Vertical Flow Component Research Articles

Vertical groundwater flow in Permo-Triassic sediments underlying two cities in the Trent River Basin (UK)

The vertical component of groundwater flow that is responsible for advective penetration of contaminants in sandstone aquifers is poorly understood. This lack of knowledge is of particular concern in urban areas where abstraction disrupts natural groundwater flow regimes and there exists an increased density of contaminant sources. Vertical hydraulic gradients that control vertical groundwater flow were investigated using bundled multilevel piezometers and a double-packer assembly in dedicated boreholes constructed to depths of between 50 and 92 m below ground level in Permo-Triassic sediments underlying two cities within the Trent River Basin of central England (Birmingham, Nottingham). The hydrostratigraphy of the Permo-Triassic sediments, indicated by geophysical logging and hydraulic (packer) testing, demonstrates considerable control over observed vertical hydraulic gradients and, hence, vertical groundwater flow. The direction and magnitude of vertical hydraulic gradients recorded in multilevel piezometers and packers are broadly complementary and range, within error, from +0.1 to −0.7. Groundwater is generally found to flow vertically toward transmissive zones within the hydrostratigraphical profile though urban abstraction from the Sherwood Sandstone aquifer also influences observed vertical hydraulic gradients. Bulk, downward Darcy velocities at two locations affected by abstraction are estimated to be in the order of several metres per year. Consistency in the distribution of hydraulic head with depth in Permo-Triassic sediments is observed over a one-year period and adds support the deduction of hydrostratigraphic control over vertical groundwater flow.

Forced stratified turbulence: successive transitions with Reynolds number.

Numerical simulations are made for forced turbulence at a sequence of increasing values of Reynolds number Re keeping fixed a strongly stable, volume-mean density stratification. At smaller values of Re, the turbulent velocity is mainly horizontal, and the momentum balance is approximately cyclostrophic and hydrostatic. This is a regime dominated by so-called pancake vortices, with only a weak excitation of internal gravity waves and large values of the local Richardson number Ri everywhere. At higher values of Re there are successive transitions to (a) overturning motions with local reversals in the density stratification and small or negative values of Ri; (b) growth of a horizontally uniform vertical shear flow component; and (c) growth of a large-scale vertical flow component. Throughout these transitions, pancake vortices continue to dominate the large-scale part of the turbulence, and the gravity wave component remains weak except at small scales.

Three-dimensional surface velocities of Storstrømmen glacier, Greenland, derived from radar interferometry and ice-sounding radar measurements

AbstractNon-steady-state vertical velocities of up to 5 m a−1exceed the vertical surface-parallel flow (SPF) components over much of the ablation area of Storstrømmen, a large outlet glacier from the East Greenland ice sheet. Neglecting a contribution to the vertical velocity of this magnitude results in substantial errors (up to 20%) also on the south–north component of horizontal velocities derived by satellite synthetic aperture radar interferometry (InSAR) measurements. In many glacier environments, the steady-state vertical velocity component required to balance the annual ablation rate is 5–10 m a−1or more. This indicates that the SPF assumption may be problematic also for glaciers in steady state. Here we derive the three-dimensional surface velocity distribution of Storstrømmen by using the principle of mass conservation (MC) to combine InSAR measurements from ascending and descending satellite tracks with airborne ice-sounding radar measurement of ice thickness. The results are compared to InSAR velocities previously derived by using the SPF assumption, and to velocities obtained by in situ global positioning system (GPS) measurements. The velocities derived by using the MC principle are in better agreement with the GPS velocities than the previously calculated velocities derived with the SPF assumption.

