Evolution of Carbon in Groundwaters

Fresh groundwaters invariably originate as meteoric waters, in most cases infiltrating through soils and into the geosphere. Along the way, dissolved inorganic carbon (DIC) is gained by dissolution of CO₂ and evolves through the weathering of carbonate and silicate parent material. As carbonate acidity is "consumed" by weathering, the pH rises and the distribution of dissolved inorganic carbonate species shifts towards bicarbonate (HCO₃^–) and carbonate (CO₃^2–). The groundwater generally approaches equilibrium with calcite, whose solubility will control pH and the equilibrium of carbonate species.

At the same time, labile organic matter from the soil can be dissolved. Oxidation of the dissolved organic matter (DOC) will take initially place by aerobic bacteria that use O₂. If the supply of DOC is exhausted before the O₂ is consumed, then redox conditions will not evolve much further unless another electron donor in the system is found (ferrous iron minerals, sulphides, etc.). If an excess of DOC accompanies the groundwater below the water table and beyond the influence of atmospheric O₂, then anaerobic bacteria will consume it using electron acceptors such as NO₃^–, Fe³⁺-oxyhydroxides or SO₄^2–. Ultimately, methanogenic reactions can take place. Redox evolution is accompanied by mineral dissolution and precipitation reactions that affect the mass balance of dissolved solids and the distribution of isotopes.

All sources of carbon are linked through these acid-base and redox reactions, which are most often mediated by bacteria. Bacterial involvement is important for two reasons. They derive their energy from redox reactions (usually oxidation of organics), and so act as catalysts, speeding up reactions that are otherwise kinetically impeded. Secondly, bacteria are isotopically selective, preferring to break the weaker, light-isotope bonds. Bacterially mediated reactions are then accompanied by large isotope fractionations. The huge range for d¹³C in various carbon reservoirs is a demonstration of isotope selectivity by bacteria (Fig. 5-1). Biologically mediated redox reactions for carbon are kinetic, proceeding in one direction only. However, for relatively stable environmental conditions, fractionation is constrained to definable ranges. Understanding the distribution of isotopes in the carbon cycle begins with a look at carbonate geochemistry.

Fig. 5-1 Ranges for d¹³C values in selected natural compounds. Especially noteworthy is the spread in ¹³C seen in different plant groups and the resulting soil CO₂.

Carbon-13 in the Carbonate System

Vegetation and soil CO₂

Carbon-13 is an excellent tracer of carbonate evolution in groundwaters because of the large variations in the various carbon reservoirs. The evolution of DIC and d¹³C_DIC begins with atmospheric CO₂ with d¹³C ~ –7% VPDB. Photosynthetic uptake of CO_2(atm) is accompanied by significant depletion in ¹³C. This occurs during CO₂ diffusion into the leaf stomata and dissolution in the cell sap, and during carboxylation (carbon fixation) by the leaf’s chloroplast, where CO₂ is converted to carbohydrate (CH₂O). The combination of these fractionating steps results in a 5 to 25‰ depletion in ¹³C (Fig). The amount of fractionation depends on the pathway followed. Three principal photosynthetic cycles are recognized: the Calvin or C₃ cycle, the Hatch-Slack or C₄ cycle, and the Crassulacean acid metabolism (CAM) cycle.

The C₃ pathway operates in about 85% of plant species and dominates in most terrestrial ecosystems. C₃ plants fix CO₂ with the Rubisco enzyme, which also catalyses CO₂ respiration through reaction with oxygen. CO₂ respiration is an inefficiency that remains as an artifact of evolution in an atmosphere with high CO₂ and increasing P_O2 (Ehleringer et al., 1991). The diffusion and dissolution of CO₂ has a net enrichment in ¹³C, whereas carboxylation imparts a 29‰ depletion on the fixed carbon (O’Leary, 1988). The result is an overall ¹³C depletion of about 22‰. Most C₃ plants have d¹³C values that range from -24 to -30‰ with an average value of about -27‰ (Vogel, 1993). The natural vegetation in temperate and high latitude regions is almost exclusively C₃. They also dominate in tropical forests. Most major crops are C₃, including wheat, rye, barley, legumes, cotton, tobacco, tubers (including sugar beats) and fallow grasses.

The more efficient C₄ pathway evolved as atmospheric CO₂ concentrations began dropping in the early Tertiary. Under low CO₂:O₂ conditions and at higher temperatures, increased respiration in C₃ plants interferes with their ability to fix CO₂. C₄ plants add an initial step where the PEP carboxylase enzyme acts to deliver more carbon to Rubisco for fixation. The result is a reduction in ¹³C fractionation during carboxylation. C₄ plants have d¹³C values that range from -10 to -16‰, with a mean value of about -12.5‰ (Vogel, 1993). C₄ species represent less than 5% of floral species, but dominate in hot open ecosystems such as tropical and temperate grasslands (Ehleringer et al., 1991). Common agricultural C₄ plants include sugar cane, corn and sorghum.

