The possibility of changing the ratio of the concentrations of NaCl and CaCl2 salts in fluid phases formed as a result of heterogenization of the H2O–CO2–NaCl–CaCl2 fluid with a decrease in P-T parameters has been studied. A well-known experimental fact regarding the ternary systems H2O–CO2–NaCl and H2O–CO2–CaCl2 is the greater tendency of the H2O–CO2–CaCl2 system to separate into coexisting predominantly aqueous-salt and aqueous-carbon dioxide phases compared to the similar system H2O–CO2–NaCl. This experimental fact can be interpreted as a greater affinity of NaCl for CO2 compared to CaCl2. Using a recently developed numerical thermodynamic model of the H2O–CO2–NaCl–CaCl2 quaternary fluid system, it was possible to identify geologically significant consequences of this difference in the interaction of NaCl and CaCl2 with CO2. Multistage heterogenization of the H2O–CO2–NaCl–CaCl2 fluid with a significant decrease in P-T parameters ultimately leads to the formation of aqueous-carbon dioxide fluid phase f2, the salt component of which is significantly enriched in NaCl and depleted in CaCl2 compared to the initial fluid. The fluid phase f1 formed at each stage of heterogenization has a predominantly water-salt composition with the ratio of the mole fractions of NaCl and CaCl2 salts, differing little from that in the initial fluid. However, the total mole fraction of salt in the f1 phase, as a rule, significantly exceeds that in the original fluid. The density of phase f1 significantly exceeds the density of phase f2. During the process of multistage heterogenization of the fluid phase f1, there is no formation of a fluid with a significant enrichment of CaCl2 compared to the initial ratio of the mole fractions of NaCl and CaCl2. At the same time, successive multiple separation of the f2 phase leads to the enrichment of its salt component in NaCl. Under favorable conditions, this process can lead to the formation of a fluid with almost pure NaCl salt. Changes in the salt composition of the fluid H2O–CO2–NaCl–CaCl2 are considered in application to the evolution of fluid composition along the regressive branch of the P-T trend of HP metamorphism and syngranulite metasomatism in the Lapland granulite belt.

A thermodynamic model of the ternary fluid system H2O–LiCl–NaCl is proposed for the temperature range from –77 to +300°C. This model incorporates low-temperature phase transitions of freezing products of water–salt inclusions. The model is based on the Pitzer equations using new interaction parameters of Na, Cl, and the corresponding equilibrium constants of reactions involving the solid and liquid phases. Based on microthermometry data of fluid inclusions (T of phase transitions during heating after freezing), the model allows determination of the salt concentrations. The characteristics (T, wt E 1pt” (ice + LiCl · 5H2O + NaCl · 2H2O), peritectic P_1^” (LiCl · 5H2O + NaCl · 2H2O + NaCl) and P_2^” (LiCl · 5H2O + LiCl · 3H2O + NaCl), and the cotectic, peritectic curves separating the phase fields (ice + L, NaCl · 2H2O + L, NaCl + L), as well as solubility isotherms of ice, hydrohalite, and halite calculated by the model, showed good agreement with the experimental data. As an example of the application of a model to a natural object, we determined the salt contents in lithium-bearing brine inclusions in late quartz veins of the Bolshie Keivy area (Fennoscandian Shield).

Properties of fluids under P–T conditions of the middle crust were studied with reference to the metasomatic alteration of metamorphic rocks (amphibolite facies) of the Bolshie Keivy nappe of the Keivy terrane of the Belomorian–Lapland collision orogen of the Fennoscandian shield. Properties of the fluids were studied in five selected types of rocks: metamorphic schists and gneisses with graphite, metasomatic quartz rocks with a high content of graphite, kyanite–quartz veins with wall-rock metasomatites, and metasomatic quartz-bearing kyanite rocks and anchimonomineral quartz veins. NaCl, CaCl2, CO2, N2, CH4, heavier hydrocarbons, and graphite were identified in the fluid inclusions using microthermometry and Raman spectroscopy. Using the method of multiequilibrium thermobarometry for mineral associations and the density of CO2 inclusions, a retrograde P–T path was calculated, which reflects the P–T exhumation history of the rocks. An explanation was proposed for the presence of water inclusions with NaCl of low salinity among inclusions of high salinity with NaCl and CaCl2. Comparison of data on the H2O activity (inferred from mineral equilibria) and salt content (data on fluid inclusions) with those of a model fluid (thermodynamic model of the H2O–NaCl–CaCl2–CO2 system) showed a good agreement between natural and model data. Natural and model data were synthesized to analyze variations in the phase state and chemical composition, fluid properties, including H2O activity, density, and salinity along the retrograde P–T trend.

The paper presents results of a study of middle crustal (amphibolite-facies level) desilicated rocks exemplified by corundum-bearing plagioclasites developing after metabasites at the unique Khitostrov corundum deposit in the Belomorian–Lapland orogen of the Fennoscandian shield, with emphasis placed onto newly acquired geological data, documentation and analysis of the metasomatic zoning, determination of the P–T conditions of its formation, and a model of the metasomatic process.

Numerical models are presented for metasomatic processes caused by the coupled heat and solute transfer from a granite source to the host metapelite of given composition in the mode of pervasive and channelized vertical fluid flow. The temperature change is calculated by the equations of conductive and advective heat transport in a permeable medium, and the results of fluid–rock interaction are calculated by means of the HCh software package. The mineral composition of rocks, the extent of their transformation, and the degree of fluid–protolith disequilibrium depend on the fluid flux, time and distance from the source. At a flux of 10 –10 m/s, only multiphase mineral assemblages characteristic of contact metamorphic zoning are formed. In permeable channels, at a flux of 10 –8 –10 –6 m/s, a vertical metasomatic zoning is formed. It changes with time as the channel is heated and the fluid/rock ratio increases. The velocity of replacement fronts in this zoning differs by several orders of magnitude. At a given composition and temperature of the fluid source and the composition of the protolith, the formation of the specific metasomatic assemblages is mainly determined by two factors: the volume fluid/rock ratio and the temperature difference between the source and the fluid. The increase in the fluid acidity with temperature decrease is most pronounced in narrow single channels, where conductive heat transfer prevails, and the temperature gradient persists for a long time. In wide closely spaced channels, the temperature is determined by advective heat transfer by fluid, its gradient disappears, and the influence of the fluid source composition becomes predominant.

A numerical thermodynamic model is proposed for one of the most important geological fluid systems, the ternary H2O–CO2–NaCl system, at P-T conditions of the middle and lower crust and crust-mantle boundary (up to P = 20 kbar and up to T = 1400°C). The form of the model is analoguous to the model developed earlier for the system H2O–CO2–CaCl2. The model is based on an equation for the Gibbs excess free energy for the fluid H2O–CO2–NaCl, also including terms responsible for the interaction of the fluid with the solid phase of NaCl. The model allows predicting physical-chemical properties of fluids, which participate in the majority of deep petrogenic processes: the phase state of the system (homogeneous or multi-phase fluid, presence or absence of solid NaCl), chemical activities of the components, densities of the fluid phases, and concentrations of the components in the co-existing phases. The P-T dependencies of coefficients of the equation for the Gibbs excess free energy are expressed via molar volumes of water and CO2 at corresponding pressure and temperature. The numerical parameters of the model are obtained by fitting experimental data on the phase state of the fluid system in the range of pressures from 1 to 9 kbar and temperatures from 500 to 930°C. Our parametrization of the P-T dependencies provides applicability of the model for pressures and temperatures beyond the experimental region, namely up to P = 20 kbar and up to T = 1400°C. The validity of the model above these P-T parameters is limited due the properties of the thermodynamic description of the CO2 employed.

Properties of fluids in high-pressure granulites were studied in HP granulites (~8.7–11 kbar, ~800–900°С) and syngranulite fluid infiltration-driven HP metasomatites (~11–9 kbar, ~920–850°С) from the Lapland granulite belt of the Fennoscandian Shield. The study involved large-scale mapping of the rocks, microthermometry of mineral-hosted fluid inclusions, multiequilibrium mineral thermobarometry, and calculations of H2O activity based on mineral equilibria. The mafic pyroxene granulites and syngranulite metasomatites (quartz blastomylonites with orthopyroxene, sillimanite, and garnet; veins and vein-like bodies of orthopyroxene–garnet and diopside–scapolite rocks) contain similar assemblages of syngenetic fluid inclusions (which are hosted mostly in quartz and also in garnet, orthopyroxene, and scapolite) of contrasting chemical composition: nearly pure СО2 (distinctly predominant), brines (the dominant salts are CaCl2 and NaCl), and N2 ± H2O. These three types of inclusions coexist in the same generations of early inclusions: rarer primary (p) and predominant primary–secondary (ps). The CO2 inclusions have either high or low densities, and the N2 inclusions are of low density. The brine inclusions show a wide range of total salt contents (up to 30–35 wt%) and variable concentration proportions of the dominant salts: p-inclusions with a salinity of 20 wt% CaCl2 + 10 wt% NaCl; ps-inclusions with a salinity of 5 wt% CaCl2 + 20 wt% NaCl; p- and ps-inclusions with a salinity of 5–23 wt% NaCl eq; and p-inclusions with halite (up to 35 wt% NaCl). In general, CaCl2 is the predominant salt component in the early p- and ps-inclusions of the rocks. Considered together, currently available data (including Sr, Nd, and O isotope systems) on these rocks indicate that the external fluid flow during the origin of granulites was evidently of mantle origin. At the peak P–T parameters, the inclusions were entrapped from a heterogeneous fluid in which immiscible water–salt and CO2-rich fluids, which initially contained N2, coexisted. Data on the chemical composition and salt concentrations of the fluids, $${{a}_{{{{{\text{H}}}_{2}}{\text{O}}}}}$$ = 0.40–0.51, are compared with the theoretically predicted phase state of the fluids and the properties of the coexisting immiscible fluid phases at the estimated P–T parameters of granulite petrogenesis on the basis of numerical models in the H2O–CO2–NaCl and H2O–CO2–CaCl2 ternary systems. The location of the tie-lines and solvus were calculated to subsequently use for the thermodynamic prediction. The paper discusses similarity and the reasons for the difference between the theoretical compositions of the generated fluid phases and the composition of fluid inclusions, geochemical consequences of the heterogenization of granulite fluids (the formation of concentrated alkaline brines and a potentially acidic CO2-rich fluid phase, the values of the mass and volume fractions of these phases depending on variations in the composition of the initial homogeneous fluid, etc.). It follows that an extensive region of the compositions of aqueous fluids with different concentrations of CO2 and Na and Ca chlorides exists at the P–T parameters of HP granulites in which originally homogeneous fluid splits into compositionally contrasting fluid phases with different properties. This region of coexisting immiscible fluids significantly expands with increasing CaCl2 concentration. Hence, the lower crust at the level of the HP granulite facies may be the region where high-temperature immiscible fluids are generated. One of these fluids is a denser phase of alkaline brines, and the other is a less dense potentially acidic phase of H2O–CO2 fluids rich in CO2. Ascending along regional permeable zones, these fluid phases of deep origin can play an important role in magmatic, metamorphic, metasomatic, and ore-forming processes in the middle and upper crust.

For the first time, the isotopic composition of oxygen, the content of trace elements, and the U–Pb zircon age were determined for kyanite–gedrite metasomatites from the Dyadina Gora ore occurrence, Belomorian Mobile Belt, Fennoscandian Shield. The zircon cores preserved from the protolith are characterized by a magmatic REE distribution and an average value of δ 18 O of about 3.0‰, and their age is close to 2400 Ma. The inner zones around the cores and rims of zircon were formed during metasomatic processes at the time of the Svecofennian metamorphism about 1870–1880 Ma ago, experienced strong fluid reworking, and are characterized by a decreased δ 18 O value to –0.9‰.

A numerical thermodynamic model is proposed for one of the most important geological fluid system – triple system H2O-CO2-CaCl2 at P-T conditions of the middle and lower crust, as well as for the crust-mantle boundary. The model is based on the equation for concentration dependence of the excess Gibbs free energy, proposed earlier, and for the first time obtained P-T dependencies of the coefficients of the equation of state (EOS) expressed via molar volumes of the components. The EOS allows predictions of the properties of the fluid, participating in the majority of the processes of depth petrogenesis: its phase state (homogeneous or multi-phase), densities of the fluid phases, concentrations of the components in the co-existing phases, and chemical activities of the components. The model precisely reproduces all available experimental data on the phase state of the ternary fluid system H2O-CO2-CaCl2 in the ranges of temperature 773.15–1073.15 K and pressures 0.1-0.9 GPa and allows, as well, correct application of the EOS beyond the experimentally studied domain of temperatures and pressures – namely up to P = 2 GPa and up to T = 1673.15 K. The possibility of the correct extrapolation of our EOS is ensured by using the parametrization of P-T dependencies via the molar volume of water. The latter remains in the experimental domain of values or very near to its boundaries, when increasing temperatures and pressures.

