Data in the Well Archive

GUNNARGUSTAFSON NG U-BU L L43 9,20 02- PAGE 21

Strategies for groundwater prospecting in hard rocks: a probabilistic approach

GUNNARGUSTAFSO N

Gustafson,G.2002:St rategiesforgroundwater prospecti nginhard rocks:aprobabi listicapproach.Norgesqeoloqiske undersekelseBulletin439,21-25.

Private wells infract ured, Precamb rian,crystalline rocks areimporta ntforruralareasandsmall communities in Sweden.Sincewellyieldsnormallyare small,systema ti capproaches to groundwaterprospecting are requiredin order to predict howto sitethe wells and whatcoststo expect.The proposed approach isto minim ise the sum of invest igat ionandexploitatio ncosts underthe assumptionofa lognormaldistributionofwellyields.The strategy involves the drillingof afairnumbe r of exploratory wells,ofwhichthebestare connected tothe supplysystem. Statistica ldataonwellyields,in this case from the SwedishWellArchive,arerequiredtosupportthe decisionsof pre-investigationsandexploratorywell drilling programmesthataresuggestedforsmall groundwaterusersand larger supplyschemes using this probabilisticapproach.

GunnarGustafson,DepartmentafGea/agy, Cha/mersUniversityofTechnalagy,S-41296Goteborq,Sweden.

Introduction

Some 10%of the Swedish population use their own private wells for domestic water supply.Most of these wells are drilled in Precambrian hardrocks that make up about 90% of the country'sbedrock.Annually,morethan 10,000new wells are drilled.Data on these wells are gathered in the National Well Archive, run by theSwedishGeological Survey (www.sgu.se/databaser/brunnsark_meny.htm).where today more than 200,000hard rock wellsare registered.Data from the Well Archive are frequently usedin regional studies and also in ad hoc approacheswhen siting bedrockwells.

Theext ensive use of wells in the crystalline basement (Gustafson&Krasny 1994)shows that the Swedish hard rock isan aquifer of significant value,albeit mostim portant for small users in rural areas.However,hard rocksalsoplay a role for water supply systems;and in that case what strategies should be usedfor groundwater prospecting?

Data in the Well Archive

Reporting of data to the Well Archive by well drillers has been compulsory in Sweden since 1974. Data comprise drilling date, yield,depth,soildepth and co-ordinatesin the Swedish survey system.The yield of thewells is normally det erminedwith asim pleair-lift testwith a duration of one to a few hours.It can also benoted thatthedrilling depth is commonly determined by the desiredyield,in thatwells are drilled until a yield of at least250IIh is reached or theyare abandoned after about 100 m depth.

The siting of thewells is normally governed by a desire to have the well close to the building and in an upstream direction from contaminant sources.In most cases no pro- fessional geological or geophysical work is made for the sit-

ing.The bulk ofthewells canthusbecon sid ered randomly site d,since theirposition isdeterm inedbythe bui ldingthey serve rat her than by hydrogeol og ical considerations. It must also be kept in mind that data accu racyislow becauseofthe approximatetesting andsam pling method s,but thereis no reason to suspect that thereis any syste mat ic bias in the data,and thusthe bulk of the wellswill givea reasonabl y good picture of the hydrogeolo gicalpropertiesof therock.

Yield statistics

Tested yieldsof the wells tend to be ap proximatel y logn or- mally distributed.A typical exam ple ofalogn ormalproba- bility plot of well yields, in this case a sam ple from the Uppsala area, Sweden, isshow nin Fig.1.As shown,itis also typicalthat very low and veryhigh yieldsdeviat efrom the straight distribution line mainly because of the imperfect testing methodology.This is most evide nt for low yields, since little effort will bepaidto awell that isconsid ereddry.

It may be debated whether theyield,Q,orthe specific capacity,Q/s_w,isthe right parameterto analysein this partic- ular case.In most aquifertypes,the specific capacity ispre- ferred since it is roughly proportionaltothetransmi ssivit y,T. However,in theSwedish crystallin erocksthereisa strong declin e of thehydraulic conductivity wit h depth (see e.g.

