au empirical na-k-ca geothepmomete~ for natural waters · 1356 r. 0. fournier and a. h. truesdell...

Geochimica et Coemochimica Acta, 1973, Vol. 37, pp. 1255 to 1275. Pergsmon Press. Printed in Northern Ireland

Au empirical Na-K-Ca geothepmomete~ for natural waters

R. 0. FOURNIER and A. H. TRUESDELL U.S. Geological Survey, i&n10 Park, California 94025, U.S.A.”

Abstract-An empiricai method of estimating the last temperature of water-rock intem,ction has been devised. It is based upon molar Xa, K, and Ca concentrations in natural waters from temperature environments ranging from 4 to 34O’C. The data for most geothermal waters cluster near a straight line when plotted as the function log (P;a/K) + /3 log [ 1/ (C&)/Sal vs reciprocal of absolute temperature, where /I is either 4 or $ depending upon whether the water equilibrated above or below 100°C. For most wsters tested, the method gives better results than the N&/K methods suggested by other workers. The ratio Na/K should not be used to estimate temperature if v’(Mc,)/ilfNB is greater than 1. The Na/K values of such waters generally yield calculated temperatures much higher than the actual temperature at which water interacted with the rock.

A comparison of the composition of boiling hot-spring water with that obtained from a neerby well (17O’C) in Yeliowstone Park shows that continued u-sbter-rock reactions may occur during ascent of water even though that ascent is so rapid that little or no heat is Iost to the country rock, i.e. the water cools adiabatically. As a result of such continued reaction, waters which dissolve additional Ca as they ascend from the taquifer to the surface will yield estimated aquifer temperatures that tbre too low. On the other hand, waters initially having enough Ca to deposit calcium carbonate during ascent may yield estimated aquifer temperatures that are too high if aqueous T\‘a, and K are prevented from further reaction with oountry rock owing to armoring by calcite or silica, miner&.

The Na-K-Ca geothermometer is of particular interest to those prospecting for geothermal energy. The method also mey be of use in interpreting compositions of fluid inclusions.

GEOTHE~~~~~TRY based upon water chemistry is of particular interest to those involved with expIoration of sources of geothermal energy. Some of the more recent papers devoted to the subject are by WHITE (1970), MAHON (1970), ELLIS (1970),

TONANI (1970), and FOURNIER and TRUESDELL (1970). Although many qualitative temperature indicators have been suggested, until now only two chemical indicators have been considered to be quantitati~~e. One is based upon the variation in solu- bihty of quartz as a function of temperature (FOURNIER and ROWE, 1966; MANON,

1966), and the other is based upon the temperature dependence of base exchange or partitioning of alkalies between solutions and solid phases.

Empirical curves showing the variation in natural waters of atomic Na/K ratios vs tem~rature for temperatures below 300°C have been presented in several

(WHITE, 1965, 1968, 1970; ELLIS and M&OX, 1967; ELLIS, 1969, 1970;

MEROADO, in press ; and FOURNIER and TRUESDELL, 1970). WHITE (1965) and ELLIS

(1970) both postulated that above approximately 175 to 2OO’C the Na/K ratios in most natural waters are controlled by equilibrium with albite and K-feldspar. Over recent years, increasing evidence indicated that waters rich in Ca, such as

* Publication authorized by the Director, U.S. Geological Survey.

1266

10

1356 R. 0. FOURNIER and A. H. TRUESDELL

Mammoth Hot Springs in Yellowstone Park and the Salton Sea geothermal brines, did not yield reasonable Na/K temperatures and that Ca content should somehow be considered.

(In this section and those that follow, superscripts showing the ionic charge of aqueous species, e.g. Naf, K+, Ca2+, are not shown where we are dealing with the sum of ionic and complexed species in solution.)

Na/K GEOTHERRIOMETER The reaction

K+ + Na-feldspar = K-feldspar + Na+, (1)

was investigated experimentally by ORVILLE (1963). HEMLEY (1967) also investigated reaction (1) in the presence of muscovite and quartz. The equilibrium constant, Ke, for that reaction is

K = [K-feldspar][Na+]

6 [Na-feldspar][K+] ’ (2)

where the square brackets denote activities of inscribed species. The variation of the equilibrium constant as a function of temperature is given by the van% Hoff equation,

d log K,

d (l/T) = AHO

-2X%’ (3)

