Endmember graphics     

Ross M. Renner  Simon R. Jurke 《Mathematical Geology》1992,24(3):287-303

Thek points inp-space corresponding to a specified set ofk (k<p) linearly independent endmember estimates associated with ap-variate (n×p) compositional datasetX, define the vertices of a (k–1) dimensional simplexH. Then estimated mixtures which together account for the systematic variation in the datasetX, are each convex combinations of thek fixed endmember estimates. Accordingly, then-points inp-space which represent these mixtures must be interior points of the simplexH. The purpose of this paper is to describe a simple graphical procedure for examining the positions of the estimated mixtures relative tok=3 or 4 putative endmembers, and for assessing their compliance or otherwise with the convexity constraints. Since the mixture coefficients must be estimated first in order to obtain the mixture estimates, the paper begins with a review of the least-squares partitioning procedure.  相似文献   

The construction of extreme compositions     

Ross M. Renner 《Mathematical Geology》1995,27(4):485-497

If a geochemical compositional dataset X (n×p)is a realization of a physical mixing process, then each of its sample (row) vectors will approximately be a convex combination (mixture) of a fixed set of (l×p)extreme compositions termed endmembers. The kpoints in p-space corresponding to a specified set of k (klinearly independent endmember estimates associated with a p-variate (n×p)compositional dataset X,define the vertices of a (k–1)dimensional simplex H.The nestimated mixtures X (n×p)which together account for the systematic variation in the dataset X,should each be convex combinations of the kfixed endmember estimates. Accordingly,the npoints in p-space which represent these mixtures should be interior points of the simplex H.Otherwise, for each sample point which lies outside H,at least one of the mixture coefficients (endmember contributions) will be negative. The purpose of this paper is to describe procedures for expanding H in the situation that its vertices are not a set of extreme points for the set which represents the mixtures.  相似文献   

Phase relations in high-pressure metapelites in the system KFMASH (K2O–FeO–MgO–Al2O3–SiO2–H2O) with application to natural rocks     

Chunjing Wei  Roger Powell 《Contributions to Mineralogy and Petrology》2003,145(3):301-315

Using a previously published, internally consistent thermodynamic dataset and updated models of activity–composition relations for solid solutions, petrogenetic grids in the model system KFMASH (K₂O–FeO–MgO–Al₂O₃–SiO₂–H₂O) and the subsystems KMASH and KFASH have been calculated with the software THERMOCALC 3.1 in the P–T range 5–36 kbar and 400–810 °C, involving garnet, chloritoid, biotite, carpholite, talc, chlorite, staurolite and kyanite/sillimanite with phengite, quartz/coesite and H₂O in excess. These grids, together with calculated AFM compatibility diagrams and pseudosections, are shown to be powerful tools for delineating the phase equilibria and P–T conditions of pelitic high-P assemblages for a variety of bulk compositions. The calculated equilibria and mineral compositions are in good agreement with petrological observation. The calculation indicates that the typical whiteschist assemblage kyanite–talc is restricted to the rocks with extremely high X_Mg values, decreasing X_Mg in a bulk composition favoring the stability of chloritoid and garnet. Also, the chloritoid–talc paragenesis is stable over 19–20 kbar in a temperature range of ca. 520–620 °C, being more petrologically important than the previously highlighted assemblage talc–phengite. Moreover, contours of the calculated Si isopleths in phengite in P–T and P–X pseudosections for different bulk compositions extend the experimentally derived phengite geobarometers to various KFMASH assemblages.  相似文献   

A type curve approach to estimatingp for ap-normal transformation     

Dachang Li  Larry W. Lake 《Mathematical Geosciences》1995,27(3):359-371

The p-normal transformation plays an important role in reservoir characterization for data sets that are neither normally nor log-normally distributed. The key step in the transformation is to estimate the value of pfor a given data set. Even though there are several ways to determine p,these are more inconvenient than the quicker and easier type curve approach to estimate pwe present in this paper. In addition, the method provides the p-normal transformation with a visual interpretation. We demonstrate the technique by analyzing reservoir permeability and porosity data from the East Velma West Block Sims Sand Unit, Oklahoma.  相似文献   

