Process and rate of dedolomitization: Mass transfer and 14C dating in a regional carbonate

WILLIAM BACK | BRUCE B. HANSHAW > 431, National Center, U.S. Geological Survey, Reston, Virginia 22092 L. NIEL PLUMMER j PERRY H. RAHN Department of and Geological Engineering, South Dakota School of Mines and Technology, Rapid City, South Dakota 57701

w'jH, . ^ ^^ I 971, National Center, U.S. Geological Survey, Reston, Virginia 22092 MEYER RUBIN I

ABSTRACT INTRODUCTION

Regional dedolomitization is the major process that controls The term "dedolomite" was originally used by von Morlot the chemical character of water in the Mississippian Pahasapa (1847), who recognized the replacement of dolomite by calcite dur- Limestone (Madison equivalent) surrounding the Black Hills, ing near-surface chemical weathering. On the basis of field, labora- South Dakota and Wyoming. The process of dedolomitization con- tory, and theoretical studies, in combination with mass-balance and sists of dolomite dissolution and concurrent precipitation of calcite; mass-transfer calculations using chemical and isotopic data, a it is driven by dissolution of gypsum. mechanism has been proposed that effectively provides a minera- Deuterium and oxygen isotopic data from the ground water, logic and geochemical explanation for the process of dedolomitiza- coupled with regional potentiometric maps, show that recharge tion (Back and Hanshaw, 1971; Plummer, 1977; Hanshaw and occurs on the western slope of the Black Hills and that the water others, 1978; Wigley and others, 1978; Hanshaw and Back, 1979; flows northward and westward toward the Powder River Basin. A Plummer and Back, 1980). According to these ideas, as ground significant part flows around the southern end of the Black Hills to water moves through a typical carbonate aquifer, it initially dis- replenish the aquifer to the east of the Hills. Depth of flow was solves calcite, dolomite, and gypsum (or anhydrite) at varying rates. inferred from interpretation of the silica geothermometer based on Once saturated with calcite and dolomite, the system continues to the temperature-dependent solubilities of quartz and chalcedony in be driven irreversibly by the dissolution of gypsum, which causes water. Chemical effects of warm water in the Pahasapa Limestone additional dissolution of dolomite and concomitant precipitation of include changes in the solubility products of minerals, conversion of calcite. The process of dedolomitization, therefore, can lead not gypsum to anhydrite, solution and precipitation of minerals, and only to the formation of dedolomite, which is calcite pseudomor- increases in the tendency for outgassing of carbon dioxide. Where phous after dolomite, but also to some vein calcites and calcareous sulfate reduction is not important, sulfur isotope data show that (1) cements. It is conceivable that both dolomitization and dedolomiti- in the Mississippian aquifer, most of the sulfate is from dissolution zation may occur simultaneously in different parts of the same of gypsum and (2) some wells and springs have a hydrologic con- geologic milieu but under subtly dissimilar chemical conditions. nection with overlying Permian and Pennsylvanian evaporites. Sul- In this paper, we show that the dedolomitization process fate ion concentration, a progress variable, shows a strong cor- occurs on a regional scale. Our field area consists of part of the relation with pH as a result of the combined effects of the dedol- regionally extensive Mississippian Madison aquifer with the work pmitization reactions. concentrated on wells and springs surrounding the Black Hills and Mass-balance and mass-transfer calculations were used to extending eastward in South Dakota (Fig. 1). Rock samples of the idjust 14C values to determine a range of ground-water flow veloci- aquifer were collected for mineralogic and isotopic analysis, and ties between 2 and 20 m/yr. These velocities are characteristic of several soil-gas samples were obtained from recharge areas in the :arbonate . The average rates of dolomite and gypsum dis- Black Hills. Chemical and isotopic analyses were made on ground- solution are 1.7 x 10~4 and 3.4 x 10"4 mmol/kg of H20/yr, respec- water samples from wells and springs producing from the Madison tively. The precipitation of calcite is occurring at the rate of 3.4 x aquifer equivalent. 10"4 mmol/kg of H20/yr. The close agreement among the model results demonstrates that dedolomitization is controlling water- REGIONAL GEOLOGIC SETTING rock interactions in this regional carbonate aquifer system. The Black Hills uplift, trending north-northwest, is about 150 km long and 100 km wide, measured from the Lower Cretaceous •Present address: TRW Energy Systems Group, 8301 Greensboro sandstone hogback that surrounds the Hills. The highest point in Drive, McLean, Virginia 22102. the Black Hills is Harney Peak, 2,207 m above sea level, consisting

jeologieal Society of America Bulletin, v. 94, p. 1415-1429, 13 figs., 9 tables, December 1983.

1415

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100°

Figure 1. Regional geologic features showing tectonic setting of the Black Hills (from Sando and others, 1976).

MONTANA

WYOMING '

UTAH ! [.• ' • '•' 1 1 V:'-^ v-

100 KILOMETERS

of Precambrian rock. Gently dipping Paleozoic and Mesozoic rock underwent carbonate and evaporite deposition during much of sequences flank the Black Hills with only the Silurian section miss- Mississippian time. ing (Darton and Paige, 1925). Under the generally shallow-water conditions that prevailed in The major aquifer of the Black Hills area is the Pahasapa the study area, shoaling conditions, reef building, and low-lying Limestone of Mississippian age, the local name applied to an equi- islands were probably common; the modern-day counterparts are valent of the Madison Limestone. These carbonate rocks were de- the Persian Gulf and the Yucatan peninsula, with their surrounding posited during Early Mississippian time, when a great seaway shallow-sea environment. At various times, a large number of low- occupied much of the area west of Wyoming. This formation ranges lying islands probably existed, as over the Great Bahama Bank in thickness from 200 m in the northern Hills to less than 100 m in today, continually changing and shifting in time and space. These the southern Hills. Petrologic studies by Schneider (1973) and Bar- low islands probably had coral patches, oolite- and crinoid-bank num (1973) show that the Pahasapa is extensively dolomitized. shoals, and lagoons associated with them (Gerhard, 1978; Peterson, During Mississippian time, the study area surrounding the 1981). The lagoonal areas probably acted as evaporating basins in Black Hills and eastward in South Dakota was part of the Cor- which gypsum crystals frequently formed and became incorporated dilleran platform (Fig. 1). This platform was bordered on the west into the limy sediments. This depositional model would explain the by the Ccirdilleran miogeosyncline, oriented approximately north- widespread occurrence of gypsum that is an important control on south in Idaho and western Montana. The miogeosynclinal trough the chemical character of present-day ground water. Sea water received both shelf-carbonate and deep-water terrigenous detritus needs to be evaporated to about 19% of original volume to precipi- (Rose, 1976; Sando and others, 1976). The highland of the Antler tate gypsum, whereas it must be further evaporated down to one- Orogenic Belt was the source for much of this terrigenous material. half of this amount to precipitate halite (Clarke, 1924, p. 214). This belt was to the west of the miogeosyncline and underwent Thus, in lagoonal environments that frequently received fresh intermittent tectonism during Mississippian time. The Transconti- influxes of sea water, gypsum could often precipitate, whereas nental Arch, south and east of the study area, was low-lying and evaporation only rarely would proceed to the point of halite precip- sporadically contributed only minor amounts of detritus to the plat- itation. In areas of more restricted circulation during Late Missis- form. The Black Hills uplift was not a regionally significant tectonic sippian time, bedded gypsum and halite would accumulate and be element until Late Cretaceous time (Agnew and Tychsen, 1965). preserved, as they are in the central Montana trough and the Willis- Mississippian rocks gradually thicken northward from south- ton Basin (Peterson, 1981). ern South Dakota to a maximum of 500 m near the North Dakota A major erosional event occurred at the end of the Mississip- state line. The state line approximately delineates the shallow-water pian. The limestone was eroded extensively to form a karst terrane carbonate facies from the thicker sequence of evaporitic facies that with caves, sinkholes, collapse features, and relief of a few tens of developed in eastern Montana and North Dakota during Late metres. The Pennsylvanian and Permian Minnelusa Formation, Mississippian time. Thus, the shallow-water Cordilleran platform which consists of sandstone, dolomite, shale, and anhydrite, was

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11.51 McNenny 580 \* Spearfish sOOOi

Jones 25.7 49 698 ifRhoadsS. E. A.F.B. ßJ8 ; Fork 443 Upton\ 68 • Philip Osage Cleghorn p Rapid City 1370 11.6 350 % Newcastle^ o 509 \ '30.5/ /15301 2q -a ^/Evans Plunge ^ÌSÓN EXPLANATION ^ Ground-water flow lines 2510*/Casca(>e ffiH _,4000~ Potentiometrie surface, in feet • Provo above mean sea level

I/75Ö R 12.9 Temperature, in °C SOUTH DAKOTA 580 Conductivity, in micromhos NEBRASKA' per centimeter at 25°C

-4200 10 20 30 40 50 MILES J——1—1 ~i—I—I—r 0 10 20 30 40 50 KILOMETERS

Figure 2. Potentiometrie map with diagrammatic flow lines of ground water in the Pahasapa Limestone (Hanshaw, 1958; Konikow, 1976), showing downgradient increase in conductivity and temperature. Shaded area shows the outcrop of the Pahasapa Limestone.

