Predicting saturated hydraulic conductivity using particle swarm optimization and genetic algorithm

Soil saturated hydraulic conductivity (K_s) is considered as soil basic hydraulic property, and its precision estimation is a key element in modeling water flow and solute transport processes both in the saturated and vadose zones. Although some predictive methods (e.g., pedotransfer functions, PTFs) have been proposed to indirectly predict K_s, the accuracy of these methods still needs to be improved. In this study, some easily available soil properties (e.g., particle size distribution, organic carbon, calcium carbonate content, electrical conductivity, and soil bulk density) are employed as input variables to predict K_s using a fuzzy inference system (FIS) trained by two different optimization techniques: particle swarm optimization (PSO) and genetic algorithm (GA). To verify the derived FIS, 113 soil samples were taken, and their required physical properties were measured (113 sample points?×?7 factors?=?791 input data). The initial FIS is compared with two methods: FIS trained by PSO (PSO-FIS) and FIS trained by GA (GA-FIS). Based on experimental results, all three methods are compared according to some evaluation criteria including correlation coefficient (r), modeling efficiency (EF), coefficient of determination (CD), root mean square error (RMSE), and maximum error (ME) statistics. The results showed that the PSO-FIS model achieved a higher level of modeling efficiency and coefficient of determination (R²) in comparison with the initial FIS and the GA-FIS model. EF and R² values obtained by the developed PSO-FIS model were 0.69 and 0.72, whereas they were 0.63 and 0.54 for the GA-FIS model. Moreover, the results of ME and RMSE indices showed that the PSO-FIS model can estimate soil saturated hydraulic conductivity more accurate than the GA-FIS model with ME?=?10.4 versus 11.5 and RMSE?=?5.2 versus 5.5 for PSO-FIS and GA-FIS, respectively.     

Under stress permeability determination of the Meuse/Haute-Marne mudstone

In the underground waste isolation projects such as the ANDRA'one in the site of Bure, the transport properties of the surrounding rock mass is of fundamental importance. To measure very low permeability, we use the modified version of the pulse test proposed by Hsieh et al. [Hsieh, P.A., Tracy, J.V., Neuzil, C.E., Bredehoeft, J.D., Silliman, S.E., 1981. A transient laboratory method for determining the hydraulic properties of ‘tight’ rocks — I. Theory. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. Vol. 18, pp. 245-252] which enables the intrinsic permeability, k, and the specific storage coefficient, S_s, of rocks such as mudstone to be characterized. In this paper, the special effort performed on the laboratory apparatus design, to ensure a good sensitivity of the rock response with respect to both parameters, k and S_s, is presented. In addition, two parameters identification procedures are proposed: the graphical method given by Hsieh et al. [Hsieh, P.A., Tracy, J.V., Neuzil, C.E., Bredehoeft, J.D., Silliman, S.E., 1981. A transient laboratory method for determining the hydraulic properties of ‘tight’ rocks — I. Theory. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. Vol. 18, pp. 245-252] and a parameter identification based on the solution of an inverse problem. The efficiency of the apparatus design and the parameters identification procedures is then demonstrated though some pulse tests performed on the Meuse/Haute-Marne mudstone.     

Vapor pressures and evaporation coefficients for melts of ferromagnesian chondrule-like compositions