Fluid-mineral equilibria and thermodynamic mixing properties of fluid systems     

L. Ya. Aranovich 《Petrology》2013,21(6):539-549

The paper presents a review of an experimental method to quantitatively constrain thermodynamic mixing properties of fluid systems at high temperature T and pressure P. The method is based on bracketing equilibrium parameters of simple fluid-mineral reactions. Experimental data obtained with this technique for the H₂O-CO₂, H₂O-N₂, and H₂O-H₂ binary systems were utilized to calculate mixing parameters corresponding to the simplified van Laar model W ₁₂ ^VL , according to which the equation for the integral excess Gibbs free energy of a binary mixture G ^ex is G ^ex =X ₁ X ₂ W ₁₂ ^VL /(X ₁ V ₁ ⁰ + X ₂ V ₂ ⁰ ), where X _i is the mole fractions of the components, and V _i ⁰ are pure species molar volumes at given P and T (in cm³). The W ₁₂ ^VL for the three mixtures correspond to 202, 219, and 331 kJ cm³/mol. The empirical correlation $W_{H_2 O - X}^{VL}$ (kJ cm³/mol) = 887.012 Q _X ? 16.674, where Q = P _c (critical pressure, bar)/T _c (critical temperature, K) for gas X (where X = CH₄, CO, H₂S, O₂, Ar, and NH₃) is used to evaluate the van Laar parameters for a number of petrologically important water-gas mixtures. The H₂O-H₂ system is characterized by the greatest positive deviation from the ideal mixing and can thus decompose into two immiscible fluid phases under the P-T parameters typical of deep lithospheric zones. The exsolution of the H₂O-CO₂ and H₂O-N₂ systems is expected to occur only under high pressure and low temperature. This combination of parameters may be expected only in the environments of cold subduction. Salts (highly soluble simple salts and/or silicates) should significantly expand the exsolution regions in petrologically important fluids.  相似文献   

Metamorphic equilibria in the siliceous dolomite system: 6 kbar experimental data and geologic implications     

R.G. Eggert  D.M. Kerrick 《Geochimica et cosmochimica acta》1981,45(7):1039-1049

Hydrothermal experiments with H₂O-CO₂ fluids at P_fluid = 6 kbar yielded the following quilibrium conditions for reactions important in metamorphosed siliceous dolomites (T = °C; X = X_co2): (3) dolomite + 2 quartz = diopside + 2 CO₂T = 620 ± 8X = 0.73 ± 0.03 (5) 5 dolomite + 8 quartz + H₂O = tremolite + 3 calcite + 7 CO₂T = 600 ± 5 550 ±5 540±5 500±5X = 0.66 ± 0.03 0.21 ± 0.03 0.21 ± 0.04 0.06 ± 0.02 (7) 3 dolomite + 4 quartz + H₂O = talc + 3 calcite + 3 CO₂T = 550±5 500±5 450 ±5X = 0.25 ± 0.05 0.07 ± 0.02 0.03 ± 0.02 (8) 2 dolomite + talc + 4 quartz = tremolite + 4 CO₂T = 550 ± 5 540 ±5 500 ± 5X = 0.22 ± 0.03 0.21 ± 0.02 0.06 ± 0.02 A thermodynamically self-consistent 6 kbar T-X_CO2, topology results by extrapolating equilibria from experimental brackets using a modified Redlich-Kwong equation for activities in H₂O-CO₂ mixtures. This topology restricts the assemblage talc + calcite to a narrow stability band in T-X_CO2 space at X_CO2 < 0.55 and T < 590°C. Accordingly, the occurrence of talc + calcite in pure siliceous dolomites metamorphosed at P_fluid = 6 kbar implies correspondingly water-rich fluids.  相似文献   

An examination of the use of the logratio transformation for the testing of endmember hypotheses     

