Pumped Ambient 2009

Analysis of flow processes in fractured chalk under pumpedand ambient conditions (UK)

A. P. Butler & S. A. Mathias & A. J. Gallagher &

D. W. Peach & A. T. Williams

Abstract An integrated set of different measurements hasbeen used to study the behavior of groundwater in anobservation well in a fractured rock formation, the UKChalk, under pumped and ambient conditions. Underpumped conditions, the response of the open borehole wasrelatively straightforward with flow mainly concentratedalong four discrete flow horizons. Furthermore, excellentcorrespondence was observed between the three methodsof borehole flow velocity measurement: impeller flowme-ter, heat-pulse flowmeter and dilution testing. Underambient conditions, the system appeared more complicat-ed. Specifically, in the upper half of the borehole, theimpeller flowmeter exhibited substantial downward flowand the heat-pulse flowmeter exhibited almost negligibleupward flow, whilst dilution testing indicated significantdilution. It was concluded that this was due to cross-flowoccurring over the upper 29 m. Analysis of drawdowndata, recovery data and a Drost analysis of the ambientcross-flow data yielded aquifer transmissivity estimates of2,049, 2,928 and > 4,388 m2/day respectively. Thediscrepancy between the drawdown and recovery esti-mates was attributed to non-linear head-losses associatedwith turbulence and inertial effects. The differencebetween the pumping test and Drost results was explainedby the flow during the pumping test bypassing thisaforementioned 29 m region of rock.

Keywords Dilution test . Fractured rocks .Hydraulic testing . Pumping test . UK

Introduction

Chalk aquifers represent some of the most importantgroundwater resources in the UK. Consequently, greateffort is incurred in developing catchment-scale ground-water models of key water-resources sites (see ENTEC2005 and references therein). These models routinely useparameters obtained from pumping test analysis (Mac-Donald and Allen 2001). However, it is often found thatwhen attempting to simulate the observed ambient (i.e.unpumped) groundwater response, a level of calibration isrequired (ENTEC 2005; Rushton et al. 1989). Thisadjustment of parameter values is due to a range ofproblems including measurement error and model uncer-tainty (Liu and Gupta 2007). However, another problem,not often discussed, is the extent that aquifer parametersderived under locally perturbed (i.e. pumped) conditionsare suitable for applying to models that represent thesystem in the ambient state.

As part of the UK Natural Environment ResearchCouncil (NERC) thematic programme on lowland catch-ment research (LOCAR; Wheater and Peach 2004), three100-m deep observation boreholes (PL10A, PL10B,PL10E) were placed around an Environment Agency riveraugmentation abstraction well at Bottom Barn (BBA)situated in the Berkshire Chalk aquifer, UK (see Fig. 1 andWilliams et al. 2006). Effort was focused on thecharacterization of PL10A, which benefited from exten-sive geophysical logging (caliper, gamma, temperature,televiewer, etc.), packer testing, flow logging (usingimpeller and heat-pulse flow meters) and dilution testing.Of particular interest is that temperature logging, flowlogging and dilution testing were undertaken underambient conditions and again when the BBA (situated32 m away) was pumping at 5,770 m3/day. In thefollowing, it is shown that the pumping of BBAfundamentally changed the flow processes withinPL10A. This local observation reflects a more generalresult, which is that the effect of pumping was to activatea different combination of flow pathways in the rockcompared to those involved during ambient flow con-ditions; thereby, raising a serious question concerning theapplication of results obtained from pumping tests infractured rock aquifers such as the Chalk. A furthercomplicating factor is that flow between the borehole and

Received: 29 April 2008 /Accepted: 29 April 2009

* Springer-Verlag 2009

A. P. Butler : S. A. Mathias ())Department of Civil and Environmental Engineering,Imperial College London,London, SW7 2AZ, UKe-mail: [email protected]

A. J. Gallagher :D. W. Peach :A. T. WilliamsBritish Geological Survey,Wallingford, OX10 8BB, UK

Hydrogeology Journal DOI 10.1007/s10040-009-0477-4

the abstraction well appeared to be through relativelylimited pathways (indicated by rapid travel times fromtracer tests) and therefore were likely to be affected bynon-linearities due to turbulent flow.

