Evaluation of flowmeter-head loss effects in the flowmeter test

Evaluation of flowmeter-head loss effects in the flowmeter test

N.C. Ruuda, Z.J. Kabalab,* , F.J. Molzc

aDepartment of Land, Air and Water Resources, University of California-Davis 9240, S. Riverbend Ave, Parlier, CA 93648, USAbDepartment of Civil and Environmental Engineering, Duke University P.O. Box 90287, Durham, NC 27708-0287, USA

cDepartment of Environmental Science and Engineering, Rich Environmental Laboratory, Clemson University, Box 340919, Clemson,SC 29634, USA

Received 2 March 1998; accepted 15 July 1999

Abstract

In this study, we develop an axisymmetric groundwater flow model to numerically simulate the hydraulic head loss across theflowmeter during a flowmeter test. Using it, we investigate the influence of flowmeter induced hydraulic head losses and filterpack effects on the calculated drawdown distributions in the vicinity of the pumping well and on the flowmeter test estimates oflayer horizontal hydraulic conductivity,Ki ; in three different aquifer–well systems: a homogeneous aquifer; a homogeneousaquifer with a filter pack surrounding the well; and a two-layer aquifer with a filter pack surrounding the well. We confirm thattheKi estimates can be significantly biased due to the head loss across the flowmeter. This head loss induces a non-uniform flowpattern in the vicinity of the well, which violates the horizontal flow assumption invoked by flowmeter test interpretationmethodologies. The effect of the hydraulic head losses alone (i.e. no cross-flow through the filter pack) can lead toKi estimationerrors as great as a factor of three even in a homogeneous aquifer. The coupled effect of hydraulic head losses and cross-flowthrough the filter pack can lead toKi estimation errors of up to a factor of 10 or greater. In actual flowmeter tests, these headlosses can be reduced by increasing the annulus of the flowmeter, by operating the flowmeter without a packer, or by choosing asmall enough pumping rate.q 1999 Elsevier Science B.V. All rights reserved.

Keywords:Axisymmetric groundwater flow model; Flowmeter head loss; Filter pack effects

1. Introduction

The flowmeter test is a single-borehole methodol-ogy designed to estimate the downhole distribution ofhorizontal hydraulic conductivity in a fully penetrat-ing well, situated in a confined aquifer. In recentyears, it has been used in a number of field investiga-tions (Hufschmied, 1983; Hess et al., 1986; Sudicky,1986; Morin et al., 1988; Rehfeldt et al., 1989, 1995;Molz et al., 1989, 1990, 1994; Taylor et al., 1990;

Hess et al., 1992; Young, 1995; Young and Pearson,1995; Boman et al., 1997; and others).

The two most popular flowmeter test interpretationmethodologies for providing these estimates weredeveloped by Molz et al. (1989) and Rehfeldt et al.(1989). Both methodologies assume that the test isperformed in a fully penetrating well situated in aconfined aquifer consisting ofn layers (Fig. 1), eachcharacterized by a horizontal hydraulic conductivityKi (L/T) and a thicknessbi (L) (for i � 1;…;n).During the test, the well is pumped at a constantrateQ (L3/T) until the wellbore drawdownsw�t� (L)reaches a quasi-steady state. Then a flowmeter islowered into the well to measure the vertical flow

Journal of Hydrology 224 (1999) 55–63

0022-1694/99/$ - see front matterq 1999 Elsevier Science B.V. All rights reserved.PII: S0022-1694(99)00119-5

* Corresponding author. Tel.:1 1-919-660-5479; fax:1 1-919-660-5219.

E-mail address:[email protected] (Z.J. Kabala)

www.elsevier.com/locate/jhydrol

velocity at each interlayer layer boundary. (In fieldinvestigations, delineating actual layer boundariesmay not be a practical task, although attempts havebeen made (Hanson and Nishikawa, 1996). Conse-quently, the locations and thicknesses of layers areoften equated to the positions of and distancesbetween successive flowmeter measurements, respec-tively.) These velocities then yield cumulativedischarge rates for each layer,Qi (L3/T).