This difference provides a tool to monitor food products marketed as "100% natural", such as fruit juices and maple syrup that can be cut with inexpensive cane sugar. Carbon-13 and other isotopes are now used routinely by customs and excise departments to check the origin of these and other imports (Hillaire-Marcel, 1986).

CAM photosynthesis is favoured by about 10% of plants and dominates in desert ecosystems with plant species such as cacti. They have the ability to switch from C₃ photosynthesis during the day to the C₄ pathway for fixing CO₂ during the night. Their isotopic composition can span the full range of both C₃ and C₄ plants, but usually is intermediate (Fig. 5-1).

As vegetation dies and accumulates within the soil, decay by aerobic bacteria converts much of it back to CO₂. Soils have CO₂ concentrations 10 to 100 times higher than the atmosphere. Microbially-respired CO₂ has much the same d¹³C as the vegetation itself. However, outgassing of CO₂ along this steep concentration gradient imparts a diffusive fractionation on the soil CO₂. Cerling et al. (1991) show that measured fractionations are over 4‰, and very close to the theoretical fractionation of 4.4‰ for CO₂ diffusion through air (see page 24). Aravena et al. (1992) provide addition field evidence for enrichment of soil CO₂ by outward diffusion. For this reason, the d¹³C of soil CO₂ in most C₃ landscapes is generally about –23‰ (Fig. 5-1). In soils hosting C₄ vegetation, it would be closer to about –9‰.
 

Dissolved Organic Carbon

The geochemical evolution of groundwaters can involve more than the CO₂-based weathering reactions discussed above. Dissolved organic carbon (DOC) plays an important role through reduction-oxidation (redox) reactions. Redox reactions involve the exchange of electrons between two complementary species or redox pairs. One species is oxidized (loss of electrons) and the other is reduced (gain of electrons). Photosynthesis is an example of an endothermic redox reaction, using energy (photons) to reduce carbon from the +IV (oxidized) to the 0 (fixed) redox state:

So what constitutes DOC? The operative boundary between DOC and particulate organic carbon is set as what will pass through a commercially available 0.45-mm filter. The decay products of vegetation form a spectrum of molecular sizes and charges. They are composed of C, O, N, H and S in varying proportions. The most common category of soil-derived organic material are the humic substances, defined as high molecular weight (up to several hundred thousand mass units), refractory, heterogeneous organic substances. In non-contaminated groundwaters, low molecular weight (LMW) compounds make up the rest. LMW DOC includes cellulose, protein, and organic acids such as carboxylic, acetic and amino acids.

The structure and formation of humic substances have yet to be fully understood, and their characterization has been based largely on methods of separation. They are alkali-soluble acids that give the dark colour to soil and wetland waters. Humic acids (HA) precipitate from solution at pH less than 2, while the fulvic acid (FA) fraction is soluble at all pH values. Insoluble humic substances or humin may be that refractory component that is strongly sorbed to the soil mineral component (Stevenson, 1985).

Structurally, humic acids appear to be networks of phenol rings bridged and fringed with carbohydrate, amino acids, fat and protein residues including various O, OH, CH₂, NH and S functional groups (Fig. 5-7). Fulvic acids are low molecular weight compounds (Stevenson, 1985; Orlov, 1995).

Fig. 5-7 Typical structure of humic and fulvic acids as proposed by Stevenson (1985) and Buffle (1977).

Compositionally, humins are C–O–H–N–S compounds, varying according to vegetation and decompositional history. Humic acids are roughly 50 to 60% carbon, with 30 to 40% oxygen (Table 5-4). Hydrogen and nitrogen represent on the order of 5% each. Fulvics tend to have slightly lower carbon contents. HA and FA result from the humification of vegetation (cellulose and other carbohydrates, proteins, lignins, tanins etc) by bacterial metabolism and oxidation. Their phenolic and amino acid products then polymerize to form humic substances.

The transport of organic carbon from the soil to groundwater is influenced by soil water conditions and soil structure. DOC in soil moisture reaches a maximum of 10 to 100 mg-C/L in the root zone, and drops off towards the water table (Aiken, 1985). Groundwaters often contain less than 1 to 2 mg-C/L, although groundwaters in certain environments can recharge with much higher DOC concentrations (Wassenaar et al., 1990). Periods of high water table and storm events can flush significant quantities of DOC to the saturated zone, particularly in agricultural areas or in the spring when soil microbial activity is low. Groundwaters recharged through saturated soils, such as in tundra and peat bogs, also typically have high DOC. Groundwaters contaminated with high dissolved organics from landfill sites or septic tanks are another example. In such cases, DOC concentrations can exceed 10 to 100 mg-C/L.