Lithostratigraphy

Traditionally, the Berkshire Chalk outcrop has beensubdivided into the Upper, Middle and Lower Chalkformations (White 1907). At a meeting of the GeologicalSociety Stratigraphy Commission at the British GeologicalSurvey (BGS) in 1999, a broadly agreed revised ChalkGroup stratigraphy was adopted (Rawson et al. 2001),which was based on the more sophisticated lithostrati-graphical classification applied by Mortimore (1986) andRobinson (1986). One of the useful markers for applyingthe new lithostratigraphical classification is a 3-m band,near the base of the Lewes Nodular Chalk (the base of theformer Upper Chalk), known as the Chalk Rock (Schurchand Buckley 2002; Woods and Aldiss 2004). This isbecause the phosphatized and glauconitized chalk-pebbleintraclasts, particularly common in the Chalk Rock, giverise to a significant increase in gamma-ray activity(Schurch and Buckley 2002). Figure 2b shows a gamma-ray log of borehole PL10A where such a gamma-ray peakis present at 27 mAOD (meters above ordinance datum).

Following Schurch and Buckley (2002) and Woodsand Aldiss (2004), the Lewes Nodular Chalk formationwas assumed to be around 20 m thick with its base locatedat the very bottom of the Chalk Rock gamma-ray

Hermitage

Streatley Goring

Pangbourne

Tilehurst

ThealeBucklebury

Cold Ash

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Fig. 1 a Location map of Bottom Barn relative to the UK. bLocation map of Bottom Barn relative to neighboring roads,villages and rivers. c Site layout at Bottom Barn

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Fig. 2 Stratigraphy, fracturing and hydraulic conductivity distributions for borehole PL10A. a Shows the variation of borehole diameterwith elevation. b Shows a natural gamma log along with the stratigraphy inferred from it. c A tadpole plot, derived from the televiewer log(see sketch to the right), showing the dip (tadpole body) and strike (tadpole tail) of the fractures. d Shows the hydraulic conductivitydistribution measured from the constant head double-packer permeameter tests, which were taken at different dates as detailed in the legend.The error bars represent the length of isolated interval (≈ 3 m)


perturbation; therefore, the uncased section of boreholePL10A can be assumed to lie in around 10 m of New PitChalk, overlain by 20 m of Lewes Nodular Chalk,overlain by 50 m of Seaford Chalk (see Fig. 2 forschematic). The New Pit formation is a firm, smooth-textured marly chalk, while the Lewes Nodular is a hard,nodular gritty chalk, with common flints, marl seams andhardgrounds. The base of the Seaford formation is at theupward change from hard, nodular, gritty chalk to soft,smooth-textured chalk (Woods and Aldiss 2004).

Fractures

To better visualize the physical structure of the aquifer atPL10A, an optical televiewer (OTV) log was obtained.The OTV log provides a 360° bitmap image of the entireborehole. Planar sub-horizontal features manifest them-selves perfectly as sine waves, from which the elevation,strike and dip of the fractures that intersect the boreholecan be obtained (Paillet and Pedler 1996). Theoretically,OTV logs can be interpreted automatically using tech-niques such as the Hough transform (Glossop et al. 1999);however, this requires that the OTV log is still intelligibleafter translating to a binary image, which, for the PL10AOTV log, was not the case; so, consequently, a manualtechnique was adopted. Ideally, this should be a simplecase of locating the minimum and maximum points of theintersecting fractures’ sine waves. However, for many ofthe fractures, the absolute locations of the peaks andtroughs were not clear. To aid a more robust analysis, asimple MATLAB program was developed (see Appendixfor a detailed description). Figure 2c shows a tadpole plotof borehole PL10A derived from the OTV log. Thetadpole body indicates the dip angle and the tail indicatesthe strike angle (or dip direction) (Williams and Paillet2002). It can be seen that there are many sub-horizontalfractures throughout the extent of the borehole.