A flowmeter test estimate of the layer horizontalhydraulic conductivity can then be calculated from(Molz et al., 1989)

Ki � Qi

Qbbi

�K �1�

whereb is the total aquifer thickness (L) and�K is aneffective aquifer hydraulic conductivity (L/T)obtained from a traditional pumping test (Theis,1935). One of the fundamental assumptions underly-ing the use of Eq. (1) is that the hydraulic head loss inthe well during the test are negligible. However, thepresence of the flowmeter creates a resistance to flowfor fluids passing through it. A large head loss acrossthe flowmeter may cause a significant change inmeasured layer discharge ratesQi in comparison tothe case where no head loss across the flowmeter werepresent. As a result, theKi estimates from Eq. (1) willbe biased.

The influence of filter pack properties on flowmetertests performed in layered confined aquifers wasinvestigated numerically by Ruud and Kabala(1997b). They assumed that the hydraulic head losses

were negligible, yet still reported significant errorsin layer hydraulic conductivity estimates due tointerlayer cross-flow through the filter pack.These errors may increase further due to theeffects of flowmeter induced head losses oncross-flow through the filter pack. Molz et al.(1996) and Boman et al. (1997) reported unrealis-tic estimates of downhole hydraulic conductivitydistributions from flowmeter tests performed inwells surrounded by a sand or gravel pack. Theysurmised that for sufficiently large pumping ratesthe head loss across the flowmeter is large enoughto induce a significant by-pass flow through thefilter pack and around the flowmeter. Thecombined influence of hydraulic head losses andfilter pack effects can be studied in numericalexperiments.

1.1. Objectives

In this study, we develop an axisymmetric ground-water flow model that numerically simulates the flow-meter test and accounts for hydraulic head lossesacross the flowmeter.

The specific objectives of this paper are:

1. To formulate an initial boundary value problemfor the the flowmeter test that accounts forhydraulic head losses on the flowmeter, and tomodify an existing numerical model to solve thisproblem.

2. To study the combined influence of flowmeterinduced hydraulic head losses and filter packeffects on the calculated drawdown distributionsin the vicinity of the pumping well.

3. To study the effects of hydraulic head losses onflowmeter test estimates of layer horizontalhydraulic conductivity in the simulated aquifer–well systems.

4. To illustrate some worst case scenarios of indiscri-minate use of the flowmeter test that may lead tointerpretations highly biased by hydraulic headlosses on the flowmeter.

Our intention is not to portray borehole flowmetertest in a negative light, but rather to emphasizethe need for careful monitoring of the flowmeterlosses.

N.C. Ruud et al. / Journal of Hydrology 224 (1999) 55–6356

Fig. 1. Diagram of a fully penetrating well surrounded by a filterpack and situated in a layered confined aquifer.

2. Head loss across an electromagnetic flowmeter

2.1. Experimental results

Foley (1997) constructed a laboratory apparatus formeasuring head loss as a function of dischargethrough an electromagnetic borehole flowmeterhaving a 0.5 in. internal annulus. The meter andpacker were placed in a 4 in. diameter vertical plasticpipe, and water was circulated through the pipe atdischarge rates varying from about 2 to 25 l min21.All testing was done with the packer inflated fully,thus water entering the meter was constricted from a4 in. diameter tube to a tube of 0.5 in. diameter. Afterpassing through the meter, a distance of about 8.9 cm,the flow field expanded back to the 4 in. diameter. Thehead losses associated with the constriction posed bythe meter were measured with a series of manometers.As one would expect, a parabolic dependence of headloss on flow rate resulted, with a least-squares fit to thedata given by

h�Qf � � 0:0034Qf 1 0:0038Q2f ; R2 � 0:999 �2�

where the flowrate across the flowmeterQf ismeasured in liters per minute and the head lossh infeet.R is the correlation coefficient resulting from thefit. Further details are provided by Foley (1997) andDinwiddie et al. (1999). Qualitative implications ofthe flowmeter head loss effects were discussed byMolz et al. (1996).

3. Mathematical model of well response

The governing equation which describes cylindri-cal axisymmetric groundwater flow to a well situatedin a 2D heterogeneous confined aquifer (Hantush,1964)

Ss�r ; z� 2s2t� K�r ; z�

r2s2r

12

2rK�r ; z� 2s

2r

� �

12

2zK�r ; z� 2s

2z

� ��3�

where s�r ; z; t� is the drawdown (L),K�r ; z� thehydraulic conductivity (L/T),Ss�r ; z� the specific stor-ativity (L21), r the radial distance from the center ofthe well (L),z the vertical distance measured from thetop of the aquifer (L), andt time.

The drawdown distribution inside and around asteadily discharging fully penetrating well with well-bore storage and a hydraulic head loss inside the wellacross a flowmeter of thicknessDzf is obtained bynumerically solving Eq. (3) subject to the followinginitial and boundary conditions

s�r ; z; 0� � 0; rw , r , ∞; 0 # z # b �4�

s�∞; z; t� � 0; t . 0; 0 # z # b �5�2s�r ; 0; t�

2z� 2s�r ;b; t�

2z� 0; t . 0; �6�

rw , r , ∞

2s�rw; z; t�2r

� 0; d , z , d 1 Dzf �7�

s�rw; z; t� � sw1�t�; 0 , z # d �8�

s�rw; z; t� � sw2�t�; d 1 Dzf # z , b �9�and to the following constraints

Q� Q1�t�1 Q2�t�1 pr2c

dsw1

dt�10�

sw2�t� � sw1�t�2 h�Q2�t�� 11�where

Q1�t� � 22prw

Zd

0K�rw; z� 2s�rw; z; t�

2rdz �12�

Q2�t� � 22prw

Zb

d 1Dzf

K�rw; z� 2s�rw; z; t�2r

dz �13�

andsw1�t� is the wellbore drawdown above the flow-meter (L), sw2�t� the wellbore drawdown below theflowmeter (L), Q1�t� the aquifer discharge rateabove the flowmeter (L3/T), Q2�t� the aquiferdischarge rate below the flowmeter (L3/T), h�Q2�t��the hydraulic head loss across the flowmeter (L),dthe distance from the top of the aquifer to top of theflowmeter (L), rw the well radius (L),rc the radius ofthe well casing (L), and2s�rw; z; t�=2r is the hydraulicgradient at the well face. The third term on the right-hand side of Eq. (10) accounts for the wellborestorage, which becomes negligible after the wellboredrawdown reaches a quasi-steady state.

In Eq. (11), h�Q2�t�� is an empirical relation

N.C. Ruud et al. / Journal of Hydrology 224 (1999) 55–63 57

between hydraulic head loss across the flowmeter andthe discharge rate below and across the flowmeter. Inthis study, we use Eq. (2) for this purpose.

The solutions to Eqs. (8) and (9) are obtained bysolving Eqs. (3)–(13) iteratively via the bisection

method until the well face boundary constraint, Eq.(10) and the empirical relation for head loss and thedischarge rate below the flowmeter, Eq. (2), are bothsatisfied. For this, we use a modified version of a fullyimplicit finite difference code developed and vali-dated by Ruud and Kabala (1996, 1997a,b).

4. Synthetic flowmeter tests

In this section, we numerically simulate the flow-meter test in three different aquifer–well systems: ahomogeneous aquifer; a homogeneous aquifer with afilter pack surrounding the well; and a two-layer aqui-fer with a filter pack surrounding the well. For eachaquifer–well system, we also consider three differentwell scenarios: a well with no flowmeter; a well with aflowmeter but no hydraulic head losses; and a wellwith a flowmeter and hydraulic head losses. Foreach of the resulting nine cases, we display the calcu-lated drawdown distributions in the vicinity of thewell, and for the systems with a flowmeter in thewell we calculate the horizontal hydraulic conductiv-ities above and below the device using Eq. (1).

