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This book is the second part of a course, “Fundamentals of Hydrogeochemistry.” It reviews spontaneous processes responsible for the formation of ground water composition and properties. It includes four major sections. The first section introduces the basics of thermodynamics and provides the concept of properties of chemical reactions. The second section is devoted to basic processes of the formation of natural waters properties and composition in the geological environment. The main attention is devoted to the water mass exchange with rock, subsurface gas, non-polar liquids and biochemical processes. The third section reviews processes of mass-transfer in the geological medium. In the fourth section methods of hydrogeochemical forecasting are described.

The textbook is intended for students specializing in geology, geochemistry, hydrogeology and ecology, and also may be of use to hydrologists and oceanologists.

Reviewer
Doctor of Geology, Prof. M. V. Charykova (S.-Petersb. State Univ.)
Published under the resolution
of the Editorial-Publishing Board
at the Geology Department
of the Sankt-Petersburg State University

This book is part II of a textbook Fundamentals of Hydrogeochemistry, part I of which was published in 2012. Whereas part I dealt with methods of study and description of the hydrochemical state of the geological medium, part II mostly touches upon spontaneous processes, which occur in ground waters. The processes are studied in consideration of the complexity of the geological environment in order to give an idea of their numerical modeling methods. In this connection the book contains four main sections.

Chapter one gives general ideas of the water solution’s thermodynamical state and spontaneous reactions in it, their laws, energy, direction and kinetics.

Chapter two reviews main processes of spontaneous formation composition of ground water as an aggregate of many similar reactions between a multitude of components in the water composition. In this connection is introduced a concept of homogenous processes (redox, acid-base, complex formation, etc.) and mass exchange between water and rock, subsurface gas and non-polar liquids (ion exchange, surface complex formation, dissolution and mineral formation, physical absorption, etc.), as well as of biochemical and isotope processes.

Chapter theree is about the element or compounds migration in the process of mixing and flow of ground water.

And lastly, chapter four gives an idea of hydrogeochemical forecasting and modeling methods.

The publication of this textbook was made due to the help by P.K. Konasavsky, A.A. Potapov and M. Gorfunkel who took upon themselves the ungrateful labor of reading the manuscript and gave helpful advice.

The author will appreciate any comments and advice about the textbook content and requests that comments be sent to:

199034 Sankt-Petersburg, University Embankment 7/9, SPbGU, Geological department, e-mail: v.tihomirov@spbu.ru.

No density or weight and no size.

They are just functions of varying rate.

All in existence due to pressure delta,

Temperature, mass, potential.

The stream of time is terribly uneven,

The space is just variety of shapes.

There is not one but many mathematics…

Maximilian Voloshin. Cosmos (1923)

Evolution of properties and composition in the geological medium is first of all change in properties and composition of ground water as a result of their reaction to the action of external factors. Cosmic, climatic, hydrological, biology-soil, anthropogenic and other factors disrupt both energy and material equilibrium of the medium, and the medium’s resistance to this action and tendency to restore the equilibrium are the substance of spontaneous processes subordinated only to the laws of thermodynamics, physics and chemistry.

Before reviewing spontaneous processes, we must have a concept of the laws of thermodynamics, physics and chemistry, which control them. At the base of hydrogeochemical processes are the multitude of elements in the composition of water solutions and chemical reactions between them. For this reason familiarity with processes should begin with familiarity with the laws of conversion of one substance in the water composition into another one.

Chapter 1

Chemical Reactions

Ground water, thermodynamically, is part of a complex heterogeneous system called the geological medium. This medium includes, beside ground water, rocks and often also underground gas or complex non-polar liquids (oil, oil products, etc.).

Rocks as aggregate of various minerals compose the largest part of the geological medium. Each mineral may be considered as an individual solid phase of the phase of constant composition. Minerals may be solid solutions and may contain substitutional impurities, which affect their chemical properties. However, hydrogeochemists more often ascribe to them permanent composition. This allows minerals to be viewed as elements of a single compound i with a molar fraction C_i = 1. The presence of impurities is usually ignored.

Ground water in its substance is a mixture of micro-particles of various size and composition poorly bonded between themselves. In terms of size these particles are drastically dominated by molecular size (less 1 nm), which in aggregate form real solution. In smaller amounts are present uniformly distributed micelles (1 to 100 nm). With the growth of their content the solution becomes colloid solution (sols), and sometimes even forms gels. Even larger particles (greater than 100 nm) form suspensions and emulsions. Poly-molecular particles of similar properties and composition (for instance, all grains of the same mineral, gas bubbles or liquid drops) may be considered as individual homogenous substances: minerals, non-polar liquids or underground gases. In such case it is convenient to merge suspended mineral particles and enclosing rock into one medium. Lastly, ground water may be treated also as a live ecosystem. The aggregate of its live organisms (plants, animals, microorganisms and fungi) form biocenose, which defines the nature of biochemical processes and plays an important role in the formation and its composition.

