Analysis of depth-dependent pressure head of slug tests in highly permeable aquifers

A curve-matching method is developed for the analysis of depth-dependent pressure head responding to a slug test in a highly permeable aquifer. The depth dependency is due to the fact that the pressure transducer is placed at depth relatively far from the initial water level. The Springer and Gelhar solution and a depth correction relation are used to generate theoretical curves of pressure head vs. time. A trial-and-error procedure is established to find the theoretical curve best fitting the field data by adjusting the two unknown parameters, the horizontal hydraulic conductivity, and the effective length of the water column. Analytic relations for some oscillation characteristics of the converted pressure head are derived. A field example indicates that the theoretical relations and the curve-matching method developed herein are suitable to deal with the oscillatory head data dependent on depth of measurement. Nevertheless, it is recognized that placing the pressure transducer close to the initial water level and using a small initial water displacement can effectively avoid complicating the data analysis, such that previous, simpler data analysis methods can be used.     

An analytical method of analysing the oscillatory pressure head measured at any depth in a well casing

When a slug test is conducted in a highly permeable aquifer, a shallow pressure transducer in the well casing produces an oscillatory pressure head that is representative of the water level fluctuation, whereas a deep pressure transducer in the well casing yields an oscillatory pressure head that is different from the water level change. Although the solutions for shallow and deep pressure head are different, it is found that the ratios of the subsequent extremity displacements are in an identical relationship (an extremity can be a maximum or a minimum in the oscillatory pressure head). Based on this relationship, an analytical data analysis method for the determination of the hydraulic conductivity is developed for both shallow and deep pressure transducer data. This analytical method is applied to the pressure head measured at different depths in the well casing of a well partially penetrating an unconfined coarse sand aquifer. Satisfactory results are obtained, validating the applicability of this analytical method for pressure transducer data at any depth in a well casing. Copyright © 2007 John Wiley & Sons, Ltd.     

An analytic data analysis method for oscillatory slug tests

An analytical data analysis method is developed for slug tests in partially penetrating wells in confined or unconfined aquifers of high hydraulic conductivity. As adapted from the van der Kamp method, the determination of the hydraulic conductivity is based on the occurrence times and the displacements of the extreme points measured from the oscillatory data and their theoretical counterparts available in the literature. This method is applied to two sets of slug test response data presented by Butler et al.: one set shows slow damping with seven discernable extremities, and the other shows rapid damping with three extreme points. The estimates of the hydraulic conductivity obtained by the analytic method are in good agreement with those determined by an available curve-matching technique.     

Effective parameters for flow in saturated heterogeneous porous media

Effective parameters for flow in saturated porous media are obtained via Taylor-Aris-Brenner moment analysis considering both periodic as well as stationary porous medium properties. It is assumed that a slug is instantaneously introduced into an unbounded, anisotropic porous medium having a compressible matrix, and that the correlation length of the local hydraulic conductivity and specific storage fluctuations is smaller than the correlation length of hydraulic head fluctuations (gradually varying flow). It is shown that the effective specific storage is equal to its volume average. The effective hydraulic conductivity is derived by a small-perturbation analysis and it is shown to consist of its volume average and of a second term which accounts for the ‘small’ local conductivity fluctuations.     

A simple correction for slug tests in small-diameter wells

A simple procedure is presented for correcting hydraulic conductivity (K) estimates obtained from slug tests performed in small-diameter installations screened in highly permeable aquifers. Previously reported discrepancies between results from slug tests in small-diameter installations and those from tests in nearby larger-diameter wells are primarily a product of frictional losses within the small-diameter pipe. These frictional losses are readily incorporated into existing models for slug tests in high-K aquifers, which then serve as the basis of a straightforward procedure for correcting previously obtained K estimates. A demonstration of the proposed procedure using data from a series of slug tests performed in a controlled field setting confirms the validity of the approach. The results of this demonstration also reveal the detailed view of spatial variations in K that can be obtained using slug tests in small-diameter installations.     

Slug Tests in Wells Screened Across the Water Table: Some Additional Considerations

The majority of slug tests done at sites of shallow groundwater contamination are performed in wells screened across the water table and are affected by mechanisms beyond those considered in the standard slug‐test models. These additional mechanisms give rise to a number of practical issues that are yet to be fully resolved; four of these are addressed here. The wells in which slug tests are performed were rarely installed for that purpose, so the well design can result in problematic (small signal to noise ratio) test data. The suitability of a particular well design should thus always be assessed prior to field testing. In slug tests of short duration, it can be difficult to identify which portion of the test represents filter‐pack drainage and which represents formation response; application of a mass balance can help confirm that test phases have been correctly identified. A key parameter required for all slug test models is the casing radius. However, in this setting, the effective casing radius (borehole radius corrected for filter‐pack porosity), not the nominal well radius, is required; this effective radius is best estimated directly from test data. Finally, although conventional slug‐test models do not consider filter‐pack drainage, these models will yield reasonable hydraulic conductivity estimates when applied to the formation‐response phase of a test from an appropriately developed well.     

Application of a nonlinear slug test model

Knowledge of the hydraulic conductivity distribution is of utmost importance in understanding the dynamics of an aquifer and in planning the consequences of any action taken upon that aquifer. Slug tests have been used extensively to measure hydraulic conductivity in the last 50 years since Hvorslev's (1951) work. A general nonlinear model based on the Navier-Stokes equation, nonlinear frictional loss, non-Darcian flow, acceleration effects, radius changes in the wellbore, and a Hvorslev model for the aquifer has been implemented in this work. The nonlinear model has three parameters: beta, which is related primarily to radius changes in the water column; A, which is related to the nonlinear head losses; and K, the hydraulic conductivity. An additional parameter has been added representing the initial velocity of the water column at slug initiation and is incorporated into an analytical solution to generate the first time step before a sequential numerical solution generates the remainder of the time solution. Corrections are made to the model output for acceleration before it is compared to the experimental data. Sensitivity analysis and least squares fitting are used to estimate the aquifer parameters and produce some diagnostic results, which indicate the accuracy of the fit. Finally, an example of field data has been presented to illustrate the application of the model to data sets that exhibit nonlinear behavior. Multiple slug tests should be taken at a given location to test for nonlinear effects and to determine repeatability.     

Analytical Interpretation of Slug Test in a Vertical Cutoff Wall

An analysis method for slug tests performed in a partially penetrating well within a vertical cutoff wall is presented. A steady‐state shape factor for evaluating hydraulic conductivity of the material within the wall was derived by applying the method of images to the previously developed analytical solution of Zlotnik et al. (2010) for an infinite aquifer. Two distinct boundary conditions were considered: constant‐head boundary for the case of direct contact between the wall and the aquifer, and no‐flux boundary representing an impermeable filter cake on the sides of the wall. The constant‐head and no‐flux boundary conditions yield significantly higher and lower shape factors, respectively, than those for the infinite aquifer. Consequently the conventional line‐fitting method for slug test analysis would yield an inaccurate estimate of the hydraulic conductivity of a vertical cutoff wall.     

Noise in pressure transducer readings produced by variations in solar radiation

Variations in solar radiation can produce noise in readings from gauge pressure transducers when the transducer cable is exposed to direct sunlight. This noise is a result of insolation-induced heating and cooling of the air column in the vent tube of the transducer cable. A controlled experiment was performed to assess the impact of variations in solar radiation on transducer readings. This experiment demonstrated that insolation-induced fluctuations in apparent pressure head can be as large as 0.03 m. The magnitude of these fluctuations is dependent on cable color, the diameter of the vent tube, and the length of the transducer cable. The most effective means of minimizing insolation-induced noise is to use integrated transducer-data logger units that fit within a well. Failure to address this source of noise can introduce considerable uncertainty into analyses of hydraulic tests when the head change is relatively small, as is often the case for tests in highly permeable aquifers or for tests using distant observation wells.     

Stochastic analysis of spatial variability in unconfined groundwater flow

In this paper, spatial variability in steady one-dimensional unconfined groundwater flow in heterogeneous formations is investigated. An approach to deriving the variance of the hydraulic head is developed using the nonlinear filter theory. The nonlinear governing equation describing the one-dimensional unconfined groundwater flow is decomposed into three linear partial differential equations using the perturbation method. The linear and quadratic frequency response functions are obtained from the first- and second-order perturbation equations using the spectral method. Furthermore, under the assumption of the exponential covariance function of log hydraulic conductivity, the analytical solutions of both the spectrum and the variance of the hydraulic head produced from the linear system are derived. The results show that the variance derived herein is less than that of Gelhar (1977). The reason is that the log transmissivity is linearized in Gelhars work. In addition, the analytical solutions of both the spectrum and the variance of the hydraulic head produced from the quadratic system are derived as well. It is found that the correlation scale and the trend in mean of log hydraulic conductivity are important to the dimensionless variance ratio.     

Green’s function of the linearized Saint-Venant equations in laminar and turbulent flows

In the present paper, an analytical expression of the Green’s function of linearized Saint-Venant equations (LSVEs) for shallow water waves is provided and applied to analyse the propagation of a perturbation superposed to a uniform flow. Independently of the kinematic character of the base flow, i.e., subcritical or supercritical uniform flow, the effects of a non-uniform vertical velocity profile and a non-constant resistance coefficient are accounted for. The use of the Darcy-Weisbach friction law allows a unified treatment of both laminar and turbulent conditions. The influence on the wave evolution of the wall roughness and the fluid viscosity are finally discussed, showing that in turbulent regime the assumption of constant friction coefficient may lead to an underestimation of both amplification and damping factors on the wave fronts, especially at low Reynolds numbers. This conclusion has to be accounted for, particularly in describing hyper-concentrated suspensions or other kinds of Newtonian mixtures, for which the high values of the kinematic viscosity may lead to relatively low Reynolds numbers.     

A Simple Pneumatic Device and Technique for Performing Rising Water Level Slug Tests

Transmissivity can be estimated by several well documented methods employing data from rising water level slug tests in wells. A very simple and relatively inexpensive system can be constructed to lower the water level in a well. Compressed air is injected through a sealed device called a well head manifold, which screws onto the casing top and contains an air pressure gauge, an air entry valve, a quick release valve and a multi-channel water level indicator or a pressure transducer. Either of the latter is lowered into the well prior to pressurization.
Compressed air is injected into the casing at a low rate through the manifold, depressing the water level a desired amount. After stabilization, the quick release valve is opened and the air pressure inside the casing is reduced to atmospheric pressure instantaneously; the water level then starts to rise. Successive elevations of the rising water level are determined with the indicator or transducer and their elapsed times from valve opening are recorded. Plots of water level recovery vs. time can then be used to estimate transmissivity by the published methods of Cooper, Bredehoeft and Papadopulos (1967), Ferris and Knowles (1954) and Hvorslev(1951).
All of the items used for construction, with the exception of the quick release valve, can be bought off the shelf. The valve can be easily constructed in a machine shop. The total cost of the device, exclusive of the transducer, should be less than $500.     

Relating millimeter-scale turbulence to meter-scale subtidal erosion and accretion across the fringe of a coastal mangrove forest

Within a wave-exposed mangrove forest, novel field observations are presented, comparing millimeter-scale turbulent water velocity fluctuations with contemporaneous subtidal bed elevation changes. High-resolution velocity and bed level measurements were collected from the unvegetated mudflat, at the mangrove forest fringe, and within the forest interior over multiple tidal cycles (flood–ebb) during a 2-week period. Measurements demonstrated that the spatial variability in vegetation density is a control on sediment transport at sub-meter scales. Scour around single and dense clusters of pneumatophores was predicted by a standard hydraulic engineering equation for wave-induced scour around regular cylinders, when the cylinder diameter in the equations was replaced with the representative diameter of the dense pneumatophore clusters. Waves were dissipated as they propagated into the forest, but dissipation at infragravity periods (> 30 s) was observed to be less than dissipation at shorter periods (< 30 s), consistent with the predictions of a simple model. Cross-wavelet analysis revealed that infragravity-frequency fluctuations in the bed level were occasionally coherent with velocity, possibly indicating scour upstream of dense pneumatophore patches when infragravity waves reinforced tidal currents. Consequently, infragravity waves were a likely driver of sediment transport within the mangrove forest. Near-bed turbulent kinetic energy, estimated from the turbulent dissipation rate, was also correlated with bed level changes. Specifically, within the mangrove forest and over the unvegetated mudflat, high-energy events were associated with erosion or near-zero bed level change, whereas low-energy events were associated with accretion. In contrast, no single relationship between bed level changes and mean current velocity was applicable across both vegetated and unvegetated regions. These observations support the theory that sediment mobilization scales with turbulent energy, rather than mean velocity, a distinction that becomes important when vegetation controls the development of turbulence.     

Analysis of slug tests in formations of high hydraulic conductivity

A new procedure is presented for the analysis of slug tests performed in partially penetrating wells in formations of high hydraulic conductivity. This approach is a simple, spreadsheet-based implementation of existing models that can be used for analysis of tests from confined or unconfined aquifers. Field examples of tests exhibiting oscillatory and nonoscillatory behavior are used to illustrate the procedure and to compare results with estimates obtained using alternative approaches. The procedure is considerably simpler than recently proposed methods for this hydrogeologic setting. Although the simplifications required by the approach can introduce error into hydraulic-conductivity estimates, this additional error becomes negligible when appropriate measures are taken in the field. These measures are summarized in a set of practical field guidelines for slug tests in highly permeable aquifers.     

Sediment transport in high‐speed flows over a fixed bed: 2. Particle impacts and abrasion prediction

Single bed load particle impacts were experimentally investigated in supercritical open channel flow over a fixed planar bed of low relative roughness height simulating high‐gradient non‐alluvial mountain streams as well as hydraulic structures. Particle impact characteristics (impact velocity, impact angle, Stokes number, restitution and dynamic friction coefficients) were determined for a wide range of hydraulic parameters and particle properties. Particle impact velocity scaled with the particle velocity, and the vertical particle impact velocity increased with excess transport stage. Particle impact and rebound angles were low and decreased with transport stage. Analysis of the particle impacts with the bed revealed almost no viscous damping effects with high normal restitution coefficients exceeding unity. The normal and resultant Stokes numbers were high and above critical thresholds for viscous damping. These results are attributed to the coherent turbulent structures near the wall region, i.e. bursting motion with ejection and sweep events responsible for turbulence generation and particle transport. The tangential restitution coefficients were slightly below unity and the dynamic friction coefficients were lower than for alluvial bed data, revealing that only a small amount of horizontal energy was transferred to the bed. The abrasion prediction model formed by Sklar and Dietrich in 2004 was revised based on the new equations on vertical impact velocity and hop length covering various bed configurations. The abrasion coefficient k_v was found to be vary around k_v ~ 10⁵ for hard materials (tensile strength f_t > 1 MPa), one order of magnitude lower than the value assumed so far for Sklar and Dietrich's model. Copyright © 2017 John Wiley & Sons, Ltd.     

Power-law velocity profile in turbulent boundary layers: An integral reynolds-number dependent solution

Geophysical flows of practical interest encompass turbulent boundary layer flows. The velocity profile in turbulent flows is generally described by a log- or a power-law applicable to certain zones of the boundary layer, or by wall-wake law for the entire zone of the boundary layer. In this study, a novel theory is proposed from which the power-law velocity profile is obtained for the turbulent boundary layer flow. The new power-law profile is based on the conservation of mass and the skin friction within the boundary layer. From the proposed theory, analytical expressions for the power-law velocity profile are presented, and their Reynolds-number dependency is highlighted. The velocity profile, skin friction coefficient and boundary layer thickness obtained from the proposed theory are validated by the reliable experimental data for zero-pressure gradient turbulent boundary layers. The expressions for Reynolds shear stress and eddy viscosity distributions across the boundary layer are also obtained and validated by the experimental data.     

Upscaling Point Velocity Measurements to Characterize a Glacial Outwash Aquifer

Small‐scale point velocity probe (PVP)‐derived velocities were compared to conventional large‐scale velocity estimates from Darcy calculations and tracer tests, and the possibility of upscaling PVP data to match the other velocity estimates was evaluated. Hydraulic conductivity was estimated from grain‐size data derived from cores, and single‐well response testing or slug tests of onsite wells. Horizontal hydraulic gradients were calculated using 3‐point estimators from all of the wells within an extensive monitoring network, as well as by representing the water table as a single best fit plane through the entire network. Velocities determined from PVP testing were generally consistent in magnitude with those from depth specific data collected from multilevel monitoring locations in the tracer test, and similar in horizontal flow direction to the average hydraulic gradient. However, scaling up velocity estimates based on PVP measurements for comparison with site‐wide Darcy‐based velocities revealed issues that challenge the use of Darcy calculations as a generally applicable standard for comparison. The Darcy calculations were shown to underestimate the groundwater velocities determined both by the PVPs and large‐scale tracer testing, in a depth‐specific sense and as a site‐wide average. Some of this discrepancy is attributable to the selective placement of the PVPs in the aquifer. Nevertheless, this result has important implications for the design of in situ treatment systems. It is concluded that Darcy estimations of velocity should be supplemented with independent assessments for these kinds of applications.     

Interaction between the Alfvén wave and turbulent sheet

The interaction between the Alfvén wave and turbulent sheet (TS) with an anomalous conductivity has been considered. High frequency turbulence causes the appearance of not only anomalous field-aligned plasma conductivity but also cross-field conductivity. Alfvén waves can be partially reflect from TS, be absorbed in this sheet, and pass through TS. When field-aligned conductivity is predominant, the relative effectiveness of these processes strongly depends on a cross-field wave scale. If TS is thin as compared to the Alfvén wavelength, the resistive Alfvén wave (λ _A ) characterized by the field-aligned resistivity and Alfvén velocity above the sheet is the characteristic parameter responsible for the wave-sheet coupling. A comparison of the loss, estimated using the analytical relationships for a thin sheet and numerically calculated based on the complete formulas for a sheet with a finite thickness, indicates that the approximation of a thin sheet results in reasonable estimates at all wave scales except very small ones. The developed model has been applied to the interpretation of the results of the works on Pi2 pulsation damping during the substorm expansion phase, which indicated that the damping decrement increases at large substorm amplitudes. The estimates indicate that this increase in damping is related to the appearance of anomalous resistivity in the case when field-aligned currents exceed the threshold values necessary for excitation of high frequency turbulence.     

Numerical Modeling of Slug Tests with MODFLOW Using Equivalent Well Blocks

Slug tests are a widely used technique to estimate aquifer hydraulic parameters and the test data are generally interpreted with analytical solutions under various assumptions. However, these solutions are not convenient when slug tests are required to be analyzed in a three‐dimensional model for complex aquifer‐aquitard systems. In this study, equivalent well blocks (EWB) are proposed in numerical modeling of slug test data with MODFLOW. Multi‐well slug tests in partially penetrating wells with skin zones can be simulated. Accuracy of the numerical method is demonstrated by benchmarking with analytical solutions. The EWB method is applied in a case study on slug tests in aquitards in the Pearl River Delta, China.