In all simulations, the total aquifer thickness isb�45 m; the well radius isrw � 0:1 m; and the skinradius is rs � 2.5rw. The specific storativity of theaquifer is assumed to beSs � 1026m21 and so is thespecific storativity of the filter pack when present. Thelength of the flowmeter packer isDzf � 0:2 m: Whenpresent in the well, the packer is placed at a distanceof d � 4:9 m from the top of the aquifer. The systemsare pumped at a constant total pumping rate ofQ�1:25 m3 h21 � 20:83 L min21 for 1 h.

A number of points concerning our choice of theconsidered synthetic cases needs to be made. First, ourtotal pumping rate was chosen such that the empiricalrelation (2) is valid for all simulated cases. Second,our solution procedure assumes that the well headlosses are negligible. One can overestimate theselosses in all considered cases by assuming that theflowrate is constant throughout the whole well andequal to the total pumping rate. The Reynolds numberfor such flow isRe� V�2rw�=n � 1912; whereV �Q=�pr2

w� � 0:011 m s21 is the mean velocity andn �1:156× 1026 m2 s21 is the kinematic viscosity ofwater at temperatureT � 158C: The flow in the wellpipe is thus laminar, and the corresponding head loss


Fig. 2. Drawdown and flowlines at timet � 1 h around a fullypenetrating well of radiusrw � 0:1 m; pumped at the rateQ�1:25 m3 h21

; and situated in a homogeneous confined aquifer withhydraulic conductivityK � 5 × 1025 m s21 and specific storativitySs � 1026 m21

: No filter pack present. No flowmeter installed.



: No filter pack present. A flowmeter is situatedbetween 4.9 and 5.1 m. No hydraulic head losses across the flow-meter.

is given by the Darcy–Weisbach formula with thefriction coefficient f � 64=Re: Thus, the well headloss, hL # f �b=2rw��V2

=�2g�� 0:08�45=0:2��0:0222

=�29:81�� 4:6 × 1024 m21 is indeed

negligible. Third, our placement of the flowmeternear the top of the aquifer is motivated by our desireto illustrate some of the worst case scenarios of indis-criminate use of the flowmeter test that may lead tointerpretations highly biased by hydraulic head losseson the flowmeter. Fourth, our selection of the rela-tively high total pumping rate would be necessary ina similar situation in the field, especially if we wantedto register measureable flow rates at the bottom of thewell—note that in the traditional flowmeter test onlyone pumping rate is selected for the flowmeter test onthe whole well.

4.1. Homogeneous aquifer

We first simulate the three well scenarios for ahomogeneous aquifer withK � 5 × 1025 m s21

: InFigs. 2–4, we present the calculated equipotentiallines and streamlines in the vicinity of a well withno flowmeter, a well with a flowmeter and no hydrau-lic head losses on it, and the well with a flowmeter andhydraulic head losses on it, respectively. As expected,in Fig. 2, the flow is perfectly horizontal around thewell with no flowmeter. It is also fairly horizontal inthe case of a flowmeter with no hydraulic head losses,except in the immediate vicinity of the well where thepresence of the flowmeter creates a no-flow boundary(Fig. 3). However, in Fig. 4, we see that the head lossacross the flowmeter causes the flow in the vicinity ofthe well to deviate from the horizontal pattern; asignificant vertical flow component is developed.Furthermore, there exists a region in the well imme-diately beneath the flowmeter where water exits thewellbore, enters the aquifer, and bypasses the flow-meter.

For the well systems possessing a flowmeter, wethen estimate the hydraulic conductivities of the aqui-fer regions above and below the flowmeter using Eq.(1). For the case with no flowmeter head losses, wefind thatK̂no head loss

above =K � 1:0 andK̂no head lossbelow =K � 1:0:

For the case with flowmeter head losses, however, wefind that K̂no head loss

above =K � 3:3 and K̂no head lossbelow =K �

0:73: In this case, the difference in head in the wellbelow and above the flowmeter induces significantupward flow around the well. This results in a corre-spondingly greater contribution of discharge to thetotal pumping rate from the region of the aquiferabove the flowmeter. Consequently, the hydraulic




: No filter pack present. A flowmeter is situatedbetween 4.9 and 5.1 m. The hydraulic head loss across the flow-meter is accounted for.