A Dupuit formulation for flow in layered, anisotropic aquifers

A new theory is presented for groundwater flow in layered, anisotropic aquifers; flow must remain semi-confined. Two main approximations are made: (1) the aquifer consists of a number of horizontal, homogeneous layers, each with its own anisotropic transmissivity, and (2) the resistance to flow in the vertical direction is neglected. Analytic solutions are derived for the head and horizontal flow in each layer by use of a comprehensive transmissivity tensor. The vertical component of flow at the layer interfaces is computed analytically by vertical integration of the horizontal divergence. The theory is applied to both uniform flow and flow to a well; solutions may be superimposed. Flow in layered, anisotropic aquifers is three-dimensional when the anisotropy between layers differs. In the context of contaminant transport, the resulting three-dimensional flow field can be of great importance. Three-dimensional flow lines become especially complicated near pumping wells. In a two-layer aquifer, the flow lines to a well may be grouped into four bundles of spiraling flow lines, referred to as groundwater whirls. These whirls are bounded by two vertical planes that intersect at the well; horizontal flow along these planes is radial. For a well in a uniform flow field, the complications of the three-dimensional flow field are illustrated by the difficulties that are encountered in delineating the capture zone of the well.

Box simulations of rotating magnetoconvection

This paper reports 3D numerical simulations of compressible, thermal convection in a small rectilinear domain placed tangentially on a rotating sphere at latitude . The spatiotemporal evolution of convection is studied in an initially non-homogeneous toroidal magnetic field located at the interface of a 2-layer unstable/stable polytropic stratification. The effects from a variation of the rotation rate and magnetic field strength are explored. In weak field convection the solutions bear close resemblance to the field-free situation with the magnetic field treated as a passive ingredient. In this case a significant amount of magnetic energy is transported downwards into the stable layer by penetrative motions where the field is concentrated in small-scale tube-like features. In the case of a dominating magnetic field, the overall structure of convection changes dramatically towards a two-dimensional, more laminar flow with convective motions occurring in columnar cells aligned with the mean magnetic field. The latter quickly becomes flat in the convection zone due to magnetic buoyancy effects. Magnetic quenching of the flow heavily influences the mixing properties of convection, thereby, reducing the fluxes of kinetic energy and enthalpy and suppressing the downward transport of magnetic energy. Adding rotation in strong field convection generates streaming motions parallel to the mean field. These motions contain a large fraction of the total kinetic energy. The horizontally-averaged (mean) flows, on the other hand, are less energetic. In the presence of strong rotation the horizontal mean flows are triggered by inertial oscillations. Averaging the mean flows over time gives an estimate for steady flows persistent in a convection zone. Whereas the vertical flow component obtained in this way shows a systematic dependence on the rotation rate and field strength, the flows in the meridional and zonal directions depend in a more complex manner on these parameters. This includes reversals in their orientation when going from moderate to strong rotation and when increasing the magnetic field strength.

An overview of water logging and salinity in southwestern Australia as related to the ‘Ucarro’ experimental catchment

Water logging and salinity are major forms of land degradation in southwestern Australia and are predicted to become even more extensive. There are basic requirements for the development of salinisation and water logging within the specific geology and geomorphology of the region. The nature, extent and consequences of water logging and secondary salinity in the agricultural areas of southern Australia is presented in overview with a particular emphasis on the type of landscape represented by the ‘Ucarro’ experimental site, near Katanning in southwestern Australia. Three types of water logging are identified. These are associated with perched aquifers in texture-contrast (duplex) soils, inundation of terraces and valleys, and saturation in surface soil due to the hydraulic pressure being above ground level in aquifers at the base of the regolith of highly weathered granites and gneisses or within channels in broad valley sediments. A dominance of the vertical component of flow in perched aquifers is identified which contributes significantly to recharge of deep aquifers and subsequent land salinisation. Water logging has reduced the potential yield by 30–80% for many crops and pastures in the >400 mm rainfall zone. Increasing land salinisation has been accompanied by increasing trends in salinity of water resources. There is an interaction between water logging and salinity where groundwater discharge occurs at the soil-surface. Water logging may be the more serious inhibitor for plant growth than salt even at low salt levels. The interaction of water and salt is synergetic for plants. Remotely-sensed techniques using surrogates such as vegetation type and condition have been developed to provide broad spatial assessments of saline and water-logged areas since 1987. In 1990, the shires to the east and west of ‘Ucarro’ had 9.1 and 2.4% of agricultural land salt-affected, respectively. In both shires, a 0.7% increase in salt-affected land has occurred in the last 8 years.

