Fe–Mg diffusion in olivine II: point defect chemistry,change of diffusion mechanisms and a model for calculation of diffusion coefficients in natural olivine

Analysis of existing data and models on point defects in pure (Fe,Mg)-olivine (Phys Chem Miner 10:27–37,1983; Phys Chem Miner 29:680–694, 2002) shows that it is necessary to consider thermodynamic non-ideality of mixing to adequately describe the concentration of point defects over the range of measurement. In spite of different sources of uncertainties, the concentrations of vacancies in octahedral sites in (Fe,Mg)-olivine are on the order of 10⁻⁴ per atomic formula unit at 1,000–1,200 °C according to both the studies. We provide the first explicit plots of vacancy concentrations in olivine as a function of temperature and oxygen fugacity according to the two models. It is found that in contrast to absolute concentrations at ∼1,100 °C and dependence on fO₂, there is considerable uncertainty in our knowledge of temperature dependence of vacancy concentrations. This needs to be considered in discussing the transport properties such as diffusion coefficients. Moreover, these defect models in pure (Fe,Mg)-olivine need to be extended by considering aliovalent impurities such as Al, Cr to describe the behavior of natural olivine. We have developed such a formulation, and used it to analyze the considerable database of diffusion coefficients in olivine from Dohmen et al. (Phys Chem Miner this volume, 2007) (Part - I) and older data in the literature. The analysis documents unequivocally for the first time a change of diffusion mechanism in a silicate mineral—from the transition metal extrinsic (TaMED) to the purely extrinsic (PED) domain, at fO₂ below 10⁻¹⁰  Pa, and consequently, temperatures below 900 °C. The change of diffusion mechanism manifests itself in a change in fO₂ dependence of diffusivity and a slight change in activation energy of diffusion—the activation energy increases at lower temperatures. These are consistent with the predictions of Chakraborty (J Geophys Res 102(B6):12317–12331, 1997). Defect formation enthalpies in the TaMED regime (distinct from intrinsic defect formation) lie between −66 and + 15 kJ/mol and migration energies of octahedral cations in olivine are most likely ∼ 260 kJ/mol, consistent with previous inferences (Phys Chem 207:147–162, 1998). Plots are shown for diffusion at various constant fO₂ as well as along fO₂ buffers, to highlight the difference in behavior between the two. Considering all the diffusion data and constraints from the point defect models, (Fe–Mg) diffusion in olivine along [001] is best described by the Master equations: (1) At oxygen fugacities greater than 10⁻¹⁰ Pa:

Role of diffusion–precipitation reactions in authigenic pyritization

Models proposed for authigenic pyritization in the literature provide good indicators of the effect of very high concentrations of available iron on decaying organisms; however, the impact of lower concentrations of iron on an actively decaying system is not so well characterised. Gel-stabilised systems are used to model the effect of extremes of iron concentration on the precipitation of pyrite and the process of organic matter preservation. The experiments show the effect of sulphate reduction decay in an environment where iron is limited or dispersed, and in iron-rich environment where diffusion is limited. The formation of discrete sulphide bands in experiments where iron is limited indicates that negative feedback, or Liesegang, reactions play a role in the development of gaps between sites of organic matter preservation and pyrite precipitation, providing a mechanism for the formation of pyrite halos, concretion rims and overgrowths. In iron-rich environments, pyrite formation is confined to the decaying organism, and the Liesegang effect is limited due to the restricted diffusion of dissolved sulphide.     

