Vertical Variations In Hydraulic Conductivity Research Articles

Quantifying the hydraulic properties of fractured rock masses along a borehole using composite geological indices: A case study in the mid and upper Choshui River Basin in Central Taiwan

Comprehensive information on vertical variations in hydraulic conductivity along a borehole is indispensable for characterizing the complexity of the hydraulic properties of fractured bedrock aquifers or for use as input data for groundwater modeling. This study presents a practical method for addressing various engineering concerns (e.g., project budget, completion time, manpower, and direct measurement of hydraulic properties from rock core specimens) when obtaining detailed and continuous hydraulic conductivity data along a borehole. Based on in-situ hydrogeological data collected from 26 boreholes located in the Choshui River Basin of Central Taiwan, eight individual and six composite geological indices were investigated to determine their correlations with the hydraulic conductivity of fractured rocks through bivariate analysis. The correlation analysis results indicate that all composite geological indices have higher correlations with the hydraulic conductivity than individual indices do. Moreover, the greater the number of individual geological indices integrated into one composite index, the higher the correlation. Based on the correlation results, quantification models for predicting the hydraulic conductivity using the composite geological indices were developed using regression analysis techniques. The performances of various statistical models were evaluated and compared. The regression analysis results for all six predictive models show that a power law relationship exists between each composite geological index and the hydraulic conductivity, and that the coefficient of determination ranges from 0.77 to 0.88. Therefore, the newly developed models can serve as an alternative for obtaining vertical hydraulic conductivity data when the budget for onsite hydraulic test is limited. • Models for predicting the hydraulic conductivity in boreholes are developed. • Eight individual and six composite geological indices are used. • All composite indices have high correlations with hydraulic conductivity. • The developed models are proven to be reliable.

Evaluation of Vertical Variations in Hydraulic Conductivity in Unconsolidated Sediments

Detailed information on vertical variations in hydraulic conductivity (K) is essential to describe the dynamics of groundwater movement at contaminated sites or as input data used for modeling. K values in high vertical resolution should be determined because K tends to be more continuous in the horizontal than in the vertical direction. To determine K in shallow unconsolidated sediments and in the vertical direction, the recently developed direct-push injection logger can be used. The information obtained by this method serves as a proxy for K and has to be calibrated to obtain quantitative K values of measured vertical profiles. In this study, we performed direct-push soil sampling, sieve analyses and direct-push slug tests to obtain K values in vertical high resolution. Using the results of direct-push slug tests, quantitative K values obtained by the direct-push injection logger could be determined successfully. The results of sieve analyses provided lower accordance with the logs due to the inherent limitations of the sieving method.

A Forward Modeling Approach for Interpreting Impeller Flow Logs

A rigorous and practical approach for interpretation of impeller flow log data to determine vertical variations in hydraulic conductivity is presented and applied to two well logs from a Chalk aquifer in England. Impeller flow logging involves measuring vertical flow speed in a pumped well and using changes in flow with depth to infer the locations and magnitudes of inflows into the well. However, the measured flow logs are typically noisy, which leads to spurious hydraulic conductivity values where simplistic interpretation approaches are applied. In this study, a new method for interpretation is presented, which first defines a series of physical models for hydraulic conductivity variation with depth and then fits the models to the data, using a regression technique. Some of the models will be rejected as they are physically unrealistic. The best model is then selected from the remaining models using a maximum likelihood approach. This balances model complexity against fit, for example, using Akaike's Information Criterion.

Field comparison of the point velocity probe with other groundwater velocity measurement methods

Field testing of a new tool for measuring groundwater velocities at the centimeter scale, the point velocity probe (PVP), was undertaken at Canadian Forces Base, Borden, Ontario, Canada. The measurements were performed in a sheet pile‐bounded alleyway in which bulk flow rate and direction could be controlled. PVP velocities were compared with those estimated from bulk flow, a Geoflo® instrument, borehole dilution, colloidal borescope measurements, and a forced gradient tracer test. In addition, the velocity profiles were compared with vertical variations in hydraulic conductivity (K) measured by permeameter testing of core samples and in situ high‐resolution slug tests. There was qualitative agreement between the trends in velocity and K among all the various methods. The PVP and Geoflo® meter tests returned average velocity magnitudes of 30.2 ± 7.7 to 34.7 ± 13.1 cm/d (depending on prior knowledge of flow direction in PVP tests) and 36.5 ± 10.6, respectively, which were near the estimated bulk velocity (20 cm/d). The other direct velocity measurement techniques yielded velocity estimates 5 to 12 times the bulk velocity. Best results with the PVP instrument were obtained by jetting the instrument into place, though this method may have introduced a slight positive bias to the measured velocities. The individual estimates of point velocity direction varied, but the average of the point velocity directions agreed quite well with the expected bulk flow direction. It was concluded that the PVP method is a viable technique for use in the field, where high‐resolution velocity data are required.