Предложена численная термодинамическая модель для одной из важнейших геологических флюидных систем – тройной системы H 2 O-CO 2 -CaCl 2 при P-T условиях средней и нижней коры и границы кора–мантия. Модель основана на ранее предложенном уравнении зависимости избыточной свободной энергии Гиббса от концентрации компонентов и впервые полученных P-T зависимостях коэффициентов уравнения состояния (EOS), выраженных через мольные объемы компонентов. Полученное уравнение состояния этой системы позволяет предсказывать свойства флюида, принимающего участие в большинстве процессов глубинного петрогенеза: фазовое состояние (гомогенное или многофазное), плотности флюидных фаз, концентрации компонентов в сосуществующих фазах, химические активности компонентов. Модель воспроизводит с высокой точностью все имеющиеся экспериментальные данные по фазовому состоянию тройной флюидной системы H 2 O-CO 2 -CaCl 2 в диапазонах температур 773.15–1073.15 K и давлений 0.1–0.9 ГПа, а также позволяет применение EOS за пределами экспериментально изученной области значений температуры и давления – до P = 2 ГПа и до T = 1673.15 K. Возможность корректной экстраполяции EOS обусловлена параметризацией P-T зависимостей через мольный объем воды, который при повышении температуры и давления либо остается в пределах его значений в экспериментальной области, либо крайне мало выходит за эти пределы.

A numerical thermodynamic model is proposed for one of the most important geological fluid system, ternary H 2 O–CO 2 –CaCl 2 system, at P-T conditions of the middle and lower crust and crust–mantle boundary. The model is based on the previously proposed equation for concentration dependence of the excess Gibbs free energy and on the first obtained P-T dependencies of the coefficients of the equation of state (EOS) expressed via molar volumes of the components. The EOS allows to predict the properties of the fluid participating in the majority of deep petrogenetic processes: its phase state (homogeneous or multi-phase), densities of fluid phases, concentrations of components in the co-existing phases, and the chemical activities of the components. The model precisely reproduces all available experimental data on the phase state of the ternary H 2 O–CO 2 –CaCl 2 fluid system in the ranges of temperatures 773.15–1073.15 K and pressures 0.1–0.9 GPa and also allows the correct application of the EOS beyond the experimentally studied range of temperatures and pressures up to P = 2 GPa and T = 1673.15 K. The possibility of the correct extrapolation of our EOS is ensured by using the parametrization of P-T dependencies via the molar volume of water. The latter remains in the experimental domain of values or falls slightly beyond its boundaries, when increasing temperatures and pressures.

One unsolved problem of Archean metallogeny of the Russian part of the Fennoscandian Shield is related to the period of formation of orogenic gold deposits, the age of which was previously considered Early Proterozoic. Comprehensive studies identified the complex evolution of ores from the Novye Peski deposit and the first Neoarchean Sm–Nd isochron isotopic age (2583 ± 16 Ma) of the formation of orogenic gold of the Karelian Craton. A significant positive ε Nd( t ) value of +4.7 of gold-bearing metasomatites probably points to the link between the ore-forming fluid and the deep mantle source.

An empirical model for the concentration dependence of the Gibbs free energy for solutions of chlorides of alkaline and alkaline earth metals in water is proposed. A simple analytical form of the Gibbs free energy makes it possible to obtain the equations of state for salt solutions that are equally accurate in the entire range of salt concentrations, from dilute solutions to solubility limits. The high accuracy of the thermodynamic description of solutions of high and intermediate concentration is ensured by the presence in the equation for the Gibbs free energy of two terms related to the Margules decomposition of the Gibbs free energy. Our form of the Gibbs free energy also contains a term that reproduces the thermodynamic behavior of solutions of electrolytes, which ensures high accuracy of the proposed model at low salt concentrations in the solution. Using the model, the equations of state for aqueous solutions of NaCl and CaCl2 at water vapor pressure in the temperature ranges of 423.15 K–573.15 K and 423.15 K–623.15 K were obtained, which corresponds to the parameters of ore-bearing solutions participating in the formation of low-temperature hydrothermal ore deposits.

Equations of state valid for all possible salt concentrations in solution are obtained for binary fluids H 2 O—NaCl and H 2 O—CaCl 2 . The equations are based on the empirical form of the Gibbs free energy for salt solutions of arbitrary concentration, developed earlier. Based on experimental data on the PVTx properties the obtained earlier thermodynamic description of H 2 O—NaCl and H 2 O—CaCl 2 solutions at saturated vapor pressure is extended towards higher pressures. For H 2 O—NaCl pressures are up to 5 kbar. For H 2 O—CaCl 2 pressures cover the range of available experimental data up to 0.7 kbar. The equations allow precise calculation of the whole set of thermodynamic parameters of the discussed salt solutions in the temperature ranges 423.15–573.15 K and 423.15–623.15 K, corresponding to low temperature hydrothermal ore deposits, that could be relevant for thermodynamic modeling of ore-bearing fluids at such deposits.