CO2 outgassing: Field measurements of precipitation rates in comparison to ... A small spring-fed stream precipitates calcite by outgassing of CO2 due to ...
Chemical Geology, 97 ( 1 9 9 2 ) 2 8 5 - 2 9 4 Elsevier Science Publishers B.V., A m s t e r d a m
285
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Geochemically controlled calcite precipitation by CO2 outgassing: Field measurements of precipitation rates in comparison to theoretical predictions W. Dreybrodt a, D. Buhmann a, J. Michaelis b and E. Usdowski b alnstitut fur Experimentelle Physik, Universitiit Bremen, W-2800 Bremen, FederalRepublic of Germany bSedimentpetrographischeslnstitut, Universitiit G6ttingen, W-3400 GOttingen, FederaIRepublic of Germany (Received June 10, 1991 ; revised and accepted January, 13, 1992 )
ABSTRACT Dreybrodt, W., Buhmann, D., Michaelis, J. and Usdowski, E., 1992. Geochemically controlled calcite precipitation by CO2 outgassing: Field measurements of precipitation rates in comparison to theoretical predictions. Chem. Geol., 97: 285-294. A small spring-fed stream precipitates calcite by outgassing of CO2 due to chemically controlled inorganic processes. The chemical composition of the water was measured along nine stations downstream with respect to Ca 2+, Mg 2+, Na +, K +, CI-, CO3-, SO42- and alkalinity. Temperature and pH were measured in situ. Small rectangular shaped tablets of limestone from the area were immersed into the stream for short periods and water analyses were carried out at the same time. From weight increase of the tablets, precipitation rates of calcite could be measured. From the data of the water analysis, they were compared to those calculated by the PWP (Plummer-Wigley-Parkhurst) rate law. The calculated rates turned out to be too high by one order of magnitude. This result is not unexpected since these calculations neglect the diffusion boundary layer between the surface of the tablets and the turbulent flowing solution, which represents a diffusive resistance. Application of a recently developed theory which takes this effect into account gives a rate dependence on the thickness E of this boundary layer. The thickness ~ can be crudely estimated by hydrodynamic correlations, or can be measured in situ by inserting gypsum tablets of equal shape as those of the limestone tablets close to them into the stream. Since dissolution of gypsum is controlled by diffusion entirely, ¢ can be determined from their weight loss. The theoretical calculations of calcite precipitation rates using these determined values of e between 0.01 and 0.03 cm are in good agreement with the field data. From this we conclude that a reasonable prediction of precipitation rates is possible by using the PWP rate equation and correcting it for the influence of the boundary layer by reducing the thus obtained rates by a factor of 10.
I. Introduction
Inorganic precipitation of calcite from spring and river water supersaturated by degassing of CO2 has been of considerable interest both experimentally in the field and theoretically. The first study was published by Jacobson and Usdowski (1975) and Usdowski et al. C o r r e s p o n d e n c e to: Dr. W. Dreybrodt, Institut fdr Experimentelle Physik, Universit~it Bremen, W-2800 Bremen, FRG.
( 1979 ), who studied calcite precipitation in the Westerhofbach, a small stream located close to the village of Westerhof, some 30 km north of G6ttingen, Germany. They investigated the chemistry of the stream water at eleven stations along the 265-m-long stream and found decreasing Pco2 due to outgassing, and also decreasing concentration of calcium as a consequence of calcite precipitation. Similar observations were performed by Michaelis et al. (1984) in calcite depositing springs in the Schw~ibische Alb, south Germany.
0 0 0 9 - 2 5 4 1 / 9 2 / $ 0 5 . 0 0 © 1992 Elsevier Science Publishers B.V. All rights reserved.