Ahlbom&Carlsson1988)which makesthe specifi c capacity approach dubious for the applied air-lifttestin g wherethe well is emptied moreor lessto its full depth.Thismeansthat the proportionality between the apparent specifi c capacit y and transmissivityis lost. For that reason the esti mate dyield, Q,is analysedin this paper.

Figure 2 shows the Cumulativ e Distribution Function (( OF) of the app roximate d lognorm al distr ibuti on of the

NG U - BU LL 439,2002 - PAGE 22 GUNNARGUSTAFSON

o

1 0.5 2.5 2 1.5 o

'"

o

<;

6

- ^o

^Cl

:;:t

.2 -0.5

o

-1 0'>

o

-1.5

:::::.. • • •

•• •

.' /'

•

Fig.1. Normalised CDF-plot of an approximately lognor- mal sample of 54 well yields in an area in Uppland.

Sweden. Log" mean,~"'"⁰= 2.30. Log" standard devia- tion,(J"",0= 0,6. Data from Pettersson (1987).

-2 -2.5

10 100 1000 10000

Fig.3.Comparison of CDFs of yieldsofwells sitedwitha VLF-surveyand a referencesample fromtheUppsala area.Data fromPett ersson(1987).

- - - - VLF-wells - - -Reference well s

100000 10000

100 1000 0.9

0.8 0.7

o 0.6 v 0.5

s!

_{et 0.4}

0.3 0.2 0.1

OL-- - - -...J

10

the difference betwe enthe groups.There is alsoa tendency forthe sp read to begreat er fo rthe less pervious rocks.

The importance of hydrogeological fieldwork and geophysics

Several low- co st approaches, i.e. lineam ent interpretation (Ericsson 1988,Wladis&Gustafson 1999),VLF measurements (Pet t ersson 1987) and sling ram electromagnetics (M Ollern 1988), havebeentakento increasethe success rate for well drillin g in Swed ish hard rocks. In the study by Pettersson (1987), a systematic comparison was made between yields ofwells sited on thebasis of a simpletectonicanalysisand Very Low Frequency (VLF) electro mag netic geophysical measurements of all wellsdril led inan area outside Uppsala.

The area isdom ina ted by intermediate granites (Up p sala granite)and has a total surfacearea of 3750 km'.Here,the rural wat er supply is based mainly on bedrock wells.The rather low enco unt ered yields have meant that VLF-mea - surements have been exten sively used as a basisfor siting. Figure3 show sCDFsof the yield sof the Vl.F-sitedwellsand 0.9

0.8 0.7

0- ^0.6

v_e 0.5

Q.et 0.4

0.3 0.2 0.1 0

10 100 1000 10000

yields for all Swedish hard rock wells based on data from 59,000 wells in the Swedish Well Arch ive (Fagerlind 1988).

Median for the population is

O ;

= 600 IIh and the average yield is

0

0

=

^{1643 IIh.}The large difference between the median and the average is the result of the skewed lo g nor- mal distribution.The distributioncan be compared to what is generally considered to be a successful wellfora single horne.O= 250 I/h.Thisis fulfilledfor abo ut80%ofthe bore- holesand,thus,there is,for pure statistical reasons,ample opportunity forwat er-di viners to take creditfor a successful well siting.

Fig.2.CDFof the approximateyielddistributionfor all Swedishhard- rock wellsbased ondata from Fagerlind(1988).

Relation between yield and lithology

There have been several effortsto correlate wellyieldsand rock type(see e.g.Carlsson & Carlstedt 1977,Liedholm 1988 and Ahlbom &Carlsson 1988). The generalresults of these st ud ies are thatbrittleacid rocks have a higher median yield than basic, ductile and more easilyweathered rocks.Median yields fallwithin an order of magnitude,abo ut400-1200IIh, and thespread within eachrock group is muchlarger than

GUNNAR GUSTAFSON NGU-BULL439,2002 - PA G E23

the reference population.VLF-siting gave an increased media n yield from 690 to 3600I/h.The difference between thepopulations was found to bestat ist icallysig nificant bya two -sampletest (Ra de&Westerg ren1990).As can be seen, the spread of the distribution s is large, indicatingthat there areseveralwellsin thereferencepopulationthat are good enoug h butalso thatsome of the VLF-wellscould be consid- eredasdry.

