A method for estimating the fresh water-salt water interface with hydraulic heads in a coastal aquif

GEOSCIENCE FRONTIERS 2(2) (2011) 199- 203available at www.sciencedirect.comGEOSCIENCEFRONTIERSChina University of Geosciences (Beijing)GEOSCIENCE FRONTIERSjournal homepage: www. esevier.com/locate/gsfORIGINAL ARTICLEA method for estimating the fresh water- -salt waterinterface with hydraulic heads in a coastal aquiferand its applicationXun Zhou*School of Water Resources and Environment, China University of Geosciences, Bejing 100083, ChinaReceived 12 November 2010; accepted 11 February 2011Available online 16 March 2011KEYWORDSAbstract Examining the descriptions of piezometric heads at two points in both the salt water and freshFresh water- -salt waterwater zones reveals that when the groundwater flow system is in steady stale and satisfies the Dupuitinterface;assumption, the location of the fresh water-salt water interface in a homogeneous, isotropic. and uncon-Sea water intrusion;fined coastal aquifer can be estimated based on a piczometric head of fresh water at a point in the freshTidal effect;water zone (from the water table to the interface) vertically lined up with a piezometric head of salt waterCoastal aquiferat a point in the salt water zone (from the interface down). Research shows that the new method isa general relation and that both the Hubbert relation describing the location of the interface and the Ghy-ben- Herzberg relation are special cases of this method. The method requires two piczometric wells to beclose to each other and cach tapping into a different zone. Measurements of piczometric heads at a wellcluster consisting of piczometric wells tapping separately into fresh water and salt water zones near Bei-hai, China at 5-day intervals for I5 months are used to ilustrate the estimation of interface location. Thedepth of the interface for well H5 ranges from 32 to 72 m below the sea level.◎2011. China University of Gcosciences (Beijing) and Peking University. Production and hosting byElsevier B.V. All rights reserved.1. Introduction●Tel: +86 10 82320674; fax: +86 10 82321081.E-mail address: zhouxun@cugb.cdu.cn.1674-9871◎2011, China University of Geoscinces (Beijing) and PekingFresh groundwater is an important source of water supply in coastalareas. Knowing the temporal and spatial evolution of the freshUniversity. Production and hosting by EIsevier B.V. All rights reserved.water- salt water interface is significant for groundwater develop-Perreview under rsosibility of China University of Geosciences ment and preventionof sea water itusion andfor undertandingthe(Biing).vulnerability of a coastal environment. Many hydrogeologicaldoi:10.016/.g.f.2011.2.000studies have discussed and used models describing a sharp interfacebetween fresh wastal areas, especially incoastal aquifers )中国煤化工rween fresh waterProduction and hosting by Eserierand salt water, orHCNMH Ginary examinationof the relation b。s needed (Glover,1959; Fetter, 1972; Bear, 1979; Essaid, 1990; Croucher and200X. Zhou / Geoscience Froniers 2(2) (2011) 199- -203O'Sullivan, 1995; Izuka and Gingerich, 1998; Cheng and Ouazar,Mq and Mp are the depth of point C below the sea level and the1999; Feseker, 2007; Tang et al, 2007; Kim et al, 2007).elevation of point C above the datum respectively; Ps and Pr arePrevious studies in determining the interface are based mainly ondensities of salt water and fresh water respectively. Fig. 1 showsthe water table in the fresh water zone with the Ghyben - Herzbergthat kK(=h,+ Ho, h{=hp + Ho, and M'=Ho - M, where Ho is therelation (ven der Veer, 1977; Reilly and Goodman, 1985; Inouchielevation of the sea level above the datum.et al, 1985; Isaacs and Hunt, 1986; Ledoux et al, 1990; MooreLet us examine the piezometric heads at two points separatelyet al.. 1992; Huyakorm et al, 1996; Person et al., 1998; Maas,in the fresh water and salt water zones in the same vertical line AE2007). By defining the piezometric heads of two fuids of dfferentin the coastal aquifer shown in Fig. 1. The piezometric bead ofdensities at a point in either fuid region, Hubbent (1940) presentedfresh water at any given point C in the fresh water zone above thea relation describing the location of the interface that relies on thearbitrary datum (P'Cr) can be described aspiezometric heads of the two fuids to be at the same point on theinterface. Izuka and Gingerich (1998) presented a method to esti-(h-M)p8mate the interface depth based on vertical head gradients usingPrPi8-+ M;=h%, .1)water-level measurements during drilling of a partially penetratingwhere Pc is the pressure at point C and g is the gravitationalwell