Carbonate dissolution and precipitation in ... - Wiley Online Library

WATER RESOURCES RESEARCH, VOL. 40, W04401, doi:10.1029/2003WR002651, 2004

Carbonate dissolution and precipitation in coastal environments: Laboratory analysis and theoretical consideration Olga Singurindy and Brian Berkowitz Department of Environmental Sciences and Energy Research, Weizmann Institute of Science, Rehovot, Israel

Robert P. Lowell School of Earth and Atmospheric Sciences, Georgia Institute of Technology, Atlanta, Georgia, USA Received 4 September 2003; revised 22 February 2004; accepted 26 February 2004; published 28 April 2004.

[1] We have conducted laboratory experiments to examine CaCO3 dissolution and

precipitation in saltwater-freshwater mixing zones, with a view to understanding and predicting porosity changes in coastal environments. Mixing of seawater or saline subsurface water with fresh water can be of major importance in the chemical diagenesis of carbonate rocks and sediments. We used artificial seawater and NaCl solutions of different concentrations under different CO2 partial pressures and with different mixing ratios. Two-dimensional flow cells filled with glass beads and crushed calcium carbonate rock were used to measure calcium carbonate precipitation and dissolution, respectively. An important feature of these experiments is that the results are shown to agree well with a relatively simple transport theory describing mineral precipitation/dissolution that results from the nonlinear dependence of CaCO3 saturation upon electrolyte concentration. The theory demonstrates that the rate of dissolution or precipitation depends on the curvature (and sign) of the solubility as a function of salinity, the square of the salinity gradient, and the macroscopic dispersion coefficient. The theory is largely scale independent and depends upon field parameters that can be determined. Analysis of data from three field sites (Yucatan peninsula, Bermuda, and Mallorca) demonstrates excellent INDEX TERMS: 1829 Hydrology: agreement between field observations and theory. Groundwater hydrology; 1832 Hydrology: Groundwater transport; 1010 Geochemistry: Chemical evolution; 4825 Oceanography: Biological and Chemical: Geochemistry; KEYWORDS: coastal aquifer, seawater interface, seawater intrusion Citation: Singurindy, O., B. Berkowitz, and R. P. Lowell (2004), Carbonate dissolution and precipitation in coastal environments: Laboratory analysis and theoretical consideration, Water Resour. Res., 40, W04401, doi:10.1029/2003WR002651.

1. Introduction [2] Dissolution and precipitation reactions in subsurface environments are linked fundamentally to the solubilities of chemical constituents in natural waters, which are nonlinear functions of temperature, salinity, pH, and other factors. When waters of different chemical composition mix, the thermodynamic activities of ions present in the solutions that control water-mineral reaction thus lead to a nonlinear dependence of the ionic strength upon mixing [Runnells, 1969]. The change in ionic strength of the resulting solution may lead to supersaturation or undersaturation of a dissolved constituent with respect to some constituent in the solid phase, thus leading to precipitation or dissolution of that constituent, respectively [Runnells, 1969; Plummer, 1975]. [3] Mixing of seawater or saline subsurface water with fresh calcium carbonate groundwater can be of major importance in the chemical diagenesis of carbonate rocks and sediments [Plummer, 1975]. For example, mixing of (CaCO3-supersaturated) seawater with CaCO3-saturated Copyright 2004 by the American Geophysical Union. 0043-1397/04/2003WR002651

groundwater can lead to carbonate dissolution (and thus to porosity enhancement [Hanshaw and Back, 1979]), provided the amount of seawater in the mixture is less than 10%, or the CO2 content of the groundwater is high [Plummer, 1975; Wigley and Plummer, 1976]. Field evidence of carbonate dissolution is found in coastal aquifers such as the Yucatan Peninsula, Mexico [Back et al., 1979; Stoessell et al., 1989], the coastal springs of Greece [Higgins, 1980], and Andors Island in the Bahamas [Smart et al., 1988]. The two latter cases showed a strong influence of CO2 content in the water on the amount of dissolved calcite. [4] On the other hand, if the fraction of seawater in the mixing region is high and pCO2 is low (normal atmospheric partial pressure), carbonate precipitation may occur upon mixing with fresh groundwaters [Plummer, 1975]. These factors could explain the absence of dissolution in the coastal aquifer of Mallorca, Spain [Price and Herman, 1991], although the situation here is complicated by the fact that a less stable (more soluble) carbonate phase, aragonite, is also present. In fact, the presence of other dissolved constituents often leads to CaCO3 precipitation in coastal aquifers [Wicks and Herman, 1996], and in some instances mixtures between fresh and saline waters that are undersaturated with respect to calcite may be supersaturated

W04401

1 of 12

W04401

SINGURINDY ET AL.: CARBONATE PRECIPITATION AND DISSOLUTION

W04401

study, we first reanalyze these experiments using a more realistic quantification of the mixing zone geometry (and thus the effective volume of mixing). We then focus on dissolution experiments, using both artificial seawater (ASW) and NaCl solutions of different concentrations, with different mixing ratios. The effect of different CO2 partial pressures is also taken into account. An important feature of these experiments is that the results are shown to agree well with a relatively simple transport theory; the theory describes mineral precipitation and dissolution resulting from the nonlinear dependence of CaCO3 saturation upon salinity [Phillips, 1991]. Because the theory is largely scale independent and depends upon field parameters that can be determined, the agreement between experiment and theory suggests that the theory may be applied to geological settings. We find that the theory is in excellent agreement with data from three coastal field sites (Yucatan peninsula, Bermuda and Mallorca), accounting for both dissolution and precipitation regimes.

2. Materials and Methods

Figure 1. Solubility of calcium carbonate as a function of (a) NaCl concentration, (b) electrolyte concentration of artificial seawater (ASW), at different pCO2, and (c) NaCl concentration in an open system. The curves in Figures 1a and 1b are derived for a closed system, from PHREEQC (with the two points shown on Figure 1a referring to batch experiments), while the curve in Figure 1c is based on batch experiments [Berkowitz et al., 2003].

with respect to dolomite [Plummer, 1975; Hanshaw et al., 1971; Badiomani, 1973; Gonzalez and Ruiz, 1991]. [5] In order to better understand and quantify mixingdriven mineral precipitation and dissolution in the context of coastal environments, we conducted a series of laboratory experiments designed to investigate CaCO3 dissolution and precipitation upon mixing between carbonatesaturated freshwater and saltwater solutions. An initial analysis of the precipitation experiments has been reported by Berkowitz et al. [2003]. With respect to this preliminary

