽  
Alexandre Puyguiraud ◽  
Philippe Gouze
Keyword(s):  
Porous Media ◽  
Large Scale ◽  
Molecular Diffusion ◽  
Pore Space ◽  
Breakthrough Curves ◽  
Heterogeneous Porous Media ◽  
Hydrodynamic Dispersion ◽  
Pore Scale ◽  
Sandstone Sample ◽  
Flow Variability

<p>Transport of dissolved substances through porous media is determined by the complexity of the pore space and diffusive mass transfer within and between pores. The interplay of diffusive pore-scale mixing and spatial flow variability are key for the understanding of transport and reaction phenomena in porous media. We study the interplay of pore-scale mixing and network-scale advection through heterogeneous porous media, and its role for the evolution and asymptotic behavior of hydrodynamic dispersion. In a Lagrangian framework, we identify three fundamental mechanisms of pore-scale mixing that determine large scale particle motion: (i) The smoothing of intra-pore velocity contrasts, (ii) the increase of the tortuosity of particle paths, and (iii) the setting of a maximum time for particle transitions. Based on these mechanisms, we derive an upscaled approach that predicts anomalous and normal hydrodynamic dispersion based on the characteristic pore length, Eulerian velocity distribution and Péclet number. The theoretical developments are supported and validated by direct numerical flow and transport simulations in a three-dimensional digitized Berea sandstone sample obtained using X-Ray microtomography. Solute breakthrough curves, are characterized by an intermediate power-law behavior and exponential cut-off, which reflect pore-scale velocity variability and intra-pore solute mixing. Similarly, dispersion evolves from molecular diffusion at early times to asymptotic hydrodynamics dispersion via an intermediate superdiffusive regime. The theory captures the full evolution form anomalous to normal transport behavior at different Péclet numbers as well as the Péclet-dependence of asymptotic dispersion. It sheds light on hydrodynamic dispersion behaviors as a consequence of the interaction between pore-scale mixing and Eulerian flow variability. </p>

Simulation of stress-strain state for ropes of closed construction during tension and torsion

2021 ◽  
pp. 2-9
Author(s):  
V. F. Danenko ◽  
◽  
L. M. Volgograd State Technical University
Keyword(s):  
Finite Element ◽  
Cross Sections ◽  
Outer Layer ◽  
Strain State ◽  
Structural Integrity ◽  
Safety Margin ◽  
Stress Strain ◽  
Stress Strain State ◽  
Axial Forces ◽  
Element Simulation

A computer finite-element simulation of the stress-strain state of elements of a closed rope under conditions of joint tension and torsion has been carried out. The redistribution of axial forces and torques in the cross sections of layers during rotation of the rope under the influence of external torque was determined, which leads to a decrease in the safety margin of the rope, a violation of the compatibility of axial and radial movements in the layers and the structural integrity of the rope in the form of wire breakage of the outer layer.

scholarly journals Mixing characterization in different helically coiled configurations by laser-induced fluorescence

2020 ◽  
Vol 61 (9) ◽  
Author(s):  
P. Kováts ◽  
C. Velten ◽  
M. Mansour ◽  
D. Thévenin ◽  
K. Zähringer
Keyword(s):  
Cross Sections ◽  
Quantitative Measure ◽  
Laser Induced Fluorescence ◽  
Helical Coil ◽  
Mixing Coefficient ◽  
Dean Vortices ◽  
Flow Mixing ◽  
Mixing Coefficients ◽  
Mass Fractions ◽  
Miscible Liquids

AbstractFlow Mixing of two miscible liquids has been characterized experimentally in three different helically coiled reactor configurations of two different lengths in the laminar flow regime at Re = 50…1000. A straight helical coil, a coiled flow inverter, and a new coiled flow reverser have been built, each in a 3-turn and a 6-turn configuration. Laser-induced fluorescence of resorufin has been used to visualize and quantify mixing in cross-sections throughout the reactors. A mixing coefficient is derived from the fluorescence images to allow for a quantitative measure and comparison of the six configurations. It becomes obvious from these experimental results, that an early flow redirection in the helical configuration is beneficial to mixing. The 3-turn reactors achieve nearly the same mixing coefficients as the 6-turn reactors with the double length. This can be explained by the stabilizing effect of the Dean vortices in the helix, which develop during the first two turns. After that, the liquid is trapped inside the vortices and further mixing is inhibited. Accordingly, the coiled flow inverter and coiled flow reverser configurations lead to much higher mixing coefficients than the straight helical coil. The results of these measurements are now used for validation of numerical simulations, which reproduce the geometrical and flow conditions of the experiments. Some exemplary results of these calculations are also shown in this article. Graphic abstract Mass fractions of tracer fluid at Re = 500 in the six examined helix configurations.