Model-Predicted Groundwater Circulation Well Performance

Groundwater circulation well (GCW) techniques are an innovative remedial technology that may effectively remediate contaminated ground water in areas unfavorable to more traditional technologies. Traditional pump-and-treat systems may be problematic where concentrated hot spots of contamination are present, aquifer drawdown due to remedial activities is unacceptable, surface discharge of treated groundwater is unwanted, or property acquisition is challenging. The vertical component of groundwater flow induced by GCW systems presents a new challenge to practitioners evaluating their potential performance. Modifications were made to two familiar pump-and-treat analysis tools—capture zone type curves and MODFLOW numerical groundwater flow modeling—to predict site specific effectiveness of GCW technologies. These techniques were used to predict the GCW treatment area dimensions, which included the capture zone, recharge zone, and circulation cell diameter. Additionally, GCW design parameters including GCW spacing, screen length, screen placement, and circulation flow rate were determined. The state of the practice is to use these predictive tools to design an instrumentation scheme that can effectively evaluate the performance of GCW systems during full-scale pilot testing.

Using precision temperature logs to estimate horizontal and vertical groundwater flow components

A new method of estimating the horizontal and vertical specific discharge components of groundwater flow from precision subsurface temperature measurements is presented. Plotting the vertical temperature gradient as a function of both Z and T and then fitting a plane to the data can provide coefficients from which the vertical and horizontal groundwater specific discharge components may be estimated. Alternatively, by considering the vertical component of groundwater to be zero, it is shown that quadric or cubic fits to temperature data provide coefficients from which horizontal groundwater flow may be estimated. These expressions along with expressions previously derived to estimate only vertical, only horizontal, or both vertical and horizontal flow components are fitted to observational data from four sites and five flow zones. It is learned for these examples (using an available fitting program) that although many of the expressions fit the observational data very well statistically, those expressions which incorporate both the vertical and horizontal flow components of specific discharge must generally be constrained so that resulting parameters will provide flow estimates consistent in direction and heat transfer with available piezometer data and/or the fundamental curvature of the temperature log. Expressions incorporating only νX or only νZ can sometimes yield estimates quite different from the estimates obtained from the expressions incorporating both νX and νZ. It is concluded that an estimate of the horizontal and vertical flow components requires both consideration of the flow calculations along with available piezometric data and the fundamental curvature of the temperature log.

FRACTURE FORMATION AND FLUID FLOW IN THE PALM VALLEY GAS FIELD, CENTRAL AUSTRALIA

Palaeo-fluid flow in the fracture network in the Palm Valley gas field (Amadeus Basin, central Australia) was investigated using fluid inclusion, isotopic and petrographic methods. The Ordovician Pacoota and Stairway Sandstone reservoir rocks have exceedingly low matrix porosity and permeability and economic gas flow rates, therefore, depend on the fracture network.Pre-fracture cementation of the matrix involved precipitation of pyrite, haematite, chlorite, illite and quartz. However, matrix cementation, as well as the fracture mineralisation, is now dominated by barite, ankerite and quartz. This indicates that subsequent to being fractured, connectivity between matrix porosity and fractures allowed invasion of the host sandstones by mineralising fluids from the fracture network. Fluid inclusion palaeo-temperature analyses indicate temperatures of 90–115°C prevailed at the time of formation of these minerals which was contemporaneous with maximum burial estimated to have occurred during the Alice Springs orogeny at ~340–240 Ma.Aqueous fluids in the sandstones were derived from three sources. Connate waters comprise one source and were parental to pre-fracture diagenetic minerals. The reservoir was accessed by two other fluids via the fracture network. Basinal brines comprise one source, whilst low salinity waters of surface meteoric origin comprise the other. One component of the basinal brine had had prior contact with Precambrian Bitter Springs Formation evaporites whilst another had been in contact with rocks characterised by high barium contents and radiogenic strontium isotope ratios. The total vertical component of fluid flow appears to have been ~7–8 km.Hydrocarbon migration was in part synchronous with fracture development and was accompanied by migration of basinal brines. Liquid hydrocarbons and wet gas migrated during cementation of the fractures. Temperatures continued to rise and dry gas was generated which displaced the wet gas now only observed in fluid inclusions in the mineral cements.