286 In a series of papers, Herman and Lorah ( 1986, 1987, 1988 ) reported on the evolution of the water chemistry along the flowpath of Warm River Cave and Falling Spring Creek, Virginia, U.S.A. The initial water chemistry is defined by mixing two chemically and thermally distinct waters inside Warm River Cave. The water chemistry was examined at a variety of stations downstream. At all the stations the water turned out to be supersaturated with respect to atmospheric CO2. Due to outgassing, the CO2 concentration decreased downstream, and as a consequence the saturation index, SI [ log ( IAP/Kc ) or log{ (ion activity product ) / (dissociation constant)}] with respect to calcite increased to values up to 1.3. Precipitation rates of calcite were estimated by measuring the stream velocity and the calcium concentrations at two neighbouring sampling stations. Assuming that all calcite precipitation takes place at the interface of water and the riverbed, an estimation of average precipitation rates between adjacent sampling sites in units of mol kg- 1 H20 s- 1 could be given (Herman and Lorah, 1988 ). This unit gives the amount of calcite deposited from 1 kg of water in 1 s. The precipitation rates thus obtained by mass balance were compared to those calculated by the PWP rate law ( P l u m m e r et al., 1978, 1979 ), which, according to Reddy et al. ( 1981 ) and Inskeep and Bloom (1985), is also valid for calcite precipitation. This rate law summarizes comprehensively laboratory data on dissolution and precipitation experiments and allows to compute reaction rates, if the activities of HCO3-, Ca 2+, H + and H2CO3"= CO2(aq ) -~H2CO 3 are known. The results obtained from the PWP rate law and those from estimations of mass transfer generally agreed within an order of magnitude. In most cases the rate law estimations turned out to be higher by a factor of ~2. However, a considerable discrepancy occurs at the sampling site where the creek breaches a small sandstone ridge and flows over a 20-m- high waterfall. Here the rate from the PWP equation underestimates the
W D R E Y B R O D T ET AL.
precipitation rates calculated from mass-transfer observations by more than a factor of 10. Since many uncertain parameters in estimating precipitation rates by mass balance must be considered, as e.g. the surface area at which precipitation takes place and the flow velocity, which both are crucial to the conversion into rates which can be compared to the rate laws, such discrepancies are to be expected. On the other hand, the agreement within a factor of 2 for most of the other sites is considered as encouraging to apply the PWP rate law for the field observations. The purpose of this work is to support this assumption by measuring both chemical composition of stream water and precipitation rates of calcite simultaneously and to compare the resulting rates directly. In applying the rate law of Plummer et al. (1978) however, one has to be careful since several restrictions have to be considered. The rates are given by the equation:
R=k~ all+ +k2an2co~.+k3 --k4aHco3 ac.,,2+ (1) where kl, k2, k2 and k4 are rate constants, given as functions of temperature, and for k4 also as function ofPco2 ( P l u m m e r et al., 1978). The activities a of Ca 2+ , HCO3-, H + and H2CO3" are those at the surface where precipitation or dissolution takes place. However, these activities can be considerably different from those in the bulk solution, since mass transport and slow conversion of CO2 into H2CO3 play an important role in controlling the reaction rates. In a series of papers, Buhmann and Dreybrodt (1985a, b) have established a comprehensive model for calcite dissolution and precipitation kinetics with respect to geologically relevant situations. This theory takes into account the three major processes occurring simultaneously during dissolution and precipitation: (1) chemical reactions at the calcitesolution interface, according to eq. 1; (2) diffusional transport of species through the solu-
287
G E O C H E M I C A L L Y C O N T R O L L E D C A L C I T E P R E C I P I T A T I O N BY C O 2 0 U T G A S S I N G
tion to the surface of the solid; and (3) slow conversion of carbon dioxide into protons and bicarbonate ions. It was shown that all the rates could be approximated by a linear equation of the form: R = o z ( [Ca ,'+ ]eq - [Ca 2+ ] )
(2)
where oe is a rate constant depending on Pco2, temperature and geometry of flow (listed in Buhmann and Dreybrodt, 1985a, b); and [ Ca2+ ]eq is the Ca 2+ concentration at saturation. The square brackets denote concentrations. In two subsequent papers we extended this theory by considering foreign ions and ion pairs ( Buhmann and Dreybrodt, 1987 ) and by a detailed investigation of turbulent flow effects (Dreybrodt and Buhmann, 1991 ). The latter paper takes into account a diffusion boundary layer, which separates the solid from the turbulent bulk of the solution and where mass
transport is determined by molecular diffusion. This b o u n d a r y layer strongly reduces dissolution and precipitation rates by the occurrence of concentration gradients across it. With these extensions it is possible to predict dissolution and precipitation rates in turbulently flowing waters of natural chemical composition. A comprehensive review on the work cited above is given by Dreybrodt ( 1988 ). The present paper is mainly based upon the theory of precipitation in a turbulently streaming solution under consideration of a diffusion b o u n d a r y layer ( D r e y b r o d t and Buhmann, 1991 ). Furthermore, this theory is extended by including foreign ions, such as Mg 2+, Na +, K ÷ , SO42 and C1-, which are always present in natural waters. Thus, we are able to calculate precipitation rates for actually measured compositions in a given system. The calculated rates are then compared to the experimentally derived precipitation rates.
12.0
5.0
311.0 10.0
~4.0
O.,..
E 9.o
3.5 (J
8.0 8..5
8.0 212 C1.
3.0 1.5
J
1.0 6n
7.5
0.5
J
7.0
,.._6.0
40
E '64.o N2o
C)
-~,2.o g ¢J a_ 0.o
t'-
~. ill
i l l l l
i11
I I s l , ,
I I t S l L L I I l l l l l l l
I l l l l l l S l l l l l l ' l ]
O I ~
r-
0
o ....... g'6 ...... 'i6g ..... '~'gi5..... ~6i5..... ~'g~
d i s t o n c e d o w n s t r e o m (m) Fig. 1. Variations of temperature, pH, Pco2, Cam, concentration and saturation index SI along the Westerhof stream on June 13. 1986 (see also Table 1).
288
w. DREYBRODTET AL.
TABLE 1 Changes in chemical species from stations I to 9 in June 1986 Station
1 2 3 4 5 6 7 8 9
T (°C)
pH
9.3 9.5 9.8 10.1 10.4 10.8 11.0 11.3 11.1
7.69 8.03 8.28 8.35 8.42 8.48 8.48 8.48 8.42
CaT (mmoll - l )
Ca 2+ (mmoll -~)
Alk, HCO3-
HCO 3-
P(;o2
(mmoll - l )
(mmoll -~)
(10 3atm)
4.63 4.51 4.47 4.53 4.45 4.38 4.33 4.29 3.91
3.81 3.68 3.62 3.66 3.58 3.51 3.47 3.45 3.15
4.96 4.96 4.96 4.96 4.96 4.96 4.86 4.4 l 4.05
4.75 4.68 4.57 4.52 4.48 4.43 4.34 3.93 3.67
5.1 2.3 1.27 1.07 0.9 0.78 0.76 0.69 0.74
Rexp-values in parentheses are from long-term measurements (cf. Fig. 3). CaT gives the analytical concentration of Ca. Alk, HCO3- is the measured alkalinity. The concentration of Ca 2+ and HCO3 , Pco2 and saturation index SI are calculated using SOLMINEQ.88. Ro is the rate calculated by the PWP equation ( 1 ) using the ionic strength I and the concentration of foreign ions: 1=22-10-3; [SO42-]=3.67 mmol l-t; [C1-]=0.42 mmol 1-~; [Mg2+]=1.58 mmol 1 ~; [Na+]=0.32 mmol l-L: [K + ] =0.05 mmol 1-~. Rcxp=values of precipitation rates found experimentally on the limestone table values in parentheses are from long-term measurements, cf. Fig. 3; R~=values calculated from the boundary layer approach; E=values of the boundary layer thickness as determined from the dissolution of gypsum; v= stream velocity at the stations.
2. Experimental methods and results In the present study we performed experiments in a natural calcite precipitating stream. The chemistry of this stream was extensively investigated in the past (Jacobson and Usdowski, 1975; Usdowski et al., 1979) and provides a suitable system for the measurement of precipitation rates. The average discharge of the spring is 5 1 s- 1 and the length of the stream is 256 m. Average stream velocities, estimated by measuring the surface velocities are also given. They vary between 0.3 and 1.3 m s -1. We analyzed water samples drawn from stations 1-9 in situ for pH, Ca, Mg and alkalinity with an error of ~ _+2%. For details of the method we refer to Jacobson and Usdowski (1975). Na +, K + , C1- and SO42- were analyzed in the laboratory. A profile of the stream is shown in Fig. 1 including the positions 1-9, which represent the stations where the precipitation rates and chemical compositions were measured. Furthermore, Fig. 1 illustrates the evolution of the stream water chemistry by profiles of pH, Pco2, Ca,or and SI with respect to calcite. It also shows the temperature evo-
lution down the stream. These data were collected in June 1986, when most of the precipitation measurements were performed. Table 1 shows further details, including alkalinity measured a s H C O 3 - . From the chemical analysis we have calculated the concentration of Ca 2+ and HCO3-ions and Pc02 by use of the computer program SOLMINEQ.88 ( 1988 ). Due to the presence of foreign ions, especially SO42-, the Ca 2÷ concentration is reduced considerably in comparison to Cato~by conversion to the ion-pairs CaSO4 °. Table 1 lists furthermore the concentrations of Mg 2÷, Na + and K +, CI- and SO42-, which remain unaltered along the stream. The ionic strength is 0.022. The concentration of sulphate shows strong seasonal fluctuations from 2- 10- 3 to 5" 10- 3 mol 1-1, while the other chemical species do not vary significantly in time. The fluctuations in sulphate concentrations are linked to high meteoric runoff, where strata with high C a S O 4 contents are reached and contribute to the chemical composition of the stream water. Sulphate concentration remains constant, however, at the same time for all sampling points. SI with respect to gypsum is ~ - 0 . 8 .
GEOCHEMICALLY CONTROLLED CALCITE PRECIPITATION BY COz OUTGASSING
SI
0.59 0.91 1.15 1.22 1.28 1.34 1.33 1.29 1.16
Ro (10-Smmolcm-2s
-1)
16 31 47 53 59 63 63 61 47
Rcxp (10-Smmolcm-2s
. . 0 1.5 4.3 4.1 6.5 2.4 0.1
R~ (10-Smmolcm-2s-l)
-l)
. .
289
.
. .
(2.2) (1.6) (1.6) (4.3) (5.6) -
e (cm)
v (cms -l )
0.02 0.01 0.02 0.025 0.015 0.03
33 66 47 91 100 133 31 -
.
. 2.3 3.8 2.8 2.5 3.5 -
TABLE 2 Area, time o f i m m e r s i o n a n d weight gain o f the e x p e r i m e n t s u s i n g the l i m e s t o n e tablets; Rexp gives the precipitation rates determ i n e d f r o m these data Station
Area ( c m 2)
Time of immersion (hr)
Weight gain (mg)
D e p o s i t i o n rate, Rexp ( 10 - s m m o l c m -2 s - l )
2 3 4 5 6 7 8 9 1 2 6 2 3 4 6 6
23.1 23.6 29.9 31.1 31.7 32.8 34.4 33.7 24.5 34.8 38.8 22.8 22.8 29.2 29.2 22.8
72 72 72 72 72 72 72 72 344 272 272 3,216 3,384 3,216 3,216 3,384
- 1.4 - 1.7 11.2 34.4 34.1 55.3 25.8 1.5 - 27.0 -3.1 196.7 325.7 932.4 627.3 1,228.2 1,368.3
-2.3 - 2.8 1.45 4.27 4.15 6.50 2.89 0.17 - 0.89 -0.09 5.20 1.23 3.36 1.86 3.63 4.93
Weight o f s a m p l e s was between 8 a n d 14 g.
290
W DREYBRODT ET AL.
8.0 I
?
E
6.0
0
E4.o E o 2.0
0.0
station number
Fig. 2. Precipitation rates measured at various stations by weight increase of limestone samples. Different symbols represent the period of time the samples were immersed in the stream (see also Table 2 ): [] = 3 days; ~ = 11 days; • = 14 days; A = 134 days (June 1986, see also Table 1). The .full lines are linear interpolations between the rates calculated from the chemical composition at each station (•) and assuming the value e for the thickness of the boundaJ3J layer indicated at the curves (see Section 4). 1.0
0.8
0.6 (,0
tz
0.4
0.2
e -
0.0
I
,
,
E (ore) Fig. 3. Ratios R / R o for the supersaturated pure CaCO3H20-COz solution with [Ca2+]=3.10-3 mol 1-~, Pc.o2=5.10 -3 atm (&), 1-10-3 (V1) and 3.10 -4 atm (•), respectively. Ro is the precipitation rate calculated from eq. 1, when no boundary layer is present, R~the rate at identical chemical composition with boundary layer of thickness e (cm) (Dreybrodt and Buhmann, 1991 ). The uncertainty of CaT and alkalinity a m o u n t s to ~ + 0.08 m m o l 1-1. Within these limits alkalinity and CaT remain constant from station 1 to 4. This is reasonable since no cal-
cite precipitation is observed between stations 1 and 3. Between stations 5 and 9 CaT decreases steadily. If one plots the values of CaT and alkalinity for all sampling points, this can be approximated by a straight line with a slope of +1.6. This means that 1.6 tool HCOBwould be reacted for every mole of Ca precipitated. Similar values have been observed by Jacobson and Usdowski ( 1975 ) who attribute the deviation from the ideal value of 2 to the analytical error. To measure precipitation rates of calcite, specimens of Carrara marble (Italy) or natural limestone of the Westerhof area, cut into rectangular samples of about 3 cm X 2 cm × 0.4 cm with an overall surface of ~ 16 cm 2, were immersed into the stream. The samples were supplied with a small central hole and mounted on top of nails of ~ 15-cm length and 8-mm diameter by a short thread with two nuts. The nails were then driven into the calcite bed of the stream, so that the samples were situated ~ 5 cm beneath the water surface. The samples with their longer edges were oriented approximately parallel to the flow direction of the stream. Most of the samples rested in this position for a time period of 3 days. Other samples were left in the stream for periods of 11, 14 and 132 days. Table 2 gives details on the experimental data. Precipitation rates were measured by weight difference of the dried samples after having been subject to calcite precipitation for a defined time. There was no difference in the precipitation rates between marble and natural limestone. The precipitation rates obtained from this procedure are shown by Fig. 2. It is interesting to note that at most stations the precipitation rates measured over different time intervals show only little variation in time, but significant variation in space. The rates increase downstream from stations 1 to 8 and then drop sharply at station 9. At station 6, two samples were immersed simultaneously for 134 days. The rates observed at these specimens agree within an accuracy of + 20% and thus give an
GEOCHEMICALLY CONTROLLED CALCITE PRECIPITATION BY CO~ OUTGASSING