scholarly journals Hydrodynamic dispersion characteristics of lateral inflow into a river tested by a laboratory model

2009 ◽  
Vol 13 (2) ◽  
pp. 217-228 ◽  
Author(s):  
P. Y. Chou ◽  
G. Wyseure
Keyword(s):  
Pore Water ◽  
Transport Model ◽  
Column Experiment ◽  
Breakthrough Curves ◽  
Water Velocity ◽  
Laboratory Model ◽  
Hydrodynamic Dispersion ◽  
Transport Parameter ◽  
Transport Parameters ◽  
Pore Water Velocity

Abstract. Groundwater and river-water have a different composition and interact in and below the riverbed. The riverbed-aquifer flux interactions have received growing interest because of their role in the exchange and transformation of nutrients and pollutants between rivers and the aquifer. In this research our main purpose is to identify the physical processes and characteristics needed for a numerical transport model, which includes the unsaturated recharge zone, the aquifer and the riverbed. In order to investigate such lateral groundwater inflow process, a laboratory J-shaped column experiment was designed. This study determined the transport parameters of the J-shaped column by fitting an analytical solution of the convective-dispersion equation for every flux on individual segments to the observed breakthrough curves of the resident concentration, and by inverse modelling for every flux simultaneously over the entire flow domain. The obtained transport-parameter relation was tested by numerical simulation using HYDRUS 2-D/3-D. Four steady-state flux conditions (i.e. 0.5 cm hr−1, 1 cm hr−1, 1.5 cm hr−1 and 2 cm hr−1) were applied, transport parameters including pore water velocity and dispersivity were determined for both unsaturated and saturated sections along the column. Results showed that under saturated conditions the dispersivity was fairly constant and independent of the flux. In contrast, dispersivity under unsaturated conditions was flux dependent and increased at lower flux. For our porous medium the dispersion coefficient related best to the quotient of the pore water velocity divided by the water content. A simulation model of riverbed-aquifer flux interaction should take this into account.

Probabilistic Analysis of Shear Resistance due to Concrete Tension

2015 ◽  
Vol 797 ◽  
pp. 35-44 ◽  
Author(s):  
Roman Jaskulski ◽  
Piotr Wiliński
Keyword(s):  
Monte Carlo ◽  
Cross Sections ◽  
Safety Margin ◽  
Shear Resistance ◽  
Distribution Functions ◽  
European Standard ◽  
Reliability Level ◽  
Average Shear ◽  
Basic Parameters ◽  
Tension Strength

The aim of the work was to assess the safety margin of reinforced rectangular concrete cross-sections subjected to shear. In the performed analyses models of shear resistance based on concrete tension strength was taken into account. Assessment was performed with use of Monte Carlo method. Utilized models of shear resistance were taken from formerly used Polish standards: PN-84/B-03264, PN-B-03264:2002 and the European standard EN-1992-1-1:2004. From the same standard necessary assumptions related with the models were taken. The safety margin and influence of the differences in assumptions on the obtained results were analyzed. The selected models was also evaluated in terms of their “sensitivity” to changes of basic parameters of distribution functions of selected random variables. Results showed that average shear resistance differs about 3 times depending of assumed model of the shear resistance and the reliability level, measured with the partial reliability exponent ΔR, differs 4-7 times.

Limitations in the use of electrical conductivity to monitor the behaviour of soil solution

Soil Research ◽  
2006 ◽  
Vol 44 (7) ◽  
pp. 695 ◽  
Author(s):  
D. A. Rose ◽  
F. Abbas ◽  
M. A. Adey
Keyword(s):  
Electrical Conductivity ◽  
Solution Concentration ◽  
Solute Concentration ◽  
Breakthrough Curves ◽  
Time Domain Reflectometry ◽  
Solid Particles ◽  
Bulk Solution ◽  
Hydrodynamic Dispersion ◽  
Wide Range ◽  
The Individual