To determine evaporation coefficients for the major gaseous species that evaporate from silicate melts, the Hertz-Knudsen equation was used to model the compositions of residues of chondrule analogs produced by evaporation in vacuum by Hashimoto [Hashimoto A. (1983) Evaporation metamorphism in the early solar nebula-evaporation experiments on the melt FeO-MgO-SiO₂-CaO-Al₂O₃ and chemical fractionations of primitive materials. Geochem. J. 17, 111-145] and Wang et al. [Wang J., Davis A. M., Clayton R. N., Mayeda T. K., Hashimoto A. (2001) Chemical and isotopic fractionation during the evaporation of the FeO-MgO-SiO₂-CaO-Al₂O₃-TiO₂ rare earth element melt system. Geochim. Cosmochim. Acta 65, 479-494], in vacuum and in H₂ by Yu et al. [Yu Y., Hewins R. H., Alexander C. M. O’D., Wang J. (2003) Experimental study of evaporation and isotopic mass fractionation of potassium in silicate melts. Geochim. Cosmochim. Acta 67, 773-786], and in H₂ by Cohen et al. [Cohen B. A., Hewins R. H., Alexander C. M. O’D. (2004) The formation of chondrules by open-system melting of nebular condensates. Geochim. Cosmochim. Acta 68, 1661-1675]. Vapor pressures were calculated using the thermodynamic model of Ghiorso and Sack [Ghiorso M. S., Sack R. O. (1995) Chemical mass transfer in magmatic processes IV. A revised and internally consistent thermodynamic model for the interpolation and extrapolation of liquid-solid equilibria in magmatic systems at elevated temperatures and pressures. Contrib. Mineral. Petrol. 119, 197-212], except for the late, FeO-free stages of the Wang et al. (2001) and Cohen et al. (2004) experiments, where the CMAS activity model of Berman [Berman R. G. (1983) A thermodynamic model for multicomponent melts, with application to the system CaO-MgO-Al₂O₃-SiO₂. Ph.D. thesis, University of British Columbia] was used. From these vapor pressures, evaporation coefficients (α) were obtained that give the best fits to the time variation of the residue compositions. Evaporation coefficients derived for Fe_(g), Mg_(g), and SiO_(g) from the Hashimoto (1983) experiments are similar to those found by Alexander [Alexander C. M. O’D. (2004) Erratum. Meteoritics Planet. Sci. 39, 163] in his EQR treatment of the same data and also adequately describe the FeO-bearing stages of the Wang et al. (2001) experiments. From the Yu et al. (2003) experiments at 1723 K, α_Na = 0.26 ± 0.05, and α_K = 0.13 ± 0.02 in vacuum, and α_Na = 0.042 ± 0.020, andα_K = 0.017 ± 0.002 in 9 × 10⁻⁵ bar H₂. In the FeO-free stages of the Wang et al. (2001) experiments, α_Mg and α_SiO are significantly different from their respective values in the FeO-bearing portions of the same experiments and from the vacuum values obtained at the same temperature by Richter [Richter F. M., Davis A. M., Ebel D. S., Hashimoto A. (2002) Elemental and isotopic fractionation of Type B calcium-, aluminum-rich inclusions: experiments, theoretical considerations, and constraints on their thermal evolution. Geochim. Cosmochim. Acta 66, 521-540] for CMAS compositions much lower in MgO. When corrected for temperature, the values of α_Mg and α_SiO that best describe the FeO-free stages of the Wang et al. (2001) experiments also adequately describe the FeO-free stage of the Cohen et al. (2004) H₂ experiments, but α_Fe that best describes the FeO-bearing stage of the latter experiment differs significantly from the temperature-corrected value derived from the Hashimoto (1983) vacuum data.     

Sap flow characteristics of four typical species in desert shelter forest and their responses to environmental factors

Sap flows of four typical species, Populus. russkii Jabl., Populus euphratica Olive., Ulmus pumila L., and Elaeagnus angustifolia L., of artificial shelter forest in a desert area were monitored in all-weather conditions using SF300 Sap flow Meter based on the theory of thermal compensation. Meanwhile, air temperature (T _a), leaf temperature (T _l), soil temperature (T _s), relative humidity (RH), and wind velocity (V _w) were simultaneously recorded by an automatic weather station. The results indicate that (1) the diurnal processes of stem sap flows of P. russkii Jabl., P. euphratica Olive., and U. pumila L., but not E. angustifolia L., show an obvious circadian rhythm. Significant differences of stem sap flow rates were found among species, but not genus. The average sap flow rate of P. russkii Jabl. is 13.8-fold of that of E. angustifolia L. The order of sap flux density (SFD) from the largest to the smallest is P. russkii Jabl., P. euphratica Olive, U. pumila L. and E. angustifolia L.; (2) compared with 373?mm, 747?mm irrigation can induce microenvironmental changes that result in the suppression of photosynthesis and transpiration and the decline of stem sap flow rates of the above four species, indicating 373?mm irrigation meets the growth needs of the above species during experiment; (3) sap flow rates are different at different stem positions: the flow rates of P. russkii Jabl., U. pumila L. and E. angustifolia L., but not P. euphratica Olive, decline gradually from cambium to pith; (4) the correlation analysis indicates that stem sap flow is negatively correlated with RH and T _s and positively correlated with T _a, T _l and saturation vapor pressure deficit (VPD). The sap flow rate of P. russkii Jabl. is significantly affected by V _w due to its large size and height. In addition, a model was established by stepwise regression analysis to estimate the relationship between the environmental factors and stem sap flows of the above four typical species of shelter forest in the desert area.     

