7.1 Hydrochemical Sequences and Facies

Nearly all groundwater originates as rain or snowmelt that infiltrates through soil into flow systems in the underlying geologic materials. The soil zone has unique and powerful capabilities to alter the water chemistry, as infiltration occurs through this thin, biologically active zone. In recharge areas the soil zone undergoes a net loss of mineral matter to the flowing water. As groundwater moves along flowlines from recharge to discharge areas, its chemistry is altered by the effects of a variety of geochemical processes. In this section, the major changes in water chemistry that commonly occur as groundwater moves along its flow paths are described. A prerequisite to this discussion is consideration of the chemistry of rain and snow, which is the input to the subsurface hydrochemical system.

Chemistry of Precipitation

The chemical composition of water that arrives on the ground surface can be determined by inspection of chemical analyses of rain and snow. Table 7.1 lists some representative results of chemical analyses of precipitation in various parts of North America. This table indicates that the dissolved solids in rain range from several milligrams per liter in continental nonindustrial areas to several tens of milligrams per liter in coastal areas. Snowmelt that contributes water to the groundwater zone can have greater dissolved solids than rain because of dissolution of dust particles that accumulate in the snow as a result of atmospheric fallout.

Rainwater and melted snow in nonurban, nonindustrial areas have pH values normally between 5 and 6. The equilibrium pH for nonsaline water in contact with CO₂ at the earth’s atmospheric value of 10^–3.5 bar is 5.7. This can be demonstrated by substituting this P_CO2 in Eq. (3.18) to obtain the activity of H₂CO₃ and then solving for H⁺ using Eq. (3.31). Because the water must be acidic, it is apparent from Figure 3.5(a) that is the only ionic species of dissolved inorganic carbon present in a significant amount; therefore, (H⁺) = ().

In industrial areas the pH of precipitation is much below 5.7, frequently as low as 3-4. In fact, acid rains are viewed as a major environmental problem in some regions of Europe and North America. The main cause of this increased acidity is sulfur spewed into the atmosphere from factories, mine processing plants, and coal- or petroleum-fired electrical generating stations. The occurrence of acid rain has now spread from industrial areas far out into the countryside. Emissions of sulfur into the atmosphere occur mainly as particulate S and SO₂. In the atmosphere this leads to increased concentrations of H⁺ and in rain and snow,

(7.1)

(7.2)

In addition to CO₂ and SO₂, the earth’s atmosphere contains other gases such as O₂, N₂, and Ar. The water becomes saturated with respect to these gases. In groundwater systems, the most important of these gases is O₂ because it imparts an appreciable oxidizing capability to the water.

In conclusion, it can be stated that rain and snowmelt are extremely dilute, slightly to moderately acidic, oxidizing solutions that can quickly cause chemical alterations in soils or in geological materials into which they infiltrate.

Carbon Dioxide in the Soil Zone

Almost all water that infiltrates into natural groundwater flow systems passes through the soil zone. In this context the term soil is used as a designation of the layer at the surface of the earth that has been sufficiently weathered by physical, chemical and biological processes to provide for the growth of rooted plants. This is a pedagogical definition, emphasizing that soil is a biological as well as a geologic medium. The soil zone exerts a strong influence on the chemistry of water that infiltrates through it. The most important effects occur as a result of the processes summarized schematically in Figure 7.1. The soil has a capability to generate relatively large amounts of acid and to consume much or all of the available dissolved oxygen in the water that infiltrates it.

Geochemically, the most important acid produced in the soil zone is H₂CO₃, derived from the reaction of CO₂ and H₂O. The CO₂ generated by the decay of organic matter and by respiration of plant roots. Organic-matter decay is the main source and can be represented by the reaction

O₂ (g) + CH₂O = CO₂(g) + H₂O (7.3)

where the simple carbohydrate CH₂O is used to designate organic matter. Other organic compounds can also be used in oxidation equations to represent CO₂ production. Anaerobic reactions such as the reduction of sulfate and nitrate also generate CO₂ (Table 3.11). These processes, however, make only minor contributions to the CO₂ budget of the soil atmosphere.

Measurements of the composition of gas samples from soils at locations in North America, Europe, and elsewhere have established that the CO₂ partial pressure of the soil atmosphere is normally much higher than that of the earth’s atmosphere. Values in the range 10^–3–10^–1 bar are typical. Because of variations of temperature, moisture conditions, microbial activity, availability of organic matter, and effects of soil structure on gas diffusion, CO₂ pressures are quite variable, both spatially and temporally. More detailed discussions of the occurrence and effect of CO₂ production in the soil zone are presented by Jakucs (1973) and Trainer and Heath (1976). When CO₂ at these partial pressures reacts with water, the pH of the water declines dramatically. For example, using the method indicated above, it can be shown that at a CO₂ partial pressure of 10^–1 bar, water in the temperature range 0–25°C will have an equilibrium pH in the range 4.3–4.5. This is much below the pH of uncontaminated rainwater.

Carbon dioxide-charged water infiltrating through the soil zone commonly encounters minerals that are dissolvable, under the influence of H₂CO₃ which is consumed by the mineral-water reactions. Examples of some H₂CO₃ leaching reactions are given by Eqs. (3.49) and (3.54). Other examples are described later in this chapter. As H₂CO₃ is consumed in the soil zone, oxidation of organic matter and root respiration is a source of replenishment of CO₂ to the soil air. The CO₂ combines with water to produce more H₂CO₃ [Eqs. (3.14) and (3.l5)]. As new water from recharge events passes through the soil, biochemical and hydrochemical processes in the soil are therefore capable of providing a continuing supply of acidity to promote mineral-water reactions. The reaction of free oxygen with reduced iron minerals such as pyrite (FeS₂) is another source of acidity. In some areas production of H⁺ by this oxidation reaction plays an important role in mineral weathering in the subsoil. The soil zone can therefore be thought of as an acid pump operating in the very thin but extensive veneer of organic-rich material that covers most of the earth’s surface.

In addition to the inorganic acid, there are many organic acids produced in the soil zone by biochemical processes. These substances, such as humic acids and fulvic acids, can play a major role in the development of soil profiles and in the transport of dissolved constituents downward toward the water table. It is believed by most geochemists however, that as a source of H⁺ involved in mineral dissolution, these acids play a minor role compared to the effect of dissolved CO₂.

Major-Ion Evolution Sequence

As groundwater moves along its flow paths in the saturated zone, increases of total dissolved solids and most of the major ions normally occur. As would be expected from this generalization, it has been observed in groundwater investigations in many parts of the world that shallow groundwater in recharge areas is lower in dissolved solids than the water deeper in the same system and lower in dissolved solids than water in shallow zones in the discharge areas.

In a classic paper based on more than 10,000 chemical analyses of well samples from Australia, Chebotarev (1955) concluded that groundwater tends to evolve chemically toward the composition of seawater. He observed that this evolution is normally accompanied by the following regional changes in dominant anion species:

Travel along flow path

Increasing age

These changes occur as the water moves from shallow zones of active flushing through intermediate zones into zones where the flow is very sluggish and the water is old. This sequence, like many others in the geological sciences, must be viewed in terms of the scale and geology of the specific setting, with allowances for interruption and incompletion. Schoeller (1959) refers to the sequence above as the Ignatovich and Souline Sequence, in recognition of the fact that two hydrogeologists in the Soviet Union developed similar generalizations independent of the contributions by Chebotarev.

For large sedimentary basins, the Chebotarev sequence can be described in terms of three main zones, which correlate in a general way with depth (Domenico, 1972):

1. The upper zone—characterized by active groundwater flushing through relatively well-leached rocks. Water in this zone has as the dominant anion and is low in total dissolved solids.
2. The intermediate zone—with less active groundwater circulation and higher total dissolved solids. Sulfate is normally the dominant anion in this zone.
3. The lower zone—with very sluggish groundwater flow. Highly soluble minerals are commonly present in this zone because very little groundwater flushing has occurred. High Cl^– concentration and high total dissolved solids are characteristic of this zone.

These three zones cannot be correlated specifically with distance of travel or time, other than to say that travel distance and time tend to increase from the upper zone to the lower zone. In some sedimentary basins, groundwater in the upper zone may be years or tens of years old, whereas in other basins ages of hundreds or thousands of years are common. Saline, chloride-rich water in the lower zone is usually very old, but the actual ages may vary from thousands to millions of years.

From a geochemical viewpoint the anion-evolution sequence described above can be explained in terms of two main variables, mineral availability and mineral solubility. The content in groundwater is normally derived from soil zone CO₂ and from dissolution of calcite and dolomite. The partial pressures of CO₂ generated in the soil zone and the solubility of calcite and dolomite are normally the limiting constraints on the level of total dissolved solids attained. Figure 3.7 indicates that at the CO₂ partial pressures typical of soil zone (10^–3–10^–1 bar), calcite and dolomite are only moderately soluble, with equilibrium concentrations in the range 100–600 mg/ℓ. Since calcite or dolomite occur in significant amounts in nearly all sedimentary basins, and because these minerals dissolve rapidly when in contact with CO₂-charged groundwater, is almost invariably the dominant anion in recharge areas.

Table 3.6 indicates that there are several soluble sedimentary minerals that release SO₄^2– or Cl^– upon dissolution. The most common of the sulfate-bearing minerals are gypsum, CaSO₄ · 2H₂O, and anhydrite, CaSO₄. These minerals dissolve readily when in contact with water. The dissolution reaction for gypsum is

(7.4)

Gypsum and anhydrite are considerably more soluble than calcite and dolomite but much less soluble than the chloride minerals such as halite (NaCl) and sylvite (KCl). If calcite (or dolomite) and gypsum dissolve in fresh water at 25°C, the water will become brackish, with total dissolved solids of about 2100 and 2400 mg/ℓ for a P_CO2, range of 10^–3–10^–1 bar. The dominant anion will be SO₄^2–, so in effect we have moved into the composition phase in the Chebotarev evolution sequence. If sufficient calcite and/or dolomite and gypsum are present to enable dissolution to proceed to equilibrium, the water will evolve quickly and directly to this phase and will not evolve beyond this phase unless it comes into contact with other soluble minerals or undergoes evaporation.

The reason that in most sedimentary terrain groundwater travels a considerable distance before SO₄^2– becomes a dominant anion is that gypsum or anhydrite are rarely present in more than trace amounts. In many shallow zones these minerals have never been present or have been previously removed by groundwater flushing. Therefore, although and SO₄^2– stages can be described in terms of simple solubility constraints exerted by only two or three minerals, the process of evolution from stage to stage is controlled by the availability of these minerals along the groundwater flow paths. Given enough time, dissolution and groundwater flushing will eventually cause the readily soluble minerals such as calcite, dolomite, gypsum, and anhydrite to be completely removed from the active-flow zone in the groundwater system. Subsurface systems rarely advance to this stage, because of the rejuvenating effects of geologic processes such as continental uplift, sedimentation, and glaciation.

In deep groundwater flow systems in sedimentary basins and in some shallower systems, groundwater evolves past the stage where SO₄^2– is the dominant anion to a Cl^–-rich brine. This occurs if the groundwater comes into contact with highly soluble chloride minerals such as halite or sylvite, which in deep sedimentary basins can occur as salt strata originally deposited during the evaporation of closed or restricted marine basins many millions of years ago. The solubilities of other chloride minerals of sedimentary origin are very high. In fact, as indicated in Table 3.6, these solubilities are orders of magnitude higher than the solubilities of calcite, dolomite, gypsum, and anhydrite. Chloride minerals of sedimentary origin dissolve rapidly in water. The general occurrence of Cl^– as a dominant anion only in deep groundwater or groundwater that has moved long distances therefore can generally be accounted for by the paucity of these minerals along the flow paths. If groundwater that has not traveled far comes into contact with abundant amounts of halite, the water will evolve directly to the Cl^– phase, regardless of the other minerals present in the system. In strata of siltstone, shale, limestone, or dolomite, where Cl^– is present in minerals occurring in only trace amounts, the rate of Cl^– acquisition by the flowing groundwater is to a large extent controlled by the process of diffusion. Cl^– moves from the small pore spaces, dead-end pores, and, in the case of fractured strata, from the matrix of the porous media to the main pores or fractures in which the bulk flow of groundwater takes place. As indicated in Section 3.4, diffusion is an extremely slow process. This, and the occurrence of sulfate- and chloride-bearing minerals in limited amounts, can account for the observation that in many groundwater systems the chemical evolution of groundwater from the to SO₄^2– and Cl^– stages proceeds very gradually rather than by distinct steps over short distances as would be expected on the basis of solubility considerations alone.

The anion evolution sequence and the tendency for total dissolved solids to increase along the paths of groundwater flow are generalizations that, when used in the context of more rigorous geochemical reasoning, can provide considerable information on the flow history of the water. At this point we wish to emphasize, however, that in some groundwater flow systems the water does not evolve past the stage or past the SO₄^2– stage. It is not uncommon in some sedimentary regions for water to undergo reversals in the sequence of dominant anions. Most notable in this regard is the increase in and decrease in SO₄^2– that can occur as a result of biochemical SO₄^2– reduction. These processes are described in Section 7.5.

Large variations in the major cations commonly occur in groundwater flow systems. Since cation exchange commonly causes alterations or reversals in the cation sequences, generalization of cation evolution sequences in the manner used by Chebotarev for anions would be of little use because there would be so many exceptions to the rule. For major cation and anion data to provide greatest insight into the nature of groundwater flow systems, interpretations must include consideration of specific hydrochemical processes that can account for the observed concentrations. Examples of this approach are included in Sections 7.3 through 7.5.

Electrochemical Evolution Sequence

Recognition of the anion evolution sequence as a characteristic feature of many groundwater systems resulted from the compilation and interpretation of chemical data from regional flow systems. It is a generalization initially founded on observation and later supported by geochemical theory. We will now look briefly at another evolution sequence, referred to as the electrochemical evolution sequence. This sequence is founded on geochemical theory, but as yet has not been rigorously appraised on the basis of field measurements.

The electrochemical evolution sequence refers to the tendency for the redox potential of groundwater to decrease as the water moves along its flow paths. This tendency was first recognized by Germanov et al. (1958). As water from rain and snow enters the subsurface flow system, it initially has a high redox potential as a result of its exposure to atmospheric oxygen. The initial redox conditions reflect high concentrations of dissolved oxygen, with pE values close to 13, or, expressed as Eh, close to 750 mV at pH 7. In the organic-rich layers of the soil zone, the oxidation of organic matter commonly removes most of the dissolved oxygen. This process, represented by Eq. (7.3), causes the redox potential to decline. The question can be asked: How far does the redox potential decline as the water passes through the soil zone to the water table? It is reasonable to expect that the consumption of oxygen in the soil zone will vary depending on numerous factors, such as the soil structure, porosity and permeability, nature and depth distribution of organic matter, frequency of infiltration events, depth to water table, and temperature. Although dissolved oxygen is an important factor in the characterization of the hydrochemical nature of groundwater, very few studies of dissolved oxygen in groundwater have been reported in the literature. From the data that are available, however, the following generalizations can be drawn:

1. In recharge areas with sandy or gravelly soils or in cavernous limestones, shallow groundwater commonly contains detectable dissolved oxygen (i.e., greater than about 0.1 mg/ℓ).
2. In recharge areas in silty or clayey soils, shallow groundwater commonly does not contain detectable dissolved oxygen.
3. In areas with little or no soil overlying permeable fractured rock, dissolved oxygen at detectable levels commonly persists far into the flow system. In some cases the entire flow system is oxygenated.