Solutions of KBr and K2SO4 of various concentrations were separately displaced by deionised water through 2 contrasting saturated materials, inert solid particles (glass ballotini), and a reactive but non-swelling aggregated clay mineral (sepiolite) over a wide range of flow rates. The concentration of the individual ions in the effluent was analysed (Br– and K+ with ion-specific electrodes, SO42+ by ion chromatography) and that of bulk solution was measured by electrical conductivity (EC). For each displacement, the individual breakthrough curves (BTCs) for the anion, the cation, and the bulk solution were optimised by CXTFIT 2.0. In ballotini, the BTCs of the anion, cation, and solution were always congruent, the retardation factors did not differ significantly from unity, and the coefficients of hydrodynamic dispersion were identical. For sepiolite, the ions were separated; the bulk solution eluted faster than the cation, slower than the anions. Retardation factors were always less than unity for the anions, greater than unity for the cation, and close to but less than unity for the bulk solution, and became more extreme as the concentration of solute decreased. Dispersion coefficients were, however, unaffected by type of solute, concentration range, or particular ion/EC. The separation of ions means that the composition as well as the concentration of a solution changes continuously during flow through a reactive soil. Estimates of solution concentration from measurements of EC may thus fail to characterise adequately the movement of the individual components of the solution in such materials. This has implications for the interpretation of any leachate monitoring in reactive soils by methods based on the measurement of EC, such as time-domain reflectometry.

Effect of Whipping on Fatigue and Extreme Loading of a 13000TEU Container Vessel in Bow Quartering Seas Based on Model Tests

2011 ◽  
Author(s):  
Gaute Storhaug ◽  
Quentin Derbanne ◽  
Byung-Ki Choi ◽  
Torgeir Moan ◽  
Ole Andreas Hermundstad
Keyword(s):  
Cross Sections ◽  
Wave Energy ◽  
Safety Margin ◽  
Fatigue Loading ◽  
Operational Experience ◽  
Sea State ◽  
Hull Girder ◽  
Numerical Tools ◽  
Vertical Vibrations ◽  
Large Container

Many large and ultra large container vessels have entered operation lately and more vessels will enter operation in the coming years. The operational experience is limited and one of the concerns is the additional effect of hull girder vibrations especially from whipping (bow impacts), but also from springing (resonance). Whipping contributes both to increased fatigue and extreme loading, while springing does mainly contribute to increased fatigue loading. MAIB recommended the industry to join forces to investigate the effect of whipping after MSC Napoli, a Post-Panamax container vessel, broke in two in January 2007. This has been followed up by a JIP initiated in 2008 with the following participants: HHI, DNV, BV, CeSOS and Marintek. In 2009 a new design 13000TEU vessel was tested in head seas and reported in [1]. The current paper deals with fatigue and extreme loading of the same vessel, but from realistic quartering sea conditions tested in 2010. Different headings and the effect of wave energy spreading have been investigated and compared to results from head seas. Further, the effect of the vibrations have been investigated on torsion and horizontal bending, as the model is also allowed to vibrate with realistic frequencies in other modes in addition to vertical bending. The findings suggest that changing the course is not effective to reduce the fatigue loading of critical fatigue sensitive details amidships. The effect of wave energy spreading did also not reduce the fatigue loading significantly. For the highest observed vertical bending moments in each sea state and for the three cross sections the wave energy spreading in average reduced the maxima, but for the highest sea state the effect of wave spreading did not consistently give reduced maxima. This is an important aspect when considering the available safety margin that may be reduced by whipping. The whipping gave also a considerable contribution to horizontal bending and torsion. This suggests that validation of numerical tools is urgent with respect to off head sea conditions and that these tools must incorporate the real structural behavior to confirm the importance of the response from torsional and horizontal as well as for vertical vibrations.

Transport of arsenic in some affected soils of Indian subtropics

Soil Research ◽  
2014 ◽  
Vol 52 (8) ◽  
pp. 822 ◽  
Author(s):  
Indranil Das ◽  
Koushik Ghosh ◽  
D. K. Das ◽  
S. K. Sanyal
Keyword(s):  
Relative Concentration ◽  
Clay Content ◽  
Breakthrough Curves ◽  
Hydrodynamic Dispersion ◽  
Aluminium Content ◽  
Vertical Column ◽  
Retention Capacity ◽  
Column Study ◽  
Solute Permeability ◽  
Frictional Coefficients

An experiment on transport of aqueous arsenic (As) from both affected and unaffected soils of West Bengal, India, was conducted with the help of double-chambered columns in the laboratory. In the vertical column study, the sigmoid shape of breakthrough curves (BTCs) suggests hydrodynamic dispersion, whereas the inflexion of BTCs at a much lesser relative concentration indicates retention of As in the affected soils. In the horizontal column study, the affected soils showed lower mechanical filtration capacity and solute permeability and higher reflection coefficient, indicating greater As retention in these soils. The frictional coefficients for soil-water solute derived from the horizontal flow also indicate As retention by the affected soils. The As retention capacity of these soils was attributed to the greater clay content, illitic minerals, organic matter, specific surface area, and amorphous iron and aluminium content.

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