Table 5-4 Mean elemental composition of humic and fulvic acids from vegetation, soils, surface water and groundwater, in weight percent (from Thurman, 1985; Orlov, 1995; Steinberg and Muenster, 1985)
 

Medium	DOC	C	H	O	N	S
	(mg-C/L)
Peat	—	58	5.6	33	2.6	0.2–0.5
Plant residue	—	50	6.3	42	2.5	—
Humic Acid
Soils	—	53–58	3.4–5.2	35–38	2.7–5.0	—
Lakes	1–30	45–52	3–5	37–47	0.7–2	0.5–4.3
Groundwaters1	<0.2–10	55–63	5.8–6.3	30–35	0.5–1.8	—
Fulvic Acid
Soils	—	53–58	3.4–5.2	35–38	2.7–5.0	—
Lakes	1–30	43–53	3–5	35–52	0.5–2.2	0.5–4.3
Groundwaters1	<0.2–10	58–62	3–5	24–30	3.2–5.8	—

1 HA and FA in groundwaters beneath agricultural areas or bogs can exceed 100 mg–C/L (e.g. Aravena et al., 1993a; 1995; Cane, 1996).
 

DOC can also be gained from organic sources within the aquifer. Buried peat is often a component of Quaternary sediments, and may also be a source of DOC in groundwaters (Aravena and Wassenaar, 1993). Marine carbonates and shales can also host sedimentary organic carbon (SOC), ranging from immature kerogen with elevated O/C ratios to highly reduced, thermally mature hydrocarbons such as bitumen. Coal horizons, besides having aquifer potential, can act as a substrate for redox reactions. In most cases, the d¹³C value of soil or aquifer-derived organic carbon is about –25 ± 2–3‰ (Fig. 5-1).
 

Biogenic methane

The generation of methane by bacteria requires a fully saturated environment that excludes atmospheric O₂ and an organic carbon substrate in the absence of other free-energy electron-acceptors such as NO₃^– and SO₄^2–. These conditions are most closely matched by wetlands and Arctic tundra, although bovine digestive tracts also meet the requirements. In natural freshwater systems, the pathways for biological methanogenesis have been reviewed by Klass (1984), and generally involve mixed bacterial populations. Fermentive bacteria begin the process by reducing complex organic structures of carbohydrates, proteins and lipids that originate in vegetation and sediments, to simpler molecules including acetate (CH₃COOH), fatty acids, CO₂ and H₂ gas. In these example reactions from Klass (1984), CH₂O is used to represent these complex organic molecules:

The simplified, "pathway-independent" reaction can be written as:

As one might expect, the ¹³C fractionation between CO₂ and CH₄ is large (e¹³C_CO2–CH4 = 75 ± 15‰). The metabolic pathway of methanogenic bacteria favours the light isotopes. From Fig. 5-9, biogenic methane in groundwater has d¹³C values depleted from coexisting CO₂ by some 50 to 80‰. This distinguishes biogenic methane from thermocatalytic and abiogenic origins.

Fig. 5-9 The distribution of ¹³C between CH₄ and coexisting CO₂ for fresh and brackish groundwaters with different sources of methane (data from Aravena et al., 1993b; 1995 — biogenic; Grossman et al., 1989 — biogenic; Barker and Fritz, 1981b — biogenic and thermocatalytic; Schoell, 1980 — biogenic, Fritz et al., 1987 — abiogenic , Fritz et al., 1992 [d¹³C_CH4 > –20‰] — abiogenic).

The fractionation of ²H can also help characterize the source of methane. The ²H contents of methane are established during methanogenesis by the ²H content of the organic substrate and the water participating in the reaction. However, these are kinetic reactions, and the fractionation factors are generally higher than for equilibrium exchange between CH₄ and H₂O. Deuterium values of -150 to -400‰ can be measured in the CH₄. Subsequent exchange of ²H with water only occurs at geothermal temperatures, well beyond the range of biogenic systems. The combination of d²H and d¹³C can then be used to distinguish biogenic methane from other sources (Fig. 5-10).

Fig. 5-10 The origin of methane in groundwater according to its d¹³C–d²H composition (data from Aravena et al., 1995, Grossman et al., 1989, Schoell, 1980 — biogenic; Fritz et al., 1987, Sherwood Lollar et al., 1993, Fritz et al., 1992 [d¹³C_CH4 > –20‰] — abiogenic; Barker and Pollock, 1984 — thermocatalytic).

The reaction pathway, i.e. acetate fermentation or CO₂ reduction, will affect differently the isotopic composition of the methane and the evolution of DIC. A two end-member model was traditionally accepted where CH₄ is produced by acetate fermentation in freshwater settings and by CO₂ reduction in marine sediments (Whiticar, 1986). In fact methanogenesis by CO₂ reduction occurs in many freshwater settings. Using ¹⁴C-labeled CO₂ and acetate at a freshwater bog, Lansdown et al. (1992) show that their observed CH₄ production is essentially via CO₂ reduction.

The most diagnostic tool to identify the pathway appears to be the ¹³C fractionation between coexisting CH₄ and CO₂, calculated as:

The ¹³C distribution is also affected by several additional factors. One is the isotopic composition of the organic substrate within the aquifer, which can be preserved in the methane (Grossman et al., 1989). Another is the bacterial oxidation of methane. This produces a positive shift in d¹³C_CH4 and corresponding depletion in the DIC (Fig. 5-11) (Barker and Fritz, 1981a). A positive shift in the ²H content of the CH₄ occurs as well.

Fig. 5-11 The d¹³C composition of biogenic methane and CO₂ or DIC in groundwater. Filled symbols indicate sites where other evidence indicates CH₄ production by CO₂ reduction. Fractionation lines for CH₄ and CO₂ provide an empirical division between the two methanogenic pathways.

Methane oxidation reactions can proceed according to a number of reactions, although the two principal electron acceptors are O₂ and SO₄^2–. Incorporation of atmospheric O₂ generally occurs in the groundwater discharge area such as at the well head, spring vent, or if the groundwaters mix with shallow groundwaters in a phreatic aquifer, oxidizing CH₄ according to:

Another important factor is whether the reaction products remain with the groundwater, or are lost (e.g. trapped as a separate gas phase within the aquifer), which may affect Rayleigh type reactions. Brackish groundwaters from 850 m depth in dolomites of the St. Lawrence Lowlands provide an example, where measured d¹³C values for DIC reach an astounding +31.6‰ and are ~-41‰ for CH₄ (Fig. 5-9). Such high d¹³C_DIC values are rarely observed in nature, and cannot be attributed to reaction with the dolomites (d¹³C = +1‰). In this case, DIC levels are over 600 mg/L (pH = 9.62). DOC reaches 120 mg-C/L and is derived from low-maturity bitumen in the dolomites. TDS reaches 2500 mg/L as NaCl salinity. In this case, reduction of DIC, producing a ~75‰-depleted CH₄ product, imparts a progressive enrichment on the residual DIC pool.

Problems and Solutions

1. What is the pH of a groundwater in equilibrium with a soil atmosphere that has P_CO2 = 10^–1.8? The groundwater temperature is 25°C. Determine the distribution of carbonate species (i.e. mH₂CO₃, mHCO₃^– and mCO₃^2–).

From Table 5-2, the dissolution constant for CO₂ can be determined: and so the concentration of dissolved CO₂ (carbonic acid) is:

We can solve for bicarbonate by assuming that [H⁺] = [HCO₃^–] considering that the dissociation of carbonic acid should produce these species in equal concentrations. This is valid as long as no other acids, such as organic acids (HA or FA), are not present. We then get:

Thus, the pH for this groundwater would be 4.81. We have determined as well that the molalities of the two principal carbonate species are: mH₂CO₃ = 10^–3.27 = 0.00054 moles/L

mHCO₃^– = 10^–4.81 = 0.000015 moles/L

The concentration of CO₃^2– is negligible at this pH:

[CO₃^2–] = 10^–10.33 · 10^–4.81 / 10^–4.81 = 10^–10.33

The P_CO2 in this case would be 0.1 or 10^–1 atmospheres. Following the same solution path as in problem 1:

= 10^–1.47 · 10^–1 = 10^–2.47

[H⁺] [HCO₃^–] = [H⁺]² = 10^–6.35 · 10^–2.47 = 10^–8.82

Thus, the pH for the sample would be 4.41, which will assure rapid exchange of ¹⁸O.

In the case where the water had an initial pH of 7.3 and 225 mg/L HCO₃^–, the system can be considered open to the CO₂ which must be assumed to be a much larger carbon reservoir than the DIC. As CO₂ dissolves and the carbonic acid so formed dissociates, both H⁺ and HCO₃^– are added to solution. This supply of H⁺ will be buffered by the high initial HCO₃^– concentration. The final HCO₃^– concentration will then be equal to the initial plus the concentration of H⁺ added to solution, which maintains a charge balance in the water:

[HCO₃^–]_final = [HCO₃^–]_initial + [H⁺]

= 10^–2.4 + [H⁺]

By iteration or mathematical solution to solve for [H⁺], the final pH is determined to be 6.82. In this case, CO₂ equilibration will not be as rapid as before, but would be attained within the conventional ~ 4 hour reaction time used for the method.

 

The fractionation between CO₂ gas and DIC varies enormously with pH due to the difference in fractionation factors between CO_2(g) and each of CO_2(aq), HCO₃^– and CO₃^2–. The solution to this problem requires that the distribution of DIC species be determined for the specified pH. The relative concentration of the DIC species is then used to weight their fractionation with soil CO₂. From Fig. 5-2, we see that for pH 5.8 and 7.3, only HCO₃^– and H₂CO₃ (CO_2(aq)) contribute significantly to DIC and so CO₃^2– can be ignored: At pH = 5.8, the DIC species ratio is: Assume that molality m is equal to activity [ ] for at low salinity, and that H₂CO₃ is essentially CO_2(aq). As only the relative concentration of DIC species are needed, we can assume that mDIC = mCO_2(aq) + mHCO₃^– = 1. The relative concentrations of HCO₃^– and CO_2(aq) are then: mHCO₃^– = 1 – mCO_2(aq)

Thus the fraction of 

and the fraction of HCO₃^– = 0.22

Accordingly, the d¹³C of the DIC for this water is then determined from the isotope mass balance equation using e¹³C values from Table 5-3:

d¹³C_DIC = 0.22 (d¹³C_CO2(g) + e¹³C_{HCO3–CO2(g)}) + 0.78 (d¹³C_CO2(g) + e¹³C_{CO2(aq)– CO2(g)})

= 0.22 (–23 + 7.9) + 0.78 (-23 – 1.1)

