Endmember graphics

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.     

The construction of extreme compositions

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.     

On the optically biaxial character and heterogeneity of anthracites

The results of the study of optical properties of 13 anthracites from different parts of the world are presented in this paper. Measurements of reflectance values were made on non-oriented vitrinite grains for a minimum of 300 points per sample. The reconstruction of Reflectance Indicating Surfaces (RIS) were made by Kilby's method [Kilby, W.E., 1988. Recognition of vitrinite with non-uniaxial negative reflectance characteristics. Int. J. Coal Geol. 9, 267–285; Kilby, W.E., 1991. Vitrinite reflectance measurement — some technique enhancements and relationships. Int. J. Coal Geol. 19, 201–218]. It was found that the use of Kilby's method for strongly anisotropic materials like anthracites did not give unambiguous results. Some improvement in Kilby's method, consisting of the division of the cumulative cross-plot into several elemental components, is suggested. Each elemental cross-plot corresponds to a textural class of anthracite, which is characterized by the values of RIS main axes R_MAX^(k), R_INT^(k) and R_MIN^(k) (k=1,2,…n; n — number of classes). The global texture of anthracite is characterized as a RIS with main axes calculated as the weighted means of , and for each class of this anthracite.The division of cumulative Kilby's cross-plot on elemental components makes possible the calculation of new coefficients H_t and H₁₀ characterizing the heterogeneity of the structure and texture of anthracites. The results of our study show that all anthracites have biaxial negative textures, but their heterogeneity varies in a wide range of H_t and H₁₀ coefficients depending upon the individual coal basin.     

Solving the kriging problem by using the Gram-Schmidt orthogonalization

This paper presents an approach to solve the kriging problem, defined in terms of projections, by using Gram-Schmidt orthogonalization. The Gram-Schmidt orthogonalization allows us to find an optimal approximationY* in then-dimensional subspaceH _n of any vectorY element of a Hilbert spaceH. This approach requiresO(n ³) multiplication operations to obtain an orthogonal basis, andO(n ²) multiplications needed to calculate kriging solution for a given point.     

H2O activity in concentrated NaCl solutions at high pressures and temperatures measured by the brucite-periclase equilibrium

 H₂O activities in concentrated NaCl solutions were measured in the ranges 600°–900° C and 2–15 kbar and at NaCl concentrations up to halite saturation by depression of the brucite (Mg(OH)₂) – periclase (MgO) dehydration equilibrium. Experiments were made in internally heated Ar pressure apparatus at 2 and 4.2 kbar and in 1.91-cm-diameter piston-cylinder apparatus with NaCl pressure medium at 4.2, 7, 10 and 15 kbar. Fluid compositions in equilibrium with brucite and periclase were reversed to closures of less than 2 mol% by measuring weight changes after drying of punctured Pt capsules. Brucite-periclase equilibrium in the binary system was redetermined using coarsely crystalline synthetic brucite and periclase to inhibit back-reaction in quenching. These data lead to a linear expression for the standard Gibbs free energy of the brucite dehydration reaction in the experimental temperature range: ΔG° (±120J)=73418–134.95T(K). Using this function as a baseline, the experimental dehydration points in the system MgO−H₂O−NaCl lead to a simple systematic relationship of high-temperature H₂O activity in NaCl solution. At low pressure and low fluid densities near 2 kbar the H₂O activity is closely approximated by its mole fraction. At pressures of 10 kbar and greater, with fluid densities approaching those of condensed H₂O, the H₂O activity becomes nearly equal to the square of its mole fraction. Isobaric halite saturation points terminating the univariant brucite-periclase curves were determined at each experimental pressure. The five temperature-composition points in the system NaCl−H₂O are in close agreement with the halite saturation curves (liquidus curves) given by existing data from differential thermal analysis to 6 kbar. Solubility of MgO in the vapor phase near halite saturation is much less than one mole percent and could not have influenced our determinations. Activity concentration relations in the experimental P-T range may be retrieved for the binary system H₂O-NaCl from our brucite-periclase data and from halite liquidus data with minor extrapolation. At two kbar, solutions closely approach an ideal gas mixture, whereas at 10 kbar and above the solutions closely approximate an ideal fused salt mixture, where the activities of H₂O and NaCl correspond to an ideal activity formulation. This profound pressure-induced change of state may be characterized by the activity (a) – concentration (X) expression: a _{H 2}O=X _{H 2}O/(1+αX _NaCl), and a _NaCl=(1+α)^(1+α)[X _NaCl/(1+αX _NaCl)]^(1+α). The parameter α is determined by regression of the brucite-periclase H₂O activity data: α=exp[A–B/ϱ_{H 2}O ]-CP/T, where A=4.226, B=2.9605, C=164.984, and P is in kbar, T is in Kelvins, and ϱ_{H 2}O is the density of H₂O at given P and T in g/cm³. These formulas reproduce both the H₂O activity data and the NaCl activity data with a standard deviation of ±0.010. The thermodynamic behavior of concentrated NaCl solutions at high temperature and pressure is thus much simpler than portrayed by extended Debye-Hückel theory. The low H₂O activity at high pressures in concentrated supercritical NaCl solutions (or hydrosaline melts) indicates that such solutions should be feasible as chemically active fluids capable of coexisting with solid rocks and silicate liquids (and a CO₂-rich vapor) in many processes of deep crustal and upper mantle metamorphism and metasomatism. Received: 1 September 1995 / Accepted: 24 March 1996     

