PHASE EQUILIBRIUM AND KINETICS OF SALINE SOIL WATER FREEZING

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1 PHASE EQUILIBRIUM AND KINETICS OF SALINE SOIL WATER FREEZING S.E. Grchishchv, A.V. Pavlov, V.V. Poomarv Vavilov strt, 30/6, room 85, Earth Cryosphr Istitut; Russia, Moscow, -mail: Abstract A thrmodyamic modl of phas quilibrium ad kitics of sali soil watr frzig ad thawig was dvlopd ad vrifid. X-ray studis of por ic formatio i watr-saturatd clays wr carrid out. Th ic phas xistc i frzig soils was studid. Th xprimts showd that aftr soil thawig th ic phas i pors xists up to +1 to +3 C. I frzig soils, th ic phas appars at tmpraturs from -2 to -4 C. Durig soil thawig th ic cott dcrasd i a stp-shapd mar. A lctromtry tchiqu for simultaous masurmt of local lctrical coductivity ad phas frot tmpratur dprssio was dvlopd. Th dpdc of th phas frot tmpratur vrsus its vlocity was obtaid for frsh ad sali watr-saturatd soils (clay, loam, sad). It was show that th phas frot tmpratur dprssio udr qual frzig vlocitis is largr if th soil particl siz is smallr ad th saliity is gratr. Thortical modl I prvious publicatios (Grchishchv t al., 1980; 1984), a kitic thory of hat - mass-trasfr i frzig - thawig watr-saturatd o-sali fi-graid soils was dvlopd. I Grchishchv t al., (1984), it was also otd that i thrmodyamic procsss with phas trasitios i soils, it is cssary to tak ito accout th coctratio of substacs dissolvd i watr. A aalysis of th litratur shows that xprimtal study of froz sali soils has rsultd i th accumulatio of sigificat iformatio about thm. Howvr, thortical ad xprimtal rsarch o phas trasitio kitics i sali soils rmais poorly dvlopd. Cosidr th thrmodyamic (physico-chmical) coditios i frzig watr-saturatd soil whr th porwatr cotais dissolvd substacs, makig it a solutio. Th frzig frot ca b cosidrd as a systm of th followig itractig phass: (1) ic, (2) watr solutio i small (ot frzig at giv tmpratur) pors, (3) watr solutio i larg (i.. frzig at giv tmpratur) pors. A thrmodyamic coditio for all phass ca b charactrizd by GibbÕs quatios (Grchishchv t al., 1984). S dt + V dp + kt dc + dm = 0 [1] j j j j j whr j - phas umbr (1 - ic, 2- solutio i small pors, 3 - solutio i larg pors), k - BoltzmaÕs costat, C j - coctratio of dissolvd substacs i j phas, S - spcific tropy, V j - spcific volum, p - prssur, T - tmpratur, m - chmical pottial. Cosidr a itractio of a solutio i small pors with a ic phas, ad writ a GibbÕs quatio for ach of ths two phass: S1 dt + V1 ds + kt dc1 + dm1 = 0 [2] ad [3] S dt + V dp + kt dc + dm = whr s - a full prssur (prssur o th ic ls), th idxs 2 ad 1 rfr to film solutio (solutio i small pors) ad to ic, rspctivly. Lt's assum as usual that th diffrcs of chmical pottials ad prssur i ighborig phass ar proportioal to phas itractio vlocity, i..: ' ' m - m = a q i j ij ij p - p = a q ' ' i j ij ij [4 ] ad [5] whr a ij - mpirical factors of proportioality, q ij - phas itractio vlocity. Subtractig ths quatios from GibbÕs quatios for film solutio ad ic ad assumig that S [6] 2 - S1 = - L/ T whr L - latt hat of fusio, ad also assumig TrzaghiÕs quatio s = s + V, 2 3 [7] S.E. Grchishchv, t al. 351