Investigation of large amplitude stratified waves in a CANDU-type 37 rod nuclear fuel channel by a real-time neutron radiography technique

A real-time neutron radiography (RTNR) system is used to determine two-phase flow parameters for a horizontal co-current two-phase flow channel with a cylindrical 37 rod bundle. Image processing techniques are applied to visualize the two-phase flow, and to determine flow regime, cross-sectional averaged void fraction, time averaged void fraction, and void distribution. The experimentally determined flow regime map disagrees with existing flow regime models developed for the cylindrical rod bundles. A new flow regime is observed and designated large amplitude stratified wavy (LASW) flow. The results show that the LASW flow regime may be due to a combination of undeveloped flow phenomena, boundary conditions, and circumferential cross flow occuring in the bundle. The rods in the bundle may act as a dampener to the vertical flow component and hinders the development of the wave into plug or slug flow by changing the momentum of the fluid in the circumferential direction. The effect of gas and liquid superficial velocities and axis position on the void fraction is observed. The existence of a cylindrical bundle in a circular flow channel is found to affect the flow regime, void fraction, void migration, and void fraction fluctuation and these effects are discussed in detail.

Ice-sheet radar layering and the development of preferred crystal orientation fabrics between Lake Vostok and Ridge B, central East Antarctica

Airborne radar data at 60 MHz are analysed to examine the flow of ice between the Ridge B ice divide and the Vostok Station subglacial lake in central East Antarctica. Interferometric SAR ice surface velocities show how three radar transects are aligned along the general direction of ice flow. Internal layering within the ice sheet is used to determine changes in the vertical component of ice flow along the transects. These data indicate ice sheet flow is related strongly to subglacial topography. In one transect, ice flows in a conventional base-parallel manner down a relatively uniform subglacial slope in the direction of ice flow. In the other two transects, internal layers show the flow of ice over a large subglacial hill upstream of Lake Vostok. Across the stoss face of this subglacial hill, analysis of the radar reflections from internal layers show that layers of ice with a preferred crystal orientation are likely to develop. This process results in layers of ice with a preferred crystal fabric across Lake Vostok at ice depths greater than ∼2.8 km. Evidence to support our analysis comes from the Vostok ice core where layers of ice with noticeable crystal alignment are abundant at ice depths greater than 2.7 km.

Wettability Effects on Liquid Flow Characteristics in a Bubbling Wall Jet along a Vertical Flat Plate.

A bubbling wall jet was generated along a vertical flat plate with different wettability by using a single-hole nozzle. Water flow characteristics in the jet were measured with a laser Doppler velocimeter. Effects of the wettability of the plate emerged on the water flow characteristics primarily in the momentum region near the nozzle tip where the inertia force of injected gas governed the flow field. In the buoyancy region located above the momentum region, the horizontal distributions of the vertical mean velocity and the root-mean-square value of the vertical turbulence component of water flow were hardly dependent on the wettability of the plate and followed their respective similar distributions.

Transient well flow in layered aquifer systems: the uniform well-face drawdown solution

Previously a hybrid analytical–numerical solution for the general problem of computing transient well flow in vertically heterogeneous aquifers was proposed by the author. The radial component of flow was treated analytically, while the finite-difference technique was used for the vertical flow component only. In the present work the hybrid solution has been modified by replacing the previously assumed uniform well-face gradient (UWG) boundary condition in such a way that the drawdown remains uniform along the well screen. The resulting uniform well-face drawdown (UWD) solution also includes the effects of a finite diameter well, wellbore storage and a thin skin, while partial penetration and vertical heterogeneity are accommodated by the one-dimensional discretization. Solutions are proposed for well flow caused by constant, variable and slug discharges. The model was verified by comparing wellbore drawdowns and well-face flux distributions with published numerical solutions. Differences between UWG and UWD well flow will occur in all situations with vertical flow components near the well, which is demonstrated by considering: (1) partially penetrating wells in confined aquifers, (2) fully penetrating wells in unconfined aquifers with delayed response and (3) layered aquifers and leaky multiaquifer systems. The presented solution can be a powerful tool for solving many well-hydraulic problems, including well tests, flowmeter tests, slug tests and pumping tests. A computer program for the analysis of pumping tests, based on the hybrid analytical–numerical technique and UWG or UWD conditions, is available from the author.