Effect of Model Scale and Particle Size Distribution on PFC3D Simulation Results

This paper investigates the effect of model scale and particle size distribution on the simulated macroscopic mechanical properties, unconfined compressive strength (UCS), Young’s modulus and Poisson’s ratio, using the three-dimensional particle flow code (PFC3D). Four different maximum to minimum particle size (d _max/d _min) ratios, all having a continuous uniform size distribution, were considered and seven model (specimen) diameter to median particle size ratios (L/d) were studied for each d _max/d _min ratio. The results indicate that the coefficients of variation (COVs) of the simulated macroscopic mechanical properties using PFC3D decrease significantly as L/d increases. The results also indicate that the simulated mechanical properties using PFC3D show much lower COVs than those in PFC2D at all model scales. The average simulated UCS and Young’s modulus using the default PFC3D procedure keep increasing with larger L/d, although the rate of increase decreases with larger L/d. This is mainly caused by the decrease of model porosity with larger L/d associated with the default PFC3D method and the better balanced contact force chains at larger L/d. After the effect of model porosity is eliminated, the results on the net model scale effect indicate that the average simulated UCS still increases with larger L/d but the rate is much smaller, the average simulated Young’s modulus decreases with larger L/d instead, and the average simulated Poisson’s ratio versus L/d relationship remains about the same. Particle size distribution also affects the simulated macroscopic mechanical properties, larger d _max/d _min leading to greater average simulated UCS and Young’s modulus and smaller average simulated Poisson’s ratio, and the changing rates become smaller at larger d _max/d _min. This study shows that it is important to properly consider the effect of model scale and particle size distribution in PFC3D simulations.     

Particle breakage of uniformly graded carbonate sands in dry/wet condition subjected to compression/shear tests

The behaviour of a granular material is primarily affected by its particle size distribution (PSD), which is not necessarily a soil constant as assumed in traditional soil mechanics. The PSD may change over time due to mechanical as well as environmental actions. In this study, a series of ring shear tests and one-dimensional compression tests were completed on carbonate sand, in both dry and saturated conditions. Samples were prepared with different initial uniform gradings, to investigate: (1) the influence of the saturation state and initial grading on mechanical and deformational behaviour of carbonate sands and (2) the evolution of the PSD as a result of breakage. The ring shear tests show that the residual friction angle remains almost constant, but dilatancy reduces with increasing saturation degree. In the one-dimensional compression test, the yield stress decreases with increasing saturation degree, but the compressibility (as defined by C_c) remains almost constant, irrespective of the saturation state. Moreover, saturated samples suffer more breakage than dry samples during ring shear tests, while there is no obvious effect of saturation state on particle breakage in one-dimensional compression. A recently proposed PSD model with only two parameters (λ_p and κ_p) is employed to model the evolution of PSD, as it can more broadly capture the whole PSD throughout the breakage process than existing breakage indices. Test results demonstrate that parameter λ_p is linearly related to Einav’s breakage index \( B_{\text{r}}^{*} \) and is dependent on initial grading, but independent of test mode. Parameter κ_p is in power relationship with \( B_{\text{r}}^{*} \) and is independent of initial grading or test mode. The evolution of parameters λ_p and κ_p is related to the input work for both ring shear and compression tests, with λ_p being hyperbolically related to input work and κ_p in power relationship with input work. Using such an evolution law provides an alternative approach to capture the effects of particle breakage in constitutive models.