2 whr s - ffctiv prssur (i soil sklto), p - prssur i solutio i larg pors; V 3 - spcific volum of watr, w driv: - L dt / T + V ds + ( V - V ) dp+ k T d( C - C ) = - V a dq + a dq whr q 32 - flow vlocity of a solutio from a larg por to a film solutio (i.. it is th flow of por solutio to th frzig frot), q 12 - vlocity of frzig of a solutio i small pors, C 1 - rsidual coctratio of dissolvd substac i ic, C 2 - coctratio of th sam substac i small pors o th ic-watr boudary. I th spcific cas wh sgrgatd ic lss ar growig, th watr flow vlocity at th frzig frot q 32 should b qual to th frzig vlocity watr q 12. Th rsidual coctratio of dissolvd substacs i ic should b proportioal to a flow of this substac from film to ic, i.. C ( q c ) b 21 whr s () 21- dissolvd substac flow from film to ic, b - mpirical factor of proportioality. Substitutig th last xprssio ito th prvious o, w driv a quatio for th kitics of phas trasitios i small pors: [8] [9] ( c) a dq + a dq + a dq = L dt / T - V ds -( V - V ) dp - kt dc [10] whr s 1, s 2, s 3 - w symbols for formr mpirical factors of proportioality. Aftr itgratig both quatios i liar approximatio w driv th followig kitic quatios: ( c) a1 dq32 + a2 dq21 + a3 dq21 = L ( T0 -T) / T0 -V1s -( V1 -V3)( p - p0) - k T C2 ( c) a dq + a dq + a dq = L ( T -T) / T -( V -V )( p- p ) - k T C [11] ad [12] whr P 0 - atmosphric prssur, T = 273 K. Ths quatios charactriz th kitics of phas trasitios i small ad larg pors accordigly ad iclud dissolvd substacs, which a formr modl did ot iclud (Grchishchv t al., 1980). From th last two quatios it follows that th mchaical prssurs s ad p act i this modl i th sam way as i our prvious modl (Grchishchv t al., 1980). Th first xprssio shows that th phas trasitio which is dvlopd i th right-had part of th quatio is ot qual to zro, ad thrfor ca rsult i flows of watr ad of substacs dissolvd i it. If th right-had part of th quatio quals zro, th quatio dscribs coditios of phas quilibrium of a solutio with ic i porous mdia i..: Figur 1. Ic phas x-ray itsity (I ) vrsus tim (t) at froz pasts thawig: (a) btoit w = 270%, (b) Yamal loam w = 33% (w - watr cott, umbrs - tmpratur). 352 Th 7th Itratioal Prmafrost Cofrc

3 Tabl 1. Th mai x-ray ivstigatio rsults L ( T -T)/ T - V s -( V - V ) ( p- p )- k T C = [13] It is asy to s that th drivd xprssio is gral by xamiig th followig wll-kow coditios of partial phas quilibrium: (a) i closd systm without dissolvd substacs, i.. at s = C= 0 L ( T - T)/ T = ( V - V ) ( p- p ) [14] (b) i op systm without dissolvd substacs, i.. at p = p 0, C = 0 L ( T [15] 0 - T)/ T = V1 s (c) i closd systm udr atmosphric prssur ad with dissolvd substacs, i.. at s = 0, p = p 0 L ( T - T)/ T = k T C 0 0 [16] Th first xprssio is th Clausius-Clapyro quatio, th scod o is Haimov-MalkovÕs quatio, ad th third o is VaÕt Hoffs Law coctig th tmpratur of phas quilibrium to th coctratio of a solutio. Th two kitic quatios giv abov, combid with quatios for hat ad watr coductivity ad diffusio of dissolvd substacs, form a kitic physicochmical modl of phas trasitios (frzig - thawig) i porous ad fi-graid mdia, saturatd with solutios. Th mpirical factors icludd i ths quatios to dscrib phas trasitio kitics ca b foud from xprimts that hav b do usig x-ray ad lctromtr tchiqus, which ar rportd blow. O of th mai problms dsrvig furthr study i this ara is th local coctratio of dissolvd sub- S.E. Grchishchv, t al. 353