The common occurrence of appreciable dissolved oxygen in shallow groundwater in sandy deposits is probably a result of low contents of organic matter in the soil and rapid rates of infiltration through the soil.

Even after dissolved oxygen is consumed to levels below detection by normal means, the redox potential can still be very high, as indicated in Section 3.9. The consumption of free molecular oxygen by bacterially catalyzed reactions that oxidize organic matter may continue until dissolved O₂ levels are considerably below the normal limits of detection. Eventually the point is reached where the aerobic bacteria involved in these reactions can no longer thrive. In the aerobic zone there are other reactions, such as those represented in Table 3.10 for the oxidation of ferrous iron, ammonia, manganese, and sulifde, that consume oxygen. Even though these oxidation processes may consume only a small portion of the total oxygen relative to the oxidation by organic matter, they can have a major effect on the chemical evolution of the water.

We will now consider what may happen as water moves deeper into the groundwater flow system. Stumm and Morgan (1970) state that in closed aqueous systems containing organic material and the other nutrients necessary for growth of bacteria, the oxidation of organic matter accompanied by consumption of O₂ is followed by reduction of . Reduction of MnO₂, if present, should occur at about the same pE or Eh as reduction, followed by the reduction of the ferric iron minerals, such as the various compounds represented by Fe(OH)₃. When sufficiently negative redox levels have been reached, the reduction of SO₄^2– to H₂S and HS^– and the reduction of organic matter to the dissolved gaseous species CO₂ and CH₄ may occur almost simultaneously. This electrochemical sequence of reduction processes is summarized in Table 3.11, with the initial processes of oxygen consumption represented in Table 3.10. Stumm and Morgan present the electrochemical evolution sequence as a phenomenon based on thermodynamic theory. They indicate that this sequence is consistent with observations of the chemical nature of nutrient-enriched lakes and batch digestors in sewage treatment facilities. With the possible exception of MnO₂ and Fe(OH)₃ reduction, the reactions described in the electrochemical evolution sequence are biologically catalyzed. The sequence of redox reactions is paralleled by an ecological succession of microorganisms, with various bacterial species adapted to the different stages of the redox sequence.

From a hydrogeologic viewpoint, the important question is whether or not the electrochemical evolution sequence occurs in the groundwater environment and, if so, where and why? The sequence, or at least parts of the sequence, are known to occur in the groundwater zone. It is known, for example, that in many areas dissolved oxygen is absent from water that recharges the groundwater zone. This is indicated by the absence of detectable dissolved oxygen in shallow wells. Presumably, the oxygen has been consumed by the processes described above. In some groundwater systems, occurs at shallow depth and diminishes in concentration as the water moves deeper into the flow system. Edmunds (1973) and Gillham and Cherry (1978) attributed this type of trend to the process of denitrification, which requires denitrifying bacteria and a moderate redox potential. It is known that in some regions groundwater has a very low redox potential. This is indicated by low SO₄^2– concentrations and H₂S odor from the water, characteristics that are attributed to the process of sulfate reduction in the presence of sulfate-reducing bacteria. Methane (CH₄) is a common constituent of deep groundwater in sedimentary basins and is observed at many locations, even in shallow groundwater. Its origin is attributed to bacterial fermentation of organic matter within the groundwater system. It is known that in some groundwater flow systems, the redox potential measured by the platinum-electrode method decreases along the apparent paths of regional flow. To illustrate this type of trend, redox potential data from two regional flow systems are presented in Figure 7.2.

In the Chebotarev evolution sequence, the gradual changes in anion composition and total dissolved solids were attributed to two limiting factors: mineral availability and rate of molecular diffusion. In the electrochemical evolution sequence, other factors must control the amount and rate of decline of the redox potential along the flow paths.

Because H₂S (or HS^–) and CH₄ are not present in significant amounts in many groundwater zones and because considerable SO₄^2– is present in these zones, it appears that it is common for groundwater not to evolve to conditions of low redox potential even during long periods of residence time. The redox reactions that would lead progressively to low redox potential probably do not proceed in many areas because of the inability of the necessary redox bacteria to thrive. The hostility of groundwater environments to bacteria is probably caused by the lack of some of the essential nutrients for bacterial growth. It may be that even in hydrogeologic regimes in which organic carbon is abundant, the carbon may not be in a form that can be utilized by the bacteria. As the emphasis in hydrochemical investigations is broadened to include organic and biochemical topics, a much greater understanding of the redox environment of subsurface systems will be developed.

7.2 Graphical Methods and Hydrochemical Facies

An important task in groundwater investigations is the compilation and presentation of chemical data in a convenient manner for visual inspection. For this purpose several commonly used graphical methods are available. The simplest of these is the bar graph. Two examples are shown in Figure 7.3. For a single sample these two graphs represent the major-ion composition in equivalents per cubic meter (or milliequivalents per liter) and in percentage of total equivalents.

The same analysis is shown on a circular graph in Figure 7.4. In Figure 7.5(a) the analysis is shown in a manner that facilitates rapid comparison as a result of distinctive graphical shapes. This is known as Stiff diagram, named after the hydrogeologist who first used it. Analysis of water with a much different composition is shown in Figure 7.5(b). The bar, circular, radial and Stiff diagrams are all easy to conduct and provide quick visual comparison of individual chemical analyses. They are not, however, convenient for graphic presentation of large numbers of analyses.

For this purpose two other diagrams are in common use. The first one, developed by Piper (1944) from a somewhat similar design by Hill (1940), is shown in Figure 7.6; the second one, introduced into the groundwater literature by Schoeller (1955, 1962), is shown in Figure 7.7. Both of these diagrams permit the cation and anion compositions of many samples to be represented on a single graph in which major groupings or trends in the data can be discerned visually. The Schoeller semilogarithmic diagram shows the total concentrations of the cations and anions. The trilinear diagram represents the concentrations as percentages. Because each analysis is represented by a single point, waters with very different total concentrations can have identical representations on this diagram. A single trilinear diagram has greater potential to accommodate a larger number of analyses without becoming confusing and is convenient for showing the effects of mixing two waters from different sources. The mixture of two different waters will plot on the straight line joining the two points. The semilogarithmic diagram has been used to directly determine the saturation indices of groundwaters with respect to minerals such as calcite and gypsum (Schoeller, 1962; Brown et al., 1972). This approach, however, is often not advisable, because of errors introduced by neglecting the effects of ion complexes and activity coefficients.

Some of the shortcomings of the trilinear graphs of the type developed by Hill and Piper are removed in the diagram introduced into the Soviet literature by S. A. Durov and described in the English-language literature by Zaporozec (1972). The basis of this diagram, shown in Figure 7.8, is percentage plotting of cations and anions in separate triangles, which in this respect is similar to the Piper diagram.

The intersection of lines extended from the two sample points on the triangles to the central rectangle fives a point that represents the major-ion composition percentage basis. From this point, lines extending to the two adjacent scaled rectangles provide for presentation of the analysis in terms of two parameters selected from possibilities such as total major-ion concentration, total dissolved solids, ionic strength, specific conductance, hardness, total dissolved inorganic carbon, or pH. Total dissolved solids and pH are represented in Figure 7.8.

The diagrams presented above are useful for visually describing differences in major-ion chemistry in groundwater flow systems. There is also a need to be able to refer in a convenient manner to water compositions by identifiable groups or categories. For this purpose, the concept of hydrochemical facies was developed by Back (1961, 1966), Morgan and Winner (1962), and Seaber (1962). The definition of hydrochemical facies is a paraphrase of the definition of facies as used by geologists: facies are identifiable parts of different nature belonging to any genetically related body or system.

Hydrochemical facies are distinct zones that have cation and anion concentrations describable within defined composition categories. The definition of a composition category is commonly based on subdivisions of the trilinear diagram in the manner suggested by Back (1961) and Back and Hanshaw (1965). These subdivisions are shown in Figure 7.9. If potassium is present in significant percentages, sodium and potassium are normally plotted as a single parameter. Definition of separate facies for the 0–10% and 90–100% domains on the diamond-shaped cation-anion graph is generally more useful than using equal 25% increments. The choice of percent categories should be made so as to best display the chemical characteristics of the water under consideration. In some situations, more subdivisions than those shown in Figure 7.9 are useful.

After arriving at a convenient classification scheme for the designation of hydrochemical facies, it is often appropriate, using maps, cross sections, of fence diagrams, to show the regional distributions of facies.

An example of a fence diagram showing the distribution of cation facies in the northern Atlantic Coastal Plain of the United States is shown in Figure 7.10. Also shown on this diagram is the generalized direction of regional groundwater flow.

In conclusion, it can be stated that there are many ways in which chemical analyses can be displayed graphically and there are many types of classifications that can be used for defining hydrochemical facies. The specific nature of the particular system under investigation usually governs the choice of graphical methods.

7.3 Groundwater in Carbonate Terrain

The theoretical framework necessary for consideration of the chemical interactions between water and carbonate minerals is outlined in Chapter 3. Garrels and Christ (1965) provide a detailed description of carbonate equilibria. The objective here is to describe how the chemistry of water evolves in various situations where groundwater flows through rocks or unconsolidated deposits comprised of significant amounts of carbonate minerals.

Open-System Dissolution

Water from rain and snow that infiltrates into terrain containing calcite and dolomite normally dissolves these minerals to saturation levels. If the dissolution occurs above the water table under conditions where abundant CO₂ is present in voids that are not entirely filled with water, the dissolution process is referred to as taking place under open-system conditions. This type of system has been described in geochemical terms in Section 3.5. If dissolution of calcite or dolomite proceeds directly to equilibrium under isothermal conditions in the open system, the chemical evolution paths and equilibrium composition of the water can be predicted. For purposes of developing a chemical evolution model, it is assumed that water moves into a soil zone where a constant partial pressure of CO₂ is maintained as a result of biochemical oxidation of organic matter and respiration of plant roots. The soil water quickly equilibrates with the CO₂ in the soil atmosphere. The water then dissolves calcite with which it is in contact in the soil pores. For computational purposes, it will be assumed that the partial pressure of CO₂ (P_CO2) is maintained at a fixed value as a result of a balance between CO₂ production and diffusion from soil.

The equilibrium values of pH and that would occur under various P_CO2, constraints prior to mineral dissolution can be computed using Eqs. (3.5), (3.18), (3.19), (3.31), and (3.32), and the method of successive approximations. Results for the P_CO2 range of 10^–4–10^–1 bar are shown as line (1) in Figure 7.11(a). This line represents the initial conditions. As dissolution of calcite or dolomite takes place, the water increases in pH and along the evolution paths for specified P_CO2 values extending upward in Figure 7.11(a) from line (1). The evolution paths are computed using a mass-balance relation for total dissolved inorganic carbon in combination with the equations indicated above. Steps along the paths are made by hypothetically dissolving small arbitrary amounts of calcite or dolomite in the water. The water composition evolves along these paths until the water is saturated.

The conditions of saturation for 15°C are represented by lines (2) and (3) for calcite and dolomite, respectively. If the temperature is higher, the saturation lines will be lower; if the temperature is lower, the lines will be higher because the solubility is greater. The positions of the evolution paths and saturation lines will be somewhat different if dissolution takes place in solutions of higher ionic strength.

Water infiltrating through the soil zone may evolve to a position on the saturation line and then evolve to disequilibrium positions off the line. For example, water under a high P_CO2 may become equilibrated with respect to calcite or dolomite in the upper horizons of the soil and then move deeper into the unsaturated zone, where different partial pressures of CO₂ exist in the soil air. If there are lower CO₂ partial pressures deeper in the unsaturated zone, the infiltrating water will lose CO₂ to the soil air. This is referred to as degassing or off-gassing. Its occurrence would cause a rise in pH of the soil water. Since degassing would normally occur much more rapidly than precipitation of carbonate minerals, the water would become supersaturated with respect to calcite or dolomite. The water would evolve above the saturation lines shown in Figure 7.11(a).

The partial pressure of CO₂ in the unsaturated zone below the CO₂ production zone in the soil is controlled mainly by the rate of gas diffusion downward from the organic-rich layers in the soil and the rate of escape to the atmosphere by way of short-circuiting paths such as deep desiccation cracks, frost cracks, root holes, and animal burrows. As a result, at some times of the year, low P_CO2 conditions can occur in the unsaturated zone below the soil. If deep infiltration occurs during these periods, conditions of supersaturation with respect to carbonate minerals will occur.

It has been indicated above that if significant amounts of carbonate minerals are present in the soil or subsoil of the unsaturated zone, dissolution to or near saturation would be expected to occur. Using a mass-balance approach, we will now determine how much mineral material must be present in order for saturation to be attained. From Figure 3.7 it is evident that at a relatively high CO₂ partial pressure of 10^–1 bar, 6.3 mmol of Ca²⁺ will occur in solution after dissolution of calcite to equilibrium under open-system conditions. Because each mole of calcite that dissolves produces 1 mol of Ca²⁺ in solution, it can be concluded that under these conditions, 6.3 mmol (0.63 g) of dissolved calcite per liter of solution is required to produce equilibrium. To determine this amount of calcite as a percentage by weight of geologic materials, it will be assumed that the materials are granular and have a porosity of 33%, and a specific gravity of 2.65. Therefore, the volumetric ratio of voids to solids is 1 : 2 and the mass of solids per liter of voids is 5300 g. If the voids are full of water and if 0.63 g of calcite from the bulk solids mass of 5300 g dissolves, the water would be saturated with respect to calcite. The 0.63 g of calcite is 0.01%, by weight of the total solids. Calcite contents of this magnitude are well below detection by the methods of mineralogical analysis normally used by geologists. This example serves to illustrate that mineral constituents present in what normally are regarded as small or even insignificant amounts can exert a strong influence on the chemistry of groundwater flowing through the materials. This generalization also applies to many other mineral species that occur in the groundwater zone.

Closed-System Conditions

In situations where there are essentially no carbonate minerals in the soil zone or in the unsaturated zone below the soil zone, infiltration water charged with CO₂ can travel to the saturated zone without much CO₂ consumption. During infiltration the CO₂ will exist in solution as H₂CO₃ and CO₂(aq) and will not be converted to . In this discussion the minor amount of CO₂ to that can occur as a result of leaching of aluminosilicate materials is neglected. The effect of these minerals on the dissolved inorganic carbon in groundwater is considered in Section 7.4.