     

BRYOCARB: A process-based model of thallose liverwort carbon isotope fractionation in response to CO2, O2, light and temperature

Evidence from laboratory experiments indicates that fractionation against the heavy stable isotope of carbon (Δ¹³C) by bryophytes (liverworts and mosses) is strongly dependent on atmospheric CO₂. This physiological response may therefore provide the basis for developing a new terrestrial CO₂ proxy [Fletcher, B.J., Beerling, D.J., Brentnall, S.J., Royer, D.L., 2005. Fossil bryophytes as recorders of ancient CO₂ levels: experimental evidence and a Cretaceous case study. Global Biogeochem. Cycles19, GB3012]. Here, we establish a theoretical basis for the proxy by developing an extended model of bryophyte carbon isotope fractionation (BRYOCARB) that integrates the biochemical theory of photosynthetic CO₂ assimilation with controls on CO₂ supply by diffusion from the atmosphere. The BRYOCARB model is evaluated against measurements of the response of liverwort photosynthesis and Δ¹³C to variations in atmospheric O₂, temperature and irradiance at different CO₂ concentrations. We show that the bryophyte proxy is at least as sensitive to variations in atmosphere CO₂ as the two other leading carbon isotope-based approaches to estimating palaeo-CO₂ levels (δ¹³C of phytoplankton and of paleosols). Mathematical inversion of BRYOCARB provides a mechanistic means of estimating atmospheric CO₂ levels from fossil bryophyte carbon that can explicitly account for the effects of past differences in O₂ and climate.     

Thermodynamic modeling of binary CH4-H2O fluid inclusions

This work reports the application of thermodynamic models, including equations of state, to binary (salt-free) CH₄-H₂O fluid inclusions. A general method is presented to calculate the compositions of CH₄-H₂O inclusions using the phase volume fractions and dissolution temperatures of CH₄ hydrate. To calculate the homogenization pressures and isolines of the CH₄-H₂O inclusions, an improved activity-fugacity model is developed to predict the vapor-liquid phase equilibrium. The phase equilibrium model can predict methane solubility in the liquid phase and water content in the vapor phase from 273 to 623 K and from 1 to 1000 bar (up to 2000 bar for the liquid phase), within or close to experimental uncertainties. Compared to reliable experimental phase equilibrium data, the average deviation of the water content in the vapor phase and methane solubility in the liquid phase is 4.29% and 3.63%, respectively. In the near-critical region, the predicted composition deviations increase to over 10%. The vapor-liquid phase equilibrium model together with the updated volumetric model of homogenous (single-phase) CH₄-H₂O fluid mixtures (Mao S., Duan Z., Hu J. and Zhang D. (2010) A model for single-phase PVTx properties of CO₂-CH₄-C₂H₆-N₂-H₂O-NaCl fluid mixtures from 273 to 1273 K and from 1 to 5000 bar. Chem. Geol.275, 148-160), is applied to calculate the isolines, homogenization pressures, homogenization volumes, and isochores at specified homogenization temperatures and compositions. Online calculation is on the website: http://www.geochem-model.org/.     

Prediction of strength parameters of sedimentary rocks using artificial neural networks and regression analysis

Accurate laboratory measurement of geo-engineering properties of intact rock including uniaxial compressive strength (UCS) and modulus of elasticity (E) involves high costs and a substantial amount of time. For this reason, it is of great necessity to develop some relationships and models for estimating these parameters in rock engineering. The present study was conducted to forecast UCS and E in the sedimentary rocks using artificial neural networks (ANNs) and multivariable regression analysis (MLR). For this purpose, a total of 196 rock samples from four rock types (i.e., sandstone, conglomerate, limestone, and marl) were cored and subjected to comprehensive laboratory tests. To develop the predictive models, physical properties of studied rocks such as P wave velocity (V_p), dry density (γ_d), porosity, and water absorption (A_b) were considered as model inputs, while UCS and E were the output parameters. We evaluated the performance of MLR and ANN models by calculating correlation coefficient (R), mean absolute error (MAE), and root-mean-square error (RMSE) indices. The comparison of the obtained results revealed that ANN outperforms MLR when predicting the UCS and E.     