Pressure, temperature and fluid composition during amphibolite facies metamorphism of graphitic metapelites, Howard Ridge, British Columbia

ABSTRACT Graphitic metapelites from the Howard Ridge area, British Columbia, have been studied to estimate the pressure, temperature and fluid composition attending amphibolite facies metamorphism. Results from thermobarometric calculations indicate that P-T conditions of 610–625°C and 6.7kbar were reached during metamorphism. The equilibrium paragonite-quartz-albite-kyanite-H₂O gives significantly different estimates of XH₂O in the metamorphic fluid using different paragonite solution models. Estimates of XH₂O range from a maximum of 0.93 (Eugster et al., 1972) to a minimum of 0.29 (Chatterjee & Flux, 1986). H₂O estimates obtained using the Eugster et al. (1972) and Chatterjee & Froese (1975) solution models give similar results (i.e. 0.8 ± 0.1 versus 0.7 ± 0.1, respectively). Non-ideal mixing in the C-O-H system provides an XH₂O estimate of 0.74 at H₂O maximum conditions, 0.5 log units below the QFM buffer. The Chatterjee & Flux (1986) paragonite solution model provides unrealistically low estimates of XH₂O relative to other paragonite solution models, C-O-H equilibria, and published fluid inclusion and mineral equilibria data. Consistent estimates of fluid composition between C-O-H and mineral equilibria suggest that a H₂O-rich fluid attended metamorphism of graphitic metapelites at Howard Ridge.     

Theory for preliminary negative impulse in storm sudden commencement inH at equatorial stations

It is shown that the storm sudden commencement (SSC) inH field at low latitude station consists of only a positive excursion when the interplanetary shock due to the solar plasma impinging on the magnetosphere is associated with a southward excursion of the interplanetary magnetic field (IMF). When the signature of SSC at low latitude station consists of a preliminary negative excursion preceding the main positive excursion of theH field, the solar plasma causing the compression is associated with a northward excursion of the IMF. It is suggested that the signature of SSC(H) at equatorial stations is the result of combined effect of the compression of magnetosphere by the solar plasma as well as due to the electric field effects associated with the velocity of the solar plasma (v) interacting with the northward component (Bz) of the interplanetary field (i.e.,E =−v _x Bz).     

Effect of salt of various concentrations on liquid limit,and hydraulic conductivity of different soil-bentonite mixtures