Ross M. Renner 《Mathematical Geology》1991,23(4):549-563

Given a compositional dataset in the absence of any prior information on any mixing process which may have formed it, a complete analysis of mixtures determines three distinct types of estimates in order. These are: (i) the estimate of the number of endmembers or fixed source compositions, of which all the sample compositions of the dataset must be approximate mixtures; (ii) the estimated compositions for each of these chosen number of endmembers; and (iii) the estimated contributions of each of these endmember estimates to each sample. Traditionally, the estimate for the number of endmembers has been assessed either by mapping or by inspection of the coefficients of determination between the observed and estimated variables. Mapping entails the plotting on a map of the region from which the samples were taken, either the contours of the contributions of each endmember to each sample, or some other portrayal of the distribution of endmember abundances. Because it requires the complete analysis, assessment by this method is too elaborate except for final confirmation and display. Alternatively, choosing a number of endmembers, which result in suitability high coefficients of determination for all or most variables, may account for elements which are not part of the conjectured mixing process or, worse, may result in the identification of endmembers which may never in fact have existed. Such an error is similar to overspecifying a multiple regression model. So, the obvious starting point from which to assess the validity, or otherwise choice of endmember numbers, is to examine the matrix of residuals. The differences between the logratio-transformed observed and estimated data form an array of residual logratios. A linear combination of these may be formed for each sample, which, under a random perturbation assumption, should follow a univariate normal distribution. Whether or not this scalar is normal can be readily tested. It can also be examined graphically for such desirable qualities as symmetry when the test for normality may be too severe. This procedure is employed to assess the decompositions of the U.S.G.S. Mid-Pacific data and the Nazca Plate Surface sediments.This paper was presented at the 18th Geochautauqua, Newark, Delaware, 13–14 October 1989.  相似文献   

Water and magmas; a mixing model     

C.Wayne Burnham 《Geochimica et cosmochimica acta》1975,39(8):1077-1084

A model for the mixing of H₂O and silicate melts has been derived from the experimentally determined effects of H₂O on the viscosity (fluidity), volumes, electrical conductivities, and especially the thermodynamic properties of hydrous aluminosilicate melts. It involves primarily the reaction of H₂O with those O^?2 ions of the melt that are shared (bridging) between adjacent (Al, Si)O₄ tetrahedra to produce OH^? ions. However, in those melts that contain trivalent ions in tetrahedral coordination, such as the Al³⁺ ion in feldspathic melts, the model further involves exchange of a proton from H₂O with a non-tetrahedrally coordinated cation that must be present to balance the net charge on the AlO₄ group. This cation exchange reaction, which goes essentially to completion, results in dissociation of the H₂O and is limited only by the availability of H₂O and the number of exchangeable cations per mole of aluminosilicate.In the system NaAlSi₃O₈-H₂O, upon which this thermodynamic model is based, there is 1 mole of exchangeable cations (Na⁺) per mole (GFW) of NaAlSi₃O₈, consequently ion exchange occurs for H₂O contents up to a 1:1 mole ratio (X^m_w = mole fraction H₂O = 0.5). For mole fractions of H₂O greater than 0.5, no further exchange can occur and the reaction with additional bridging oxygens of the melt produces 2 moles of associated OH^? ions per mole of H₂O dissolved. These reactions lead to a linear dependence of the thermodynamic activity of H₂O (a^m_w) on the square of its mole fraction (X^m_w) for values of X^m_w, up to 0.5 and an exponential dependence on X^m_w at higher H₂O contents. Thus, for values of $\text{X}{}^{\mathrm{m}}{}_{\mathrm{w}}\text{? 0.5, a}{}^{\mathrm{m}}{}_{\mathrm{w}}\text{= k(X}{}^{\mathrm{m}}{}_{\mathrm{w}}\text{)}{}^2$, where k is a Henry's law constant for the dissociated solute.Extension of the thermodynamic model for NaAlSi₃O₈-H₂O to predict H₂O solubilities and other behavior of compositionally more complex aluminosilicate melts (magmas) requires placing these melts on an equimolal basis with NaAlSi₃O₈. This is readily accomplished using chemical analyses of quenched glasses by normalizing to the stoichiometric requirements of NaAlSi₃O₈, first in terms of equal numbers of exchangeable cations for mole fractions of H₂O up to 0.5 and secondly in terms of 8 moles of oxygen for higher H₂O contents. Chemical analyses of three igneous-rock glasses, ranging in composition from tholeiitic basalt to lithium-rich pegmatite, were thus recast and the experimental H₂O solubilities were computed on this equimolal basis. The resulting equimolal solubilities are all the same, within experimental error, as the solubility of H₂O in NaAlSi₃O₈ melt calculated from the thermodynamic relations.The equivalence of equimolal solubilities implies that the Henry's law constant (k), which is a function of temperature and pressure, is independent of aluminosilicate composition over a wide range. Moreover, as a consequence of the Gibbs-Duhem relation and the properties of exact differentials, it is clear that the silicate components of the melt, properly defined, mix ideally. Thus, a relatively simple mixing model for H₂O in silicate melts has led to a quantitative thermodynamic model for magmas that has far-reaching consequences in igneous petrogenesis.  相似文献   