idea of the error in the measurements. No precipitation Was observed at stations 1-3 for the short-term measurements. This results from the fact that the saturation index is too low for precipitation to start. Similar observations were m a d e by Suarez ( 1983 ) and Troester and White ( 1986 ). This behaviour results from the fact that for precipitation to start, nuclei of a critical size have to be formed at the mineral surface. This nucleation process requires a critical supersaturation of the solution. For details see Berner (1980). From the chemical data in Table 1 and the PWP rate equation, we were able to calculate the expected rates. These are listed in Table 1 and are generally too high by a factor of 10 compared to the data observed. This behaviour can be explained by considering our recent paper (Dreybrodt and Buhmann, 1991 ) on dissolution and precipitation of calcite from solutions in turbulent motion. In this work we investigated the influence of the diffusion boundary layer o f thickness c between the wellmixed, turbulently flowing solution and the calcite surface on the dissolution and precipitation rates. Since mass transport of the respective ions from and to the calcite surface proceeds by molecular diffusion through this layer, it represents a diffusive resistance and both dissolution and precipitation rates are reduced. We have calculated this influence onto the precipitation rates for the pure system C a C O 3 - H 2 0 - C O 2 in the region of Pco: of several 11) - 3 atm and Ca 2+ concentrations of up to 3- 10 - 3 mol 1-i. Fig. 3 shows the ratio o f the rate R~, when the layer is present, to the rate Ro given by eq. 1, i.e. when no layer is present. These data are taken from fig. 6 of Dreybrodt and B u h m a n n (1991) for [ C a 2 + ] = 3 " 1 0 -3 mol 1- l and for Pco2-values as given in the figure caption. The most important result of Fig. 3 is that for e between 0.01 and 0.02 cm the rates R~ are reduced to values between 0.2Ro and 0.15Ro. The reason for this behaviour lies in the fact that the slow conversion of CO2 into H2CO3 takes place entirely in the boundary
29 l
layer if e > 0.01 cm. For details see Dreybrodt and B u h m a n n ( 1991 ).
3. Determination of the boundary layer thickness Because of its importance in explaining measured precipitation rates by a theoretical approach, the thickness e of the diffusion boundary layer must be known. A crude way to estimate e is to use h y d r o d y n a m i c correlations (Skelland, 1974). For a flat plate of length L with the long side into the direction of the stream lines one finds for water at 10°C:
L/~=Nsh;
Nsh..~O.37(vL/u) °s
(3)
where Nsh is the Sherwood number; v the stream velocity; and u the viscosity of water. For our samples, the length L is 3 cm, and the stream velocities range between 20 and 50 cm s -1. Thus, we obtain values ofe between 0.005 and 0.01 cm. These estimations of e show that the observed low precipitation rates can be explained reasonably (cf. Fig. 3 ). A better way to estimate the boundary layer thickness e has been proposed by Opdyke et al. ( 1987 ). If dissolution of a material of a given shape is controlled entirely by diffusion through the boundary layer, the dissolution rate is given by:
R=Dm(C~q --CB)/e
(4)
where Dm is the constant of molecular diffusion; Ceq is the saturation concentration; and C~ the actual concentration in the solution. CaSO4 or gypsum (CaSO4"2H20) are such materials. Therefore, by placing gypsum samples of the same shape as the limestone samples close to them into the stream and measuring their weight loss, we were able to estimate much more accurately. We have done this for the short-term measurements (3 days) and found values of e between 0.01 and 0.03 cm (Table 1 ). This m e t h o d has been verified by measure-