Ca–Mg diffusion in diopside: tracer and chemical inter-diffusion coefficients

We have experimentally determined the tracer diffusion coefficients (D*) of ⁴⁴Ca and ²⁶Mg in a natural diopside (~Di₉₆) as function of crystallographic direction and temperature in the range of 950–1,150 °C at 1 bar and f(O₂) corresponding to those of the WI buffer. The experimental data parallel to the a*, b, and c crystallographic directions show significant diffusion anisotropy in the a–c and b–c planes, with the fastest diffusion being parallel to the c axis. With the exception of logD*(²⁶Mg) parallel to the a* axis, the experimental data conform to the empirical diffusion “compensation relation”, converging to logD ~ −19.3 m²/s and T ~ 1,155 °C. Our data do not show any change of diffusion mechanism within the temperature range of the experiments. Assuming that D* varies roughly linearly as a function of angle with respect to the c axis in the a–c plane, at least within a limited domain of ~20° from the c-axis, our data do not suggest any significant difference between D*(//c) and D*(⊥(001)), the latter being the diffusion data required to model compositional zoning in the (001) augite exsolution lamellae in natural clinopyroxenes. Since the thermodynamic mixing property of Ca and Mg is highly nonideal, calculation of chemical diffusion coefficient of Ca and Mg must take into account the effect of thermodynamic factor (TF) on diffusion coefficient. We calculate the dependence of the TF and the chemical interdiffusion coefficient, D(Ca–Mg), on composition in the diopside–clinoenstatite mixture, using the available data on mixing property in this binary system. Our D*(Ca) values parallel to the c axis are about 1–1.5 log units larger than those Dimanov et al. (1996). Incorporating the effect of TF, the D(Ca–Mg) values calculated from our data at 1,100–1,200 °C is ~0.6–0.7 log unit greater than the experimental quasibinary D((Ca–Mg + Fe)) data of Fujino et al. (1990) at 1 bar, and ~0.6 log unit smaller than that of Brady and McCallister (1983) at 25 kb, 1,150 °C, if our data are normalized to 25 kb using activation volume (~4 and ~6 cm³/mol for Mg and Ca diffusion, respectively) calculated from theoretical considerations.     

Rare earth element diffusion in a natural pyrope single crystal at 2.8 GPa

Volume diffusion rates of Ce, Sm, Dy, and Yb have been measured in a natural pyrope-rich garnet single crystal (Py₇₁Alm₁₆Gr₁₃) at a pressure of 2.8 GPa and temperatures of 1,200-1,450 °C. Pieces of a single gem-quality pyrope megacryst were polished, coated with a thin layer of polycrystalline REE oxide, then annealed in a piston cylinder device for times between 2.6 and 90 h. Diffusion profiles in the annealed samples were measured by SIMS depth profiling. The dependence of diffusion rates on temperature can be described by the following Arrhenius equations (diffusion coefficients in m²/s): % MathType!MTEF!2!1!+- % feaaeaart1ev0aaatCvAUfKttLearuavTnhis1MBaeXatLxBI9gBam % XvP5wqSXMqHnxAJn0BKvguHDwzZbqegm0B1jxALjhiov2DaeHbuLwB % Lnhiov2DGi1BTfMBaebbfv3ySLgzGueE0jxyaibaieYlf9irVeeu0d % Xdh9vqqj-hEeeu0xXdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9 % pgea0dXdar-Jb9hs0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaaca % qabeaadaabauaaaOqaauaabeqaeeaaaaqaaiGbcYgaSjabc+gaVjab % cEgaNnaaBaaaleaacqaIXaqmcqaIWaamaeqaaOGaemiraq0aaSbaaS % qaaiabbMfazjabbkgaIbqabaGccqGH9aqpcqGGOaakcqGHsislcqaI % 3aWncqGGUaGlcqaI3aWncqaIZaWmcqGHXcqScqaIWaamcqGGUaGlcq % aI5aqocqaI3aWncqGGPaqkcqGHsisldaqadaqaaiabiodaZiabisda % 0iabiodaZiabgglaXkabiodaZiabicdaWiaaysW7cqqGRbWAcqqGkb % GscaaMe8UaeeyBa0Maee4Ba8MaeeiBaW2aaWbaaSqabeaacqqGTaql % cqqGXaqmaaGccqGGVaWlcqaIYaGmcqGGUaGlcqaIZaWmcqaIWaamcq % aIZaWmcqWGsbGucqWGubavaiaawIcacaGLPaaaaeaacyGGSbaBcqGG % VbWBcqGGNbWzdaWgaaWcbaGaeGymaeJaeGimaadabeaakiabdseaen % aaBaaaleaacqqGebarcqqG5bqEaeqaaOGaeyypa0JaeiikaGIaeyOe % I0IaeGyoaKJaeiOla4IaeGimaaJaeGinaqJaeyySaeRaeGimaaJaei % Ola4IaeGyoaKJaeG4naCJaeiykaKIaeyOeI0YaaeWaaeaacqaIZaWm % cqaIWaamcqaIYaGmcqGHXcqScqaIZaWmcqaIWaamcaaMe8Uaee4AaS % MaeeOsaOKaaGjbVlabb2gaTjabb+gaVjabbYgaSnaaCaaaleqabaGa % eeyla0IaeeymaedaaOGaei4la8IaeGOmaiJaeiOla4IaeG4mamJaeG % imaaJaeG4mamJaemOuaiLaemivaqfacaGLOaGaayzkaaaabaGagiiB % aWMaei4Ba8Maei4zaC2aaSbaaSqaaiabigdaXiabicdaWaqabaGccq % WGebardaWgaaWcbaGaee4uamLaeeyBa0gabeaakiabg2da9iabcIca % OiabgkHiTiabiMda5iabc6caUiabikdaYiabigdaXiabgglaXkabic % daWiabc6caUiabiMda5iabiEda3iabcMcaPiabgkHiTmaabmaabaGa % eG4mamJaeGimaaJaeGimaaJaeyySaeRaeG4mamJaeGimaaJaaGjbVl % abbUgaRjabbQeakjaaysW7cqqGTbqBcqqGVbWBcqqGSbaBdaahaaWc % beqaaiabb2caTiabbgdaXaaakiabc+caViabikdaYiabc6caUiabio % daZiabicdaWiabiodaZiabdkfasjabdsfaubGaayjkaiaawMcaaaqa % aiGbcYgaSjabc+gaVjabcEgaNnaaBaaaleaacqaIXaqmcqaIWaamae % qaaOGaemiraq0aaSbaaSqaaiabboeadjabbwgaLbqabaGccqGH9aqp % cqGGOaakcqGHsislcqaI5aqocqGGUaGlcqaI3aWncqaI0aancqGHXc % qScqaIYaGmcqGGUaGlcqaI4aaocqaI0aancqGGPaqkcqGHsisldaqa % daqaaiabikdaYiabiIda4iabisda0iabgglaXkabiMda5iabigdaXi % aaysW7cqqGRbWAcqqGkbGscaaMe8UaeeyBa0Maee4Ba8MaeeiBaW2a % aWbaaSqabeaacqqGTaqlcqqGXaqmaaGccqGGVaWlcqaIYaGmcqGGUa % GlcqaIZaWmcqaIWaamcqaIZaWmcqWGsbGucqWGubavaiaawIcacaGL % Paaaaaaaaa!0C76!