An elastoplastic constitutive model for frozen saline coarse sandy soil undergoing particle breakage

The mechanical property of frozen saline sandy soil is complicated due to its complex components and sensitivity to salt content and confining pressure. Thus, a series of triaxial compression tests were carried out on sandy samples with different Na₂SO₄ contents under different confining pressures to explore the effects of particle breakage, pressure melting, shear dilation and strain softening or hardening. The test results indicate that the stress–strain curves exhibit strain softening/hardening phenomena when the confining pressures are below or above 6 MPa, respectively. A shear dilation phenomenon was observed in the loading process. With increasing confining pressure, the strength firstly increases and then decreases. By taking into consideration the changes between the grain size distributions before and after triaxial compression tests, a failure strength line incorporating the influences of both particle breakage and pressure melting is proposed. In order to describe the deformation characteristics of frozen saline sandy soil, an elastoplastic incremental constitutive model is established based on the test results. The proposed model considers the plastic compressive, plastic shear and breakage mechanisms by adopting the non-associated flow rule. The breakage mechanism can be reflected by an index related to the initial, current and ultimate grain size distributions. The hardening parameters corresponding to compressive and shear mechanisms consider the influence of particle breakage. Then the effect of particle breakage on both the stress–strain and volumetric strain curves is analyzed. The calculated results fit well with the test results, indicating that the developed constitutive model can well describe the mechanical and deformation features of frozen saline sandy soil under various stress levels and stress paths. In addition, the strain softening/hardening, contraction, high dilation and particle breakage can be well captured.

     

Temperature independent thermal expansivities of calcium aluminosilicate melts between 1150 and 1973 K in the system anorthite-wollastonite-gehlenite (An-Wo-Geh): A density model

The thermal expansivities of 10 compositions from within the anorthite-wollastonite-gehlenite (An-Wo-Geh) compatibility triangle have been investigated using a combination of calorimetry and dilatometry on the glassy and liquid samples. The volumes at room temperature were derived from densities measured using the Archimedean buoyancy method. For each sample, density was measured at 298 K using glass that had a cooling-heating history of 10-10 K min⁻¹. The thermal expansion coefficient of the glass from 298 K to the glass transition interval was measured by a dilatometer and the heat capacity was measured using a differential scanning calorimeter from 298 to 1135 K. The thermal expansion coefficient and the heat flow were determined at a heating rate of 10 K min⁻¹ on glasses which were previously cooled at 10 K min⁻¹. Supercooled liquid density, molar volume and molar thermal expansivities were indirectly determined by combining differential scanning calorimetric and dilatometric measurements assuming that the kinetics of enthalpy and shear relaxation are equivalent. The data obtained on supercooled liquids were compared to high-temperature predictions from the models of (Lange, R.A., Carmichael, I.S.E., 1987. Densities of Na₂O-K₂O-CaO-MgO-FeO-Fe₂O₃-Al₂O₃-TiO₂-SiO₂ liquids: New measurements and derived partial molar properties. Geochim. Cosmochim. Acta51, 2931-2946; Courtial, P., Dingwell, D.B., 1995. Nonlinear composition dependence of molar volume of melts in the CaO-Al₂O₃-SiO₂ system. Geochim. Cosmochim. Acta59 (18), 3685-3695; Lange, R.A., 1997. A revised model for the density and thermal expansivity of K₂O-Na₂O-CaO-MgO-Al₂O₃-SiO₂ liquids from 700 to 1900 K: extension to crustal magmatic temperatures. Contrib. Mineral. Petrol.130, 1-11). The best linear fit combines the supercooled liquid data presented in this study and the high temperature data calculated using the Courtial and Dingwell (1995) model. This dilatometric/calorimetric method of determining supercooled liquid molar thermal expansivity greatly increases the temperature range accessible for thermal expansion. It represents a substantial increase in precision and understanding of the thermodynamics of calcium aluminosilicate melts. This enhanced precision demonstrates clearly the temperature independence of the melt expansions in the An-Wo-Geh system. This contrasts strongly with observations for neighboring system such as anorthite-diopside and raises the question of the compositional/structural origins of temperature dependence of thermal expansivity in multicomponent silicate melts.     