If the recharge water infiltrates to the water table without significant CO₂ consumption and then encounters carbonate minerals along its flow paths in the saturated zone, dissolution will take place in this zone under closed-system conditions. As H₂CO₃ is converted to (see Eq. 3.54), the H₂CO₃ concentration and the CO₂ partial pressure will decline. In carbonate rocks and in most other calcareous strata there is no CO₂ replenishment below the water table. Exceptions to this generalization are discussed in Section 7.5. As in the open-system case, the water will proceed from some initial condition defined by the P_CO2 and pH to a condition of saturation with respect to the carbonate minerals present in the system. Figure 7.11(b) shows initial conditions, saturation conditions, and some representative evolution paths for closed-system dissolution. The evolution paths and saturation lines were calculated using procedures similar to the open-system case, except that P_CO2 is variable and total dissolved inorganic carbon is the sum of the initial CO₂ and the carbon from carbonate-mineral dissolution.

Comparison of Figure 7.11(a) and (b) indicates that the equilibrium pH and values that result from calcite or dolomite dissolution under open- and closed-system conditions are different. Because the solubility is greater for a given initial P_CO2, open-system pH values at saturation are lower and the and Ca²⁺ concentrations are higher. At high initial P_CO2 conditions, the difference in water chemistry between the two systems is smallest. Figure 7.11(b) indicates that it is possible, within part of the soil-zone P_CO2 range, to evolve under closed-system conditions to pH values well above 8. Under open-system conditions, however, equilibrium pH values are below 8. In carbonate terrain the pH of natural groundwater is almost invariably between 7.0 and 8.0, which suggests that open-system conditions are common.

In the discussion above, the chemical evolution of groundwater was considered within the convenient constraints of open and closed CO₂ systems under specified time-independent boundary conditions. In nature, variations in CO₂ partial pressures, soil temperatures, and slow diffusion-controlled reaction processes can cause significant deviations from the conditions prescribed in our hydrochemical models. In some situations infiltrating groundwater may proceed partway along open-system evolution paths and then move below the water table and evolve the rest of the way to saturation under closed-system conditions. Other factors, such as adsorption, cation exchange, gas diffusion, and mechanical dispersion, may influence the chemical evolution of the water. Closed-system or partly closed-system dissolution above the water table can arise in some situations. Nevertheless, open- and closed-system models provide a useful framework within which to interpret chemical data from many hydrogeologic settings. There is a need, however, for more studies of the distribution of CO₂ partial pressures in the unsaturated zone to provide a better basis for the adoption of these models in the interpretation of field data.

Incongruent Dissolution

The concept of incongruent dissolution is introduced in Section 3.5. Specific application of this concept to the calcite-dolomite-water system is presented below. The preceding discussion was based on the premise that calcite and dolomite, if present in the hydrogeologic system, dissolve independently of each other. Although Figure 7.11 shows saturation lines for both calcite and dolomite, it should be kept in mind that these lines were calculated for dissolution of these minerals in separate systems. If these two minerals occur in the same hydrogeologic system, which is often the case, they may dissolve simultaneously or sequentially. This can lead to much different equilibrium relations than those displayed in these diagrams.

In terms of equilibrium constants and activities, the saturation conditions for calcite and dolomite can be expressed as

(7.5)

(7.6)

where the subscripts c and d designate calcite and dolomite, respectively. If groundwater at 10°C dissolves dolomite to saturation and then flows into a zone that contains calcite, no calcite dissolution will occur, because the water would be saturated with respect to calcite. This conclusion is based on the K_c and K_d values listed in Table 3.7. At equilibrium with respect to dolomite, the ion-activity product [Ca²⁺][CO₃^2–] would equal , which at about 10°C is equal to K_c (Table 3.7). Comparison of and K_c values using data from Table 3.7, indicates that > K_c at temperatures below 10°C, and < K_c above 10°C. Therefore, if groundwater dissolves dolomite to equilibrium at the lower temperatures, the water will become supersaturated with respect to calcite, causing precipitation. The system evolves toward a condition whereby the rate of dolomite dissolution equals the rate of calcite precipitation. The coexisting processes of dolomite dissolution and calcite precipitation are implied in the expression incongruent dissolution of dolomite.

When groundwater dissolves dolomite to equilibrium at temperatures above 10°C and then moves into a zone where calcite exists, the water will be able to dissolve calcite because < K_c. Calcite dissolution increases [Ca²⁺] and [CO₃^2–] and the water will therefore become supersaturated with respect to dolomite. Because the dolomite precipitation reaction is so sluggish, supersaturation could persist for long periods of time with little or no dolomite precipitation. If significant amounts of dolomite were to form, however, the calcite dissolution process would be incongruent. Over long periods of time, the incongruency of the dolomite and calcite reactions may exert an important influence on the chemical evolution of the water and on the mineralogical evolution of the host rock.

When groundwater dissolves calcite to equilibrium first and then encounters dolomite, dolomite dissolves regardless of the temperature because the water must acquire appreciable Mg²⁺ activity before dolomite equilibrium is attained [Eq. (7.6)]. Even from the initial stages of dolomite dissolution, however, the water becomes supersaturated with respect to calcite as a result of the influx of [Ca²⁺] and [CO₃^2–] from the dolomite, and calcite precipitates. The dolomite dissolution would therefore be incongruent. As calcite precipitates, the water would tend to become undersaturated with respect to dolomite. If this occurs in a zone in which dolomite exists, dolomite would continue to dissolve as calcite precipitates. As a result, there would be a decrease in the Ca²⁺/Mg²⁺ molal ratio.

In the above discussion, the concept of incongruent dissolution of calcite and dolomite was illustrated by assuming that the groundwater encounters calcite and dolomite sequentially along its flow paths; that is, we let the water react with one mineral and then the other. In many hydrogeologic systems, such as those in glacial till or partly dolomitized limestone, calcite and dolomite exist together in the same strata and hence would be expected to dissolve simultaneously if contacted by water undersaturated with respect to both of these minerals. The incongruency relations would therefore be controlled by the differences in effective dissolution rates as well as temperature and P_CO2. The differences in dissolution rates determine the Ca²⁺/Mg²⁺ molal ratio. For example, if water infiltrates into a soil and becomes charged with CO₂, and then moves into a soil horizon that contains both calcite and dolomite, dissolution of both of these minerals occurs. If calcite dissolves much more rapidly than dolomite, calcite saturation would be attained much before dolomite saturation. After calcite saturation is reached, dolomite would continue to dissolve, but incongruently, until dolomite saturation is reached. The Ca²⁺/Mg²⁺ molal ratio would evolve from a high initial value to a much lower value as Mg²⁺ is contributed from dolomite and as Ca²⁺ is lost through calcite precipitation. Under these circumstances, calcite supersaturation may persist a considerable distance along the groundwater flow paths.

If, on the other hand, dolomite dissolves more rapidly than calcite, the Ca²⁺/Mg²⁺ molal ratio would be much smaller than in the case described above. This could occur if dolomite is much more abundant in the geologic materials, so the surface area of reaction would be much larger than that of calcite. If dolomite saturation is attained quickly, there would be little opportunity for calcite to dissolve. The reasoning here is similar to the case of sequential dolomite-calcite dissolution described above. The water temperature could also affect the tendency for incongruency to develop.

In conclusion, it can be stated that in groundwater systems that contain calcite and dolomite, Ca²⁺/Mg²⁺ molal ratios can develop within a wide range, both above and below unity, depending on the influence of sequential distribution, simultaneous dissolution, incongruent dissolution, CO₂ partial pressures, temperatures, and other factors. Interpretation of water composition from carbonate systems within the strict confines of simple open- and closed-system dissolution models can in some situations be misleading. Cation exchange reactions can also produce variations in the Ca²⁺/Mg²⁺ ratio of groundwater but, as indicated in the discussion above, they need not necessarily be invoked to explain these variations.

Other Factors

As indicated in Table 3.7, the solubilities of calcite and dolomite are quite strongly dependent on temperature. The solubility-temperature relations for these minerals are unusual in that larger solubilities occur at lower temperatures, because CO₂ is more soluble at lower temperature and because values of K_c and K_d are larger. Nearly all other mineral types have the reverse relationship; they are more soluble at higher temperatures. In the preceding section, the effect of temperature on the incongruency relations was noted. Our purpose now is to take a broader look at the effects of temperature on the chemical evolution of groundwater in carbonate terrain.

In climatic regions where snowfall accumulates on the ground during the winter, the largest groundwater recharge event commonly takes place in the spring-time as snowmelt infiltrates through the cold or even partially frozen soil zone and moves downward to the water table. In vast areas of Canada and the northern United States, carbonate minerals occur in abundant amounts in the soil or subsoil at very shallow depths. During spring recharge, dissolution can proceed at very low temperatures under open- or nearly open-system conditions. At depths greater than a few meters below ground surface, temperatures are normally at least several degrees higher. Calcite and dolomite-saturated water that infiltrates downward from the cold upper zone into the underlying warmer zones will become supersaturated with respect to these minerals as a result of this temperature increase.

A situation where water is initially saturated with respect to calcite at a temperature of 0°C is taken as an example. This may represent water that infiltrates through the soil during a period of spring snowmelt. If the water moves below the frost zone to depths at which the geologic materials have temperatures closer to the average annual air temperature, the water will become supersaturated with respect to calcite. If the water moves deeper in the groundwater flow system, the temperature will continue to rise as a result of the regional geothermal gradient. The water will become progressively more supersaturated, unless the temperature effect is balanced by Ca²⁺ and CO₃^2– losses as a result of calcite precipitation. At 25°C and at a CO₂ partial pressure of 10^–2 bar, calcite is half as soluble as at 0°C. This example illustrates that the total dissolved solids in groundwater do not necessarily increase along the flow paths. If the groundwater chemistry is controlled almost entirely by interactions with carbonate minerals, it is possible for differences in temperature along the flow paths to cause decreases in total dissolved solids. In nature, however, decreases caused by carbonate-mineral precipitation can be masked by increases in dissolved solids caused by dissolution of other minerals.

Considering carbonate mineral dissolution and precipitation in terms of a regional groundwater flow system, water moves from recharge areas in which temperatures can be low, to deeper zones at higher temperatures, and then back to shallow colder zones in the discharge areas. For waters that become saturated with respect to calcite and dolomite in the recharge areas, the deeper zones would be calcite or dolomite precipitation zones. In the colder discharge areas, dissolution would once again occur if carbonate minerals are present and if other mineral-water interactions have not appreciably altered the saturation levels.

In the hydrochemical evolution processes considered above, the effects of non- carbonate salts in the water were neglected. If the water contains significant contents of noncarbonate mineral-forming ions such as Na⁺, K⁺, Cl^–, and SO₄^2–, the carbonate-mineral equilibrium is influenced by the effects of ionic strength and complex-ion formation. This can be deduced from the discussions in Sections 3.3 and 3.5. Greater salinity is reflected in higher ionic strength, which in turn causes lower values for the activity coefficients of all major ions in solution (Figure 3.3). The solubilities of calcite and dolomite therefore increase. In the development of hydrochemical models, the effect of ionic strength in the fresh- to brackish-water salinity range can be taken into account quantitatively. The modeling of saline or brine solutions, however, involves greater uncertainties associated with the activity coefficient relations.

Groundwater that is influenced chemically by dissolution of calcite or dolomite is also commonly influenced by other minerals that exert some control on the concentrations of Ca²⁺ and Mg²⁺. For example, dissolution of gypsum (CaSO₄ · 2H₂O) can cause large increases in Ca²⁺ concentrations. Through the common-ion effect described in Section 3.5, this can cause supersaturation of the water with respect to calcite or dolomite or greatly limit the amount of calcite or dolomite that will dissolve when the water encounters these minerals along its flow paths. If clay minerals are present, cation exchange processes may cause large changes in the cation ratios and thereby alter the saturation levels of the water with respect to carbonate minerals. The roles of the common-ion effect and cation exchange in the chemical evolution of groundwater are described in more detail in Section 7.5.

In the development of geochemical models to describe equilibria between groundwater and carbonate minerals, the use of thermodynamic data obtained from experiments on relatively pure forms of the minerals is common practice. In natural systems, however, calcite and dolomite may deviate significant ly from the ideal composition. For example, calcite can contain as much as several percent Mg in solid solution with Ca. Impurities such as Sr and Fe commonly occur in carbonate minerals. Although these impurities may be an important source of these elements in groundwater, their effect on the equilibrium constants of calcite and dolomite is generally small. In some situations, however, oxidation and hydrolysis reactions with the impurities may cause a significant production of H⁺ and therefore a lower pH. It is necessary to emphasize that in our consideration of the carbonate system, the processes of dissolution and precipitation of carbonate minerals were isolated from the many other processes that in nature commonly occur concurrently within the hydrochemical system. In the interpretation of chemical data from real groundwater systems, it is usually necessary to take into account a more complex set of interacting hydrochemical processes.

Interpretation of Chemical Analyses

Calcite and dolomite exist in virtually all regions of the world in which sedimentary rocks are abundant. To describe the chemical evolution of groundwater in all these regions or even in a representative number of regions would be an insurmountable task, even if many chapters could be devoted to the cause. Instead, our approach will be to briefly summarize the hydrochemical characteristics of groundwater in a small number of carbonate-rock systems and then describe some geochemical interpretations developed for these systems. For this purpose, carbonate-rock aquifers in central Pennsylvania, central Florida, and south-central Manitoba were chosen. These three aquifers are located in very different climatic and hydrologic settings. The locations, geology, and groundwater conditions of the three aquifer systems are summarized in Table 7.2. Information on the aquifier system in Pennsylvania was obtained from Jacobson and Langmuir (1970) and Langmuir (1971). The Floridan system is described by Back and Hanshaw (1970) and Hanshaw et al. (1971). The hydrogeology of the portion of the Manitoban dolomite aquifer used in this comparison has been described by Goff (1971). Render (1970) reported on a regional study of this aquifer system.

In the hydrochemical investigations, careful pH measurements were made in the field. The charge-balance errors of the chemical analyses used in the data compilation are less than 5% (acceptable limit of charge-balance error indicated in Section 3.3).

In the study in Pennsylvania, chemical analyses of 29 springs and 29 wells were conducted. Of the 29 wells, 20 are in dolomite and 9 in limestone. Twenty-two of the springs discharge from limestone and 7 from dolomite. In the hydrochemical investigation of the Floridan aquifer, samples from 53 wells were analyzed. In this discussion, data from 39 of the wells are used. The other wells were excluded to avoid the effects of mixing in saltwater zones near the ocean. In the hydrochemical investigation of the Manitoban aquifer, samples from the 74 wells were analyzed.