Packer testing

The vertical distribution of hydraulic conductivity wasmeasured using a constant head double-packer permea-meter. The double-packer permeameter used in boreholePL10A incorporates a pump, to abstract water from theisolated section, and a transducer to measure the pressurewithin the section (see Price and Williams 1993 for moredetails). Once the section to be tested is isolated byinflating the packers, water is pumped out of the isolatedinterval at a constant rate, Q [L3T−1]. The head in thesection is monitored using the transducer and pumpingcontinues until a steady-state drawdown is measured, �0

[L]. In typical UK Chalk boreholes, this takes around20 min. The horizontal hydraulic conductivity of thetested section, K [LT−1] is then calculated using (Hvorslev1951) K = QF / �0 where F [L] is a shape factordependant on the ratio of horizontal and vertical hydraulicconductivity and the geometry of the packered abstraction

system. The appropriate shape factor for the double packerpermeameter is given in the form of a simple polynomialapproximation by Mathias and Butler (2007). This isbased on an underlying semi-analytical solution, whichassumes that the aquifer is isotropic and homogeneous (inpractice the length of aquifer between and including thepackered sections and for about the the same lengthradiating out from the borehole) and that the boreholeabove and below the packered length can be treated as aconstant-head boundary condition. Applying this resultgives the hydraulic conductivity profile shown in Fig. 2d.It can be seen that the hydraulic conductivity values spanalmost five orders of magnitude. Generally there is alinear-log trend with elevation combined with around anorder of magnitude of fluctuation. The profile is similar tothose obtained at a number of other Chalk boreholes in theUK (Price et al. 1982; Price and Williams 1993; Allen etal. 1997) and Israel (Nativ et al. 2003).

Pumping test analysis

As previously stated, the abstraction well, BBA waspumped at 5,770 m3/day for 34 h. Drawdown andrecovery (after the cessation of pumping) were continu-ously monitored using pressure transducers in the threeobservation boreholes and the abstraction well (Fig. 3). Inview of the early time data being affected by variousprocesses operating in the vicinity of the well (e.g. wellstorage), estimates of effective transmissivities wereobtained using Jacob’s method on the late time datafollowing Meier et al. (1998). This assumes that theaquifer is homogeneous and isotropic, well bore storagecan be ignored, pumping was at a constant rate, flowobeys Darcy’s law and, for the pumping and recovery timeperiods analysed, the effects of delayed yield and elasticstorage and are negligible. Although, on the scale of thetest, it is unlikely that the aquifer can be truly consideredto be isotropic and homogeneous, this assumption is stillconsidered reasonable for allowing comparisons in trans-missivity values to be made. The focus on late time datameans that any effects from storativity or initial variationsin pumping rate should be negligible. It is argued later thatevidence of fast flow pathways connecting observationand abstraction wells could indicate turbulent flow in thevicinity of the abstraction well and this may mean that thetransmissivities from the pumping test analyses are under-estimated.

Note that recovery data is plotted on a transformed axis(Agarwal 1980; Samani and Pasandi 2003) such that it canalso be analysed using Jacob’s method. The resultingtransmissivity estimates are given in Table 1. The meantransmissivity is calculated to be 2,049 ± 230 m2/day fromthe drawdown phase results and 2,928 ± 229m2/day from therecovery. These are well within the national ranges for theChalk (MacDonald and Allen 2001), further supporting thatthis is a relatively typical site.

The discrepancy between the drawdown and recoverytransmissivities is a common occurrence although rarely


addressed. Rushton and Chan (1976) showed that thediscrepancy between drawdown and recovery data couldsometimes be explained by vertical variations in hydraulicconductivity. Rushton and Booth (1976) and Shapiro et al.(1998) suggest that the discrepancy can also be due tonon-linear head losses within the well-bore. However, theidea that non-linear head losses only occur within thewell-bore is a common misconception dating back tothe empirical work of Jacob (1946). In fact, non-linearhead losses due to turbulence, microscopic inertia andmicroscopic drag (Giorgi 1997) are likely to occur over alarge region within the aquifer around the well-bore due tothe fast velocities caused by the convergence of flow-lines(Mathias et al. 2008). This is likely to be particularlyimportant in Chalk aquifers where groundwater flow inthe saturated zone is often largely confined to a limitednumber of well-connected flow pathways (e.g. Mathias etal. 2007, Hartmann et al. 2007).

Flow logging

To gain information about which portions of the aquiferare likely to be contributing to this transmissivity, upflowlogs were obtained using both impeller and heat-pulse

flowmeters. Impeller flowmeter measurement involveslowering an impeller down a borehole at a fixed rate andlogging the rotation rate of the impeller. The net upflowvelocity is obtained from a simple calibration equation,which in turn can be converted to an estimated flow rateby multiplying by the borehole cross-sectional areaobtained from caliper log measurements; note thereforethat noise in the flow impeller profiles is partially due toerror in the borehole area measurement. The mainshortcoming of impeller flowmeters is their lack ofsensitivity to low-velocity flow For smaller flow rates, aheat-pulse flowmeter is more appropriate.

Table 1 Transmissivity data obtained from Jacob analysis (see Fig. 3).Note BBA refers to the abstraction well. SD standard deviation

Borehole Radial distance Drawdowna Recoverya

BBA N/A 1,782 2,933PL10A 31.9 m 2,328 3,076PL10B 53.9 m 2,219 3,147PL10E 36.8 m 866 2,555Mean N/A 2,049 2,928SD N/A 230 229

aUnits are in m2 /day

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Fig. 3 Plots of drawdown and recovery whilst pumping BBA at 5770 m3/day for PL10B (a), PL10E (b), PL10A (c) and BBA (d). a–dNote that tp and sp refers to the time the pump was switched off and the corresponding drawdown. For drawdown, s is plotted against t,whereas for recovery, sp – s is plotted against tp(t – tp)/t


The heat-pulse flowmeter was originally developed byDudgeon et al. (1975). An electrical heating grid, locatedbetween two thermistors, is heated by a short pulse ofelectrical current. The heated lens of water is movedtowards one of the thermistors by the vertical componentof flow in the borehole. The arrival time of the heat-pulseat the thermistor is recorded. If the heat-pulse is detectedby the upper one, flow is upwards and vice versa. The flowvelocity can then be calculated by dividing the distancebetween the element and thermistor by the respective traveltime. Again, the flow-rate is estimated by multiplying thevelocity by the local cross-sectional area from the caliperlog; note that neither the impeller nor heat-pulse flowmetersused in this study were capable of measuring flow across theborehole. The direct measurement of cross-flow requiresmore sophisticated instrumentation (e.g. James et al. 2006;Su et al. 2006).

Figures 4a and 5a show measured upflow profiles forborehole PL10A whilst pumping BBA and under ambientconditions respectively. As the results obtained duringpumping are more straightforward to interpret, these arediscussed first. It can be observed that there is relativelygood correspondence between the impeller and heat-pulseflowmeters. The step changes in the impeller log areindicative of discrete flow horizons. It is apparent thatthere is an upflow at the base of the borehole, followed byan additional inflow at 27 mAOD, which corresponds tothe Chalk Rock (compare Fig. 2b). There is a smalloutflow at 57 mAOD followed by a much larger outflowat 74 mAOD, which is sufficient to change the flowdirection. Finally, the impeller and heat-pulse logs suggestthat there is an inflow in the vicinity of the water table.

This description is further supported by the temperaturelog in Fig. 4b, where inflections can be seen at 27 mAODand 74 mAOD.

Under ambient conditions, the picture is more compli-cated. First, flow rates are generally around a quarter ofthose for the pumped condition. Second, the impellerflowmeter log in Fig. 5a shows an upflow from the base ofthe hole and an outflow at 57 mAOD that appears tochange the flow direction such that there is a substantialdownward flow in the upper part of the borehole (the largepeak at 63 mAOD is probably due to the flowmeter hittingthe side of the borehole). From 57 to 85 mAOD, theimpeller flowmeter results are very variable and alwaysnegative, which could be indicative of some downwardmovement or cross-flow. The temperature log indicates asteep gradient from 57 to 74 mAOD and is consistent withthe relatively low flows recorded by both heat pulse andimpeller measurements in this interval. Above 74 mAOD,the temperature gradient is almost zero, which may be dueto downward flow, as suggested by the impeller measure-ments in this region of the borehole, although thisexplanation is not supported by heat pulse measurements.Between 57 and 74 mAOD there are only two heat pulsemeasurements, one positive and similar to those at greaterdepth, and one of zero at 65 mAOD. The higher heat-pulse measurements (measuring zero) are found in theregion above 74 mAOD. It seems likely that thedisagreement in these various results is indicative of lowvertical flows but significant cross-flow The distribution ofthe cross-flow is impossible to estimate but seems likely tobe highest at 74 mAOD or just above this point, with lesssignificant flow between 57 and 74 mAOD.