Effect of the various concentrations of NaCl and CaCl₂ on the four different soil-bentonite mixtures has been evaluated. The results show that the liquid limit of the mixtures decreases with an increase in the salt concentration. Liquid limit decreased significantly with an increase in CaCl₂ concentration from 0 to 0.1 N. However, a further increase in the concentration did not produce any significant decrease in liquid limit. A quite opposite trend was observed for the NaCl solution. An increase in NaCl concentration from 0 to 0.1 N did not produce any major decrease in the liquid limit, but a further increase in concentration from 0.1 to 1 N decreased the liquid limit significantly. Consolidation tests were carried out on the mixtures to evaluate the effect of mineralogical composition of the bentonite on the hydraulic conductivity (k) of the mixture in the presence of various salts concentrations. The k for any mixtures was found to be decreasing with decrease in the salt concentration. At relatively low concentration, Ca²⁺ had more effect on the k in comparison to the same concentration of Na⁺. However, at 1 N of NaCl and CaCl₂ almost an equal value of k was observed. A comparison of the performance of four bentonites showed that the mixture with bentonite having highest exchangeable sodium percentage (ESP) exhibited the lowest k when permeated with de-ionized (DI) water, however, k increased with an increase in the salt concentration. Similarly, mixture with a bentonite of lower ESP exhibited a higher k with DI water but with the increase in the salt concentration alteration in the k, compared to all other mixtures, was relatively less.     

A type curve approach to estimatingp for ap-normal transformation

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.     

Simulation of geological surfaces using fractals

Methods suggested in the past for simulated ore concentration or pollution concentration over an area of interest, subject to the condition that the simulated surface is passing through specifying points, are based on the assumption of normality. A new method is introduced here which is a generalization of the subdivision method used in fractals. This method is based on the construction of a fractal plane-to-line functionf(x, y, R, e, u), where(x, y) is in[a, b]×[c, d], R is the autocorrelation function,e is the resolution limit, andu is a random real function on [–1, 1]. The simulation using fractals escapes from any distribution assumptions of the data. The given network of points is connected to form quadrilaterals; each one of the quadrilaterals is split based on ways which are extensions of the well-known subdivision method. The quadrilaterals continue to split and grow until resolution obtained in bothx andy directions is smaller than a prespecified resolution. If thex coordinate of theith quadrilateral is in[a _i ,b _i ] and they coordinate is in[c _i ,d _i ], the growth of this quadrilateral is a function of(b _i –a _i ) and(d _i –c _i ); the quadrilateral could grow toward the positive or negativez axis with equal probability forming four new quadrilaterals having a common vertex.This paper was presented at Emerging Concepts, MGUS-87 Conference, Redwood City, California, 13–15 April 1987.     

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

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.     

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

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).     

Ri-μi/μm-Ci dependent oblateness of deformed pebbles in the Baraitha conglomerate,Central India and tectonic implications

Strain analysis of the Baraitha conglomerate is attempted by direct measurements on extracted pebbles and by micrometric analysis. The overall deformation is of flattening type, with thek value lower by more than half in the matrix than in the pebbles. The viscosity contrast between pebbles and matrix (μ _i/μ_m) is in the ratio of 2:1 and the bulk deformation appears to be strongly controlled by C_i (concentration of pebbles expressed as percentage). The total shortening (≃35%) in the Baraitha conglomerate is comparable with the shortening accomplished in the folding of the overlying Bijawar Group volcanosedimentary sequence. The bulk strain axesX _t, Y_t andZ _t, as determined from the analysis of the deformed conglomerate, are unsymmetrically oriented with reference to folds formed by oblique flexural-slip with neitherX _t norY _tcoincident with the fold hinges. The lack of transection of folds by cleavage again suggests flattening deformation. The extension in theY _tdirection is greater in the matrix than in the pebbles.     