2.1. Batch Experiments and Theoretical Calculations of Solubility [6] The software package PHREEQC [Parkhurst, 1995] was used to determine the solubility of CaCO3 as a function of salinity for NaCl-water solutions and for ASW-pure water mixtures in a closed system for different fixed pCO2 conditions. PHREEQC is based on an ion-pairing aqueous model. It is designed to solve thermodynamic equations and to assess the potential for geochemical reactions. This program uses analytical expressions for the dependence of ionic strength on activity coefficients and contains many thermodynamic equilibrium constants. In order to compare the theoretical results from PHREEQC with real solutions, some batch experiments were then performed using double deionized water without salt and 40g/L NaCl at pCO2 of 1 atm. We also performed batch experiments in an open system (pCO2 = 103.5 atm), corresponding to the concentration of CO2 in the atmosphere. This was the situation for the precipitation experiments. Concentrations of Ca2+ in the solutions were measured using atomic absorption spectroscopy. [7] Figures 1a, 1b, and 1c depict the solubility of calcium carbonate as a function of NaCl (or electrolyte concentration in the case of ASW) at different pCO2 as determined by PHREEQC or batch experiments. Concentrations are expressed as kilogram of solute per kilogram of solution. When NaCl is added to a solution, dissolution and/or precipitation of CaCO3 is controlled by factors that act to maintain a constant ion activity product in solution. Increasing the ionic strength of the solution increases CaCO3 solubility, because it decreases the thermodynamic activity of the dissolved ions as a result of increased mutual electrostatic interaction [Plummer, 1975]. On the other hand, the decrease in the dielectric constant of water and the decrease of free water molecules due to solvation of the ions enhance CaCO3 precipitation [Runnells, 1969]. The shapes of the solubility curves (Figure 1) thus result from the nonlinear nature of the simultaneously competing interactions among ions and solvents.

2 of 12

W04401


W04401

Figure 2. Schematic diagram of the experimental apparatus. The flow cell was filled with glass beads for the precipitation experiments and with CaCO3 particles for the dissolution experiments. The CO2 sources were present only for the precipitation experiments. [8] For values of pCO2 102 atm, the curves in the Figures 1a and 1b are concave downward. From this it can be predicted that mixing of two waters, both saturated with Ca2+ but containing different amounts of dissolved salts, should result in undersaturation of the mixed waters. Therefore, if adjacent carbonate rock were available, dissolution would occur. The initial increase in solubility with the addition of the electrolyte causes the decrease in the thermodynamic activity of the dissolved ions, and more of the solid must dissolve to maintain a constant ion activity product in solution [Runnells, 1969]. At high concentrations of dissolved salts, the major factors are a decrease in the dielectric constant of water and the removal of free water due to solvation of ions. Runnells [1969] noted that the solubility curve becomes more linear with increasing temperature, therefore the diagenetic effects of mixing decrease with rising temperature. For pCO2 = 103 and 103.5 atm (open system), the solubility curves are concave upward (Figures 1b and 1c). In this case mixing of two solutions that are both saturated with Ca2+ and with different salinities should result in supersaturation of the mixed waters, and precipitation should occur [Berkowitz et al., 2003]. The variation in curvature and change in behavior from concave downward to concave upward in the case of the ASW solutions can be attributed to interactions of ions other than Na+ and Cl. In particular, Garrels and Thompson [1962] have shown that ion association reduces the amount of free Ca2+ and CO2 3 in seawater, 2+ uniting especially with SO2 4 and Mg , respectively. These kinds of reactions reduce the concentration of the free Ca2+ to about 91% of its analytical value, and that of CO2 3 to about 9% of its analytical value. Wigley and Plummer [1976] observed that in some circumstances redistribution of ion pairs, such as MgHCO+3, MgOH+, and CaSO4 may augment nonlinear mixing behavior and may significantly change CaCO3 solubility in seawater. 2.2. Flow Experiments 2.2.1. Basic Arrangement and Mixing Zone Estimates [9] The laboratory setup (Figure 2) consisted of a 2-D polymethylmethacrylate flow cell (internal dimensions

0.16 m 0.16 m 0.01 m) packed with either 1 mm diameter glass beads (for precipitation experiments) or 0.65 mm crushed and sieved carbonate particles (for dissolution experiments) and saturated with double deionized water. The flow cell was connected to two inlet reservoirs, one containing double deionized water and the other containing ASW or a NaCl-water solution. The waters in each reservoir were saturated with CaCO3 and either open to the atmosphere (for precipitation experiments), or closed and connected to a CO2 source to maintain the fluids at pCO2 = 1 atm (for dissolution experiments). The fluids were pumped into the flow cell at specified flow rates where they mixed and, depending on the experimental conditions, calcium carbonate either precipitated or dissolved. The inlet and outlet faces of the flow cell system were designed to allow water to enter (and exit) evenly along the entire length of each face. The cumulative amount of Ca2+ in the exiting fluids was recorded as a function of time, and the rate of precipitation or dissolution was determined. All the experiments took place at room temperature (23C). [10] When dissolution or precipitation occurs upon fluid mixing in the flow cell, it is important to determine whether thermodynamic equilibrium conditions are achieved within the cell. It is also necessary to realize that mixing does not take place uniformly throughout the flow cell. In order to check whether thermodynamic equilibrium was reached during the flow cell experiments, we carried out another series of batch experiments. [11] For dissolution, batch experiments were performed under the same conditions as the flow experiments (i.e., closed system, pCO2 = 1 atm, and volume of liquid equal to the pore volume). The Ca2+ concentration was measured after specified time periods in the liquid phase. The results of batch experiments and the outlet Ca2+ concentration measurements clearly showed that the liquid and solid phases were in equilibrium. From these experiments, equilibrium was reached after 50– 60 min; to compare, the average cell residence time in the flow cell experiments was 88 min for the overall volumetric flow rate of 0.0014 m3/d. (In actuality, of course, fluid velocities dif-

3 of 12

W04401


W04401

Figure 3. Schematic diagram used to calculate the width of the mixing zone, L, for (a) 1:1 flow ratio and (b) unequal flow ratios. In both Figures 3a and 3b, L is given by the distance AB.

fered in parts of the flow cell, so that chemical equilibrium may not have been reached in the higher velocity sections of the cell.) The equilibrium concentrations obtained in batch experiments agreed well with PHREEQC calculations. [12] Similarly, for precipitation, we mixed equal volumes of fluid corresponding to the amount contained within one flow cell volume, and determined when equilibrium was reached. Results of batch experiments indicated nonequilibrium conditions for the flow cell experiment with 30 g/L salt water. Specifically, the batch fluid remains oversaturated for mixing times corresponding to the liquid residence time in this flow cell experiment. In contrast, the flow cell experiments in the 80 and 120 g/L cases were in equilibrium. [13] The effective volume Ve of the mixing zone in the flow cell can be estimated for the given rate of CaCO3 input Ci1 and Ci2 from the fluid reservoirs and the rate of CaCO3 output C01 and C02 measured in the outlet reservoirs, from the individual flow cell experiments. This parameter is used in our analyses below. For a total volumetric flow rate Q, Ve ¼ V ½ðC01 Q01 þ C02 Q02 Þ ðCi1 Qi1 þ Ci2 Qi2 Þ =DCQ