where T is absolute temperature and AH”,,, is the standard heat of reaction at given temperature. Equation (3) allows AH“(r) to be determined graphically by a plot of log K', values, derived from experimental studies, vs 1/T. Of great importance to this paper is the fact that the AH’(r) of reaction (1) varies only slightly with temperature. Because of this, a plot of log K, vs l/T yields a line with small curvature that can be interpolated and extrapolated with more confidence than a simple K, vs temperature plot. Once such a curve were established it would be advantageous to use it to determine an unknown temperature of equilibration from a given value of K,. However, it is not always possible to evaluate K, rigorously owing to un- certainties about both the purity of the solid reactants and the activity coefficients of the aqueous species. When the equilibration temperature is unknown, it is impossible to evaluate K, rigorously. For practical purposes we are forced to assume pure solid phases (unit activity by convention) and that activity coefficients for Na and K cancel each other so that K B a molar Na/K. Unfortunately, activity coefficients for Na and K may differ widely in high temperature aqueous solutions. Even so, when measured molal concentrations of Na and K for water-mineral reactions are plotted as log (Na/K) vs l/T, approximately straight lines result. The empirical curves based on natural water compositions and experimental points for the sanjdine-high-albite series are shown as such a plot in Fig. 1. Also shown for comparison is the theoretical variation in K, for equation (l), derived from low-temperature thermochemical data of ROBIE and WALDBAUM (1968) for microcline plus low-albite and calculated as suggested by HEL~ESON (1969), making use of average heat capacities (CRISS and COBBLE, 1964) for the aqueous ions computed from absolute entropies.

~~~ra~~~~i~~ either of the ~~~~~~ ~~963~ or ETEXLEY ~~9~~~ ex~rimental data to lower temperatures yields curves in the 100 to 300°C interval with significantly greater Ha/W: values than the ~o~~~nding theo~t~~al and empirical curves shown in Pig. 1, CMcuIations based upon molar volumes of microline and low-albite and partial molar volumes of aqueous NaCl and IiCI as functions of temperature and pressure (ELLIS and MCFADDEK, 1972) show that onIy a small part of this discrepancy may be due to the higher pressures at which the experimental work was perfurmed: 2000 bars for Orviflo’s work arzd fOOO bars for Hemley’s work, compared to hydrostatic pressure in s column of water everywhere at its boiling point for the theoretical curve, ~toi~hiometri~ a~t~vity-~e~~ien~s ap~ro~r~a~ to the experimental conditions were not known. Their omission may be the main cause for the discrepancy.

h’a/K ratios of waters from geothermal bores and cold-water wells and springs listed in Table 1 are plotted in z;‘ig. 2. Generally, thy maximum measured in-hole temperature is plotted. Unfortunately, the maximum measured temperature in a drilled hole is not always the tempera,ture of the aquifer in which a given sample of water equilibrates. W&er may enter a drilled hole through permeable channels from a still hotter region at depth, or the aquifer may be at a Iolver temperatnre. In the worst exampIe for chemical interpretations the water sample may be a mixture of waters from two di%rent a*quifers at different temperatures.

Ae~ording to EXLIS (f9?0), the silica method ~&LEON, 1966; ~~~~~~~~ and ROWE, 1966) of estimating temperature of underground hot water supplying a discharging well may be better than ~~ys~ca~ measurements in the same well. Where measured in-hole temperatures a.re not reported or are suspect, aquifer tem- ~era~ures have been estimated from the silica content of the water, silica-estimated tempernturcs are not used exclusively in this report because some of the silica data

1258 R. 0. FOURWER and A. H. TRUESDELL

Table 1. Chemical data for waters from known temperature environments. * Molal concentrations are given for Na, K, and Ca

Ref. Ns, Ii C& t + m, -

CzocHosLovalcr.i~t 201 Marklin 1 202 Loket 2 205 Lokct 5 203 V. Kamen 3 204 V. Kamen 4 206 Udoli G 208 Marianska 8 209 Krasovice 9 210 Lochousice 10 EL SALVADOR

13 Ahuac~i~pan 8 ICELAND

17 Akranes IS &beer I 20 Braiitarholt 1 21 FXioaar G23 22 Fludir 4 25 He@1 G3 26 H~Ilisholt I 27 Hlemmiskoid I 28 Husatottir 3 29 Husavik 31 Hvergcrdi 03 32 La&and 1 33 Laugarnas c;4 34 Loira 36 Namafjall 3 37 Reykir I 39 Reykjanes 40 Iloykjanes 2 41 Keykjancs 8 42 Rcykjsvik 43 Selfoss 7 44 SPlfOss 8 45 Srltjarnarnes S-1 1 46 Spoestadir 1

JAPAN 61 Hatchobaru 1 64 Otake 7 66 otdie 8 66 Otake 9 57 Otako 10

Mlwco 05 Mexicsli 5 66 Mesicali 8

Nnw ZEAI.:WD 69 Broadlands 1

72 Brosdlands 3 73 Broadlands 4 74 Broadlands 9 75 RroadlaxIds 10 ‘76 Broadlands 11 77 Broadlands 13 79 Kawrlzu 4 80 Ra\r-rrau 7A 81 Kawrau 7h 83 Kaw~rau 712

1 0~000238 0000064 OO00449 3 1 0000457 ~000102 0.00166 3 1 0‘000326 0‘000115 UG00641 4 1 0~000109 0000051 0~000254 2 1 0~000100 0000051 0~000210 3 1 0~00039I G~oooos9 0~00120 8 I 0~000130 ~ooaaz6 a.00~00 8 1 0.000196 0,000128 0,000524 10 1 0~000435 0~000089 0~00190 10

2 0.210 0.0223 0,00851 228

3 0.0591 0~000435 0,014o 110 4 0.00297 0~000036 0~000047 4 o.ao64~ 0.0~~~2 0.000439 72 3 0.00298 0~000090 0~000111 102 4 0~00324 0.000069 0.0000 18 3 0~00809 0.000468 OXIOOO4O 220 4 0~00301 ~0~~49 0~0000~~~ 4 0.00673 0.000095 0.000369 63 4 3 5

3

6

3 6 6

0.00604 0~000133 0.000254 0.0433 0~000803 0.00629 0~00923 0.000691 0~000037 0.00309 O~OOOG2 1 0*000158 0.00270 0~000059 0~000047 0.00852 ~000107 0.00135 0.00578 0000716 0~000027 Oa?4 18 G.0~~59 G.GO~G6 0.518 0.0435 0.0508 0.495 0.0411 0.0478 0.36: 0.0322 0.0413 0~00413 O.GO~33 0~000013

i0

94 216

47 136

74 265 69

225 190 253

4 0.00722 0~000123 0~000706 84 4 0~00:4s 0~000130 0~000783 79 3 0.00946 0~000151 0~00151 83 4 ct.00343 0~00005 1 0~000106 74

8 0.0607 0.00739 0.000247 293 8 0.0368 0.30269 0~000247 8 8

9 10

11 11

11

11 11 0.0404 0.00319 0~000050 292 11 G+l396 0.00366 0.~00027 2SO 11 G.0443 GaxiGO @O#OlH2 271 11 0.0426 0~00611 0~000060 258 12 O.Olh7 0~00143 0~000180 200 12 O.Oli4 0~00141 0~000102 ZOO 12 0.0398 0@0389 @~000087 2% 13 O~0324 WrlRl ii 0+nYlfi.i

0.0350 0.0407 0.0477

O-00276 0.00335 0.003F6

0,253 0.8402 0.487 0.0855

0.0463 0*00389 0.0457 0.00537 @C457 O~OOBi3 0.0454 0.00454 0.0467 0.00558

0~000494 0-000307 0~000502

0.00699 340 0~0180 355

0~000115 275 0~000055 260 G.00~55 255 0~000125 280 0.0(10076 270