W. DREYBRODTET AL.
292
ments in the laboratory. We drilled a hole 5.8 cm long in a block of crystalline gypsum (Marienglas, Harz Mountains, Germany). The diameter of the hole was d = 1 cm and its surface area A = 18.2 c m 2. We pumped water through this tube and measured the weight loss of the block for given time periods and flow velocities. In all cases flow was turbulent with a Reynolds number: Re = (vL/v) >2000 The dissolution rates R were calculated by the expression:
R= (Am/At)A
(5)
where )Im is the weight loss expressed in grams; At the time of exposure to dissolution; and A the surface area of the tube wall. Using eq. 4 w i t h O m = 10 - 5 c m 2 s - 1 , C e q = 1.93 g 1-1 at 10°C (Blount and Dickson, 1973) and CB=0 we obtain e. Table 2 shows the experimentally obtained values of ~. From hydrodynamic correlations (Skelland, 1974) one obtains for a straight circular tube: =43.5 (vL/u) - 0 8 ( D m / P ) -0.33
(6)
The values of e calculated for each experiment by using this equation are also listed in Table 3 and are in close agreement to the values observed experimentally. TABLE 3 Thickness e of the boundary layer determined from CaSO4" 2H:O dissolution experiments Flow velocity (cms 1)
20 100 200
~ (cm) measured
calculated
0.016 0.0024 0.001
0.01 0.0027 0.0016
4. Calculation of the precipitation rates Using the species concentrations from the water analysis listed in Table 1 we have calculated the precipitation rates for values of
~=5"10 -3, 1"10 -2, 2"10 -2 and 3-10 -2 cm. These calculations were performed using the theoretical approach which considers the influence of the boundary layer (Dreybrodt and Buhmann, 1991 ) and is furthermore extended to include the presence of the foreign ion species Mg 2+, Na +, K +, C1- and 8 0 4 2 (Buhmann and Dreybrodt, 1987 ). The precipitation rates for e = 0.01 cm are listed in Table 1. The lines in Fig. 2 interpolate the calculated precipitation rates from stations 1 to 9 for given thicknesses e of the boundary layer as indicated at the curves. The uppermost curve gives the result calculated from the PWP rate equation (1), assuming no boundary layer to be present. Note that the scale is changed for these rates by a factor of 10. The experimental data (cf. Section 2 ) show precipitation rates in accordance to boundary layers of a few tenths of millimetres, as have been also observed by the dissolution experiments using gypsum tablets. Considering the variations in stream velocity and changing water chemistry, which become important in the long-time runs, the agreement between experimental data and theoretical predictions is acceptable. To estimate the variations of the precipitation rates, which result from long-term chemical variations, we have used the data of chemical analysis of the stream water during three different field studies between 1977 and 1986. Fig. 4 illustrates the precipitation rates calculated from these three sets of data for e = 0.01 cm. They show that the long-term variations of the water chemistry cause changes in the precipitation rates, which are in the limits between 1.5.10-s mmol c m - 2 s - 1. This means that although the chemical composition varies by some extent, the precipitation rates remain fairly constant. Finally, we compare the rates with those estimated by mass balance. The average discharge of the spring is 5 1 s - l and the loss in Ca concentration between station 1 and 9 amounts to 7.2-10-4 mol 1-1. The geometrical surface area of the river-bed is estimated
G E O C H E M I C A L L Y C O N T R O L L E D CALCITE PRECIPITATION BY C O 2 0 U T G A S S I N G
5.0 I
O]
?
4.0
E --3.0 0
E E
? 2.0
//
L-
0.0
' " ~ . . . . ~ . . . . 4 . . . . ~ . . . . ~ . . . . -~. . . . ~ . . . . 9
station number Fig. 4. Precipitation rates calculated with e=0.01 cm for various chemical compositions observed in the stream at the corresponding station for different observation times from 1977 to 1986, (observations listed in Table 1): A = August 30, 1977; Fq= June 19, 1 9 8 4 ; ~ = June 13, 1986. Data from Usdowski et al. (1979).