A comparative study of the mollusc communities of two oligohaline intertidal marshes: Spatial and temporal distribution of abundance and biomass     

T. Dale Bishop  Courtney T. Hackney 《Estuaries and Coasts》1987,10(2):141-152

Molluscs were collected monthly for a year from two low salinity (0–9‰) intertidal marshes dominated by the macrophytesJuncus roemerianus orSpartina cynosuroides in St. Louis Bay, Mississippi. TheJuncus marsh had lower soil organic matter, higher pH and was more frequently inundated than theSpartina marsh. Eight species of gastropods were abundant and dominated in the higherSpartina marsh, while three bivalve species were dominant in theJuncus marsh. Of the common species,Succinea ovalis, Vertigo ovata andDeroceras laeve are gastropods of terrestrial origins;Geukensia demissa granosissima (bivalve) andMelampus bidentatus (gastropod) are euryhaline estuarine species and the remaining gastropods (Detracia floridana, Littoridinops palustris, Onobops jacksoni) and bivalves (Polymesoda caroliniana, Cyrenoida floridana) are brackish species. Most species were capable of continuous recruitment (based on size class analysis), but exhibited peak activity in particular seasons. Bivalve abundance correlated to temperature, and gastropod abundance was negatively correlated to soil pH. These correlations reflect the influence of flooding regime at the two sites. Biomass was greater in theJuncus marsh because of the increased presence of the large-bodiedPolymesoda. Polymesoda represented >90% and >50% of the total biomass in theJuncus andSpartina (except summer) marshes respectively but always <-5% of the individuals collected. Gastropod biomass was the same in both marshes. Species diversity (H′) was greater inSpartina except for summer months. TheJuncus marsh always exhibited greater species richness. Evenness (J′) determined seasonal changes in diversity (H′). Similarity values (C_z) were always quite low, with highest values in spring In contrast to faunal studies from Gulf and East Coast salt marshes, we found 1) fewer species, 2) communities comprised of unique species combinations, 3) greatest mean densities in summer, and 4) potentially less productivity by the molluscs of our sites. These mollusc communities exhibit structural characteristics that emphasize the unique ecotonal nature of the oligohaline marshes within which they are found.  相似文献   

Molecular mimicry of the bond length-bond strength variations in oxide crystals     

G. V. Gibbs  L. W. Finger  M. B. Boisen Jr. 《Physics and Chemistry of Minerals》1987,14(4):327-331

Minimum energy theoretical bond lengths R _t obtained with robust split-basis molecular orbital calculations for 27 hydroxyacid molecules containing first- and second-row cations X ⁿ⁺ reproduce XO bond lengths in crystals. Plots of ln(R _t ) vs. ln(s), where s is the Pauling bond strength, define two different but essentially parallel trends (for first- and second-row cations, respectively) as observed for crystals. A new bond strength parameter p=s/r is defined where r=1 for first- and r=2 for second-row main-group cations. When a ln(R _t ) vs. ln(p) plot is prepared with these theoretical bond lengths, a single trend is obtained. A regression analysis of this data set shows that more than 99 percent of the variation of ln(R _t can be explained in terms of a linear dependence on ln(p), yielding R=1.39 p ^?0.22 as an estimator of the bond lengths. A comparison of 153 mean XO bond lengths compiled by Shannon (1976) for main-group closed-shell X-cations from all 6 rows of the periodic table with those estimated with this formula for r=1, 2, ..., 6, respectively, shows that these bond lengths are estimated within 0.05 Å on average with nearly 85 percent estimated within 0.10 Å of the observed value. More than 97 percent of the variation of these observed bond lengths can be ranked in terms of a linear dependence on the estimated bond lengths. The success of these calculations is further evidence that the forces that govern bond length variations in oxide crystals behave as if they are short-ranged.  相似文献   

Analysis of some aromatic hydrocarbons in a benzene-soluble bitumen from Green River shale     

D.E. Anders  F.G. Doolittle  W.E. Robinson 《Geochimica et cosmochimica acta》1973,37(5):1213-1228

The hydrocarbon content of an aromatic fraction, isolated from the bitumen of Green River shale, was studied by mass spectrometry, infra-red spectrometry, gas chromatography and a dehydrogenation technique. The hydrocarbon types and their distribution in this aromatic fraction, as determined by mass spectrometry, include the following: C_nH_2n?6(10%), C_nH_{2n?8 (31 %)}, C_nH_2n?10(18%), C_nH_2n?12(12%), C_nH_2n?14(8%) and a series of alkenylbenzenes (20%). The carbon-number range, empirical formulae and quantity of each compound in the major types are reported. Mass spectra of several compounds and homologous mixtures of compounds isolated from the aromatic fraction are also given.  相似文献   

Synthesis of tourmaline solid solutions in the system Na2O–MgO–Al2O3–SiO2–B2O3–H2O–HCl and the distribution of Na between tourmaline and fluid at 300 to 700 °C and 200 MPa     

G. v. Goerne  G. Franz  W. Heinrich 《Contributions to Mineralogy and Petrology》2001,141(2):160-173

Tourmaline has been synthesized hydrothermally at 200 MPa between 300 and 700 °C from oxide mixtures with Mg-Al ratios for the end members dravite NaMg₃Al₆(Si₆O₁₈)(BO₃)₃(OH)₃(OH) and Mg-foitite &ding6F;(Mg₂Al)Al₆ (Si₆O₁₈)(BO₃)₃(OH)₃(OH). Six different Na concentrations were investigated to determine the distribution of Na between tourmaline and fluid in the SiO₂-saturated system Na₂O-MgO-Al₂O₃-SiO₂-B₂O₃-H₂O-HCl. Synthetic tourmaline ranges from X-site vacant (&ding6F;) tourmaline (Mg-foitite) to nearly ideal dravite with Na=0.95 apfu. There are small, but significant, amounts of proton deficiency and negligible tetrahedral Al. Chemical variation is primarily caused by the substitutions Al&ding6F;Mg_-1Na_-1 and minor AlMg_-1H_-1. Varying amounts of Na and &ding6F; determine the Mg/Al ratios. Besides tourmaline and quartz, additional Mg-Al phases are chlorite and, at 700 °C, cordierite. Albite is also present at high Na concentrations in the bulk composition. The c dimension of the tourmaline crystals increases with Na in tourmaline. The amount of Na in the X-site depends strongly on the bulk concentration of Na in the system as well as on the temperature. These factors in turn control the phase assemblage and the composition of the fluid phase. For the assemblage tourmaline + quartz + chlorite/cordierite + fluid, a linear relationship exists between Na concentration in the fluid (quenched after the run) and tourmaline with temperature: T °C [ᆭ °C]=(Na_fluid/Na_tur)앾.878-14.692 (r²=0.96). For the assemblage tourmaline + albite + quartz + fluid, it is: T °C [ᆣ °C]=(Na_fluid/Na_tur)욝.813-6.231 (r²=0.95), where Na_fluid is the concentration of Na⁺ in the final fluid (mol/l) and Na_tur is the number of Na cations in the X-site of tourmaline. The equations are valid in the temperature range of 500-715 °C. Our experiments demonstrate that the occupancy of the X-site in combination with the changing concentrations of Al and Mg can be used to monitor changes in the fluid composition in equilibrium with a growing tourmaline crystal. Currently, this relation can be applied qualitatively to natural tourmaline to explain zoning in Na- and Al/(Al+Mg).  相似文献   

Seasonal abundance and diversity of spiders in two intertidal marsh plant communities     

Mark W. LaSalle  Armando A. de la Cruz 《Estuaries and Coasts》1985,8(4):381-393

The spiders of two Mississippi marsh communities were studied from January 1982 through March 1983. Monthly collections were made in two adjacent marsh plant zones dominated bySpartina cynosuroides (L.) Roth andJuncus roemerianus Scheele respectively. A total of 38 species of spiders (36 inSpartina, 33 inJuncus) representing 13 families were collected. The dominant species in theSpartina zone includedPirata mayaca Gertsch,Lycosa watsoni Gertsch (Lycosidae),Clubiona saltitans Emerton,Scotinella formica (Banks) (Clubionidae),Floricormus sp. (Linyphiidae),Dictyna sylvania Chamberlin & Ivie (Dictynidae),Paramaevia hobbsae (Barnes) (Salticidae), andAgelenopsis barrowsi Gertsch (Agelenidae). The dominant species in theJuncus zone includedLycosa watsoni, Pirata mayaca, Clubiona saltitans andSarinda hentzi (Banks) (Salticidae). Density, biomass, species richness and equitability peaked in May in theJuncus zone and in June in theSpartina zone. Peak levels of density and biomass corresponded to the reproductive activity of the common species, while diversity patterns were attributable to the reproductive activity of the less common species. Mean values of density and biomass over the study period were 84.8 spiders per m² and 155.6 mg per m² in theSpartina zone and 39.4 spiders per m² and 133.0 mg per m² inJuncus zone. The Juncus zone was flooded more frequently, contained less litter, and supported lower overall density and diversity of spiders.  相似文献   

The system pargasite-H₂O-CO₂: a model for melting of a hydrous mineral with a mixed-volatile fluid—I. Experimental results to 8 kbar     

J.R Holloway 《Geochimica et cosmochimica acta》1973,37(3):651-666

The stability of the amphibole pargasite [NaCa₂Mg₄Al(Al₂Si₆))O₂₂(OH)₂] in the melting range has been determined at total pressures (P) of 1.2 to 8 kbar. The activity of H₂O was controlled independently of P by using mixtures of H₂O + CO₂ in the fluid phase. The mole fraction of H₂O in the fluid ($\text{X}{}_{\mathrm{H}}{}_2\text{O}{}^{\mathrm{1fl}}$) ranged from 1.0 to 0.2.At P < 4 kbar the stability temperature (T) of pargasite decreases with decreasing $\text{X}{}_{\mathrm{H}}{}_2\text{O}{}^{\mathrm{1fl}}$ at constant P. Above P ? 4 kbar stability T increases as $\text{X}{}_{\mathrm{H}}{}_2\text{O}{}^{\mathrm{1fl}}$ is decreased below one, passes through a T maximum and then decreases with a further decrease in $\text{X}{}_{\mathrm{H}}{}_2\text{O}{}^{\mathrm{1fl}}$. This behavior is due to a decrease in the H₂O content of the silicate liquid as $\text{X}{}_{\mathrm{H}}{}_2\text{O}{}^{\mathrm{1fl}}$ decreases. The magnitude of the T maximum increases from about 10°C (relative to the stability T for $\text{X}{}_{\mathrm{H}}{}_2\text{O}{}^{\mathrm{1fl}}\text{= 1}$) at P = 5 kbar to about 30°C at P = 8 kbar, and the position of the maximum shifts from $\text{X}{}_{\mathrm{H}}{}_2\text{O}{}^{\mathrm{1fl}}\text{? 0.6}$ at P = 5 kbar to $\text{X}{}_{\mathrm{H}}{}_2\text{O}{}^{\mathrm{1fl}}\text{? 0.4}$ at P = 8 kbar.The H₂O content of liquid coexisting with pargasite has been estimated as a function of at 5 and 8 kbar P, and can be used to estimate the H₂O content of magmas. Because pargasite is stable at low values of $\text{X}{}_{\mathrm{H}}{}_2\text{O}{}^{\mathrm{1fl}}$ at high P and T, hornblende can be an important phase in igneous processes even at relatively low H₂O fugacities.  相似文献   

