THERMODYNAMIC MODEL FOR PREDICTING INTERACTIONS OF GEOTHERMAL BRINES WITH HYDROTHERMAL ALUMINUM SILICATE MINERALS

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1 PROCEEDINGS, Thrty-Second Workshop on Geothermal Reservor Engneerng Stanford Unversty, Stanford, Calforna, January 22-24, 27 SGP-TR-183 THERMODYNAMIC MODEL FOR PREDICTING INTERACTIONS OF GEOTHERMAL BRINES WITH HYDROTHERMAL ALUMINUM SILICATE MINERALS Nancy Moller, Chrstomr Chrstov and John Weare Unversty of Calforna San Dego La Jolla, Calforna, 9293 emal: ABSTRACT We report our contnued progress on the development of a thermochemcal model of alumnum slcate mneral solubltes n aqueous solutons contanng H +, Na +, K +, Al 3+, Cl, S(OH) 4, SO(OH) 3, OH, Al(OH) 2+, Al(OH) + 2, Al(OH) 3, Al(OH) 4 as a functon of ph to hgh salt concentratons (I 5 m). Pror conference proceedngs outlned our progress n developng an accurate model for the potassum free system to 1 o C, and some prelmnary results for that system to 3 o C. In ths artcle we report a fully developed model for the potassum free system to 3 o C and prelmnary results to 1 o C for the full system. The model, whch ncorporates the Ptzer specfc nteracton equatons (PITZER, 1987) accurately predcts flud compostons for the low Al (< 1-5 m) and S(OH) 4 (< 1-4 m) concentratons commonly encountered n the ntermedate ph ranges typcal of most natural fluds. Wth avalable solublty or free energy of reacton data, the solublty of complex Na and K hydrothermal alumnoslcate mnerals can now be predcted as a functon of soluton composton and ph n ths system to hgh temperature. Phase equlbrum dagrams llustratng the capabltes of ths model are presented. INTRODUCTION Adequate flud flow n a hydrothermal formaton s essental to effcently extract geothermal energy from the thermal energy of natural and enhanced formaton fluds. Whle there are many other factors nvolved n the complex processes of the development or degradaton of reservor permeablty, the dssoluton and precptaton of mnerals n the pore and fracture structure of a hydrothermal formaton has a sgnfcant nfluence on the flow volume. Therefore, the ablty to correctly predct the saturaton condtons (supersaturaton or undersaturaton) of the reservor fluds wth respect to the mneralogy of the reservor formaton and potental replacement mnerals s a crtcal frst step n understandng and controllng permeablty. The saturaton condtons of a hydrothermal flud are a complex functon of the concentraton of all the solutes n the flud phase, the temperature and the pressure on the system. Because the saturaton chemstry s so senstve to the composton of the hydrothermal flud, t s not generally possble to extrapolate behavor from laboratory measurements on fluds wth composton approxmatng those extracted from the reservor. However, n our research program we have shown that we can develop a comprehensve model of saturaton based on the Ptzer lqud densty equaton of state (EOS) for the hghly complex soluton nteractons occurng n the system H +, Na +, K +, Al 3+, Cl, S(OH) 4, SO(OH) 3, OH, Al(OH) 2+, Al(OH) 2 +, Al(OH) 3, Al(OH) 4, H 2 O (n addton to Ca 2+, HSO 4, SO 4 2, HCO 3, CO 3 2, CO 2 (aq), dscussed elsewhere MOLLER, 1998 and references theren). TABLE 1: MINERALS TO BE INCLUDED IN MODEL Mneral Composton All Evaporte and Carbonate Mnerals presently n TEQUIL* Al (III) mnerals Alumnum chlorde AlCl 3.6H 2O(s) hexahydrate Gbbste Al(OH) 3(s) Boehmte AlOOH(s) S (IV) mnerals Quartz SO 2(s) Chalcedony SO 2(s) Crystobalte SO 2(s) Amorphous slca SO 2(s) Amorphous slca SO 2.2H 2O(s) Al(III)-S (IV) mnerals Kaolnte Al 2S 2O 5(OH) 4 (s) Dckte Al 2S 2O 5(OH) 4 (s) Na(I)-Al(III)-S (IV) mnerals Low albte NaAlS 3O 8(s) Hgh albte NaAlS 3O 8(s) K(I)-Al(III)-S (IV) mnerals Mcroclne KAlS 3O 8(s) Sandne KAlS 3O 8(s) Sodum and potassum zeoltes Analcme 1 (S/Al = 2.) NaAlS 2O 6.H 2(s) Analcme 2 (S/Al = 2.5) Na.85Al.85S 2.15O 6.H 2(s) Na-clnoptlolte (S/Al = Na 1.1Al 1.1S 4.9O H 2(s) 4.5) K-clnoptlolte (S/Al = K 1.1Al 1.1S 4.9O H 2(s) 4.5) *see TEQUIL models on geotherm.ucsd.edu webste.

