EAS44600 Groundwater Hydrology Lecture 8: Storage Properties of Aquifers Dr. Pengfei Zhang


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1 EAS44600 Groundatr Hydrology Lctur 8: Storag Proprtis of Aquifrs Dr. Pngfi Zhang Moistur Contnt Rcall that th porosity (n) of arth matrials is th ratio of th volum of th voids (V v ) to th total volum (V ) of th sampl. h volum of th voids may b furthr dividd into th volum of th atr (V ) and th volum of th air (V a ). h volumtric moistur contnt θ is dfind as: V = V θ (81) For saturatd zons V = V v and θ = n; for unsaturatd zons V < V v and θ < n. Watr abl A atr tabl is dfind as th surfac on hich th fluid prssur in th pors of a porous mdium is xactly atmosphric. W commonly think that th atr tabl is th boundary btn th unsaturatd zon and th saturatd zon. Hovr, a saturatd capillary fring oftn xistd abov th atr tabl (Figur 81). h capillary fring is diffrnt from th typical saturatd zon in that its prssur is lss than on atmosphr. hrfor, a hydrologic systm is oftn dividd into thr zons: an unsaturatd zon, a capillary fring (somtims also calld tnsionsaturatd zon), and a saturatd zon (Figur 81). Figur 81. A hydrologic systm consists of an unsaturatd zon, a capillary fring and a saturatd zon (Frz and Chrry). If on placs a ll a f ft or so blo th atr tabl, th atr in that ll ill ris to th lvation of th atr tabl at th location of th ll (abl 81). h prssur hydraulic had 81
2 (h p ) on th atr tabl is zro sinc th prssur on th atr tabl is xactly atmosphric. Rcall that th total hydraulic had (h) is th sum of th lvation had (z) and th prssur had (h p ). hrfor, th total hydraulic had at any point on th atr tabl must b qual to th lvation had (i.., h = z). On figurs th position of th atr tabl is oftn indicatd by a small invrtd triangl, as in Figur 81. h atr tabl oftn follos topography, although th rlif of th atr tabl is lss than th topography (Figur 82). Groundatr gnrally flos from topographic highs to topographic los, and dischargs at th topographic lo spots. Figur 82. Unconfind, or atr tabl aquifr (Fttr). Aquifr An aquifr is a gologic unit that can stor and transmit atr at sufficint rats to supply lls. his rquirs an intrinsic prmability of 102 darcy and abov. A confining layr is a gologic unit that has lo to no intrinsic prmability (.g., 102 darcy or lss), such as in clays and till. Confining layrs ar subdividd into aquifugs (absolutly imprmabl) and aquitards (imprmabl rlativ to th adjacnt units). Watr tabl aquifrs, thos ith no confining layr abov, ar calld unconfind aquifrs (Figur 82). Aquifrs ovrlain by a confining layr ar calld confind aquifrs (Figur 83). Whn you think about it, th aquifr insid th pip usd in Darcy s xprimnt as a confind aquifr. h pip itslf as a confining layr. Bcaus this aquifr as confind, any atr that as introducd to th pip fastr than it as rlasd causd prssur in th pip. Natural confind aquifrs act th sam ay. As atr rchargs th confind aquifr, prssur may build up in th aquifr. If on r to drill a ll in a prssurd confind aquifr, th atr 82
3 lvl in th ll (pizomtr) might ris far abov th aquifr. An artsian ll is a ll in hich th atr riss abov th top of th aquifr. In som cass th atr lvl may ris abov th ground surfac, in hich cas th ll is calld as a floing ll (Figur 84). Rcharg Confining Layr Confind Aquifr Figur 83. Confind aquifr (Fttr). Figur 84. Artsian and floing ll in confind aquifr (Fttr). Whr do aquifrs gt thir atr? In th cas of an unconfind aquifr, th atr largly coms dirctly from prcipitation sinc thr is no obstruction prvnting infiltrating atr from raching th atr tabl. You can imagin thn that th atr tabl may fluctuat significantly through th sasons bcaus of changs in prcipitation and vapotranspiration that srv to add and rmov atr from th subsurfac. h cas of th confind aquifr is lss straightforard, sinc thr is a confining layr atop th aquifr; its rcharg must com from mans othr than from dirct infiltration. An important mans of rcharg to confind aquifrs is by infiltration of prcipitation into portions of th aquifr that outcrop at th surfac (Figur 83). For xampl, 83