TABLE I. CHEMICAL ANALYSES OF GROUND WATER FROM THE BLACK HILLS AREA

Concentration, mg/1

ample no, T(°C) Cond.* Field TDS Si02 Ca Mg Sr Na K CI so4 HCOj F nd location pH

¡1 Rhoads Fork 5.7 443 7.35 256 8.8 66 23 0.07 0.9 0.6 0.4 3.1 309 0.10 ¡2 Jones Spgs 12.9 476 7.20 269 8.4 71 22 0.12 1.5 0.6 0.5 5.8 324 0.10 3 Spearfish 13.2 435 7.39 233 10.0 52 23 0.15 2.1 I.I 0.6 8.2 279 0.20 4 Cleghorn Spgs 11.6 390 7.41 203 11.0 42 19 0.13 4.9 2.7 2.2 23 198 0.03 5 Newcastle 25.0 509 7.20 302 12.0 64 29 0.38 2.6 1.7 1.2 47 290 0.30 6 Osage 23.4 526 7.20 311 11.0 70 27 0.32 2.1 1.4 0.7 50 298 0.40 7 McNenny 11.5 605 7.18 362 12.0 87 24 0.89 2.1 1.4 0.6 103 269 0.30 i Upton 25.7 698 7.12 456 12.0 88 41 2.9 2.6 2.2 " 0.8 169 276 1.20 3 Ellsworth AFB 49.0 678 7.01 461 21.0 91 33 0.94 4.9 3.7 1.0 204 204 0.60 b Provo 60.0 1730 6.97 1070 30.0 110 30 2.2 203 18 269 319 180 1.30 1 Evans Plunge 30.5 1530 6.90 1140 23.0 206 41 2.9 86 11 108 545 234 1.10 i Philip 68.0 1370 6.78 1080 33.0 218 58 4.5 18 7.3 22 641 160 2.60 |i Midland 71.0 1570 6.69 1310 35.0 266 66 5.5 25 9.7 28 802 146 2.80 ¡1 Bear Butte 13.6 2250 6.91 2080 11.0 462 96 4.2 3.9 2.5 0.9 1400 198 1.20 !> Cascade Spgs 20.0 2510 6.89 2280 15.0 535 83 6.2 27 5.2 31 1450 244 1.60

•Specific conductance, micromhos at 25 °C.

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8500

6500 £ Ui u. z t— 5500 5

1200

1500 5 10 20 30 40 50 60 70 « 2 TEMPERATURE, ° CELSIUS cc 2500 § u. Figure 3. Relation of water temperature to depth of well com- O pleted in the Pahasapa Limestone. z £ 1500 ¡y Q deposited on the karstified Mississippian Pahasapa Limestone (Gries, 1971). The Black Hills uplift, which began in the Late Cre- 500 taceous, separates the Paleozoic Williston Basin in the northeast from the post-Cretaceous Powder River Basin on the southwest (Agnew and Tychsen, 1965). As a result of uplift, sediments overly- 0 10.0 20.0 30.0 35.0 ing the Pahasapa were removed by erosion; then was SiOj, MILLIGRAMS PER LITER able to infiltrate the cavern system. The Minnelusa Formation that overlies the Pahasapa Limestone seems to be hydrologically con- Figure 4. Depth of ground-water flow as deduced from nected to the Pahasapa as indicated by discharge of dye from temperature of water estimated from chalcedony and quartz ther- springs in the Minnelusa that was injected into sinkholes in the mometer. Saturation index for chalcedony is shown at each sample Pahasapa (Rahn and Gries, 1973). Our interpretation of sulfur iso- number. tope data, discussed below, suggests hydrologic connection from the lower elevations, with most of the precipitation occurring dur- the Pahasapa up through Pennsylvanian and Permian rocks in at ing the months of April through July. Streamflow is also highest least part of the study area. during these months. Those streams draining the Precambrian crys- talline core of the Black Hills are generally perennial. Sinkholes GROUND-WATER OCCURRENCE AND FLOW PATTERN occur where streams cross the outcrop of Paleozoic carbonate rocks, and many streams lose their water to underground drainage. The average annual precipitation ranges from 26 in. (66.0 cm) The relatively impermeable Permian and Triassic Spearfish Forma- in the high areas of the northern Black Hills to 16 in. (40.6 cm) in tion dams the subsurface flow and causes large springs to occur

TABLE 2. COMPARISON OF POSSIBLE DEPTH OF GROUND-WATER FLOW BASED ON MEASURED TEMPERATURE. QUARTZ THERMOMETER. AND CHALCEDONY THERMOMETER

Location T °C Reported Geothermal , SI + T'c' Depth from SI T"C" Depth from depth gradient depth quartz quartz quartz chalcedony chalcedony chalcedony (ft) (ft) thermometer (ft) thermometer (ft)

1 Rhoads Fork 5.7 Spr 70 0.49 35.5 3,050 -0.08 0.4 2 Jones Springs 12.9 Spr 790 0.35 34.0 2.900 -0.19 1.1 3 Spearfish 13.2 725 820 0.42 39.6 3.460 -0.12 4.6 4 Cleghorn Springs 1 1.6 Spr 660 0.48 42.7 3.760 -0.06 7.7 270 5 Newcastle 25.0 2,680 2,000 0.31 45.6 4,060 -0.18 10.7 1,570 6 Osage 23.4 2.560 1.840 0.29 42.7 3.760 -0.20 88.7 270 7 MeNenny 11.5 650 0.52 45.6 4,060 -0.02 10.7 1,570 8 Upton 25.7 2.900 2,070 0.30 45.6 4.060 -0.18 10.7 1,570 9 Ellsworth AFB 49.0 4.640 4.400 0.21 65.5 6.050 -0.19 31.4 2.640 10 Provo 60.0 3.920 5.500 0.23 79.6 7.460 -0.13 46.3 4,130 11 Evans P unge 30.5 Spr 2.550 0.51 69.0 6,400 »0.05 35.1 3,010 12 Philip 68.0 4.000 6.300 0.17 83.6 7.860 -0.16 50.5 4,550 LI Midland 71.0 3.300 6,600 0.16 86.0 8.100 -0.16 53.1 4,810 14 Bear Butte 13.6 1.440 860 0.45 42.7 3.760 -0.08 7.7 270 15 Cascade Springs 20.0 Spr 1.500 0.49 53.2 4.820 -0.02 18.6 1.360

+ ä 273l5: 1 21iA5 Depth - ttemp-5 -C) > IOO: SL Saturation Index = log-j^E: 1 Q,z - (5.20i-tog Si02) ~ " Chalc " (4.655-log Si02) ~ '

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Values of conductivity and temperature of ground water plot- ted on this potentiometric map (Fig. 2) show a typical downgra- dient increase; in this case, conductivity ranges from about 400 micromhos in the recharge area to about 1,500 micromhos at Philip and Midland. Conductivity values are anomalously high at Cas- cade, Bear Butte, and Provo. These samples have high sulfate con- centrations that represent the dissolution of dispersed gypsum or anhydrite, probably from the overlying Minnelusa Formation. The high chloride content at Provo, unlike Cascade and Bear Butte, indicates that the Provo sample may be influenced by solution of bedded evaporites of the bittern type. Temperatures of springs in the outcrop area range from approximately 5 to 13 °C (Table 1). The mean air temperature in the Black Hills is about 7 °C. Schoon and McGregor (1974) estab- lished geothermal gradients for deep wells in several aquifers in South Dakota that show an unusually high geothermal gradient in south-central South Dakota. For example, a plot of temperature versus depth (Fig. 3) shows that several wells, particularly Provo, CALCULATED DEPTH, IN FEET Philip, and Midland, have higher temperatures than would be expected from the normal geothermal gradient. On the basis of Figure 6. Trilinear diagram showing chemical character of thickness and depth of the aquifer, any reasonable flow path from ground water in the Pahasapa Limestone and the reactions control- the Black Hills to Philip and Midland would indicate that the water ling its chemical evolution; data in percentage of meq/1. was never at a depth greater than 1,400 m and that the temperature, therefore, should be between 40 and 50 °C at Midland and Philip instead of the 70 °C observed. Rahn and Gries (1973) made iso- along many stream valleys at the outer edge of the outcrop of the thermal plots of springs discharging from the Madison outcrops in ;arbonate rocks. Rahn and Gries (1973) determined that streams the Black Hills and suggested that the hot water possibly resulted lose an average of 44 cfs (1.25 m/s) to the sinkholes and that the from the high thermal conductivity of Precambrian rocks. springs discharge an average of 190 cfs (5.38 m/s). The excess of Additional information on depth of flow paths may be inferred spring discharge over streamflow loss results from recharge of pre- by consideration of the silica geothermometer that is based on the cipitation falling directly on outcrops of Paleozoic carbonate rocks. temperature-dependent solubilities of quartz and chalcedony in On the basis of spring discharge measurements from ground- water. Saturation indices' (Langmuir, 1971) of these minerals (Table water drainage areas, Rahn and Gries (1973) estimated that the 2), calculated by means of the computer program WATEQF recharge to the carbonate aquifer is greater than 6.8 in. (17.3 cm) (Plummer and others, 1976), show the water is supersaturated with per year in the northern Black Hills and is about 0.6 in. (1.5 cm) per respect to quartz and generally subsaturated with respect to chal- year in the southern Black Hills. cedony. Curves for the solubility products for quartz and chalce- The configuration of the potentiometric surface (Fig. 2) of the dony as a function of temperature are shown in Figure 4. The depth Pahasapa indicates that the Black Hills uplift is the major source of corresponding to the "normal" geothermal gradient of 1 °C/33 m, recharge for the aquifer in our study area. Water from the west given on the right-hand ordinate, shows the probable range of lank of the Black Hills flows both westerly toward the Powder depths based on the silica geothermometer; that is, if the water were River Basin and easterly around the southern tip; water recharging in equilibrium with either quartz or chalcedony and no additional an the north, south, and east sides of the Black Hills moves gener- solution or precipitation occurred after the water was at the indi- illy in an easterly direction. cated temperature along the solubility curve, the depth from which the water has migrated is shown by the right-hand ordinate (Fourn- TABLE 3. ISOTONIC ANALYSES OK GROUND WATER FROM THE BLACK HILLS AREA ier and Rowe, 1966). The calculated depths are shown (Fig. 5) in relation to the actual depth of sampling points. The depths calcu- 1S Location 6 0 SD s'-'c 6 !, (S04 ) TU lated from the temperature of the quartz thermometer are all appre- ciably greater than those calculated from the chalcedony geo-