Transient well flow in vertically heterogeneous aquifers

A solution for the general problem of computing well flow in vertically heterogeneous aquifers is found by an integration of both analytical and numerical techniques. The radial component of flow is treated analytically; the drawdown is a continuous function of the distance to the well. The finite-difference technique is used for the vertical flow component only. The aquifer is discretized in the vertical dimension and the heterogeneous aquifer is considered to be a layered (stratified) formation with a finite number of homogeneous sublayers, where each sublayer may have different properties. The transient part of the differential equation is solved with Stehfest's algorithm, a numerical inversion technique of the Laplace transform. The well is of constant discharge and penetrates one or more of the sublayers. The effect of wellbore storage on early drawdown data is taken into account. In this way drawdowns are found for a finite number of sublayers as a continuous function of radial distance to the well and of time since the pumping started. The model is verified by comparing results with published analytical and numerical solutions for well flow in homogeneous and heterogeneous, confined and unconfined aquifers. Instantaneous and delayed drainage of water from above the water table are considered, combined with the effects of partially penetrating and finite-diameter wells. The model is applied to demonstrate that the transient effects of wellbore storage in unconfined aquifers are less pronounced than previous numerical experiments suggest. Other applications of the presented solution technique are given for partially penetrating wells in heterogeneous formations, including a demonstration of the effect of decreasing specific storage values with depth in an otherwise homogeneous aquifer. The presented solution can be a powerful tool for the analysis of drawdown from pumping tests, because hydraulic properties of layered heterogeneous aquifer systems with partially penetrating wells may be estimated without the need to construct transient numerical models. A computer program based on the hybrid analytical-numerical technique is available from the author.

Wettability Effects on Bubble Characteristics in a Bubbling Wall Jet along a Vertical Flat Plate.

A bubbling wall jet was generated along a vertical flat plate with different wettability by using a single-hole nozzle. Water flow characteristics in the jet were measured with a laser Doppler velocimeter. Effects of the wettability of the plate emerged on the water flow characteristics primarily in the momentum region near the nozzle tip where the inertia force of injected gas governed the flow field. In the buoyancy region located above the momentum region, the horizontal distributions of the vertical mean velocity and the root-mean-square value of the vertical turbulence component of water flow were hardly dependent on the wettability of the plate and followed their respective similar distributions.

Spatial instability of planar channel flow with fluid injection through porous walls

The present paper deals with the stability properties of a planar channel flow driven by air injection through porous walls. Experimental investigations have been carried out in the so-called VECLA facility and a theoretical linear stability analysis has been performed. The nonparallel effects are studied by using three different stability approaches. They appear to be very significant for this particular flow. This study provides indeed an interesting example of an instability mechanism strongly related to the vertical component (usually negligible) of the mean flow. The obtained results finally agree very well with the measurements with respect to the amplified frequency range and to the streamwise amplification of the instability waves.

A numerical model of ground deformation induced by single well pumping

Abstract In this paper, a numerical model is proposed to study ground deformation caused by lowering of the water table from a single pumping well. The model uses the finite element method to study the problem. In the model, the Dupuit assumption is not used due to errors that might be introduced by ignoring the seepage face and vertical flow component. Instead, a two-step iteration procedure is used to determine the actual flow paths. Field testing is performed to verify the numerical calculations. Ground deformations were measured under different pumping rates. The field measurements of the ground deformation matched well with the calculated values.

Subglacial groundwater flow during the last glaciation in northwestern Germany

Reconstruction of groundwater flow in overpressured soft sediments overridden by the last (Weichselian) ice sheet in northwestern Germany about 18,000 ka B.P, based on numerical modelling, reveals a complete reorganisation of groundwater dynamics as compared to the present system. Groundwater flow, controlled by potentiometric surface high up in the ice sheet and by a steep hydraulic gradient at the glacier periphery, was here up to 30 times faster than at present and a vertical flow component penetrated the entire thickness of Quaternary sediments reaching some 200 m in places.