log (r;a,‘K) f 1035 j3 log I:t/(w/Nal -

tat T )q=Gi /q=f7)q=f** -

218 2.00 0.97 0.86

109 100

2.23

135 212 137

2.62 2.13 2.68 1.92 2.89 1.90 2.67 1.62 2.45 1*61 2.03 1.24 2.53 I.79 2.98 1.83 2.91 1.66 2.72 1.78 2.05 1.13 3.12 2.15 2.44 1.66 2.88 1.90 I.65 0.91 2.92 1.55 2.01 1.08 2.16 I.08 1.90 la06 2.52 2*03 2.80 I.77 2.t4 1.76 2.81 I.$0 2.8s I,S3

1.71 1.71 1.20 1.96

1.06

1.80

270 0.W

200 226 247 155 75 85 79 7s

0.5G 0.96 0.97 2.01 1.96 1.95 2.00 I.98

291 1.57 216 2.05 227 2.00 246 1‘93 241 l%J

0*72 0.99 1.04 0.96 1.01

1.63 1Y59

0.63 O-56

234 1.82 264 1% 264 1.75 259 1.81 273 I.64 264 1.77 243 I-80 264 l.S4 259 I.88 183 2.11 179 2.11 260 I.81 262 I.88

0.91 1.14 1.10 1,09 1.12

0,:9 0.75

I.08 0.93 0.90 0.92 0.92 0.89 1.03 0*90 0.92 I.12 I a9 I.01 1.01

0.86 @67 G+i 0.7% 0.68 0.64 0.74 @7% 0.68 1.07 1.01 *a1 0.79

3.62 0.73 3.17 3.62 0.65 3.23 3‘61 0.45 2‘97 3.64 0.33 3.24 3.62 0.29 3.17 3,56 0.64 3.24 3.56 0.71 3.42 3.53 0.19 2.94 3.53 0.69 3.35

2.54 2.41 2.58 2.25 1.82

2‘44 2,46 2.22 2.06

2.99 2.20 2.75

2.57

2.53 2.52 2.61 243

Teble I-(Co:onkZ.)

An empirical Na-K-G geothermometer for natural waters

Ref. Ns K Cn. tmt a

83 Kawereu 8 84 Kawerctu 8 86 Kawersu 8 86 Kawerau 10 87 Kawerau 17 88 Neawha, 1

6 O-0362 270 285

250

230

260 234 220

0.000027 0~000050 0-000050 0.000699

0.000723 0~000013 0~000025 0.00125 0~000349

0.0110 0~00103 0.0663 0~00450 0.0554 0~00570 0.0272 0.00225 oa374 0.00396 0~0%~ 0,004Ql 0.0517 0~00192

275 220

0.0502 0.00192 0.0565 0.00523 0.0487 0.00320 0.0522 0.00512 0.0522 0,00512 0~0611 0.00440 0.0511 0.00334 0.0574 0.00575 0.0522 0~00511 0.45’3 0.00972

0.000225 0~000250 0~000574 0.000873 0~000823 0~000449 0~000549 0.000437 0~000499 0.0~~99 O-000674 0.000425 0.000437 0~0100

260 253 214 231 260

261 1.84 0.98 0.64 257 1.79 0.98 @70 266 1.86 0.99 0.72 221 1.91 1,17 0. Y6 259 l-88 0.99 0.79 221 1.99 1.31 1.24 223 2.02 1.29 1.24 223 Ie-GY 1.24 0% 232 1% 1‘03 O.Y2 217 2.03 1.17 0.94 256 1.89 0.99 O-83 199 2.12 1.08 0.99 247 1.82 0.97 0.85 231 2.03 1,06 0.94 192 2.13 1,43 1.35 193 2.15 1.42 1.34 243 1.94 1.00 O-86 197 2.13 1.18 1.12 245 1.91 1.01 0.88 248 1.90 1.01 0.89 231 2% 1.06 @96 221 1.98 1.12 I.03 245 1.88 1.00 0.65 245 1.93 1.01 0.88

4 3.61 I.67 1.45

0.00425 0~000060 200 175 2.11 1.15 0.86

0.000767 0~000020 0.00166 0.00132

236

0.0174 0-000921 0~000044 0.000023

0~000565 0~000161 0~000143 0~000281 0.5i4 0.00226 0,465 0.00427 0.600 0.00381 0.283 0~00250 0.343 0.00239 0.273 0~00281 0.244 0.00192 0.333 0-00299 0.271 O-00203 0.308 0.00264 0.565 0.00389 0.170 0.00241 0.163 0~00241 0.134 0~00192 2.19 0.448 2.31 0,422 0.461 0.0320 O-0290 0~00161 0.0332 0~00192 0.0129 0~000358 0.0133 0~000460 0.0141 0~000384

0~00107 0.0~998 0.00137 0.00230 0~00157 0.00230 0~00140 0.0199 0~0250 0.0424 0.0174 0.0247 0~106 0.0377 0,111 0.0444 0~0509 0.0521 0~00254 0.000766 0.000766 0699 0.719 O-0280

175 10 11 10 11 10 9

11 11

231 181 185

1.00 I.32 1.13

wt 99 97

100 102 109 101

0~000042

0~0000~7 0.0110072

101

101 100 9s

135 136 136 340 300 190 186

178 196 1”O

83 118 105 114 112 125 121 116 119 115 110 143 150 134

o.oooj74 0~000167

175 203

1% I-12 2.20 l-31 2.23 1.28 3.53 0.28 3.52 0.23 3.53 0.16 3.52 0.37 3.53 0.71 3.54 0.27 3.52 0.55 3.52 0.71 2.18@ 2.41 2.56 2.04 2&?J Z-20 2.58 Z-05 2.60 2.16 2.51 1.99 2.54 2.10 2.57 2.05 2.55 2.12 2.58 2.08 2.61 2.16 2.40 1.85 2.36 1.83 2,46 1.85 1.63 0,69 I.75 O.iP 2.16 1.16 2.18 1.26 2.11 I.24 2.23 1.56 2.13 I.46 2.26 1.56

2.20 1.88 2.04 1.94 2.05 2.01 1.91 2.05 2.09 2.04 2.03 1.67 1.57 1.52 @65 0.59 1,01 1.20 I.10 1.45 I.41 1.49

12 0.0384 13 0.0322 12 13 5

13 14 13 S

13 15 13 13 16 17 13 16 18 18 18 1S 5 a

19

20

21 21 21 22 22 22 22 22 22 22 22 23 23 23 23 23 23 23 23 23 23 23 23 23 23 24 26 24 26 21 27 27 21

0.0310 0.0299 0.0413

89 N;awhs 1 91 Orakeikorako 2 92 Orakeikomko 3 94 Rotokaua 2

100 Taupe 1 105 Waiotapu 6 106 Waiotapu 6 109 Wairakei 4/l 110 Wairakoi 9

oa391 0.0239

111 Wairakoi 9 112 Wairskei 20 113 Wairakci 21 114 Wairakei 27 115 Wairakei 28 116 Wairakei 41 I.17 Waxakei 43 118 Wairakoi 44 1 IQ Wairskoi 48 OCEAN

TCBKEY 120 Kizildern KDl UNlTED STATeES 134 Beowawa 2 137 Bradv’s 2 139 Casabiablo 3 2 I1 Center County Ps. 12 212 Center county Pa. 16 2 13 center County Pa. 40 214 center county Pa. 66 215 Center county Pa. 75 2 16 center county Pe. 88 217 Center County Pa. 91 218 Contar county Pa. 179 2 19 Kettleman Hills 72

0~0600

0.0101 0.0339

4.11 4306 3.70 3*76 3.76 4.1 t 3.11 3.93

220 Kettleman Hills 12 221 Kettlom~n Hills 73 222 Kett.leman Hills 48 223 Kettleman Hills 74 224 Kettlem:m Hills 13 225 Kottlemtura Hills 21 226 Ksttlamsn Hills 31 227 Kettleman Hills 32 228 Kettleman Hills 102 229 Kettleman Hills 84 230 K&tleman Hills I 231 Kettlemarl Hills 2 232 Kettleman Hills 5 144 Salton Sea I.I.D. 1 145 Saltcn SOS I.T.D. 2 146 Seltun Sea I.I.D. 3 150 Stsambnst Spgs. 1 151 Steemborzt. Spgs. 2 165 Yello;vstono Park Y3 166 Yellorvstone Park 1-4 167 Yellowatonc Park 1’5

1260

Table I-(Co&.)

R. 0. FOURNIER and A. H. TRUESDELL

log (Na/K) + 1 oq /9 log [dWa)/Nal

Ref. Na K Ca tmt t*S r ,f?=oi/ /3=+ap= ;**

168 Yellowstone Park Y6 169 Yellowstone Park Y8 170 Yellowstone Park Y9 171 Yellowstone Park Y 10 172 Yollowstone Park Y13 U.&S .R. 177 Pauzhetsk 4 182 Kamchatka 35 WEST PAKISTAN 184 Shadman 27 FLUID INC~~USIONS Providencia 62-S-146 Providencia 62-S-145 Provide&a 60-H-67 Providencia 60-H-67 Providencia 60-H-57 Providencia 60-H-57 Providoncia 60-H-57 Providencia 63-R-22 Providencia 63-R-22 Providencia 62-S-320 Providencia 63-R-39 Providencia 63-R-39

27 0.0148 0.000563 0.000250 181 2.20 1.42 1.43 27 0.0164 0.000563 0.000147 170 2.26 1.47 1.42 27 0.0117 0~000409 0~000020 196 2.13 1.45 1.32 27 0~00700 0.00176 0.0112 72 2.89 0.60 2.17 27 0.0130 O.OOOi16 0.000037 195 2.14 1.26 1.15

28 0.0429 0.00269 0~00130 28 0.0141 0.000639 0.000574

195 194 2.14 174 2.24

3.32

1.20 1.34

1.18 1.42

29

30 30 30 30 30 30 30 30 30 30 30 30

0.00152 0~000128 0~00105 28 1.08 2.85

0.513 0.123 0.0624 0.970 0.261 0.250 0.296 0.0639 0.170 0335 0.0767 0.0749 0935 0.212 0.302 0.861 0.174 0.594 0.948 0.230 0.384 0.352 0.0’742 0.105 0.365 0.0870 0.130 2.77 1.19 1.43 0.948 @179 0.217 3.48 1.29 2.24

;;“,” II

358 358 365 365 365 365 365 365 290 372

1.66 0.62 0.62 1.66 0.57 0.47 1.58 0.66 0.71 1.58 0.64 0.61 1.57 0.64 0.57 1.57 0.69 0.68 1.57 0.61 0.55 1.57 0.68 0.66 1.51 0.62 0.62 1.57 0.37 0.24 1.78 0.72 0.62 1.55 0.43 0.31