The mean values and standard deviations of the temperature, major-ion concentrations, pH, P_CO2, and saturation indices for calcite, dolomite, and gypsum for groundwater in the three study areas are listed in Table 7.3, which indicates important similarities and differences between the three areas. In each of the areas is the dominant anion and SO₄^2– the second most abundant anion. Concentrations of Cl^– are generally very low. The average content in the Manitoban aquifer is more than twice as large as the averages for the Floridan aquifer and for the spring samples from the Pennsylvania aquifer. The average value for the well samples from the Pennsylvanian study area is between these two extremes. The average pH values for the Manitoban and Floridan aquifers are similar. The pH of the Pennsylvanian aquifer is slightly lower. Nearly all samples, however, lie in the relatively narrow pH range 7–8. In the Manitoban aquifer, the average Ca²⁺/Mg²⁺ molal ratio is less than unity, whereas in the other areas it is greater than unity.

	Pennsylvania limestone and dolomite aquifer				Florida limestone aquifer		Manitoba dolomite aquifer
	Springs		Wells
Parameter		σ		σ		σ		σ
Temperature (°C)	10.9	1.3	18.0	1.2	24.4	1.2	5.1	0.9
pH	7.37	1.5	7.47	0.3	7.69	0.25	7.61	0.25
K+	1.6	0.6	1.5	1.4	1.0	0.8	9	7
Na+	3.8	1.8	3.1	3	7.9	5.3	37	36
Ca2+	48	11	55	22	56	25	60	15
Mg2+	14	11	28	14	12	13	60	21
	183	43	265	83	160	40	417	101
Cl–	8.2	3.5	10	9	12	9	27	26
SO42-	22	5	20	15	53	94	96	127
PCO2 (atm)	10–2.2±0.15		10–2.15±0.43		10–2.51±0.35		10–2.11±0.33
SIcal‡	–0.39	0.25	–0.16	0.12	+0.12	0.18	+0.44	0.17
SIdol‡	–1.2	0.74	–0.36	0.23	–0.23	0.49	+0.27	0.35
SIgyp‡	–2.0	0.14	–2.2	0.46	–2.3	0.8	–1.8	0.53

*, mean.
†σ, standard deviation.
‡Saturation index expressed in logarithmic form:
SI_cal = log ([Ca²⁺][CO₃^2–]/K_cal)
SI_dol = log ([Ca²⁺][Mg²⁺][CO₃^2–]²/K_dol)
SI_gyp = log ([Ca²⁺][SO₄^2–]/K_gyp)
SOURCE: Back, written communications; Goff, 1971; and Langmuir, 1971.

In our interpretation of this hydrochemical information we will begin by noting that the calculated P_CO2 values for the groundwaters in all three areas are considerably above the P_CO2 of the earth’s atmosphere (10^–3.5 bar). This indicates that the groundwater in these aquifers became charged with CO₂ during infiltration through soil zones. A second important observation is that there are large groundwater temperature differences between the three areas. The Floridan aquifer is warmest, with temperatures close to 25°C. In the Pennsylvanian aquifer the average groundwater temperature is close to 11°C and in the Manitoban aquifer the temperatures are near 5°C.

The pH of water in the three aquifers is significant ly above 7 and below 8. Figure 3.5(a) indicates therefore that the dissolved inorganic carbon exists almost entirely as . The concentrations of are highest in groundwater in the Manitoba aquifer, which indicates that more calcite or dolomite has dissolved in the water in this aquifer than in the other aquifers. The amount dissolved in the Pennsylvanian aquifer is intermediate between the Manitoban and Floridan aquifers. These differences can be attributed to three main factors. The first factor is temperature. As would be expected from the solubility considerations, the coldest water has the highest content of carbonate-mineral dissolution products. This cannot account for all the differences, however. The second factor is the partial pressure of CO₂. The Manitoban water has the highest calculated partial pressure and the Floridan water has the lowest. The differences are large enough to account for much of the difference in values. Trainer and Heath (1976) have attributed the relatively low CO₂ partial pressures in groundwater in the Floridan aquifer to the occurrence of permeable sands in the main recharge areas of this aquifer. The region of major recharge is shown in Figure 7.12(a). These authors suggest that relatively little CO₂ is produced in the soil zone in these areas because of the lack of abundant organic matter. They also suggest that because of the high permeability of the sand, CO₂ readily escapes from the soil to the atmosphere.

The third factor is the degree of saturation with respect to calcite and dolomite. In this regard the procedure of Langmuir (1971) is adopted; a sample is designated as being saturated if its saturation index, expressed in logarithmic form, is in the range –0.1 to +0.1. Sixty-two percent of the Manitoban samples were saturated with respect to both calcite and dolomite, 12% were supersaturated, and 8%, were significant ly undersaturated. Sixty-six percent of the Floridan samples were supersaturated with respect to calcite, 24% were saturated, and 10% were undersaturated. With respect to dolomite, 59%, were supersaturated, 21%, saturated, and 20% undersaturated. Results for the Pennsylvanian springs and well samples are very different: 20% were saturated and 80% were undersaturated with respect to calcite. With respect to dolomite, 4% were saturated and the rest were undersaturated. If all the undersaturated waters in the Pennsylvanian aquifer were to be brought to saturation by dissolution of calcite or dolomite, the average and pH values would be much closer to the average values for the Manitoban aquifer.

Since only 10% of the Floridan samples are undersaturated with respect to calcite, dissolution to saturation for these waters would not greatly increase the mean and pH values.

It is reasonable at this point to draw the conclusion that conditions of disequilibrium (i.e., undersaturation or supersaturation) are not uncommon in carbonate aquifers. One of the most enigmatic of disequilibrium conditions in hydrogeochemical systems is the existence of undersaturation with respect to calcite and dolomite in situations where these minerals occur in abundance. Laboratory experiments on rates of calcite dissolution indicate that equilibrium should be achieved in a matter of hours or days (Howard and Howard, 1967; Rauch and White, 1977), and yet in the Pennsylvanian and Floridan carbonate-rock aquifers, much older water in contact with calcite and dolomite persists in a state of undersaturation. Dye tracer tests conducted by Jacobson and Langmuir (1970) in parts of the Pennsylvanian aquifer indicated groundwater residence times of 2–6 days over flow distances of about 7000 m. They concluded that the residence times of many of the spring waters are generally somewhat longer than 2–6 days and that the waters sampled from the wells are much older than this. Langmuir (1971) noted that the pH and values of the spring waters tend to increase with their subsurface residence times. A much larger percentage of the well samples was saturated because the water had sufficient time to equilibrate with the calcite and dolomite in the aquifer. This investigation suggests that in field situations, weeks or even months of residence time can be necessary for dissolution to proceed to equilibrium with respect to calcite and dolomite. Because none of the spring or well waters was supersaturated with respect to calcite or dolomite, Langmuir concluded that the solubilities of calcite and dolomite based on thermodynamic data represent the controlling limits on the concentrations of Ca²⁺, Mg²⁺, , and H⁺ in the groundwater of this carbonate-rock system. Langmuir also concluded that the evolution of the water chemistry roughly follows the open-system dissolution model. At a more detailed level of analysis, he noted that incongruent dissolution of dolomite at times of low water-table levels and dilution by recharging groundwaters at times of higher water levels are processes that account for many of the data trends, including the Ca²⁺/Mg²⁺ molal ratios.

The few undersaturated samples from the Manitoban aquifer represent the effect of short local flow paths along fracture or bedding plane conduits in recharge areas. Although detailed age estimates cannot be derived from existing data, these waters are expected to be very young.

In the Floridan aquifer, where groundwater is much older, widespread conditions of undersaturation with respect to calcite and dolomite [Figure 7.12(b)] are much more perplexing than in the Pennsylvanian aquifer. Average velocities in the Floridan aquifer determined by ¹⁴C dates are 8 m/y (Back and Hanshaw, 1970). Within the region of undersaturation, the groundwater attains ages of hundreds to thousands of years. Back and Hanshaw suggest that perhaps in some areas a significant amount of water reaches the aquifer through sand-filled solution openings and has not been in intimate contact with the limestone. They also suggest that armoring of the limestone surface by inorganic ionic species or by organic substances may produce a state of pseudo-equilibrium between crystal surfaces and the solution. There is also the possibility that some of the well samples appear undersaturated because the well water represents a mixture of waters of different compositions that flow into the well bores from different strata or zones within the aquifer. Most of the wells in the Floridan aquifer have intake zones over large vertical intervals. The occurrence of undersaturation in waters that are a mixture of two or more saturated waters was established by Runnels (1969) and Thraikill (1968) and was demonstrated in computer simulation studies by Wigley and Plummer (1976).

In an extensive part of the Floridan aquifer, groundwater is significant ly supersaturated with respect to calcite and dolomite. Back and Hanshaw (1970) and Langmuir (1971) suggest that this is caused by dissolution of trace amounts of gypsum and that the condition of supersaturation is maintained by an imbalance in rates of gypsum dissolution relative to precipitation rates of calcium carbonate (calcite or aragonite). This interpretation is consistent with the results of a kinetically based model of water chemistry evolution in this aquifer described by Palciauskas and Domenico (1976). These authors have developed a mathematical framework that indicates that the distance that groundwater must travel to attain saturation with respect to individual mineral phases increases with increasing rates of mixing and velocity and decreases with increasing rates of reaction. Their analysis shows that steady-state chemical concentrations can exist and can cause a steady level of supersaturation or undersaturation. This can occur when the rate of production of one or more dissolved species due to the dissolution of one mineral species is balanced by the rate of consumption of these species by precipitation of a second mineral species.

Much of the water in the Manitoban aquifer is supersaturated with respect to calcite and dolomite. In Figure 7.13, the water chemistry expressed in terms of pH, , Ca²⁺, and Mg²⁺ is compared to the simple open-system models for the dissolution of dolomite and calcite separately and in sequence. This comparison indicates that the data generally plot above the equilibrium lines (i.e., above the levels that would be attained if the water evolved directly to saturation under open-system dissolution). Cherry (1972) attributed this condition of disequilibrium to the combined influence of temperature change, degassing, cation exchange, and the common-ion effect caused by gypsum dissolution. Most of the recharge to the aquifer occurs in areas where the aquifer is overlain by glacial till. The till is rich in dolomite, calcite, quartz, feldspars, and clay minerals, and at shallow depth has small amounts of gypsum. A small part of the supersaturation is caused by the increase in temperature that occurs as the water moves from the colder zone in the upper meter or two of soil into the deeper parts of the flow system.

In some recharge areas, it is likely that during part of the year the CO₂ partial pressure in the unsaturated zone below the soil is often lower than the partial pressures in the organic-rich soil horizons in which CO₂ is generated. If CO₂ in the infiltrating recharge water degasses as it flows through this zone, the pH of the water would rise. This could account for the fact that in Figure 7.13, the water composition expressed as , Ca²⁺, and Mg²⁺ versus pH generally plots above the equilibrium lines (Cherry, 1972).

One of the most striking aspects of hydrochemical data from the three aquifer systems described above is a rather common occurrence of disequilibrium with respect to calcite-dolomite-water interactions. Because of this, one might be inclined to question the use of equilibrium concepts as an important means of interpreting hydrochemical data from carbonate rocks. However, the equilibrium concepts provided a useful framework for interpretation of the field data. Recognition of the deviations from thermodynamic equilibrium and the development of hypotheses to account for these deviations are an important part of the interpretive process. Eventually, it may be possible to interpret hydrochemical data from field settings within a quantitative framework that includes equations that describe the irreversible and kinetically controlled parts of the system, combined with the hydrodynamic processes of transport.

Hydrochemical data from aquifer systems can be used to develop interpretations of the evolution of aquifer permeability. For example, in the parts of the aquifers that are undersaturated with respect to calcite or dolomite, flowing groundwater is dissolving the aquifer rock. The porosity and permeability are therefore increasing. In terms of human history, these changes are probably imperceptible, but over periods of geologic time they are the basis for the development of permeability networks and even major landscape alterations. This aspect of groundwater processes is considered further in Chapter 11.

7.4 Groundwater in Crystalline Rocks

Crystalline rocks of igneous or metamorphic origin generally have at least one characteristic in common: they contain appreciable amounts of quartz and aluminosilicate minerals such as feldspars and micas. These minerals were originally formed at temperatures and pressures far above those occurring at or near the earth’s surface. On the land surface, in the soil zone, and in the groundwater zone to depths of many hundreds or thousands of meters, these minerals are thermodynamically unstable and tend to dissolve when in contact with water. The dissolution processes cause the water to acquire dissolved constituents and the rock to become altered mineralogically.

As in the chemical evolution of groundwater in carbonate rocks, the dissolution of feldspars, micas, and other silicate minerals is strongly influenced by the chemically aggressive nature of water caused by dissolved CO₂. When CO₂ charged waters that are low in dissolved solids encounter silicate minerals high in cations, aluminum, and silica, cations and silica are leached, leaving an aluminosilicate residue with increased Al/Si ratio. This residue is usually a clay mineral such as kaolinite, illite, or montmorillonite. The cations released to the water are normally Na⁺, K⁺, Mg²⁺, and Ca²⁺. Another consequence of this process of incongruent dissolution is a rise in pH and in concentration. Equations that can be used to describe these chemical changes in the water and host rock, and interpretations of hydrochemical data from igneous and metamorphic rocks, are described below.

Theoretical Considerations

Of all the minerals with which groundwater comes into contact, quartz is the most abundant, both in areal distribution and bulk composition. This discussion will therefore commence with consideration of quartz dissolution and solubility. The solubility of quartz (SiO₂) can be characterized (Stumm and Morgan, 1970) by the following equilibria (K values at 25°C):

The dissolved silicon species can also be written in the form H₂SiO₄, , and so on, which portrays their acidic nature. With these equations it can be shown that in the pH that includes nearly all groundwater (pH 6–9), the dominant dissolved silicon species is Si(OH)₄, At high pH values, other species are dominant in solution, and silica is more soluble. The results of analyses of Si concentrations in water are generally expressed as SiO₂. Expressed in this manner, quartz solubility is only about 6 mg/ℓ at 25°C (Morey et al., 1962). There is considerable evidence to indicate, however, that an amorphous or noncrystalline form of SiO₂, rather than quartz, controls the solubility of SiO₂ in water. The solubility of amorphous silica is approximately 115 to 140 mg/ℓ at 25°C (Krauskopf, 1956; Morey et al., 1964). The solubility increases considerably with temperature. Over long periods of time amorphous silica can evolve toward a crystalline structure and eventually become quartz.

Based on the solubility of amorphous silica and the abundance of quartz in most hydrogeologic systems, one might expect that SiO₂ would occur in major concentrations in most groundwaters. In nature, however, this is not the case. Davis (1964) compiled thousands of groundwater analyses from various areas in the United States and found that values for dissolved SiO₂ typically range from 10 to 30 mg/ℓ, with an average value of 17 mg/ℓ. Studies done elsewhere indicate that these values are reasonably representative on a global scale. Groundwater is therefore almost invariably greatly undersaturated with respect to amorphous silica. Quartz and amorphous silica generally do not exert an important influence on the level of silica in groundwater. More important in this regard are aluminosilicate minerals such as feldspars and micas.