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Dilution test

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Background2– 6min11– 15min32– 36min55– 60min76– 80minmodel

26 m3/day

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19 m3/day

57 m3/day

26 m3/day

–

Fig. 4 Flow logging, temperature logging and dilution testing in PL10Awhilst pumping the Bottom Barn abstraction well (≈ 35 m away)


Flow processes within the abstraction well

Unfortunately, the pump broke down before the loggingteam had time to carry out geophysical logging in theabstraction well (BBA). Consequently, it was restartedfive days later at a reduced rate of 4,750 m3/day. The ratereduction was required for operational reasons and wasunfortunate as it made direct comparison with the results

from PL10A more problematic. Nevertheless, Fig. 6shows gamma, temperature, fluid electrical conductivity(FEC) and impeller flowmeter logging under pumped andambient conditions. The gamma log indicates the eleva-tion of the Chalk Rock horizon to be a little higher at 28mAOD than found in PL10A. The temperature log isrelatively flat although there is evidence of warming at23.6 mAOD where the pump is located. Under ambient

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Fig. 6 Gamma, temperature, fluid electrical conductivity and impeller flowmeter logging in BBA. Note that this logging was undertaken 5days after the previously discussed pumping test and the BBA was pumped at a reduced rate of 4,750 m3/day

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Background2– 8min22– 29min74– 81min283– 293min461– 468min587– 593min

~2 m3/day

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Fig. 5 Flow logging, temperature logging and dilution testing in PL10A under ambient conditions


conditions, the FEC log shows a distinct step change at 45mAOD, which is replaced under pumped conditions bythree separate changes at 48, 61 and 82 mAOD. Thesechanges are likely to mark the main flowing horizons.

Figure 6d shows impeller flowmeter data. Underambient conditions, flow rates are comparable with thoseobserved in PL10A. Under pumped conditions, it appearsthat 2,000 m3/day enters the borehole between 82 and79 mAOD, below which there is a steady increase indown-flow to 61 mAOD. At this point, a flow ofapproximately 3,600 m3/day is achieved, which isincreased to 4,750 m3/day by 48 mAOD. There isconsiderable uncertainty over this interpretation becausethe variability in borehole diameter is unknown. Never-theless, the significant fluctuations about clear trends arebelieved to be largely due to borehole diameter variability.A caliper log was not available so a constant boreholediameter of 0.762 m was assumed (based on the originalcompletion report). However, as the abstraction boreholewas acidized during development to increase the yield(Harker 1974), it would be reasonable to assume thatvariations in diameter were accentuated and that activefractures were opened significantly by this process. Theacidization process would have depressed the water tableconsiderably and pushed the acid well into the Chalkalong open fractures, increasing the permeability greatly.

Dilution testing

Dilution tests were also performed to complement thelogged flow data from PL10A (see Figs. 4c and 5c). Theseinvolve lowering a fluid electrical conductivity (FEC)probe down the borehole to obtain a measure ofbackground conductivity with depth. A tube is lowereddown to the base of the borehole and filled with a well-mixed saline solution. The tube is then retrieved so as toprovide a close to uniform, elevated FEC along theborehole. As water enters and leaves the borehole vianatural flow horizons the saline solution is diluted. Therate of dilution is then monitored by subsequent FEClogging. The result is a series of FEC profiles for a rangeof different times.

Dilution test data can be inverted to acquire flow ratesassociated with discrete flow horizons using a dilution testmodel. Such models generally assume steady-state flowand that the borehole is fully mixed laterally. In this way,solute concentrations within the borehole can be describedby a one-dimensional advection dispersion equationsubjected to discrete sources and sinks associated withflowing horizons (Tsang et al. 1990).