= –22.1

The identical calculation using pH 7.3 gives:

HCO₃^– = 0.90

d¹³C_DIC = 0.10 (–23 – 1.1) + 0.90 (-23 + 7.9) = –16.0‰

For the third pH of 9.8, fractionation with CO_2(aq) is negligible, although CO₃^2– must now be considered. A similar solution path is followed:

As mCO_2(aq) is negligible, the relative concentrations of the major DIC species HCO₃^– and HCO₃^2– are then: mCO₃^2– = 1 – mHCO₃^–

Thus the fraction of 

and the fraction of CO₃^2– = 0.23

Accordingly, the d¹³C of the DIC for this water is then determined from the isotope mass balance equation using e¹³C values from Table 5-3:

d¹³C_DIC = 0.77 (d¹³C_CO2(g) + e¹³C_{HCO3–CO2(g)}) + 0.23 (d¹³C_CO2(g) + e¹³C_CO3–CO2(g))

= 0.77 (–23 + 7.9) + 0.23 (–23 + 7.6)

= –15.2‰

pH	5.8	7.3	9.8
	0.28	8.91	>100
		<0.001	0.30
fraction CO2(aq)	0.78	0.10	0.00
fraction HCO3–	0.22	0.90	0.77
fraction CO32–	0.00	0.00	0.23
d13CDIC	–22.1	–16.0	–15.2

Calculation of the equilibrium P_CO2 and calcite saturation index requires the activities of DIC species (aH₂CO₃, aHCO₃^– and aCO₃^2–), which are calculated with activity coefficients using ionic strength and the Debye-Hückel equation. The ionic strength is calculated from: I_JR1 =½ (63.0/40080´ 4 + 1.3/24300´ 4 + 3.1/23000 + 205/61000 + 2.8/35453) = 0.005 and I_YK1 = ½ (25.5/40080´ 4 + 0.3/24300´ 4 + 2.7/23000 + 79.1/61000 + 4.1/35453) = 0.0021 The activity coefficients for Ca²⁺ and the DIC species are then calculated from the Debye-Hückel equation:

and the activity of Ca²⁺ and HCO₃^– are determined from (for JR1):

[Ca²⁺] = mCa²⁺ · g_Ca

= 63.0/40080 · 0.72 = 10^–2.95

[HCO3^–] = 205/61000 · 0.92 = 10^–2.51

The activities of H₂CO₃ and CO₃^2– are then determined from the activity of HCO₃^– and pH:

and

The calculations for YK1 are the same, with the exception that the reaction constants (K₁ and K₂) for 5°C must be used.

The equilibrium P_CO2 is the calculated from (for JR1):

And the saturation of calcite is determined from the saturation index (SI) which is calculated from the ion activity product for calcite (IAP_CaCO3) and the solubility constant for calcite (K_CaCO3): IAP_CaCO3 = [Ca²⁺][CO₃^2–] = 10^–2.95 · 10^–5.53 = 10^–8.48

K_CaCO3 = 10^–8.48 at 25°C, from Table 5-2

log SI_CaCO3 = log (IAP/K_CaCO3) = log (10^–8.48/10^–8.48) = 0

This value for YK1 is 1.4‰ more depleted than that which was measured (–11.3‰). Although the difference is not huge, it does fit with our thermodynamic calculations which show that calcite dissolution took place under closed system conditions. The d¹³C mass balance equation used here is for open system conditions, as only the d¹³C of the soil CO₂ is considered. For closed system conditions, a d¹³C mass balance equation including the isotope value of the calcite (d¹³C_carb) must be used. We first start with a calculation of the initial DIC, based on the soil P_CO2 of 10^–2.0: and so the activity of dissolved CO₂ (carbonic acid) is: [H₂CO₃] = [CO_2(aq)] = mCO_2(aq) = 10^–3.19 = 6.46 · 10^–4 moles/L and the bicarbonate concentration mHCO₃^– is calculated as:

[H⁺] [HCO₃^–] = [HCO₃^–]² = 10^–9.71

[HCO₃^–] = 10^–4.86

Under the low salinity conditions prior to calcite dissolution g_HCO3 will be ~ 1. mHCO₃^– = [HCO₃^–] / g_HCO3 = 10^–4.86 = 1.38 · 10^–5 moles/L and so the concentration of DIC at the time of recharge (mDIC_rech), prior to closed system calcite dissolution, is: mDIC_rech = mCO_2(aq) + mHCO₃^–

= 6.46 · 10^–4 + 1.38 · 10^–5 = 6.60 · 10^–4 moles/L

and the d¹³C value for the DIC at this time is (ignoring the effect of CO₃^2–): d¹³C_DIC-rech = [mCO_2(aq) (d¹³C_CO2(g) + e¹³C_{CO2(aq)–CO2(g)}) + mHCO₃^– (d¹³C_CO2(g) + e¹³C_{HCO3–CO2(g)})] / ( mCO_2(aq) + mHCO₃^– )

= [6.46 · 10^–4 (–23 – 1.2) + 1.38 · 10^–5 (–23 + 10.2)] / (6.46 · 10^–4 + 1.38 · 10^–5)