Rhoads Fork -17.2 -125 -11.0 6.2 62 ± 2 thermometer or from a "normal" gradient. There appear to be two Jones Springs -14.6 -110 -11.6 6.7 276 ± 10 Spearfish -17.1 -126 -10.7 3.2 90 + 5 temperature regimes and, therefore, two depth regimes: one for Cleghorn Springs -13.2 -103 - 9.6 5.7 182 ± 8 wells less than about 3,000 ft (914.4 m) deep (except Spearfish), Newcastle -17.7 -130 -10.4 9.8 0.1 ± 0.2 6 Osage -18.1 -135 -10.0 10.4 0.5 ± 0.2 where the depths calculated from the chalcedony thermometer and 7 McNenny -17.4 -127 -11.5 11.4 116 I 5 8 Upton -18.2 -133 - 8.2 12.2 a normal gradient are less than the actual depths and another for 9 Ellsworth AFB -14.1 -107 - 9.1 wells deeper than 3,000 ft, where the calculated depths are greater 3 Provo -17.1 -131 - 9.4 10.9 1 Evans Plunge -16.7 -121 - 9.7 than the actual depths. These relationships are interpreted to mean 2 Philip -17.5 -125 - 7.2 14.52 3 Midland -17.6 -128 - 6.2 15.0 that loss of heat has occurred in shallower wells, presumably from 4 Bear Butte -16.7 -122 - 4.1 12,9 0.3 ± 0.2 5 Cascade Springs -16.0 -118 - 9.1 12.5 4.7 ± 1.0

... ,, , . loll dlllvll^ OIUUUCI . . Sole: Precision for ß'^O. rt' . and ii^S is ±0.2" m; precision for 6D is ±2" m>. Data in 1 n respective to 'Saturation index, SI = log equilibrium constant SI = 0 means equilibrium MOWIi'V

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Sample Site

Rhoads Fork 9. E.A.F.B. Jones Spring 10. Provo Spearfish 11. Evans Plunge Cleghorn 12. Philip Newcastle 13. Midland Osage 14. Bear Butte McKenny 15. Cascade Spring Upton Sample number increases with increasing sulfate concentration

Figure 6. Trilinear dia- gram showing chemical charac- ter of ground water in the Pahasapa Limestone and the reactions controlling its chemi- cal evolution; data in percent- age of meq/1.

greater amount of ground-water circulation on the western flanks thermal gradient and therefore show no effect of either appreciable of the Black Hills, and that the deeper wells (except Ellsworth Air ground-water flow or an additional heat source. As is shown below Force Base) have an additional source of heat. The structural posi- on the basis of isotopic evidence, the EAFB well is apparently not in tion of the aquifer and the less permeable rocks beneath the aquifer hydrologic continuity with other wells to the east of it. would seem to preclude significant upward migration of deeper hot The presence of this hot water can have pronounced effects on water. The likely source of heat, therefore, is associated with young geochemical reactions that do not occur in aquifers with cooler shallow-igneous intrusives (Jack A. Redden, 1973, oral commun.). water. These effects, discussed below, include: changes in solubility The wells at Spearfish and EAFB show essentially a normal geo- product (Ksp) of minerals, conversion of gypsum to anhydrite, increased poten tial for outgassing, and changes in locations of solu- tion and precipitation of minerals.

GEOCHEMISTRY AND ISOTOPIC COMPOSITION OF GROUND WATER

Of the 15 samples (Tables 1, 3) used in this study, 10 are from wells, and 5 are from springs. Three springs (Cleghorn, Rhoads Fork, and Jones), which are part of a local flow system, occur within the regional recharge area, that is, within the outcrop area of the Pahasapa Limestone. The other two springs, Evans Plunge and Cascade, are on the flanks of the Black Hills and represent upward discharge from the aquifer considerably downgradient from the recharge area. Rhoads Fork and Jones Springs have similar chemical compo- sitions. Except for their isotopic composition, either of these could be considered representative of water within the recharge area that has entered the Pahasapa, reacted with the rock, and discharged in the springs. This water is typical of that moving from the recharge Figure 7. Deuterium and l8oxygen content of ground water in area into the artesian aquifer system. In that Jones Spring and the Pahasapa Limestone compared to the world-wide rainfall line. Rhoads Fork Spring are on opposite sides of the uplift, there is

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—3400~. POTENTIOMETRIC SURFACE IN FEET ABOVE MEAN SEA LEVEL

17.55, ¿"0 PERMIL, IN REFERENCE TOSMOW 1 0 50 ÒD PERMIL, IN REFERENCE KILOMETERS TOSMOW

Figure 8. Map showing isotopie depletion of deuterium and l8oxygen in ground water on the west side of the Black Hills. Shaded area shows the outcrop of the Pahasapa Limestone.

good reason to believe that these analyses are regionally representa- major springs at the south end of the Black Hills, Evans Plunge tive of recharge water. On the other hand, Cleghorn Spring, which (sample 11) and Cascade (sample 15), and the easternmost sampling should also be representative of recharge, differs chemically from points of Philip (sample 12) and Midland (sample 13) are character- the other two springs in several significant ways: both dissolved ized by calcium and sulfate ions. The index numbers correspond to bicarbonate and total carbon content are lower at Cleghorn, and an increase of sulfate concentration, and their position on the dia- the sulfate is significantly higher (Table 1) than in the other two gram (Fig. 6) indicates typical evolution of chemical character of springs in the recharge area. Cleghorn probably represents Paha- water in carbonate aquifers that contain gypsum (Hanshaw and sapa water that has been slightly influenced by minor solution of Back, 1979, Fig. 1) wherein the percentage of dissolved sulfate evaporites from the Minnelusa. This is confirmed by examination gradually increases. of detailed geology at the three springs: Cleghorn discharges from Distribution of the oxygen and hydrogen isotope data (Fig. 7) Minnelusa outcrops, whereas Rhoads Fork and Jones Springs dis- shows that the isotopically lightest water occurs on the west side of charge from the Pahasapa. the Black Hills, where 5lsO ranges from about -18 to -16.5 per mil As shown in the trilinear diagram (Fig. 6), samples 1 through 7, (%„), which contrasts significantly with the range of -15 to -13 %o which include those in the recharge area, Newcastle and Osage on on the east side. A graph of SD versus 6 lsO (Fig. 8) shows that most the western flanks of the Black Hills, and McNenny on the north, of the sample points plot near the world meteoric water line first ls are all calcium-carbonate-type water. Water from Upton and Ells- identified by Craig (1961). The distribution of SD and S O in the worth (EAFB) (samples 8, 9) is predominantly a calcium-sulfate- Black Hills is particularly significant in delineating the ground- bicarbonate water. Evans Plunge (sample 11) is a calcium-sodium- water flow pattern. The three eastern samples, Jones, Cleghorn, and sulfate water, and Provo (sample 10) is the only sodium-chlo- EAFB, are enriched in the heavy isotopes of hydrogen and oxygen, ride-type water. The remaining four samples, which include the two whereas samples on the west side are depleted. This is interpreted to