4 confind aquifrs in intrmontan basins may ris latrally ith th topography, and actually outcrop in th adjacnt foothills. Hnc, th outcrops in th foothills catch prcipitation and thn transmit th atr to lor lvation in th aquifr hr it bcoms confind. Potntiomtric surfac If th atr lvls in lls tappd in a confind aquifr ar plottd on a map and contourd, th rsulting surfac, hich is actually a map of th hydraulic had in th aquifr, is rfrrd to as a potntiomtric surfac (Figurs 85 and 86). If th aquifr is unconfind, th contour map is rfrrd to as th map of th atr tabl. Groundatr ill flo in th gnral dirction that th potntiomtric surfac is sloping, i.., from highr hydraulic had to lor hydraulic had (Figur 86). Figur 85. Unconfind aquifr and its atr tabl; confind aquifr and its potntiomtric surfac (Fttr). Figur 86. Potntiomtric surfac of th Dakota Sandston (Darton, 1909). 84
5 Comprssibility of Watr Fluids ar comprssibl,.g., an incras in prssur dp ill lad to a dcras in th volum of a givn mass of atr (V ). h comprssibility of atr (β) is dfind as: dv / V β = (82) dp hr dv is th chang in th volum of th atr, V is th original volum of th atr, and dp is th chang in prssur. h ngativ sign is ncssary to nsur a positiv β. Effctiv Strss h ight of ovrlying rock and atr crats a donard strss (σ ) on a saturatd aquifr (Figur 87). his strss is born by th granular sklton of th porous mdium and th fluid prssur p of th atr in th por spacs (Figur 87). Mathmatically spaking, hav: σ = σ p (83) + hr σ is th ffctiv strss, th portion of th total strss that is born by th granular sklton. In trms of th changs in ths paramtrs, hav: = dp (84) + hr is th chang in total strss, is th chang in ffctiv strss, and dp is th chang in fluid prssur. otal Strss σ p Fluid Prssur σ Effctiv Strss Figur 87. otal strss, ffctiv strss, and fluid prssur on an arbitrary plan through a saturatd porous mdium (Frz and Chrry). 85
6 At a givn point of th saturatd porous mdium, th ight of th ovrlying rock and atr rmains ssntially th sam ovr tim. In such cass, th chang in th total strss = 0, and = dp (85) In plain ords, quation 85 stats that if th fluid prssur incrass, th ffctiv strss dcrass by an qual amount; and if th fluid prssur dcrass, th ffctiv strss incrass by an qual amount. Rcall that p = ρgh, hr ρ is th dnsity of th fluid and g is th p gravitational constant. Also rcall that h = h p + z, hr h is th total hydraulic had and z is th lvation had. hrfor, th fluid prssur can b xprssd in trms of th hydraulic had as: Sinc z is a constant, diffrntiating quation 86 givs Substituting quation 87 into quation 85 yilds: p = ρ ghp = ρg( h z) (86) dp = ρ gdhp = ρgd( h z) = ρgdh (87) = ρgdh (88) Equation 88 stats that th chang in th ffctiv strss ( ) at a givn point in a saturatd aquifr is govrnd by th chang in th hydraulic had at that point. Comprssibility of a Porous Mdium h comprssibility of a porous mdium, α, is dfind as α dv / V = (89) hr V is th total volum of th porous mdium, dv is th chang in th volum of th porous mdium, and is th chang in ffctiv strss. Rcall that V = V s + V v, hr V s is th volum of th solids and V v is th volum of th atrsaturatd voids. An incras in ffctiv strss lads to a rduction dv in th total volum of th porous mdium. In granular matrials th rduction in th total volum of th porous mdium is almost ntirly du to grain rarrangmnt. In gnral, dv = dvs + dvv ; but th volum chang for individual grains du to th chang in ffctiv strss is ngligibl (in othr ords, individual grains ar almost incomprssibl). hrfor, can assum dv = dv (810) v 86