above the interface. Kim et al. (2007) estimated the interfacedepth using two sets of pressure data obtained from both fresh wateracceleration.and salt water zones in a single borehole. Zhou et al. (2008) andFor point A in the salt water zone on the same vertical line, weZhou (2008) introduced methods for determining the location of thecan also describe the piczometric head of salt water above thefresh water- -salt water interface in coastal zones using hydraulicdatum (中As) asheads. In this paper, application of the developed method is given to(M' - M)p,8+ (M{ -M )Arg+Pcillustrate the estimation of the interface, with hydraulic headsψ% =A +M,;=+M,， (2)measured in the fresh water zone and the salt water zone in theP.gcoastal aquifer near Beihai, China, where the groundwater flowwhere PA is the pressure at point A. Pc in Eq. (2) can be expressedsystem is thought to be in a steady state and meets the Dupuitassumption.Pc=('c - M})ag.3)2. MethodSubtituing Eq. (3) into Eq. (2) givesAs shown in Fig.1, it is assumed that (1) the coastal unconfined%=(M -M) +(M-Mr)°+(oa-M)°+M, (4)aquifer is homogeneous and isotropic; (2) groundwater flowdischarges into the sea and is in steady state and; (3) thegroundwater flow system satisfies the Dupuit assumption. ARearrangement of Eq. (4) yieldsvertical line AE intersects the water table at point D, any point inthe fresh water zone at C, the interface at point B, and any point in%s=RM +yver(5)the salt water zone below the interface at point A. As ilustrated inFig. 1, h, and n stand for the elevations of the piezometric headsFrom Eq. (5), we obtain:of salt water measured at point A above the mean sea level andoCr=(1 + 8)uw - 8o'cs, .6)above an arbitrary datum respectively; hp and h are the elevationsP,-PyAs Pg- Prof the water table at point D above the sea level and an arbitrarywheredatum respectively; M and M' are the depth of the interface belowsea level and the elevation of the interface above the datumδ=_Pu7)respectively; M, and M。are the depth of point A below the seaρ.-Pilevel and the elevation of point A above the datum respectively;Note that φCr=φcr + Ho,PAs=φas + Ho, and M' =Ho - M ,where φcr and φAs are the piezometric head of fresh water_ELand surfacemeasured at point C and the piezometric head of salt watermeasured at point A above the mean sea level, we can also obtaingWater tablelthe following relation from Eq. (6) when the sea level is used asthe datum:|Sea1s|.Mean sea levelM== P! σφcr-_ρqψn=δφcr-(1 +8)pw.8)Mρ,一PP。- PrEq. (8) or (6) gives the depth of the inteface below sea level or|hsM_ |MFresh waterthe elevation of the interface above the datum, which is deter-Hemined by the piezometric head of salt water at point A in the saltSalt waterB，water zone, PAs or φAs , and the piezometric head of fresh water atInterfacepoint c on the same vertical line in the fresh water zone, 4cr orDatumJ| 中国煤化工Sure. This methodrequires two pietapping separatelyFigure 1 Schematic diagram showing a fresh water- -salt waterinto the salt walMHCNMHGinterface that generally occurs in a homogeneous, isotropic, andIf points A and C tap simultaneously at the same point B on theunconfined aquifer in a coastal zone.interface, Eq. (6) or (8) becomes the Hubbert relation describingX. Zhou / Geoscience Frontiers 2(2) (2011) 199- -203_201identical to the sea level, i.e,, h. = 0 or K=Ho, Eq. (10) or (9)9，1kmreduces into the Ghyben-Herzberg relation:Beibuwan GulfM=oht(11)W10一jIH5。oH3M'=(1 + 8)Ho- oh.(12)s1921 H69 H4●W2Since points A and C are arbitrary, Eq. (8) or (6) is a generalBeihal●W6relation that can be used to estimate the location of the freshwater- -salt water interface when the previously mentionedassumptions are met in coastal zones. The Hubbert relation isa special case of Eq. (8) or (6) and the Ghyben-Herzberg relationFigure2 Map showing locaion of the observation well clustersin is a special case of Eq (10) or (9).the northwestern coastal area of Beihai, Guangxi, China.the relationship among the fresh water head, salt water head, and3. Applicationthe location of a point on the fresh water- -salt water interface. TheHubbert rlation is difiult to apply since both the fresh water The groundwater sysem in the Beihai coasal region of southemhead and the salt water head at the same point on the interface are Guangxi, China. is used to ilustrale the aplication of thenot known if the interface's location is previously unknown.developed principle. The coastal plain is underlain by QuatemarySince %=k at point A and心r=h in Eq. (1), from Eq. (6) and Neogene !unconsolidated sedimentswe obtain:gravel and scattered lenses of clay or sandy clay; the total thick-ness ranges from 5 to 350 m. The unconsolidated sediments in theM'=_ Ps_K.