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be a function of the rainfall pattern where the west side of the Black range from less than 10 mg/1 in the recharge water to values of Hills is influenced by isotopically depleted rainfall from northwes- about 800 mg/1, excluding the two values above 1,400, which are terly storms. Rainfall on the east side is isotopically enriched discussed below. The S34S values have an approximately curvilinear because its source is partially from Gulf Coast storms that, owing to distribution when plotted against sulfate content; a similar distribu- absence of high elevations, have not been isotopically depleted, and tion has been observed in the Floridan aquifer (Rightmire and oth- these storms generally do not reach the west side. Intermediate ers, 1974). Sulfate concentration values are controlled by dissolu- values of ground water mixed from the two sources occur on the tion of gypsum or anhydrite, bacterial reduction of sulfate, and north and south ends of the Black Hills. Hydrogen and oxygen oxidation of sulfide minerals or hydrogen-sulfide gas. The isotopic isotope values at Philip and Midland do not resemble those of the equilibrium fractionation factor for SO| - HS" is approximately springs on the eastern side of the Black Hills. Rather, their isotopic 1.065 at 25 °C, which means that coexisting sulfate and sulfide at composition is similar to that of Rhoads Fork, which is typical of isotopic equilibrium have a difference in 534S of 65 °/oo. That is, if recharge water from the western side of the Black Hills. A flow path S34S for the sulfate ion of 18%o is typical for gypsum of Mississip- from the southwestern side of the Black Hills (Fig. 2) indicates that pian age, at isotopic equilibrium the 534S for sulfide is about -47 the water sweeps around the southern end of the Hills and flows °/oo. If pyrite formed during reduction of Mississippian-age gypsum, toward the area of Philip and Midland. Much of the water, there- subsequent oxidation of this sulfide will tend to decrease the S34S fore, in the southern part of the aquifer in South Dakota originates value for sulfate. The sulfate ion depleted in <534S (less than 8 °/oo) from recharge in the western and southwestern Black Hills. This (Fig. 9) in water with low concentration results from sulfide oxida- interpretation has been substantiated by additional isotopic data in tion, either of minerals in the aquifer or of industrial gases in the a regional study of the Madison aquifer (J. F. Busby and others, atmosphere. Bacterial reduction of sulfate tends to increase the <534S 1983). of sulfate, because the light isotope, 32S, will fractionate to the gas The <534S isotopic value of the dissolved sulfate ion in the H2S or the ion HS~. It is known (Holser and Kaplan, 1966; Clay- ground water increases downgradient from less than + 7 °/oo in the pool and others, 1980) that the sulfur isotopic composition of the recharge area to about + 15 °/oo at Midland. Concentrations of SO4 Mississippian sulfate is considerably heavier than that of the Penn- sylvanian and Permian. The range of values is about +16°/oo to +21°/oo for the Mississippian evaporites and as light as +10°/oo for Permian evaporites (Fig. 9), with intermediate values for the Penn- sylvanian and lowermost Permian rocks (Minnelusa Formation). Water from the Madison Limestone (Fig. 9) that has greater than about 10 millimoles of sulfate is isotopically similar to Missis- sippian evaporites. Water with lower sulfate concentration has iso- topic values that indicate a mixed sulfate origin from oxidation of Mississippian evaporites sulfides and dissolution of evaporites. The Bear Butte and Cascade water samples (Fig. 9) are from a well and a spring that produce water partly from the Minnelusa Formation of Pennsylvanian and Permian age; consequently, the isotopic values of the dissolved sul- fate from those evaporites are significantly lighter than the sulfate dissolved from the Mississippian evaporites. Minnelusa Formation - The total dissolved inorganic carbon (DIC or I.CO2) content ranges from more than 5 mmol/1 in the recharge area to about 3 mmol/1 downgradient. The partial pressure of CO2 is lowest in all Permian evaporites of the springs in the recharge area except Cleghorn and, in general, increases systematically downgradient. The loss of DIC results mainly from precipitation of calcite and possibly from outgassing associated with pumping. Water from wells with temperatures above 50 °C typically contains bubbles of CO2, which are visible • Madison project proof of outgassing. Furthermore, wells in South Dakota and Mon- X This study (Black Hills) tana have been observed with extensive calcium-carbonate deposits at the surface; perhaps other wells have calcium-carbonate deposits on or near the casing. Additionally, at many springs in the Black Hills, calcareous tufa accumulates in the stream bed within ~ 1 mi below the spring, presumably due to outgassing of CO2. The 513C for the dissolved carbonate species ranges from -11.6°/oo near the recharge area to -4.1°/oo downgradient. This 0.0 5.0 10 15.0 20.0 progressive enrichment in l3C is characteristic of limestone aquifers SO,"', MILLIMOLES PER LITER where the principal reaction is dissolution of marine-carbonate Figure 9. Graph showing <534S difference between Mississip- minerals with typical 513C values of 0 ± 2°/oo. pian (Pahasapa) and Permian evaporites and the relation of <534S Soil-gas composition and carbon and oxygen isotopic values of and sulfate concentration in ground water from both the Pahasapa CO2 in soil gas were determined for a number of samples at three Limestone and the Madison Limestone (after Hanshaw and others, locations within the recharge area. These locations were selected on 1978). the basis of variations in native vegetation and thus probably

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TABLE 4. MEASURED AND ADJUSTED VALUES OF ' X' IN GROUND WATER AND derived from the half-life equation given in the footnotes of Table 4, CALCULATED AGES IN YEARS BEFORE PRESENT (YBP) may be written:

14 Location «l4C'\„ c YBP* YBPt YBpS l4C(% mdn, adj) = % mdn(lab) l3 l3 l4 <5 Csoil-<5 Ccarb 1 Rhoads Fork - 71 92.9 610 >mdn C(% mdn, lab) 13 3 2 Jones Springs 0 100 0 >mdn ö Cwater-ö' Ccarb 3 Spearfish -257 74.3 2.460 >mdn >mdn 4 Cleghorn Springs - 84 91.6 730 > mdn 5 Newcastle -5.18 46.2 6.380 1.850 700 where: 6 Osage -453 54.7 4.990 130 >mdn 7 McNenny -204 79.6 1.890 >mdn >mdn l4 l4 8 Upton -853 14.7 15.850 9.350 8,700 C(%mdn, adj) is the C adjusted for dissolution of carbonate 9 Ellsworth AFB -942 5.8 23.540 17.900 17,300 rocks with known <5I3C value. 10 Provo -927 7.3 21,640 16,270 • -*• l4 l4 11 Evans Plunge -715 28.5 10.380 5.270 1.900 C(%mdn, lab) is the C content measure in the laboratory and 12 Philip -972 2.8 29,560 21.980 20.000 1.1 Midland -976 2.4 30,830 22.020 20,100 given in Table 4. 14 Bear Butte -776 22.4 12,370 138 • •** Sl3C is the isotopic composition of soil-gas CO2, assumed to 15 Cascade Springs -806 19.4 13,560 7.920 soil have an average value of — 18°/oo in this study.

•Unadjusted ages: t - |n 2 "' A l3 8 Cwaterthe isotopic composition of the D1C at any sample ^Using method of Pearson and White (1967); where rt' Y of limestone = 0" and Ä "C of soil point and is given in Table 3. 100 , _ .„» . _ 5,730/', In d'~*C ter ) 3 gas--18 " "In~2v "Ä wa lì f ^' Ccarb is the isotopic composition of the marine-carbonate 6 C "' C02gas 14_ minerals in the study area. §The lime of flow (in years) between Rhoads Fork and the well. At, is calculated from the C activity (% Ji+ modern) observed at thee wellw< . A. and the C activity calculated at the well assuming no decay. An(j, ( Table 6). An, d As discussed below, the <5'3C of calcite and dolomite from the study •Water is not dated because of possible mixing (see text). area has an average value of about 0°/oo, in which case the preceding equation can be reduced to:

l4 represent the maximum range in carbon isotope content in the soil C(%mdn, adj) =

CO2. A location near Spearfish was identified as a "prairie- l4 l3 C(%mdn, lab) -^il grassland" site where soil CO2 is expected to be enriched in C by 6 Cwater root respiration and by decay of Hatch-Slack (C4) vegetation (Bender, 1968). A site near Jones Spring was chosen to represent a The values in the column labeled "YBP2" were determined by "normal woodland" on the east flank of the Black Hills and another means of this equation. This l4C-age-adjustment method does not "normal woodland" site was selected in the center of the Black Hills take into account the possible loss of l4C from DIC owing to pre- uplift near Jenny Gulch; these latter two areas have predominantly cipitation of calcite caused by the dedolomitization process. Calvin (C3) photosynthetic plants, which are generally isotopically The Pahasapa Limestone is an assemblage of calcite and lighter than C4 plants. As expected, the two types of sites yielded dolomite with minor amounts of gypsum and possibly traces of l3 soil gases with noticeably different C contents. Samples from the other minerals. As ground water contacts such a mineral assem- I3 Spearfish site have an average S C of-15.3°/oo, which is typical for blage, it is possible to dissolve calcite until saturation is achieved C4-type vegetation, and an average log Pco2 of-1.9. On the other and have the water remain undersaturated with respect to dolomite I3 hand, samples from the Jones Spring site yielded an average S C and gypsum. A model depicting this reaction sequence is developed value of-19.8%o and an average log Pcc>2 of-2.26. Samples from by mass-balance calculations that consider differences between the the Jenny Gulch, with similar vegetative environment but different beginning recharge water of Rhoads Fork and end-member I3 soil conditions, yielded a similar average S C value, -20.1%o, but a ground-water downgradient. A second set of adjusted l4C ages was 13 higher C02 content, with an average log Pco2 -1-9. Carbon determined by incorporating S C data into mass-transfer calcula- isotope values from these two sites are typical of mixed C3-C4 tions (Table 4, column labeled "YBP3") in accordance with both vegetation locales (Rightmire and Hanshaw, 1973). These data, congruent and incongruent carbonate-mineral reactions in the sys- viewed in conjunction with the climatological data from the area, tem. The two methods will produce identical results if there is no suggest that if recharge occurs during the growing season in the calcite precipitation; where they yield similar ages, the indication is Black Hills, which are largely woodland, the C02 input from the that calcite precipitation is not a major influence on the radiocar- I3 soil gas will have a S C of about -18°/oo and an equilibrium log bon age. Further credence is given to the two methods when tritium l4 PCo2 about -2.0. data are also examined in light of the C adjustment methodolo- The percentage of modern l4C as determined in the laboratory gies. Consequences of these calculations are discussed in the follow- (Table 4, column labeled "l4C°/oo mdn, lab") ranges from 2.4% to ing section. 100%. These values give raw or unadjusted ages (Table 4, column As would be expected, exceptionally high tritium concentra- labeled "YBP1") that range from about 30,000 YBP (years before tions (TU) exist in springs (Rhoads Fork, Jones, and Cleghorn) present) to essentially "modern." As shown by Pearson and Han- (Table 3) in the recharge area and indicate a predominant amount shaw (1970), sources of dissolved organic-carbonate species can be of post-hydrogen bomb (1952) water. The wells at Spearfish and identified by means of the ratio of the stable isotopes of carbon, McNenny also have high, post-bomb tritium levels. These tritium SI3C. Pearson and White (1967) showed derivation of an elegantly concentrations substantiate the l4C adjustments that indicate the simple equation to account for the contribution of D1C from the water from these five sample points is "greater-than-modern" in l4 congruent dissolution of carbonate rocks by aggressive C02 that is adjusted age owing to incorporation of bomb-produced C. Dur- introduced into the aquifer from the soil zone. Their equation, ing the mid-1960s, the 3H content of rainfall in the Northern Hem-