Overall liquid ground water is also a complex heterogeneous system, in which should be discerned: 1) real solution; 2) inert suspended substance; 3) biocenose (live dispersed matter).

1.1 Real Water Solution

Real solutions where individual components are visually indistinguishable compose most of the ground water volume and define its properties and composition. As a rule, it is identified with ground water in hydrogeochemistry studies.

Properties and composition parameters of this solution are called thermodynamic state parameters. They are subdivided into extensive and intensive ones. The extensive parameters include those which depend on the size of the medium or system, are proportionate with them and, therefore, are additive. Such are mass – m, volume – V, amount of the matter, heat, energy, etc. The intensive parameters include parameters, whose value does not depend on the size of the system or phase, namely, pressure – P, temperature – T, density – d, concentration – C, etc. They reflect change in the state of water.

Extensive and intensive parameters are tied between themselves. Change in any of them results in changes in the other ones. The ideas of cause and effect interrelation between these parameters define the model of solution state, and the mathematical expression of a given interrelation is the equation of state of the solution. It is sufficient to know some minimum number of its parameters for the complete description of the solution properties. As a rule, as such parameters of state serve first of all most easily measured, namely: volume, pressure, temperature and composition (V, P, T, C_i). Equations of state for the complex solutions are constructed based on equations of state of pure substances, which make its composition. For this are needed additional parameters, associated with the mixing processes (mixing proportions, interaction coefficients, etc.). Parameter values and their interrelation are determined both theoretically, i.e., according to logic, and experimentally. For this reason, equations of state for the solutions, as a rule, include semi-empirical functional interrelations.

1.1.1 Properties of Water Solution

Solutions have special properties, which identify them among other substances. Real water solution is no exception.

1. First of all, it has variable composition, and the concentration of its substances are not constant. H₂O, as the dominant substance – solvent has most stable concentration, the others are present as admixtures. Their content varies within a very vide range and is usually quoted in values of concentration (molarity, molality, molar fraction, etc.).

2. Any solution is a medium with distributed parameters. This means that within its limits composition and properties may change, but gradually. For this reason, specific stable boundaries between the waters of different composition are absent. On the contrary, concentration and property changes within the space coordinate of a single solution display gradients, i.e., values of parameter changes attributed to a unit of distance.

3. Real water solutions are capable of mixing with one another in unlimited proportions. At mixing, their extensive parameters are summed up whereas the intensive ones are levelling off.

If we treat mixing of different water solutions as a purely physical process, with no consideration of their chemical interaction, the mixture composition may be easily calculated.

Let us assume that mixed are only two solutions with salinities m₀ and m₁ and concentrations of component i respectively C_0,i and C_1,i. If the fraction of one of them in unit volume of the mixture is equal to α, then the corresponding fraction of the other one will be equal to 1 − α, a salinity and concentration of the component i in the mixture will be the sum of the two addends:

If mixed are two waters with known content of the component i, which does not enter chemical interaction, then from the composition of the mixture it is possible to determine proportions of the mixed waters:

The value α, which may range between 0 and 1, is often called fractional mixture concentration. If the component i is not present in one of mixed waters (C_1,i = 0), the fractional concentration is equal to the ratio C_i/C_i,0.

To determine the fractional concentration of mixing are used, as a rule, strong acids or bases, which poorly form insoluble salt. For instance, to study the fraction of sea or fresh water in their mixture are used Cl⁻ or Na+ but not sulphates, varbonates, Ca²⁺ or Mg²⁺. In particular, the fraction of sea water in such mixture is determined from the following equation:

where C_water,Cl C_water,Cl,sea and C_{water,Cl,fresh} are weight contents of Cl⁻, correspondingly, in mixtures, sea and fresh waters. If the chlorine content in fresh water is negligibly low and may be disregarded (C_{water,Cl,fresh} ≈ 0), then

In the absence of chemical interaction value α_i does not depend on the nature of the component. That is why the mixture composition may be calculated if the composition’s mixed solutions are known. For this it is necessary to equate Equations (1.4) for two different components (or one component i and salinity) and to unfold the obtained equation as a function of interrelation between their concentrations in the mixture:

Equation (1.6) shows that at mixing of two waters concentration of their components, which do not take part in chemical reactions are not removed from the solution, are tied between themselves in direct linear relation. For this reason the discovery of such linear interrelation in the ground water composition may indicate the participation in their formation of the mixing process.

4. All solution parameters are tied between themselves by the equation of state. The most important component of such an equation is the connection between intensive and extensive parameters. This interrelation has a complex, not fully studied nature. However, it noticeably simplifies and is amenable to experimental studies in ideal double-component solutions with dominance of one component – solvent.