Importance of the vertical component of groundwater flow: a hydrogeochemical approach in the valley of San Luis Potosi, Mexico

Fractured volcanics exert a control on groundwater flow in the San Luis Potosi (SLP) valley. The chemical composition and temperature of water pumped from boreholes partially penetrating the fractured volcanics indicate that the produced water originates from an upward vertical flow. Most of the thermal groundwater has been detected in areas related to regional faults and lineaments. Intensive and uncontrolled pumping from the upper 1 4 of the aquifer (total depth > 1500 m) causes the rise of water from a deep regional flow system that mixes with the shallower waters. The deep waters contain high fluoride concentrations that contaminate the mixture and cause substantial health related effects. The recharge controls on the regional flow system require further research; however, hydrogeochemical evidence supports the view that the origin of this recharge is limited to the western bounding Sierra Madre Occidental. Higher levels of dissolved Na +, Li +, F − (and SO 4 −2) derived from Tertiary volcanics have been introduced into the exploited region; the concentrations indicate lengthy and deep circulation flow. Li + concentration was used as an indicator of groundwater residence time, and therefore of the length of the groundwater flow path. Hydrogeochemical interpretation indicates the presence of three flow systems: a shallow local one controlled by a clay layer that subcrops most of the valley floor, an intermediate system in which water infiltrates just beyond the boundary of the clay layer, and a deep regional system which originates outside the surface catchment. The local and intermediate systems circulate through materials with comparatively low hydraulic conductivity. Low Cl − concentrations suggest rapid flow in the regional system. Concentrations of Li + and F − can be used to calculate percentages of waters in mixtures of regional and intermediate flows. Concentrations of Na +, Ca 2+ and SO 4 −2 appear to be controlled by water-rock reactions. Uncontrolled pumping increases will tend to enhance fluoride concentration and its undesirable effects. Lack of management of aquifers in basins similar to the SLP valley can result in groundwater contamination, not only from surface anthropogenic sources, but also from natural water-rock interactions.

Variations in Capture‐Zone Geometry of a Partially Penetrating Pumping Well in an Unconfined Aquifer

AbstractDesign of effective and efficient pump‐and‐treat systems requires capture zones of recovery wells to closely circumscribe the contaminant plume. Overestimation of capture zones incurs the undesired expense of treating clean water. Underestimation of capture zones enables contaminants to escape downgradient. Recovery wells in unconfined aquifers commonly penetrate only part of the aquifer either because of its large saturated thickness or the shallow vertical extent of contamination. The capture‐zone geometry of a partially penetrating pumping well can differ greatly from that of a fully penetrating one because of vertical flow components near the well. The differences in geometry are far greater if the medium is anisotropic (Kh≠ Kv).To estimate the capture‐zone geometry of a partially penetrating pumping well, a steady‐state, finite‐difference model was constructed to simulate flow to a well in a regional flow system. The model was used to simulate differences in the velocity field created by changes in (1) the depth of well penetration, (2) the magnitude of the regional hydraulic gradient, and (3) the degree of anisotropy. Following each simulation particle tracking was performed to determine the maximum width, depth, and distance to the stagnation point of the capture zone. Graphs were developed between capture‐zone width, relative capture‐zone depth, distance to the stagnation point, versus the ratio of Q/q (pumping rate/specific discharge). The graphs enable estimates to be made of these geometric parameters for a variety of pumping rates, regional hydraulic gradients, hydraulic conductivities, anisotropy ratios, and degrees of partial penetration. The results show that for isotropic conditions, particularly for small ratios of Q/q and wells that penetrate less than 40 percent of the aquifer, the shape of a capture zone can deviate significantly from that of a fully penetrating well. For anisotropic conditions, these differences are more pronounced and apply to a wider range of Q/q ratios and well penetration depths.In sequences of sediment, anisotropy is produced by textural, architectural, and stratigraphic elements that occur at different scales. Capture zones should be estimated using Kh:Kv ratios determined from pumping tests. This assures that the measured degree of anisotropy is commensurate with the scale of elements encountered by the stress created by a pumping well. Tabulated Kh:Kv ratios from analysis of pumping tests in unconfined aquifers suggest there are few isotropic sand and gravel aquifers. Recognition of this characteristic and consideration of the effects of partial penetration and regional hydraulic gradient on the geometry of capture zones may lead to the design of more efficient and effective pump‐and‐treat systems.