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TABLE 5. VALUES OF SATURA HON INDEX OF MINERALS FOR GROUND WATER with respect to those minerals, provides the basis for identification FROM THE BLACK HILLS AREA« of controlling chemical reactions. Interpretation of the values of saturation index (Table 5) for the important minerals in the Location Total Log sit sit siB SI** co Calcite Gypsum 2 PC02 Aragonite Dolomite system—calcite, aragonite, dolomite, and gypsum (including anhy- mmol (aim) drite for the high-temperature water)—shows that the significant

1 Khoads Fork 5.711 -1.98 -0.09 -0.25 -0.61 -3.04 reactions are essentially the same as those identified for the system 2 Jones Springs 6.121 -1.77 -0.08 -0.24 -0.53 -2.77 in Florida (Back and Hanshaw, 1971). The mass-balance relations 3 Spearfish 5.018 -2.03 -0.07 -0.23 -0.35 -2.73 4 Cleghorn Springs 3.560 -2.20 -0.30 -0.46 -0.83 -2.34 developed for Florida (Plummer, 1977) and further refined with 5 Newcastle 5.339 -1.76 -0.01 -0.17 -0.09 -1.96 6 Osage 5.499 -1.75 +0.01 -0.14 -0.13 -1.89 data from the present study (Plummer and Back, 1980) show that 7 McNenny 5.128 -1.85 -0.15 -0.31 -0.75 -1.49 the amounts of calcite (cal), dolomite (dol), and gypsum (gyp) dis- 8 Upton 5.178 -1.70 -0.03 -0.18 -0.11 -1.36 9 Ellsworth 3.875 -1.56 +0.03 -0.10 + 0.02 -1.25 solved or precipitated during chemical evolution of the ground 10 Provo 3.443 -1.51 + 0.06 -0.06 -0.06 -1.07 II Evans Plunge 4.672 -1.54 -0.02 -0.17 -0.42 -0.69 water can be estimated by the following chemical mass-balance 12 Philip 3.309 -1.32 + 0.14 + 0.03 + 0.05 (-0.56) relations: 13 Midland 3.167 -1.25 +0.09 -0.01 -0.10 (-0.43) 14 Bear Butte 4.082 -1.75 + 0.02 -0.13 -0.48 -0.55 15 Cascade 4.956 -1.61 + 0.11 -0.05 -0.35 -0.07 ACa = Acal + Adol + Agyp

•SI. Saturation Index, = log (1AP/Ke^). Precision is ±0.05, except for dolomite, which is ±0.10. All AMg = Adol calculations use the thermodynamic data of WATEQF (Plummer and others. 1976) except as noted. ^Calculai ions based on the ion pairing model and thermodynamic data for calcite and aragonite of ASO4 = Agyp Plummer and Busenberg ( 1982). ASC02 = Acal + 2 Adol + AC02 gas "Log KDo1 for the reaction CaMg(C03)2 - Ca Mg t 2CO -17.02 and AH" was taken as -8.29 Kcal/mole as in WATEQF.

"Log K0yp = 82.090-3853.94/T-29.811 log J where T is in °K. T his expression is calculated from the where A denotes the change in the number of moles of the dissolved gypsum solubility data of Marshall and Slusher (1966) using the WATEQF aqueous model. (-0.56) and (-0.43) constituent between the initial and final points along the flow path. are values for anhydrite owing to high temperature of the water. This assumes the only sources of calcium are the three major miner- als, and the only sources of magnesium and sulfate are dolomite and gypsum, respectively. This approach further assumes that ¡sphere was as high as 5,000 TU; the average 3H content of rainfall (1) the moles of calcium from dolomite are equal to the moles of expected in the Black Hills area would have been in the range of magnesium from dolomite due to congruent dissolution of stoichi- 2,500 TU (Stewart and Farns worth, 1968). The post-bomb 14C con- ometric dolomite and that (2) the moles of calcium from gypsum tent of the atmosphere was as high as 200% of modern. These five equal the moles of total sulfate in the system. This second assump- springs and wells, therefore, show (Table 4) an adjusted 14C "age" tion requires conservancy of sulfate; that is, there is little or no that is greater than modern. reduction to sulfide species. This assumption has been shown to be reasonable for other carbonate systems (Rye and others, 1981). GEOCHEMICAL REACTIONS AND MASS TRANSFER These reactions, in either the forward or reverse direction, are the principal controls of ground-water chemistry. Their effects are The mineralogy of the aquifer, together with the saturation manifested in several significant relationships discussed throughout indices that indicate the departure from equilibrium of the water the rest of this section. For example, the saturation indices for the

Figure 10. Downgradient increase in saturation index for calcite, dolomite, and gypsum using sulfate as a progress vari- able indicating extent of reac- tions.

WM 0.0 -.06 Equilibrium SI for Gypsum M$^0.0:.06 Equilibrium SI for Calcita ÌIIIIIIIII! 0.0M0 EquMbrium SI for Dolomit«

3 so;' MILLIMOLES PER LITER

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minerals in this system (Table 5) are plotted against the dissolved As seen below, pH decreases systematically as SOj2concentration sulfate concentration (Fig. 10). For this graph and several of the increases, which would be expected from the above reactions. following graphs, the sulfate concentrations, which increase with Dolomite is near equilibrium at 25 °C in a ground water that is either the length of the flow path and/or residence time, are used as also in equilibrium with calcite and has a Mg/Ca = 1 (Hanshaw and a progress variable to show the extent to which the controlling others, 1971); where ratios occur that are greater than 1, dolomite reactions have proceeded. The saturation index for gypsum or an- can form, and at lower ratios, dolomite will dissolve. A critical hydrite shows that water is greatly undersaturated in the recharge contribution of gypsum to the process of dedolomitization is to area; although the saturation index increases progressively as a provide an abundant supply of calcium in order to maintain a low function of sulfate concentration, the water does not obtain equili- Mg/Ca ratio. Although von Morlot (1847) recognized that sulfate brium with respect to either gypsum or anhydrite. The saturation was associated with the process, it was not understood that the index for dolomite indicates that water in the recharge area is presence of sulfate was a consequence of obtaining the necessary greatly undersaturated but that, with increasing dissolution of gyp- calcium and was not a primary cause of dedolomitization. Our field sum, the water approaches equilibrium with respect to dolomite. data (Fig. 6) verify the significance of the Mg/Ca ratio; regardless Water is nearly in equilibrium with calcite. However, the two sam- of the absolute concentration of Mg or Ca or their relative percen- ples with highest temperatures (12, Philip; and 13, Midland) are in tages, all samples have a ratio less than 1. The other critical aspect equilibrium with aragonite. On the basis of kinetic considerations, of maintaining dolomite subsaturation is the precipitation of cal- one would expect aragonite, not the less soluble calcite, to precipi- cite. The main role of calcite is removal of carbonate ion; for every tate from hot water in the presence of magnesium ions. mole of dolomite dissolved, two moles of carbonate are released to In a carbonate aquifer that does not contain gypsum or anhy- the water. If this carbonate were not removed, the water would drite, calcite would dissolve until equilibrium was attained; if attain equilibrium with dolomite and the reaction would cease. If dolomite was present, it, too, would dissolve until equilibrium was gypsum stops dissolving, then the precipitation of calcite would reached—probably taking longer than calcite. As a result, we would cease and the water would attain equilibrium with dolomite and expect some of the calcite, originally dissolved, to precipitate when therefore the process of dedolomitization would not continue. As dolomite saturation is approached. Without the presence of gyp- indicated by reversal of the dedolomitization arrow in the cation sum, little else would occur. However, in the presence of gypsum, triangle (Fig. 6), as the process continues, the percentage of calcium ground water will remain at saturation or be slightly supersaturated increases because the amount of calcite precipitation decreases, with calcite owing to the contribution of calcium ions from the owing to deficiency of the CO3 ion not being replenished by C02 dissolution of gypsum. The continual addition of calcium from gas from the soil zone. gypsum thus leads to the precipitation of calcite owing to the It follows that the pH must decrease as a function of increasing common-ion effect. The precipitation of calcite decreases the pH gypsum dissolution. This is, indeed, the case and an excellent corre- and removes carbonate from solution, thereby causing further dis- lation exists between pH decrease and sulfate increase (Fig. 11).