A siting strategy for the small user

The most likely yield of a log normal population is the medianvalue.Thismeansthatthere is a50%chanceofget- ting690 l/hormore inarandoml y sitedwell intheinvesti- gated area.The chanceofgetting more ismuch high er ina VLF-sited well, but howthatinfluencestheeconomyof the project canbe analysedwit ha simple riskanalysis.Therisk, or riskcost,R,isdefinedas theprob abilityof failure ofapro- ject,p.,multipliedby the econo micconsequences(cost)of a failure,

c,

^Thus:

R=pt-c, (1)

Ifwe drillthe well inarandomposition,thecostofafail- ure is thesameasthe costof drillinga drywell,B.lnthecase of aVLF-sited well, we also haveto add the invest igat ion cost,V, if thewellisdry.Ifweassumethat the drilling of a well costsB

=

20,000SEK, and wehave a need for a yield of 1000 I/h,we find from Fig. 3 that the probability of failure for the randomlysited wellisp,=P(Q<1000l/h)

=

0.6.The risk cost will then be:

Rw

=

0.6.20,000

=

12,000 5EK (2)

For theVLF-sited well the probability of failure isonly 0.15and the risk cost for thewellwill only be:

Rv =0.15·20,000

=

^{3,000 5EK (3)}

The obviousthing to do is to useVLF-siting if it costsless thanRw-Rv =9,0005EK.ln reality,thecompleterisk calcula- tion isa bit more complicatedsince thedesired yieldcanbe obtained from morethan one well.

Thestrategy for asmallwell user would then be to first check the data in theWellArchiveand if thereis a highprob-

abilityofsuccess- drill!In an area wit h lessperviou srocks, useasimple tectonic analysis combined wit h VLF for posi- tioningthe well.

A strategy for large users

For larger usersit is likely that a well-field ,i.e.two or more wells, willhave to beused.Inorder to opti mise this system wehavetoconsiderthatthewellswill have to be spread to allow for recharge,and thatthey have to be connected to thedistrib ut ion syste mandinstal ledwit h pumps, elect ricity supp ly,etc.

Assumethat:

• Bisthe cost ofdrilling a boreholethatlat er canbe used as a product ionwelland thatb boreholes are drilled dur- ingpre-investigatio n andexploit at ion.

• 1is thecostof connect ing a borehole to makeita pro- duct ion well and that iboreholes are connected to the production syste m.

• Thereis anaveragerelat ionbetween the costs sothat l=cB

Ourst rategywill betomini misethe cost:

C

=

bB+il

=

B(b

+

ic) given a demand0 (4)

Ournexttask isto esti mate the yieldsofNdrilled wells.

Given aCDFforalargenumberofwellssuch thatp(O<On)

=F[OJ,the probable yield forwellninanordered sequence of yieldsusing equal densitysampling in the CDFcan be esti mate d to be (Kite 1977):

On=F-l[nl(N+7)J (5)

Thus,it is possibleto construct acumul ativediagramof the sum of expect ed well yields star ting with the largest ones.Since thelognorm aldistrib ut ion is rather skewed one finds that the best wells contribu te proport ionally much moreto the sumand,what is moreimportant,the sumofthe i best wellsofalarge sample b will beconsiderablygreater than thesum of i randomlydrilled wells.

"LO(i,b)

= "2:F

^{1[(b-n+7)1(b+}7)J forn

=

1toi (6)

If theCDF for theVLF-w ells, wit h median 3600l/h and log sta ndard deviation 0.6,in the example above isused,

O -='''--- - - - - - - - - - -

^----l

S

:is' 100000 _{~1 6 wel l s}

0~ _ 8wells

~

:!2

- . -4wells

.S!>. 50000 _ 2wells

(5ra - -1well

I-

150000

Numberof boreholes,i

o

2 4 6 8 10 12 ^{Fig. 4.} Cumulat iveplot s

of predicted borehole yields from the i best wellsout of b drilled.