-.Pth=(1+)h,- 6h{.(9)southern part of the region can roughly be grouped into oneunconfined aquifer and three confined aquifers. Because of reliefPg-Pf° P.- Pfon the basement- sediment interface, only one unconfined aquiferFrom Eq. (9) or (8) we can also obtain the fllowing relation and one conined aquifer are present in the northern part of thewhen the sea level is used as the datum:study area. Hydraulic connections exist among the aquifers,especially among the confined aquifers due to the semi-pervi-ousness and termination of clay. The three confined aquifers,M=- PLhn-_Ps_h,=8hn-(1+ a)h,(10)therefore, can be treated as one confined aquifer. A detailedPs-Pr° Ps- Prdescription of the hydrogeological setting was given by Zhou et al.Eq. (10) or (9) gives the depth of the interface below sea level(2000, 2006). .or the elevation of the interface above the datum, which isEleven clusters of wells were drilled in the northwestemndetermined by piezometric head of salt water at point A in the salt coastal zone in the city of Beihai (Fig. 2. excerpt well S19-1).water zone, hs or n, , and the water table of fresh water on the Each of the well clusters has three piezometric wells of differentsame vertical line in the fresh water zone, hq or h If pointCison depths in very close proximity. The three piezometric wells at wellthe water table and the piezometric head of salt water at pointAis cluster H5 from upper to lower zones were named H5-1, H5-2,aH5-2田H5-32461214 15Time (Month)20- b官40608100中国煤化工Figure 3 Changes in (a) average piezometric heads in wells H5-2 and H5-3 and (b) calculatJYHCNMH G,water interfacebelow sea level from January, 1996 to March, 1997.202X. Zhou / Geoscience Frontiers 2(2) (2011) 199 -203and HS-3. Piezometric wells H5-2 and HS-3 are thought to tapsatisfied, especially approaching or far from the coast. This methodseparately into the fresh water and salt water zones. Measurementsrequires the two nearest piezometric wells to penetrate separatelyof the piezometric heads were carried out once every five daysinto the fresh water and salt water zones.from January, 1996 to March, 1997. During the measurementperiod, the piezometric heads at well H5-3 tapping into the saltAcknowledgmentswater zone were lower than the mean sea level in the dry seasonand higher than the sea level in the rainy season. This observationThis work was supported by the Fund for the Special Research ofmay suggest that the change in location of the fresh water- -saltDoctorate Subjects of the Ministry of Education of Chinawater interface depends on both the piezometric head of fresh(No. 20070491522).water above the interface and the piezometric head of salt waterbelow the interface. Both heads should be considered in esti-mating the location of the interface.ReferencesForρ= 1.0 and Ps = 1.025, Eq. (8) becomes:Bear, J.1979. Hydraulics of Groundwater. McGraw-ill, In.. London.M= 40中cr - 4lφAs;(13)p. 566.:heng, Ah.D., Ouazar, D. 1999. Analytical Solution. In: Bear, J,assuming that the aquifer near well cluster H5 satisfies theCheng, Ah.D., Sorek, S. Ouazar, D.. Herrera, I. (Eds.), Seawaterpreviously mentioned assumptions.Intrusion in Coastal Aquifers - Concepts, Methods and Practice.Kluwer Academic Publishers. London. Dp.163-191.Eq. (13) is used to estimate the interface depth in the north-ishers, London, P.163-19westem coastal zone in Beihai, with the assumption that a sharpE.. O'Sullivan, MJ.. 1995. The Henry problem for saltwaterinterface exists between the fresh water and salt water zones.Essaid, HI. 1990. A multilayered sharp interface model of coupledPiezometric heads at well cluster H5 are used since the aquitardfreshwater and seawater flow in coastal systems: model developmentbetween the unconfined and confined aquifers terminates near thisand application. Water Resources Research 26 (7), 1431-1454.well cluster. Piezometric head relative to sea level at H5-2 representsFeseker, T, 2007. Numerical studies on saltwater intrusion in a coastalthe hydraulic head of fresh water above the interface (φcr) andaquifer in northwestern Germany. Hydrogeology Joumal 15, 267- -279.piezometric head relative to sea level at HS-3 represents theFetter Jr, C.W. 1972. Position of the saline water interface beneathhydraulic bead of salt water at a point in the salt water zone belowoceanic islands. Water Resources Research 8 (5). 