* The tabulated waters are from wells, except for the fluid inclusion waters from Providencia, Mexico. t t, is generally the maximum measured temperature in a given well. Where a reservoir temperature is known to be different

than the maximum temperature, the reservoir temperature is given. 2 t, is temperature of last water-rock equilibration estimated from the silica content of the water. 9 Reciprocal of absolute temperature. If different t, and t, values are listed, the reciprocal oft, is given. 11 Tabulated values for log (Na/K). 7 Tabulated values for log (Na/K) + j log[l/(Ca)/Na] are given only where they are less than 2.3 01‘ where d(Ca)/Na is

less than one. ** Tabulated values for log (Na/K) + $ log [d(Ca)/Na] are given only where they are greater than 2.0 and 2/(Ca)/Na is

greater than one. tt The waters listed from Czechoslovakia are from wells in granitic rock. These are typical of spring waters in granitic rocks

found elsewhere, e.g. the Sierra Nevada of California described by FETH et al. (1964). $$ Temperatures of the Kettleman Hills waters estimated from the geothermal gradient and depth of the producing zone. @ The reciprocal of silica temperature is listed for the Kettleman Hills waters. We believe that thie is a more reliable tem-

perature than the geothermal gradient estimate. (j 11 The average filling temperature is given for the fluid inclusion data.

1. PACES (1972). 16. SARBUTT (1964). 2. SI~VALDSON and CUELIAR (1970). 17. MARON (1967). 3. ARNASON and TO~IAS&N (in press). 18. MAHON (1966). 4. ARN&SSON (1970). 19. RANKAMA and SAEAMA (1950). 6. EIJ.IS (1969). 20. DO~MINCO and SAMILGIL (1970). 6. BJ +NSSON et a~?. (1970). 21. D. E. White (unpublished data). 7. ELLIS (1967). 22. LANQMUIR (1971). 8. KOGA (in press). 23. KHARAKA (1971). 9. ELLIS (1970). 24. MUIPFLER and WHITE (1969).

10. MERCADO (1967). 25. WHITE (1968). 11. BROWNE and ELLIS (1970). 26. WHITE (1964). 12. bfAHON (1962). 27. R. 0. Four&r and R. D. Barnes (unpublished data. 13. MAHON (in press). 28. VARIN et cd. (in press).

14. ELLIS (1966). 29. BARNES and CLARXE (1969). 15. i+hHON (1964). 30. RYE and HABBTY (1969).

,4n empirical Na-K-Ca geothermometer for natural waters

a Geoiherm. grad. temp; ailfield water A Silica temp; oil field water

z ~.~~t!pt,,p’ \ICo/Na -=I . I

D Measured tBmR; G/Na z 1 f Fluid inclusion filling temp. 0 HEMLEY (1967) D ~vrue(l963)

1261

0 t

400 300 203 loo 50 25 0 II IiII / I I I L 1 1 , i / 1

1.4 I.6 22 2-6 3.0 3.4

lO3/T

Fig. 2. Na/K values for natural waters vs assumed equilibration temperature. The lower dashed line combines the empirical curves of ELLIS (1970) and WHITE

(1965, curve E). See text for details.

in Table I may not be reliable owing to variations both in analytical technique and in sample storage and treatment procedures prior to analysis. Also, the method and conditions of sample collection are not always specified, so that one must guess about possible evaporative concentration of the sample owing to steam loss. A correction for steam loss would be necessary in order to use silica to estimate underground temperature. Evaporative concentrations do not affect Na/K ratios.

In Pig. 2, a line extrapolated from HEBILEY’S (1967) experimental results sets an upper limit for the Na/K data points of the natural waters. Above 200°C most points cluster close to the empirical curves of ELLIS (1970) and WHITE (1965), but below 200°C there is much more scatter. This might be attributed to disequilibrium states of the low-temperature waters, including ocean water. However, most Na/K values for water from oil wells at the Kettleman Hills (California) and from drill holes in Yellowstone Park plot significantly above the empirical curve. The Yellowstone Park waters issue from potassium-rich rocks, and it is unlikely that the high Na/K values result entirely from disequilibrium. Some waters at higher temperatures from other places also have relatively high Na/K values, such as No. 88 from Ngawha, New Zealand (23O”C), and No. 91 from Orakeikorako, New Zealand (260°C). If one were using the empirical curves and the compositions of these New Zealand waters to estimate subsurface temperature, the estimates would be too low by approximately 65 and 7O”C, respectively.

Sample 171 from Mammoth Hot Springs, Yellowstone Park, is particularly noteworthy. In terms of total dissolved solids, it is the most concentrated water in


the Park. The water is very rich in calcium, it deposits travertine, and has a very low Na/K ratio. The subsurface temperature estimated from the Na/K ratio in that water would be in excess of 400°C. The temperature found by drilling leveled off at 72OC, which is compatible both with the low silica content and high calcium content of the water, as will be discussed later.

It is evident that a geothermometer based on the simple Na/K ratio in natural waters must be used with extreme caution. It should be used only for waters showing other evidences for a high temperature source, e.g. high SiO,, low Ca, etc. Very high estimated subsurface temperatures may be obtained for waters from low- to moderate-temperature environments. Conversely, using the empirical curve of ELLIS (1970) and WHITE (1966), Na/K ratios of some waters may indicate temperatures as much as 60 to 70°C too low.

EFFECT OF OTHER REACTIONS

One of the main reasons for the scatter of points in Fig. 2 is that at any given temperature the Na/K ratio depends upon the specific reaction taking place (FOURNIER and TRUESDELL, 1970). For example, HEMLEY (1967) showed that at the same temperature the Na/K ratios are different in solutions equilibrated with K-feldspar and albite compared to muscovite and albite. A whole spectrum of Na/K vs temperature curves is possible, depending upon which minerals control solution composition.

Other cations also may have an effect upon the Na/K ratio. For instance, for a reaction in which plagioclase alters to K-feldspar with the liberation of Na+ and Ca2+,

Kf + Na,Ca, plagioclase + 4y quartz = K-feldspar + zNa+ + yCa2+, (4)

neglecting activity coefficients, an approximate equilibrium constant, K*, is

Nao-%)Cau K*= K . (5)