NGU-BULL 43 9 , 2002 - PAGE 24 GUNNARGUSTAFSON

Exp lanation of symbolsused

usanyt hingabout the rechargeconditions andwater qual- ity. These also have to be investigated,but since the well yield normally isthe limiti ng factor in the Swedish hard rocks, the approach gives agood basisfor str ategi c deci- sions.

cumulat ive plotsof the yield for i boreholes out ofbdrilled will be as showninFig.4.

If we assume thatthe need isQ

=

20,000 l/h

=

480 m3/d , we find that it is not likelythat we can cover itif we drilljust one ortwo wells.If we drill4wells we will probablyneed all 4 of them but withoutanysafetymargin. Ifwe drill 8 wells we might cover the need with one but mostprobably with two andif we drill16,one wellwill probablybe sufficient.

Going back to Equation 4 we will analyse what that means for the economy.Assuming a water need of 20,000 l/h,the drilling cost per well ofB=20,000 SEKand the cost factors c

=

^{3 and c}

=

5 we obtain the values of the cost func- tion C giveninTable 1.

Table1.Optimisationofcostfora wellsyst em.

Number of drilled Required numberof Cost function, Costfunction, borehol es,b co nnect ed boreholes,i C(SEK) c

=

^{3 C(SEK)} c

=

s

1 Notlikely,i>b 2 Not likely,i>b

4 4 320,000 480,000

8 2(1?) 280,000 360,000

16 1 380,000 410,000

The magnitudeof the costfactor c can be debated.The result s above are not too sensitive for that, as there is,in both cases, a minimum for 8 drilled exploratorywells.The analysis shows,however,thatit is better to siteanddrill a fair number of exploratorywells in a well organised drilling cam- paign than to drill them one by one.This isfurther enhanced by the fact thatan efficientsiting process and better prices for drillingcan be obtai ned for a campaign ofseveral bore- holes.

Symbol B b c

CDF C, nO]

N n

P,

o

0, Om 0, O/s.

R Rv Rw T V 11"",o 0""' 0 'L.O(i,b)

Unit (SEK) (-) (-)

(-) (SEK) (-)

(SEK)

(-) (-) (-)

(-) (I/h) (I/h) (I/h) (I/h) (m'/s) (SEK) (SEK) (SEK) (m'/s) (SEK) (lo g[I/h]) (-) (I/h)

The cost of drilling a well Num be rof exploratorywells Cost relat io nbet w een drillingand conne ct in g aborehole

Cumulativedistrib uti o n function Econo m ic consequencesofa failure Distribution funct ionfor a sample of wellyields

Co st ofconnec ti nga borehole to the supply syst em

Number ofconnected boreholes Tota lnumberofwells ina sample Seq uen t ialnumber of a wellin an ordered sam ple

Prob abilit y of failure Wellyield

Aver age well yieldof a sample Medi anwell yieldof a sample Yieldofwellnina sequence Specificcapaci ty

Riskco st

Risk cost for a VLF-sitedwell Risk cost for adry well Transm issivity

Investigati o n orsitingcost for a well MeanoflogarithmsofQ

Standarddeviatio n oflogarithmsofQ Sumof the yield of theibestwells outofb drilled

Conclusions

As Fagerlind (1988) pointed out,the crystalline bedrock of Sweden is an underestimated aquifer.The main reasons for this lie bothinthe conceptionthatthecryst allinebedrock is best suited for the rural water supply to single farms and othersmall uses,and that adequate strategiesfor ground- water prospecting have been lacking inthesehydraulically inhomogeneous rocks.A certainamount of economiccau- tion by those responsibleforwat er supplyin small commu- nitieshas also prevented extensiveexploratorydrillingcam- paigns ("please drill the best wells first"). However, the importance of the approach liesin the factthatitis possible to follow a strategy that isbased on a simple reasoningthat mostdecisionmakerscan accept.

Examples of the methodology proposed are the water works for the communities of Amotfors,Varrnland county, Sweden, and Rakkestad in SENorway, where the authorwas heavily involved in the groundwat er exploration.In both cases,groundwa terfrom the fractured crystalline rockswas shown to bethe most cost-effective system for the water supply.Finally,aword of caution - the approach doesnot tell

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