From studies of the mineralogical and chemical nature of weathered igneous and metamorphic rocks and from thermodynamic considerations, it is known that the feldspar minerals are altered to clay minerals and other decomposition products. Table 7.4 indicates some of the common reactions that describe these dissolution processes.

Gibbsite-kaolinite
Na-montmorillonite-kaolinite
Ca-montmorillonite-kaolinite
Illite-kaolinite
Biotite-kaolinite
Albite-kaolinite
Albite-Na-kaolinite
Microcline-kaolinite
Anorthite-kaolinite
Andesine-kaolinite

­

For simplicity the feldspar minerals will be considered only in terms of idealized end members; K-feldspar, Na-feldspar (albite). and Ca-feldspar (anorthite). In nature, however, feldspars contain impurities. Many feldspar minerals contain Na and Ca in various ratios as solid-solution mixtures of the two Na and Ca end members. Also included in Table 7.4 are reactions that describe the alteration of clay minerals. The incongruent dissolution reactions in Table 7.4 are written simply by introducing the appropriate dissolved species and then adjusting for mass balance in the normal manner. A major assumption inherent in this approach is the conservation of Al. That is, because the solubilities of aluminum compounds in water are extremely low, the total concentration of Al species (including complexes and polymers) removed from the solid phase is assumed to be negligible. The dissolution of feldspars is therefore assumed to produce mineral products that include all the Al removed from the feldspars. Field and laboratory studies have shown that in most circumstances this assumption is reasonable.

We will now make use of thermodynamic data within an equilibrium framework to gain some insight into some of the more specific results of groundwater interactions with the feldspars and clays. Consider, for example, the albite dissolution reaction in Table 7.4. Expressed in mass-action form, it becomes

(7.11)

where K_alb-kaol is the equilibrium constant and the bracketed quantities are activities. In this development the activities of the mineral phases and water are taken as unity. This is a valid approach when considering minerals of ideal compositions in nonsaline solutions. Equation (7.11) can be expressed in logarithmic form as

(7.12)

(7.13)

which indicates that the equilibrium condition for the albite-kaolinite reaction can be expressed in terms of pH and activities of Na⁺ and Si(OH)₄. The kaolinite-Na montmorillonite reaction and the gibbsite-kaolinite reaction (Table 7.4) can be expressed in terms of Na⁺, Si(OH)₄, and H⁺ or pH. These equilibrium relations are the basis for construction of diagrams known as stability diagrams or as activity-activity diagrams. Examples of these diagrams are shown in Figure 7.14. The lines that separate the mineral phases of these diagrams represent equilibrium relations such as Eq. (7.11). Since minerals in real systems do not have ideal chemical compositions, the stability lines based on thermodynamic data for relatively pure mineral phases probably do not accurately represent real systems. Nevertheless, these types of diagrams have been found by many investigators to serve a useful purpose in the interpretation of chemical data from hydrogeological systems.

It is apparent from Table 7.4 that the incongruent dissolution of feldspars, micas, and clays involves consumption of H⁺. Production of CO₂ in the soil zone is usually considered to be the main source of H⁺. As these reactions proceed, there is a progressive increase in pH of the water. If the reactions occur in the soil zone or elsewhere in the unsaturated zone where CO₂ replenishment is significant, H₂CO₃, which is controlled by the partial pressure of CO₂ [Eq. (3.18)], remains constant while the concentrations and CO₃^2– increase. The concentration of total dissolved inorganic carbon therefore increases. If the reactions occur below the water table, where CO₂ replenishment does not occur, H⁺ consumption causes H₂CO₃ decline, P_CO2 decline, increase, and CO₃^2– increase, while the concentration of total inorganic carbon remains constant. Within this theoretical framework it can be seen that if the reactions proceed far enough, groundwater in rocks comprised of feldspar and mica can acquire pH values above 7 or 8, and concentrations of many tens or even hundreds of milligrams per liter.

The stoichiometries of the dissolution reactions for calcite and Ca-feldspar (anorthite) are identical; that is, for every mole of Ca²⁺ that goes into solution, 2 mol of H⁺ are consumed. The charge balance of cations and anions in solution is maintained as H₂CO₃ dissociates to form and CO₃^2–, as can be deduced from Figure 3.5(a). Although in theory Ca--type groundwater can evolve in rocks or unconsolidated deposits that contain Ca-feldspar, in nature this is uncommon, probably because of slow dissolution rates that develop as the feldspar acquires coatings of clay, which forms as a product at the incongruent reaction.

We will now consider the chemical evolution that may occur when fresh, slightly acidic water such as rain infiltrates through geologic materials in which feldspars are the only mineral phases that undergo significant dissolution. An initial assumption is that only Na-feldspar dissolves at a significant rate. When dissolution begins, the water contains negligible concentrations of Si(OH)₄, and Na. As the concentrations of these constituents increase, the water composition, expressed in terms of Si(OH)₄ and Na⁺/H⁺, will plot in the gibbsite stability field of Figure 7.14(a). This indicates that from a thermodynamic viewpoint, Na-feldspar will dissolve incongruently to produce gibbsite and dissolved products. As dissolution continues, Si(OH)₄ and the [Na⁺]/[H⁺] ratio increase and the water composition moves through the gibbsite stability field into the kaolinite field. In the kaolinite field, incongruent dissolution of Na-feldspar produces kaolinite. Some of the gibbsite formed during the early stage is converted to kaolinite. As dissolution of the feldspar continues, the values of Si(OH)₄ and [Na⁺]/[H⁺] increase further and the water chemistry evolves to the Na-montmorillonite stability field or more directly toward the Na-feldspar field. When the composition evolves to the boundary of the Na-feldspar field, equilibrium with respect to this feldspar is attained. Feldspar dissolution then ceases. For water to achieve equilibrium with respect to feldspar minerals, long periods of time and sluggish flow conditions are required. The water, however, is in equilibrium or near equilibrium with at least one other mineral phase. When the water composition plots in the kaolinite field, for example, equilibrium or near equilibrium exists with respect to this mineral. If the water composition plots on the boundary between kaolinite and montmorillonite, equilibrium or near equilibrium exists with respect to both these minerals.

Laboratory Experiments

The preceding discussion of silicate mineral dissolution was based on stoichiometric concentrations and on equilibrium concepts. This approach indicates nothing about the rates at which dissolution takes place or about the microscopic nature of the dissolution processes. For this type of information, laboratory experiments are useful.

Experiments on silicate mineral dissolution reported in the literature can generally be placed in two categories. Experiments in the first category involve dissolution systems where water and minerals are reacted in containers in which there is no through-flow (Garrels and Howard, 1957; Wollast, 1967; Houston, 1972). The second category includes experiments in which water is passed through mineral materials packed as porous media in cylindrical containers (Bricker, 1967; Bricker et al., 1968; Deju, 1971). Experiments in both categories have indicated that dissolution of feldspars and micas proceeds in two main stages. The first stage, which occurs in a matter of minutes after water is brought in contact with the mineral surfaces, involves the exchange of cations on the mineral surfaces for hydrogen ions in the water. This exchange is followed by a much slower and gradually decreasing rate of dissolution. The dissolution stage contributes appreciable amounts of dissolved products to the water over a period of hours or days before the dissolution is normally congruent. During the second stage dissolution gradually becomes incongruent.

The type of results that have been obtained from silicate-mineral dissolution experiments in which there was no water through-flow (Bricker, 1967; Houston, 1972) are shown in schematic form in Figure 7.15. In these experiments the increases in the rates of concentration in the solution are controlled by the kinetics of mineral dissolution. If the mineral occurs in a porous medium, however, and if water is flowing through the medium, the concentration at a given point along a flow path will depend on dissolution kinetics and on the flow rate. If the flow rate is rapid compared to the rate of mineral dissolution, the concentration of dissolution products at a specified distance along the flow path may be small compared to the concentrations achieved after the same period of leaching under no-flow conditions. This topic is discussed further in Section 7.8.

Although experiments on the dissolution of feldspars and other silicate minerals in aqueous solutions have been conducted by numerous investigators, the mechanisms that control the slow rate of dissolution of these minerals are still problematic. For feldspar, Petrovic et al. (1976) summarized the hypotheses that have been advanced to account for the slow dissolution rates. They indicate that numerous authors have suggested that the dissolution rate is controlled by the rate of diffusion of ions through layers or coatings on the mineral surfaces. For example, continuous coatings of hydrated amorphous silica-alumina precipitates have been suggested by some investigators; others favor hypotheses involving crystalline precipitates through which diffusion is presumed to occur. In another hypothesis it is presumed that diffusion occurs through a residual layer of leached feldspar consisting mainly of silica and alumina formed on feldspar surfaces. Based on detailed examination of actual surfaces of feldspar grains that had undergone appreciable dissolution in distilled water, Petrovic and coworkers concluded, however, that even when there is no significant layer or coating on feldspar surfaces, dissolution during the second stage is very slow. They did this by examining in great detail the nature of feldspar surfaces at which dissolution in laboratory vessels had occurred. As a result of this work, the concept of relatively thick continuous coatings of incongruent dissolution products on silicate minerals is now in doubt.

The discussion above indicated in a general way how silicate minerals can influence the chemical evolution of groundwater in silicate terrain. It should be kept in mind, however, that groundwater in real hydrogeologic systems reacts simultaneously with a large number of silicate minerals that have nonideal compositions. The solid products that form on the mineral surfaces as a result of incongruent dissolution are in some cases amorphous substances that require long periods of time for conversion to crystalline forms. The amorphous and clay mineral dissolution products commonly have appreciable cation exchange capacities and therefore have the capability of altering the cation ratios in the groundwater. For the water to evolve toward equilibrium with respect to the primary silicates such as feldspars, it is necessary for the concentrations of Si(OH)₄ and cations to progressively increase as the dissolution proceeds. If the reaction products in the pore water are continually flushed out by groundwater flow at rates that are appreciable relative to the reaction rates, equilibrium with respect to primary silicate minerals will never be attained. The nature of the clay-mineral weathering products produced in the system can therefore be dependent on the hydrodynamic and hydrochemical conditions as well as on mineralogic factors. An example of the interpretation of hydrochemical data from granitic rock using both hydrodynamic and mineral dissolution concepts is provided by Paces (1973).

In the next section, interpretations of chemical analyses of groundwater from silicate terrain are briefly appraised in light of the theoretical considerations developed above.

Interpretation of Field Data

A group of chemical analyses of samples from wells, springs, and stream baseflow from crystalline rock terrain (granites, diorites, basalts, and amphibolites) in various parts of the world are shown in Table 7.5. All these waters have very low major-ion concentrations. Without exception, is the dominant anion and SiO₂ is present in major concentrations relative to the cations. The anions Cl^– and SO₄^2– occur in only minor or trace concentrations. Their occurrence can normally be attributed to atmospheric sources, to the decomposition of organic matter in soil, and to the trace impurities in rocks and minerals. K⁺ is generally the least abundant of the cations.

	Location*	Number	pH		Cl–	SO42-	SiO2	Na+	K+	Ca2+	Mg2+
(1)	Vosges, France	51	6.1	15.9	3.4	10.9	11.5	3.3	1.2	5.8	2.4
(2)	Brittany, France	7	6.5	13.4	16.2	3.9	15.0	13.3	1.3	4.4	2.6
(3)	Central Massif, France	10	7.7	12.2	2.6	3.7	15.1	4.2	1.2	4.6	1.3
(4)	Alrance Spring F, France	77	5.9	6.9	< 3	1.15	5.9	2.3	0.6	1.0	0.4
(5)	Alrance Spring A, France	47	6.0	8.1	< 3	1.1	11.5	2.6	0.6	0.7	0.3
(6)	Corsica	25	6.7	40.3	22.0	8.6	13.2	16.5	1.4	8.1	4.0
(7)	Senegal	7	7.1	43.9	4.2	0.8	46.2	8.4	2.2	8.3	3.7
(8)	Chad	2	7.9	54.4	< 3	1.4	85	15.7	3.4	8.0	2.5
(9)	Ivory Coast (Korhogo, dry season)	54	5.5	6.1	< 3	0.4	10.8	0.8	1.0	1.0	0.10
(10)	Ivory Coast (Korhogo, wet season)	59	5.5	6.1	< 3	0.5	8.0	0.2	0.6	< 1	< 0.1
(11)	Malagasy (high plateaus)	2	5.7	6.1	1	0.7	10.6	0.95	0.62	0.04	0.12
(12)	Sierra Nevada, Calif. (ephemeral springs)		6.2	2.0	0.5	1.0	16.4	3.03	1.09	3.11	0.70
(13)	Sierra Nevada, Calif. (perennial springs)		6.8	54.6	1.06	2.38	24.6	5.95	1.57	10.4	1.70
(14)	Kenora, NW Ontario (unconfined aquifer)	12	6.3	24.0	0.6	1.1	18.7	2.07	0.59	4.8	1.54
(15)	Kenora, NW Ontario (confined aquifer)	6	6.9	59.2	0.7	0.8	22.1	3.04	1.05	11.9	4.94

It should be noted that Cl^– and SO₄^2– are not significant constituents in silicate rocks and there is no tendency toward development of SO₄^2– and Cl^– facies as groundwater moves along flow paths in these rocks. This is the case even in regional flow systems where flow paths and water ages are very large. The Chebotarev hydrochemical evolution sequence is therefore not relevant in these systems.

The geochemical interpretation of chemical analyses of water from silicate- mineral terrain commonly involves two main approaches. The first involves plotting of data on stability diagrams to determine what may be the stable alteration products. The other approach involves calculation of reaction sequences that can account for the observed concentrations‘ of major cations, and H⁺.

Numerous investigators have observed that in igneous terrain nearly all groundwaters within several hundred meters of ground surface, and groundwater-derived surface waters such as springs and baseflow, plot in the kaolinite fields of stability diagrams such as those in Figure 7.14 (Garrels, 1967; Garrels and MacKenzie, 1967; Tardy, 1971; Bricker et al., 1968; Bottomley, 1974). A small percentage of samples plot in the montmorillonite fields and hardly any occur in the gibbsite, mica, or feldspar fields or exceed the solubility limit of amorphous silica. This suggests that alteration of feldspars and micas to kaolinite is a widespread process in groundwater flow systems in igneous materials. In a few investigations this has been substantiated by investigations of the surface coatings on the primary igneous materials. In general, however, there is little information on the weathering products that form in these subsurface systems, other than what can be inferred from water chemistry and stability diagrams. Unstable amorphous precipitates or metastable clay mineral intermediates may persist for long periods of time before clay minerals actually crystallize.