In most natural systems the amount of Ca in solution is controlled by the solubility of a calcium-bearing carbonate (generally calcite) at given conditions of temperature, pH, and partial pressure of CO,. On the other hand, except for the alkali lake environment, the amounts of aqueous Na and K are not controlled by the solution and deposition of alkali-bearing carbonates. With this in mind it is inter- esting to observe the distinct temperature-dependent trend obtained when log [1/(Ca)/K] is plotted vs 103/T, as shown in Fig. 3. Except for ocean water, even the low temperature waters follow this trend. Similarly, in Fig. 4 a plot of log [+‘(Ca)/Na] vs 103/T shows a linear trend, but with more scatter of the data points. These linear temperature-dependent trends throughout the entire temperature range are contrary to the result shown in Fig. 2, where log (Na/K) values for low temperature waters depart drastically from the trend defined by the high-temperature data.

We interpret these results as follows: although absolute quantities of aqueous Ca generally are controlled by the solubility of carbonate, Ca also enters into silicate reactions in competition with K and Na. Therefore, the amounts of aqueous Na and K are influenced by the aqueous Ca concentration. In general, natural waters

An empirical Na-K-Ca geothermometer for natural waters 1263

30 0 Measured temp.

). Sllico tsmp. 0

*Geothermal gradient temp.,

20 OSilica temp; oil well Hz0

+ Fluid- inclusion temp.

5 IO

I. oc 6M) 400 300 200 100 50 25 0

III Irii 1 I I I I I 1 1.0 ’ 1 r l ’ ’ i 1 8 / / 1 I

I.4 16 2.2 2.6 30 34

103/T

Fig, 3. Log [1/(&)/K] vs reciprocal of absolute temperature for naturrtl waters.

3of- Eb

o Measured temperature 0”

A Silica temperature

2.0 - 0 Geothermal gradient temperature; oil well $0 k

2

OSilica temperature; oil well I+,0

@ ,.,1

i-Fluid-inclusion filling temperofure 0 0

0-

oocean

-lo 600 4 2 0

I I I I I I I IO 14 18 22 28 30 34 36

to3/ T

Fig. 4. Log [ACNE] vs reciproaal of absolute ~0rnper~t~~ for natural waters.

contain much less K than Na. Therefore, for a given amount of reaction in response to a change in Ca concentration, a change in aqueous K will be more evident than a change in Na concentration, i.e. aqueous K tends to change so as to ahow any given ratio of aqueous Ca to Na to satisfy an equilibrium expression such as equation (5). Thus, aa expected, the correlation of K with Ca shown in Fig. 3 is better than the

correlation of Na with Ca shown in Fig. 4. However, in the low-temperature waters shown in Fig. 4 the absolute Na concentrations are. so low that changes in Na are evident in response to changes in Ca concentrations.

In view of the above considerations, we believe that aqueous Na-K-Ca relationships generally can be explained entirely in terms of silicate reactions even though


the absolute quantity of aqueous Ca is controlled by the solubility of carbonate. Many different reactions may occur involving only aqueous Na+, K+, and Ca2+, but all are limited to three configurations:

(x + 2y)K+ + solid = xNa+ + yCa2+ + solid (6)

(2~ - x)K+ + xNa+ + solid = yCa2+ + solid (7)

(z - 2y)K+ + yCa2+ + solid = xNa+ + solid. (9)

To facilitate comparison, equations (6), (7) and (8) can be written in terms of a single potassium ion participating in the net reaction so that the approximate equilibrium constant, K*, for all possible reactions can be transposed to a generalized

form,

2/G logK* =logg+/3log=,

in which the value of p depends upon the stoichiometry of the reaction. In formulating equation (9), the following assumptions were made : (1) excess

silica is present. In general, this is a valid assumption because quartz, chalcedony, or cristobalite is commonly present in hydrothermally altered rocks. (2) Aluminum is conserved in the solid phases. In actuality, this is not true because the aluminum content of a given volume of rock commonly changes in the course of hydrothermal alteration. However, except in rare acid waters, so little aqueous aluminum is present compared to other cations that it can be neglected. (3) The formation of a hydroxyl-bearing mineral on one side of an equation is balanced by the decomposition of a hydroxyl-bearing mineral on the other side, i.e. hydrogen ions involved in hydrolysis cancel out of the net equation. This assumption may not be valid everywhere. From a practical point of view, however, the incorporation of hydrogen ion into an expression used for estimating subsurface temperature must be avoided. The pH of a water ascending from a hot environment to a cooler environment generally will change owing to continued reaction with wall-rocks, to loss of gases such as CO, as the water boils, and to the change with temperature of dissociation constants for various hydrogen-bearing species such as H&3,. In order to correct for these effects, subsurface temperature and CO, partial pressure must be known.

For reactions (6) and (7), b = 2y, and for reaction (8), B = -2~. For the alkali feldspar reaction shown in equation (l), or any reaction involving only Na- and K- bearing minerals, j3 = 0 and equation (9) simplifies to log K* = log (Na/K). For reactions involving only Ca- and K-bearing minerals, /3 = 1 and equation (9) simplifies to log K* = log [2/(Ca)/K]. For any reaction in the configuration of equation (6) in which one unit of K+ is fixed in the solid and appropriate amounts of Na+ and Ca2+ are released, such as in equation (4), the value of /? is between 0 and 1. For reactions in the configuration of equation (7), p is greater than 1, and for reactions in the configuration of equation (S), p is a negative number.

Figure 5 shows the distribution of data points for well waters plotted in terms of log (Na/K) + B log [d(Ca)/Na] for p = 0, (K,, exchanged for Na,,), compared to b = 2, (K,, + Ca,, exchanged for 3NaJ. Above lOL”C, the points are more scattered using fi = 2 than using p = 0, and the reverse is true below 100°C. We reasoned


i

olog(Na/K). p=O rlog(Na/K)+2log(~/No)

t

5

f4

0 .

3

Z-

1

0

A

No.171, p=2

No. 66 0

I ’ I ’ I I I ’ I ’ I t IO I .4 I.8 22 2.6 3.0 3-4

103/T

Fig. 5. Distribution of data points for well waters using ,L? = 0 compare to p = 2, plotted vs the reciprocal of absolute temperature.