Effect of confining pressure on the diffusion of HTO, 36Cl− and 125I− in a layered argillaceous rock (Opalinus Clay): diffusion perpendicular to the fabric

The through- and out-diffusion of HTO, ³⁶Cl⁻ and ¹²⁵I⁻ in Opalinus Clay, an argillaceous rock from the northern part of Switzerland, was studied under different confining pressures between 4 and 15 MPa. The direction of diffusion and the confining pressure were perpendicular to the bedding. Confining pressure had only a small effect on diffusion. An increase in pressure from 4 to 15 MPa resulted in a decrease of the effective diffusion coefficient of ∼20%. Diffusion accessible porosities were not measurably affected. The values of the effective diffusion coefficients, D_e, ranged between (5.6±0.4)×10⁻¹² and (6.7±0.4)×10⁻¹² m² s⁻¹ for HTO, (7.1±0.5)×10⁻¹³ and (9.1±0.6)×10⁻¹³ m² s⁻¹ for ³⁶Cl⁻ and (4.5±0.3)×10⁻¹³ and (6.6±0.4)×10⁻¹³ m² s⁻¹ for ¹²⁵I⁻. The rock capacity factors, α, measured were circa 0.14 for HTO, 0.040 for ³⁶Cl⁻ and 0.080 for ¹²⁵I⁻. Because of anion exclusion effects, anions diffuse slower and exhibit smaller diffusion accessible porosities than the uncharged HTO. Unlike ³⁶Cl⁻, ¹²⁵I⁻ sorbs weakly on Opalinus Clay resulting in a larger rock capacity factor. The sorption coefficient, K_d, for ¹²⁵I⁻ is of the order of 1–2×10⁻⁵ m³ kg⁻¹. The effective diffusion coefficient for HTO is in good agreement with values measured in other sedimentary rocks and can be related to the porosity using Archie's Law with exponent m=2.5.     

Analysis of influencing factors of clay particle diffusion in electric double layer北大核心CSCD

双电层结构对研究黏土力学特性、冻土水分迁移等具有重要意义。为了探究不同影响因素对黏土颗粒扩散双电层电势分布的影响,借鉴Gouy-Chapman-Stern双电层理论,基于Nernst-Planck方程和Poisson-Boltzmann方程,利用数值软件COMSOL定量分析了温度、浓度、颗粒尺寸、颗粒形状以及溶液相对介电常数对扩散双电层电势分布的影响规律。研究表明：温度对电势分布的影响不明显,但随着温度以及Stern层厚度增加,黏土颗粒表面电势和Stern电势均增加;而随着溶液浓度以及相对介电常数减小,表面电势值增加;在矿物成分、表面电荷密度以及颗粒形状确定的情况下,尺寸对于扩散双电层电势分布的影响不显著;但颗粒的不规则形状对电势分布的影响较为明显,当颗粒形状存在夹角时,夹角处的表面电势远大于其他位置,且夹角越小,夹角处表面电势值越大。     

Volume diffusion of Ytterbium in YAG: thin-film experiments and combined TEM–RBS analysis

In this study, we address volume diffusion of ytterbium in yttrium aluminum garnet (YAG) using thin-film single crystal diffusion couples. We employ analytical transmission electron microscopy (ATEM) as a tool for combined microstructural and microchemical analysis and compare the results to Rutherford backscattering (RBS) analysis. Given the high spatial resolution of the method, we focus on microstructural changes of the thin-film diffusant source during the diffusion anneal. We evaluate the potential influence of the associated changes in its transport properties on the evolution of concentration profiles in the single crystal substrate. This approach allows us to test the reliability of determination of volume diffusion coefficients from thin-film diffusion experiments. We found that for the chosen experimental setting, the influence of thin-film re-crystallization is small when compared with the experimental uncertainty and good estimates for the volume diffusion coefficients of Yb in YAG can be obtained using standard assumptions. Both Yb-concentration profiles analyzed with ATEM and with RBS give similar results. At 1,450°C and 1 bar, we infer log D _Yb (m²/s) values of −19.37 ± 0.07 (TEM) and −19.84 ± 0.02 (RBS). Although the change in thin-film transport properties associated with successive crystallization during the diffusion anneal does not play a major role for our experimental setup, this effect cannot generally be ignored.     

Application of the cBΩ model to the calculation of diffusion parameters of He in olivine

The validity of the thermodynamic cBΩ model is tested in terms of the experimentally determined diffusion coefficients of He in a natural Fe-bearing olivine (Fo₉₀) and a synthetic end-member forsterite (Mg₂SiO₄) over a broad temperature range (250–950 °C), as reported recently by Cherniak and Watson (Geochem Cosmochim Acta 84:269–279, 2012). The calculated activation enthalpies for each of the three crystallographic axes were found to be (134 ± 5), (137 ± 13) and (158 ± 4) kJ mol^?1 for the [100], [010] and [001] directions in forsterite, and (141 ± 9) kJ mol^?1 for the [010] direction in olivine, exhibiting a deviation of <1 % with the corresponding reported experimental values. Additional point defect parameters such as activation volume, activation entropy and activation Gibbs free energy were calculated as a function of temperature. The estimated activation volumes (3.2–3.9 ± 0.3 cm³ mol^?1) of He diffusion in olivine are comparable with other reported results for hydrogen and tracer diffusion of Mg cations in olivine. The pressure dependence of He diffusion coefficients was also determined, based on single experimental diffusion measurements at 2.6 and 2.7 GPa along the [001] direction in forsterite at 400 and 650 °C.     

Multicomponent diffusion in garnets I: general theoretical considerations and experimental data for Fe–Mg systems

We have carried out a combined theoretical and experimental study of multicomponent diffusion in garnets to address some unresolved issues and to better constrain the diffusion behavior of Fe and Mg in almandine–pyrope-rich garnets. We have (1) improved the convolution correction of concentration profiles measured using electron microprobes, (2) studied the effect of thermodynamic non-ideality on diffusion and (3) explored the use of a mathematical error minimization routine (the Nelder-Mead downhill simplex method) compared to the visual fitting of concentration profiles used in earlier studies. We conclude that incorporation of thermodynamic non-ideality alters the shapes of calculated profiles, resulting in better fits to measured shapes, but retrieved diffusion coefficients do not differ from those retrieved using ideal models by more than a factor of 1.2 for most natural garnet compositions. Diffusion coefficients retrieved using the two kinds of models differ only significantly for some unusual Mg–Mn–Ca-rich garnets. We found that when one of the diffusion coefficients becomes much faster or slower than the rest, or when the diffusion couple has a composition that is dominated by one component (>75 %), then profile shapes become insensitive to one or more tracer diffusion coefficients. Visual fitting and numerical fitting using the Nelder-Mead algorithm give identical results for idealized profile shapes, but for data with strong analytical noise or asymmetric profile shapes, visual fitting returns values closer to the known inputs. Finally, we have carried out four additional diffusion couple experiments (25–35 kbar, 1,260–1,400 °C) in a piston-cylinder apparatus using natural pyrope- and almandine-rich garnets. We have combined our results with a reanalysis of the profiles from Ganguly et al. (1998) using the tools developed in this work to obtain the following Arrhenius parameters in D = D ₀ exp{–[Q _1bar + (P–1)ΔV ⁺]/RT} for D _Mg^* and D _Fe^*: Mg: Q _1bar = 228.3 ± 20.3 kJ/mol, D ₀ = 2.72 (±4.52) × 10⁻¹⁰ m²/s, Fe: Q _1bar = 226.9 ± 18.6 kJ/mol, D ₀ = 1.64 (±2.54) × 10⁻¹⁰ m²/s. ΔV ⁺ values were assumed to be the same as those obtained by Chakraborty and Ganguly (1992).     

Analytical solution of advection–diffusion equation in heterogeneous infinite medium using Green’s function method

Some analytical solutions of one-dimensional advection–diffusion equation (ADE) with variable dispersion coefficient and velocity are obtained using Green’s function method (GFM). The variability attributes to the heterogeneity of hydro-geological media like river bed or aquifer in more general ways than that in the previous works. Dispersion coefficient is considered temporally dependent, while velocity is considered spatially and temporally dependent. The spatial dependence is considered to be linear and temporal dependence is considered to be of linear, exponential and asymptotic. The spatio-temporal dependence of velocity is considered in three ways. Results of previous works are also derived validating the results of the present work. To use GFM, a moving coordinate transformation is developed through which this ADE is reduced into a form, whose analytical solution is already known. Analytical solutions are obtained for the pollutant’s mass dispersion from an instantaneous point source as well as from a continuous point source in a heterogeneous medium. The effect of such dependence on the mass transport is explained through the illustrations of the analytical solutions.     

Coupling simulation of microbially induced carbonate precipitation and bacterial growth using reaction–diffusion and homogenisation systems

Acta Geotechnica - Soil improvement techniques have been developed experimentally and empirically from various geotechnical standpoints based on physical, chemical, and biological findings. The...     

Effects of grain dissolution–diffusion sliding and hydro-mechanical interaction on the creep deformation of soft rocks

Acta Geotechnica - The creep deformation behaviour of soft rocks is one of the most important research fields in geotechnical engineering. In this study, a theoretical model was developed to...     

Experimental growth of åkermanite reaction rims between wollastonite and monticellite: evidence for volume diffusion control

Growth rates of monomineralic, polycrystalline åkermanite (Ca₂MgSi₂O₇) rims produced by solid-state reactions between monticellite (CaMgSiO₄) and wollastonite (CaSiO₃) single crystals were determined at 0.5 GPa dry argon pressure, 1,000–1,200°C and 5 min to 60 h, using an internally heated pressure vessel. Inert Pt-markers, initially placed at the monticellite–wollastonite interface, indicate symmetrical growth into both directions. This and mass balance considerations demonstrate that rim growth is controlled by transport of MgO. At 1,200°C and run durations between 5 min and 60 h, rim growth follows a parabolic rate law with rim widths ranging from 0.4 to 16.3 μm indicating diffusion-controlled rim growth. The effective bulk diffusion coefficient \( D_{\text{eff,MgO}}^{\text{Ak}} \) is calculated to 10^?15.8±0.1 m² s^?1. Between 1,000°C and 1,200°C, the effective bulk diffusion coefficient follows an Arrhenius law with E _a = 204 ± 18 kJ/mol and D ₀ = 10^?8.6±1.6 m² s^?1. Åkermanite grains display a palisade texture with elongation perpendicular to the reaction interface. At 1,200°C, average grain widths measured normal to elongation, increase with the square root of time and range from 0.4 to 5.4 μm leading to a successive decrease in the grain boundary area fraction, which, however, does not affect \( D_{\text{eff,MgO}}^{\text{Ak}} \) to a detectible extent. This implies that grain boundary diffusion only accounts for a minor fraction of the overall chemical mass transfer, and rim growth is essentially controlled by volume diffusion. This is corroborated by the agreement between our estimates of the effective MgO bulk diffusion coefficient and experimentally determined volume diffusion data for Mg and O in åkermanite from the literature. There is sharp contrast to the MgO–SiO₂ binary system, where grain boundary diffusion controls rim growth.     

Constraints on the early cooling rates of Mt. Dabie from diffusion modeling of chemical zoning of garnet

Diffusion modeling of zoning profiles in eclogite garnets from three different tectonic units of Mt. Dabie, UHPM unit, HPM unit and northern Dabie, was used to estimate the relative time span and cooling rates of these rocks. Modeling result for the Huangzhen eclogite garnet shows that the maximal time span for the diffusion-adjustment process is about 22 Ma since the peak-temperature metamorphism, which is the maximum time span from amphibolite facies metamorphism to greenschist facies metamorphism. The Bixiling eclogites had subjected to a cooling process at a rate of - 10℃/Ma from 750℃ to 560℃ during 20 Ma. The second cooling stage of the Raobazhai eclogite following granulite-facies metamorphism is an initial fast cooling process at a rate of about 25℃/Ma and then slowed down gradually. All these belong to a coherent Dabie collision orogen with differences in subduction depth and exhumation/uplifting path.     

Decoding near-concordant U–Pb zircon ages spanning several hundred million years: recrystallisation,metamictisation or diffusion?

In situ isotopic (U–Pb, Lu–Hf) and trace element analyses of zircon populations in six samples of the intrusive Mawson Charnockite, east Antarctica, emphasise complex zircon behaviour during very high-grade metamorphism. The combination of geochemical data sets is used to distinguish xenocrysts and identify a population of primary igneous zircon in situations where U–Pb data spread close to concordia over a few hundred Myr. The population is filtered to exclude grains with: (1) U–Pb ages >2% discordant, (2) anomalous trace element-content (Th, U, Y, REE) and (3) outlying Hf-isotopic values. Rare metamorphic-type grains were also excluded. Upon filtering the population, minimum emplacement ages for each sample were determined using the oldest grain(s). This approach improves upon age determinations in complex data sets that use weighted mean or isochron methods. Our results suggest that the Mawson Charnockite was emplaced episodically at c. 1145–1140 Ma, c. 1080–1050 Ma and c. 985–960 Ma. Core-outer core-rim and core-rim textures were identified but are not correlated with U–Pb ages. We establish that recrystallisation (mainly of zircon rims) must have occurred shortly following igneous crystallisation and that metamictisation/cracking is a Paleozoic to Recent event. Therefore, intra-zircon diffusion in a high-T, high-strain environment during Meso-Neoproterozoic orogenesis is inferred to have caused the extensive U–Pb isotopic disturbance. Charnockitic magmatism prior to c. 1,000 Ma has not previously been recorded in the Mawson region and indicates that orogenesis may have commenced c. 150 Myr earlier than previously thought. Correlations with similar aged rocks in adjacent regions have implications for supercontinent reconstructions.     

Grain boundary and volume diffusion experiments in yttrium aluminium garnet bicrystals at 1,723 K: a miniaturized study

Yb-Y inter-diffusion along a single grain boundary of a synthetic yttrium aluminium garnet (YAG) bicrystal has been studied using analytical transmission electron microscopy (ATEM). To investigate the diffusion, a thin-film containing Yb as the diffusant was deposited perpendicular to the bicrystal grain boundary by pulsed laser deposition (PLD). Structural properties and their change with time in both the diffusant source and the grain boundary are reported. The diffusion profiles are incorporated in a numerical diffusion model, which is applied to determine the grain boundary diffusion coefficient, D _gb , at 1.723 K it is equal to 3 × 10⁻¹⁵ m²/s. We find that grain boundary diffusion is 4.85 orders of magnitude faster than volume diffusion, which was determined from the same diffusion experiment. This result is discussed in the context of special versus general grain boundaries. Finally, we successfully tested the capability of synchrotron-based nano-X-ray fluorescence analysis to map micro-chemical patterns in two dimensions with sub-micrometre resolution.     

Experimental measurements of the diffusion parameters of light hydrocarbons in water-saturated sedimentary rocks—I. A new experimental procedure

An automatic experimental set-up has been developed for the determination of diffusion parameters of hydrocarbon gases through water-saturated rock samples. Diffusive flow of hydrocarbons through rock slices is monitored by gas chromatography. Experiments are carried out according to the time lag method yielding diffusion coefficients, solubility coefficients, and diffusion permeabilities. Diffusion coefficients down to 10⁻¹² m² s⁻¹ (10⁻⁸ cm⁻² s⁻¹) may be determined routinely on rock samples of 2–10 mm thickness. Maximum errors in diffusion coefficients are estimated around 20% and reproducibility was found to range between 10 and 20%. Specific features of this set-up are automatic sampling and data acquistion, high sampling frequency, and maintenance of water-saturation of the rock samples throughout the experiment.     

Operator splitting methods for degenerate convection–diffusion equations II: numerical examples with emphasis on reservoir simulation and sedimentation

We present an accurate numerical method for a large class of scalar, strongly degenerate convection–diffusion equations. Important subclasses are hyperbolic conservation laws, porous medium type equations, two-phase reservoir flow equations, and strongly degenerate equations coming from the recent theory of sedimentation–consolidation processes. The method is based on splitting the convective and the diffusive terms. The nonlinear, convective part is solved using front tracking and dimensional splitting, while the nonlinear diffusion part is solved by an implicit–explicit finite difference scheme. In addition, one version of the implemented operator splitting method has a mechanism built in for detecting and correcting unphysical entropy loss, which may occur when the time step is large. This mechanism helps us gain a large time step ability for practical computations. A detailed convergence analysis of the operator splitting method was given in Part I. Here we present numerical experiments with the method for examples modelling secondary oil recovery and sedimentation–consolidation processes. We demonstrate that the splitting method resolves sharp gradients accurately, may use large time steps, has first order convergence, exhibits small grid orientation effects, has small mass balance errors, and is rather efficient.     

Review of the use of Péclet numbers to determine the relative importance of advection and diffusion in low permeability environments

In low permeability environments, transport by advection is often neglected based on a Péclet number criterion. Such a criterion usually states that if the Péclet number (Pe) is much smaller than 1, diffusion dominates over advection and transport may be modeled considering diffusion only. Unfortunately, up to 10 different Péclet number definitions exist and for a particular case these different definitions lead to very diverse Péclet number values, differing several orders of magnitude from each other. In this paper, the different Péclet number definitions are therefore evaluated on their ability to determine the relative importance of transport by advection and by diffusion in low permeability environments. This is done by comparing the results of the analytical solution for pure diffusion with the analytical solution for diffusion, advection and dispersion for a large number of different input parameter values. The relation between the different Péclet numbers and the difference between the calculated concentration considering diffusion only and the calculated concentration considering both diffusion and advection is studied. These calculations show that some Péclet number definitions are not well suited to decide whether advection may be neglected in low permeability media.

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Resumen Frecuentemente se descuida el transporte por avección en ambientes de baja permeabilidad sobre la base del criterio del número de Péclet. Dicho criterio usualmente sostiene que si el número de Péclet (Pe) es mucho menor a 1, la difusión domina sobre la avección y es posible modelar el transporte considerando la difusión únicamente. Desafortunadamente existen 10 definiciones diferentes del número de Péclet y para un caso en particular estas diferentes definiciones conducen a valores de número de Péclet muy diversos los cuales difieren entre sí en varias magnitudes. Por lo tanto, en este artículo se evalúan las diferentes definiciones en base a su habilidad para determinar la importancia relativa del transporte por avección y difusión en ambientes de baja permeabilidad. Esto se lleva a cabo mediante la comparación de los resultados de la solución analítica para difusión pura con los de la solución analítica por difusión, avección y dispersión para un número amplio de diferentes valores como parámetro. Se ha estudiado la relación entre los diferentes números de Péclet y las diferencias entre la concentración calculada considerando difusión únicamente y considerando tanto difusión como avección. Estos cálculos muestran que algunas de las definiciones de los números de Péclet no son muy apropiadas par decidir si se puede descuidar la avección en medios de baja permeabilidad.

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Résumé Dans les milieux à faible perméabilité, le transport par advection est souvent négligeable lorsquon se base sur le critère du nombre de Péclet. Un tel critère suggère habituellement que pour un nombre de Péclet beaucoup plus petit que 1, la diffusion domine sur ladvection et que le transport peut être modélisé par diffusion seulement. Malheureusement, il existe jusquà environ dix définitions du nombre de Péclet et pour un cas spécifique, ces différentes définitions mènent à des valeurs du nombre de Péclet très différentes, et qui varient entre elles de plusieurs ordres de grandeur. Dans cet article, les différentes définitions du nombre de Péclet sont évaluées en fonction de leur habileté à déterminer limportance relative du transport par advection et par diffusion dans les milieux à faible perméabilité. Ceci est fait en comparant les résultats de la solution analytique pour la diffusion pure à la solution analytique pour la diffusion, ladvection et la dispersion, et ce, pour un grand nombre de valeurs différentes comme paramètre dentrée. La relation entre les différents nombres de Péclet et la différence entre la concentration calculée en considérant la diffusion seulement et la concentration calculée considérant simultanément la diffusion et ladvection est étudiée. Ces calculs prouvent que certaines définitions de nombre de Péclet ne sont pas appropriées afin de décider si ladvection peut être négligée dans les milieux à faible perméabilité.

     

Origin of zoned spinel by coupled dissolution–precipitation and inter-crystalline diffusion: evidence from serpentinized wehrlite, Bangriposi, Eastern India

Textural and mineral–chemical characteristics in the Bangriposi wehrlites (Eastern India) provide insight into metamorphic processes that morphologically and chemically modified magmatic spinel during serpentinization of wehrlite. Aluminous chromite included in unaltered magmatic olivine is chemically homogenous. In sub-cm to 10s-of-micron-wide veins, magnetite associated with antigorite and clinochlore comprising the serpentine matrix is near-stoichiometric. But Al–Cr–Fe³⁺ spinels in the chlorite–magnetite veins are invariably zoned, e.g., chemically homogenous Al-rich chromite interior successively mantled by ferritchromite/Cr-rich magnetite zone and magnetite continuous with vein magnetite in the serpentine matrix. In aluminous chromite, ferritchromite/Cr-rich magnetite zones are symmetrically disposed adjacent to fracture-controlled magnetite veins that are physically continuous with magnetite rim. The morphology of ferritchromite–Cr-rich magnetite mimics the morphology of aluminous chromite interior but is incongruous with the exterior margin of magnetite mantle. Micropores are abundant in magnetite veins, but are fewer in and do not appear to be integral to the adjacent ferritchromite–Cr-rich magnetite zones. Sandwiched between chemically homogenous aluminous chromite interior and magnetite mantle, ferritchromite–Cr-rich magnetite zones show rim-ward decrease in Cr₂O₃, Al₂O₃ and MgO and complementary increase in Fe₂O₃ at constant FeO. In diffusion profiles, Fe₂O₃–Cr₂O₃ crossover coincides with Al₂O₃ decrease to values <0.5 wt% in ferritchromite zone, with Cr₂O₃ continuing to decrease within magnetite mantle. Following fluid-mediated (hydrous) dissolution of magmatic olivine and olivine + Al–chromite aggregates, antigorite + magnetite and chlorite + magnetite were transported in 10s-of-microns to sub-cm-wide veins and precipitated along porosity networks during serpentinization (T: 550–600 °C, f(O₂): ?19 to ?22 log units). These veins acted as conduits for precipitation of magnetite as mantles and veins apophytic in chemically/morphologically modified magmatic Al-rich chromite. Inter-crystalline diffusion induced by chemical gradient at interfaces separating aluminous chromite interiors and magnetite mantles/veins led to the growth of ferritchromite/Cr-rich magnetite zones, mimicking the morphology of chemically modified Al–Cr–Fe–Mg spinel interiors. Inter-crystalline diffusion outlasted fluid-mediated aluminous chromite dissolution, mass transfer and magnetite precipitation.