solution of dolomite. In other words, the process of dedolomifiza- As no likely source or sink exists for C02 gas within the tion is driven by the dissolution of gypsum. We believe that aquifer, the Pahasapa is considered a closed system downgradient

'dedolomitization" will not occur in low-temperature environments from the recharge area. In this closed system, Pco2 increases and without the presence of gypsum or some other source of additional 2C02 decreases (Fig. 12) as a result of calcite precipitation. If this calcium ions. Furthermore, the resulting calcite is not only a were an open system from which C02 could escape, Pco2 would not replacement of dolomite to form dedolomite but, we believe, the increase as observed. process may account for some vein calcites and secondary cements. The quantitative effect of these dedolomitization reactions can The process may be viewed mechanistically as follows: be expressed in a model involving transfer of mass from one phase to another. Such a model will evaluate dissolution of minerals and (A) dissolution of calcite gases, precipitation of minerals and other solid phases, and outgass- ing. Rearranging the mass-balance equations given above, the H20 + C02s + CaC03 — 2 implied mass transfer of calcite (Acal), dolomite (Adol), gypsum Ca!c + 2HCOJs; , c (Agyp), and C02 gas (AC02 gas), is: (B) dissolution of dolomite Acal = ACa - AMg - ASO4 2H20 + 2C02s + CaMg(C03)2 — Adol = AMg Ca^2 Mg+2 + 4HCOj + s d Agyp = ASO4 ACO, = A£C0 + ASO4 - ACa - AMg (C) dissolution of gypsum gas 2

CaS04-2H20 — where ACa, AMg, ASO4, and AC02 are differences in total concen- 2 2 Ca; + SO4 + 2H20 trations (mmole/kg H20) of calcium, magnesium, sulfate, and total inorganic carbon between the recharge water and downgradient where c, d, and g represent ions from calcite, dolomite, and gypsum; ground water. The term "AC02 gas" can be obtained by subtracting ind s represents C02 from soil gas. When occurring simultane- Acal and 2Adol from total inorganic carbon (A2C02). This value ity, CaCOj will precipitate as follows: can be used to determine which reactions are open or closed to C02 gas. AC02 gas will be zero if there is no source for C02 in the Ca!2 + Ca!2 + Ca;2 + 6HCOT , — c a g 3c, d, s reaction and no outgassing of C02. + 3Cac d, g C03c d s + 3HCOj + 3H • The philosophical approach and method of reaction modeling Sic, «TO were discussed by Plummer and Back (1980). The detailed reaction simulations have been determined by the computer program ^s calcite is precipitated, the pH of the ground water will decrease. PHREEQE (Parkhurst and others, 1980), which uses an aqueous

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Figure 11. Downgradient de- crease in pH for each sample with sul- fate shown as a progress variable.

model with the constraints of mass balance and charge balance to thermodynamic data for the system, CaC03-C02-H20 (Plummer predict pH and equilibrium distribution of inorganic species in and Busenberg, 1982). solution as a function of reaction progress. In addition, the simula- The chemical character of water at Rhoads Fork is assumed to tion scheme predicts the amount of mineral dissolution and precipi- be typical of recharge water for the system. We have modeled the tation required to maintain equilibrium. The aqueous model used is net chemical transfer between Rhoads Fork and selected sampling similar to that of WATEQ (Truesdell and Jones, 1974) and points downgradient from the recharge area. The results of these WATEQF (Plummer and others, 1976), modified to include new mass-transfe r calculations (Table 6) give the amount of gypsum and

TABLE 6. MASS TRANSFER REACTIONS'

Step 1 Step 2

End member +.Acal + Adolo +Agyp Water at + Acal + AC02 ~~* Water at Sample water depth well head no. (calculated) (observed)

Rhoads Fork - .187 •0.0 • .054 Spearfish -.216 -.290 ~* Spearfish 3 P jt = -l.99 P = -1% p 203 CO C02 co2 = - pH = 7,35 pH = 7.36 pH = 7.39

Rhoads Fork - .684 + .247 • .458 Newcastle -.070 -.111 ~~* Newcastle 5

PC02 = -1.73 PC02 = -1.75 pH - 7.18 pH = 7.2

Rhoads Fork - .571 * .165 • .489 Osage + .018 + .013 ""'' Osage 6

PC02 = -I.75 PC02 = -I.75 pH = 7.19 pH = 7.20 Rhoads Fork - .366 • .041 • 1.041 McNenny -.191 -.108 ~* McNenny 7

PCOj,-1.90 PC02 = -I.85 pH = 7.27 pH = 7.18

Rhoads Fork -1.844 • .741 • 1.728 Upton -.076 -.095 ~* Upton 8 69 PC02 = PCO2 = -1.70 pH = 7.12 pH = 7.12 Rhoads Fork -1.528 • .412 • 2.093 * Ellsworth AFB -.352 -.778 ~* Ellsworth AFB 9 p PC02 = -1.31 C02=-l» pH = 6.84 pH = 7.01

Rhoads Fork -2.389 • .289 + 3.293 ~* Provo -.093 -.347 ~* Provo 10

PC02 = -1.33 PC02 = -1.49 pH = 6.83 pH = 6.97

Rhoads Fork -3.077 • .742 + 5.648 ' Evans Plunge + .185 + .378 —* Evans Plunge 11 P 1 54 PC02 = -I65 C02 " " pH = 6.97 pH = 6.90

Rhoads Fork -4.048 + 1.442 • 6.648 -* Philip -.245 -.989 ~* Philip 12

PCO2 = -1.00 PC02 = -I.3I pH = 6.54 pH = 6.78 Rhoads Fork -4.846 +1.773 + 8.328 -'' Midland -.257 -.982 Midland 13

PC02 = -0.97 PC02 = -1.25 pH = 6.49 pH = 6.69

Rhoads Fork -7.605 + 3.012 + 14.574 —* Bear Butte -.076 + .037 Bear Butte 14

PC02 = -I.8I PC02---I.75 pH " 6.99 pH = 6.91

Rhoads Fork -6.032 • 2.476 + 15.099 ~* Cascade Springs + .190 + .137 Cascade Springs 15

Pc02 = -I.58 PC02 = -1.61 pH = 6.83 pH = 6.89

•Mass transfer coefficients in millimoles per Kg of water; positive sign indicates dissolution and negative sign indicates precipitati on. +1\;( )2 stands for log Pc02'

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Figure 12. Graph showing corresponding downgradient de- Figure 13. Mass transfer of the three principal minerals from

crease in XC02 with increase in Pc02- recharge water to water downgradient.

dolomite dissolution and the amount of calcite precipitation as a rium, the calculations in the first step permit determination of consequence of the dissolution of gypsum and dolomite. chemistry of ground water for an unobtainable sample and thereby Because the calculated log Pco2 and pH differed significantly permit estimation of the mass transfer of calcite (Fig. 13). In esti- from observed values for several wells (Table 6), the mass transfer mating the mass transfer associated with outgassing, the computer from the recharge area to the wellhead was evaluated in two steps. model uses the ground-water chemistry predicted from the first The first step involves reactions that occur between the recharge step, together with the thermodynamic constraints imposed by the area and the bottom of the well, where a sample is not obtainable. calcite saturation index and Pcc>2 observed at the wellhead. The second step evaluates the effects that pumping has on CO2 outgassing and calcite precipitation in the vicinity of the well. HYDROLOGIC CONSEQUENCES OF Because the saturation index shows that the water is nearly in equil- MASS-TRANSFER MODELS ibrium with calcite, it is only through the mass-transfer calculations that we can demonstrate quantitatively that dolomite continues to Ground-water reactions involve dissolution and precipitation dissolve and calcite continues to precipitate. As gypsum and dolo- of carbonate minerals and changes in £C02 that cause changes in mite continue to dissolve, we use the constraint of calcite equilib- S13C and Sl4C. The l4C values measured in the laboratory therefore rium to define the amount of calcite precipitated (Fig. 13). must be adjusted to account for these reactions. A model has been In simulation of water chemistry at the bottom of each well, developed that simulates chemical reactions to predict quantita- the mass balance on magnesium and sulfate was used to estimate tively the changes in carbon isotope composition and the amount of the amounts of dolomite and gypsum dissolving between the 14C lost from the water owing to calcite precipitation during dedo- recharge area (Rhoads Fork) and the bottom of the well. It was lomitization. Consequently, by using the laboratory-determined assumed that no further changes occur in total sulfate or magne- 14C value, initial chemistry, including 5I3C, and all changes in car- sium during the second step. In the calculations, calcium, magne- bon chemistry, it is possible to calculate an adjusted l4C value and, sium, sulfate, and carbon were added to the Rhoads Fork ground hence, an apparent age of ground water. Unfortunately, some water water, as dictated by the stoichiometry of gypsum and dolomite could not be dated in this way because of uncertainties in its mixing (Table 6 and Fig. 13). Slight variations in the stoichiometry of and flow path. In adjusting I4C data for effects of chemical reac- dolomite do not affect the results. By maintaining calcite equilib- tions, the calculation requires knowing the l4C content of the water as a function of reaction progress along the flow path (Wigley and 1AB1.E 7. a'-'c AND 14C ACTIVITY ALONG REACTION PATH FROM RHOADS FORK* others, 1978). In the absence of this information for Cascade, Bear Butte, Provo, and Cleghorn samples, we were unable to determine Location Cale, at Cale, at Observed at depth^ wellhead^ wellhead the age of the water. For the remaining samples, the isotopic com- S'3c 14c 6'3C I4C SI3C I4C position of the water was simulated using the equations of Wigley