4 Figur 2. Phas frot tmpratur dprssio modulus DT vrsus frzig or thawig vlocity for o-sali soils (1 - Kudiovskay clay, 2 - Sakhali loam, 3 - Yamal loam) ad for frsh watr (4). stacs i small ad larg pors. Th local xclusio of th salts from larg to small pors ad th origi of "sali pockts" aftr passag of th frzig frot could b importat for phas trasitio kitics. X-ray ivstigatios Th X-ray difractomtry tchiqu givs valuabl iformatio about frzig of soil moistur i por spac (Adrso ad Hokstra, 1965a; 1965b; Norrish ad Raussl-Colom, 1962; Filatov, 1981; Grchishchv t al., 1992; Grchishchv ad Pavlov, 1994). It is applid to rsarch o ic structur formd i pors of diffrt sizs, ad chags of th crystal lattic of clayy mirals i frzig soils. This problm is importat for th corrct applicatio of thrmodyamics to frzig soils, as soil proprtis ar closly coctd to th proprtis of por ic. I arlir work (Grchishchv t al., 1992; Grchishchv ad Pavlov, 1994) whr x-ray ad lctromtric mthods wr usd, it was stablishd that (a) durig thawig, at th phas trasitio of ic to watr, with disapparac of ic, rflctios had a wavy form o difractograms at tmpraturs from -1 to -2 C; i Na-askagl-clay with a watr cott of 384%, this procss was rcordd at + 1 C ; (b) th dpdc of tmpratur dprssio o crystallizatio frot vrsus frzig vlocity i watr-saturatd sady-clayy soils, is symmtrical i rlatio to frzig ad thawig as i watr. Th lattr mas, that for umrically qual frzig ad thawig vlocitis, th valus of phas trasitio frot tmpratur dviatios from 0 C ar qual to ach othr. Rctly w xtdd th low tmpratur rag of x-ray ivstigatios of frzig kitics i clayy soils. A improvd low tmpratur attachabl x-ray dvic to th difractomtr, usig thrmolctrical lmts ad a w systm of tmpratur rgulatio, with thrmocoupls that masur tmpratur dirctly i sampls, was dvlopd for th study of phas trasitios. This rsarch was carrid out o pasts of kaoliit ad btoit of various watr cott ad dsity, ad o Yamal loam ad its grai-siz fractios. Th aims of th ivstigatios wr to stimat: (a) th ifluc of grai- miralogical compositio upo th mchaics of ic ad ufroz moistur formatio; (b) th mchaics of ic formatio i pors of various diamtrs, dow to micropors ad microcapillaris, ad th ufroz moistur migratio i por spac btw th crystal lattic of mirals ad th por spac of soil. Th mai tchiqus of th studis wr dscribd i Grchishchv t al. (1992). Th mai rsults of th ivstigatios ar show i Tabl 1. W first masurd xprimtal curvs of chags i ic phas itsity i tim. Ths curvs rgistr prcisly th momt of occurrc of th ic crystal phas, coct it i tim to a tmpratur jump, which is rgistrd by th thrmocoupl i a sampl, stimat growth of th ic phas i tim, quatify th magitud of this phas, ad stimat chag i ic particl oritatio. I xprimts, a diffrc i th charactr of ic phas itsity vrsus tim (trmd hr "curv IPIT") at frzig ad at thawig was obsrvd. A frzig curv IPIT has a mootoous charactr (xcpt for th iitial jump at th momt of occurrc of th ic phas), ad at thawig is stp-shapd with jumps (s for xampl Figur 1). This is vidc that i froz Tabl 2. Soil proprtis bfor o-dimsioal frzig watr cott 354 Th 7th Itratioal Prmafrost Cofrc