= –24.0‰

Under closed system conditions, the amount of carbonate dissolved by the groundwater is equal to mCa²⁺, and is also equal to mDIC – mDIC_rech: mCa²⁺ = 25.5/40080 = 6.36 · 10^–4 moles/L

mDIC – mDIC_rech = 79.1/61000 – 6.60 · 10^–4 = 6.37 · 10^–4 moles/L

Our d¹³C mass balance equation to calculate a final d¹³C_DIC is then: d¹³C_DIC-calc = [ (mDIC_rech · d¹³C_DIC-rech) + (mCa²⁺ · d¹³C_carb))]

/ ( mDIC_rech + mCa²⁺)

= [6.60 · 10^–4 (-24.0) + 6.36 · 10^–4 (1.5)]

/ (6.60 · 10^–4 + 6.36 · 10^–4)

= –11.5‰

This calculated value for the d¹³C of the DIC in YK1 is much closer to the measured value of –11.4‰, and supports the P_CO2 data indicating closed system dissolution of carbonate.
 

The concentration and d¹³C value of the DIC can be accounted for by equilibration with the soil CO₂. In this case, we will assume that activity coefficients are equal to 1 and therefore molalities equal activities. Thermodynamic constants (K_T values) used in this problem are calculated for the sample temperatures from the equations given earlier in this chapter (page 119) or can be interpolated from data in Table 5-2. The equilibrium P_CO2 of BC1 is:

[H₂CO₃] = 10^–3.34 · 10^–7.00 / 10^–6.47 = 10^–3.87

This is the same P_CO2 as was measured in the recharge area soils, and suggests that this water is then in equilibrium with soil CO₂. The calculation of d¹³C should bear this out: d¹³C_DIC-calc = [mCO_2(aq) · (d¹³C_soil + e¹³C_{CO2(aq)–CO2(g)}) + mHCO₃^– · (d¹³C_soil + e¹³C_{HCO3–CO2(g)})] / (mCO_2(aq) + mHCO₃^–)

= [10^-3.87 · (–23 – 1.1) + 10^–3.34 · (–23 + 9.6)] / (10^-3.87 + 10^–3.34)

= –15.84

This is precisely the value measured in the BC1 sample, and so this groundwater has evolved under open system conditions with the soil CO₂.

However, the P_CO2 in the BC2 to BC4 groundwaters decreases, showing that in this part of the aquifer, weathering takes place under closed system conditions. For the example of BC2:

[H₂CO₃] = 10^–3.17 · 10^–7.30 / 10^–6.43 = 10^–4.04

Similarly, P_CO2 for BC3 = 10^–3.22

and P_CO2 for BC4 = 10^–3.42

As no calcite has been observed in this aquifer, the weathering reactions that have consumed CO₂ and increased the pH must be the alteration of primary silicates (see silicate weathering on page 21). The increase in Ca²⁺ and Na⁺ would be produced by weathering of feldspars. The sulphate and much of the calcium can be attributed to gypsum dissolution.

Using the appropriate geochemical reactions, show the process responsible for the evolution of DIC and d¹³C_DIC in this groundwater flow system. From your reaction pathway, calculate a final HCO₃^– concentration and d¹³C_DIC for BC4 and compare with the measured values.

The principal changes we observe in the evolution from BC1 to BC4 are a decrease to 0 in sulphate and DOC, and an increase from 0 to 11 in sulphide. These are the key changes that we would observe during the process of sulphate reduction. The progressive increase in bicarbonate and depletion in ¹³C is consistent with this.

The geochemical reaction for sulphate reduction can be written as (from Fig. 5-8):

2CH₂O + SO₄^2– ® H₂S + 2HCO₃^– In this reaction, two moles of DOC produce two moles of bicarbonate and one mole of dissolved sulphide. Although H₂S is produced in this equation, it is the HS^– species that will dominate due to the high pH from silicate weathering (K_HS-H2S = 10^–7.0). The final DIC will then be equal to the initial DIC in BC1 plus the bicarbonate produced during sulphate reduction.

The DIC of BC1 was determined above from HCO₃^– and pH data:

mDIC_BC1 = (mCO_2(aq) + mHCO₃^–)

= (10^-3.87 + 10^–3.34) = 10^–3.23 = 5.89 · 10^–4 moles /L

For samples BC2 to BC4, this is calculated as: mDIC_calc(H2S) = mDIC_BC1 + 2mHS^–

=5.89 · 10^–4 + 2 (2.8/33,000)

= 7.59 · 10^–4 moles/L

The actual DIC in BC2 is calculated from mHCO₃^– and pH (as in previous examples):

and assuming that molalities equal activities: mHCO₃^– = 41.1/61,000 = 6.74 · 10^–4 moles/L

mH₂CO₃ = mHCO₃^– / 7.41 = 9.10 · 10^–5 moles/L

and mDIC = 6.74 · 10^–4 + 9.10 · 10^–5 = 7.65 · 10^–4 moles/L

Thus, our calculation of mDIC_BC2, assuming that the increase in bicarbonate is due to sulphate reduction, is the same as that for the actual value determined from measured HCO₃^– and pH. The same calculations for BC3 and BC4 give the same conclusion that the additions to the DIC pool are derived through sulphate reduction, and oxidation of DOC:

A similar calculation of DIC could be made on the basis of the decrease in DOC for each sample, whereby:

mDIC_calc(DOC) = mDIC_BC1 + (mDOC_BC1 – mDOC) Finally, the evolution of d¹³C_DIC can also be calculated for comparison with measured values. BC1 was shown to be sampled from the recharge area, and so can be used in this calculation: d¹³C_DIC-calc = (d¹³C_BC1 ·mDIC_BC1 + d¹³C_DOC ·2mHS^–)/(mDIC_BC1 + 2mHS^–) The results of this calculation for each sample is compared with the other calculations of DIC in the following table:

For these calculations, we must use the thermodynamic approach developed in problem 7 above, including calculation of:

Ionic strength: 

Activity coefficients: 

Ion activities: [Ca²⁺] = mCa²⁺ · g_Ca

[HCO3^–] = (mg–HCO₃/L)/61,000 · g_HCO3

Ion molalities: mHCO₃^– = (mg-HCO₃^–/L)/61,000 mCO_2(aq) =[H₂CO₃]

mDIC = mHCO₃^– + mCO_2(aq)

P_CO2: 

In fresh waters, methanogenesis generally proceeds via the CO₂ reduction pathway, which imparts a strong enrichment on the residual DIC. The d¹³C enrichment trend observed in this aquifer is consistent with CH₄ generation by CO₂ reduction. A rough calculation of this enrichment can be made on the basis of a d¹³C mass balance and a Rayleigh distillation of the DIC pool during methanogenesis, if we presume that no carbon has been lost from the groundwater.

The d¹³C of the DIC in FR1 can be calculated using the closed system approach we saw in problem 7 for YK1. First, we calculate mDIC_rech from the soil P_CO2 of 10^–1.8 and then the d¹³C of DIC in the recharge water prior to closed system dissolution of calcite. Enrichment values are from Table 5-3, for 5°C:

[H₂CO₃] = [CO_2(aq)] = mCO_2(aq) = 10^–2.99 = 1.02 · 10^–3 moles/L

and the bicarbonate concentration mHCO₃^– is calculated as:

[H⁺] [HCO₃^–] = [HCO₃^–]² = 10^–9.51

[HCO₃^–] = 10^–4.76

Again, under the low salinity conditions prior to calcite dissolution g_HCO3 will be ~ 1, and so: mHCO₃^– = [HCO₃^–] / g_HCO3 = 10^–4.76 = 1.74 · 10^–5 moles/L and so the concentration of DIC at the time of recharge (mDIC_rech), prior to closed system calcite dissolution, is: mDIC_rech = mCO_2(aq) + mHCO₃^–

= 1.02 · 10^–3 + 1.74 · 10^–5 = 1.04 · 10^–3 moles/L

The contribution of bicarbonate is insignificant in this high P_CO2– low pH soil and can be ignored in the d¹³C mass balance equation, which simplifies to: d¹³C_DIC-rech = [mCO_2(aq) (d¹³C_CO2(g) + e¹³C_{CO2(aq)–CO2(g)})] / ( mCO_2(aq))

= (–23 – 1.2)

= –24.2‰

Under closed system conditions, the amount of carbonate dissolved by the groundwater at FR1 is equal to mCa²⁺: mCa²⁺ = 31/40080 = 7.73 · 10^–4 moles/L The d¹³C mass balance equation to calculate a final d¹³C_DIC for FR1 is then: d¹³C_DIC-calc = [ (mDIC_rech · d¹³C_DIC-rech) + (mCa²⁺ · d¹³C_carb))]

/ ( mDIC_rech + mCa²⁺)

= [1.04 · 10^–3 (-24.2) + 7.73 · 10^–4 (0)] / (1.04 · 10^–3 + 7.73 · 10^–4)

= –13.9‰

This value is close the measured value of –13.7‰ for FR1 and supports the assumption that calcite is dissolved under closed system conditions.

The enrichment in d¹³C observed in FR2, FR3 and FR4 was attributed to the strong fractionation due to methanogenesis. During bacterial CO₂ reduction (see equation above) ¹²CO₂ is preferentially used over ¹³CO₂. The enrichment factor e¹³C_CO2–CH4 is between 60 and 90‰ (Whiticar et al., 1986). The ¹³C enrichment in the residual DIC during this reaction can be likened to a Rayleigh distillation. It is for this reason that d¹³C enrichments DIC in methanogenic groundwaters can reach 20‰ and more (Fig. 5-9). This can be simulated on the basis of a d¹³C mass balance equation and Rayleigh equation.