CO₂-H₂O mixtures in the geological sequestration of CO₂. I. Assessment and calculation of mutual solubilities from 12 to 100°C and up to 600 bar     

Nicolas Spycher  Karsten Pruess 《Geochimica et cosmochimica acta》2003,67(16):3015-3031

Evaluating the feasibility of CO₂ geologic sequestration requires the use of pressure-temperature-composition (P-T-X) data for mixtures of CO₂ and H₂O at moderate pressures and temperatures (typically below 500 bar and below 100°C). For this purpose, published experimental P-T-X data in this temperature and pressure range are reviewed. These data cover the two-phase region where a CO₂-rich phase (generally gas) and an H₂O-rich liquid coexist and are reported as the mutual solubilities of H₂O and CO₂ in the two coexisting phases. For the most part, mutual solubilities reported from various sources are in good agreement. In this paper, a noniterative procedure is presented to calculate the composition of the compressed CO₂ and liquid H₂O phases at equilibrium, based on equating chemical potentials and using the Redlich-Kwong equation of state to express departure from ideal behavior. The procedure is an extension of that used by King et al. (1992), covering a broader range of temperatures and experimental data than those authors, and is readily expandable to a nonideal liquid phase. The calculation method and formulation are kept as simple as possible to avoid degrading the performance of numerical models of water-CO₂ flows for which they are intended. The method is implemented in a computer routine, and inverse modeling is used to determine, simultaneously, (1) new Redlich-Kwong parameters for the CO₂-H₂O mixture, and (2) aqueous solubility constants for gaseous and liquid CO₂ as a function of temperature. In doing so, mutual solubilities of H₂O from 15 to 100°C and CO₂ from 12 to 110°C and up to 600 bar are generally reproduced within a few percent of experimental values. Fugacity coefficients of pure CO₂ are reproduced mostly within one percent of published reference data.  相似文献   

Water speciation and diffusion in haploandesitic melts at 743-873 K and 100 MPa     

Huaiwei Ni  Yang Liu  Lijin Wang  Youxue Zhang 《Geochimica et cosmochimica acta》2009,73(12):3630-124

Water is an important volatile component in andesitic eruptions and deep-seated andesitic magma chambers. We report an investigation of H₂O speciation and diffusion by dehydrating haploandesitic melts containing ?2.5 wt.% water at 743-873 K and 100 MPa in cold-seal pressure vessels. FTIR microspectroscopy was utilized to measure species [molecular H₂O (H₂O_m) and hydroxyl group (OH)] and total H₂O (H₂O_t) concentration profiles on the quenched glasses from the dehydration experiments. The equilibrium constant of the H₂O speciation reaction H₂O_m+O?2OH, K = (X_OH)²/(X_H2OmX_O) where X means mole fraction on a single oxygen basis, in this Fe-free andesite varies with temperature as ln K = 1.547-2453/T where T is in K. Comparison with previous speciation data on rhyolitic and dacitic melts indicates that, for a given water concentration, Fe-free andesitic melt contains more hydroxyl groups. Water diffusivity at the experimental conditions increases rapidly with H₂O concentration, contrary to previous H₂O diffusion data in an andesitic melt at 1608-1848 K. The diffusion profiles are consistent with the model that molecular H₂O is the diffusion species. Based on the above speciation model, H₂O_m and H₂O_t diffusivity (in m²/s) in haploandesite at 743-873 K, 100 MPa, and H₂O_t ? 2.5 wt.% can be formulated as