For characterization of the interrelation between the composition and extensive properties of the solution the outstanding American physicochemist Gilbert Newton Lewis (1875–1946) introduced additional intensive parameters under the common name partial molar quantity. Among them are partial molar volume, partial molar heat capacity, chemical potential, etc.

If we add to a water solution ΔN_i moles of any component i, its volume, heat, energy and other extensive properties will change by some value Δg. Such change of an extensive parameter, related to one mole solved component i, is called mean partial quantity

where

is mean partial molar value of any extensive property, for instance volume (cm³·mole⁻¹) or heat capacity (cal·mole⁻¹·deg⁻¹). It depends on concentration. That is why the derivative of this interrelation should be considered:

Which characterized real partial molar values. Thus, true partial quantity of a component i is partial derivative of any extensive property of its ideal solution (g_i) over its concentration at constant temperature and pressure.

The partial molar values per se are intensive properties as they do not depend on the total amount of solution and may be both positive and negative. If the solution pressure and temperature do not change, any of its extensive property is a function only of its composition:

Let us assume that to a solution are added sequentially all its components by infinitely small amounts at constant pressure and temperature. At each addition any extensive parameter changes by values ∂g₁, ∂g₂,… ∂g_k, which respectively are equal:

In which case the derivative of the change of any extensive property at the addition of one component i may be represented as the sum of two addends:

And at the addition of all components total value of the extensive properties G will change by

If the amounts ∂N₁, ∂N₂, ∂N₃,…, ∂N_k have the same proportions as in the initial solution, the composition of the latter does not change. This is the same as mixing two solutions of the same composition: the solution amount increases, and its composition does not. In this case the very partial molar values g_j also do not change, and ΣN_i∂g_i in the second addend in Equation (1.11) are equal to 0. Then

Integrating Equation (1.12), on condition of constancy median partial molar values

we obtain Equation

Which is called the first Gibbs-Duhem equation. It shows that any extensive property g, for instance volume, heat capacity or energy of the solution, may be determined from its composition, if corresponding median partial molar values of its components are known. For instance, if the mole amount of individual components in the composition of a solution and their partial molar volumes are known, then the volume of the entire solution will be equal to the sum of their products.

At the addition of not all components or all but in other proportions, the composition of the source solution noticeably changes, but the addend in the equation (1.11) ΣN_i∂g_i ≠ 0. Equating equations (1.11) and (1.12), we abtain the second Gibbs-Duhem Equation:

It describes the association between partial molar values of different components in one solution at constant temperature and pressure. It follows from it that if content of only one component changes, the partial molar values of all components change, but so that

In other words, an increase in an extensive parameter of a solution due to addition of a component i is compensated by a decrease of median partial molar values of the remaining components in its composition.

If both parts of Gibbs-Duhem equation is divided by ΣN_i, i.e., if they are related to 1 mole of the solution, the equations (1.13) and (1.14) will assume the form:

where G_M is median extensive parameter (volume, mass, heat capacity, etc.) of 1 mole of the solution.

Equations (1.13), (1.14), (1.16) and (1.17) are very important for further understanding of the effect of change in water composition of solutions on their extensive properties, first of all on volume and energy. In this connection very significant are median partial molar values of the components in water solutions, which are determined experimentally in pure solutions of individual components at an increase of concentration by 1 mole. The obtained results may be found in reference literature (Naumov et al., 1971; Wagman et al., 1982; CRC Handbook of Chemistry and Physics, 2004–2005, etc.).

1.1.2 Composition of Water Solution

Real composition of ground water is much more complex than the analytical one. It is a whole and very brittle formation created by the forces of inter-atomic and inter-molecular interactions. Participants in it are almost all elements of Mendeleyev’s table, whose chemical properties are defined first of all by the number and potential energy of outer valence electrons. Only elements in the eights group of the Mendeleyev’s table, the so-called inert gases, have completely occupied outer electron shells and refuse either to incorporate or give away electrons. As a result they are chemically most passive and are present in water only in atomic state. All other elements interact between themselves. For this reason the overwhelming majority of atoms in natural water are in a bonded state.

Such bonds may be interatomic (interatomic bonding) and intermolecular (intermolecular bonding). Forces of interatomic interaction are very strong (on the order of 10² kJ·mole⁻¹) and form the strongest chemical bonds, namely, molecules and ions. Forces of intermolecular interaction are weaker (0.1–1 kJ·mole⁻¹) and control bonds between molecules and ions. Among them are noticeably identified hydrogen bonds, which hold an intermediate position with energy close to 10–50 kJ·mole⁻¹. The less energetic bonds are, the weaker they are and the easier destroyed, so it is more difficult to discover and analytically study them. Most methods of chemical analysis destroy intermolecular and hydrogen bonds and determine the content of components with the strongest interatomic bonds. However, weak bonds are most common and play an important role in the formation and real properties of ground water in static conditions of the geological medium.

Interatomic chemical interactions are most energetic. Their multitude, according to quantum theory, may be boiled down to three major types: covalent, polar and ion. In the absence of differences in electric negativity, the bond between atoms has non-polar covalent nature, at very large difference (more than by 1.7 times) – ion and in the intermediate case – polar.

Covalent and polar bonds form due to communization of one or several electrons. Covalent bonding is typical of atoms with identical or similar properties, mostly non-metals. If these atoms are positioned symmetrically, molecules with covalent bonding have no charge or polarity. Such non-polar compounds, as a rule, have no inter-molecular bonds, and they are chemically very passive. Molecules with covalent bond poorly interact with H₂O and are poorly soluble in water. They are mostly numerous organic (C₅H₁₂, C₆H₆, etc.) and gas components (N₂, CH₄, C₂H₆, etc.).

The polar bonding is a covalent bonding where the atoms are positioned asymmetrically relative to the electron orbits, causing thereby the molecule polarity. Such molecules form dipoles with positively and negatively charged ends. They form when interacting atoms are too different in their electric negativity to be able to form only a covalent bond insufficiently different to convert it to an ion bond. The polar bond is resident first of all in H₂O, and also HCl, NH₃, SO₂, etc. Their properties depend on values of dipole momentum, which is equal to the product of their positive charge and distance between the charges (Table 1.1). Substantial dipole momentum is intrinsic in in H₂O and ammonia (NH₃), alcohols, organic acids, ethers. But the main dipole in water solutions composition is obviously H₂O, which determines main water properties. Other polar chemical compounds are sufficiently active and relatively well soluble in water.

Table 1.1 Dipole momentums of individual molecules in gas (Debye units, 1D = 3.34·10⁻³⁰ Kl·m) (CRC Handbook of Chemistry and Physics, 2004–2005).

In a case of ion bonding one or more electrons is/are lost by some atoms or their groups, and acquired by other atoms or their groups. A result is the formation of particles with electrostatic charge – ions. The distinguishing feature of such ions is that the bond between them and their behaviour to a substantial extent is determined by forces of the electrostatic field. By the sign of the charge are distinguished cations (positively charged) and anions (negatively charged). By the size they may be monoatomic (K⁺, Mg²⁺, Cl⁻, etc.) and polyatomic (HCO₃⁻, SO₄²⁻, etc.), by the charge values – mono-(Na⁺, Cl⁻, etc.) and poly-charged (Cu²⁺, Al³⁺, S²⁻, etc.). The capacity of these ions to interact between themselves and with other compounds to a substantial extent depends on their size and charge, and also on the charge density (ion potential), i.e., the ratio of ion z_i charge and the values of its radius r_i. Ions are well soluble in natural water and are main among the analysed components.

Intermolecular interaction has mostly an electrical nature and depends on the distances between molecules. At very large distances molecules do not interact but on approach they first are pulled to each other, and then repel. Depending on the type of a molecule, three major types of their interaction are distinguished: the dispersion, induction and orientation ones.

The dispersion interaction is observed between non-polar neutral molecules. It occurs only at the moment of the approach of these molecules due to the appearance in them of a short-time induced dipole momentum. In natural waters composition so interact mostly gas or organic components at encounter. This interaction is relatively rare, brief and too weak. For this reason its effect on ground water composition is insignificant.

Inductive interaction occurs between polar and non-polar compounds. At the moment of their approach under the influence of the dipole charge occurs inductive polarization of non-polar molecules. In water, most common inductive interaction is established between dipoles H₂O and electrically neutral gas and organic compounds. But this interaction is also relatively weak and does not form firm super-molecule bonds. Moreover, non-polar molecules rather obstruct stronger orientation interactions between H₂O dipoles. Non-polar molecules of a large size increase the distance between H₂O dipoles, weaken hydrogen bonds between them and therewith decrease internal pressure. The greater the size of non-polar molecules, the smaller their solubility in water whereas its invasion of tetrahedral structure of water requires additional energy proportionate to the values of external pressure. That is why solution of non-polar compounds facilitates decrease of the density of a water solution and increase of its compressibility factor and freezing temperature.

Orientation interaction is observed between charged particles and is most important in the formation and composition of water properties. Three major types of such interaction are distinguished: 1) between dipoles, 2) between ions and dipoles, 3) between ions.

The first type is linked mainly with interaction of H₂O molecules between themselves and much more rarely with dipoles of organic compounds. Dipoles, when they meet, orient to one another by opposite charges and interact. Exactly at inter-dipole interaction often arise hydrogen bonds, strengthening supra-molecule formations.

The second type is typical of interaction between H₂O and ions. When they meet, water dipoles orient in the electrostatic field of ions, pulled in by the end with the opposite charge and become less mobile. This way form super-molecule associations of the aquatic complex type – [ion(H₂O)_n]. Such process is called hydration, and formed complexes – hydrates. Diluted solutions are dominated by saturated aquatic complexes where each ion is surrounded by water molecules, for instance,

. Even ions of hydrogen H⁺ and hydroxyl OH⁻ do not exist in water individually but form complexes H[H₂O]⁺ (hydroxonium) and OH[H₂O]⁻ (hydroxide hydrate).

The third type is associated with interaction of ions between themselves. A water solution with high relative dielectric permeability substantially weakens forces of electrostatic attraction between oppositely charged ions, which prevents them from interaction between themselves. Because of this cations and anions coexist in water separately. Only at very high their concentration and deficit of water they are capable of interacting with one another forming more complex associations, often joined by donor-acceptor bonds, i.e., at the expense of undivided pair of electrons from the donor-atom and free orbital of acceptor-atom.

That is exactly the competition between different forms of orientation interaction, which determines the composition and chemical properties of ground water. In very fresh water dominates orientation interaction between H₂O dipoles. As salinity and concentration of the dissociated ions, i.e., the simplest anions and cations (Na+, Ca²⁺, Cl⁻, CO₃²⁻, etc.) grows, also increases the role of interaction between water and ions. At relatively high salinity ions have to interact between themselves, forming more complex associated ions (CaHCO₃⁺, NaHCO₃⁻, HSiO₃⁻, HCO₃, etc.), capable of decomposing into simpler ones with freshening water. At this, the number of associated ions increases. Thus form complex super-molecular compounds with relatively weak bonds (PbCl₃⁻, AlF₆³⁻, Fe₂OH₂⁴⁺, etc.). Moreover, one and the same dissociated ion may be part of the composition of different associated ones. For instance, calcium in the sea water may exist simultaneously as Ca²⁺, [CaHCO₃]⁺, [CaCO₃], [CaSO₄], etc.

The simplest associated ions, which include only two ions (for instance, FeOH⁺, AlF²⁺, NaSO₄⁻, CaCO₃, etc.), are called ion pairs. Associated formations from a large number of cations and anions are called complex or coordination compounds. Cations (Al³⁺, Cu²⁺, Fe³⁺, NH₄⁺, H₃O⁺, etc.) are positioned in the venter of these complex formations and are called central atoms or central groups. Anions (OH⁻, Cl⁻, CO₃²⁻, SO₄²⁻, etc.) and more rarely polar compounds (H₂O, NH₃, etc.) are positioned around cations and are called ligands or addends. Central atoms and their closest ligands form an internal sphere of complex compounds. Outside of this sphere may be additional ligands, which are called off-spherical. In writing the composition of complicated complexes it is customary to include the compound of the central atom with ligands of internal sphere in square brackets, and with ligands of the external sphere – in squiggle brackets ({[Cu(H₂O)₆]²⁺Cl⁻}, {[Mn(H₂O)₆]²⁺SO₄²⁻}, {[Al(H₂O)₆]³⁺}, etc.).

The nature of bonds in complex compounds may be diverse – inter-dipole, ion-dipole, sometimes hydrogen but most common is donor-acceptor, which is covalent with some polarity. At that, ligands play a role of donor and the central atom – of acceptor of electrons.

The number of donor atoms in the composition of an individual ligand determines its denticity (toothiness). If a ligand have only one such atom (OH⁻, Cl⁻, F⁻, etc.), it is called monodentate, i.e., single-toothed. A ligand with several such atoms is called polydentate, i.e., multi-toothed. Polydentate ligands have 2 and more bonds with one and the same central atom, clamming up on it like a claw. That is why such complexes with polydentate ligands are especially strong and are called cyclical or chelate, i.e., claw-like. They are often called simply chelates. To the polydentate are attributed ligands of the type CO₃²⁻, SO₄²⁻, PO₄²⁻ and many organic acids. Complex formations may include various ligands. Then they are called mixed complexes) ([AlF₂(OH)]⁰, [BF₂(OH)]⁰, [BeF(OH)₂]⁻, etc.). At incomplete utilization of their donor capacity the ligands can have coordination tie with the second cation. Then ligands serve as a bridge. Such complexes with several central atoms are called polynuclear complexes. The bridges are capable of forming both monodentate and polydentate ligands. In particular, in the formation of such bridges quite often participates OH⁻. Various polynuclear hydroxide complexes are typical for metals Zr, Hf, Nb, Ta, Sc, Pb, Zn, Th (Th₂(OH)₂⁶⁺, Th₄(OH)₈⁸⁺, Th₆(OH)₁₅⁹⁺, etc.). Polynuclear complexes with various central atoms are called heteropolynuclear complexes.

Ligands are positioned around the central cations in a certain order. The number of ligands which can append the central cation is called the coordination number, which in interrelation with and depending on the size of interacting ions has the values 2, 4, 6 and greater. The charge of a complex formation is equal to the sum of charges of intertied cations and anions and may be positive, negative and neutral. At that, neutral complexes may have analogue minerals. For instance, Al(OH)₃⁰ and gibbsite, BaSO₄⁰ and barite, CaCO₃⁰ and calcite, CaSO₄⁰ and anhydrite, etc.

The appearance of polynuclear complexes sometimes facilitates polymerization and formation of large macromolecules, which are capable of making solution into colloid. For instance, at hydrolysis of oxide iron Fe³⁺ may form a complex compound Fe(OH)₃⁰, which polymerizes and forms large colloid molecules [Fe(OH)₃]_n. In such solutions precipitates mineral of iron hydroxide – the limonite. Similar colloid forms occurrence are typical of many chelate complex compounds with organic ligands.

Overall real composition of ground water is a result of complex mostly orientation inter-molecular interactions. Their role increases with a decrease in solution particle mobility, i.e., lowering of temperature and flow velocity. A more detailed description of these interactions and their role in the ground water composition formation is given in the section Homogenous processes.

1.1.3 Structure of the Water Solution

Affected by the forces of inter-atomic and inter-molecular interactions, almost all atoms in ground water turn out to be to some extent associated. Numerous weak intermolecular bonds, not taken into account at chemical analysis, whose effect grows with increase in pressure, salinity and with the decrease in temperature and rate of flow, have special significance. All these bonds obstruct translation mobility of individual atoms and thereby facilitate the formation of some structure of the solution, which determines its physical and chemical properties in reservoir conditions. Aqueous solution structure is some relatively stable in space and time optimum orderliness of inter-atomic and inter-molecular bonds in the specifically set conditions. This structure depends on temperature, pressure and composition of water in the reservoir conditions.

As mentioned above, in the absence of alien components H₂O molecules are positioned in a certain order, forming their own structures, similar to a tetrahedron. Moreover, the strength of these structures and orderliness of the O and H atoms decrease with the growth in temperature.

Alien components forming solution disrupt the orderliness of pure water. The nature of such disruptions depends first of all on the properties of these components.

Non-polar hydrophobic components do not interact with dipoles H₂O but extend and weaken hydrogen bonds between them and thereby increase internal pressure. They as if loosen the solution by increasing its volume, compressibility factor and decreasing density. This effect of non-polar components on the ground water structure is limited at shallow depths due to low external pressure but may increase with depth with growth of their content. In conditions of low temperatures and pressures H₂O dipoles can form around non-polar components peculiar spheres, which are called gas hydrates or clathrates. Within such clathrates, as in a trap, are positioned chemically non-associated molecules O₂, N₂, H₂S, CH₄, noble gas atoms, etc. (Figure 1.1). At sufficient methane content such gas hydrates are capable of forming solid substances similar to snow with density of up to 1.24 g·ml⁻¹. Gas-hydrates are capable of settling and accumulating in tubes, which results in their plugging in silts of shelf zones.

Much greater effect on the structure of ground water render polar hydrophilic components, among which ions play the main role. For them, water serves as a strong protolytic solvent, which:

1. has very high dielectric permeability (81.0 units GHz);

2. is capable of entering orientation interaction with them, creating hydrates;

3. itself forms ions H+ and OH⁻ and for this reason has amphoterous properties.

Due to this water it is as if a mix of two solutions with opposite charges, which are uniformly distributed in its entire volume, electrically neutralize each other but almost do not interact between themselves. Such solutions with discrete oppositely-charged particles – ions, whose total charge is always equal zero, are called stoichiometric solutions. In them, the sum of cations charges is always equal to the sum of anion charges.

Such specifics of interaction between dipoles of H₂O, cations and anions mostly determine the structure of water solution. The simplest idea of it is provided by the statistical theory of diluted solutions of strong electrolytes proposed by Peter Joseph Debye (1884–1966) and Erich Armand Hückel (1896–1980) in 1923. Under this theory ions are treated as rigid non-polarizable spheres separated by a uniform medium with high value of the dielectric constant. At that, structure of the solution is function of distances dipoles H₂O and ions. Depending on it, it is customary to distinguish molecular and supramolecular structure. Molecular structure is determined by a direct effect of ions on the orientation and mobility of water dipoles and is manifested first of all by the formation of hydrates. Supramolecular structure is caused by undisturbed interaction of H₂O molecules between each other (Figure 1.2).

The physical sense of molecular structure is not fully understood. But studies of water solutions by various methods indicate that the area of its distribution oversteps boundaries of the hydrates. In this connection in the molecular structure around each ion are identified two spheres of the molecular structure: inner, or internal hydration shell (Figure 1.2), and outer, or external hydration shell (Figure 1.2). Inner or primary hydration shell is positioned within the hydrate and is caused by direct orientation interaction of H₂O with ions. Outer hydration shell is caused by the competitive effect on H₂O from the ion, on the one hand, and from inter-dipole hydrogen bonds on the other. Such disrupted H₂O dipole structure is sometimes called cybotactic state.

There are two ways to approach the hydration nature: the thermodynamic and kinetic. The thermodynamic approach treats hydration as a reversible process of joining H₂O dipoles with the formation of peculiar aquatic complexes with a set coordination number. Such an approach is handy when studying the thermodynamics of chemical processes, in particular complex formation, and will be used in the sections dealing with these processes. The kinetic approach was introduced by O.Ya. Samoylov (1921–1980), who proposed a first model of clathrate type of water structure as early as 1946.

According to Samoylov’s kinetic model, ions do not join H₂O dipoles but just affect their mobility. In this connection hydration is evaluated not by bonds energy but by the comparison of the duration of relative immobility of H₂O dipoles near the ion – t_i and far from it – t_H2O, i.e., at different levels of activation energy. In the pure water without dissolved components at thermal activation energy E_a,0 H₂O dipoles have median immobility duration

where Ar_i is pre-exponential factor; R is universal gas constant; T is absolute temperature. Near the ion i activation energy, i.e., hydration potential, changes to ΔΕ_a,i. = E_a,i – E₀, and median H₂O dipole delay time becomes

The ratio of H₂O dipoles delay duration near the ion and far from it may be determined from the following Equation

The change amount of activation energy depends ΔΕ_a,i on ionic radius and structure of its electron shell (Table 1.2). If the activation energy of the an ion is higher, dipoles H₂O will linger longer near him, as ΔΕ_a,i > 0 and t_i/t_H2O > 1. Such hydration is called positive hydration. If the activation energy near the ion decreases, the H₂O dipoles near it exchange more often than far from it as ΔΕ_a,i < 0 and t_i/t_H2O < 1. Such hydration is called negative hydration.

Table 1.2 Values of H₂O activation ΔE_a,i (kJ·mole⁻¹) change due to hydration at temperature 21.5 °C (Goncharov, V.V. et al., 1967)

As Table 1.2 shows, positive hydration is inherent in ions of small size but with substantial charge, i.e., with great charge density, mostly cations (Na⁺, Ca²⁺, Mg²⁺, Li⁺, Al³⁺, etc.). Such ions well fit within structural voids of water and facilitate lowered mobility of its molecules. Negative hydration is observed near large ions with small charge density (Cl⁻, Br⁻, I⁻, K⁺, Cs⁺ and almost all double- and triple-charged metal cations). They do not fit into structural voids of water, hence they facilitate weakening of its hydrogen bonds. As their charge is small, these hydrogen bonds are not replaced by the others, and H₂O dipoles acquire greater mobility than without the ion. What happens is as if partial melting of earlier existing water structure.

These Samoylov concepts of positive and negative hydration agree well with the concept of dual-layer hydration. According to V.M. Vdovenko (1907–1978), the ΔE_i value describes total hydration potential, i.e., the sum of median hydration potential of both layers, which have opposite signs. It was experimentally established that the time of H₂O lodging in the first sphere at positive hydration is on the order of 10⁻¹¹ s (for Li⁺ and Na⁺), and at negative one – 10⁻¹² s (for K⁺, Rb⁺ and Cs⁺), whereas the time of exchange for the same dipoles in pure water is on average 4·10⁻¹¹ s (Goncharov et al., 1967).

At positive hydration dipoles of the inner layer do not have hydrogen bonds between them and are ordered by the coordination number. At negative, hydrogen bonds may be preserved even at inner hydration. At outer hydration the competition occurs between the striving of H₂O dipoles to orient relative to the ion and form hydrogen bonds between themselves. Because of this H₂O dipoles turn out disorderly and more mobile than in pure water.

The effect of ions on the solution structure increases with the growth of their concentration. As salinity grows, the relative role of the supramolecular structure declines and the relative role of the molecular one increases. In a very diluted solution ions are far from one another and practically do not interact between themselves (Figure 1.3, a). Such solutions, in which dominate supramolecular structure of pure water and the interaction between ions may be disregarded, are called ideal or diluted. With increase in salinity a moment occurs when disparate areas of the molecular structure begin to join. At this stage competition between ions for possessing H₂O dipoles drastically increases, the extent of their hydration begins to drop, and they interact, forming first ionic pairs and then more complicated complex compounds (Figure 1.3, b). The salinity, at which free hydration stops, are called critical, and solutions with salinity above it are considered moderately concentrated. As salinity increases further, supramolecular structure disappears and the moment onsets when all H₂O dipoles are controlled by an electrostatic field of ions (Figure 1.3, c). In this case it is called complete hydration. Ions and dipoles of the solution at high salinity occupy the most stable position, which is determined by the outer and inner hydration. Solutions with such structure are called concentrated. Further increase in salinity results in the disappearance of the outer hydration structure, i.e., in a state of full hydration. X-ray studies showed that it is similar to the structure of the corresponding solid crystallohydrate.

Figure 1.3 Schematic water hydrate layers position around ions in conditions of different salinity.

(After A.M. Blohk1969). Structure around ion: A – inner hydration shell, B – outer hydration shell, C – unbroken water structure. State of solution: a – diluted; b – critical; c – quasi-orderly.

From a kinetic viewpoint, salinity action on the water solution structure is similar to the action of temperature and pressure. This was a reason to compare the effect of temperature and pressure, on the one hand, and salinity, on the other, on the mobility of solution components, and therefore, on its structure. In this connection John Desmond Bernal (1901–1971) and Ralph Howard Fowler (1889–1944) introduced the concept of structural temperature of the solution. Under their definition, structural temperature of a given solution is equal to the temperature of pure water with the solution’s structural properties (viscosity, density, refraction, etc.). Ions with positive hydration work as lowering of temperature and have structural temperature below the solution temperature; ions with negative hydration – as increase of temperature, and their structural temperature is higher than the solution’s temperature. Non-polar compounds occupy plentiful space, thereby lowering the intensity of translation motion of the water molecules, lowering the structural temperature of the solution, as in a case of positive hydration.

1.1.4 Basis Components of a Solution

Thus, ground water is a product of a complex interaction between atoms and molecules, which to a different extent are tied between themselves. Thermodynamics subdivides any system into components. However, the content of this term is to a substantial extent tentative and depends on the nature of studied objects and tasks to be solved. One must remember that the components, as wrote Anderson (2005) are only “building blocks”, which form the overall system composition.

If a system includes several media, the universal “blocks” are selected, which are good for construction in any medium – in solution, in rock and in natural gas. Then components may have a tentative nature and not represent real compounds in compared media. For instance, in such cases may be used as components of water such formations as NaCl, SiO₂, Al₂O₃, etc., which are not present in the solution. Such tentative formal components are commonly used when media of different aggregate state are compared (solid, liquid or gaseous), and they are called components of the system or traditional components (Physical chemistry, 2001; Anderson, 2005).

The selection of components in the composition of water solution is associated with the need to take into account chemical reactions among them. In this connection its composition is characterized by chemical species, which are atoms, ions, molecules or their fragments and are capable of participation in chemical reactions between themselves. All plurality of components in the solutions is conveniently divided into two groups: independent (basis) and dependent (secondary).

Independent or basis components (basis species) of water solutions are the minimum number of mutually independent components, which do not change their elemental and stoichiometric composition during the course of reactions but are capable of forming any phase and any chemical component of the system. Basis components can be individual atoms (He, Ar, etc.), compounds with covalent bond (CH₄, N₂, O₂, etc.) and dissociated ions (Cl⁻, SO₄²⁻, CO₃²⁻, COOH⁻, etc.).

Dependent or secondary components (secondary, auxiliary species) are numerous combinations of basis components, ion pairs (CaHCO₃⁺, NaCO₃⁻, etc.) and complex formations (PbCl₃⁻, AlF₆³⁻, Fe₂OH₂⁴+, etc.). In this case salts and minerals, which can exist outside of solution, also may be considered as secondary as they are products of reactions between basis components.

Basis components, as a rule, determine analytical composition of natural waters. Their concentration are viewed as their total content per unit volume, including those which are part of the composition of secondary components. For instance, a basis ion of carbonate in the solution forms secondary compounds CO₃⁻, HCO₃⁻, CO₂, CaHCO₃⁺, NaCO₃⁻, etc. In this connection the content of basis components in the solution may be equal to the analytical one and is associated with concentrations of secondary components by the equation

Here, [C_i]_M is concentration of the basis component i in the solution, which sometimes is called general molar concentration; C_M,i is concentration of nonassociated basis component in the solution; C_M,j is concentration of its secondary component with sequential number j; v_ij is number of basis component i in the composition of secondary j. That is why a nonassociated basis component may be regarded as secondary. If a chemical component does not participate in chemical reactions, its identification as basis and secondary does not make sense as the concentration does not change.

The set of basis components determines calculation basis,₂₃⁻₂₃⁻