ð1Þ

where V is the volume of the flow cell. For the case of dissolution, DC is the amount (in units of kg/m3) of CaCO 3 predicted to dissolve (using PHREEQC) or precipitate (determined by batch experiments) in order to reach saturation after mixing. The inlet and outlet CaCO3 concentrations were measured by atomic absorption spectroscopy. [14] In addition to an estimate for Ve in each experiment, we also require (sections 4.2 and 4.3) an estimate of the width L of the mixing zone. Because we cannot directly visualize L during the experiments, we estimate it by considering the effective volume of mixing from equation (1). [15] Figure 3 presents schematically the mixing zone used to estimate the width L for the flow experiments with

flow ratios between the two inlets of 1:1 (Figure 3a) and different from 1:1 (Figure 3b). In Figure 3a, Ve is given by the area ACBDA, multiplied by the cell thickness h (with h = 1 cm), while in Figure 3b, Ve is given by the area ABCA, multiplied by h. The width of the mixing zone for all precipitation experiments (see section 2.2.3), and for the dissolution experiment with equal freshwater and saltwater flow rates of 7.2 104 m3/d (see section 2.2.2), was calculated according to: L ¼ AB ¼ 2 Ve =ð DC hÞ

ð2Þ

where DC = 0.23 m is the diagonal length of the flow cell. The width of the mixing zone for the other dissolution cases (see section 2.2.2) was calculated as: L ¼ AB ¼ 2 Ve =ð EC hÞ

ð3Þ

where EC = 0.16 m is the length of the flow cell. [16] Details of experimental conditions for specific experiments are given in the following subsections. Clearly, our definitions of Ve and L are (convenient) simplifications: they are based on the amount of calcium carbonate dissolved in relation to the total amount predicted to dissolve, with the assumption that all mixing occurs at a single mixing ratio over a finite volume fraction of the flow cell. Empirical support for these definitions is given in section 3.2, while the sensitivities of our calculations to these definitions are discussed in section 5.1. 2.2.2. Dissolution Experiments [17] The flow cell was packed with crushed and sieved 0.65 – 0.7 mm particles of calcareous sandstone (97.5% CaCO3, 2.5% SiO2) obtained from the Rosh-Hanikra coast of northern Israel. The porosity of the calcium carbonate particle packing was measured to be n 0.33. One inlet reservoir contained 40 g/L NaCl dissolved in double deionized water or ASW [Guillard and Ryther, 1962; Harrison et al., 1980] (see Table 1); a second inlet reservoir contained

4 of 12


W04401

Table 1. Chemical Composition of Artificial Seawater (ASW) Salt

Formula

H2O, mol kg1

Sodium chloride Potassium chloride Sodium hydrogen carbonate Potassium bromide Boric acid Sodium fluoride

Anhydrous Salts NaCl KCl NaHCO3 KBr H3BO4 NaF

4.504 9.022 1.979 8.110 3.186 6.754

101 103 103 104 104 105

Magnesium chloride Calcium chloride Strontium chloride Magnesium sulphate

Hydrated Salts MgCl2 6H2O CaCl2 2H2O SrCl2 2H2O MgSO4 7H2O

2.375 9.920 8.689 2.725

102 103 105 102

only double deionized water. The waters in each reservoir were then fully saturated with CO2 and Ca2+; the only source of Ca2+ was the dissolved solid phase CaCO3. Note that the ASW was supersaturated with respect to the dissolved Ca2+. The flow experiments were done in closed system, with both inlet reservoirs being sealed from the atmosphere and connected to a CO2 source. A permanent connection to the CO2 source during the experiment maintained full saturation with CO2 of the injected solution while pressurizing the space above the draining reservoir and preventing a vacuum effect. By adding 0.4 psi CO2 above atmospheric pressure (and thus balancing the water vapor pressure), we obtained a pCO2 of 1 atm. The fluids were injected simultaneously at the different flow ratios such that the total overall volumetric flow rate was 0.0014 m3/d. The volumetric flow rates for the different experiments are summarized in Table 2. [18] Between experiments, the system was unpacked, cleaned, and repacked, thus providing multiple ‘‘realizations’’ of the (homogeneous) porous medium structure with fresh material. The two adjacent outlet faces were free flow boundaries at atmospheric pressure. On the basis of the difference between inlet and outlet concentrations of Ca2+, and the known concentration and molar volume of CaCO3, the amount of solid CaCO3 that was dissolved within the flow cell was calculated as a function of time. The flow experiments were repeated twice in order to check reproducibility of the results. 2.2.3. Precipitation Experiments [19] Full details of the precipitation experiments are given by Berkowitz et al. [2003]; for completeness and because we reanalyze some of the data, we describe the basic arrangement here. The flow cell described above was packed with 1 mm diameter glass beads and saturated with double deionized water. The porosity of the glass bead

W04401

packing was measured to be n 0.29. One inlet reservoir contained NaCl dissolved into double deionized water (NaCl concentrations of 30 g/L, 80 g/L, and 120 g/L); the second reservoir contained double deionized water. The flow system was open with pCO2 = 103.5 atm. The waters in each reservoir were fully saturated with CaCO3 and then injected simultaneously at an equal, prescribed volumetric flow rate 0.0576 m3/d along each of two adjacent inlet faces. The two adjacent outlet faces were free flow boundaries at atmospheric pressure. Precipitation patterns of CaCO3 within the flow cell were photographed, and outlet fluid was collected at intervals of 20 minutes and analyzed for chemical content. As described for the dissolution experiments, the amount of precipitated CaCO3 within the flow cell was calculated as a function of time.

3. Results 3.1. Dissolution [20] Figure 4 presents the accumulated amounts of solid calcium carbonate that dissolved during the flow experiments, from which we can determine the dissolution rates of solid CaCO3 within the flow cell during the various flow experiments. Because mixing does not occur uniformly throughout the flow cell, the dissolution rate of CaCO3 was normalized by the volume Ve of mixing zone estimated from equation (1). The CaCO3 dissolution rate was relatively constant throughout the duration of all flow experiments. Estimates of Ve and of the CaCO3 dissolution rates for the various flow experiments are summarized in Table 2. Note that the mixtures with higher ratios of fresh water have higher dissolution rates, in agreement with mixing theory predictions (see section 4), and that, as expected, the calculated Ve is highest for the equal ratio mixtures. 3.2. Precipitation [21] Figure 5 shows the pattern of calcium carbonate precipitation in the flow cell at selected times for the case of equal mixing between fresh water and 120 g/L NaCl, carbonate-saturated solutions. The pattern of the precipitation region motivated definition of Ve and L in section 2.2.1 and the geometry shown schematically in Figure 3a. [22] The development of a precipitation zone along the diagonal interface is clearly visible already in the initial stages (Figure 5, t = 1, 2 hr). Once established, precipitation continued along the diagonal interface, with more deposition occurring nearer the outflow region (Figure 5, t = 4 hr). The reproducibility of this behavior was demonstrated by running a second, identical experiment, and by the occurrence of similar results with an experiment that used a 80 g/L NaCl, carbonate-saturated solution [Berkowitz et

Table 2. Estimates of Effective Volume of Flow Cell Mixing Zone (Ve) and Rates of CaCO3 Dissolution in the Flow Experimentsa Flow Ratio and Type of Saline Fluid 4

3

4

3

7.2 10 m /d fresh water, 7.2 10 m /d NaCl solution (ratio: 0.5 fresh/0.5 salt) 10.1 104 m3/d fresh water, 4.3 104 m3/d NaCl solution (ratio: 0.7 fresh/0.3 salt) 4.3 104 m3/d fresh water, 10.1 104 m3/d NaCl solution (ratio: 0.3 fresh/0.7 salt) 1.15 103 m3/d fresh water, 2.9 104 m3/d ASW (ratio: 0.8 fresh/0.2 ASW)

Ve 4

CaCO3 Dissolution Rate

m (equation (2))

1.8 104 kg/m3/d (Figure 4a)

Ve 1.01 104 m3 (equation (3))

7.2 104 kg/m3/d (Figure 4a)

Ve 1.18 104 m3 (equation (3))

1.3 104 kg/m3/d (Figure 4b)

Ve 9.6 105 m3 (equation (3))

6.2 104 kg/m3/d (Figure 4b)

Ve 2.32 10

The total flow cell volume is 2.66 104 m3.

a

5 of 12

3

W04401


W04401

obtained from batch experiments. For all precipitation experiments, with equal flow rates of 0.0576 m3/d for the fresh and salt water, Ve 2.2 104 m3 (in comparison to the total volume of the flow cell is 2.66 104 m3).

4. Theory and Comparison to Experiments 4.1. Solute Transport and Evolution of Porosity [24] Consider fluid containing solute of concentration C flowing with specific discharge (Darcian velocity) u through a porous medium. If during flow through an elemental volume dx3 solute precipitates or additional solute enters solution, the rate of change of porosity is given by the simple mass balance rs

Figure 4. Calcium carbonate dissolution during flow experiments. The overall volumetric flow rate is 1.44 103 m3/d, and different ratios of fresh and saline water are employed. Experiments with specific combinations of liquid ratios are (a) 7.2 104 m3/d fresh water, 7.2 104 m3/d salt (NaCl only); 4.3 104 m3/d fresh water, 10.1 104 m3/d salt (NaCl only), (b) 10.1 104 m3/d fresh water, 4.3 104 m3/d salt (NaCl only); 1.15 103 m3/d fresh water, 2.9 104 m3/d ASW. Also shown are best fit lines for each experiment. al., 2003]. On the other hand, the quantity of precipitated carbonate was too small to be easily visible in an experiment performed with a 30 g/L NaCl, carbonate-saturated solution. Between experiments, the system was unpacked, cleaned, and repacked. [23] The rates of CaCO3 precipitation for the flow experiments using the 30, 80 and 120 g/L NaCl solutions are shown in Figure 6. These results are from experiments by Berkowitz et al. [2003] that have been reanalyzed to take into account the effective volume of mixing. Here we have plotted measurements only from the first 150– 200 min in the case of 80 and 120 g/L NaCl, to avoid the influence of redistribution of precipitated material and changes in mixing zone conditions (also as a result of precipitated material) [Berkowitz et al., 2003]. We also slightly modified the timescale and removed very early time measurements to account for the small delays in response associated with the dead volumes of the inlet and outlet chambers. Estimates of the mixing zone volumes were made in the same way as for the dissolution experiments, using equation (1). The DC value used in equation (1) was calculated from PHREEQC for the cases of 80 and 120 g/L; for the 30 g/L case, in which the system did not reach equilibrium (as noted in section 2.2.1), the DC value used in equation (1) was

dn ¼ rf u rC rf nDr2 C dt

ð4Þ

where rf is the density of the fluid, rs is the density of the solid material that is either dissolving or precipitating, D is the macroscopic dispersion coefficient, and t is the time. The concentration C is written as a mass fraction (kg solute/kg water). Equation (4) is the three dimensional analogue of that given by Wood and Hewett [1982] and Lowell et al. [1993]. [25] If we now put rf inside the derivative terms and assume that the ce = rfC is the concentration in kg/m3 in thermodynamic equilibrium, the right-hand side of equation (5) can be written Qs ¼ u rce nDr2 ce

ð5Þ

[26] The equilibrium concentration in equation (5) is typically a function of temperature, salinity, pressure, pH, and perhaps other factors that may change from place to place within the medium; consequently, precipitation or dissolution effectively occurs along gradients in these parameters. The rate of reaction Qs given by equation (5) is thus termed a ‘‘gradient reaction’’ [Phillips, 1991]. It is a valid description of precipitation and dissolution processes provided the rate of precipitation or dissolution is sufficiently rapid to maintain thermodynamic equilibrium along the property gradient. In the situation considered here we mix fluids that are in equilibrium with respect to CaCO3 but of different salinities. In this case, one can show [Phillips, 1991] that Qs ¼ nD

2 @ ce ðrsÞ2 @s2

ð6Þ

so that the initial rate of dissolution (or precipitation) is proportional to the macroscopic dispersion coefficient, the curvature of ce(s), and to the square of the salinity gradient. Upon combining equations (5) and (6), and substituting into equation (4), the rate of change of porosity can be related to the reaction rate Qs that results from mixing of the fluids. Thus rs

2 dn @ ce ðrsÞ2 ¼ nD @s2 dt

ð7Þ

Dissolution occurs when @ 2ce/@s2 < 0 and precipitation occurs when @ 2ce/@s2 > 0.

6 of 12

W04401


W04401

Figure 5. Photographs of calcium carbonate precipitation during a flow experiment. The flow rate is 0.0576 m3/d along each of the two inlet faces, with both salt and fresh water at equilibrium concentration of CaCO3 at the inlets. Concentration of inlet salt water is 120 g/L NaCl. Calcium carbonate (white material) is seen to precipitate along the diagonal of the flow cell, which coincides with the mixing (interface) zone between fresh and salt water. Compare the shape of the precipitation region with the approximate mixing zone shown in Figure 3. See color version of this figure at back of this issue. [27] The importance of the relatively simple result given by equation (6) is that Qs is a function of field parameters that can be determined, and does not depend upon the scale at which the measurements are made. Thus, if equation (6) can be tested successfully against laboratory data, we suggest that this approach to investigating dissolution and precipitation processes and changes in porosity resulting from mixing of saturated solutions can be applied to the large scale natural environment. 4.2. Comparison of Theory to Dissolution Results [28] To compare the theory to experimental data on dissolution, using equation (6), we first estimate nD. The dispersion coefficient is approximated as D av (ignoring effects of molecular diffusion), where a is essentially the transverse dispersivity and v is the magnitude of the interstitial velocity in the principal flow direction. We set a = 6.5 104 m, the mean diameter of the calcium

carbonate particles in the flow cell [Dullien, 1979]. The interstitial velocity v = F/nA, where F is the volumetric flow rate and A is the cross-sectional inflow area. Consequently, nD aF/A. For these experiments, the area of each inlet face is 0.163 m 0.01 m, so the total inlet area is A = 3.26 103 m2, and the total volumetric fluid flow F = 0.0014 m3/d. Thus nD 2.8 104 m2/d. [29] We then determine the parameter @ 2ce/@s2 from Figure 1. To estimate @ 2ce/@s2, a parabolic curve was fit to the data shown in Figure 1a, for pCO2 = 1 atm, with R2 = 0.96. Differentiating the fitted function twice yields a value of @ 2ce/@s2 = 0.024. As noted above, a negative value indicates a dissolution-dominated system. This value of @ 2ce/@s2 is used throughout our analysis below for the NaCl experiments. A value of @ 2ce/@s2 = 0.028 was estimated for the ASW experiment. [30] Finally, the parameter (rs)2 (Ds/L)2, where Ds is the difference between the salinity of the fresh and saline

7 of 12

W04401


W04401

and from equation (6), Qs 2.8 104 (0.024 103) 0.04 106 = 2.7 104 (kg/m3/d). The experimental value (from Table 3 and Figure 4a) for the calcium carbonate dissolution rate is Qs 1.8 104 (kg/m3/d). [32] The results of similar calculations for the three other dissolution experiments are summarized in Table 3, together with estimated changes in porosity; theoretical values are calculated from equation (7). Overall, there is reasonably good agreement between the theoretically and experimentally obtained calcium carbonate dissolution rates.

Figure 6. Calcium carbonate precipitation during flow experiments, with saltwater concentrations of 30, 80, and 120 g/L NaCl, for a flow rate of 0.0576 m3/d along each of the two inlet faces. Also shown are best fit lines for each experiment. Note that two experiments were completed for the 120 g/L NaCl case.

waters and L is the width of the mixing zone, whose method of estimation is given in section 2.2.1. Because Ds is known directly from the experimental setup, the key is to determine L. [31] We first consider the experiments with the NaCl solution of 0.04 kg/kg. For the flow experiment with flow rates 7.2 104 m3/d fresh and 7.2 104 m3/d salt water, (2) gives L = 0.2 m. Thus (rs)2 ((0.04 kg/kg 0 kg/kg) 103 kg/m3/0.2 m)2 = 0.04 106 (kg/m3/m)2,

4.3. Comparison of Theory to Precipitation Results [33] Similar calculations can be carried out for the precipitation experiments (Table 4). In this case, we set the dispersivity a = 103 m, equal to the diameter of the glass beads used to pack the flow cell. The flow cell had the same dimensions as before; the area of each inlet face is 0.163 m 0.01 m, so the total inlet area is A = 3.26 103 m2. For a volumetric flow rate of F = 0.11 m3/d, then nD aF/A 0.034 m2/d. [34] We reanalyze the precipitation experiments reported upon previously [Berkowitz et al., 2003], taking into account our improved estimates of the mixing zone (using equations (1) and (2)). For this purpose, we also unify all units to those employed here, preferring to work with concentrations expressed as kilogram of solute per kilogram of solution. Thus reanalysis of the precipitation results gives @ 2ce/@s2 = 0.06 103 m3/kg. [35] We compare the theory with the experimental results for the solution with 80 g/L NaCl. From equation (1) we find Ve 2.2 104 m3 and using this in equation (2), we obtain L = 0.19 m. For the 80 g/L NaCl solution, rs ((0.08 kg/kg 0 kg/kg) 103 kg/m3/0.19 m)2 = 0.18 106 (kg/m3/m)2, and from equation (6), Qs 0.034 (0.06 103) 0.18 106 = 0.37 (kg/m3/d). Note that the negative sign indicates precipitation. To compare, the rate of CaCO3 precipitation derived from the (negative) slope of the reanalyzed data (Figure 6b) is Qs 0.39 kg/m3/d. The poor correspondence between theory and experiment for the 30 g/L flow experiment can be explained [Berkowitz et al., 2003] by the fact that equilibrium conditions do not prevail for this particular case.

5. Discussion 5.1. Agreement Between Theory and Experiment [36] With regard to the theoretical estimates of precipitation and dissolution rates, and their comparison to the

Table 3. Theoretical and Experimental Estimates of Dissolution Rates and Porosity Changea

Flow Ratio and Type of Saline Fluid 7.2 104 m3/d fresh water, 7.2 104 m3/d NaCl solution (ratio: 0.5 fresh/0.5 salt) 10.1 104 m3/d fresh water, 4.3 104 m3/d NaCl solution (ratio: 0.7 fresh/0.3 salt) 4.3 104 m3/d fresh water, 10.1 104 m3/d NaCl solution (ratio: 0.3 fresh/0.7 salt) 1.15 103 m3/d fresh water, 2.9 104 m3/d ASW (ratio: 0.8 fresh/0.2 ASW)

dn

dn

2.7 104 1.8 104

0.36

0.24

0.11

7.4 104 7.2 104

0.99

0.97

0.15

0.072

4.8 104 1.3 104

0.64

0.17

0.12

0.079

6.2 104 6.2 104

0.83

0.83

@ 2ce/@s2 103, m3/kg

L, m

(rs 10 ) , (kg/m3/m)2

0.024

0.2

0.04

0.024

0.12

0.024 0.028

3 2

Qs Theory, kg/m3/d

Qs dt dt Experiment, Theory, Experiment, 3 4 kg/m /d per 10 years per 104 years

a Note that the sum of the initial porosity of the system and the value of dn/dt cannot exceed unity; larger values simply indicate that the medium has become fully dissolved.

8 of 12

W04401


W04401

Table 4. Theoretical and Experimental Estimates of Precipitation Rates and Porosity Changea

Saltwater Contentb 30 g/L NaCl solution (nonequilibrium case) 80 g/L NaCl solution 120 g/L NaCl solution

@ 2ce/@s2 103, m3/kg

(rs 103)2, (kg/m3/m)2

Qs Theory, kg/m3/d

Qs Experiment, kg/m3/d

dn dt

dn dt

L, m

Theory, per year

Experiment, per year

0.06

0.19

0.025

5.2 102

5.7 103

0.1

0.01

0.06 0.06

0.19 0.19

0.18 0.4

0.37 0.82

0.39 0.87, 0.96

0.05 0.11

0.05 0.12, 0.13

a

Negative signs denote precipitation and reduction in porosity. Equal ratios of fresh and salt water.

b

experimentally obtained values, it is clear that minor changes in the value of L can improve further the agreement between theory and experiment. This is because L appears as a squared term in equation (6), within (rs)2. Moreover, it should be noted that the theoretical estimates are sensitive to the choice of functional fit for CaCO3 solubility vs. salinity (e.g., as obtained from Figure 1a), which determines @ 2ce/@s2 in equation (6). We chose to fit a parabolic function, because the constant second derivative provides some ‘‘consistency’’ between the precipitation and dissolution analyses. [37] Analysis of the flow experiments with different flow ratios (but with the same total inlet flow rate) shows that the volume of the mixing zone is largest when the flow ratio between the two inlets is 1:1. A reduction in flow ratio with respect to one of the inlets (whether salt water or fresh water) causes a reduction in the volume and width of the mixing zone (recall Figure 3). The effect of the volume ratio is included in the theory (equation (6)) only implicitly, through the mixing zone width L which appears in the term (rs)2. [38] There are two cases in which the agreement between theory and experiment is somewhat poorer (see Table 3): the 0.3 freshwater/0.7 saltwater mixing ratio; and the 0.5 freshwater/0.5 saltwater mixing ratio. We first note that the observed values of dissolution rate are indeed different at different mixing ratios. Some of this difference may stem from changes in mixing zone volume, and hence length L; recall from section 2.2.1 that our definitions of Ve and L are simplifications which assume particular mixing zone geometries and mixing ratios. For example, as the freshwater fraction increases, between rows 1 and 2 in Table 3, L decreases by almost a factor of 2 (thereby increasing the dissolution rate by nearly 3). There is a fourfold difference in the observed dissolution rate, however, so comparison with theory suggests that the curvature of the solubility curve also has an effect. For the theoretical calculations, however, we simply assumed a parabolic fit to the solubility curves in Figure 1 and hence obtained a constant value of @ 2ce/@s2. Visual inspection of Figure 1a, however, indicates that the curvature decreases with increasing saltwater fraction. Had we taken this into account, we could have produced a better fit between theory and experiment. [39] The good agreement between the flow cell measurements on dissolution and precipitation during mixing of CaCO3-saturated fluids of different salinities and the theory derived from Phillips [1991] suggests that the simple result given by equations (6) and (7) can be extrapolated to the natural environment. This extrapolation is valid because equations (6) and (7) are essentially independent of scale (given the assumption of thermodynamic equilibrium con-

ditions). This result is important because there are few currently available formalisms from which one can estimate rates of dissolution or precipitation, and hence porosity changes, in nature that use measurable field parameters. Below we discuss the general usefulness and limitations of equations (6) and (7). Then we provide some examples applying equations (6) and (7) to the natural environment and compare our results to those based on the simulation results for a hypothetical situation given by Sanford and Konikow [1989a]. 5.2. Model Robustness [40] Equation (7) provides useful insights into precipitation and dissolution processes in coastal environments where fresh and saline waters mix. It shows that the rate of dissolution depends linearly on the dispersivity, specific discharge, and curvature of the solubility as a function of salinity, but varies as L2. Of these parameters, specific discharge, and L can be estimated in the field, as can pCO2. The latter parameter affects @ 2ce/@s2. The greatest uncertainty then is the dispersivity a. If a can be estimated at the field scale, then equation (7) should be widely applicable. [41] There are a number of other assumptions inherent in this equation, however, that must be taken into account that prevent its use in all situations. First of all, the rate of change in porosity inside the mixing zone tends to be slow under steady experimental conditions. On the other hand, continuous dissolution may cause changes in porosity structure and flow patterns with time (at the advanced stages of experiment, after months or years), which can also cause changes in the CaCO3 dissolution rate. Secondly, the medium is assumed to be homogeneous, and hence equation (7) is not easily applied if permeability is controlled by discrete fractures. Some degree of inhomogeneity can be accommodated through the parameter a, however. Thirdly, the precipitation or dissolution reactions must be rapid enough for thermodynamic equilibrium to be maintained. Finally, the two fluids that are mixing must each be initially saturated with respect to the solid phase. 5.3. Comparisons to Other Modeling and Experimental Analyses [42] Sanford and Konikow [1989b] showed that dissolution rates of calcium carbonate in coastal areas are sensitive to fluid flux. According to their results the rate of porosity increase is a linear function of specific discharge. They expressed the porosity increase empirically, based on an analysis of numerical simulations, by

9 of 12

R ¼ 0:45CCa u

ð8Þ

W04401


W04401

Table 5. Estimates of Porosity Change Compared to Model Simulation and Field Sitesa Parameter

Model Simulationb

Yucatan Peninsula

Mallorca

Bermuda

n a u (F/A) L pCO2 Qs nD @ 2ce/@s2 (rs)2 dn dt (over 10 ka)

0.3 (1) 1 m (1) 0.68 m/d (1) 20 m (1) 102 atm (1) 0.23 1010 kg/m3/d (2) 0.68 m2/d 0.015 103 m3/kg (3) 2.5 106 (4) 0.04 (5)

0.3 (6) 1 m (7) 8 m/d (8) 10 m (9) 102 – 101.5 atm (8) 1.1 109 kg/m3/d (2) 8 m2/d 0.015 103 m3/kg (3) 9 106 (4) 0.7 (over 5 ka) (5)

0.34 (10) 0.1 m (7) 0.23 m/d (10) 2.8 m (10) 103.5 atm (10) 1.5 1010 kg/m3/d (2) 0.024 m2/d (4) 0.06 103 m3/kg (11) 1.1 104 (4) 0.06 (5)

0.3 (7) 1 m (7) 0.065 m/d (6) 4.5 m (12) 102 atm (12) 0.44 1010 kg/m3/d (2) 0.065 m2/d 0.015 103 m3/kg (3) 4.5 105 (4) 0.06 (5)

a

Numbers in parentheses refer to the following sources: 1, Sanford and Konikow [1989a]; 2, equation (6); 3, Figure 1b, best fit parabola; 4, section 4.2; 5, equation (7); 6, Sanford and Konikow [1989b]; 7, assumed; 8, Back et al. [1979]; 9, Stoessel et al. [1989, Figure 2]; 10, Price and Herman [1991]; 11, Figure 1c, best fit parabola; 12, Smart et al. [1988]. b Sanford and Konikow [1989a].

where R is the change in percent porosity per 10 ka, CCa is the maximum amount of calcium carbonate predicted to dissolve to reach saturation per liter of water after mixing (mg/L); and u is the specific discharge in the system (m/d). Although their results gave reasonable agreement with some field comparisons, there are a number of built in assumptions that make this equation difficult to test adequately. [43] First of all, it does not address systems in which precipitation is occurring rather than dissolution. Secondly, their model simulations include assumptions regarding both dispersivity and permeability, neither of which is often well constrained by field data. As a result, (8) may not be scale independent and thus cannot be tested directly against laboratory data. If we test this relation against our data, for example, we find poor agreement. The total specific discharge in the flow cell described in section 3 was 0.63 m/d. For example, using PHREEQC, the maximum amount of calcium carbonate predicted to dissolve was 45 mg/L. Thus according to (8), the porosity increases after 10 ka by about 0.13. However, according to the results of our experiments presented in Table 3, the porosity change is 0.97 after 10ka; note again that this estimate is in excellent agreement with the value obtained by the theory described in section 4.1. [44] We next examine how well the result given by equation (7) compares to results of numerical simulations by Sanford and Konikow [1989a]. Sanford and Konikow [1989a] consider a range of parameter values. We consider the case L = 20 m and u = 250 m/yr and find (see Table 5 for all values; we assume that the seawater-freshwater salinity difference is 30 g/L) that the porosity increases to about 0.04 over 10 ka. This value is well within the range of porosities predicted in the simulations of Sanford and Konikow [1989a], who found that model porosities increased from 0.3 to greater than 0.4 over their range model parameter values. [45] We next consider existing data from three field sites, considering them in the context of equations (6) and (7) and of previously published estimates of porosity changes. Table 5 includes the pertinent field data. [46] Several studies have focused on the Yucatan peninsula [Back et al., 1979, 1986; Stoessell et al., 1989]. According to their results, mixing of fresh and saline water causes calcite dissolution and dramatic geomorphic evolution in both fresh and saline groundwater environments in

Yucatan peninsula coastal aquifer. Our estimates (Table 5) show that the carbonate formation could dissolve completely in about 5000 years; i.e., for the initial porosity is 0.3, and the estimated porosity change is 0.7. Our results are in general agreement with an estimate of Hanshaw and Back [1980], which predicts that complete dissolution will occur in 8.7 ka. Back et al. [1979] also observed that there are regions with high specific discharge where complete dissolution of the carbonate aquifer could occur in the mixing zone in less than 10 ka years. [47] A second site that has received attention is that of Mallorca, Spain (Table 5). The geochemistry of this region is still uncertain, and whether precipitation and/or dissolution are occurring, if at all, remains a subject of debate. This is in part because of the additional presence of aragonite, which is a highly soluble calcium carbonate phase. The situation is further complicated by the low recharge rates in the region, leading to a relatively narrow mixing zone and possibly rather localized infiltration of rainfall. Thus it is estimated that the mixing zone ranges in thickness from 0.3 m to 2.8 m in different locations [Price and Herman, 1991]; consequently rates of precipitation or dissolution may range over two orders of magnitude according to our model. Sanford and Konikow [1989b] predict a modest amount of dissolution, whereas Price and Herman [1991] and Berkowitz et al. [2003] suggest the occurrence of some precipitation. Sanford and Konikow [1989b] used a coupled reaction-transport model to calculate the porosity increase resulting from calcite dissolution, using the same input data. They assumed an initial porosity of 0.30, and predicted porosity values were between 0.31 and 0.45 (after 10 ka). On the other hand, although Price and Herman [1991] did not predict the magnitude of the change in porosity, they concluded that dissolution is not to be expected within the present mixing zone because water is supersaturated with respect to the carbonate minerals. Assuming open conditions (pCO2 = 103.5 atm), precipitation occurs according to our model, and the parameters in Table 5 yield a small porosity decrease of 0.06 over 10 ka. Assuming a thinner mixing zone would increase the rate of porosity decrease. It should be noted that the theoretical estimate given here supercedes that given previously by Berkowitz et al. [2003]. [48] Finally, we consider data from a field site in Bermuda (Table 5). Plummer et al. [1976] observed both precipitation and dissolution processes there. In most cases,

10 of 12

W04401


where pCO2 = 102 atm, our estimates agree with those of Sanford and Konikow [1989b], yielding a relatively small increase in porosity of 0.06 over 10 ka. According to Plummer et al. [1976], some regions were found where pCO2 = 103 atm, because of outgassing processes. It is worthwhile to note that in this case, our method of estimation predicts precipitation. We find that @ 2ce/@s2 = 0.06 103 from the fit of a parabolic curve to the data shown in Figure 1b (over the range of 0 – 0.025 kg/kg), for a pCO2 = 103 atm. In this case, a porosity reduction following precipitation reaches 0.24. [49] We stress that, notwithstanding the above comparisons between theoretical calculations and field observations, caution must be exercised when extrapolating from our laboratory-scale experiments to the field scale. Clearly, actual field conditions are far more heterogeneous and complex than what is accounted for in the theory and our laboratory experiments. First, in terms of the liquids, the theory assumes that each of the two waters in the mixing zone is at equilibrium with calcite. While many of our experiments use a NaCl solution, seawater has different properties, as evidenced by our experiments with ASW. In particular, (end-member) seawater (as relevant to the three field sites we examine above) and ASW are supersaturated with respect to calcite (dissolved Ca2+), whereas the NaCl solutions are saturated. Also, complexation, which influences solubility, is different in seawater (or ASW) and in NaCl solutions, even if the ionic strengths are identical. The theory itself does not account explicitly for the effect of the mixing ratio, nor for the fact that the flow rate varies from one part of the mixing zone to another. The theory also assumes a uniform mixing zone width and thermodynamic equilibrium. The predictions of the theory are sensitive to choices of these parameter values, as well as to the curvature of the equilibrium concentration curve: variability in any of these parameter values may lead to over/under prediction of dissolution/precipitation. [50] Finally, our extrapolation of equations (6) and (7) to the field scale assumes that the (field) system is in (thermodynamic) equilibrium. In our laboratory dissolution experiments, for example, equilibrium was reached within about 1 hr. The laboratory flow cell also had a relatively high surface area per unit volume of rock. In contrast, field systems such as those considered above will generally have much lower surface areas per unit volume of rock, but this is countered by flow rates in the field which tend to be much lower than those used in the laboratory. We note, however, that kinetic effects may be significant where flow is focused through fractures and other highpermeability conduits.

6. Conclusions [51] Carbonate dissolution or precipitation during seawater-freshwater mixing in coastal environments is difficult to assess quantitatively. The laboratory experiments conducted here provide estimates of both carbonate precipitation and dissolution rates in a controlled setting. More importantly, however, the laboratory experimental results are shown to agree well with a relatively simple transport model that, in principal, can be scaled from the laboratory to the field setting. Moreover, the transport

W04401

model depends upon field parameters that are readily attainable. The model gives reasonable results when applied to a variety of field settings that involve both dissolution and precipitation over a broad range of rates. Thus we suggest that the approach developed here provides a robust tool for analyzing carbonate dissolution and precipitation in coastal environments. [52] Acknowledgments. The financial support of the US-Israel Binational Science Foundation (contract 1999142) and BP International is gratefully acknowledged. The authors thank Roberto Ventrella for preparing the ASW solutions, and Ward Sanford, an anonymous reviewer and the Associate Editor for detailed and constructive comments.

References Back, W., B. B. Hanshaw, T. E. Pyle, L. N. Plummer, and A. E. Weidie (1979), Geochemical significance of groundwater discharge and carbonate solution to the formation of Caleta Xel Ha, Quintana Roo, Mexico, Water Resour. Res., 15, 1521 – 1525. Back, W., B. B. Hanshaw, J. S. Herman, and J. N. Van Driel (1986), Differential dissolution of a Pleistocene reel in the ground-water mixing zone of coastal Yucatan, Mexico, Geology, 14, 137 – 140. Badiomani, K. (1973), The Dorag dolomitization model—Application to the Middle Ordovician of Wisconsin, J. Sediment. Petrol., 43, 965 – 984. Berkowitz, B., O. Singurindy, and R. P. Lowell (2003), Mixing-driven diagenesis and mineral deposition: CaCO3 precipitation in salt waterfresh water mixing zones, Geophys. Res. Lett., 30(5), 1253, doi:10.1029/2002GL016208. Dullien, F. A. L. (1979), Porous Media: Fluid Transport and Pore Structure, Academic, San Diego, Calif. Garrels, R. M., and M. E. Thompson (1962), A chemical model for seawater, Am. J. Sci., 260, 57 – 66. Gonzalez, L. A., and H. M. Ruiz (1991), Diagenesis of middle tertiary carbonates in the Toa Baja Well, Puerto Rico, Geophys. Res. Lett., 18, 513 – 516. Guillard, R. R. L., and J. H. Ryther (1962), Studies of marine planktonic diatoms. I. Cyclotella nana Hustedt and Detonula confervacea Cleve, Can. J. Microbiol., 8, 229 – 239. Hanshaw, B. B., and W. Back (1979), Major geochemical processes in the evolution of carbonate aquifer systems, J. Hydrol., 43, 287 – 312. Hanshaw, B. B., and W. Back (1980), Chemical mass-wasting of the northern Yucatan Peninsula by groundwater dissolution, Geology, 8, 222 – 224. Hanshaw, B. B., W. Back, and R. G. Deike (1971), A geochemical hypothesis for dolomitization by groundwater, Econ. Geol., 66, 710 – 724. Harrison, P. J., R. E. Waters, and F. J. R. Taylor (1980), A broad spectrum artificial seawater medium for coastal and open ocean phytoplankton, J. Phycol., 16, 28 – 35. Higgins, C. G. (1980), Nips, notches, and the solution of coastal limestone: An overview of the problem with examples from Greece, Estuarine Coastal Mar. Sci., 10, 15 – 30. Lowell, R. P., P. Van Cappellen, and L. N. Germanovich (1993), Silica precipitation in fractures and the evolution of permeability in hydrothermal upflow zones, Science, 260, 192 – 194. Parkhurst, D. L. (1995), User’s guide to PHREEQC—A computer program for speciation, reaction-path, advective-transport, and inverse geochemical calculations, U.S. Geol. Surv. Water Resour. Invest. Rep., 95-4227, 143 pp. Phillips, O. M. (1991), Flow and Reactions in Permeable Rocks, Cambridge Univ. Press, New York. Plummer, L. N. (1975), Mixing of sea water with calcium carbonate ground water, Mem. Geol. Soc. Am., 142, 219 – 236. Plummer, L. N., H. L. Vacher, F. T. Mackenzie, O. P. Bricker, and L. S. Land (1976), Hydrogeochemistry of Bermuda: A case history of groundwater diagenesis of bicarbonates, Geol. Soc. Am. Bull., 87, 1301 – 1316. Price, R. M., and J. S. Herman (1991), Geochemical investigation of saltwater intrusion into a coastal carbonate aquifer: Mallorca, Spain, Geol. Soc. Am. Bull., 103, 1270 – 1279. Runnells, D. D. (1969), Diagenesis, chemical sediments, and the mixing of natural waters, J. Sediment. Petrol., 39, 1188 – 1201. Sanford, W. E., and L. F. Konikow (1989a), Simulation of calcite dissolution and porosity changes in saltwater mixing zones in coastal aquifers, Water Resour. Res., 25, 655 – 667.

11 of 12

W04401


Sanford, W. E., and L. F. Konikow (1989b), Porosity development in coastal carbonate aquifers, Geology, 17, 249 – 252. Smart, P. L., J. M. Dawans, and F. Wheeler (1988), Carbonate dissolution in a modern mixing zone, South Andros Island, Bahamas, Nature, 335, 811 – 813. Stoessell, R. K., W. C. Ward, B. H. Ford, and J. D. Schuffert (1989), Water chemistry and CaCO3 dissolution in the saline part of an open-flow mixing zone, coastal Yucatan Peninsula, Mexico, Geol. Soc. Am. Bull., 101, 159 – 169. Wicks, C. M., and J. S. Herman (1996), Regional hydrogeochemistry of a modern coastal mixing zone, Water Resour. Res., 32, 401 – 407. Wigley, T. M. L., and L. N. Plummer (1976), Mixing of carbonate waters, Geochim. Cosmochim. Acta, 40, 989 – 995.

W04401

Wood, J. R., and T. A. Hewett (1982), Fluid convection and mass transfer in porous sandstone—A theoretical model, Geochim. Cosmochim. Acta, 46, 1707 – 1713.

B. Berkowitz and O. Singurindy, Department of Environmental Sciences and Energy Research, Weizmann Institute of Science, Rehovot 76100, Israel. ([email protected]; [email protected]) R. P. Lowell, School of Earth and Atmospheric Sciences, Georgia Institute of Technology, 311 Ferst Drive, Atlanta, GA 30332-0340, USA. ([email protected])

12 of 12

W04401


W04401

Figure 5. Photographs of calcium carbonate precipitation during a flow experiment. The flow rate is 0.0576 m3/d along each of the two inlet faces, with both salt and fresh water at equilibrium concentration of CaCO3 at the inlets. Concentration of inlet salt water is 120 g/L NaCl. Calcium carbonate (white material) is seen to precipitate along the diagonal of the flow cell, which coincides with the mixing (interface) zone between fresh and salt water. Compare the shape of the precipitation region with the approximate mixing zone shown in Figure 3.

7 of 12