that at some intermediate value of p between 0 and 2, the log K* values calculated for most waters would fall closer to a temperature-dependent line. In order to find an average value of B that would yield less scatter in the log K* values, we used a subjective graphical method based upon the relations shown in Fig. 5. For example, the log K* value for ,9 = 1 lies half way between the points for /? = 0 and @ = 2, and the log K* value for /? = 4 lies one-fourth the distance from the ,5 = 0 to the @ = 2 point. It is evident that the positions of some points, such as Nos. 66 and 171, are greatly affected by changes in p, and other points, such as No. 22, are hardly changed at all. All the corresponding pairs of data points depicted in Fig. 5 were connected by vertical tie lines, and a slanting straight line was then drawn through them so that it intersected the ‘most important’ vertical tie lines at about the same relative position along each tie line. (Our plot is not illustrated in this paper because at a scale necessary for reproduction it would show only an incomprehensible jumble of overlapping lines. The ‘most important’ data points were selected on the basis both of our estimation of the reliability of the temperature and chemical data and upon an effort to insure widespread geographic representation,) To a great extent, the position of the resulting line was fixed by pairs of data points with small vertical distance between them. This line passes through the points 103/T = 1.70, log K* = 0.560 and 103/T = 3.20, log K* = 3.031. Above 100°C it intersects most tie lines about one-sixth the distance from /? = 0 to @ = 2 (4 the distance from ,!l = 0 to /? = l), so that log K* data points cluster along a linear trend when a b value of Q is used, as shown in Fig. 6. Below lOO”C, log K* values plot near a linear extension


-Fluid inciusion filling temp. DMeasured temp. ~Silico temp. *011 well water. geothermui

gradient temp. AOit weli water, silica temp.

q Measured temp., p = 4/3

Fig. 6. Suggested curve for geothemometry of natural waters. The two dashed lines show f 15*C and - 15% with respect to the middle curve. Superimposed am the data points for the well waters listed in Table 1. See text for details.

of this line when b = 4 is used. [Previously @'OBRNIER and TRUESDELL, 1971), we suggested a line with a slightly diEerent slope and the use of p = 8 for low- temperature environments. Additional data acquired recently have caused us to change our original curve.] Most data points fall within about & 15 to 3U°C of this line. An exception is in the 5 to 15OC region, where many points plot either above or below the curve. In this temperature interval, the points that faI1 below the curve are generally for waters from granitic rocks, and the points above the curve are for waters from limestones and dolomites. The scatter of points may reflect departures frum chemical equilibrium and/or different net reactions taking place in rocks of greatly different compositions.

For @ = Q, the net reaction is

K+ f solid + iCa2+ + $??a+ + solid,

and for ,!? = s, the net reaction is

K+ + $Na+ + solid F+ @a2+ + solid.

We do not mean to imply that all reactions above 100°C in hot-spring systems have the stoichiometry of equation (10) or that all reactions in the weathering environment have the stoichiometry of equation (I 1). However, it appears that the combined /3 = 6 and /! = + straight-line curve may serve as a useful reference for geother- momet,ryof manywaters. It should be particularly useful for waters in which the silica geothermometer of FCNJRWIER and ROWE (1966) is ambiguous, i.e. high-siliea values may be due to equilibria with quartz at high temperatures deep underground or to metastable equilibrium with amorphous silica at low temperatures near or at the surface. Neither the SO, nor the Na-K-Ca geothormometers are reliable for acid suIfate-rich waters that contain little chloride.


In considering equations (10) and (ll), it should be remembered that a net reaction cannot be deduced only from the composition of water flowing from a rock or only from the mineralogy of an alteration assemblage. One must know either the change in composition of water as it flows through a given volume of rock or the change in bulk composition of that given volume of rock in response to water-rock reactions. In the real situation, new Na- and Ca-bearing minerals may form con- currently with decomposition of other Na- and Ca-bearing minerals. If, during this alteration, there is a net decrease in Na and Ca in the solid phases per given volume of original rock, then the new Na- and Ca-bearing minerals cancel out of the net equation.

Equation (10) is entirely consistent with the usual changes in bulk chemistry of igneous rocks that result from hydrothermal alteration associated with ore deposition. Generally, progressing from fresh to more altered rock, there is first a progressive leaching of Na and Ca with simultaneous fixation of K. Potassium is removed from the rock only after Na and Ca are essentially depleted. The situation in regard to equation (11) and the weathering environment is less clear cut. Most chemical studies ofweathered rocks give only the composition of the least and most weathered portions of rock with little regard for the bulk chemistry of the main portion of intermediate weathered material. The situation is further complicated by seasonal fluctuations in water tables and a tendency toward non-equilibrium conditions as rates of reaction decrease with decreasing temperature.

Na-K-Ca GEOTHERMOMETER

We suggest that Fig. 6 may be used to estimate temperature of last rock-water equilibration as follows: (1) express the concentrations of dissolved species in units of molality. (2) Using molality values, calculate log [2/(Ca)/Na]. If this number is negative, calculate log K* for p = $, and use Fig. 6 to estimate temperature. (3) If log d(Ca)/Na is positive, calculate log K* for /3 = $, and determine whether the temperature estimated from Fig. 6 is greater or less than 10G”C. If greater than lOO”C, recalculate log K* using ,5 = 4, and use that value to estimate the temperature. Otherwise, use /I = $ to estimate the temperature.

Table 2 lists subsurface temperatures estimated by the silica (FOURR’IER and ROWE, 1966), log (Na/K) (Fig. 1) and log (Na/K) + /? log [d(Ca)/Na] (Fig. 6) methods using compositions of hot-spring waters from several regions where reservoir temperatures are known in nearby drill holes. Obviously, no single method works best for all waters. However, the silica method and calcium-corrected method (Fig. 6) are better than either the ELLIS (197( ) or extrapolated experimental (HENLEY, 1967) curves for most waters. In comparing the results shown in Table 3, it should be remembered that hot-spring waters may come from aquifers or reservoirs at more shallow depths or lower temperatures or both than the main reservoir supplying a given geothermal well. Thus, some of the low estimated temperatures, compared to measured temperatures in drill holes, may be real in the sense that shallow aquifers or reservoirs do exist at the lower temperatures. This is in contrast to a situation in which water compositions change either by continued water- rock reaction or by mixing with near-surface water during travel from a deep reservoir to the surface.