5 Tabl 3. Distributios of watr W, dry dsity rd ad watr saturatio G with dpth h of frzig Sakhali loam sampl (frzig from blow with vlocity 6 mm pr hour) soil durig ic crystal growth, a discrt spctrum of tmpraturs of phas quilibrium is formd. As th displacmt of thrmodyamic quilibrium occurs udr th ifluc of adsorptio forcs i th soil sklto, th stp-lik bhavior of tmpraturs of phas quilibrium vidtly rflcts a stp-lik bhavior of por siz distributio. Fluctuatios of curvs IPIT ar of itrst also durig thawig of a soil (s Figur 1). Thy show that durig a gral thaw of ic, short-trm local frzig of thawd or prviously ufroz watr i pors is possibl. W otd prviously (Grchishchv t al., 1992) that durig frzig from larg pors through smallsizd ad ultra small-sizd pors ad capillaris, watr outflow occurs from itrlayr spacs of a crystal lattic. This is show by a x-ray difractomtry of th siz of th itrlayr distac of a crystal lattic of motmorilloit mirals (btoit). As rsarch has show (s Tabl 1), at frzig of watr-motmorilloit pasts, itrlayr watr, xcpt 2 to 3 moomolcular layrs, movs ito por spac formig ordiary ic. Th rmaiig itrlayr watr is "ufroz" watr. Th ufroz itrlayr watr quatity basically dpds o tmpratur ad o th atur of th xchag catios. Th disapparac of th ic phas i btoit pasts with watr cotts of 270%, 100% ad 60% occurrd at tmpraturs from + 4 to + 1 C. Th xistc of ÒwarmÓ ic is probably coctd to spcial thrmodyamic coditios i spcific por spac of clays. Thus thr is th activ rorgaizatio of ic ad btoit particls, togthr with thir aggrgats ad Figur 3. Phas frot tmpratur dprssio modulus DT vrsus coctratio C ad frzig vlocity v for (a) watr solutio of NaCl ad (b) Yamal loam saturatd with watr solutio of NaCl; xprimtal data S.E. Grchishchv, t al. 355

6 Tabl 4. Tmpratur (T) of th crystallizatio frot of NaCl solutios vrsus coctratio ( C) ad frzig vlocity (v). (T q - phas quilibrium tmpratur, T pw - tmpratur of frsh watr frzig) blocks, that is markd by brightly xprssd fluctuatios of ic ad btoit phas rflctio itsity. Aftr btoit pasts thaw, th watr from larg pors through small-sizd os coms back to th crystal lattic, which icrass but ot quit up to th iitial d 001. Elctromtry ivstigatios Th purpos of our lctromtry studis was to assss th tmpratur dpdc of phas trasitio frots (watr frzig or ic thawig) o phas trasitio vlocity (frzig or thawig) i fi-graid watr-saturatd o-sali ad sali soils. This dpdc charactrizs phas trasitio kitics i figraid (sady-clayy) soils, which i tur, dfis th procss of ic sgrgatio at frzig. Th lctromtry study tchiqu was publishd prviously (Grchishchv t al., 1994). This tchiqu ivolvs th simultaous masurmts of (a) local frzig (or thawig) vlocity ad (b) tmpratur of frzig (or thawig) frot with hlp of a dvic dvlopd by th authors - th lctrothrmomtr "spidr". Th lattr cosists of thr lctrods, locatd o corrs of a right-agld triagl with ach lg big 3 mm log. Th lctrods ar placd such that o of th lgs is placd horizotally ad othr o vrtically. With th hlp of ths lctrods, lctrical coductivity is masurd cotiuously at a "poit" i a soil i vrtical ad horizotal dirctios udr frzig or thawig. Th frzig vlocity is coutd durig a itrval of tim btw bgiigs of th rcssio of lctrical coductivity i vrtical ad horizotal dirctios. A thrmocoupl idicatd th momt of crystallizatio frot passag, which was tak as th phas frot tmpratur. Th frzig of sampls 4 cm i hight ad 3 cm i diamtr was mad i a systm that was op from blow. Th lctrothrmomtr "spidr" is placd 15 mm from th bottom of a glass. Th lctromtric studis of por moistur frzig kitics wr carrid out usig o-dimsioal crystallizatio. Matrials ivstigatd wr o-sali Kudiovsky clay ad Sakhali loam, o-sali ad sali Yamal loam, frsh watr, ad NaCl solutios. I Figur 2, th