The second interpretive approach is to model the water chemistry through calculation procedures. This can be done by reacting the primary minerals to produce clay minerals and dissolved products or by reconstituting the primary minerals through combining the clay minerals with the dissolved products observed in the water. To illustrate the mineral reconstitution approach, we will use an example presented by Garrels and MacKenzie (1967) in an interpretation of the geochemical evolution of ephemeral spring water in a granite area of the Sierra Nevada of California. The calculations are summarized in Table 7.6. At the top of this table the average concentrations of dissolved constituents in the spring water are listed. Below this, the mean concentrations in snow samples are indicated. These values are assumed to be representative of water that recharges the groundwater zone feeding the springs. To obtain the concentrations derived from the rock during subsurface flow, the snow values are subtracted from the mean spring concentrations. A slight deficiency of anions results after this subtraction is made. This imbalance was corrected by assigning a slightly higher value. As a first step in the reconstitution of primary granitic minerals from the water chemistry, kaolinite is converted to plagioclase in an amount that consumes all the Na⁺ and Ca⁺ in the water (step 2, Table 7.6). Kaolinite is chosen as the secondary mineral because all the analyses of spring water plot in the kaolinite stability field of diagrams such as those shown in Figure 7.14. Garrels and MacKenzie (1967) note that the calculated plagioclase feldspar resulting from this step is, in fact, similar to that found in the rocks of the region. In the next step, all Mg²⁺ and enough K⁺, , and SiO₂ are reacted with kaolinite to form the biotite mica. The small residue of K⁺, , and SiO₂ is then reacted to form K-feldspar. After this step a residue of 4% of the total original silica remains. This is within the limits of error of the original values of concentration used for the mean composition of the spring water. Garrels and MacKenzie (1967) conclude that the reactions work out too well to leave much doubt that the system is indeed a closed system reacting with CO² and that the weathering product is kaolinite.

Reaction (coefficients × 10-4)		Water concentrations (mol/ℓ × 10–4)								Mineral products (mol/ℓ × 10–4)
		Na+	Ca2+	Mg2+	K+		SO42–	Cl–	SiO2
	Initial concentrations in spring water	1.34	0.78	0.29	0.28	3.28	0.10	014	2.73
(1)	Minus concentrations in snow water	1.10	0.68	0.22	0.20	3.10	–	–	2.70
(2)	Change kaolinite back into plagioclase
	1.23Al2Si2O5(OH)4 + 1.10Na+ + 0.68Ca2+ + 2.44 + 2.20SiO22– =
	1.77Na0.62Ca0.38Al1.38Si2.62O8 + 2.44CO2 + 3.67 H2O	0.00	0.00	0.22	0.20	0.64	0.00	0.00	0.50	1.77Na0.62Ca0.38 feldspar
(3)	Change kaolinite back into biotite
	0.037Al2Si2O5(OH)4 + 0.073K+ + 0.22Mg2+ + 0.15SiO2 + 0.51 = 0.0073
	KMg3AlSi3O10(OH)2 + 0.51CO2 + 0.26H2O	0.00	0.00	0.00	0.13	0.13	0.00	0.00	0.35	0.073 biotite
(4)	Change kaolinite back into K-feldspar
	0.065Al2Si2O5(OH)4 + 0,13K+ + 0,13 + 0.26SiO22– =
	0.13KAlSi3O8 + 0.13CO2 + 0.195H2O	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.12	0.13 K-feldspar

An alternative computational approach is to react a specified group of primary minerals with CO²-charged water to produce the observed cation and concentrations. This approach has been used by Cleaves et al. (1970) and Bottomley (1974). If reasonable assumptions can be made regarding the initial P_CO2, the pH of the water can also be accounted for. The difference between the mineral reconstitution approach and the mineral dissolution approach is just a matter of bookkeeping. Adherence to stoichiometric reactions and the mass- and charge-balance principles is inherent in both methods. It is perhaps somewhat surprising that although terrain characterized by silicate minerals has many different mineral species and many variations from ideality in mineral compositions, it is often possible to account for the observed water chemistry using a relatively small number of reactions with minerals of ideal composition. More rigorous analyses of the chemical evolution of groundwater in silicate terrain are currently hindered by the lack of suitable information on reaction kinetics, on the behavior of mineral assemblages of nonideal compositions, and on the effects of dispersion and other factors. The chemical evolution of groundwater that moves to great depth in crystalline rock is influenced by increases in temperature and pressure. The necessity of incorporating these two factors renders the interpretative process much more difficult. Some groundwater systems in terrain formed primarily of silicate minerals have water compositions that are very anomalous when considered in light of the generalities presented above. For example, in some areas pH values exceed 9 or 10 and SiO₂ concentrations exceed 100 mg/ℓ. The reader is referred to Klein (1974) for an example of a study of this type of groundwater.

7.5 Groundwater in Complex Sedimentary Systems

In Sections 7.3 and 7.4, the geochemical evolution of groundwater in carbonate rocks and in relatively simple crystalline rock assemblages was described. Many sedimentary rocks or unconsolidated deposits, however, consist of mixed assemblages of minerals derived from various sedimentary, igneous, or metamorphic sources. Even individual strata commonly comprise mixed mineralogic assemblages. The assemblages can vary from bed to bed in layered sequences. These variations can cause large differences in the chemistry of groundwater from bed to bed and from region to region. We will now look at the factors that control these variations and at some approaches that can be used in the interpretation of data from these systems.

Order of Encounter

One of the most important factors in the chemical evolution of groundwater in mixed or layered assemblages is the order of encounter. This refers to the order in which various minerals or groups of minerals are encountered by the water as it moves through the flow system. This will be illustrated by considering chemical evolution sequences that would occur in a hypothetical hydrogeologic system that has four types of strata: sandstone, limestone, gypsum, and shale. As we proceed, further assumptions will be made.

In the first evolution sequence, the water passes through a soil developed on a limestone aquifer. The water becomes charged with CO₂ at a partial pressure of 10^–2 bar, and then infiltrates to the water-table zone. During infiltration, saturation with respect to calcite is attained by open-system dissolution. The water passes through the limestone and enters a zone of gypsum, where dissolution to gypsum saturation occurs. From the gypsum zone the water flows into a sandstone aquifer and then into a zone of shale.

The chemical evolution of the groundwater in the various stages of this sequence was estimated based on various assumptions regarding the mineralogy and geochemical processes in the flow system. The results are tabulated in Table 7.7. The chemistry of the water in the soil zone is assumed to be controlled entirely by the carbon dioxide regime. All other chemical inputs are assumed to be insignificant. The soil-water composition was computed using the approach outlined in Section 3.5. The calculations were simplified by noting that in the charge-balance relation H⁺ is balanced entirely by , because the pH is below 8. Table 7.7 indicates that the pH of the soil water is 4.9.

During infiltration in the limestone, open-system dissolution of calcite to saturation causes the pH to rise to 7.3. In this zone, the water acquires a Ca—HCO₃ composition with low total dissolved solids (Table 7.7). When the water enters the gypsum bed, dissolution of gypsum to saturation causes the water to become brackish, with Ca²⁺ and SO₄^2– as the dominant ions. At this stage in the calculation of the water composition, it was assumed that although gypsum dissolution causes supersaturation with respect to calcite, calcite precipitation does not proceed at a significant rate. Thus, the saturation index (SI_c) for calcite is large, as indicated in Table 7.7. Supersaturation with respect to calcite is caused by the common-ion effect.

It is assumed that as the water passes through the sandstone, gradual precipitation of calcite causes reestablishment of calcite equilibrium. The sandstone is composed of quartz and feldspar. It is assumed that these minerals have no significant effect on the water composition. The precipitation of calcite causes the pH to decline from 7.3 to 6.7 and the P_CO2 to increase from 10^–2 to 10^–1.6 bar. The Ca²⁺ and concentrations decrease, and as a result the total dissolved solids also decrease, by a small percentage. Ca²⁺ and SO₄^2– remain as the dominant ions.

As the water flows from the sandstone into the montmorillonitic shale, the process of cation exchange causes the Ca²⁺ concentration to decrease to a value that we arbitrarily specify as 20 mg/ℓ. This causes the Na⁺ content to rise to 725 mg/ℓ. The cation exchange process is represented by Eq. (3.109). Because each mole of Ca²⁺ adsorbed is replaced by 2 mol of Na⁺, cation exchange causes a slight increase in total dissolved solids but no change in pH and . The loss of Ca²⁺ causes the water to become undersaturated with respect to both calcite and gypsum (Table 7.7).

In the second evolution sequence, the water passes through the surface soil and then through sandstone, shale, limestone, and finally into a gypsum zone. The P_CO2 in the soil is 10^–2 bar, and the water composition is the same as in the first stage of the previous example. In the sandstone plagioclase feldspar dissolves incongruently (for the dissolution reaction, see Table 7.4). It is assumed that under closed-system conditions 0.2 mmol of H₂CO₃ is consumed by this reaction. A major portion of the dissolved CO₂ is thus converted to . The water acquires small concentrations of Na⁺ and Ca²⁺, the pH rises to 6.5, and the P_CO2 declines to 10^–2.4 bar (Table 7.8).

When the water moves from the sandstone into the limestone, dissolution of calcite to saturation causes the pH to rise to 8.9 as H⁺ is consumed by the conversion of dissolved CO₂ to . The P_CO2 decreases from 10^–2.4–10^–4.4 bar. The low Ca²⁺ and concentrations of this water relative to the limestone water in the previous example illustrates the difference between closed- and open-system dissolution.

When the water enters the gypsum zone, gypsum dissolution causes it to become brackish, with Ca²⁺ and SO₄^2– as the dominant ions. A high degree of supersaturation with respect to calcite develops (Table 7.8). For computational purposes it is assumed that calcite does not precipitate. In nature, however, calcite would gradually precipitate, and such high levels of supersaturation would not persist. Precipitation of calcite would cause a loss of Ca²⁺ and dissolution of more gypsum. In some situations equilibrium with respect to both gypsum and calcite can occur. Although in these examples limestone and gypsum strata control the chemical evolution of the groundwater, similar results could be attained if the water flowed through strata with only very small amounts of calcite and gypsum. It was shown in Section 7.3 that porous materials with only a fraction of a percent by weight of calcite can produce calcite-saturated water.

These two hypothetical evolution sequences indicate that the order in which groundwater encounters strata of different mineralogical composition can exert an important control on the water chemistry. As groundwater flows through strata of different mineralogical compositions, the water composition undergoes adjustments caused by imposition of new mineralogically controlled thermodynamic constraints. Although in some strata the water may attain local equilibrium with respect to some mineral phases, the continuous flow of the water causes disequilibrium to develop as the water moves into other strata comprised of different minerals. Considering that hydrogeologic systems contain numerous types of strata arranged in an almost limitless variety of geometric configurations, it is not unreasonable to expect that in many areas the chemistry of groundwater exhibits complex spatial patterns that are difficult to interpret, even when good stratigraphic and hydraulic head information is available.

Water Composition in Glacial Deposits

The chemistry of groundwater in glacial deposits is quite variable, because these deposits are composed of mixtures of mineralogical assemblages derived by glacial erosion of bedrock strata and of preexisting glacial sediments. Some generalizations can be made, however, with regard to the composition of groundwater in these materials. In North America there are three main composition categories into which most natural groundwaters in glacial deposits can be placed.

1. Type I Waters: Slightly acidic, very fresh waters (< 100 mg/ℓ TDS), in which Na⁺, Ca²⁺, and/or Mg²⁺ are the dominant cations and is the abundant anion. These waters are soft or very soft. (For a definition of water hardness and softness, see Section 9.1.)
2. Type II Waters: Slightly alkaline, fresh waters (< 1000 mg/ℓ TDS), in which Ca²⁺ and Mg²⁺ are the dominant cations and is the dominant anion. These waters are hard or very hard.
3. Type III Waters: Slightly alkaline, brackish waters (< 1000 to 10,000 mg/ℓ TDS), in which Na⁺, Mg²⁺, Ca²⁺, , and SO₄^2– generally occur in major concentrations. Most of this water has SO₄^2– as the dominant anion.

Type I water occurs in glacial deposits in parts of the Precambrian Shield in Canada and northern Minnesota, northern Wisconsin, and northern Michigan. These waters also occur in parts of Maine, Vermont, and New Hampshire, where the glacial overburden has been derived from igneous rock. Type II water is typical of the glacial materials in the midwestern region of the United States and in southern Ontario. Type III water occurs extensively in the Interior Plains region of the United States and Canada (North Dakota, Montana, Manitoba, Saskatchewan, and Alberta). (Type II water also exists in the Interior Plains region but is less common than Type III water.)

In situations where contamination from agricultural activities or sewage systems is significant, each of these water types can have appreciable concentrations of or Cl^–. Deposits formed as a result of glacial processes in mountainous regions also contain groundwater, but because of the more local nature and variability of these deposits, they will not be included in our discussion. The general categories above refer only to groundwaters that owe their chemical development to processes that take place in glacial deposits or in soils developed on these deposits. During the course of their flow histories, some groundwaters in glacial deposits have passed through bedrock or other nonglacial materials. The chemical composition of this water is commonly influenced by processes that occurred in these nonglacial materials.

The glacial deposits in which Type I water is common were derived from igneous or metamorphic rock. The chemical evolution of this water is controlled by interactions with aluminosilicate minerals in the manner described in Section 7.4. Because the weathering of these minerals proceeds slowly relative to the rates of groundwater movement, the groundwaters are very low in dissolved solids, with pH values that normally do not evolve above 7. Even though Ca²⁺ and Mg²⁺ are sometimes the dominant cations, the waters are soft because the total concentrations of these cations are very low. Although Type I water occurs in glacial deposits in many parts of the Precambrian shield, there are extensive areas in the Shield Region that have Type II water. This occurs because of carbonate minerals derived by glacial erosion of Paleozoic bedrock near the Shield, erosion of Paleozoic outliers on the Shield, or erosion of local zones of marble or other metamorphic rocks that contain carbonate minerals. Streams and lakes on the Shield that are fed by groundwater have acidic or alkaline waters, depending on their proximity to glacial deposits that contain carbonate minerals.

Type II waters are primarily a result of carbonate-mineral dissolution under open or partially open system CO₂ conditions. Cation exchange processes are commonly a modifying influence. Cl^– and SO₄^2– concentrations rarely exceed 100 mg/ℓ because minerals such as gypsum, anhydrite, and halite are generally absent. The effects of dissolution of primary silicate minerals such as feldspars and micas are largely obliterated by the much larger concentrations of cations and from the calcite and dolomite.

From a geochemical viewpoint, the most enigmatic waters in glacial deposits are those in the Type III category. This water is distinguished from Type II waters by much higher Mg²⁺, Na⁺, and SO₄^2–, and to a lesser extent by higher Ca²⁺ concentrations. Because of its brackish nature and high SO₄^2– contents, Type III water is, from a water utilization viewpoint, an unfortunate characteristic of this region. The water is generally unsuitable for irrigation and in many cases even unsuitable for human or animal consumption.