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Table 3. Composition (parts per million) of hot spring YF 392 in Yellow- stone National Park compared with the composition of water from the

nearby Y-5 drill hole. (Roberta Barnes, analyst)

T(“C) SiO, PH ca fifg Xia K Li NH, HCO,* SO, Cl F B

1

170

6.7 2.9 0.10

324 I5

3.1 0.21

423 15

234 19

2.4

2

3.38 0.12

377 I7

3.6 0.24

493 17

273 22

2.8

3

92 (boiling) 210

8.44 0.4 0.005

360 9.1 3.2

to.1 467

16 268

25 2.8

4

7.25 20.0

0.90 1.65 0.97

0.91 0.94 0.87 0.76 0.86

1. LVater collected in a stainless steel bottle (FOURNIER and MORGAN- STERN, 1971) from 75 m deep in the Y-5 drill hole, Yellowstone Park. The hole is 164 m deep and penetrated just one aquifer at a depth of 76 m and temperature of 17O’C.

2. Calculated composition of water from the Y-5 drill hole after loss of 14.2 per cent water through adiabatic cooling and separation of the resulting steam, but no loss of dissolved constituents.

3. Composition of hot spring YF 392.

4. Ratios of constituents in aquifer to constituents in the hot-spring water. If the aquifer water cooled entirely adiabatically from 170 to 92”C, without loss or gain of dissolved constituents, the ratios would be 0.86.

* Total alkalinity expressed as HCO,-.

In many places, significant water-rock reaction occurs during the upward movement of an increment of water from a reservoir to the surface. Table 3 com- pares the composition of water in a hot spring with that in the reservoir feeding that spring. The reservoir was found 76 m deep with a temperature of 170%. It is a highly fractured zone in otherwise impermeable ash-flow tuff. The fractured zone may be stratigraphically controlled, possibly caused by a discontinuity in the cooling history of the ash-flow tuff (L. J. I?. Muffler, oral communication, 1972). Water in tl e spring, 30 m distant from the drill hole, is boiling and flows at an estimated rate of 20 liters per minute. Taking the silica content, 210 ppm, of the hot-spring water and assuming cooling entirely by adiabatic processes as the water moves from the reservoir to the surface, a reservoir temperature of 172% is estimated by the method of FOURKIER and ROWE (19GG). This is in excellent agreement with the measured reservoir temperature of 170°C. Therefore, it appears that an assumption of adia-

batic cooling is good. The ratio of chloride in the deep water to that in the hot-spring water also supports this assumption (see Table 3, column 4). In order for the water to cool adiabatically (without loss of heat by conduction), the water must have risen

1270 R. 0. FO~JRNIER and A. H. TRUESDELL

to the surface relatively quickly. Yet, a great deal ofwater-rock reaction has occurred during the ascent, as shown by the decrease in calcium and potassium, instead of the expected increase. Thus, we can expect that the Na-K-Ca geothermometer will commonly yield temperatures lower than the reservoir temperature because of continued reaction with wallrocks at lower temperatures during ascent. In the example just described, the reservoir temperature estimated from the Na-K-Ca content of spring YF 393 is 153”C, 17% less than the actual temperature. In a few hot spring systems, such continued reaction may be minimal because the channelways are lined with non-reactive silica (FOURNIER and TRUESDELL, 1970).

EFFECT OF pH

When a water emerges from a spring or well, its hydrogen ion activity may be over an order of magnitude different from the original hydrogen ion activity of that water at depth. Furthermore, the original pH at depth can be calculated only if subsurface temperature and partial pressures of gases such as CO, are known. Therefore, as previously noted, hydrogen ion cannot be incorporated into an expression used for estimating subsurface temperature. In formulating our empirical expression relating water composition to subsurface equilibration temperature we have assumed, for practical purposes, that hydrogen ions do not enter into the reaction. This is equivalent to saying that, although several different simultaneous reactions may be taking place, one reaction can be written in which the solid products and reactants undergo a change in Na, K and Ca, but not hydrogen ion. Such a reaction will define a Na-K-Ca relationship, such as equation (9), which is inde- pendent of other simultaneous reactions in which hydrogen ion does participate. The fact that the data points shown in Fig. 6 show so good a correlation with temperature suggests that this is generally the case.

For situations in which hydrogen ion does enter into the net reaction equations similar to (6), (7), and (8) may be formulated :

K+ + zH+ + solid = xNa + 1+2--x

~ Ca2+ + solid

Kf + xNa + zH+ + solid = 1+x+2

2 Ca2+ + solid

x-l-z K++ 2

Ca2+ + zH+ + solid = xNa + solid.

(10)

(11)

(12)

The corresponding approximate equilibrium constant, I<**, for each of these reactions is :

NW logK** &log; -log; +(I f.2 4)logH (13)

log R*" = d/(C4 -xlog~-log;+(l +z+x)log~

log K** =

(14)

(15)

An empirical Na-K-C& geothermometer for natural waters 1271

Equations (13) and (15) are identical, except that x is larger in (15) than in (13).

For better comparison with equation (Q), equations (13) and (14) may be recast, respectively, into the following forms :

log K** = log N; + (1 - 2) log d(Ca) d(Ca) Na + 2 log H

log K** = log ; + (1 + x) log 2/(Ca) 2/(Ca) Na + ZlogH. (17)

Equations (16) and (17) are similar to equation (9) except for the additional term z log [2/(Ca)/H]. As yet, we have not evaluated whether addition of this term would increase or decrease the scatter of points shown in Fig. 6.

EFFECT OF CARBON DIOXIDE