Topological relations in multisystems of more than n+ 3 phases 1

Multisystems of n+k (k > 3) phases are very complicated and knowledge of them has suffered as a result. The successful solution of the topological relationships in n+ 3 phase multisystems by Zen (1966, 1967) and Zen & Roseboom (1972) has aroused much interest regarding what will happen in a multisystem of more than n+ 3 phases. Since 1979, some important research results on this topic have been published. These results have expounded the substantial rules governing the appearance of phase relations in phase diagrams of n - k (k > 3) phase multisystems. The most significant conclusions include: (1) It is impossible to incorporate all the possible phase relations in an n+k (k > 3) phase multisystem in a single closed net. Therefore, it is no longer enough to use only a single closed net to depict the topological relations involved in these types of multisystems. Instead, one or more groups of closed nets, namely the complete system(s) of closed nets are necessary for this purpose. (2) A principle called the Combination Principle has been proposed and proved. It states: Any closed net of one n+k (k > 3) phase multisystem must be a combination of two or more distinct n+ 3 order submultisystem closed nets belonging to the given n+k phase multisystem, if it is not one of the n+ 3 order submultisystem closed nets itself. The combination principle provides both a theoretical basis and a practical method for the construction of closed nets and, hence, for the derivation of the real phase diagrams for any n+k (k > 3) phase multisystem. (3) A theorem on divariant-assemblage-characteristic-stability-polygons is also important to our understanding of the n+k (k± 3) phase multisystem closed nets. This theorem can be stated as follows: A divariant assemblage of an n+k (k± 3) phase multisystem will be stable in an l-polygon lacking diagonals in an appropriate set of closed-net-diagrams, and this l-polygon may be at least a triangle, and at most a k-polygon. In addition, the closed-net-diagrams of unary and binary n+ 4 phase multisystems derived respectively by Guo (1980b, 1980c, 1981a) and by Roseboom & Zen (1982) have also been summarized. The combination principle is applied to a practical petrological problem in this paper, dealing with 7 phases in the system FeO-Fe₂O₃-SiO₂.     

Social vulnerability index for coastal communities at risk to hurricane hazard and a changing climate

This paper presents the development of the Coastal Community Social Vulnerability Index (CCSVI) in order to quantify the social vulnerability of hurricane-prone areas under various scenarios of climate change. The 2004–2005 Atlantic hurricane seasons is estimated to have caused 150 billion dollars in damages, and in recent years, the annual hurricane damage in the United States is estimated at around150 billion dollars in damages, and in recent years, the annual hurricane damage in the United States is estimated at around 6 billion. Hurricane intensity or/and frequency may change due to the increase in sea surface temperature as a result of climate change. Climate change is also predicted to cause a rise in sea levels, potentially resulting in higher storm surges. The CCSVI combines the intensity of hurricanes and hurricane-induced surge to create a comprehensive index that considers the effects of a changing climate. The main contributing factors of social vulnerability (such as race, age, gender, and socioeconomic status) in hurricane-prone areas are identified through a principal components analysis. The impact of social characteristics on the potential hurricane damage under various scenarios of climate change are evaluated using Miami-Dade County, Florida, as a case study location. This study finds that climate change may have a significant impact on the CCSVI.     

Rn solution by the circulating fluids in a “hot dry rock” geothermal reservoir

The mechanism of²²²Rn release into fracture fluids by direct alpha-recoil, lattice and grain boundary/micro-crack diffusion is discussed. Experimental measurements of²²²Rn release into surrounding air and water phases have been made for crystalline rock specimens with well defined surface areas. The²²²Rn flux from an infinite plane surface and hence the effective diffusion length of²²²Rn in the rock matrix has been estimated.The²²²Rn flux from plane crystalline rock surfaces has been used in conjunction with a simple hydrological model of the reservoir to calculate the²²²Rn content of the return fluids of a geothermal doublet circulation system. For given production rate and piezometric difference between the injection and production wells, the²²²Rn content of the return fluid is dependent upon the distribution of flow path lengths and fracture apertures in the reservoir. Matching of the calculated and experimental²²²Rn contents of the return fluids has been used to select appropriate parameters for the reservoir model and hence to estimate the extent of the heat-transfer surface. The model estimates the fracture width of the flow paths, total swept surface area and fracture volume within the reservoir.     

222Rn solution by the circulating fluids in a “hot dry rock” geothermal reservoir

The mechanism of²²²Rn release into fracture fluids by direct alpha-recoil, lattice and grain boundary/micro-crack diffusion is discussed. Experimental measurements of²²²Rn release into surrounding air and water phases have been made for crystalline rock specimens with well defined surface areas. The²²²Rn flux from an infinite plane surface and hence the effective diffusion length of²²²Rn in the rock matrix has been estimated.The²²²Rn flux from plane crystalline rock surfaces has been used in conjunction with a simple hydrological model of the reservoir to calculate the²²²Rn content of the return fluids of a geothermal doublet circulation system. For given production rate and piezometric difference between the injection and production wells, the²²²Rn content of the return fluid is dependent upon the distribution of flow path lengths and fracture apertures in the reservoir. Matching of the calculated and experimental²²²Rn contents of the return fluids has been used to select appropriate parameters for the reservoir model and hence to estimate the extent of the heat-transfer surface. The model estimates the fracture width of the flow paths, total swept surface area and fracture volume within the reservoir.     