1307- 1315.the interface (PAs). Data from piezometric heads at H5-2 and HS-3Glover, R.E. 1959. The patterm of fresh-water flow in a coastal aquifer.are frst smoothed out using the Haning formula of running averageJourna] of Geophysical Research 64 (4), 457- -459.to eliminate minor fuctuations in the measured piezometric headsHubbert, M.K., 1940. The theory of ground-water motion. Joumal ofGeology 48, 785- -944.caused by tide (Fig. 3a). The estimated interface depths at welll H5Huyakom, PS.. Wu, Y.S., Park, N.S, 1996. Multiphase approach to theaccording to Eq, (13) at every time step during the measurementnumerical solution of a sharp interface saltwater intrusion problem.period are shown in Fig. 3b, and the depths range from 32 to 72 mWater Resources Research 32 (1), 93-102.below the sea level. The interface was lower in dry season than inInouchi, K., Kishi, Y, Kakinuma, T.1985. The regional unsteady interfacerainy season due to the raising of piezometric heads in salt water.between fresh water and salt water in a confined coastal aquifer.The results suggest that both the fresh water head in the fresh waterJourmal of Hydrology 77. 307- -331.zone and salt water head in the salt water zone have an importantIsaacs, L.T, Hunt, B.. 1986. A simple approximation for a moving inter-bearing on the interface location.Lzuka, S.K.. Gingerich, S.B.,. 1998. Estimation of the depth to the fresh-water/salt-water interface from vertical head gradients in wells in4. Conclusioncoastal and island aquifers. Hydrogeology Joumal 6. 365-373.Kim, K.Y., Chon, C.M.. Park, K.H.. 2007. A simple method for locatingWhen the groundwater flow in a coastal aquifer is in a steady statethe fresh wate-salt water interface using pressure data. Ground Waterand satisfes the Dupuit assumption, the location of the fresh45 (6), 723- -738.water- salt water interface in a homogeneous, isotropic, anLedoux, E. Sauvagnac, S.. Rivera, A.. 1990. A compatible single pha-unconfined coastal aquifer can be estimated using a piezometricse/two-phase numerical model: 1. Modeling the transient salt- water/-head of fresh water measured at any point in the fresh water zonefresh-water interface motion. Ground Water 28(I), 79- -87.(from the interface to the water table) in combination withMaas, K.2007. Influence of climate change on a Chjben-Herzberg lens.Joumal of Hydrology 347. 223- -228a piezometric head of salt water measured at any point in the saltMoore, Y.H. Stoessell, R.K.. Easley, D.H.. 1992. Fresh-water/sea-waterwater zone (from the interface down) on the same vertical line.relationship within a groundwater fow system, northeasternist ofThe Hubbert relation describing the interface location is a specialthe Yucatan Peninsula. Ground Water:case with two points simultaneously tapping the same point on thePerson, M.sula. Ground V1., Taylor, J.Z., Dingman, S.L.. 1998. Sharp interface models ofiterface. The Ghyben- -Herzberg relation is also a special casesalt water intrusion and wellhead delineation on Nantucket Island,with the fresh water piezometric head tapping the water table andthe salt water piezometric head being at the sea level.Reilly, TE.. Goodman, A.S., 1985. Quantitative analysis of saltwater-Measurements at 5-day intervals from piezometric heads of saltfreshwater relationships in groundwaler systems - a historicalperspective. Journal of Hydrology 80, 125-160.water and piezometric heads of fresh water at well cluster H5 nearTang. X.Q. Wang, H. Zuo, FH, Ohtoshi, K., 2007. Numerical simulationBeihai, China, show that the salt water heads can be lower or higherof fresh-saline water interface regularities in coastal areas duo to thethan the mean sea level. At every measured time, the measurementsof piezometric heads are used to estimate the location of the freshtidal fuctuati中国煤化工nment 7 (4),84-92(in Chinese "water- salt water interface. During the measurement period, theven der Veer, PMHCNMHGadyiterfccefowin.calculated interface depth for well HS range from 32 to 72 m belowa coastal aquifer involving a phreatic subsurface with precipitation.the sea level. Eror may exist if the Dupuit assumption is notJoumal of Hydrology 34, 1-11.X. Zhou / Geoscience Frontiers 2(2) (2011) 199- -203203Zhou, X.. 2008. An introduction to determination of the location of freshZhou, x.. Ruan, C. Yang, Y, Fang, B.. Ou, Y. 2006. Tidal efects ofwater-salt water interface in coastal zones. Geoscience 22 (1),groundwater levels in the coastal aquifers near Beihai, China. Envi-123- 128 (in Chinese with English abstract).ronmental Geology 51 (4), 517-525.Zhou, X., Chen, M., Ju, X.. Ning, X., Wang, J, 2000. Numerical simu-Zhou, X., Zhou, H., Zhang, L., 2008. Characteristics of piezometric headslation of seawater intrusion near Beihai, China. Environmentaland determination of fresh water- -salt water interface in the coastalGeology 40 (1/2), 223- -233.zone near Beihai, China. Environmental Geology 54 (1), 67-75.中国煤化工MHCNMHG