Simulation assessment of the direct‐push permeameter for characterizing vertical variations in hydraulic conductivity

The direct‐push permeameter (DPP) is a tool for the in situ characterization of hydraulic conductivity (K) in shallow, unconsolidated formations. This device, which consists of a short screened section with a pair of pressure transducers near the screen, is advanced into the subsurface with direct‐push technology. K is determined through a series of injection tests conducted between advancements. Recent field work by Butler et al. (2007) has shown that the DPP holds great potential for describing vertical variations in K at an unprecedented level of detail, accuracy and speed. In this paper, the fundamental efficacy of the DPP is evaluated through a series of numerical simulations. These simulations demonstrate that the DPP can provide accurate K information under conditions commonly faced in the field. A single DPP test provides an effective K for the domain immediately surrounding the interval between the injection screen and the most distant pressure transducer. Features that are thinner than that interval can be quantified by reducing the vertical distance between successive tests and analyzing the data from all tests simultaneously. A particular advantage of the DPP is that, unlike most other single borehole techniques, a low‐K skin or a clogged screen has a minimal impact on the K estimate. In addition, the requirement that only steady‐shape conditions be attained allows for a dramatic reduction in the time required for each injection test.

A Rapid Method for Hydraulic Profiling in Unconsolidated Formations

Information on vertical variations in hydraulic conductivity (K) can often shed much light on how a contaminant will move in the subsurface. The direct-push injection logger has been developed to rapidly obtain such information in shallow unconsolidated settings. This small-diameter tool consists of a short screen located just behind a drive point. The tool is advanced into the subsurface while water is injected through the screen to keep it clear. Upon reaching a depth at which information about K is desired, advancement ceases and the injection rate and pressure are measured on the land surface. The rate and pressure values are used in a ratio that serves as a proxy for K. A vertical profile of this ratio can be transformed into a K profile through regressions with K estimates determined using other techniques. The viability of the approach was assessed at an extensively studied field site in eastern Germany. The assessment demonstrated that this tool can rapidly identify zones that may serve as conduits for or barriers to contaminant movement.

Characterizing Hydraulic Conductivity with the Direct‐Push Permeameter

The direct-push permeameter (DPP) is a promising approach for obtaining high-resolution information about vertical variations in hydraulic conductivity (K) in shallow unconsolidated settings. This small-diameter tool, which consists of a short screened section with a pair of transducers inset in the tool near the screen, is pushed into the subsurface to a depth at which a K estimate is desired. A short hydraulic test is then performed by injecting water through the screen at a constant rate (less than 4 L/min) while pressure changes are monitored at the transducer locations. Hydraulic conductivity is calculated using the injection rate and the pressure changes in simple expressions based on Darcy's Law. In units of moderate or higher hydraulic conductivity (more than 1 m/d), testing at a single level can be completed within 10 to 15 min. Two major advantages of the method are its speed and the insensitivity of the K estimates to the zone of compaction created by tool advancement. The potential of the approach has been assessed at two extensively studied sites in the United States and Germany over a K range commonly faced in practical field investigations (0.02 to 500 m/d). The results of this assessment demonstrate that the DPP can provide high-resolution K estimates that are in good agreement with estimates obtained through other means.

Characterising the vertical variations in hydraulic conductivity within the Chalk aquifer

Summary Various field methods have been used to examine and quantify the vertical variations in aquifer properties within the Chalk aquifer at a LOCAR site in Berkshire, UK. The site contains three 100 m open boreholes and three sets of two nested piezometers within an area of about 100 m 2 . There is also an 86 m deep abstraction borehole about 40 m from the site. The techniques that have been used at the site include: geophysical logging, borehole imaging, packer testing, dilution testing and pumping tests. The packer test results show that the permeability of the aquifer varies by three orders of magnitude over the 70 m of tested material with a strongly non-linear decrease with depth below ground level. Comparison with the borehole images show that some of the highly permeable zones appear to be associated with obvious fractures. However, large fractures can be seen in zones which have much lower permeability while some highly permeable zones appear to be associated with poorly developed fractures. Single borehole dilution tests have shown that there are differences in flow velocity depth profiles over a few tens of meters across the site. These are inferred to be because the different boreholes, although of similar drilled depth and very close proximity, intersect slightly different parts of the fracture network and hence the groundwater flow system. In particular, a flowing feature at the base of one borehole is not intersected by the second, which is drilled from a slightly higher elevation. A dilution test carried out whilst the aquifer was being pumped shows that different fractures become active when the aquifer is stressed. This has implications for the interpretation of flow logs performed under pumping.