The main chemical characteristics of Type III groundwater can be accounted for by a combination of the following processes: open or partially open system dissolution of calcite and dolomite to produce pH values in the range 7–8 and values in the range 300–700 mg/ℓ, dissolution of gypsum (CaSO₄, 2 H₂O) and anhydrite (CaSO₄) to produce SO₄^2– values in the range of several hundred to 2000 mg/ℓ and as much as several hundred milligrams per liter of Ca²⁺, and alteration of the cation ratios by ion exchange. All these geochemical processes are interrelated. Cherry (1972), Grisak et al. (1976) and Davison (1976) have used stoichiometric combinations of the preceding four processes to account for Type III water in various areas in the Great Interior Plains Region of Manitoba and Saskatchewan. Since calcite and dolomite are ubiquitous in the soils and glacial deposits of the region, and since soil-zone P_CO2 values are generally high, dissolution of calcite and dolomite is a most reasonable way to account for the observed pH and values. Type III water is characteristically saturated to moderately supersaturated with respect to calcite and dolomite. For SO₄^2– to occur as the dominant anion in most Type III water, only very small amounts of gypsum need to be dissolved. Type III water is generally undersaturated with respect to gypsum. As the water moves along its flow paths, the dissolution of gypsum is the major cause of increases in the total dissolved solids. Because of the common-ion effect, the additional Ca²⁺ often produces water that is supersaturated with respect to calcite and dolomite.

By means of the mineral-dissolution processes described above, the pH, TDS, , and SO₄^2– values characteristic of Type III water can be accounted for but not the high Mg²⁺ and Na⁺ concentrations and not the small but significant concentrations of Ca^–. There is also an unaccountable deficiency of Ca²⁺ in relation to SO₄^2–. A reasonable explanation for the major features of the Type III water involves the combined influence of carbonate-mineral dissolution by water charged with CO₂ in the soil zone, dissolution of small amounts of gypsum, and exchange of Ca²⁺ for Na⁺ and Mg²⁺ on montmorillonitic clays. The availability of gypsum for dissolution is the governing factor in the evolution from freshwater to brackish-water conditions. The influx of Ca²⁺ derived from gypsum causes increased Na⁺ and Mg²⁺ concentrations as the cation exchange reactions [Eqs. (3.106) and (3.109)] adjust to maintain equilibrium. Gypsum appears to be the main source of SO₄^2–, which is the dominant anion in most Type III waters.

The origin of the gypsum in the glacial deposits is a topic of considerable speculation. Various lines of evidence suggest that it was not contained in the glacial deposits at the time of their deposition. Cherry (1972) has suggested a hypothesis in which small but significant amounts of gypsum precipitated in these deposits as a result of penetration by brine water forced into shallow zones from deep formations during glacial loading of the regional sedimentary basin. This may have occurred in the upper zones of the various till units during the numerous episodes of glacial retreat in the Pleistocene epoch. In another hypothesis, the origin of gypsum is attributed to oxidation of small amounts of iron sulfides such as pyrite (FeS₂) in the soil and subsoil. The combined effects of infiltration, iron sulfide oxidation, calcite dissolution, and subsequent evapotranspiration cause gypsum precipitation at shallow depth. These hypotheses have not been evaluated in detail. The origin of the most important mineral in the chemical evolution of Type III water therefore remains a subject of controversy.

Groundwater in Stratified Sedimentary Rocks

Sequences of stratified sedimentary rocks of continental, deltaic, or marine origin are common in North America. These sequences normally include sandstones, siltstones, shales, limestones, and dolomites. Many of the geochemical processes that have already been considered in our discussions of other hydrogeologlc environments are also important in these stratified sequences. For example, dissolution of carbonate minerals and of small amounts of gypsum, anhydrite, or halite commonly influence the major-ion composition. Alteration of feldspars, micas, and clay minerals can also be important. The purpose of this section is to describe four geochemical processes that are generally much more important in stratified sedimentary rocks than in the hydrogeologic environments considered previously. These are (1) cation exchange, (2) CO₂ generation below the soil zone, (3) biochemical reduction of sulfate, and (4) oxidation of sulfide minerals. The discussion focuses on the evolution of fresh or brackish groundwater within several hundred meters of ground surface. Deeper systems in which saline or brine waters develop are considered in Section 7.7.

A striking characteristic of many groundwaters in stratified sedimentary sequences is the occurrence of Na⁺ and as the dominant ions. In some situations the concentrations are as high as 2500 mg/ℓ, which is more than half an order of magnitude above values typical of groundwater in limestone or dolomite. Na–HCO₃-type waters occur in Tertiary and Cretaceous deposits of the Atlantic and Gulf Coastal Plains of the United States (Foster, 1950; Back, 1966), in the Tertiary and Cretaceous bedrock of western North Dakota, Montana, southern Saskatchewan, and Wyoming (Hamilton, 1970; Moran et al., 1978a; Groenewold et al., in press), and elsewhere. The occurrence of Na⁺ and as the dominant ions can be explained by the combined effects of cation exchange and calcite or dolomite dissolution. High Na–HCO₃ waters can be produced in sequences of strata that have significant amounts of calcite or dolomite and clay minerals with exchangeable Na⁺.

The two geochemical processes are represented by the reactions

(7.14)

(7.15)

where (ad) denotes cations absorbed on clays. The equilibrium for Eq. (7.15) is far to the right as long as there is appreciable Na⁺ on the exchange sites of the clays. Equation (7.14) proceeds to the right as long as the activity product [Ca²⁺][CO₃^2–] is less than the equilibrium constant for calcite (i.e., as long as SI_calcite < 1) and as long as calcite is available for dissolution. The removal of Ca²⁺ from solution by the exchange reaction causes the water to become or remain undersaturated with respect to calcite, thereby enabling calcite dissolution to continue. When these two processes operate below the water table, carbonate-mineral dissolution occurs under closed-system conditions. Dissolved CO₂, which is expressed as H₂CO₃, is consumed as the pH, and Na⁺ values rise. The relations between pH, Ca²⁺, and concentrations for low-salinity water in which calcite has dissolved to equilibrium are shown in Figure 7.16. For the pH range that is common for groundwater, this graph indicates that when Ca²⁺ is maintained at low concentrations, equilibrium concentrations are high.

In the Tertiary and Cretaceous strata in the regions mentioned above, groundwaters with less than a few tens of milligrams per liter of Ca²⁺ and Mg²⁺ and more than 1000 mg/ℓ of are common. The pH of these waters is typically in the range 7.0–8.5.

For groundwater in this pH range to evolve to such high concentrations, high production of H⁺ is necessary. In the Plains Regions a major source of H⁺ is the oxidation of pyrite (FeS₂), which is a common constituent in the bedrock of this region (Moran et al., 1978). Hydrogen ions are released as a result of the reaction

(7.16)

The oxidation occurs in the soil-moisture zone as oxygen is supplied from the earth’s atmosphere. Oxidation of a very small amount of pyrite relative to a given mass of the geologic material produces a large decrease in the pH of the pore water. An additional source of H⁺ arises from CO₂ production in the soil zone in the usual manner.

To account for the chemical characteristics of Na–HCO₃-type groundwaters in the Atlantic and Gulf Coastal Plains, Foster (1950), Pearson and Friedman (1970), and Winograd and Farlekas (1974) have concluded that CO₂ is generated within the groundwater flow system at depths far below the water table. The CO₂ combines with H₂O to form H₂CO₃, which causes calcite dissolution. Mechanisms such as the following have been suggested for generation of CO₂ at depth:

Oxidation of organic matter by sulfate:

(7.17)

Coalification (diagenesis) of lignite:

(7.18)

In anaerobic groundwater environments, oxidation of organic matter can be accomplished through SO₄^2– reduction. This process, which requires the catalyzing action of anaerobic bacteria, is often identifiable in well samples by the rotten-egg smell of H₂S gas (HS^– + H⁺ = H₂S). Groundwater in which CO₂ has been generated by SO₄^2– reduction typically has low SO₄^2– concentrations and because of this can be clearly distinguished from high-NaHCO₃ water that has evolved only through calcite dissolution and ion exchange processes.

Some stratified sequences of continental and deltaic deposits contain appreciable amounts of lignite. Foster (1950) and Winograd and Farlekas (1974) have suggested that lignite coalification, a process whereby temperature and pressure in an anaerobic environment progressively eliminate reduced volatile matter that subsequently oxidizes in the conversion of lignite to coal, is an important source of CO₂ in some groundwater zones in the Atlantic and Gulf Coastal Plain regions. However, this may not be an important CO₂ source in the lignite-rich deposits of the Great Plains Region.

We have illustrated how groundwater in stratified or mixed assemblages of unconsolidated sediments or rocks can follow many different geochemical evolution paths, depending on factors such as the sequence of encounter, relative rates of mineral dissolution, mineral availability and solubility, presence of organic matter and bacteria, CO₂ conditions, and temperature. Although it is often possible to explain the present-day composition of groundwater in terms of models based on the factors indicated above, the hydrochemistry of groundwater flow systems undergoes progressive and mainly irreversible changes over long periods of geologic time as groundwater continually passes through the geologic materials. The small amounts of gypsum and other soluble minerals that have strongly influenced the chemical evolution of groundwater in many hydrogeologic systems are gradually being removed from these systems. Sodium that is being exchanged for Ca²⁺ in the development of Na-rich groundwaters is being removed from the exchange sites of clay minerals. Silicate minerals such as feldspars and micas are continually being transformed to clay minerals. The characteristics of soil profiles in recharge areas that control the initial composition of groundwater as it begins to travel along its evolutionary paths are slowly changing due to flushing by repeated infiltration events. Over time periods of many thousands or millions of years, these changes affect the composition and shape of the earth’s crust. The effects of groundwater geochemistry on a geological time scale are considered further in Chapter 11. On a much more recent time scale, during the last few tens or hundreds of years, man’s activities have been affecting the chemical evolution of groundwater. In Chapter 9, some of the specific ways in which these activities are degrading groundwater quality are described.

7.6 Geochemical Interpretation of ¹⁴C Dates

In Section 3.8, the principles of the ¹⁴C method of groundwater age dating were introduced. Our purpose here is to describe some of the ways in which geochemical processes can cause adjusted or corrected groundwater ages to differ from decay ages or unadjusted ¹⁴C ages. The initial step in the determination of the ¹⁴C age of groundwater is to precipitate several grams or more of inorganic carbon, usually in the form of BaCO₃ or SrCO₃, from a 50- to 100-ℓ water sample. The next step is to determine by radiometric counting the percent of ¹⁴C (i.e., specific activity) in the carbon extracted from the precipitate. The measured ¹⁴C content is normally expressed as the ratio (R) of the ¹⁴C in the sample to the ¹⁴C content of modern carbon.

Based on this ratio, Eq. (3.111) indicates the unadjusted age of a ¹⁴C sample. To account for the effect of dead carbon that entered the water as a result of mineral dissolution below the water table, we will use an adjustment factor denoted as Q, where

t = —8270 ln R + 8270 ln Q (7.19)

Q is the fraction of the total dissolved inorganic carbon derived below the water table by mineral dissolution or by oxidation of organic matter. It is assumed that this added carbon contains no ¹⁴C. Inorganic carbon that enters the water by mineral dissolution above the water table is assumed to have little influence on the ¹⁴C content of the water because of rapid equilibration with the ¹⁴C in the soil air, which has ¹⁴C at “modern” levels. This definition of Q is consistent with that presented by Wigley (1975). This discussion will focus on the factors that affect Q and ways in which numerical estimates of Q can be obtained. Q is the ratio of inorganic carbon initially contributed to the groundwater under conditions where the carbon going into solution maintains a ¹⁴C content equal to that of modern carbon to the total dissolved inorganic carbon in the sample.

The significance of Q will be illustrated by several examples in which it is assumed that mixing of waters from different sources does not occur. Consider a situation where water infiltrates into a soil zone and, while in the zone of CO₂ production in the soil, acquires 100 mg/ℓ of dissolved inorganic carbon from CO₂ and from calcite dissolution. The water then moves through the groundwater flow system with no further calcite dissolution, to some location where it is sampled. For this case, the Q value for the sampled water will be 1, because soil-zone dissolution of carbonate minerals produces a ¹⁴C content in the water that is the same as the ¹⁴C content of modern carbon, regardless of whether the calcite or dolomite that dissolves in the soil zone has significant amounts of ¹⁴C. When carbonate-mineral dissolution takes place in the unsaturated zone, there is usually sufficient CO₂ generated by decay of modern organic matter to maintain equilibrium of ¹⁴C contents between the water and the soil atmosphere. Whether the organic matter in the soil is tens of years old or a few hundreds of years old is of little consequence, because these time periods are short relative to the half-life of ¹⁴C (5730 years).

In a second example, the water acquires 100 mg/ℓ of dissolved inorganic carbon in the soil zone under open-system conditions and then acquires another 100 mg/ℓ of inorganic carbon by dissolution of calcite and dolomite below the water table. In this case, Q has a value of 0.5. Nearly all calcite and dolomite that occurs in hydrogeologic systems is devoid of measurable ¹⁴C because these minerals were originally formed hundreds of thousands or millions of years ago. When these minerals are this old, their original ¹⁴C content has been lost by radioactive decay. The dissolved inorganic carbon contributed to groundwater through closed-system dissolution causes the original inorganic carbon in the water to be diluted with the nonradioactive carbon. The value of Q in this example is 0.5, because this is the ratio of carbon that initially had a modern ¹⁴C value to the total carbon, which includes the original carbon plus the additional nonradioactive carbon.

In the third example the groundwater described above moves along its flow paths into a zone in which the total content of dissolved organic carbon derived from carbonate minerals is increased further. The value of Q therefore becomes smaller. For example, if the water enters a zone in which CO₂ is being generated by sulfate reduction and calcite is being dissolved as a result of the CO₂ increase and Na–Ca exchange, the additional carbon would be expected to be devoid of ¹⁴C. Organic matter that occurs in geologic strata is normally very old, and therefore generally has no significant ¹⁴C content. If the water acquires 100 mg/ℓ of inorganic carbon from the organic matter and from the calcite, the value of Q will be 100/300 = 0.33.

As another example, we will consider groundwater that moves along flow paths in granitic rock that is completely devoid of carbonate minerals. The water moves through a soil zone in the recharge area, where it becomes charged with CO₂ at a partial pressure of 10^–2 bar at 15°C. The dissolved inorganic carbon content is therefore 21 mg/ℓ, and because the pH of the water in equilibrium with this P_CO2, would be 5.0, the dissolved inorganic carbon is nearly all in the form of H₂CO₃. These values were obtained using the type of calculation procedure outlined in Section 3.5. The fact that most of the dissolved inorganic carbon exists as H₂CO₃ can be deduced from Figure 3.5(a). As the water moves along flow paths in the granite, the pH and values will gradually rise as dissolution of silicate minerals such as feldspars and micas occurs. Eventually, the pH may rise above 7 and nearly all the dissolved inorganic carbon will exist as . The value of Q, however, will remain at unity while these changes occur, because no new inorganic carbon is introduced into the groundwater from the rock mass.