GEOCARBSULF: A combined model for Phanerozoic atmospheric O2 and CO2

A model for the combined long-term cycles of carbon and sulfur has been constructed which combines all the factors modifying weathering and degassing of the GEOCARB III model [Berner R.A., Kothavala Z., 2001. GEOCARB III: a revised model of atmospheric CO₂ over Phanerozoic time. Am. J. Sci. 301, 182-204] for CO₂ with rapid recycling and oxygen dependent carbon and sulfur isotope fractionation of an isotope mass balance model for O₂ [Berner R.A., 2001. Modeling atmospheric O₂ over Phanerozoic time. Geochim. Cosmochim. Acta65, 685-694]. New isotopic data for both carbon and sulfur are used and new feedbacks are created by combining the models. Sensitivity analysis is done by determining (1) the effect on weathering rates of using rapid recycling (rapid recycling treats carbon and sulfur weathering in terms of young rapidly weathering rocks and older more slowly weathering rocks); (2) the effect on O₂ of using different initial starting conditions; (3) the effect on O₂ of using different data for carbon isotope fractionation during photosynthesis and alternative values of oceanic δ¹³C for the past 200 million years; (4) the effect on sulfur isotope fractionation and on O₂ of varying the size of O₂ feedback during sedimentary pyrite formation; (5) the effect on O₂ of varying the dependence of organic matter and pyrite weathering on tectonic uplift plus erosion, and the degree of exposure of coastal lands by sea level change; (6) the effect on CO₂ of adding the variability of volcanic rock weathering over time [Berner, R.A., 2006. Inclusion of the weathering of volcanic rocks in the GEOCARBSULF model. Am. J. Sci.306 (in press)]. Results show a similar trend of atmospheric CO₂ over the Phanerozoic to the results of GEOCARB III, but with some differences during the early Paleozoic and, for variable volcanic rock weathering, lower CO₂ values during the Mesozoic. Atmospheric oxygen shows a major broad late Paleozoic peak with a maximum value of about 30% O₂ in the Permian, a secondary less-broad peak centered near the Silurian/Devonian boundary, variation between 15% and 20% O₂ during the Cambrian and Ordovician, a very sharp drop from 30% to 15% O₂ at the Permo-Triassic boundary, and a more-or less continuous rise in O₂ from the late Triassic to the present.     

Inhibition of calcium carbonate precipitation in NaCl brines from 25 to 90°C

The nucleation induction period of CaCO₃ in NaCl brines in the absence and presence of scale inhibitors was experimentally measured at temperatures from 25 to 90°C. A semi-empirical mathematical inhibitor model is presented for the CaCO₃ scale control in industrial processes based upon nucleation theory and experimental observations. Results show that the minimum inhibitor dosage (C_inh) may be obtained from: C_inh=f(s)/b_inh log [t_inh/t₀], where t_inh is the inhibition time, e.g., 20 min, t₀ is the nucleation induction period in the absence of inhibitors, b_inh is the inhibitor efficiency, and f(s) is the safety factor, e.g., 2. Important factors for the kinetics of both nucleation and inhibition have been incorporated in this model including the calcite saturation index (SI), temperature (T), and the molar ratio of Ca to HCO₃ alkalinity (R). In this paper, model parameters are presented for commonly used inhibitors, including 1-hydroxyethylidene-1,1-diphosphonic-acid (HEDP) and nitrilotri(methylene phosphonic) acid (NTMP). Results show that HEDP and NTMP are the best inhibitors for calcite scaling in the systems examined.     

Determination of ground thermal properties for energy piles by thermal response tests

Thermal properties of ground heat exchanger (GHE) such as effective thermal conductivity and borehole thermal resistance are commonly measured in the field by thermal response tests (TRTs). TRT has been proved to be a consolidated method to determine thermal properties of traditional borehole heat exchangers (BHEs). However, there is still lack of data for adopting TRT on energy piles with often a large diameter and deficiency in validation of TRT results with geological materials. In this study, ground thermal properties for typical configured GHEs of energy piles are investigated. Three TRTs are conducted and the obtained results are analyzed. Effective thermal conductivity, λ_eff, of the ground derived by following the traditional linear source model shows large deviation as compared to the thermal conductivity of the geological materials. In order to determine λ_eff properly, the linear source model is modified and an equivalent radius, r_eq, of energy piles is considered. The λ_eff estimated by the modified model shows a good agreement with thermal conductivity of the in situ geological materials. In addition, there has been no obvious correlation between borehole thermal resistances and thermal efficiency due to heat transport of energy piles that depends not only by borehole thermal resistance but also by the pile’s diameter and ground conditions. The findings drawn from this study indicate that the modified model is reasonable and useful in determining thermal properties of energy piles.     