The approach is to calculate the total DIC reservoir which will be equal to the DIC from previous sample (mDIC_FR1), plus the amount of DOC oxidized (DDOC) plus the amount of carbonate dissolved (DCa²⁺). The ratio of this calculation of total DIC to actual DIC (after CO₂ reduction and generation of CH₄) represents the residual fraction, f, for the Rayleigh calculation. The ¹³C fractionation factor during methanogenesis can be set at a median value of say e¹³C_CO2–CH4 = 75‰. The value of d¹³C_DOC is set at –26‰ and the aquifer carbonate has d¹³C_carb = 0‰.

Here we will run through this calculation for FR2, which is the first of the series to show evidence of methanogenesis. The d¹³C of the total DIC pool prior to CO₂ reduction is then determined from the Rayleigh equation:

d¹³C_DIC–FR2 = d¹³C_DIC–init – e¹³C_CO2–CH4 · ln (mDIC_FR2 / mDIC_init)

For this calculation:

mDIC_FR2 = 2.91 · 10^–3 moles/L (from table above)

mDIC_init–FR2 = mDIC_FR1 + (mDOC_FR1 – mDOC_FR2) + (mCa²⁺_FR2 – mCa²⁺_FR1) = 1.81 · 10^–3 + (44 – 28)/12,000 + (48 – 31)/40,080

= 1.81 · 10^–3 + 1.33 · 10^–3 + 4.24 · 10^–4

= 3.57 · 10^–3 moles/L

f = mDIC_FR2 / mDIC_init

= 2.91 · 10^–3 / 3.57 · 10^–3

= 0.815

d¹³C_{DIC–init–FR2} = [d¹³C_DIC–FR1 · mDIC_FR1 + (d¹³C_DOC · (mDOC_FR1 – mDOC_FR2) + d¹³C_carb · (mCa²⁺_FR2 – mCa²⁺_FR1)] / [mDIC_FR1 + (mDOC_FR1 – mDOC_FR2) + (mCa²⁺_FR2 – mCa²⁺_FR1)]

= [–13.7 · 1.81 · 10^–3 + (–26) · 1.33 · 10^–3 + (0) · 4.24 · 10^–4] / [1.81 · 10^–3 + 1.33 · 10^–3 + 4.24 · 10^–4]

= –16.7‰

Now applying the Rayleigh distillation: d¹³C_DIC–FR2 = d¹³C_{DIC–init–FR2} – e¹³C_CO2–CH4 · ln (mDIC_FR2 / mDIC_init)

= –16.7 – 75 · ln (2.91 · 10^–3 / 3.57 · 10^–3)

= –16.7 – 75 · ln (0.815)

= –1.36‰

This value is close to the measured value for FR2 of –2.1‰, and so our interpretation of a rayleigh enrichment during CO₂ reduction must be correct.

Carrying out these calculations for FR3 and FR4 also produce values similar to those measured:

mDIC_init–FR3 = mDIC_FR2 + (mDOC_FR2 – mDOC_FR3) + (mCa²⁺_FR3 – mCa²⁺_FR2) = 2.91 · 10^–3 + (28–12)/12,000 + (61–48)/40,080

= 4.57 · 10^–3 moles/L

d¹³C_{DIC–init–FR3} = [d¹³C_DIC–FR2 · mDIC_FR2 + (d¹³C_DOC · (mDOC_FR2 – mDOC_FR3) + d¹³C_carb · (mCa²⁺_FR3 – mCa²⁺_FR2)] / [mDIC_FR2 + (mDOC_FR2 – mDOC_FR3) + (mCa²⁺_FR3 – mCa²⁺_FR2)]

= [–2.1 · 2.91 · 10^–3 + (–26) · 1.33 · 10^–3] / [2.91 · 10^–3 + 1.33 · 10^–3 + 3.24 · 10^–4]

= –8.91‰ d¹³C_DIC–FR3 = d¹³C_{DIC–init–FR3} – e¹³C_CO2–CH4 · ln (mDIC_FR3 / mDIC_init–FR3)

= –8.91 – 75 · ln (3.90 · 10^–3 / 4.57 · 10^–3)

= 3.0‰

mDIC_init–FR4 = mDIC_FR3 + (mDOC_FR3 – mDOC_FR4) + (mCa²⁺_FR4 – mCa²⁺_FR3) = 3.90 · 10^–3 + (12–2)/12,000 + (68–61)/40,080

= 4.90 · 10^–3 moles/L

d¹³C_{DIC–init–FR4} = [d¹³C_DIC–FR3 · mDIC_FR3 + (d¹³C_DOC · (mDOC_FR3 – mDOC_FR4) + d¹³C_carb · (mCa²⁺_FR4 – mCa²⁺_FR3)] / [mDIC_FR3 + (mDOC_FR3 – mDOC_FR4) + (mCa²⁺_FR4 – mCa²⁺_FR3)]

= [3.1 · 3.90 · 10^–3 + (–26) · 8.33 · 10^–4] / [3.90 · 10^–3 + 8.33 · 10^–4 + 1.74 · 10^–4]

= –1.95‰ d¹³C_DIC–FR4 = d¹³C_{DIC–init–FR4} – e¹³C_CO2–CH4 · ln (mDIC_FR4 / mDIC_init–FR4)

= –1.95 – 75 · ln (4.49 · 10^–3 / 4.90 · 10^–3)

= 4.6‰