spearfish -10.9 54.5 -10.5 54.5 -10.7 74.3 and others (1978) and the mass transfer of Table 6. Mewcastle -10.3 50.5 -10.2 50.5 -10.4 46.2 Usage -10.5 51.8 -10.5 51.5 -10.0 54.7 In calculating the isotopic evolution, the starting isotopic com- McNenrtv -10.9 53.9 -10.8 53.9 -11.5 79.6 13 Jpton - 8.9 42.2 - 8.8 42.2 - 8.2 14.7 position of Rhoads Fork water was taken as S C = -11.0°/oo and 55 Ellsworth AFB -10.1 47.2 - 9.5 47.2 - 9.1 5.8 l4 I3 Evans Plunge - 9.2 40.6 - 8.1 35.7 - 9.7 28.5 °/oo modern C; average S C of dolomite was assumed to be 0°/oo. Jhilip - 8.2 31.5 - 7.8 31.5 - 7.2 2.8 14 viidland - 7.7 IIA - 7.4 27.4 - 6.2 2.4 The laboratory analysis gives a § C value of 92.9%. However, we conclude that this sample is contaminated by atmospheric isotopes. •Rhoads Fork dl3C = -11.0; 14C calculated to be 55% modern. By using calculations based on chemical mass balances, a value of ^ '^C in " i,u PDB; '4C in % modern using mass balance calculations. 55% was thus determined to be representative of the water leaving

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TABLE 8. VELOCITY OF GROUND-WATER FLOW AND HYDRAULIC CONDUCTIVITY, K, Evans Plunge is estimated to be 5,270 yr old, but when adjusted for l4 DETERMINED FROM C ANALYSES both congruent and incongruent reactions, the age is only 1,900 yr. The younger age for Evans Plunge is more in keeping with our Velocity* A Head .1 Length Gradient^ K§ (m/yr) (ft) (km) 1 (m/s) understanding of the hydrogeology of the Pahasapa aquifer. These adjusted 14C ages can be used to determine velocity of From Rhoads Fork to: ground-water flow, hydraulic conductivity of the aquifer (Hanshaw 5 Newcastle 21.4 1,850 15 38 X 10"' 1.8 X IO-6 8 Upton 4.6 1,900 40 14 X I0~3 1.0 X IO-6 and Back, 1974), and rates of chemical reactions. Velocity of 9 Ellsworth AFB 1.2 500 20 7.6 X 10"' 0.5 X IO"6 ground-water flow (Table 7) was calculated by assuming that the 3 11 Evans Plunge 10.5 300 20 4.6 X IO" 7.3 X IO"6 14C 12 Philip 11.0 1,325 220 1.8 X IO"3 19 X IO"6 age is the time required for water to flow from recharge area to 13 Midland 12.9 1,450 260 1.7 X IO-3 24 X IO-6 sampling point. An assumed horizontal flow line was measured 'Velocity - ^Agtft'yrl"^ where Aage is the calculated flowtime between Rhoads Fork and the well and from the outer edge of the outcrop of the Pahasapa around the •iage is based on the '4C adjusted for both congruent and incongruent reaction (Table 4). Black Hills to the well sampled. Distance divided by age gives a

tCradient.i= ^¡eadjm) range of velocities of ground-water flow from less than 2 to more ^Length of flow path (m) than 20 m per yr; the mean velocity of 10.3 m/year for ground- ; where porosity, d, has an assumed value of 10%. water flow in the Pahasapa compares favorably with the average flow velocity of 7 m/yr determined by l4C in the principal artesian aquifer of Florida (Hanshaw and others, 1965). the recharge area in a closed system. Table 7 includes the predicted The hydraulic conductivity, K (Table 8), was calculated from a <5i3C and I4C activity of the downhole ground water at the end of the form of Darcv's law, K = ^f where V is velocity determined from first step and similar values at the end of the second step. Most SI3C l4C; I is hydraulic gradient, equal to-^where AH is total head loss values predicted at the wellhead are within l°/o of the measured 0 from recharge area to sample point; AL is the length of an assumed values. horizontal flow line; and 6 is porosity, assumed to be 10% for these One way to further test the reliability of the mass-transfer l3 calculations. The hydraulic conductivity for the Pahasapa dolomite values is to calculate for each water sample the <5 C value for 6 l3 in the area studied ranges from a low of 0.5 x 10~ m/s to a high of dolomite that was required to match the predicted S C of the water 6 about 24 x 10" m/s, which are characteristic values for limestone with the observed 6,3C. These values average +1.0c/'oo with a range 13 aquifers. of -4.6°/oo to +2.9°/oo. This calculated average and range of S for l4 By combining the C ages of ground water (Table 4) with the the dolomite compares well with measurements of eight dolomite mass-transfer calculations (Table 6), rates of dolomite and gypsum samples from the Pahasapa that average +0.1°/oo and range from I3 dissolution and calcite precipitation can be determined (Table 9). -5.5°/oo to +5.1°/oo. The relatively large spread of <5 C for dolomite 4 Dolomite dissolution ranges from a high of 3.9 x 10" mmol/yr/kg derived from reaction simulation thus seems to reflect the true iso- 5 4 of H20 to a low of 2.4 x 10" ; the mean is about 1.7 x 10" mmol/kg topic heterogeneity of dolomite in the Pahasapa. of H20/yr. Eliminating the high values for solution of gypsum and 14 Finally, the C activity has been adjusted for all reactions precipitation of calcite at Evans Plunge, the mean gypsum dissolu- (Table 4) to estimate the most reliable 14C age of the ground water. 4 tion rate is about 3.4 x 10" mmol/kg of H20/yr, and the average As was mentioned previously, two adjustments were made to the 4 precipitation rate of calcite is near 3.4 x 10" mmol/kg of H20/yr. l4 14 C age of the ground water. For example, the C laboratory value As discussed earlier, dissolution of dolomite and precipitation of gives the Midland ground water an age of 30,830 yr. Each adjust- calcite are driven irreversibly by the solution of gypsum. While ment for chemical reactions leads to a younger age; the Pearson and maintaining dolomite and calcite equilibrium in a system with White adjustment (1967), based solely on congruent dissolution of approximately constant composition, we would expect the rate of calcite, gives an age of 22,020 yr, whereas consideration of both calcite precipitation to be equal to the gypsum dissolution rate. congruent and incongruent reactions gives an age of 20,100 yr. Stoichiometry dictates that, owing to the common carbonate ion, Although the final adjustment is not particularly significant in dat- the dolomite dissolution rate would be half the calcite precipitation ing older water such as the Midland sample, large errors can result rate. The observance of these relationships in the average calcu- for younger water, such as that at Evans Plunge, if precipitation of lated rates further supports the mechanism of dedolomitization in calcite is ignored. On the basis of congruent solution only, water at the Madison Limestone aquifer.

TABLE 9. RATES OF CHEMICAL REACTIONS

Sample number ( ' age. .} dolo Dolomite -A £Vp Gypsum -i cal Calcite and location YBP mmol/kg of mmol/kg of mmol/kg of

H20/yr H20/yr HjO/yr

From Rhoads Fork to:

5 Newcastle 700 . 247 3.5 X 10~4 .458 6.5 X I0~4 - .684 8 Upton 8.700 .741 8.5 X 10"5 1.728 2.0 X I0-4 -1.844 9 Ellsworth AFB 17,300 . 412 2.4 X I0~5 2.093 I.2XI0"4 -1.528

11 Evans Plunge 1,900 .742 3.9 X I0"4 5.648 3.0 X I0-3 -3.077 12 Philip 20,000 1.442 7.2 X 10"5 6.648 3.3 X I0~4 -4.048 13 Midland 20,100 1.773 8.8 X 10"5 8.328 4.1 XIO"4 -4.846

Note: Positive value indicates dissolution of dolomite and gypsum; negative value indicates precipitation of calcite.

