GroundwaJer. Past Achie1.ements and Fw..re ChaJ1enges. Sii1« at (ecs) i; 2C(X}Eakma. ~ ,.. ~ gq 5i5C!JTs:Ji

Droundwater reservoir characterization based on pumping test curve

diagnosis in fractured fonnation

LBardenhagenlJeparrmenta/Wo/er Affairs, WindJwek,Namibia

ABSTRACT: In this paper methods and techniques for the diagnosis of pumping tests in fractured aquifersare reviewed and extended. These techniques, which include the comparison of drawdown and recovery data,straight-line analysis, special plotS, derivatives, and pseudo-skin analysis are demonstrated on a continuousfractured model (double porosity case) and a discontinuous model (single fracture case) using theoretical andpractical examples.

1 INTRODUCTION

Pumping tests are the most important tool for theaquifer investigation in the groundwater industry, asthey are the only method that provides informationon the hydraulic behavior of the well, and reservoirboundaries. These are essential information for anefficient aquifer and well field management mId fre-quently, togetlter with drilling results, are the onlyinformation available for. tlte establishment ofgroundwater extraction schemes. To achieve reliablereservoir information in fractured aquifers, a soundunderstanding of tlte drawdown behavior is of highimportance. A detailed diagnosis of drawdown datain combination witlt geological data can help tocomprehend tlte reactions in a llactured aquifer. Thispaper will briefly review the two important and

- well-known models for fractured aquifers, the con-tinuous model for double porosity or natural frac-lUred aquifers and the discontinuous model for asingle fracture or fault embedded in a homogenousmatrix. These models will be used to demonslratethe diagnostic tools available to identify tlte differentflow phases tltat can occur during a pumping test in. fractured environment. Field data will be presentedto illustrate and discuss some of these cases.

2 THEORY

2.1 Double porosity models

The concept of double porosity introduced by8arenblatt et al. (1960) considers homogenous dis-lributed conductive fractures embedded in a ho-mogenous distributed matrix. Two matrix types are

generally discussed: tlte spherical block matri,x'(Warren & Root 1964) used to represent aquiferslike quartzite and tlte layered matrix (Kazemi 1969)adopted for example for sandstones with beddingplanes. Commonly a pseudo-steady state block-to-fracture flow is assumed, which is a special case oftransient flow reslricted by skin, as illustrated byMoench (1984). ,

Moench (1984) considers that two representativeelementary volumes (REV), one for ~ fractu&sand'one for the matrix, are necessaryJor tlte matlte-matical description of tlte flow in such aquifers. Theclassic concept of double porosity cannot be appliedif tlte cone Qf depression is not considerably largertItan botlt REV because tlte influence of tlte singleftactures is not negligible as demonstrated by Wei etal. (1998).

The typical drawdown curve in a double porosityaquifer is shown in Figure 1. Initially, mainly tltefracture network releases water and tlte drawdown ischaracterized by a straight line in a semi logarithmic(scmilog) plot. The flattening of the curve is origi-nated by the ever-increasing additional contributionfrom the matrix. Thc later drawdown is the responseof tlte matrix alone, which. is represented by aslraight line parallel to tlte initial one in the semilogplot. In a double logarithmic (log-log) plot, botlt theinitial and tlte late drawdowns are characterized byTheis curves shifted horizontally from each oilier.The distance between tlte two parallels or two Theiscurves depends on .the fracture/matrix storage coef-ficient ratio.

Both tlte pseudo-steady state and transient modelsshow an almost horizontal flattening when block-to-fissure skin is present. The flattening in tlte transientmodel witltout block to fissure skin is not horizontal.

it,

. 81

It has a slope of half the slope of the two parallels(Fig. 1).

0

E..

4

8

9-lOO 10.' 10"

I (mini

Figure 1. Drawdown in slab-shaped double porosity aquiferand transient block to fissure flow, A = fracture/formation skin-factor of 5. B = fracture/formation skin-factor ofO.

2.2 Singlefracture models

In Iow permeability rock, features like fractures,faults, dykes, or bedding plains can represent zonesof high permeability that act as conduits. Basicallyfive models can be applied for these features:

Finite vertical fracture with infinite fracture con-ductivity (Gringarten et al. 1974)Finite vertical fracture with finite fracture con-ductivity (Cinco-Ley & Samaniego 1978)Infinite vertical fracture with finite fracture con-ductivity (Boehmer & Boonstra 1986dyke/formation m'6del) .

Finite horizontal fracture with infinite conductiv-ity (Gringarten & Ramey 1974)Finite horizontal fracture with finite conductivity(Valk6 & Economides 1997)

Whether a vertical feature is finite or infiniteconductive depends on the relative conductivity Crdefined as:

Cr=Kr'w/(7t'Km'Xr) [-] (1)

where:

Kr =conductivity of the fracture [lit]w - fracture'swidth[I]Km - conductivity of the matrix [I/t]Xr .. holf-Iength of the frneture [I]

Cll1co-LtlY& Snll1nnlcgo(l97K) dol1H1nMlrnlcdthat for nil practicalpurposesa single vertical frae.ture with Cr ~ 100could be regardedas an infiniteconductive fracture that coincides with the Gringar-ten et nl. (\ 974) Infinite nux model fOf Infinite con.dudlvl! tfnctures.

IfCf < \00. then the fracture has finite conductiv-

\~. 1\\,,-'t""\.~ \\\t'lM~ thnt ro"!1.\t'~~ tht t~\\\~ l'1.""

dUtti\'ity "ms\ be applied (Cinco.Ley&. Snmn-niego 1978,Boehmer& Boonstra1986),

Additionally, Cr is used to classify the differentflow phases that can occur while pumping from. avertical fracture as follows:- Cr < 0.1, bilinear flow (after well bore storage or

linear fracture flow), thereafter pseudo-radialflow

- . 0.1 :s Cr < 100, bilinear flow, linear formationflow appears masked in the transition zone

- Cr ~ lOO,linear formation flowWhen these single vertical fractures are repre-

sented in a log-log plot, the following characteristicscan be depicted (Cinco-Ley & Samaniego (198Ia):

Linear fracture flow appears as a straight-linewith slope 0.5 in the very early time dataBilinear flow is plotted as a straight-line with ...

slope 0.25 in the early time data (Fig. 2)Linear formation flow shows a str!rightline withslope 0.5 in the intermediate time data (Fig. 2).

The radial-acting flow phase plots on a straightline in a semilog plot. .

~.

I (minI

Figure 2, Drawdown diagnoses for vertical fractures with dif-ferent relative conductivity Cr.

The characteristic slopes found for a single hori-zontal fracture with infinite conductivity (Gringarten& Ramey 1974)are depending on the dimensionlessformation thickness h.Jdefined as

h.J=h ' Kr I(re Kv) [-] (2)

where:

h =reservoir thickness [I]rr ...fractureradius[I]Kr .. radialCrnctureconductivity [1/1]Ky '" wrliclIl f(mnnlionconductivity [1/11

When hi.< 1, the following characteristicnowphasesareobservedin a log-logplot:

Very early time data shows a slope of 1 that in-dicntcsfmct\l\'Cstorn~cnowEnt'ly time lIntn showstI slopeot' 0,5 tOr IIn@l\tnow

h\tt'n\\C\\i:\tt'ti\\\~ dnh\ ~h\,,\~ :\ ~\\'t'Cof \ ~I\\I\tbr tntl\sict\tnow innuct\ccJby the limitedt~ture reservoir

82

The flow phases for h.t~ 1, when represented in alog-log plot. are reduced to a slope of 0.5 from veryearly time data to intermediate time data, indicatinglinear flow.

However, due to the very short early time period,this phase might be masked by wellbore storage orsimplY be missed. Va1k6& Economides (1997) in-vestigated the behavior of a horizontal penny-shapedfracture with finite conductivity, but did not findcharacteristic slopes over the dimensionless time t.Jperiod in the range ofO.! to 100.

In all these cases the radial-acting flow phasecommences approximately at the dimensionless timet.J==15, which is defined as:

t.J=T.tI(S'x() [-]

where:t =Real time [t]T =Formation transmissivity [l2/t]S =Formation storage coefficient [-]

Only after the radial~acting flow phase is reachedcan the common analysis methods for primary aqui-fers be applied to determine the transmissivity T,e.g. Jacob or Thcis. The storage coefficient S can beestimated with equation (3), if the fracture half-length Xc is known. Figure 3 illustrates the ex-tremely large error made in the calculation of Swhen the Jacob straight-line method for time draw-down data is applied to.the data measured in an ob-servation well located near an infinite conductivevertical fracture with uniform flux. The straight-linemethod is only applicable when the distance of theobservation well is at least 5 times that of the frac-ture half-length (which is in fact the REV of such asystem).

100

10

to .. ......

,... f/ .......-'-....---:!:,i.. 1

0

0 2 3Dlm lonl... dllWlCl If'"

Figure 3. Deviation from the real storage coefficient calculated

using the lacob's straight-line method for data of the radial-acting flow phase in obserVation wells in the vicinity of a sin-

gle vertical infmite conductive fracture with uniform flux.

One must bear in mind that the determination ofthe storage coefficient S is a function of its locationand not the extraction time although the radial-actingflow phase in the observa~on well has been reached!

However, Figure 3 can also be used to either deter-mine the correct storage coefficient if the relativeposition of the observation well to the fracture isknown or to determine the fracture half-length if thestorage coefficient is known.

The influence of the fracture storage can be de-. scribedwith the relativestoragecapacityCOf afterRamey & Gringarten (1976) defined as:

COf= Sf' w/(S' xc) [-] (4)

where Sc =Fracture storage coefficient [-].

(3)

Figure 4 shows the drawdown in a vertical frac-ture with infmite conductivi~ and infinite flux withCOf between 10-0and IQ-IO.All curves commencewith linear flow (slope 0.5). All curves withCOf < 10-4describe the drawdown in high storagecapacity fractures and their behavior is' significantlydifferent to that of well bore storage. In these curvesthe slope of 0.5 indicates linear fracture flow and notlinear formation flow and indicates that all dis-charged water is provided solely by the fracture. The

. curves show a transitionzone characterizedby anincreasing slope from 0.5 to I with increasing COfas a result of the leakage from the formation thatgradually replaces the storage in the fl!icture. Oncethe radial-acting flow phase is.reached, all water isprovided by the formation. ,... .

,..'2LFa__""", 1Iopo0.5

,,," ILM a Inoor fonnllion ""'" IIopo 0.5

Ba""""" b<uIdaty, IIopo 11...0.'.0-1

1.0-4

1.0-$

.....'.""..1'.""""'.0-4'.""."".."".0'.."'...2

Id 1.1

Figure 4. Drawdown in an infinite conductive vertical fracture(Cr - 10000) with various relative fracture capacity CDf (di-mensionless dJ-awdown pd - 11 . T . 5/(2 . Q) [-] where: s -drawdown,Q ~ discharge rate, T - formation transmissivity)

The drawdown curve for COf =10-0in Figure 4coincides exactly with the drawdown curve observedin a isolated single fracture for the early time dataand partly with the transient phase. It confums thefact that the transition zone is caused by the limitedextent of the fmite fracture because the waterpumped from such a isolated single fracture is pro-vided only by the fracture storage. This observationleads to the interpretation that these effects i.e.,wellbore storage, fracture storage, and the closedboundary reservoir can be described by the sameprinciple of pumping from a limited reservoir.

83

3 DIAGNOSIS METIIODS AND TOOLS

The following methods and tools can be applied for.the diagnose of pumping test data in fractured aqui-fu~: .

Comparison of drawdown and recovery dataPseudo-skin analysisStraight-line analysis in log-log and semilogplotsSpecial plotsFirst and second derivative of the drawdown data

3.1 Comparison of drawdown and recovery phase

The fIrSt check during a pumping test data evalua-tion should be the comparison of the drawdown andrecovery behavior of the data if both are available.Due to the superimposing theory, both should showthe same principal curve shapes. If a flattening isobserved in the drawdown curve, the same typicalflattening must appear in the recovery data. If this isnot the case, the flattening in the drawdown wascaused by:

Variation of the discharge rate during the draw-down phaseDischarge from a closed reservoir (limited reser-voir) .

In the first case, only the recovery data after atime correction (Birsoy & Summers 1980) can beused. In the second case, the late time recovery datawill show a horizontal flattening instead of a steepincreaseas it is observedduringthe latetimedataofthe drawdown phase (Streltsowa 1988). This flatten-ing of the recovery data should never be confusedwith a leaky boundary. A leaky boundary would leadto a fully recovery, which is never the c~e in a lim-ited reservoir.

3.2 Pseudo-skin anf!lysis

A well located within or in the vicinity of a conduit(if the distance is below the REV) shows less draw-down than expected for wells in a homogeneousformation. This effect is known as pseudo-skin(Gringarten & Ramey 1974). The application of theskin determination methods as in wells situated inhomogenous aquifers would lead to a negative skin-factor sf [-]. The skin factor sf and the drilled radiusrw are related to the effective radius roffas follows(Sabet 1991):

roff= rw.e-sf [I] (5)

The equation shows that a negative skin-factor(well in a fracture) would lead to an effective radiusof the well larger than the real radius. In the case ofa positive skin-factor (well in homogenous aquifer)the well is effectively acting with a radius smallerthan the actual one.

However, the pseudo-skin effect can be used todetermine whether a well is located in a fracturezone or not, due to the fact that, in principle, nonegative skin factor or enlarged effective radius canbe observed in a primary or continuous fractured aq-ui(er. One useful application is for example to dis-tinguish between the drawdown of a horizontal frac-ture with infinite conductivity and the drawdown ofa well in a homogenous aquifer with wellborestor-age. Unfortunately this holds true only for h.i:S 1where the skin-factor is always negative, because theskin-factor increases towards positive values withh.i> I. Similarly, the method can be used for verticalfeatures.

3.3 Straight-line analysis

As already discussed most of the flow phases thatappear during a pumping test in a fractured aquifershow characteristic straight-lines either in a log-logor in a semilog plot. However, the log-log plot pro-vides additional information as follows:

Well bore storage shows a slope of 1Fracture storage shows a slope between 0.5 and1 for linear flow and 0.25 to 1 for bilinear flow.Two parallel closed boundaries show a slope 0.5.

0 (Ehlig-Economides & Economides 1985)Three equidistant closed boundaries U-shapedshow a slope 0.5Limited reservoir (four closed boundaries) showsa slope of 1.

The semilog plot provides additional informationregarding the presence of negative boundaries: .

One closed boundary doubles the slope of theradial-acting flow straight-line

. Two perpendicularsclosedboundaryquadruplesthe slopeof the radial-actingflowstraight-line..

Only one straight-line will be observed when allthe boundaries .are located equidistant to the pump-ing well. If this is not the case, each boundary willincrease the slope of the previous straight-linereached. .

3.4 Special plots

Besides ~e semilog and log-log plots, the followingthree additional plots are very useful for the diag-nose of pumping test data (Cinco-Ley & Samaniego1981b):

Linear drawdown ve~uS square root of timeLinear drawdown ve~us fourth square root oftimeLinear drawdown versus one divided by squareroot oftime

The first plot is useful for the determination of thelinear flow behavior. The drawdown data of linearand bilinear phases will plot on a straight line thatcommences at the origin of the diagram. In the sec-ond plot the drawdown data of the bilinear flow

84

phase will plot on a straight line starting at the ori-gin. The drawdown data of a spherical flow will ploton a straight line that commences in the origin in thethirdplot. .

Cinco-Ley & Samaniego (l981b) demonstratedthat the first two diagrams are very useful to deter-mine skin effects in drawdown data of wells in sin-gle fractures with either linear or bilinear drawdownbehavior. Such skin effects cause an additionaldrawdown that increases clogging phenomena and inextreme cases can even destroy the stimulation ef-fect of drilling. in a fracture zone (Economides &Nolte 1989).

Cinco-Ley & Samaniego (1981b) found that, dueto skin effects, the early time linear flow data in alog-log plot are represented as an almost horizontalOnethat develops into the radial-acting phase (bilin-car flow would plot similarly). Plotting the samedata in a linear drawdown versus square root of timediagram will also show a straight-line, but will beshifted downwards from the origin. Both authorsstated that, by data from the pumped well only, it isnot possible to. obtain a Unique solution for the de-termination of the skin location, which could be 10-c:atedat the well, or between fracture and formation,or at both. However, Bardenhagen (1999) showed anunique evaluation method for the skin location for asingle vertical fault with a relative conductivityCr ~ 100 by using the plot linear drawdown versussquare root of time for drawdown data of a pumpedwell and an observation well located in the samefiwlt.