Most studies have looked at dilution-test modelinversions for pumped wells (Tsang et al. 1990; Tsangand Doughty 2003; Evans 1995; Karasaki et al. 2000;Doughty 2005). This is generally straightforward; provid-ing the pumping rate is large enough, only inflowingfeatures are present. These can be easily located at thebeginning of the test as discrete dilution features.However, when the borehole is not directly pumped (as

is the case for both ambient and pumped conditions in thispaper), the presence of outflowing horizons is likely.Unfortunately, outflow locations are not apparent untillater on in the test, by which time the conductivity profilesare generally complex due to the interactions differentfeatures (Doughty 2005). Therefore, outflow horizons, andconsequently non-pumped wells, are much harder tointerpret (Michalski and Klepp 1990; Williams et al.2006; Mathias et al. 2007).

Pumped conditionsNote that the pumped condition did not involve pumpingPL10A, but a neighboring abstraction well 35 m away(BBA). The dilution test was undertaken once pseudosteady-state conditions had been achieved giving steadyflow both in the vicinity of the observation well andwithin the open borehole—this was also the case for asimilar test undertaken during ambient (i.e. no pumping)conditions. An analysis of the flowmeter and temperaturedata shows that inflows appear to occur at 10 and 27mAOD, and outflows at 57 and 74 mAOD. Inspection ofthe dilution test data indicates that an additional inflowprobably exists at 79 mAOD. Using a model similar to thatof Tsang et al. (1990), Mathias et al. (2007) obtained the setof calibrated inflows and outflows listed in the flow chart tothe right of the dilution test data (Fig. 4c). The comparisonbetween the resulting simulated and observed upflow andsalt concentration data is very convincing (see Fig. 4a, c).

From these results, it is clear that water-table observa-tions made in PL10A whilst pumping, do not necessarilyreflect the overall aquifer response. Rather, they representthe integrated response of the four discrete flow horizonsand the upflow from the base of the borehole.

Ambient conditionsThe dilution test performed under ambient conditions ismuch harder to interpret (Fig. 5c). There is definitely anupflow from the base; most of which leaves the boreholeat 57 mAOD. The difficulty arises in the upper region ofthe borehole (>57 mAOD). At a glance, it appears thatthere are two major inflows at 74 and 79 mAOD, whichpush the salt down to the outflow at 57 mAOD. However,this conflicts with the heat-pulse flowmeter and tempera-ture data (compare Fig. 5a, b), which suggest that there isvery low vertical flow in this region. Furthermore,although salt arising from the bottom of the hole initiallylooks as though it does not pass the 57 mAOD horizon,the final profile recorded after 587 min shows somepassing (subsequent testing has shown that this feature isrepeatable). This implies that the vertical flow above 57mAOD is very small in an upward direction, this isconfirmed by the heat-pulse measurement at 59 mAOD,but which is in complete contrast to the impellerflowmeter data. Therefore, it is assumed that the dilutiontaking place in the upper region is due to a complexdistribution of cross-flow, with major contributions at 74and 79 mAOD. As they are specifically designed for


vertical flow, the cross-flows are not recorded at all by theheat pulse flowmeter and lead to erroneous results in theimpeller measurements.

Due to the number of degrees of freedom, it is difficultto delineate the vertical distribution of cross-flow using theaforementioned dilution test model. However, an estimateof the total cross-flow, Qc [L3T–1] in that region can beobtained using the analytical solution of Drost et al. (1968)

c� c0ci � c0

¼ exp � Vt

Qc

� �ð1Þ

where c [ML−3], c0 [ML−3] and ci [ML−3] are the meancurrent, mean background and mean initial salt concen-trations respectively, V [L3] is volume of borehole underconsideration and t [T] is time after tracer injection.

Figure 7 shows a plot of mean concentration againsttime in borehole PL10A for z>57 mAOD under ambientconditions. Interestingly it does not converge on to themean background value, c0 , during the time studied. Thisis because salt is moving up (albeit at a very slow rate)past the 57 mAOD horizon. Therefore, when fitting theDrost et al. (1968) formula, the c0 parameter should beconsidered unknown.