7 Equation 810 stats that th chang in th total volum of a porous mdium is qual to th chang in th volum of voids (or porosity) du to th rarrangmnt of th grains undr incrasd ffctiv strss. Aquifr Comprssibility Pumping from a ll ill rduc th prssur had in a saturatd aquifr, lading to incrasd ffctiv strss (quation 88). h aquifr sklton may consolidat or compact du to this incrasd ffctiv strss by th rarrangmnt of th grains (Figur 88). Aquifr comprssibility is dfind as db / b α = (811) hr α is th aquifr comprssibility, db is th chang in aquifr thicknss, b is th original aquifr thicknss, and is th chang in ffctiv strss (Figur 88). h ngativ sign indicats that th aquifr thicknss rducs as th ffctiv strss incrass. Figur 88. Aquifr compaction causd by groundatr pumping (Frz and Chrry). Sinc as = dp (quation 85) and dp = ρgdh (quation 87), quation 811 can also b rittn db / b db / b α = = (812) dp ρgdh Spcific Storag h spcific storag (S s ) of a saturatd aquifr is dfind as th volum of atr rlasd from th storag pr unit volum of th aquifr pr unit dclin in hydraulic had. As discussd arlir, a dcras in hydraulic had h ill lad to a dcras in fluid prssur p and an incras in ffctiv strss σ. A dcras in fluid prssur ill caus th fluid to xpand; and an incras in ffctiv strss ill caus th compaction of th aquifr. hrfor, th atr rlasd from 87
8 th storag du to a dcras in h is producd by to mchanisms: 1) th xpansion of th atr causd by dcrasing p, and 2) th compaction of th aquifr causd by incrasing σ. h volum of atr producd (dv ) by th xpansion of th atr can b drivd from quation 82: dv = βv dp (813) Rcall that for a saturatd aquifr V = V v = nv, hr n is th porosity. With V = 1 (unit volum of aquifr), dp = ρgdh (quation 87), and dh = 1 (unit dclin in hydraulic had), quation 813 bcoms dv = β ( nv )( ρgdh) = βnρg (814) h volum of atr xplld (dv ) from th unit volum of aquifr during compaction is qual to th rduction in volum of th aquifr (dv ). From quation 89, hav: dv = αv (815) Rcall that dv = dv v (quation 810), and V = V v for a saturatd aquifr. hrfor, dv = (816) dv h ngativ sign is addd sinc th volumtric rduction dv is ngativ, but th amount of atr producd dv is positiv. Combining quations 815 and 816, hav: dv = dv = αv (817) For V = 1 (unit volum of aquifr), dh = 1 (unit dclin in hydraulic had), and (quation 88), quation 816 bcoms: = ρgdh dv = αρg (818) h spcific storag S s is th sum of th to trms givn by quations 814 and 818: S s = ρg( α + nβ ) (819) ransmissivity and Storativity of a Confind Aquifr W hav mntiond transmissivity () and storativity (S) arlir in th cours. For a confind aquifr of thicknss b, th transmissivity is dfind as = bk (820) 88
9 hr K is th hydraulic conductivity, and th storativity (or storag cofficint) S is dfind as Substituting quation 819 into quation 821 givs: S = S s b (821) S = ρgb( α + nβ ) (822) In plain ords, th storativity of a confind aquifr of thicknss b is th volum of atr rlasd from th storag pr unit surfac ara of th aquifr pr unit dclin in hydraulic had or potntiomtric surfac (Figur 89). Figur 89. Diagrams illustrating th concpt of storativity in (a) an unconfind aquifr and (b) a confind aquifr (Domnico and Schartz). ransmissivity and Spcific Yild in an Unconfind Aquifr In an unconfind aquifr, th transmissivity is dfind by th sam quation (820) but b is th saturatd thicknss of th aquifr or th hight of th atr tabl abov th top of th undrlying confining aquifr. In an unconfind aquifr, th rlas of atr from storag is primary du to th datring of th por spacs. his datring is dirctly rlatd to th spcific yild S y of th aquifr matrials. Watr may also b rlasd in an unconfind aquifr du to th scondary ffcts of atr xpansion and aquifr compaction. hrfor, th storativity of an unconfind aquifr is dfind as S = S S b (823) y + s 89
10 For an unconfind aquifr th valu of S y is typically svral ordrs of magnitud gratr than th valu of S s b, and th storativity is oftn takn to b qual to S y. h volum of atr draind from an aquifr du to th drop in hydraulic had can b stimatd from th formula V = SA h (824) hr V is th volum of atr draind, S is th storativity, A is th surfac ara ovrlying th draind aquifr, and h is th dclin in hydraulic had. Storativity valus for confind aquifrs rang from to 0.005; storativity valus for unconfind aquifrs ar much highr, ranging from 0.02 to hrfor, for th sam dclin in hydraulic had, th volum of atr rlasd from an unconfind aquifr ill b much gratr than th volum of atr rlasd from a confind aquifr. 810
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