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CONCLUSIONS Clarke, F. W., 1924, The data of (5th edition): U.S. Geological Survey Bulletin 770, 841 p. Claypool, G., Holser. W. T., Kaplan, 1. R., Sakai, H., Zak, I., 1980, The age curves of sulfur and oxygen isotopes in marine sulfate and their mutual interpretation: Chemical Geology, v. 28, p. 199-260. Craig, H., 1961, Isotopic variations in meteoric waters: Science, v. 13, p. 1702-1703. This paper demonstrates that the principal controls on the Darton, N. H., and Paige, Sidney, 1925, Central Black Hills: U.S. Geological Survey Atlas, Folio 219, 34 p. chemical character of water in carbonate aquifers is commonly Fournier, R. O., and Rowe, J. J., 1966, Estimation of underground temperatures from silica content of water from hot springs and wet steam wells: American Journal of Science, v. 264, p. 685-697. implanted during deposition and early diagenesis. For example, the Gerhard, L. C., 1978, Some modern carbonate studies applied to the Williston Basin: Montana Geological Society, 24th Annual Conference: Williston Basin Symposium, Billings, Montana, p. 35-55. shallow-marine environment in which the Pahasapa Limestone was Gries, J. P., 1971, potential of the Pahasapa limestone: Proceedings of the South Dakota deposited allowed the development of restricted lagoons in which Academy of Science, v. 50, p. 61-65. Hanshaw, B. B., and Back, W., 1974, Determination of regional hydraulic conductivity through C dating of ocean water evaporated to the point where gypsum precipitated and ground water: Mémoires de l'Association Internationale des Hydrogéologues, Congres de Montpellier, v. X-l, p. 195-196. became disseminated throughout the limestone. This presence of 1979, Major geochemical processes in the evolution of carbonate-aquifer systems: Journal of Hydrol- gypsum permits the process of dedolomitization to be a major con- ogy, v. 43, p. 287-312. Hanshaw, B. B„ Back, W., and Rubin, M„ 1965, Radiocarbon determinations for estimating ground-water trol in the chemical character of present-day ground water. This flow velocities in central Florida: Science, v. 148, p. 494-495. Hanshaw, B. B., Back, W., and Deike, R. G., 1971, A geochemical hypothesis for dolomitization by ground paper further demonstrates that dedolomitization is occurring on a water: Economic Geology, v. 66(5), p. 710-724. regional basis and that sulfate alone is not the critical ion, as earlier Hanshaw, B. B., Busby, John, and Lee, Roger, 1978, Geochemical aspects of the Madison Aquifer System: Montana Geological Society, 24th Annual Conference: Williston Basin Symposium, Billings: Montana believed, but, rather, the calcium associated with sulfate derived Geological Society, p. 385-390. Holser, W. T., and Kaplan, I. R., 1966, Isotope geochemistry of sedimentary sulfates: Chemical Geology, v. I, from gypsum is the driving mechanism for dissolution of dolomite p. 93-135. and the concurrent precipitation of calcite. Deuterium and oxygen Konikow, L. F., 1976, Preliminary digital model of ground-water flow in the Madison Group. Powder River Basin and adjacent areas, Wyoming, Montana, South Dakota, North Dakota, and Nebraska: U.S. isotope data for the ground water substantiate the hypothesis of Geological Survey Water Resources Investigations 63-75, 44 p. Langmuir, D., 1971, The geochemistry of some carbonate ground waters in central Pennsylvania: Geochimica mass transport of water along flow paths deduced from the potenti- et Cosmochimica Acta, v. 35(10), p. 1023-1045. ometric surface. Geothermometry based on chalcedony and quartz Marshall, W. L., and Slusher, R., 1966, Thermodynamics of calcium sulfate dihydrate in aqueous sodium chloride solutions, 0-110°: Journal of Physical Chemistry, v. 70, p. 4015-4027. solubility in ground water provides a basis for interpreting the Parkhurst, D. L., Thorstenson, D. C., and Plummer, L. N., 1980, PHREEQE-A computer program for geochemical calculations: U.S. Geological Survey Water Resources Investigation 80-96, 210 p. depth of the flow system. Sulfur isotope data provide a greater Pearson, F. J., and Hanshaw, B. B., 1970, Sources of dissolved carbonate species in ground water and their understanding of the of the system and suggest areas effects on carbon-14 dating: Isotope Hydrology 1970, International Atomic Energy Agency, p. 271-286. Pearson, F. J., Jr., and White, D. E., 1967, Carbon 14 ages and flow rates of water in Carrizo sand, Atascosa with hydrologic connection between the Mississippian limestone County, Texas: Water Resources Research, v. 3, 251 p. Peterson, J. A., 1981, Stratigraphy and sedimentary facies of the Madison limestone and associated rocks in and overlying Pennsylvanian and Permian evaporites. Mass- part of Montana, North Dakota, South Dakota, Wyoming, and Nebraska: U.S. Geological Survey l4 transfer calculations provide a refinement to adjustment of C Open-File Report 81-642, 83 p. Plummer, L. N., 1977, Defining reactions and mass transfer in part of the Floridan Aquifer: Water Resources values used to determine the age and velocity of ground water. In Research, v. 13(5), p. 801-812. the Madison aquifer, this improved adjustment is less important for Plummer, L. N„ and Back, William, 1980, The mass balance approach: Applications to interpreting the chemical evolution of hydrologic systems: American Journal of Science, v. 280, p. 130-142. older water but can be significant for young water with high con- Plummer, L. N., and Busenberg. E., 1982, The solubilities of calcite, aragonite and vaterite in CO2-H2O 14 solutions between 0 and 90°C, and an evaluation of the aqueous model for the system CaCO^-CC^- centration of C. Mass-transfer calculations refine and quantify H2O: Geochimica et Cosmochimica Acta, v. 46, p. 1011-1040. the controlling chemical reactions and provide reaction coefficients Plummer, L. N„ Jones, B. F., and Truesdell, A. H„ 1976, WATEQF A Fortran IV version of WATEQ, a computer program for calculating chemical equilibrium of natural waters: U.S. Geological Survey that show both the amount and rate of mineral solution and Water Research Investigation 76-13, 61 p. Rahn, P. H., and Gries, J. P., 1973, Large springs in the Black Hills, South Dakota and Wyoming: South precipitation. Dakota Geological Survey Report of Investigations, no. 107, 46 p. Rightmire, C. T., and Hanshaw, B. B., 1973, Relationships between the carbon isotope composition of soil CO2 and dissolved carbonate species in groundwater: Water Resources Research, v, 9, p. 958-967. Rightmire, C. T., Pearson, F. J., Back, W„ Rye, R. O., and Hanshaw, B. B„ 1974, Distribution of sulfur ACKNOWLEDGMENTS isotopes of sulfates in from the Principal Artesian Aquifer of Florida and the Edwards Aquifer of Texas, U.S.A., Isotopes Technology in Groundwater, v. II: International Atomic Energy Agency, p. 191-207. We greatly appreciate the review of the manuscript by Owen Rose, P. R., 1976, Mississippian carbonate shelf margins, western : U.S. Geological Survey Journal of Research, v. 4. p. 449-466. Bricker, U.S. Geological Survey; Jan Veizer, University of Ottawa; Rye, R., Back, W., Hanshaw, B. B., Rightmire, C., and Pearson, F. J.. 1981, The origin and isotopic composi- tion of dissolved sulfide in ground water from carbonate aquifers in Florida and Texas: Gcochimica et and an anonymous reviewer selected by Editors of the Geological Cosmochimica Acta, v. 45, p. 1941-1950. Society of America. Sando. W., Dutro, J., Sandberg, C., and Mamet, B., 1976, Revision of Mississippian stratigraphy, eastern Idaho and northeastern Utah: U.S. Geological Survey Journal of Research, v. 4, p. 467-479. Schneider, G. B., 1973, Petrology of the Pahasapa (Madison) limestone of the northeastern Black Hills of South Dakota [Ph.D. thesis]: Rapid City. South Dakota. South Dakota School of Mines and Technology, 63 p. Schoon, Robert A., and McGregor, Duncan J., 1974, Geothermal potentials in South Dakota: South Dakota REFERENCES CITED Geological Survey Report, no. 110, 76 p. Stewart, G. L.. and Farnsworth, R. K., 1968. United States tritium rainout and its hydrologic implications: \gnew, A. F., and Tychsen, P. C., 1965, A guide to the stratigraphy of South Dakota: South Dakota Water Resources Research, v. 4, p. 273-289. Geological Survey Bulletin, v. 14, 195 p. Truesdell, A. H„ and Jones, B. F., 1974, WATEQ, a computer program for calculating chemical equilibria in Back, William, and Hanshaw, B. B., 1971, Rates of physical and chemical processes in a carbonate aquifer: natural waters: National Technical Institute Service PB-220 464, 173, U.S. Geological Survey Journal of Nonequilibrium systems in national water chemistry: Advances in Chemistry Series 106, p. 77-93. Research, v. 2, p. 233-248. Barnum, D. C., 1973, A petrologic, stratigraphie, and crushing properties study of the Pahasapa (Madison) von Morlot, A., 1847, Veber Dolomit and seine kunstliche Darstellung aus kalkstein: Naturwissenschaftliche limestone of the northern Black Hills, South Dakota [Ph.D. thesis]: Rapid City, South Dakota, South Abhandlungen, gesammelt und durch Subscription lursg. von Wilhelm Haidinger, v. I, p. 305-315. Dakota School of Mines and Technology, 142 p. Wigley, T.M.L., Plummer, L. N., and Pearson, F. J., Jr., 1978, Mass transfer and carbon isotope evolution of Bender, M. M., 1968, Mass spectrometric studies of C variations in corn and other grasses: Radiocarbon, natural water systems: Geochimica et Cosmochimica Acta, v. 42, p. 1117-1139. v. 10, p. 468-472. Busby. J. F., Lee, Roger, and Hanshaw, B. B., 1983, Major geochemical processes related to the hydrology of MAM.'SI R1PI Rlil'EIVtD BY II IH SoCIKTY MARCH 8, 1982 the Madison aquifer system and associated rocks in parts of Montana, South Dakota, and Wyoming: Revised Manusckipi Received Novhmhkr 18, 1982 U.S. Geological Survey Water Resources Investigation Report 88-83-4093. Manuscript Accepted December 14, 1982

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