: A filter pack is present withrs=rw � 2:5 andKs �1:5 × 1024 m s21

: No flowmeter installed.

conductivity in the aquifer above the flowmeter isoverestimated and that below it is underestimated.

4.2. Homogeneous aquifer with a filter pack

We next simulate the three well scenarios for ahomogeneous aquifer with a filter pack surroundingthe well where the system is defined byK �5 × 1025 m s21

; Ks=K � 3:0; and rs=rw � 2:5; whereKs is the filter pack hydraulic conductivity (L) andrs

is the radius of the filter pack from the center of thewell (L). In Figs. 5–7, we again present the calculatedequipotential lines and streamlines in the vicinity of awell with no flowmeter, a well with a flowmeter andno hydraulic head losses on it, and the well with aflowmeter and hydraulic head losses on it, respec-tively. At the well face, the filter pack/aquifer inter-face is denoted by a thick dashed line in the threefigures.

The flow is again perfectly horizontal around thewell with no flowmeter (Fig. 5) and nearly horizontalwith a flowmeter and no hydraulic head losses on it(Fig. 6). As in Fig. 4, the flowmeter head lossproduces a significant vertical flow component inthe vicinity of the well (Fig. 7).

For the case with no flowmeter head losses, we find

again thatK̂no head lossabove =K � 1:0 and K̂no head loss

below =K �1:0; For the case with flowmeter head losses, however,we obtain K̂no head loss


0:68: We note that the hydraulic conductivity estimates





: A flowmeter is situated between 4.9 and 5.1 m.No hydraulic head loss across the flowmeter.




: A flowmeter is situated between 4.9 and 5.1 m.The hydraulic head loss across the flowmeter is accounted for.


; and situated in a two-layer confined aquifer whereb1 � 5 m; b2 � 40 m; K2 � 5 × 1025 m s21 and K2=K1 � 10: Afilter pack is present wherers=rw � 2:5 and Ks � 1:5 ×1024 m s21

: No flowmeter is installed.

are slightly more biased than in the previous section.The reason is that the filter pack of higher conductiv-ity than that of the aquifer serves now as a verticalflow short cut. This is also evident from the compar-ison of the streamline shapes in Figs. 4 and 7.

4.3. Two-layer aquifer with a filter pack

Finally, we simulate the three well scenarios for atwo-layer aquifer with a filter pack surrounding thewell where the system is defined byK2 �5 × 1025 m s21

; K2=K1 � 10; Ks=K2 � 3:0; rs=rw �2:5; rs=rw � 2:5; b1 � 5 m; andb2 � 40 m; whereb1

andb2 are the thicknesses of layers 1 and 2, respec-tively. In Figs. 8–10, we present the calculated equi-potential lines and streamlines in the vicinity of thewell for the three well scenarios as in the previous twosections. At the well face and the filter pack/aquiferinterface, the layer interface is denoted by a thickdashed line.

The flow patterns are now more complicated.Although they are still horizontally dominated in thefirst two cases, a significant cross-flow developsbetween the layers and even larger one through thefilter pack. This is due the hydraulic conductivitycontrast between the layers and the filter pack. For

the case with no flowmeter head losses, we find thatK̂no head loss

above =K � 1:2 and K̂no head lossbelow =K � 0:99: For

the case with flowmeter head losses, however, weobtain K̂no head loss


0:85:When a head loss is present, the increased

drawdown above the flowmeter induces an increasein the measured cross-flow through the filter pack.Consequently, the measured flow rate attributed tothe first layer is artificially increased above what itwould be with no head loss and the drawdownconstant along the entire well face. Had the situationbeen reversed andK1=K2 � 10; then the head losswould have led to a significant underestimation ofK2, by again artificially increasing the cross-flowfrom layer 2 into layer 1 through the filter pack.These examples provide an excellent illustration ofthe combined influence that the head loss and thesubsequent cross-flow through the filter pack exerton the flowmeter test estimates in a simple layeredsystem.