from its geometrical dimensions as 5.3-106 cm2. From this, an average precipitation rate o f 6 . 8 " 1 0 - 7 mmol cm -2 s -1 results. Compared to the measured data, this is too high by a factor of 10. However, considering the natural roughness of the stream bed as well as the precipitation by leaves, twigs, grain size of sediments, etc., an increase in surface area by a factor of 10 is not unlikely. This reduces the precipitation rate calculated from mass balance down to ~ 7.10 - 8 mmol cm - 2 s - 1 5. Discussion of the results and conclusions Our results show that if inorganic processes are controlling calcite precipitation in natural systems, precipitation rates cannot be estim a t e d by using the rate equation (eq. 1, by P l u m m e r et al., 1978 ), since the ion activities at the surface where precipitation takes place, are different from those in the bulk solution. To account for these differences one needs a complicated computational procedure and furthermore knowledge o f the thickness of the hydrodynamic b o u n d a r y layer. This knowledge is not easily to obtain for true surfaces of
293
stream beds, since surface roughness has to be taken into account. At small protrusions, considered for instance as small spheres with diameters of a few millimetres, and flow velocities of several 10 cm s - 1, one obtains values of in the order of several 10-3 cm (Skelland, 1974), whereas in between the peaks of the protrusions c will be considerably larger. Therefore, on average, considering the weak dependence of R, for e > 0.01 cm, a reduction of the rates as calculated by the rate law of eq. 1 by a factor of ~ 10 is reasonable. Experimentally, one might gain further information by gypsum dissolution experiments on casts of Paris plaster, which replace the natural bed at the corresponding site of the riverbed. Our data further give some evidence that the actual surface area may be a factor of 10 higher than that calculated from the geometrical dimensions of the river-bed. If we use the surface area calculated by the geometrical dimensions, the average rates along the river-bed calculated by mass balance are lower by ~ 50% than those calculated directly from the rate law of eq. 1. This is in close agreement to the resuits of H e r m a n and Lorah (1988). By using the geometrical surface of the river-bed and converting the rates calculated from eq. 1 in mol c m - 1 s - ' into the units of those obtained from mass balance (mol kg- ~ HRO s-~ ), these authors also found the rates obtained from eq. I generally higher within a factor between 1 and 2. We would expect that measurements of precipitation rates in Falling Spring Creek by limestone tablets, as suggested here, would yield actual precipitation rates similar to those we have observed in the Westerhof stream. These are lower by about a factor of 10 and therefore represent the actual precipitation. In conclusion, we would like to propose that it is possible to estimate precipitation rates of calcite in natural streams within an accuracy of a factor between 2 and 3. By chemical analysis of the stream water, the activities of Ca 2+. H C O 3 - , H + and H2CO3" can be obtained using current programs, such as SOLM~NEQ.88.
294
From these data, rates can be calculated by use of the rate law of Plummer et al. ( 1978 ). A reduction of these rates by a factor of 10 takes into account the existence of the diffusional boundary layer and gives a good estimation of the actual precipitation rates. To confirm this method, it would be useful to conduct further precipitation experiments on limestone tablets in comparison to mass-balance estimations elsewhere. Acknowledgements
The authors thank the Deutsche Forschungsgemeinschaft (Schwerpunktprogramm: Hydrogeochemische Vorg~inge im Wasserkreislauf der ges~ittigten and unges~ittigten Zone and the DFG-Sonderforschungsbereich 261 ) for financial support of this work. References Berner, R.A., 1980. Early Diagenesis - - A Theoretical Approach. Princeton University Press, Princeton, N.J., 241 pp. Blount, C.W. and Dickson, F.W., 1973. Gypsum-anhydrite equilibria in systems CaSO4-H20 and CaCO3NaCI-H20. Am. Mineral., 58:323-331. Buhmann, D. and Dreybrodt, W., 1985a. The kinetics of calcite dissolution and precipitation in geologically relevant situations of karst areas, 1. Open system. Chem. Geol., 48:189-211. Buhmann, D. and Dreybrodt, W., 1985b. The kinetics of calcite dissolution and precipitation in geologically relevant situations of karst areas, 2. Closed system. Chem. Geol., 53: 109-124. Buhmann, D. and Dreybrodt, W., 1987. Calcite dissolution kinetics in the system HzO-CO2-CaCO3 with participation of foreign ions. Chem. Geol., 64: 89-102. Dreybrodt, W., 1988. Processes in Karst Systems-- Physics, Chemistry, and Geology. Springer, Berlin, 288 pp. Dreybrodt, W. and Buhmann, D., 1991. A mass transfer model for dissolution and precipitation of calcite from solutions in turbulent motion. Chem. Geol., 90: 107122. Herman, J.S. and Lorah, M.M., 1986. Groundwater geochemistry in Warm River Cave, Virginia. Natl. Soc. Speleol. Bull., 48: 54-61. Herman, J.S. and Lorah, M.M., 1987. CO2 outgassing and calcite precipitation in Falling Spring Creek, Virginia, U.S.A. Chem. Geol., 62: 251-262.
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