These examples illustrate that as groundwater evolves chemically during its movement along regional flow paths, Q can in some situations decrease. If one wishes to obtain useful estimates of the “true” age of groundwater from ¹⁴C data, it is necessary to first acquire a relatively detailed understanding of the geochemical origin of the inorganic carbon in the water. This can be done using conceptual geochemical models such as those outlined in the previous sections of this chapter. These models can be tested and improved using data on the ¹³C content of the inorganic carbon in the groundwater and of the carbon sources in the porous media. More detailed discussions of methods for adjustment of ¹⁴C ages based on interpretation of hydrochemical and ¹³C data are provided by Pearson and Hanshaw (1970), Wigley (1975), and Reardon and Fritz (1978).

Although in the examples above, attention has been drawn to the fact that dilution of ¹⁴C by geochemical processes can exert a major influence on ¹⁴C dates of groundwater, it should be emphasized that ¹⁴C ages can nevertheless be useful in many types of subsurface hydrologic investigations. ¹⁴C data can contribute invaluable information, even if there is considerable uncertainty in the estimates of Q values. Detailed age estimates are often not necessary for a solution to a problem. For example, whether or not the water is 15,000 or 30,000 years old may not be crucial if one has a reasonable degree of confidence in information that indicates that the age is somewhere in this range, or even older. With this approach in mind, it is fortunate that large uncertainties in Q estimates for old groundwater have a relatively small influence on the calculated groundwater age.

For example, if the unadjusted age of a groundwater sample is 40,000 years and if the Q value is 0.7, the adjusted or corrected age obtained using Eq. (7.19) is 37,050 years. If the uncertainty associated with Q is large, for example ±0.2, the corresponding range in ¹⁴C age is 34,250–39,135 years. Because of the logarithmic form of the terms in Eq. (7.19), the effect of Q is small at large values of t.

In one of the hypothetical cases presented above, a Q value of 0.3 was obtained. It should be noted that in real situations this would be considered an extreme value. As a general guide, Mook (1972) has suggested that a Q value of 0.85 is a reasonable estimate for many situations. Wigley (1975) has shown that in situations where CO₂ is not generated below the water table, it is very unlikely that Q values smaller than 0.5 will develop.

We expect that in the next few decades there will be an increasing interest in the identification of zones in which old groundwater occurs. This will occur as society develops a greater desire to consume water that has been unblemished by the almost limitless variety of chemicals that are now being released into the hydrologic cycle. Some deep groundwater zones that contain saline or brine waters that can be identified as being isolated from the hydrosphere may have special value as waste disposal zones. For these and other reasons, the identification of the distribution of ¹⁴C in groundwater in the upper few thousand meters of the earth’s crust will be important in the years ahead.

7.7 Membrane Effects in Deep Sedimentary Basins

In this text, emphasis is placed primarily on the processes and characteristics of groundwater systems in the upper few hundred meters of the earth’s crust. In these zones the temperatures are generally less than 30°C and the confining stresses are not large. However, most groundwater in the earth’s crust exists at greater depths, where temperatures and pressures are much above those considered in our previous discussions. The chemical characteristics of waters at these depths are commonly very different from those at shallow depths. The effect of temperature and pressure on mineral solubilities and ion complexing and the great age of deep groundwaters are factors that produce different water compositions. Saline or brine waters are common at these depths, although in some areas brackish waters occur.

Of the various effects that have a distinctive influence on the chemical evolution of groundwater in deep flow systems, we will choose only one, known as the membrane effect, as a basis for further discussion. Other effects result from extensions of the chemical processes that have been described for shallow systems. The membrane effect, however, is relatively unique to deep systems in stratified sedimentary rocks. For more general discussions of the geochemistry of deep groundwaters, the reader is referred to White (1957), Graf et al. (1965), Clayton et al. (1966), van Everdingen (1968b), Billings et al. (1969), and Hitchon et al. (1971). For a review of geochemical investigations of groundwaters noted for their high temperatures, the reader is referred to Barnes and Hem (1973).

When water and solutes are driven under the influence of hydraulic head gradients across semipermeable membranes, the passage of ionic solutes through the membranes is restricted relative to the water (see Section 3.4). The concentrations of solutes on the input side of the membrane therefore increase relative to the concentrations in the output. This ion-exclusion effect is referred to as salt filtering, ultrafiltration, or hyperfiltration. Salt filtering can also occur in the absence of significant hydraulic gradients in situations where differential movement of ions takes place because of molecular diffusion. Salt filtration effects caused by shales were first suggested by Berry (1959) as an important process in sedimentary basins. The concept was also used by Bredehoeft et al. (1963) to explain the concentration of brine in layered sedimentary rocks. The process has been demonstrated in the laboratory by Hanshaw (1962), McKelvey and Milne (1962), Hanshaw and Coplen (1973), Kharaka and Berry (1973), and Kharaka and Smalley (1976). The membrane properties of clayey materials are believed to be caused by unbalanced surface charges on the surfaces and edges of the clay particles. As indicated in Section 3.7, the net charge on clay particles is negative. This results in the adsorption of a large number of hydrated cations onto the clay mineral surfaces. Owing to a much smaller number of positively charged sites on the edges of the clay particles and the local charge imbalance caused by the layer or layers of adsorbed cations, there is also some tendency for anions to be included in this microzone of ions and water molecules around the clay particles. The ability of compacted clays and shales to cause salt filtering develops when clay particles are squeezed so close together that the adsorbed layers of ions and associated water molecules occupy much of the remaining pore space. Since cations are the dominant charged species in the adsorbed microzones around the clay particles, the relatively immobile fluid in the compressed pores develops a net positive charge. Therefore, when an aqueous electrolyte solution moves through the pores as a result of an external gradient or molecular diffusion, cations in the solution are repelled. In order to maintain electrical neutrality across the membrane, anions are also restricted from passage through the membrane. Slight charge differences, referred to as streaming potentials, caused by a small degree of differential migration of cations and anions, produce electrical currents across the membrane. The streaming potential also contributes to the retardation of cations in the fluid being forced through the membrane.

As a convenient way of expressing the efficiency of the clay membrane for retarding the flow of ionic species, Kharaka and Smalley (1976) have defined the filtration ratio as the concentration of species in the input solution divided by the concentration in the effluent solution.

Berry (1969) and van Everdingen (1968c) have described the relative factors influencing membrane filtration effects in geologic environments. Because of differences in ionic size and charge, there are relatively large differences in filtration ratios for the major cations that occur in groundwater. Divalent cations are filtered more effectively than monovalent cations. The membrane effect is stronger at lower groundwater flow rates. Distinctive differences in filtration ratios between monovalent and divalent cations do not always occur, and under some experimental conditions the trend in filtration ratios is reversed (Kharaka and Smalley, 1976). Temperature of the fluid also has a significant effect on the filtration ratios. In laboratory experiments using compacted bentonite, Kharaka and Smalley observed that the filtration ratios for alkali and alkaline earth metals decrease by as much as a factor of 2 between 25 and 80°C. They attribute this change to the effect of temperature on the nature and degree of cation hydration. Coplen (1970) observed experimentally that both hydrogen and oxygen are fractionated across montmorillonite membranes. Because of mass differences, ²H and ¹⁸O accumulated at the high-pressure side of the membrane. Another important conclusion derived from laboratory experiments using different types of clays is that clays with higher cation exchange capacities have greater ion-filtering efficiencies. Montmorillonitic clays, therefore, are generally much more efficient than kaolinitic clays.

If salt filtering does, in fact, exert a significant influence on the geochemical evolution of groundwater in sedimentary basins, the effects should be evident when the spatial distributions of cations and anions are investigated in deep sedimentary basins where groundwater flows or diffuses across clay or shale strata. Combinations of chemical and potentiometric data that unequivocally show the effects of salt filtering in deep zones within sedimentary basins are extremely difficult to obtain because hydrodynamic and stratigraphic conditions are generally quite complex relative to the number and distribution of groundwater monitoring wells or boreholes that are normally available for investigations of this type. Nevertheless, the salt filtering hypothesis has been found by numerous investigators to be a reasonable explanation for anomalous water compositions in various zones in deep sedimentary basins in North America and Europe. Although alternative explanations based on water-rock interactions or different hydrodynamic interpretations may be tenable as an explanation of some of these situations, there appears to be little doubt that salt filtering is in many cases an important factor. In some investigations the distributions of the stable isotopes ¹⁸O and ²H have been used as an aid in the interpretation of the chemical and hydrodynamic data (Graf et al. 1965; Hitchon and Friedman, 1969; Kharaka et al., 1973).

All laboratory experiments that have been conducted on the membrane properties of clays and shales have shown that large effective stresses must be applied for significant salt filtering efficiencies to be achieved. On the basis of laboratory evidence, it seems very unlikely that salt filtering will occur in most sedimentary deposits at depths below the ground surface of less than about 500–1000 m. If salt filtering were to commonly occur at shallower depths, the well-known generalization that states that total dissolved solids in groundwater tend to increase along flow paths would, of course, be invalid in many areas.

An unresolved problem, however, is whether or not clayey deposits such as clayey till that have been subjected to very high effective confining stresses at some time in the geologic past can maintain significant membrane properties long after the confining stresses have been removed. This question is of particular relevance in regions of sedimentary terrain that have been overridden by glaciers. The continental glaciers that traversed most of Canada and the northern part of the United States had thicknesses of several kilometers. In situations where the subglacial fluid pressures were able to dissipate during the period of glacial loading, the clayey deposits beneath the glaciers were subjected to large effective vertical stresses. Whether or not these deposits maintained significant membrane capabilities following deglaciation and crustal rebound remains to be established. Schwartz (1974) and Wood (1976) have invoked salt filtering in clayey glacial deposits as a hypothesis to explain some anomalous chemical trends in data from shallow wells in areas of clayey tills in southern Ontario and Michigan. Their field evidence is not unequivocal. The hypothesis has yet to be evaluated by studies in other areas or by laboratory tests on the deposits to ascertain whether they are capable of causing salt filtration.

7.8 Process Rates and Molecular Diffusion

To this point in our discussion of the chemical evolution of groundwater, emphasis has been placed on mineral dissolution and exchange reactions operating within an equilibrium framework. Equilibrium conditions are commonly observed in laboratory experiments and are conveniently amenable to description using thermodynamic concepts. In nature, however, hydrochemical processes often proceed extremely slowly, even when considered on a geological time scale. Because the rates of many reactions are slow, the bulk mass of the groundwater often remains undersaturated with respect to minerals that occur in the porous media. The rates can be slow because ions are not easily released from the crystal structures, or because the flux of water and reaction products between the bulk mass of the flowing water and the crystal surfaces is slow, or because series of reactions are involved, one of which is slow and therefore rate-determining for the system. Porous unfractured geological materials such as gravel, sand, silt, and clay are characterized by a large range of pore sizes. The bulk of the flowing water moves through the largest pores. It is this water that is obtained when wells or piezometers are sampled. The surface area over which reactions occur, however, is primarily the area that encompasses the smaller pores. The surface area that encompasses the large pores in which most of the flow occurs is usually only a small fraction of the surface area of the small pores. The processes whereby the bulk mass of the flowing groundwater acquires its chemical composition can therefore be strongly influenced by the rate of transfer of water and reaction products from the reaction surfaces in the smaller pores to the water in the larger pores. This rate can be slow. It is reasonable to expect that in many situations this rate is controlled by molecular diffusion of the reaction products through the fluid in the smaller pores into the larger pores, where they are then transported in the active, hydraulically controlled flow regime. From this line of reasoning it is apparent that the time required for equilibrium to be achieved in an experiment in which particulate mineral matter is reacted in a vessel in which the solids and liquid are stirred or agitated is normally less than the equilibration time in a situation where water is passed through a column packed with the mineral matter as a porous medium.

The effect of the rate of transfer of reaction products from the reaction surfaces to the bulk mass of flowing water is illustrated schematically in Figure 7.17. In a uniform flow field, the distance of attainment to saturation, referred to as the saturation distance, increases as the effective rate of transfer of reaction products between the reaction surfaces and bulk mass of flowing water decreases [Figure 7.17(a)]. In a given flow system different minerals can have different saturation distances. Figure 7.17(b) illustrates the effect of flow rate on the saturation distance for a single mineral species. In many situations the relation between the flow rate and the effective reaction rate is such that the water passes through complete groundwater flow systems without attaining saturation with respect to many of the mineral species in the host rock. This is particularly the case for aluminosilicate minerals, which have effective reaction rates that are limited by both the rate of transfer by diffusion of reaction products through the smaller to the larger pores and by slow rates of ionic release from crystal structures. For a more detailed discussion of the effect of reaction rates and diffusion on the chemical evolution of groundwater, the reader is referred to Paces (1976). Domenico (1977) has reviewed the theory of transport process and rate phenomenon in sediments. Laboratory experiments are described by Howard and Howard (1967) and Kemper et al. (1975).

In many flow systems the dominant movement of groundwater is through fractures or along bedding planes. Fractured rocks such as limestones, siltstone, shale, and basalt, and fractured nonindurated deposits such as some clays and clayey tills, have appreciable porosity in the unfractured matrix of the materials. Although the matrix has significant porosity, its permeability is commonly so low that flow in the matrix is small relative to the flow in the fracture networks. When wells or piezometers in these fractured materials are sampled, the samples represent the water flowing in the fracture system rather than the water present in the bulk mass of the porous medium. The chemistry of this water, however, can strongly reflect the results of diffusion of reaction products from the porous matrix to the fractures. Fracture openings are commonly small, even in strata with large fracture permeability. In comparison to the flux of solutes into fractures as a result of diffusion from the porous matrix, the volume of water in the fracture network is commonly small. The diffusive flux from the matrix can therefore be the controlling factor in the chemical evolution of the groundwater flowing in the fracture network. The chemical evolution of groundwater in fracture flow systems can depend on the mineralogy of the matrix material, the effective diffusion coefficients of ions in the matrix, the fracture spacing, and variations of rates of flow in the fractures. The commonly observed phenomenon of gradual increases in major ions along flow paths in regional flow systems can often be attributed to the effect of matrix diffusion.

Suggested Readings

BACK, W., and B. B. HANSHAW. 1965. Chemical geohydrology. Adv. Hydrosci., 1, pp. 49–109.

GARRELS, R. M., and C. L. CHRIST. 1965. Solutions, Minerals, and Equilibria. Harper & Row, New York, pp. 74–91.

HEM, J. D. 1970. Study and interpretation of the chemical characteristics of natural water. U.S. Geol. Surv. Water-Supply Paper 1973, pp. 103–230.

PACES, T. 1976. Kinetics of natural water systems. Proc. Symp. Interpretation of Environmental Isotopes and Hydrochemical Data in Groundwater Hydrology, Intern. Atomic Energy Agency Spec. Publ., Vienna, pp. 85–108.

STUMM, W., and J. J. MORGAN. 1970. Aquatic Chemistry. Wiley-Interscience, New York, pp. 383–417.

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