If c0 and ci are known, Eq. (1) can be fitted to the datausing linear regression (by applying a loge transformationto the concentration data). However, because this is notthe case, a non-linear method is required. Specifically, theRMSE (root mean squared error)

RMSE ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

N

XNn¼1

cn � cobs;n� �2

vuut ð2Þ

was minimized using a simplex search method availablewith MATLAB called FMINSEARCH. N [–] is thenumber of data samples, cn [ML−3] and cobs;n [ML−3] arethe nth modelled and observed concentration values.

A plot of the calibrated curve alongside the data isshown in Fig. 6. The final parameter and RMSE valueswere Qc/V=0.015 min−1, c0=0.48 kg/m3 and RMSE =0.02 kg/m3. The ci was estimated by averaging the 2–8-min profile. From the calliper log, the volume of thisportion of the borehole was calculated to be V=0.97 m3.Therefore, the estimated value of total cross-flow wasfound to be Qc=22 m3/day.

Implications for transmissivity

The above-calculated value of cross-flow, in conjunctionwith the local hydraulic gradient, can be used to calculatean additional estimate of aquifer transmissivity that isindependent of the perturbation caused by pumping BBA.From the water-level elevations in PL10A, PL10B andPL10E prior to pumping BBA, the local hydraulicgradient, Jx [–] was estimated to be 1/(224 ± 53) (erroris based on 0.5 cm error on water level elevations). Anestimate of the regional groundwater flow, q [L3T−1L−1]can be obtained from q = Qc/(αD) where D [L] is theborehole diameter and α [–] is a dimensionless boreholefactor. Assuming that the well is perfectly circular and theaquifer is isotropic and homogenous, Bidaux and Tsang(1991) calculated that α=2. From the caliper log (Fig. 2a)the average diameter of PL10A over the region 57 mAOD< z<86 mAOD was 0.206 m. It follows that an estimate ofthe regional groundwater flow around PL10A is 22/(2 x0.206) = 53.4 m2/day. Applying Darcy’s Law then leads toa transmissivity estimate of 11,945 ± 974 m2/day, an orderof magnitude larger than the values obtained from thepumping test analysis (in Fig. 3) and outside the nationalstatistical distributions presented by MacDonald and Allen(2001). However, for a well-developed borehole, Bidauxand Tsang (1991) suggest that α might be more around 5,which leads to a more realistic transmissivity value of4,778 ± 390 m2/day.

0 100 200 300 400 500 6000

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

Time (min)

Mea

n sa

linity

(kg

/m3 )

(for

z >

57

mA

OD

)

Drost (1968)Observed dataObserved background

Fig. 7 Plot of mean concentration against time in borehole PL10Afor z>57 mAOD under ambient conditions

N E S W N60.75

61

61.25

Ele

vatio

n (m

AO

D)

∆ Z = 0.15 m

Strike = 151o

(θ1, z

1)

(θ2, z

2)

(θ3, z

3)

Fig. 8 An example of a sine wave fit to a fracture in boreholePL10A


Given the difference in flow distributions in PL10Aunder pumped and ambient conditions, the discrepancy intransmissivity estimates is not surprising. Under pumpedconditions, flow was concentrated in just four discretehorizons, where as under ambient conditions, flowappeared to be distributed over a region of around 29 mthickness; however, it seems likely that most cross-flowoccurs above 79 mAOD. However, if this was really thecase, it is expected that the integrated value of the packertest results should also be of the order 5,000 m2/day. Thepacker test data in Fig. 2d would therefore suggest thatthere must be features above those measured of signifi-cantly greater permeability. Unfortunately, it was notpossible to observe these as the borehole at this elevationwas too wide for the packers.

Note that PL10A was chosen for the detailed discus-sion because we had the most information about it. Theother boreholes did not have workable televiewer logs andadequate packer test coverage. PL10B was also dilutiontested (see Mathias et al. 2007). Under pumped conditionsit behaved very similarly to PL10A. Under ambientconditions it behaved in a more complex way showingevidence of simultaneous down and cross-flow.