Prediction of vapor-liquid equilibrium and PVTx properties of geological fluid system with SAFT-LJ EOS including multi-polar contribution. Part I: Application to H2O-CO2 system

Molecular based equations of state (EOS) are attractive because they can take into account the energetic contribution of the main types of molecular interactions. This study models vapor-liquid equilibrium (VLE) and PVTx properties of the H₂O-CO₂ binary system using a Lennard-Jones (LJ) referenced SAFT (Statistical Associating Fluid Theory) EOS. The improved SAFT-LJ EOS is defined in terms of the residual molar Helmholtz energy, which is a sum of four terms representing the contributions from LJ segment-segment interactions, chain-forming among the LJ segments, short-range associations and long-range multi-polar interactions. CO₂ is modeled as a linear chain molecule with a constant quadrupole moment, and H₂O is modeled as a spherical molecule with four association sites and a dipole moment. The multi-polar contribution to Helmholtz energy, including the dipole-dipole, dipole-quadrupole, and quadrupole-quadrupole contribution for H₂O-CO₂ system, is calculated using the theory of Gubbins and Twu (1978). Six parameters for pure H₂O and four parameters for pure CO₂ are needed in our model. The Van der Waals one-fluid mixing rule is used to calculate the Lennard-Jones energy parameter and volume parameter for the mixture. Two or three binary parameters are needed for CO₂-H₂O mixtures, which are evaluated from phase equilibrium data of the binary system. Comparison with the experimental data shows that our model represents the PVT properties of CO₂ better than other SAFT EOS without a quadrupole contribution. For the CO₂-H₂O system, our model agrees well with the vapor-liquid equilibrium data from 323-623 K. The average relative deviation for CO₂ solubility (expressed in mole fraction) in water is within 6%. Our model can also predict the PVTx properties of CO₂-H₂O mixtures up to 1073 K and 3000 bar. The good performance of this model indicates that: (1) taking account of the multi-polar contribution explicitly improves the agreement of calculated properties with experimental data at high temperatures and high pressures, (2) the molecular-based EOS with just a few parameters fit to data in the sub-critical region can predict the thermodynamic properties of fluids over a wide range of P-T conditions.     

Neodymium diffusion in orthopyroxene: Experimental studies and applications to geological and planetary problems

We have determined the Nd³⁺ diffusion kinetics in natural enstatite crystals as a function of temperature, f(O₂) and crystallographic direction at 1 bar pressure and applied these data to several terrestrial and planetary problems. The diffusion is found to be anisotropic with the diffusion parallel to the c-axial direction being significantly greater than that parallel to a- and b-axis. Also, D(//a) is likely to be somewhat greater than D(//b). Diffusion experiments parallel to the b-axial direction as a function of f(O₂) do not show a significant dependence of D(Nd³⁺) on f(O₂) within the range defined by the IW buffer and 1.5 log unit above the WM buffer. The observed diffusion anisotropy and weak f(O₂) effect on D(Nd³⁺) may be understood by considering the crystal structure of enstatite and the likely diffusion pathways. Using the experimental data for D(Nd³⁺), we calculated the closure temperature of the Sm-Nd geochronological system in enstatite during cooling as a function of cooling rate, grain size and geometry, initial (peak) temperature and diffusion direction. We have also evaluated the approximate domain of validity of closure temperatures calculated on the basis of an infinite plane sheet model for finite plane sheets showing anisotropic diffusion. These results provide a quantitative framework for the interpretation of Sm-Nd mineral ages of orthopyroxene in planetary samples. We discuss the implications of our experimental data to the problems of melting and subsolidus cooling of mantle rocks, and the resetting of Sm-Nd mineral ages in mesosiderites. It is found that a cooling model proposed earlier [Ganguly J., Yang H., Ghose S., 1994. Thermal history of mesosiderites: Quantitative constraints from compositional zoning and Fe-Mg ordering in orthopyroxene. Geochim. Cosmochim. Acta 58, 2711-2723] could lead to the observed ∼90 Ma difference between the U-Pb age and Sm-Nd mineral age for mesosiderites, thus obviating the need for a model of resetting of the Sm-Nd mineral age by an “impulsive disturbance” [Prinzhoffer A, Papanastassiou D.A, Wasserburg G.J., 1992. Samarium-neodymium evolution of meteorites. Geochim. Cosmochim. Acta 56, 797-815].     