5. Conclusions

In this study, we developed a numerical model for




: A flowmeter is situated between 4.9 and 5.1 m. Nohydraulic head loss across the flowmeter.



: A flowmeter is situated between 4.9 and 5.1 m. Thehydraulic head loss across the flowmeter is accounted for.

solving the initial boundary-value problem for theflowmeter test with a head loss across the flowmeter.Using this model, we simulated the flowmeter test inthree different aquifer–well systems: a homogeneousaquifer; a homogeneous aquifer with a filter packsurrounding the well; and a two-layer aquifer with afilter pack surrounding the well. For each aquifer–well system, we also considered three different wellscenarios: a well with no flowmeter; a well with aflowmeter but no hydraulic head losses; and a wellwith a flowmeter and hydraulic head losses. Wepresented figures of the calculated drawdown distribu-tions in the vicinity of the well and estimated thehorizontal hydraulic conductivities above and belowthe device using Eq. (1). The main conclusions fromour study are the following:

1. We confirm the findings of Molz et al. (1996) andBoman et al. (1997) that the hydraulic conductivityestimates from the flowmeter test can be signifi-cantly biased due to a head loss across the flow-meter. This head loss induces a non-uniform flowpattern in the vicinity of the well, which is in viola-tion of the horizontal flow assumption invoked bythe flowmeter test interpretation methodologies.

2. The effect of flowmeter induced hydraulic headlosses alone (i.e. no cross-flow through the filterpack) can lead to hydraulic conductivity overesti-mates of half an order of magnitude even in ahomogeneous aquifer and more than an order ofmagnitude in layered systems.

3. The coupled effect of hydraulic head losses acrossthe flowmeter and of cross-flow through the filterpack can lead to hydraulic conductivity overesti-mates of up to a factor of 10 or greater.

4. In every flowmeter test, care should be taken in theselection of the pumping rate to avoid significanthead losses across the flowmeter. These headlosses can be reduced by increasing the annulusof the meter, or by operating the meter without apacker. These options have been studiedexperimentally by Arnold (1997), and both appearfeasible. A third possible solution is to performflowmeter measurements at multiple rates. A hightotal pumping rate could be used for deepmeasurements where the flowrate through themeter is still small, whereas a low total pumping

rate could be used for shallow measurementswhere the flowrate through the meter is significant.

Acknowledgements

We express our gratitude to Dr K. Rehfeldt and ananonymous reviewer for their in-depth comments.This research was partially supported by the USGeological Survey, USGS Agreement\# 1434-HQ-96-GR-02689 and North Carolina Water ResourcesResearch Institute, WRRI Project\# 70165.

References

Arnold, K.B., 1997. Calibration of an electromagnetic BoreholeFlowmeter in an artificial well without a packer. Master’s thesis,EE and S Department, Clemson University.

Boman, G.K., Molz, F.J., Boone, K.D., 1997. Borehole flowmeterapplication in fluvial sediments: methodology, results, andassessment. Ground Water 35 (3), 443–450.

Dinwiddie, C.L., Foley, N.A., Molz, F.J., 1999. In-well hydraulicsof the electromagnetic borehole flowmeter. Ground Water 37(2), 305–315.

Foley, N.A., 1997. Pressure distribution around an electromagneticborehole flowmeter in an artificial well. Masters thesis, Envir-onmental, Engineering & Science Department, ClemsonUniversity, Anderson, SC.

Hanson, R.T., Nishikawa, T., 1996. Combined use of flowmeter andtime-drawdown data to estimate hydraulic conductivities inlayered aquifer systems. Ground Water 34, 84–94.

Hantush, M.S., 1964 Hydraulics of wells. In: Chow, V.T. (Ed.),Advances in Hydroscience, vol. 1, Academic Press, NewYork, pp. 281–442.