At a constant partial pressure of CO, the stability of calcite decreases as temperature increases. Depending upon pH relationships, the solubility of calcite may either increase or decrease as the partial pressure of CO, increases. Where pH is controlled or buffered by silicate hydrolysis reaction, an increase in Yco, decreases the amount. of Ca in solution, thus decreasing the solubility of calcite. On the other hand, where pH may decrease in response to an increase in P,,, the solubility of calcite also will increase as Pco, is increased. In general, silicate reactions will control pH deep in hot spring systems where temperatures are high and rates of reaction are rapid. On the other hand, in cooler environments where high partial pressures of CO, exist pH is likely to be controlled by carbonate equilibria. In any event, the important consideration is the amount of aqueous Ca in the water. High aqueous Ca contents require smaller Na/K ratios according to equation (9). This accounts for the very low Na/K values in Ca-rich waters, such as those at Mammoth hot springs, Yellowstone Park, and, in fact, most other travertine- depositing thermal waters. For CO,-rich or Ca,,-rich environments, the Na-K-Ca geothermometer will give good results provided that calcium carbonate was not deposited after the water left the reservoir. Where calcium carbonate has been deposited, the Na-K-Ca geothermometer may give anomalously high temperatures.

EXPERIMENTAL RESULTS

A few experimental results with little or no CO, present bear upon the empirical geothermometer presented in this paper. The most significant are some experiments by J. J. Hemley (oral communication, 1971) conducted at 1000 bars and 300 and

5OO’C in which chloride solutions were equilibrated with mixtures of K-feldspar plus andesine. The resulting solutions were analyzed for Na, K, and Ca. The analytical results are plotted in Fig. 7. The log (Na/K) values plot far below the empirical Na/K curve from ELLIS (1970) and WHITE (1965, curve E) and the experimental curves for albite plus K-feldspar (HEMLEY, 1967 ; ORVILLE, 1963). When the

B = $ correction is applied, however, the data plot very close to the empirical @ = + curve derived from natural water compositions. This experimental work was not taken into account when the /3 = 6 empirical curve was drawn.

One of us (Fournier) has carried out some experiments at temperatures below 300°C, and the results of these are also plotted in Fig. 7. In two experiments, basalt

11


K-fe1d.t andesine

altered to clinop-

tilolite(Fournier. unpub.)

Elasalt(Fournier, unpub.)

q Na/K alb. + K-feld.(ORVILLE. 1963)

“C 600 500 400 300 200 100

I lb

I I I I I I I I 14 l-8 22 2.6

103/ T

Fig. 7. Comparison of experimental and empirical results. The dashed line is the Na/K empirical curve combined from ELLIS (1970) and WHITE (1965, curve E).

The lower solid line is the empirical p = & curve from Fig. 6 of this paper.

was dissolved in pure water at 200° for 30 days and at 194°C for 37 days, and the resulting solutions were chemically analyzed. Again the data fall on or close to the empirical curve for /l = 4. Similar results also were obtained at 200°C when clinoptilolite-rich rock was reacted with 0.05 m NaCl for 13 days. In another group of experiments clinoptilolite-rich rock was dissolved at 150°C for 13 days; one part was reacted with 0.05 m NaCI, and a second part was reacted with a 50: 50 mixture of NaCl plus KC1 (0.09 m total chloride). Base exchange occurred and the resulting solutions approached each other in composition. The data bracket the empirical b = g curve, but plotted as Na/K are far off the empirical curves of ELLIS (1970) and WHITE (in press).

Additional experimental work will be necessary to calibrate the Na-K-Ca geothermometer and to understand its implications. However, the initial agreement between experimental results and the empirical curve is very encouraging.

CoNCLUsIoNs

The ratio Na/K should be used for geothermometry with great caution, and preferably only for near-neutral and alkaline waters that do not deposit travertine and/or waters with log [2/(Ca)/N a ] 1 ess than 0.5. In Table 3 it is evident that some waters give better results when referred to the ELLIS (1970) curve, and others give better results when referred to the extrapolated experimental curve of HEMLEP (1967).

Much of this ambiguity is removed when a correction is made for the calcium content of the water. The function, log (Na/K) + @ log [2/(Ca)/Na], appears to work well for most geothermal waters when /3 is assumed to be i or +, according to the criteria in a preceding section. However, in some places the net rock-water


reaction may be such that /? is greatly different than our assumed value. If this is true, our calcium correction method may fail to yield the correct temperature.

All ‘water composition’ geothermometers may be adversely affected by continued water-rock reaction as the waters ascend and cool. Waters that initially have little calcium will generally yield low estimated aquifer temperatures owing to continued water-rock reaction during ascent. However, waters initially CO,- and calcium-rich may yield high estimated subsurface temperatures owing to the rapid deposition of calcium carbonate and slower reactions invoking Na and K.

Another obvious problem is mixing of deep water with shallow water of different composition. If the shallow water is very dilute relative to the deep water, mixing will have little effect upon Na/K ratios. Such mixing will, however, have an effect upon the calcium-corrected geothermometer because the square root of calcium is involved in the calculation. But, if the original calcium concentration is small relative to sodium, mixing may have little effect.

The NrlrK-Ca geothermometer also may be of use in interpreting compositions of fluid inclusions trapped in minerals. Chemical data for fluid inclusions from Providencia, Mexico (RYE and HAFFTY, 1969) are plotted vs filling temperature in Figs. 2 and 6. In Fig. 2, if the Providencia Na/K data are referred to the experimental curve defined by the work of HEMLEY (1967) and ORVILLE (1963), temperatures of 500 to 700°C are suggested (Fig. 2). If the data are referred to the empirical curve of ELLIS (1970), temperatures of 400 to 500°C are suggested (Fig. 2). In contrast, if the chemical data are referred to the calcium-corrected curve of Fig. 6, temperatures of 300 to 375’C are suggested; this temperature interval is in reasonable agreement with the range in filling temperatures.

Acknowledgenaents-The manuscript was reviewed by L. J. P. MUFFLER, D. E. WHITE, G. K. CZA~NSKE, A. J. ELLIS, and TOMAS PACES. We wish to acknowledge their many helpful com- ments and suggestions. We are particularly grateful to J. J. HEMLEY for allowing us to use his unpublished experimental data in our Fig. 7.

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au empirical na-k-ca geothepmomete~ for natural waters · 1356 r. 0. fournier and a. h. truesdell...

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