A dual-tube direct-push method for vertical profiling of hydraulic conductivity in unconsolidated formations

Abstract A new direct-push procedure has been developed for the purpose of conducting discrete-interval slug tests to define vertical variations in hydraulic conductivity (K.) This approach is an extension of existing dual-tube methods developed for soil sampling. In this procedure, nested rods (tubes) are simultaneously advanced to predetermined test intervals. The inner rods are then removed and a screen is inserted into the formation for slug testing and possible water sampling. Once testing and sampling are completed, the screen is retrieved, the inner rods reinserted, and the system is advanced to the next test interval. A series of field tests were performed in a highly permeable sand and gravel aquifer to assess the effectiveness of this new approach. Dual-tube profiling results were compared to multilevel slug tests conducted in conventional monitoring wells for intervals in which hydraulic conductivity ranged from 175 ft/day to over 800 ft/day. An initial evaluation found that the dual-tube profiling results were in good agreement (< or =12 percent difference) with K values obtained from multilevel slug tests in the closest monitoring well. Two more-detailed profiles demonstrate that the dual-tube method can effectively delineate small-scale vertical and horizontal variations in hydraulic conductivity. This field assessment shows that the dual-tube method is an accurate and efficient procedure for obtaining information about spatial variations in hydraulic conductivity. This information can be useful for selecting intervals for well installations, for assessment of various remediation alternatives, and for identifying preferential flow paths and other features that can control contaminant movement in the subsurface. The information is obtained without the need for permanent wells. Because this is a direct-push procedure, drill cuttings are eliminated and the volume of development water generated is significantly reduced.

Dipole Probe: Design and Field Applications of a Single‐Borehole Device for Measurements of Vertical Variations of Hydraulic Conductivity

AbstractA dipole probe (DP) for measuring vertical variations of hydraulic conductivity has been designed, constructed, and tested in field conditions. The variable‐length device designed for the dipole flow test (DFT) consists of three packers separated by changeable spacer rods. The assembled DP is lowered into a well with a long screened interval. The packers are inflated, isolating two screened sections (chambers) between them. A small submersible pump, mounted on the central packer, transfers water from the upper (extraction) chamber into the lower (injection) chamber. This simultaneous injection and extraction creates a recirculatory flow within the aquifer. The chamber head responses are measured by two pressure transducers in the DP chambers. The DP can be used at discrete intervals along the entire well screen length. The DP has been successfully tested in a specially constructed well with a continuous screen in a highly conductive sand and gravel aquifer. During drilling, disturbed samples were collected using the split spoon method and the vertical profile of K was estimated from grain‐size analysis. A total of 153 DFTs were performed with various DP geometries. Results indicate that the chamber head changes are sensitive to aquifer properties, reach steady state rapidly, vary linearly with redrculation pumping rate, and can be controlled by changes in DP dimensions. Vertical profiles of K compare well with grain‐size analysis estimates.

Hydraulics of a partially penetrating well: solution to a mixed-type boundary value problem via dual integral equations

New semi-analytic solutions are obtained for well response to the pumping test and slug test performed on a partially penetrating well. The solutions account not only for the wellbore storage, infinitesimal skin, and aquifer anisotropy, but also for the mixed-type boundary condition at the well face, which is novel. The solutions are obtained via the method of dual integral equations (DE). The new solutions are computationally robust and efficient, about one to two orders of magnitude faster than the corresponding finite difference solutions. Existing approximate solutions obtained with flux–flux discontinuous boundary conditions are compared to our DE solutions. The accuracy of the approximate solutions appears to be adequate for slender well screens. Our DE solution is computationally more efficient than the approximate solutions. In the range where the approximate solutions are less accurate the DE solution is about an order of magnitude faster. More important, the new solutions provide the correct distribution of the point flux (local velocity) along the well screen, unlike all existing solutions. This feature is essential in cases where vertical variations of hydraulic conductivity are sought (e.g. in flowmeter tests), and for tracer tests.

The use of slug tests to describe vertical variations in hydraulic conductivity

Multilevel slug tests provide one means of obtaining estimates of hydraulic conductivity on a scale of relevance for contaminant transport investigations. A numerical model is employed here to assess the potential of multilevel slug tests to provide information about vertical variations in hydraulic conductivity under conditions commonly faced in field settings. The results of the numerical simulations raise several important issues concerning the effectiveness of this technique. If the length of the test interval is of the order of the average layer thickness, considerable error may be introduced into the conductivity estimates owing to the effects of adjoining layers. The influence of adjoining layers is dependent on the aspect ratio (length of test interval/well radius) of the tesy interval and the flow properties of the individual layers. If a low-permeability skin is present at the well, the measured vertical variations will be much less than the actual variations, owing to the influence of the skin conductivity on the parameter estimates. A high-permeability skin can also produce apparent vertical variations that are much less than the actual, owing to water flowing vertically along the conductive skin. In cases where the test interval spans a number of layers, a slug test will yield an approximate thickness-weighted average of the hydraulic conductivities of the intersected layers. In most cases, packer circumvention should not be a major concern when packers of 0.75 m or longer are employed. Results of this study are substantiated by recently reported field tests that demonstrate the importance of well emplacement and development activities for obtaining meaningful estimates from a program of multilevel slug tests.

Numerical simulations of steady-state subsurface drainage with vertically decreasing hydraulic conductivity

Most subsurface drainage equations assume either homogeneous, two-layer or three-layer soil conditions. Finite difference simulations were performed to quantify the effect of gradually decreasing hydraulic conductivity on watertable depths for steady-state subsurface drainage. For vertically decreasing hydraulic conductivity, and for cases where drain spacing was based on effective hydraulic conductivity of the 0.5 to 2.0 m layer, mid-spacing watertable depth ranged from 0.282 to 0.900 m. The average value was 0.718 m, which is considerably shallower than the 0.9 m design value used for determining drain spacing. These higher watertables may have detrimental effects on crop yield, especially in arid areas where soil salinity is a problem. The importance of the difference between actual and design watertable depths was mostly related to the type of hydraulic conductivity decrease function, drain depth, and drainage rate. These differences are explained by the position of the drain within the soil profile and the effect of the spacing on the equivalent depth of flow. Using effective hydraulic conductivity of the 0.5 to 3.0 m layer for determining drain spacing reduced the error. For an effective hydraulic conductivity value of 0.3 m/d, the average watertable depth increased from 0.748 m for the 2.0 m auger hole to 0.829 m for the 3.0 m hole. The results presented can be used to estimate the error on watertable depth resulting from ignoring the vertical variations of hydraulic conductivity.

An Analysis of Dispersion in a Stratified Aquifer

The dispersion of a conservative solute produced as a result of vertical variations of hydraulic conductivity in a horizontal stratified aquifer of finite thickness is analyzed by applying the moment method of Aris to solve the governing advection‐dispersion equation describing mass transport. In the analysis it is assumed that the aquifer is of constant thickness and of infinite lateral extent, the hydraulic conductivity is a known function of the vertical coordinate only, and the flow is unidirectional, parallel to the stratification. The applicable Aris moment equations are developed in a suitable nondimensional form. Analytical solutions are obtained for the zeroth and first moments and for the time derivative of the second moment of the longitudinal concentration distribution for the case of an instantaneous plane source for several idealized hydraulic conductivity profiles (parabolic, linear, step function, and cosine profiles and their even periodic extensions). The analysis gives the time‐dependent variation of the longitudinal macrodispersivity for these idealized cases throughout the transient development of the dispersion process. The results of the analysis are applied to a field‐measured hydraulic conductivity profile, and predicted values of the longitudinal macrodispersivity are compared with field results. An important conclusion from the analyses is that nonuniformities in the hydraulic conductivity profile which persist over long distances may produce rather large values of longitudinal macrodispersivity which are comparable to those observed in some aquifers and which are much larger than those predicted by some previous stochastic analyses. Implications of the analytical results for field dispersion problems are discussed.

Stochastic analysis of macrodispersion in a stratified aquifer

The longitudinal dispersion produced as a result of vertical variations of hydraulic conductivity in a stratified aquifer is analyzed by treating the variability of conductivity and concentration as homogeneous stochastic processes. The mass transport process is described using a first‐order approximation which is analogous to that of G. I. Taylor for flow in tubes. The resulting stochastic differential equation describing the concentration field is solved using spectral representations. The results of the analysis demonstrate that for large time the longitudinal dispersivity approaches a constant value which is dependent on statistical properties of the medium. The analysis also describes the transient development of the dispersive process and some non‐Fickian effects which occur early in the displacement process.