Hess, A.E., 1986. Identifying hydraulic conductive fractures with aslow-velocity borehole flowmeter. Canadian Geotechnical J. 23,69–78.

Hess, K.M., Wolf, S.H., Celia, M.A., 1992. Large-scale naturalgradient tracer testing sand and gravel Cape Cod, Massachu-setts. 3. Hydraulic Conductivity Variability and CalculatedMacrodispersivities. Water Resour. Res. 28 (8), 2011–2027.

Hufschmied, P., 1983. Ermittlung der Durchlassigkeit von Lock-ergesteins-rundwasserleitern, eine Vergleichende Untersuchungverschiedener Feldmethoden, Doctoral Dissertation No. 7397,ETH, Zurich, Switzerland.

Molz, F.J., Foley, N., Dinwiddie, C.L., 1996. In-well hydraulics ofborehole flowmeters: problems and solutions. Eos Trans. Am.Geophys. Union 77 (46), F236 Fall Meeting.

Molz, F.J., Morin, H., Hess, A.E., Melville, J.G., Gu¨ven, O., 1989.The impeller meter for measuring aquifer permeabilityvariations: evaluation and comparison with other tests. WaterResour. Res. 25, 1677–1683.

Molz, F.J., Gu¨ven, O., Melville, J.G., 1990. A new approach andmethodologies for characterizing the hydrogeologic properties


of aquifers, Report EPA/600/2-90/002, US EnvironmentalProtection Agency, Ada, OK.

Molz, F.J., Boman, G.K., Young, S.S., Waldrop, W.R., 1994.Borehole flowmeters: field application and data analysis. J.Hydrol. 163, 347–371.

Morin, R.H., Hess, A.E., Paillet, F.L., 1988. Determining the distri-bution of hydraulic conductivity in a fractured limestone aquiferby simultaneous injection and geophysical logging. GroundWater 26, 587–595.

Rehfeldt, K.R., Hufschmied, P., Gelhar, L.W., Schaefer, M.E.,1989. The borehole flowmeter technique for measuring hydrau-lic conductivity variability, Report No. EN 6511, Electric PowerResearch Institute, Palo Alto, CA.

Rehfeldt, K.R., Boggs, J.M., Gelhar, L.W., 1995. Field study ofdispersion in a heterogeneous aquifer. 3. Geostatistical analysisof hydraulic conductivity. Water Resour. Res. 28 (12), 3309–3325.

Ruud, N.C., Kabala, Z.J., 1996. Numerical evaluation of flowmetertest interpretation methodologies. Water Resour. Res. 32 (4),845–852.

Ruud, N.C., Kabala, Z.J., 1997a. Response of a partially penetratingwell in a heterogeneous aquifer: integrated well-face flux versus

uniform well-face flux boundary conditions. J. Hydrol. 194 (1–4), 76–94.

Ruud, N.C., Kabala, Z.J., 1997b. Numerical evaluation of the flow-meter test in a layered aquifer with a skin zone. J. Hydrol. 203(1–4), 101–108.

Sudicky, E.A., 1986. A natural gradient experiment on solute trans-port in a sand aquifer: Spatial variability of hydraulic conduc-tivity and its role in the dispersion process. Water Resour. Res.22, 2069–2082.

Taylor, K., Wheatcraft, S.W., Hess, J., Hayworth, J.S., Molz,F.J., 1990. Evaluation of methods for determining the verti-cal distribution of hydraulic conductivity. Ground Water 28,88–98.

Theis, C.V., 1935. The relation between the lowering of the piezo-metric surface and the rate and duration of discharge of a wellusing ground-water storage. Trans. Am. Geophys. Union 16,519–524.

Young, S.C., 1995. Characterization of high-K pathways by bore-hole flowmeter and tracer tests. Ground Water 33, 311–318.

Young, S.C., Pearson, H.S., 1995. The electromagnetic boreholeflowmeter: description and application. Ground Water Monit.Rem. Fall, 138–146.


Documents

Evaluation of flowmeter-head loss effects in the flowmeter test