Summary and conclusions

This integrated study has revealed significant new insightsinto the behavior of groundwater flow and head in anobservation and abstraction borehole in the UK fracturedChalk aquifer under pumped and ambient conditions.Under pumped conditions, the system behaved in arelatively straightforward manner flow being mainlyconcentrated in four discrete flow horizons. Furthermore,excellent correspondence was observed between the threemethods of borehole flow velocity measurement: impellerflowmeter, heat-pulse flowmeter and dilution test inver-sion. Under ambient conditions the system appeared muchmore complicated. Specifically, in the upper half of theborehole, the impeller flowmeter suggested a substantialdownward flow, the heat-pulse flowmeter suggested aclose to negligible upward flow, whilst the dilution testingprovided evidence of significant dilution. It was concludedthat this was due to the significant cross-flow occurringover a region of 29 m thickness. Analysis of drawdowndata, recovery data and a Drost analysis of the ambientcrossflow data yielded aquifer transmissivity estimates of2,049, 2,928 and > 4,388 m2/day, respectively. Thediscrepancy between the drawdown and recovery estimatesis assumed to be caused by non-linear head-lossesassociated with turbulence and inertial effects. The differ-ence between the pumping test and Drost results was thenexplained by the groundwater flow during pumpingbypassing this aforementioned 29 m region of aquifer.

Changes in observation-well flow profiles induced bypumping in another well are primarily thought to occurdue to changes in the head distribution of the large-scaleflowpaths (Le Borgne et al. 2006). Previously, thisphenomenon has been exploited to identify and charac-

terize those features that are directly connected to theabstraction well (Williams and Paillet 2002; Le Borgne etal. 2006). However, in many instances, aquifer parametersare sought for modeling groundwater or catchmentbehavior away from the presence of abstraction wells.These might, for example, be to evaluate water resources,minimum environmental stream flows or responses toextreme events (droughts and floods). This emphasises thegreat care that must be taken in the extrapolation ofpumping test results to ambient flow conditions. Themarked change in flow pathways also implies that similarcaution is required when applying transport parametersobtained during pumping to such conditions.

Acknowledgements Funding through the NERC LOCAR researchprogram is gratefully acknowledged (project NER/T/S/2001/00941). The authors would like to thank T. Scott at the EnvironmentAgency, UK, for access to and use of the Bottom Barn abstractionwell. The assistance of L. Maurice, D. Buckley, and I. Woods fromthe British Geological Survey for help in collecting the field data isalso gratefully acknowledged.

Appendix

Details of the strike and dip program are as follows. Afracture is identified from a visual inspection of the OTVbitmap image. The user then selects three points anywherealong the fracture intersect: (θ1, z1), (θ2, z2) and (θ3, z3),where 0 < θ<2π (i.e. north = 0 and south = π) and z [L] iselevation. The program then superimposes the sine wave

z ¼ Dz sin q þ að Þ þ z0 ð3Þ

where

Dz ¼ a sec að Þ ð4Þ

tan að Þ ¼ �b=a ð5Þ

z0 ¼ z3 sin q1 � q2ð Þ þ z2 sin q3 � q1ð Þ þ z1 sin q2 � q3ð Þsin q1 � q2ð Þ þ sin q3 � q1ð Þ þ sin q2 � q3ð Þ

ð6Þand

a ¼ z3 � z2ð Þ cos �1ð Þ þ z1 � z3ð Þ cos �2ð Þ þ z2 � z1ð Þ cos �3ð Þsin �1 � �2ð Þ þ sin �3 � �1ð Þ þ sin �2 � �3ð Þ

ð7Þ

b ¼ z3 � z2ð Þ sin �1ð Þ þ z1 � z3ð Þ sin �2ð Þ þ z2 � z1ð Þ sin �3ð Þsin �1 � �2ð Þ þ sin �3 � �1ð Þ þ sin �2 � �3ð Þ

ð8ÞThe three points can then be moved independently, and

the sine wave automatically corrects itself to fit them. Theuser can keep moving the points until an appropriatevisual fit between the sine wave and the fracture intersectis achieved (see Fig. 8). The final values of (θ1, z1), (θ2, z2)


and (θ3, z3) are subsequently stored. The strike and dip ofthe fracture can then be obtained from

strike ¼ �=2� �; Dz < 03�=2� �; Dz � 0

�ð9Þ

dip ¼ arctan 2 Dzj j=Dð Þ ð10Þ

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