rsults ar show for th avrag dpdc of th modul of phas frot tmpratur dprssio o phas frot vlocity (i.. o frzig or thawig vlocity). Th rsults displayd ar for osali soils ad frsh watr. Th variability of xprimtal masurmt was up to 20% of DT. Th soil proprtis ar giv i Tabl 2. Durig fractioig of Kudiovsky clay ad Sakhali loam, it was obsrvd that th clay cott of ths soils icrasd from Yamal loam to Sakhali loam to Kudiovsky clay, i.. i th sam ordr as th modul of phas frot tmpratur dprssio. I Tabl 3, for xampl, data dscribig th distributio of th watr cott of a miral sklto dsity ad ic saturatio of frzig sampls ar show for a Sakhali loam. Th frzig vlocity was 6-7 mm/h. Th froz thickss was 25 mm i both cass. Th ic saturatio was calculatd for two masurmts of ic dsity: 910 ad 700 kg/m 3. A aomalously low dsity for sgrgatd ic (700 kg/m 3 ) was foud i arlir xprimts o havig proprtis of Sakhali loam (Grchishchv ad Shakov, 1993) ad is usd i Tabl 3 for compariso. Th ic saturatio of th froz part of th Sakhali loam at ic dsitis of 910 to 700 kg/m 3 is cosidrably largr tha 1. It shows a xtra ic sgrgatio, arisig i this cas durig uidirctioal frzig from blow. Th rsults of xprimts with NaCl solutios ad sampls of Yamal loam saturatd with NaCl solutios ar giv i Tabl 4 ad o Figur 3. Ths data allow us to stablish a importat mpirical xprssio for watr solutios TvC (, ) = T( C) + T () v q pw [17] 356 Th 7th Itratioal Prmafrost Cofrc

7 whr v ad C - frzig vlocity ad solutio coctratio, rspctivly; T(v,C) - th frzig frot tmpratur at giv v ad C, C: T q (C); - tmpratur of phas quilibrium at giv C ad at v =0, C; T pw (v) - tmpratur of frzig frot for frsh watr at giv v, C. Ths xprimtal data allowd us to stimat th mpirical costats that ar icludd i our kitic modl. Ackowldgmts Th authors ar plasd to xprss thir gratitud to th rviwrs for thir assistac i laguag ad stylistic chags i th papr. Th rsarch was supportd by th Russia Fud of Fudamtal Ivstigatios (Grat RFFI ). Rfrcs Adrso, D.Y. ad Hokstra, P. (1965 a). Crystallizatio of clay adsorbd watr. Scic, 149, No. 3681, Adrso, D.Y. ad Hokstra, P. (1965 b). Migratio of itr lamllar watr durig frzig ad thawig of Wyomig btoit. Soil Scic Socity of Amrica Procdigs, 29, o. 5, Filatov, A.O. (1981). Ic structur ad dtails of ic formatio i clays. Fild ad xprimtal ivstigatios of froz groud (i Russia). Yakutsk, Prmafrost Istitutio of Sibria Brach of RAS, pp Grchishchv, S.E., Chistotiov, L.V. ad Shur, Y.L. (1980). Cryogic physic-gological procsss ad thir forcast. (i Russia), Ndra, Moscow, (326 pp.). Grchishchv, S.E., Chistotiov, L.V. ad Shur, Y.L. (1984). Fudamtals of cryogic physic-gological procsss simulatio. (i Russia). Nauka, Moscow, (232 pp.). Grchishchv, S.E., Pavlov, A.V. ad Poomarv, V.V. (1992). Chags i microstructur of fi-graid soils du to frzig. Prmafrost ad Priglacial Procsss, 5, Grchishchv, S.E. ad Shakov, V.V. (1993). Dvlopmt of physic-chmical modl for cryogic havig ad largmt of sgrgatd ic i frzig sady-clayy soils. I Procdigs of th Sixth Itratioal Cofrc o Prmafrost, Bijig, Chia. Vol. 1, pp Grchishchv, S.E. ad Pavlov, A.V. (1994). Frzig - thawig kitics i watr ad watr saturatd soils. I Procdigs of th Sv Itratioal Symposium o Groud Frzig, Nacy, Frac. pp Norrish, K. ad Raussl-Colom, I.F. (1962). Effcts of frzig o th swllig of clay mirals. Clay Miral Bullti, 5, S.E. Grchishchv, t al. 357