Specific Methods for the Evaluation of Hydraulic Properties in Fractured Hard-rock Aquifers

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1 Speciic Methods o the Evaluation o Hydaulic Popeties in Factued Had-ock Aquies Jean-Chistophe Maéchal, Benoît Dewandel,. Subahmanyam, Ricado Toi To cite this vesion: Jean-Chistophe Maéchal, Benoît Dewandel,. Subahmanyam, Ricado Toi. Speciic Methods o the Evaluation o Hydaulic Popeties in Factued Had-ock Aquies. Cuent Science, Indian Academy o Sciences, 003, 85 (4), pp <hal > HAL Id: hal Submitted on 8 Ma 010 HAL is a multi-disciplinay open access achive o the deposit and dissemination o scientiic eseach documents, whethe they ae published o not. The documents may come om teaching and eseach institutions in Fance o aboad, o om public o pivate eseach centes. L achive ouvete pluidisciplinaie HAL, est destinée au dépôt et à la diusion de documents scientiiques de niveau echeche, publiés ou non, émanant des établissements d enseignement et de echeche ançais ou étanges, des laboatoies publics ou pivés.

2 Speciic Methods o the Evaluation o Hydaulic Popeties in Factued Had-ock Aquies J.C. Maéchal a,*, B. Dewandel a,. Subahmanyam b and R. Toi a a BRGM, WATER Depatment, Unit «Wate esouces, Discontinuous media», Indo-Fench Cente o Goundwate Reseach, NGRI, Uppal Road, Hydeabad, India b National Geophysical Reseach Institute, Indo-Fench Cente o Goundwate Reseach, Uppal Road, Hydeabad, India * Coespondence: Indo-Fench Cente o Goundwate Reseach, National Geophysical Reseach Institute, Uppal Road, Hydeabad, India, Tel: , Fax: , maechal@ngi.es.in Abstact: Blocs undelined by actues netwoks mainly compose had-ock aquies. The complexity o lows though actues makes inadequate the use o classical techniques o the intepetation o hydaulic tests. Fou dieent methods, well adapted to the complexity o goundwate lows in had-ock aquies, ae pesented o pumping wells and/o obsevation wells intepetations. The Neuman method is suited o unconined anisotopic aquies while Gingaten method is developed o the case o a single hoizontal actue. The thid method (Waen and Root) takes into consideation the heteogeneity o the medium, allowing the intoduction o a double poosity aquie (tansmissive actues and capacitive matix). Finally, the outh method, Bake theoy, assesses the low dimension elated to spatial distibution o conductive actues and thei connectivity. All these methods ae pesented and illustated on pumping tests caied out in a ganite teain, south o Hydeabad, India. eywods: hydogeology, hydaulic test, had-ock, anisotopy, heteogeneity INTRODUCTION Lage tacts o South India ae undelained by had cystalline ock teain (ganite, gneiss, basalt ). The aea also is classiied as semiaid to aid, geneally pone to dought conditions, equiing optimal management o goundwate esouces against inceasing demands o wate o vaious activities (agicultual, industial, domestic). Estimating the hydaulic chaactes o wate beaing layes is an essential pat o goundwate studies. The most eective way o detemining these chaacteistics is to conduct and analyse in-situ hydaulic tests. One o the ealy ecods o pumping tests on a lage scale in India was done by Vincent and Shama (1). The study indicates that well losses compise a signiicant potion o the total dawdown in a numbe o low- and high-yielding wells. aanth and Pakash () obseved that the tansmissivity values (T) obtained by slug-tests ae moe than pump test values o low T values, and that they vay om negligible up to a acto o about thee o highe T values. Padeep Raj et al. (3) om hydological tests on dug wells in the cystalline ocks, estimated a ange o T values om 6.5 to m /d, o the weatheed zone based on intepetation made by Papodopulos and Coope method (4). Ballukaya (5) om a study in anataka postulates that the yield luctuation in the pe- and post-monsoon peiods is lagely dependent on echage that is esticted to about 60m depth. All these studies consideed hadock aquie as isotopic and homogeneous, which is not the case as demonstated below. The esh unalteed massive had ock is not wate beaing, but the (i) weatheed zone and (ii) issued and jointed zones ae poductive. In geneal, the weatheed hoizon, when it is wate satuated, is pooly tansmissive with high stoage while the issued and jointed zones ae pooly capacitive, but highly tansmissive. The poblem o low though actues o a actued envionment is pimaily a poblem o low though a dual poosity media, which 1

3 includes the poous matix and the actued netwok. These two components ae hydaulically inteconnected and cannot be teated sepaately. The degee o inteconnection between these two media deines the chaacte o the entie low domain, and is a unction o the hydaulic popeties o each o them. These popeties include matix hydaulic conductivity and actue-netwok distibution, oientation, apetues, connectivity and thus, bulk hydaulic conductivity. They will also detemine the heteogeneity and anisotopy o the whole aquie. The complexity o lows though actues makes inadequate the use o classical techniques such as Theis and Jacob methods o the intepetation o hydaulic tests. Basically, in had ock context, assumptions (homogeneity and isotopy) attached to such methods ae not coheent with the eality. Thus, thee is a need o altenative techniques o the evaluation o aquie paametes able to involve the speciicity o had-ock aquies. Fou dieent methods ae pesented below, o the intepetation o pumping tests, well adapted to the complexity o goundwate lows in had-ock aquies. The method o Neuman (6) is suited o unconined anisotopic aquies while Gingaten method (7) was developed o the case o a single (hoizontal) actue intesecting the pumping well. These methods ae complementay because dealing both with anisotopy at the obsevation and at pumping wells espectively. The Waen and Root (8) method takes into consideation the heteogeneity o the medium, allowing the intoduction o a double poosity aquie (tansmissive actues and capacitive matix). Finally, the outh method Bake theoy (9)- opens the way o the assessment o the low dimension and o the degee o connectivity between the actues. All these methods ae incopoated and illustated on obsevations obtained om pumping tests caied out in the same study aea. The Maheshwaam wateshed located in India (Andha Padesh, Ranga Reddy Distict) is the main study aea o the Indo-Fench Cente o Goundwate Reseach (Fench Geological Suvey / National Geophysical Reseach Institute). This wateshed, located at 30 kilometes away om Hydeabad, coves a suace o about 55 km and is mainly constituted by Achean ganites. The weatheing poiles ae obsevable though many dugwells ealie used by the ames o iigation. Poiles ae geneally tuncated by eosion: unde a ew decimetes o ed soils, the alteites ae thick with less than 5 metes. A high density o hoizontal actues is obseved in the issued zone (10). Vetical actues with a tectonic oigin ae also pesent. Due to the oveexploitation o goundwate esouces, wate levels ae a below gound level and the alteites ae dy while only the issued zone is satuated. This speciicity was used to ealise pumping tests with the objective to test the ou intepetation methods mentioned above and thus to chaacteise the hydodynamic popeties o the issued laye only. ANISOTROPY OF PERMEABILITY USING NEUMAN METHOD AT OBSERVATION WELLS Fo instance, on a bi-logaithmic plot (Figue 1), the dawdown cuves at obsevation wells IFP-1/1 and IFP-1/ duing pumping tests at IFP-1 well have a complex shape, diicult to intepet with classical methods (Theis o example). Dawdown cuves ae composed by thee pats: the ist one, at shot times, with stong slopes, is ollowed by an intemediate peiod duing which wate level stabilisation occus; a thid pat o long times shows a new incease in slopes. The theoy initially developed by Boulton (11) to intepet some special cuves obtained in obsevation wells takes into account the notion o «delayed yield om stoage in unconined aquies» (1). It was impoved by Neuman (6, 13) who developed an analytical solution adapted to anisotopic unconined aquies, whee is the adial pemeability paallel to the aquie extension and z is the vetical pemeability. Neuman method consides an

4 unconined and ininite aquie. When a constant dischage ate is pumped in a complete well, the wate comes o one pat om the stoage in the aquie and o the othe pat om gavitational dainage at the ee suace. The Neuman solution, unde abacus, gives educed dawdowns in an obsevation well located at a adial distance om the pumping well, 4T s DN as a unction o : Q - Reduced time t s o type A cuves; Tt S Tt - Reduced time t o type B cuves; y S y whee T is the tansmissivity o the aquie, S the stoage coeicient, S y the speciic yield, t the time since the stating o pumping. The intepetation using this method consists in itting the obseved dawdowns on the abacus constituted by two types o cuves: type A cuve o shot times and type B cuve o late times. Both cuves ae chaacteised by the same D Z paamete, which is a unction o the pemeability anisotopy, the D b thickness o the aquie b and the distance between the obsevation and pumping wells. The application o this method (Table 1a) to the obsevation wells IFP-1/1 and IFP-1/ leads to the evaluation o tansmissivities, stoage coeicients (S) and speciic yields (S y ). Vey simila values ae obtained in each obsevation wells o T A and T B showing the coheence o the intepetation o this pumping test using Neuman method. The values obtained o speciic yields ae consistent with othe ones deduced both om indiect methods by Magnetic Resonance soundings (14) and om diect methods by adjustment o wate levels luctuations using a global model (15). The detemination o D needs the knowledge o the aquie thickness b. Flowmete measuements duing injection tests in eight wells o the basin have shown that the esh basement does not contain any conductive actue. It is namely the case in pumping well IFP- 1. Thus, the top o this laye was chosen as the bottom o the aquie. As o classical methods, the uncetainty on the value o makes diicult any intepetation o dawdown in pumping wells. The esults o this intepetation, included in Table 1b, show an anisotopy o the pemeability tenso, in accodance with geological obsevations: hoizontal pemeability is systematically highe than vetical one. This esult is consistent with the obsevation o many hoizontal actues in dugwells. HORIZONTAL FRACTURE INTERSECTING THE PUMPING WELL USING GRINGARTEN METHOD Flowmete vetical poile in IFP-9 (10) shows that only one actue is conductive (at 9 metes depth) and is satuated duing the whole pumping test. Moeove, the analysis by Neuman method aises the existence o hydaulic anisotopy due to the existence o hoizontal actues (10). Thus, the method developed by Gingaten and Ramey (16) o a vetical well intesecting a single hoizontal actue in an anisotopic aquie (Figue ), applicable to the pumping well, is well adapted to the hydogeological context o IFP-9 well. The complexity o the analytical solution necessitates an intepetation though the adjustment o obseved dawdowns on theoetical cuves o an abacus (7) giving the educed dawdowns in a pumping well as a unction o educed time o vaious geometical coniguations 3

5 epesented by the paamete H DG, when the actue is located at the cente o the aquie z ), with ( 0. 5 H t t, s DG S s 4 Q z and DG s H, H DG whee z is the distance between the actue and the bottom o the aquie, H the aquie thickness., the pemeability along the adial diection paallel to the actue, can be intepeted as the pemeability inceased by the existence o the hoizontal actue. z, the vetical pemeability, epesents the matix pemeability, S s the speciic stoage coeicient, t the time since the pumping stating, the adius o the hoizontal actue, s the dawdown and Q the pumping dischage ate. Adjustment o obseved dawdowns by Gingaten theoetical cuves (Figue 3) leads to high value o H DG, suggesting a high pemeability anisotopy. Dieence between obsevations and theoetical cuve at shot times is attibuted to well losses in the pumping well. nowing the geomety o the case (i.e. the thickness H o the aquie), supposing the distance z between the bottom o the aquie and the actue equal to 0.5*H and using the value detemined by Maéchal et al. (10) using Neuman method o Ss ( at IFP-9), the hydodynamic popeties o the aquie ae evaluated (Table ): the hoizontal pemeability, z the vetical pemeability and the adius o the hoizontal actue. It is obseved that the anisotopy o the aquie is shown in the pumping wells while estimated actue adius is coheent with ield obsevations. DOUBLE POROSITY MODEL USING WARREN AND ROOT METHOD Due to the act that blocs sepaated by actues compose had-ock aquies, one method allowing descibing such behaviou is poposed. This method deives om the conceptual double poosity model developed by Baenblatt et al. (17). The concept (Figue 4) supposes a conined aquie constituted by two media: the actues, tansmissive but pooly capacitive, and the matix capacitive but pooly tansmissive. Each medium is chaacteised by its hydaulic popeties: and S ae the pemeability and the stoage coeicient o the actue medium espectively and m and S m ae the pemeability and the stoage coeicient o the matix espectively. The low, adial to the pumping well is only contolled by the tansmissivity o actues (low om matix to pumping well is nil, >> m ) and the actues netwok dains the matix whee the low is stationay (spatial vaiation o the * hydaulic head is neglected). The expession o the dawndown is: s, t F u,, u * T t m, and S S S m S S m z Q ; 4T whee is intepoosity low coeicient (dimensionless), 4n( n ) / l shape acto, paamete chaacteistic o the geomety o the actues and aquie matix whee n (dimensionless) is the numbe o actue sets (n = 1,, 3; see Figue 4), l the width o matix blocs (in mete),, a acto, o ealy time analysis equal to 0 and o late time analysis equal to 1/3 (othogonal system, n=, 3) o 1 (n=1), a adial distance om the pumping well, T the actues tansmissivity (T =H ; H: aquie thickness), Q the pumping ate and t the time. This method is well illustated at pumping well IFP-16. The logaithmic deivatives o dawdowns in IFP-16 have the typical shape o a double poosity aquie (Figue 5a): (i) well eects and low tough actues to pumping well, (ii) tansitional peiod: the U illustates 4

6 the contibution o the matix low though actues to the pumping (note that in most case the U o deivatives is oten masked by well eects) and (iii) low in actues and matix. The application o Waen and Root method is then justiied o this data set (Figue 5b). Fo the intepetation, accoding to lowmete measuements and geological obsevations, n=3 and l=1 m wee used. The hydaulic conductivity o actue netwok = 5, m/s and that one o matix m = 7, m/s. On igue 5b is also pesented the intepetation using Theis method, which cannot popely intepet the dawdown ate 470 min o pumping. This shows the limit o such models o hydaulic tests in had-ock teain, and consequently the necessity to use moe sophisticated models. CONNECTIVITY AND FRACTIONAL DIMENSION FLOW USING BARER THEORY In actued aquie, low popeties ae contolled by the actues distibution. Bake model (9) takes account o the dimension o the low, which esults om the distibution and connectivity o the conductive actues (Figue 6). This theoy is a genealisation o the Theis theoy consideing a adial low, n-dimensional, into a homogeneous, conined and isotopic actued medium chaacteised by a hydaulic conductivity and speciic stoage S s. This Genealised Flow Model intoduces the actional dimension o low, n, which chaacteises the vaiation law o low section accoding to distance om the pumping well. Values o n vay om 0 to 3, when n=3 the low is spheical (Figue 6), cylindical when n= (that coesponds to Theis model) and linea when n=1. Paamete n can take any values, entie o not, evealing the complex geomety o the low. Expession o tansient dawdown in the aquie (s(,t)) is given as ollowing: s Q n n, t 1, u 4 n b 3 n, u S s 4 t whee t a 1 ( a, x) e t dt is the incomplete gamma unction, the adial distance om the x pumping well, Q the pumping ate and t the time. This method has been applied to pumping well IFP-9 (Figue 7). The genealised tansmissivity b 3-n is evaluated: m 1.5 /s. The low dimension is equal to.5, and thus coesponds to an intemediate low between cylindical (like Theis) and spheical. The low seems to be geneated by one sub-hoizontal actues netwok, o only one single hoizontal actue as suggested by lowmete tests, connected to a second actue netwok pobably sub-vetical to vetical. CONCLUSIONS Aquie tests in had-ock teain (ganite, gneiss, basalt) make inadequate the use o classical techniques such as Theis o Jacob methods and need speciic methods allowing taking into account the complexity o goundwate low. The methods adopted in the pesent pape conside the heteogeneity and the anisotopy o the media: anisotopy o pemeability (6), single hoizontal actue intesecting the pumping well (7), double poosity behaviou (8) o connectivity and actional dimension low (9). These methods ae successully applied to case studies in Achean ganites and allow to chaacteise the complexity o lows though 5

7 actues. These techniques should be widely used by scientists and enginees o actued aquie chaacteisation (stuctue, anisotopy, heteogeneity) and evaluation (pemeability, stoage, wate supply ). Reeences 1. Vincent W. Uhl, J and Shama, G.., Goundwate, 1978, 16(3), aanth,. R. and Pakash, V.S., Jounal o the Geological Society o India, 3, 1988, Padeep Raj, Nandulal, L. and Soni, G.., Jounal o the Geological Society o India, 1996, 48, Papadopulos, I.S. and Coope, H.H., Wate Resouces Reseach, 1967, Ballukaya, P.N., Jounal o the Geological Society o India, 1997, 50, Neuman, S.P., Wate Resouces Reseach, 1975, 11/, Gingaten, A.C. and Withespoon, P.A., Pecolation though issued ock, Deutsche Gesellschat u Red and Gundbau, Stuttgat, 197, T3B1-T3B8. 8. Waen, J.E. and Root, P.J, Engineeing Jounal, 1963, 3, Bake, J.A., Wate Resouces Reseach, 1988, 4, Maéchal, J.C., Wyns, R., Lachassagne, P., Subahmanyam,., Jounal o the Geological Society o India, submitted. 11. Boulton, N.S., J. Hydol., 1970, 10, Boulton, N.S. and Pontin, J.M.A., J. Hydol., 1971, 14, Neuman, S.P., Wate Resouces Reseach, 197, 8/4, Wyns, R., Baltassat, J.M., Lachassagne, P., Legchenko, A., Vaion, J., Mathieu, F., Bull. Soc. géol. Fance, to be published. 15. Engeand, C., PhD Thesis Univesity Pais VI, Gingaten, A.C. and Ramey, H.J., Tans. Am. Inst. Min. Eng., 1974, 57, Baenblatt, G.E., Zheltov, I.P. and ochina, I.N., Jounal o Applied Mathematic Mechanics Tansl., 1960, 4/10, Black, J.H. Applied Hydogeology, 1994, 3, Acknowledgements: This wok has been achieved by the scientists belonging to the Indo- Fench Cente o Goundwate Reseach (BRGM-NGRI). The authos thank the Fench Ministy o Extenal Aais and the Sevice o Coopeation and Cultual Action o the Fench Embassy in New Delhi, which has suppoted exchanges o scientists between Fance and India. The Indo-Fench Cente o Goundwate Reseach eceived also a unding om CNRS (Fench National Cente o Scientiic Reseach) in the ACI Pogam «Wate and Envionment». 6

8 Dawdown at pumping well (m) Dawdown at obsevation wells (m) Figues 10 Theoetical cuves Type A Type B B B 1 A IFP-1/1 A IFP-1/ Time (min) Figue 1 : Adjustment o dawdown in obsevation wells IFP-1/1 and IFP-1/ using Neuman theoetical cuves o types A and B. Figue : Schematic section o the Gingaten aquie model (one single hoizontal actue). 10 Obsevations Gingaten model H DG = Time (min) Figue 3: Adjustment o dawdown in pumping well IFP-9 using Gingaten theoetical cuves. 7

9 Dawdown at pumping well [m] Dawdown at pumping well [m] Figue 4: Double poosity model. (a): natually actued ock omation, (b) and (c) Waen and Root idealised actued system; (b) othogonal actues netwok (n=3) and (c) hoizontal actues netwok (n=1). 10 w ell eects + low in actues tansitional peiod low in actues+matix 1 Deivative Time [min] 4 w ell eects + low in actues tansitional peiod low in actues+matix 3 Waen and Root Theis measuement Theis Waen & Root Time [min] Figue 5: Intepetation at pumping well IFP-16 using a double poosity model. (a) logaithmic deivative at IFP-16 and (b) adjustment o dawdown using Waen and Root (double poosity) and Theis method. 8

10 D awd o wn at p u mp in g we ll (m ) Figue 6: The concept o low dimension (om (18)) O bs evations B ak e Tim e (m in) Figue 7: Adjustment o dawdown at pumping well IFP-9 using Bake theoy. 9

11 Tables Obsevation well Pumping well (m) T A (m /s) T B (m /s) T A /T B T AB (m /s) S Sy IFP-1/1 IFP E E E E E-03 IFP-1/ IFP E E E E E-03 Table 1a : tansmissivity and stoage paametes obtained by adjustment o dawdown ((T A : tansmissivity obtained by adjustment on type A cuve, T B : tansmissivity obtained by adjustment on type B cuve, T AB : aveage o T A and T B ). Obsevation well (m) b (m) (m/s) Z (m/s) D 1/ D IFP-1/ E-07 5.E IFP-1/ E E Table 1b : pemeability and anisotopy degee detemined at obsevation wells using Neuman method Pumping Well H (m) nown paametes Fissue z z (m) H S s * (1/m) H DG Paametes detemined by adjustment z (m) (m/s) (m/s) IFP F9/ E E-05 5.E Table : pemeability, anisotopy degee and adius o the hoizontal actue detemined at pumping wells using Gingaten method (* : Ss is the aveage o speciic stoage coeicient detemined o each site using Neuman method at obsevation wells). z 10