Equation of state of the H2O, CO2, and H2O-CO2 systems up to 10 GPa and 2573.15 K: Molecular dynamics simulations with ab initio potential surface

Based on our previous development of the molecular interaction potential for pure H₂O and CO₂ [Zhang, Z.G., Duan, Z.H. 2005a. Isothermal-isobaric molecular dynamics simulations of the PVT properties of water over wide range of temperatures and pressures. Phys. Earth Planet Interiors149, 335-354; Zhang, Z.G., Duan, Z.H. 2005b. An optimized molecular potential for carbon dioxide. J. Chem. Phys.122, 214507] and the ab initio potential surface across CO₂-H₂O molecules constructed in this study, we carried out more than one thousand molecular dynamics simulations of the PVTx properties of the CO₂-H₂O mixtures in the temperature-pressure range from 673.15 to 2573.15 K up to 10.0 GPa. Comparison with extensive experimental PVTx data indicates that the simulated results generally agree with experimental data within 2% in density, equivalent to experimental uncertainty. Even the data under the highest experimental temperature-pressure conditions (up to 1673 K and 1.94 GPa) are well predicted with the agreement within 1.0% in density, indicating that the high accuracy of the simulation is well retained as the temperature and pressure increase. The consistent and stable predictability of the simulation from low to high temperature-pressure and the fact that the molecular dynamics simulation resort to no experimental data but to ab initio molecular potential makes us convinced that the simulation results should be reliable up to at least 2573 K and 10 GPa with errors less than 2% in density. In order to integrate all the simulation results of this study and previous studies [Zhang and Duan, 2005a, 2005b] and the experimental data for the calculation of volumetric properties (volume, density, and excess volume), heat properties, and chemical properties (fugacity, activity, and possibly supercritical phase separation), an equation of state (EOS) is laboriously developed for the CO₂, H₂O, and CO₂-H₂O systems. This EOS reproduces all the experimental and simulated data covering a wide temperature and pressure range from 673.15 to 2573.15 K and from 0 to 10.0 GPa within experimental or simulation uncertainty.     

Refinements in a site-mixing model for illites: local electrostatic balance and the quasi-chemical approximation

A quasi-chemical model for illites has been derived, and local electrostatic balance has been added to a random regular solution site-mixing model for illites (Stoessell, 1979). Each model assumes similar order-disorder conditions for both the end-members micas and the solid solution. Thermodynamic properties of illites predicted by the random, electrostatic, and quasi-chemical models are compared as a function of composition. For natural illite compositions, molar entropies of mixing in the electrostatic model are about 1 entropy unit less than those in the random model. Intermediate values are given by the quasi-chemical model. Each model predicts an increased entropy of mixing in dominantly trioctahedral illites as compared to dioctahedral illites. Each model also predicts destabilization of trioctahedral illites using absolute molar exchange energies greater than 2 RT/Z_x, where Z_x is the number of adjacent cation interactions per site in the Xth site class. The most negative free energies of mixing are predicted by the quasi-chemical model. Intermediate values predicted by the random model are apparently the result of error cancellation due to overestimation of both the entropy and enthalpy of mixing.     

Kinetics of fine wet grinding of zeolite in a steel ball mill in comparison to dry grinding

Batch wet grinding of zeolite was studied with emphasis on a kinetic study in a laboratory size steel ball mill of 200 mm diameter. The breakage parameters were determined by using the single sized feed fractions of − 850 + 600 µm, − 600 + 425 µm and − 425 + 300 µm for the zeolite samples. The S_i (specific rate of breakage) and B_i,j (primary breakage distribution) values were obtained for those feed size fractions in order to predict the product size distributions by simulation for comparison to the experimental data. The specific rates of breakage values for wet grinding in the first-order breakage region were higher than the dry values reported previously by a factor 1.7 at the same experimental conditions, but the primary breakage distribution (B_i,j) values were approximately the same. The simulations of the product size distributions of zeolite were in good agreement with the experimental data using a standard ball mill simulation program. The wet grinding of zeolite was subjected to slowing-down effect in the mill at 2 min of grinding, corresponding to an 80% passing size of about 400 µm. On the other hand, the slowing down effect in the dry grinding of zeolite was also seen at 4 min of grinding. In addition, effects of some operational parameters on dry and wet grinding of zeolite were determined by simulation using the breakage parameters obtained experimentally.