2 Ths system contans most of the solutes commonly encountered n hgh concentraton n hydrothermal solutons. The saturaton level of mnerals whose composton are wthn ths system can be predcted wth hgh accuracy provded free energy data defnng ther stablty are avalable. Table 1 lsts the hydrothermal alumnoslcate mnerals for whch we have found suffcent data to nclude them n the model. METHODOLOGY The temperatures of the hydrothermal systems accessed by present day and projected geothermal systems are well below the crtcal pont of pure water. In ths stuaton the fluds are nearly ncompressble and the largest varaton n the soluton free energy comes from changes n solute composton and temperature. A very accurate representaton of the compostonal behavor of ncompressble aqueous soluton phase s gven by the free energy equatons ntroduced by Ptzer (PITZER, 1987; HARVIE, 1984). In the model dscussed here an deal mxture or mxng equaton of state s used for the vapor phase and the sold phases are assumed to be pure. These equatons have been presented n several publcatons. They are ncluded below for reference. Detaled explanatons of these expressons can be found n the earler references (PITZER, 1987; HARVIE, 1984). As s usual n aqueous soluton theory, the thermodynamcs of the system are summarzed n the chemcal potentals of ndvdual speces, µ. The µ are gven n terms of the actvty of speces, γ va the Eq. (1), o µ = µ + RT ln γ m (1) γ s gven by an equaton of state (PITZER, 1987). Chemcal equlbrum between reservor rocks and the soluton phase s determned by a chemcal potental balance equaton determned by the stochometry of the reacton. For example, the formaton or dssoluton of K-spar s gven by the mass balance expresson, KAlS O ( s) 8 H O Al( OH ) ( aq) K ( aq) 3H SO + = + +, (2) whch leads to the chemcal potental balance equaton, K spar G ( T ) = µ + µ + 3µ 8 µ. + o f Al ( OH ) K H SO H O (3) If the chemcal potental sum on the rght hand sde of Eq. (3) does not equal the free energy of formaton on the rght hand sde, the sold K-spar dssolves or precptates untl balance s obtaned. Ths balance relaton can also be replaced by a free energy mnmzaton problem (HARVIE, 1987). In the model we are developng, our (HARVIE, 198; HARVIE, 1984; WEARE, 1987) mplementaton of the Ptzer actvty expressons for the aqueous soluton phase s used. 2 ln γ z F m (2 B ZC ) M M a Ma Ma a m (2Φ m ) c Mc + ψ + a Mca c a = mmψ + z mmc a a ' Maa ' M c a ca a a< a ' c a + m (2 λ ) + m m ς n nm (4) n a nam n n a φ.5.5 F = A { I ( I ) mmb + mm Φ.5 (2 1.2) ln(1 1.2 I )} c a ca c c cc c a c c < c mm a a a, a a a < a + Φ (5) B g I g I = β + β ( α, ) + β (12 ), ma Ma Ma Ma x g( x) = 2(1 (1 + x) e ) x, 2 E Φ = Θ + Θ ( ), Z = z m (6) j j j I Ths expresson s symmetrc for catons and anons. The B coeffcents descrbe the onc strength dependence of bnary solutons. When ether the caton or anon for an electrolyte s unvalent, we set α equal to 2. and omt the β (2) term. For 2-2 or hgher valence pars, α = 1.4. In addton the β (2) term accounts for the ncreased tendency of these hgher charged speces to assocate n soluton. When strong on assocaton s present the on par speces must be added to the speces lst (HARVIE, 1984). Examples for the complcated Al system nclude the monomerc hydrolyss speces, Al(OH) 2+, Al(OH) + o 2, Al(OH) 3 and Al(OH) 4 speces. The onc strength dependence of the ternary mxng coeffcents s found n the Φ terms, whch account for mxng between two ons of lke charges. In Φ j, Θ s the only adjustable j E parameter. The onc strength dependent Θ ( I ) term j accounts for electrostatc unsymmetrc mxng effects that depend only on the charges of ons and j and the total onc strength. The terms wth λ and ζ account for neutral speces nteractons wth anons and catons (FELMY, 1986). In ths model the thrd vral coeffcents, C, and the ψ terms, are ndependent of onc strength.

3 All these parameters are adjusted to ft the avalable data n bnary and ternary systems usng a non-lnear least squares method (HARVIE, 1987). Note that only bnary and ternary data are requred to evaluate all the parameters n the Ptzer equatons descrbed here no matter how many components are n the soluton. Eq s. 4-6, therefore, provde a means to extrapolate data from ternary and lower systems to systems of hgher order. We (CHRISTOV, 24 ab; HARVIE, 1984) have shown that these equatons can provde solublty predctons for a range of onc strengths that nclude most of the compostons found n nature. Temperature dependence (MOLLER, 1988; GREENBERG, 1989; CHRISTOV, 24ab) of the soluton parameters s bult nto the model by adjustng selected constants n the followng equaton, parameter (T) = a 1 +a 2 T + a 3 (T 2 ) + a 4 (T 3 ) + a 5 /T + a 6 ln T + a 7 (1/(T-263)) + a 8 (1/(68-T)). (7) To constran our parameter evaluaton as much as possble n our modelng program we nclude all measurements avalable n our data base. Ths, for example, means that data for very low and hgh ph values not usually encountered n natural waters are used to evaluate the parameters n the aqueous Al system. Due to the strong hydrolyss n ths system, the Al 3+ on domnates the solute Al compostons only at low ph. Ths s the regon where measured thermodynamc propertes are most senstve to Al 3+,1 parameters (e.g. β and Θ n Eq s. 4-6). Ths Al, Cl Al, H focus on ncludng all the data not only generalzes the model to treat very low and hgh ph hydrothermal brnes but also allows the evaluaton of parameters n composton regons where they make the largest and most ndependent contrbuton. Thereby, the relablty of the model s ncreased. RECENT MODEL IMPROVEMENTS A hgher temperature model (T<3 o C) for the H +, Na +, Al 3+, Cl, OH, Al(OH) 2+, Al(OH) 2 +, Al(OH) 3, Al(OH) 4 system In the prevous conference proceedngs, we presented a model for ths system, o -12 o C. Ths model was constraned by all the data avalable for ths temperature range. Results for a prelmnary model for hgher temperatures were also gven. Here, we present results of recent efforts to better defne the hgh temperature behavor of ths system to 3 o C. The solublty of Al mnerals n water s relatvely hgh n very low and very hgh ph solutons. However, n the near neutral range the low solublty of Al contanng mnerals (gbbste, boehmte, kaolnte, etc., Table 1) constrans the concentraton of Al n most natural waters to levels below 1-5 m. At these almost trace levels, the knd of experments that provde free energy data for the varous solute speces (e.g., Al(OH) 2+, Al(OH) 2 +, Al(OH) 3, Al(OH) 4 ) s lmted to solublty measurements n varous background medum. Fortunately, due to the great mportance of ths system to the predcton of rock-water nteractons there have been a number of efforts to carefully measure solubltes for temperatures up to 3 o C (e.g., CASTET, 1993; PALMER, 21; BOURCIER, 1993; BENEZETH, 21; KUYUNKO, 1983 and references theren). Usng these data, we have parameterzed a model to 3 o C. The agreement of the model over the composton and temperature range of the data s very good as shown n Fgs. 1-3 below. log [ m(al)] Al(OH) 4 - m(al) o C;.1 m (NaCl) Al(OH) 2 + Al 3+ Al(OH) ++ Al(OH) ph Fgure 1: Model predctons of the solublty of boehmte (sold lne) vs. the data of PALMER, 21. log [ m(al)] Al(OH) o C; 1. m m(al) Al(OH) ++ + Al(OH) 2 Al 3+ Al(OH) ph Fgure 2: Model predctons of the solublty of boehmte (sold lne) vs. the data of PALMER, 21. In Fg. 3. we have ncluded all the avalable data for T 25 o C. Note the consderable scatter n the measurements. Generally the hgh ph solublty data are the most relable. The process of smultaneously

4 fttng the data from all temperatures reduces the uncertanty of the parameterzaton. log [ m(al)] o C;.3 m (NaCl) m(al) + Al(OH) 2 Al 3+ Al(OH) ++ Al(OH) 4 - Al(OH) ph Fgure 3: Model predctons of the solublty of boehmte vs. ph (sold lne) vs. expermental data. Open squares: BENEZETH, 21; flled squares: Kuyunko, 1983; flled damonds: CASTET, 1993; flled trangles: BOURCIER, Addton of K + to alumnum soluton model A sgnfcant advantage of usng the Ptzer equaton of state approach defned by Eq s. 4-6, s that many of the parameters requred for a very complex system can be (are best) establshed n much smpler systems for whch there are more precse data. Our evaluaton of the parameters for the potassum contanng system Na +, K +, Al 3+, Cl, OH, Al(OH) 2+, Al(OH) + 2, Al(OH) 3, Al(OH) 4 llustrates ths. Low ph solublty data for AlCl 3 n KCl solutons were used to evaluate the Al-K nteractons (e.g., θ ). The agreement of Al, K model predctons wth these acd sde data s llustrated n Fg. 4. m (AlCl 3 ) AlCl 3.6H 2 O o C Sylvte o C m (KCl) Fgure 4: The predcted solublty (sold lnes) of AlCl 3.6H 2 O as a functon of KCl concentraton. Data, crcles: MALQUORI, 1928 (see Lnke, 1965); trangles: PATEL 1966 (see Lnke, 1965). As the ph s ncreased, the Al 3+ on reacts wth waters of hydraton formng hydrolyss speces, Al(OH) (3-n)+ 4, fnally arrvng at the tetrahedrally coordnated Al(OH) 4 speces at suffcently hgh ph. The most mportant parameters for postvely charged speces (n<3) are the bnary nteractons wth Cl (e.g., β,1 ; see Eq s. 4-6). These parameters Al( OH ) +, Cl 2 were establshed n the better determned Na system and, consstent wth the Ptzer mxng approach, are accepted for the K system whch has few data. The negatvely charged Al(OH) 4 on s expected to nteract strongly wth the postve K + on. Fortunately, there s enough data (WESOLOWSKI, 1992) to evaluate the mportant bnary parameters (e.g. β,1 ; see Eq s. 4-6). The agreement of the Al( OH ), K + 4 parameterzed model wth the avalable data s llustrated n Fg. 4. m (KAl(OH)4) Gbbste solublty n K-OH-Al(OH) 4 -H 2O solutons; symbols: data of Wesolowsk, o C 5 o C o C m (KOH) Fgure 5: Gbbste solublty (sold lnes) n K solutons for varous temperatures. Data of WESOLOWSKI (1992). PREDICTION OF MINERAL SOLUBILITIES Wth the parameterzaton of the soluton model, the free energes (chemcal potentals, see Eq s. 1-6) of the solute speces are avalable. Gven the standard free energes of formaton of the sold phases, as n Eq. (3), as a functon of temperature, the saturaton status of hydrothermal brnes wthn the H +, Na +, K +, Al 3+, Cl, S(OH) 4, SO(OH) 3, OH, Al(OH) 2+, Al(OH) + 2, Al(OH) 3, Al(OH) 4, H 2 O system wth respect to mnerals n ths system (see Table 1) may be predcted. The sources for the mneral free energes are compled n Table 2. Ths model was developed for use n predctng the saturaton status of hydrothermal brnes havng many compostonal degrees of freedom wth respect reservor rocks. However, to llustrate the capabltes of the model we present below solublty dagrams for some ternary and quaternary systems.

5 TABLE 2 Mneral: Data used n parameterzaton Al (III) mnerals AlCl 3.6H 2 O LINKE, 1965 Al(OH) 3 WESOLOWSKI, 1992 PALMER, 1992 WESOLOWSKI, 1994 AlOOH CASTET, 1993; DIAKONOV, 1996; BENEZETH 21; PALMER., 21 S (IV) mnerals Quartz SO 2 HEMLEY, 198; GUNARSSON, 2 Chalcedony: ARNORSSON, 1982 SO 2 Crystobalte: GUNARSSON, 2 SO 2 Amorphous: GUNARSSON 2 SO 2 Amorphous: CHEN,1982 SO 2.2H 2 O Al(III)-S (IV) mnerals Kaolnte DEVIDAL, 1996 Al 2 S 2 O 5 (OH) 4 Dckte: ZOTOV, 1998; FIALIPS, 23 Al 2 S 2 O 5 (OH) 4 Na(I)-Al(III)-S (IV) mnerals Low NaAlS 3 O 8 ARNORSSON, 1999 Hgh NaAlS 3 O 8 ARNORSSON, 1999 K(I)-Al(III)-S (IV) mnerals Mcroclne ARNORSSON 1999 KAlS 3 O 8 Sandne: ARNORSSON, 1999 KAlS 3 O 8 Sodum and potassum zeoltes NaAlS 2 O 6.H 2 WILKIN, 1998 Na.85 Al.85 S 2.15 WILKIN, 1998 O 6.H 2 (s) Na 1.1 Al 1.1 S 4.9 O 12. WILKIN, H 2 K 1.1 Al 1.1 S 4.9 O 12. WILKIN, H 2 Ternary Systems Fg. 6 shows the stablty felds of the mnerals, sandne and hgh albte, n aqueous solutons at 1 predcted by the model. The composton of the soluton phase s dstrbuted accordng to the complex specaton scheme ncluded n the model. However the total composton of any soluton on ths dagram may be wrtten n terms of the compostons of the mnerals as shown. In geothermal applcatons, the stabltes of mneral phases n hghly concentrated salt solutons are often requred. Fg. 7 llustrates the effect of dssolved salt concentraton on plagoclase mneral coexstence. The ntal concentratons of the soluton before the addton of excess solds are gven on the axes. The flow of an NaCl rch brne through a formaton of coexstng hgh-albte and sanadne wll convert the sanadne to albte, substantally changng the concentraton of K n the soluton phase. However as llustrated n Fg.7 the total solublty of sold mneral s stll small. For example, n the example llustrated n Fg. 7 t was assumed excess sold phase (sandne and hgh-albte) were equlbrated wth 1gm of water contanng x moles of dssolved NaCl. For x=1. n equlbratng the system.15 moles of K were transferred to the soluton. However, the total Al n soluton remaned at 1.7x1-5. Snce the volumes of mnerals are dfferent ths replacement process could affect the pore volumes n the reservor. m (KAlS 3 O 8 ).1.5 pure water solublty m(k + )=3.94d-5 ph=6.49 m(s tot)=1.17d-4; m(a ltot)=3.77d-5 1 o C; hgh seres plagoclases sandne pure water solublty m(na + )=1.3d-4 ph=6.67; hgh-albte m(s tot)=3.89d-4; m(a ltot)=1.28d m (NaAlS 3 O 8 ) Fgure 6: Solublty n the sandne/hgh albte ternary. m (Altotal) o C low-albte&mcroclne saturaton hgh-albte&sandne saturaton m (NaCl) Fgure 7: Total Al concentraton at coexstence n the plagoclase seres.

6 Quaternary systems As a further llustraton of the capabltes of the model we show n Fg. 8 the quaternary solublty dagram for the system SO 2, low-albte, mcroclne, H 2 O. Note the domnance of the SO 2 concentraton n most of the dagram. Fgure 8: Solublty of mnerals n the low-albte, mcroclne, quartz, H 2 O. T=1 o C. ACKNOWLEDGEMENTS Ths research was supported by DOE Grant DE- FG36-4GO143, NSF Grant NSF-EAR and DOE BES grant DE-FG2-6ER15767 REFERENCES Arnorsson S., Sgurdsson S. and Svavarsson H. (1982) The chemstry of geothermal waters of Iceland. I. Calculaton of aqueous chemstry from o to 37 o C. Geochm. Cosmochm. Acta 46, Arnorsson S. and Stefansson (1999) Assessment of feldspar solublty constants n water n the range o to 35 o C at vapour saturaton pressures. Amer. J. Sc. 299, Benezeth P., Palmer D. A. and Wesolowsk D. J. (21) Aqueous hgh-temperature solubltes studes. II. The solublty of boehmte at.3 m onc strength as a functon of temperature and ph as determned by n stu measurements. Geochm. Cosmochm. Acta 63, Bourcer W. L., Knauss K. G. and Jackson K. J. (1993) Alumnum hydrolyss constants to 259 o C from boehmte solublty measurements. Geochm. Cosmochm. Acta 57, Castet S., Dansurand J. L., Schott J., and Gout R. (1993) Boehmte solublty and aqueous alumnum specaton n hydrothermal solutons (9-35 o C): Expermental study and modelng. Geochm. Cosmochm. Acta 57, Chen C.T. and Marshal W. (1982) Amorphous slca solubltes IV. Behavor n pure water and aqueous sodum chlorde, sodum sulphate, magnesum chlorde, and magnesum sulphate solutons up to 35 o C. Geochm. Cosmochm. Acta 46, Chrstov C. and Moller N. (24a) A chemcal equlbrum model of soluton behavor and solublty n the H-Na-K-OH-Cl-HSO 4 -SO 4 -H 2 O system to hgh concentraton and temperature. Geochm. Cosmochm. Acta 68(6), Chrstov C. and Moller N. (24b) A chemcal equlbrum model of soluton behavor and solublty n the H-Na-K-Ca-OH-Cl-HSO 4 -SO 4 -H 2 O system to hgh concentraton and temperature. Geochm. Cosmochm. Acta 68(18), Devdal J.-L., Dandurand J.-L. and Gout R. (1996) Gbbs free energy of formaton of kaolnte from solublty measurement n basc solutons between 6 and 17 o C. Geochm. Cosmochm. Acta 6, Dakonov I., Pokrovsk G., Schott J., Castet S. and Gout R. (1996) An expermental and computatonal study of sodum-alumnum complexng n crustal fluds. Geochm. Cosmochm. Acta 6, Falps C.-I., Majzlan J., Beaufort D. and Navrotsky (23) A. New thermodynamc evdence on the stablty of dckte vs. kaolnte. Am. Mneralogst 88, Greenberg J. and Moller N. (1989) The predcton of mneral solubltes n natural waters: A chemcal equlbrum model for the The Na-K-Ca-Cl-SO4- H2O system to hgh concentraton from to 25oC. Geochm. Cosmochm. Acta 53, Gunarsson I. and Arnorsson S. (2) Amorphous slca solublty and the thermodynamc propertes of H 4 SO 4 o n the range of o to 35 o C at P sat. Geochm. Cosmochm. Acta 64, Harve C., Greenberg J. P. (1987) A chemcal equlbrum algorthm for hghly non-deal multphase systems: Free energy mnmzaton. Geochm. Cosmochm. Acta 51: Harve C., Moller N., and Weare J. (1984) The predcton of mneral solubltes n natural waters: The Na-K-Mg-Ca-H-Cl-SO 4 -OH-HCO 3 -CO 3 -CO 2 - H 2 O system from zero to hgh concentraton at 25 C. Geochm. Cosmochm. Acta 48, Hemley J., Montoya M. and Luke R. (198) Equlbra n the system Al 2 O 3 -SO 2 -H 2 O and some general mplcatons for alteraton/mneralzaton processes. Econ. Geol.. 75, Kuyunko N., Malnn S. and Khodakovsk I. (1983) An expermental study of alumnum ons hydrolyss at 15, 2 and 25 o C. Geochem. Intl. 2, Lnke W., Solubltes Inorganc and Metal-organc Compounds 4 th Ed., vols. 1 and 2. Amer. Chem. Soc. Washngton (1958, 1965). Moller, N., Greenberg J. P., and Weare, J. (1998). Computer modelng for geothermal systems: Predctng carbonate and slca scale formaton, CO 2 breakout and H 2 S exchange. Transport n Porous Meda 33(1-2):

7 Moller N. (1988) The predcton of mneral solubltes n natural waters: A chemcal equlbrum model for the Na-Ca-Cl-SO4-H2O system to hgh temperature and concentraton. Geochm. Cosmochm. Acta 52, Palmer D. A. and D. J. Wesolowsk (1992) Alumnum specaton and equlbra n aqueous solutons: II. The solublty of gbbste n acdc chlorde solutons from 3 to 7 o C. Geochm. Cosmochm. Acta 56, Palmer D. A., Benezeth P., and Wesolowsk D. J. (21) Aqueous hgh-temperature solublty studes. I. The solublty of boehmte as functons of onc strength (to 5 molal, NaCl), temperature (1-29 o C), and ph as determned by n stu measurements. Geochm. Cosmochm. Acta 65(13), Palmer D. A. and Wesolowsk D. J. (1992) Ptzer K. S. (1987) Thermodynamc model for aqueous solutons of lqud-lke denstes. In Revews n Mneralogy--Thermodynamc Modelng of Geologcal Materals: Mnerals Fluds and Melts, Vol. 17 (ed's. I. S. E. Carmchael and H. P. Eugster), pp Mneralogcal Socety of Amerca. Weare J. H. (1987) Models of mneral solublty n concentrated brnes wth applcaton to feld observatons. In Thermodynamc Modelng of Geologcal Materals: Mnerals, Fluds and Melts, 17 (ed's. I. S. E. Carmchael and H. P. Eugster), pp Mneralogcal Socety of Amerca. Wesolowsk D. J. (1992) Alumnum specaton and equlbra n aqueous solutons: I. The solublty of gbbste n the system Na-K-Cl-OH-Al(OH) 4 from - 1 o C. Geochm. Cosmochm. Acta 56, Wesolowsk D. J. and Palmer D. A. (1994) Alumnum specaton and equlbra n aqueous soluton: V. Gbbste solublty at 5 o C and ph 3-9 n.1 molal NaCl soluton (a general model for alumnum specaton; analytc methods). Geochm. Cosmochm. Acta 58, Wlkn R. and Barnes H. (1998) Solublty and stablty of zeoltes n aqueous solutons: I. Analcme, Na-, and K-clnoptlolte. Amercam Mneralogst 83, Zotov A., Mukhamed-Galeev A. and Schott J. (1998) An expermental study of kaolnte and dckte relatve stablty at 15-3 o C and the thermodynamc propertes of dckte. Am. Mneralogst 83,