All these plots can also be applied for horizontalfeatures as they are only related to the flow regime.

3.5 Derivatives

The additional use of curve derivatives is of great8dvantage because they are sensitive to smallchanges in the rlrawdown curve and are independentof skin effects, as illustrated in Figure 6. Usually, thederivative is plotted as (tW6.t . t), which providesthe following advantages:. All characteristic straight-line slopes remain the

same. Radial-acting flow phase is plotted as a horizon-

tal fuie, which eases the identification for thehuman eye

Unfortunately, derivatives applied to real data of-reo show too much noise. Smoothing of the deriva-tives would overcome this problem, but it cannot beensured that the applied mathematical algorithmwould not produce misleading artifacts. However,recovery data are usually less noisy as they are notiDfluenced by variations in the discharge rate andcan be used. Nevertheless, with some experienceeven noisy derivative curves can be interpreted.

!

4 FIELD EXAMPLES

4.1 Field example 1

Two boreholes located 133.5 m apart were sitedon a 15 km long, sub-vertical (77°S) fault zonecrossing the Fish River in the southern part of Na-mibia, which might be a potential recharge source.The fault partly separates two low yielding forma-tions composed at horizontal intercalated layers ofclaystone, siltstone and sandstone. Both boreholesintersect the fault at 27m below the surface. The wa-ter level in both boteholes rose immediately after thefault was struck at a level of 906.1 m amsl (8.3 mbelow surface in BHl and 5.3 m below surface inBH2). The airlift yield was estimated at more than100 m3fh in each borehole. Screens with 0.5 mmslots were installed to avoid borehole collapse. Fig-ure 5 shows the drawdown measured during one ofthe constant discharge tests. Only the drawdown inthe. observation well shows a slope of 0.5 indicatinglinear formation flow. However, the drawdown inthe pumped well starts almost horizontal and devel-opes at late time to radial-acting flow. This behavioris typical for a skin that is located at the well.

10

I.0.1

0.011 10 100 1000

11"*'1

Figure 5. Example for a restticted drawdown in a pumped well.The slope of.0.5 in the drawdown data of the observation wellindicates linear formation flow. Simulation for a vertical infi-nite conductive fracture with uniform flux results: T -200 m2/d; S = 0.0007; xf=.460 m; sf= 1.78.

10000 100000

4.2 Field example 2A borehole was drilled into the dolomites of the

Tsumeb area, northern Naplibia. The constant dis-charge test indicated a short period of linear flux to afracture in the early stages. Water strikes were re-corded at depths between 14m and 27 m below thewater table. As soon as the water level in thepumped well fell to the level of the rust water strikea significant increase in the drawdown was meas-ured, with a further increase as the water level fellbelow to the second strike (Fig. 6). This behavior isa clear indication of over-abstracting at a rate of20 m3fh.However, due to unknown reasons an addi-tional drawdown of 7 m can be determined from thespecial plot.

85

E.

30-0.0 10.0 20.0

t~(mInJ~

Figure 6. Graphical skin evaluation using the linear flow periodof draw down curve.

5 CONCLUSION

It is demonstrated that pumping tests can providevarious types of useful information regarding thereservoir behavior of fractured rock aquifers, if reli-able data and principal structural geologicalinformation are available. Furthermore, it is shownthat only a detailed data analysis can producereliable results, using a combination of diagnosticmethods and tools. Some of the most importantfunctions are assuring data quality by comparingdrawdownand recoverydata.

Use pseqqo-skin analysis to overcome maskingor coinciilentaleffectsIdentify different flow regimes with detailedstraight-line diagnosis -Obtain skin effects with application of specialplotsUse derivatives from real data. This requiresmuch experience. Nevertheless, they are espe-cially useful to identify radial-acting flow, be-cause they are not affected by skin effects.

However, further investigations are necessary,especially for the Cjvaluationof data from pumpingtests performed in discontinuous aquifers below therepresentative elementary volume (REV).

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