Thermodynamics of hydration of Na- and K-clinoptilolite to 300 °C

The hydration state of Na- and K-exchanged clinoptilolite from Castle Creek (Idaho, U.S.A.) has been measured by a pressure titration method to 300 °C and P _H2O<30 bars. The water content of clinoptilolite can be predicted as a function of water activity and temperature with the equation: a _H2O = [exp[[−ΔH _h ^∘/nRT] + [ΔS _h ^∘/nR] − 1/nRT· [W₁ X _h + W₂ X _{h 2}]− ln(X _a/X _h)]]⁻¹ where T is degrees in Kelvin, ΔH _h ^∘ is the standard molal enthalpy of hydration, ΔS _h ^∘ is the entropy of hydration, X _h and X _a are, respectively, the mole fractions of the hydrous and anhydrous components of the solid solution, W ₁ and W ₂ are interaction parameters, n is the maximum number of moles of H₂O per formula unit (based on 12 oxygens), and R is the gas constant. This equation can be used to locate clinoptilolite-H₂O isohydrons in a _H2O-T space below the liquid-vapor equilibrium curve of water. The standard molal Gibbs free energy of hydration is −47.62 ± 5.52 kJ/mol H₂O and −5.40 ± 2.71 kJ/mol H₂O for the Na- and K-clinoptilolite, respectively. These standard-state thermodynamic properties of clinoptilolite hydration are in good agreement with previous data at low H₂O pressures. The experiments indicate that clinoptilolite progressively dehydrates with increasing temperature at pressures along the liquid-vapor equilibrium curve. Kinetic data above 150 °C show that clinoptilolite dehydration and hydration reactions are fast and reversible and that steady-state hydration states are attained in minutes. Received: 19 June 1998 / Revision, accepted 14 December 1998     

Operator error in petrographic point-count analysis: A theoretical approach

Operator error in petrographic point-count analysis introduces bias into the estimates of proportion in a thin section. A correction for this bias, leading to an unbiased estimator of the true proportion in that thin section, is here proposed. Operator error also affects the confidence interval, and in this situation, too, an adjustment is possible. The approach proposed requires that the probabilities associated with operator error, categorized into A-type and B-type errors, are known or assumed. The A-type operator error tends to underestimate the true proportion in a thin section, whereas the B-type operator error tends to overestimate it.     

Calcite dissolution kinetics in saline waters

The effect of ionic strength (I), pCO₂, and temperature on the dissolution rate of calcite was investigated in magnesium-free, phosphate-free, low calcium (m_Ca2+ ≈ 0.01 m) simple KCl and NaCl solutions over the undersaturation range of 0.4 ≤ Ω_calcite ≤ 0.8. First-order kinetics were found sufficient to describe the rate data where the rate constant (k) is dependent on the solution composition. Rates decreased with increasing I and were faster in KCl than NaCl solutions at the same I indicating that Na⁺ interacts more strongly with the calcite surface than K⁺ or that water is less available in NaCl solutions. Rates increased with increasing pCO₂ and temperature, and their influences diminished at high I. Arrhenius plots yielded a relatively high activation energy (E_a ≈ 20 ± 2 kJ mol^− 1) which indicated that dissolution was dominated by surface-controlled processes. The multiple regression model (MR) of Gledhill and Morse (2006a) was found to adequately describe the results at high I in NaCl solutions, but caution must be used when extrapolating to low I or pCO₂ values. These results are consistent with the hypothesis that the mole fraction of “free” solvent (X_{“free”H2O}) plays a significant role in the dissolution kinetics of calcite with a minimum value of  45–55% required for dissolution to proceed in undersaturated solutions at 25–55 °C and pCO₂ = 0.1–1 atm. This hypothesis has been incorporated into a modified version of the MR model of Gledhill and Morse (2006a) where X_{“free”H2O} has replaced I and the Ca²⁺ and Mg²⁺ terms have been dropped: