A numerical Lagrangian stochastic approach to upscaling of dispersivity in solute transport

The upscaling of dispersivity in solute transport in heterogeneous aquifers is addressed with a numerical stochastic formulation. This work represents progress toward converting theory into scalable numerical models that can be compared to laboratory experiments. Traditional global assumptions of low variance, ergodicity, single correlation scale, stationarity, and the like are avoided through the use of a flexible Lagrangian numerical, not analytical, framework, which allows assumptions to be local. A method of calculating grid-block upscaled dispersivities is presented. Computational results are obtained for a heterogeneous tank experiment, with reasonable behavior.     

Diurnal sea breeze effects on inner-shelf cross-shore exchange

Cross-shore exchange by strong (cross-shore wind stress, τ_sx>0.05 Pa) diurnal (7–25 h) sea breeze events are investigated using two years of continuous wind, wave, and ocean velocity profiles in 13 m water depth on the inner-shelf in Marina, Monterey bay, California. The diurnal surface wind stress, waves, and currents have spectral peaks at 1, 2, and 3 cpd and the diurnal variability represents about 50% of the total variability. During sea breeze relaxation (−0.05<τ_sx<0.05 Pa), a background wave-driven inner-shelf Eulerian undertow profile exists, which is equal and opposite to the Lagrangian Stokes drift profile, resulting in a net zero Lagrangian transport at depth. In the presence of a sea breeze (τ_sx>0.05 Pa), a uniform offshore profile develops that is different from the background undertow profile allowing cross-shore Lagrangian transport to develop, while including Lagrangian Stokes drift. The diurnal cross-shore current response is similar to subtidal (>25 h) cross-shore current response, as found by Fewings et al. (2008). The seasonality of waves and winds modify the diurnal sea breeze impact. It is suggested that material is not transported cross-shore except during sea breeze events owing to near zero transport during relaxation periods. During sea breeze events, cross-shore exchange of material appears to occur onshore near the surface and offshore near the sea bed. Since sea breeze events last for a few hours, the long-term cross-shore transport is incremental each day.     

Fluids in the lithosphere, 1. Experimentally-determined wetting characteristics of CO2H2O fluids and their implications for fluid transport, host-rock physical properties, and fluid inclusion formation

The equilibrium distribution of CO₂H₂O fluids in synthetic rock samples (principally dunite and quartzite) has been characterized by measurements of the dihedral wetting angle, θ, resulting from 5-day annealing periods at 950–1150°C and 1 GPa. For fluids in equilibrium with polycrystalline quartz, θ varies systematically from 57° for pure H₂O to 90° at X_CO2 0.9. Similarly, for San Carlos olivine, θ varies from 65° for pure H₂O to 90° at X_CO2 0.9. The addition of solutes (NaCl, KCl, CaF₂, Na₂CO₃) to H₂O causes a major decrease in θ in the quartz/fluid system (to values as low as 40°), but has no effect on fluid wetting in dunite. Reconnaissance experiments on other mono- and polymineralic aggregates indicate universally high wetting angles (θ 60°) in upper mantle assemblages and for CO₂ in felsic compositions. For diopside + H₂O, θ 80°, with large variation due to crystalline anisotropy. In no case does θ approach 0°, the condition necessary for fluid to be present along all grain boundaries.Because a value of θ greater than 60° precludes the existence of an interconnected fluid phase in a rock, our results have important implications not only for fluid transport but also for the physical properties of the bulk fluid/rock system. Any static fluid present in the upper mantle must exist as isolated pores located primarily at grain corners, and transport can occur only by hydrofracture. In the continental crust, aqueous fluids (especially saline ones) are likely to form an interconnected network along grain edges, thus contributing to high electrical conductivity and allowing the possibility of fluid transport by porous flow or surface energy-driven infiltration.     

Investigating soil moisture feedbacks on precipitation with tests of Granger causality

Granger causality (GC) is used in the econometrics literature to identify the presence of one- and two-way coupling between terms in noisy multivariate dynamical systems. Here we test for the presence of GC to identify a soil moisture (S) feedback on precipitation (P) using data from Illinois. In this framework S is said to Granger cause P if F(P_t|Ω_t−Δt)≠F(P_t|Ω_t−Δt−S_t−Δt) where F denotes the conditional distribution of P, Ω_t−Δt represents the set of all knowledge available at time t−Δt, and Ω_t−Δt−S_t−Δt represents all knowledge except S. Critical for land–atmosphere interaction research is that Ω_t−Δt includes all past information on P as well as S. Therefore that part of the relation between past soil moisture and current precipitation which results from precipitation autocorrelation and soil water balance will be accounted for and not attributed to causality. Tests for GC usually specify all relevant variables in a coupled vector autoregressive (VAR) model and then calculate the significance level of decreased predictability as various coupling coefficients are omitted. But because the data (daily precipitation and soil moisture) are distinctly non-Gaussian, we avoid using a VAR and instead express the daily precipitation events as a Markov model. We then test whether the probability of storm occurrence, conditioned on past information on precipitation, changes with information on soil moisture. Past information on precipitation is expressed both as the occurrence of previous day precipitation (to account for storm-scale persistence) and as a simple soil moisture-like precipitation-wetness index derived solely from precipitation (to account for seasonal-scale persistence). In this way only those fluctuations in moisture not attributable to past fluctuations in precipitation (e.g., those due to temperature) can influence the outcome of the test. The null hypothesis (no moisture influence) is evaluated by comparing observed changes in storm probability to Monte-Carlo simulated differences generated with unconditional occurrence probabilities. The null hypothesis is not rejected (p>0.5) suggesting that contrary to recently published results, insufficient evidence exists to support an influence of soil moisture on precipitation in Illinois.     

Temperature dependence of the oxygen isotopic fractionation between diatom silica and water

We present a new paleotemperature scale, based on the oxygen isotopic ratio of the non-exchangeable fraction of the oxygen from diatom silica. The equation t = 17.2 − 2.4 (δ¹⁸O_silica − δ¹⁸O_water − 40) − 0.2 (δ¹⁸O_silica − δ¹⁸O_water − 40)² was derived using recent sediment samples from different oceanic areas, the temperature and isotopic composition of the local surface water. Comparison of our results with other relationships established for quartz-water or amorphous silica-water at higher temperature suggests no difference in isotopic fractionation between quartz-water and biogenic silica-water couples.     

Upscaling relative permeabilities in a structured porous medium

Upscaling of multi-phase flow problems for a heterogeneous porous medium requires modification of constitutive functions at the grid-block scale. A particular type of heterogeneity that has important environmental consequences involves thin, continuous streaks of high permeability through lower-permeability background rocks. These streaks, which may correspond to features like abandoned wells in mature sedimentary basins, can become preferential flow paths for an invading fluid. Quantification of flow through these types of heterogeneities in deep, geological formations is necessary for estimates of migration and possible leakage of injected fluids such as hazardous liquid wastes, municipal liquid wastes, and, possibly, carbon dioxide. One of the important constitutive functions for proper estimation of flow through these flow paths is the relative permeability function. In the simple case of a single high-permeability streak in a uniform rock matrix, with both materials having identical (local) relative permeability functions, the upscaled relative permeability must be changed significantly to capture the proper leakage. Standard petroleum reservoir pseudo-functions for relative permeability capture the general features of the upscaled function, but they still produce errors of several hundred percent in the leakage estimation. Detailed three-dimensional numerical simulations and associated upscaled calculations demonstrate the proper form for the upscaled relative permeability, and provide a modified derivation of pseudo-functions to capture the leakage behavior in upscaled models.     

Constrains on gravity wave induced diffusion in the middle atmosphere

A review of the important constraints on gravity wave induced diffusion of chemical tracers, heat, and momentum is given. Ground-based microwave spectroscopy measurements of H₂O and CO and rocket-based mass spectrometer measurements of Ar constrain the eddy diffusion coefficient for constituent transport (K _zz ) to be (1–3)×10⁵ cm²s^–1 in the upper mesosphere. Atomic oxygen data also limitsK _zz to a comparable value at the mesopause. From the energy balance of the upper mesosphere the eddy diffusion coefficient for heat transport (D _H ) is, at most 6×10⁵ cm²s^–1 at the mesopause and decreasing substantially with decreasing altitude. The available evidence for mean wind deceleration and the corresponding eddy diffusion coefficient for momentum stresses (D _M ) suggests that it is at least 1×10⁶ cm²s^–1, in the upper mesosphere. Consequently the eddy Prandtl number for macroscopic scale lengths is >3.     

Exploring the nature of non-Fickian transport in laboratory experiments

Observations of non-Fickian transport in sandbox experiments [Levy M, Berkowitz B. Measurement and analysis of non-Fickian dispersion in heterogeneous porous media. J Contam Hydrol 2003;64:203–26] were analyzed previously using a power law tail ψ(t) ∼ t^−1−β with 0 < β < 2 for the spectrum of transition times comprising a tracer plume migration. For each sandbox medium a choice of β resulted in an excellent fit to the breakthrough curve (BTC) data, and the value of β decreased slowly with increasing flow velocity. Here, the data are reanalyzed with the full spectrum of ψ(t) gleaned from analytical calculations [Cortis A, Chen Y, Scher H, Berkowitz B. Quantitative characterization of pore-scale disorder effects on transport in “homogeneous” granular media. Phys Rev E 2004;10(70):041108. doi: 10.1103/PhysRevE.70.041108], numerical simulations [Bijeljic B, Blunt MJ. Pore-scale modeling and continuous time random walk analysis of dispersion in porous media. Water Resour Res 2006;42:W01202. doi: 10.1029/2005WR004578] and permeability fields [Di Donato G, Obi E-O, Blunt MJ. Anomalous transport in heterogeneous media demonstrated by streamline-based simulation. Geophys Res Lett 2003;30:1608–12s. doi: 10.1029/2003GL017196]. We represent the main features of the full spectrum of transition times with a truncated power law (TPL), ψ(t) ∼ (t₁ + t)^−1−βexp(−t/t₂), where t₁ and t₂ are the limits of the power law spectrum. An excellent fit to the entire BTC data set, including the changes in flow velocity, for each sandbox medium is obtained with a single set of values of t₁, β, t₂. The influence of the cutoff time t₂ is apparent even in the regime t < t₂. Significantly, we demonstrate that the previous apparent velocity dependence of β is a result of choosing a pure power law tail for ψ(t). The key is the change in the log–log slope of the TPL form of ψ(t) with a shifting observational time window caused by the change in the mean velocity. Hence, the use of the full spectrum of ψ(t) is not only necessary for the transition to Fickian behavior, but also to account for the dynamics of these laboratory observations of non-Fickian transport.     

Stored mafic/ultramafic crust and early Archean mantle depletion

Both early and late Archean rocks from greenstone belts and felsic gneiss complexes exhibit positive ε_Nd values of +1 to +5 by 3.5 Ga, demonstrating that a depleted mantle reservoir existed very early. The amount of preserved pre-3.0 Ga continental crust cannot explain such high ε values in the depleted residue unless the volume of residual mantle was very small: a layer less than 70 km thick by 3.0 Ga. Repeated and exclusive sampling of such a thin layer, especially in forming the felsic gneiss complexes, is implausible. Extraction of enough continental crust to deplete the early mantle and its destructive recycling before 3.0 Ga ago requires another implausibility, that the sites of crustal generation and of recycling were substantially distinct. In contrast, formation of mafic or ultramafic crust analogous to present-day oceanic crust was continuous from very early times. Recycled subducted oceanic lithosphere is a likely contributor to present-day hotspot magmas, and forms a reservoir at least comparable in volume to continental crust. Subduction of an early mafic/ultramafic “oceanic” crust and temporary storage rather than immediate mixing back into undifferentiated mantle may be responsible for the depletion and high ε_Nd values of the Archean upper mantle. Using oceanic crustal production proportional to heat productivity, we show that temporary storage in the mantle of that crust, whether basaltic as formed by 5–20% partial melting, or partly komatiitic and formed by higher extents of melting is sufficient to balance an early depleted mantle of significant volume with ε_Nd at least +3.0.     

Diapirism in the earth's mantle: Experiments on the motion of a hot sphere in a fluid with temperature-dependent viscosity

The ascent of magma diapirs through the earth's mantle is modelled experimentally by the motion of a hot metal sphere through a fluid whose viscosity varies strongly with temperature. The dimensionless drag on the sphere (drag number D) and the heat transfer from it (Nusselt number Nu) are found as functions of the dimensionless velocity of the sphere (Peclet number Pe) and the viscosity contrast μ_∞/μ₀ = 10^γ, where μ_∞ and μ₀ are the viscosities of the fluid far from the sphere and at its surface. The drag D = D(Pe, γ) has two limits. For large Pe and small γ (“Stokes” limit), the drag approaches the Stokes' Law result. For small Pe and large γ (“lubrication” limit), the drag is orders of magnitude less than that predicted by Stokes' Law. Nu is a function of Pe alone. For reasonable values of the diapir radius and the viscosity contrast, the dimensionless scale height Pe/3 Nu may exceed a critical value, resulting in progressive melting during ascent. This suggests that diapirs may ascend great distances through the mantle while remaining largely molten. Lamont-Doherty Geological Observatory Contribution No. 3414.     

Explicit solution of a free boundary problem for a nonlinear absorption model of mixed saturated-unsaturated flow

In wet soils, zones of saturation naturally develop in the vicinity of impermeable strata, surface ponds and subterranean cavities. Hydrology must be then concerned with transient flow through coexisting unsaturated and saturated zones. The models of advancing saturated zones necessarily involve a nonlinear free boundary problem.A closed-form analytic solution is presented for a nonlinear diffusion model under conditions of ponding at the surface. The soil water diffusivity is restricted to the special functional form D(θ) = a/(b − θ)², where θ is the water content field to be determined and a, b are positive constants. The explicit solution depends on a parameter C (determined by the data of the problem), according to two cases: 1 < C < C₁ or C ≥ C₁, where C₁ is a constant which is obtained as the unique solution of an equation. This result complements the study given in P. Broadbridge, Water Resources Research, 1990, 26, 2435–2443, in order to established when the explicit solution is available. The behavior of the bifurcation parameter C₁ as a function of the driving potential is studied with the corresponding limits for small and large values. Moreover, the sorptivity is proven to be continuously differentiable function of the variable C.     

Geochemistry and isotopes of fluids from sulphur springs, Valles Caldera, New Mexico

Detailed geochemistry supported by geologic mapping has been used to investigate Sulphur Springs, an acid-sulfate hot spring system that issues from the western flank of the resurgent dome inside Valles Caldera. The most intense activity occurs at the intersection of faults offsetting caldera-fill deposits and post-caldera rhyolites. Three geothermal wells in the area have encountered pressures <1 MPa and temperatures of 200°C at depths of 600 to 1000 m. Hot spring and fumarole fluids may discharge at boiling temperatures with pH 1.0 and SO₄ 8000 mg/l. These conditions cause argillic alterations throughout a large area.Non-condensible gases consist of roughly 99% CO₂ with minor amounts of H₂S, H₂, and CH₄. Empirical gas geothermometry suggests a deep reservoir temperature of 215 to 280°C. Comparison of ¹³C and ¹⁸O between CaCO₃ from well cuttings and CO₂ from fumarole steam indicates a fractionation temperature between 200 and 300°C by decarbonation of hydrothermally altered Paleozoic limestone and vein calcite in the reservoir rocks. Tritium concentrations obtained from steam condensed in a mudpot and deep reservoir fluids (Baca #13, 278°C) are 2.1 and 1.0 T.U. respectively, suggesting the steam originates from a reservoir whose water is mostly >50 yrs old. Deuterium contents of fumarole steam, deep reservoir fluid, and local meteoric water are practically identical even though ¹⁸O contents range through 4‰, thus, precipitation on the resurgent dome of the caldera could recharge the hydrothermal system by slow percolation. From analysis of D and ¹⁸O values between fumarol steam and deep reservoir fluid, steam reaches the surface either (1) by vaporizing relatively shallow groundwater at 200°C or (2) by means of a two-stage boiling process through an intermediate level reservoir at roughly 200°C.Although many characteristics of known vapor-dominated geothermal systems are found at Sulphur Springs, fundamental differences exist in temperature and pressure of our postulated vapor-zone. We propose that the reservoir beneath Sulphur Springs is too small or too poorly confined to sustain a “true” vapor-dominated system and that the Sulphur Springs system may be a “dying” vapor-dominated system that has practically boiled itself dry.     

Paleomagnetism of the triassic nicola volcanics and geotectonics of the quesnellia subterrane of terrane I, British Columbia

Paleomagnetic data from 46 sites (674 specimens) of the Westcoast Crystalline Gneiss Complex on the west coast of Vancouver Island using AF and thermal demagnetization methods yields a high blocking temperature WCB component (> 560°C) with a pole at 335°W, 66°N (δ_p = 4°, δ_m = 6°) and a lower coercivity WCA component ( 25 mT, < 500°C) with a pole at 52°W, 79°N (δ_p = 7°, δ_m = 8°). Further thermal demagnetization data from 24 sites in the Jurassic Island Intrusions also defines two high blocking temperature components. The IIA component pole is at 59°W, 79°N (δ_p = 7°, δ_m = 8°) and IIB pole at 130°W, 73°N (δ_p = 12°, δ_m = 13°). Combined with previous data from the Karmutsen Basalts and mid-Tertiary units on Vancouver Island and from the adjacent Coast Plutonic Complex, the geotectonic motions are examined for the Vancouver Island segment of the Wrangellian Subterrane of composite Terrane II of the Cordillera. The simplest hypothesis invokes relatively uniform translation for Terrane II from Upper Triassic to Eocene time producing 39° ± 6° of northward motion relative to the North American craton, combined with 40° of clockwise rotation during the Lower Tertiary.     

Fluids in the lithosphere, 2. Experimental constraints on CO2 transport in dunite and quartzite at elevated P-T conditions with implications for mantle and crustal decarbonation processes

In a series of experiments at 0.5–1.3 GPa and 1050–1200°C we have monitored the transport, via crack propagation, of CO₂ into well-annealed olivine and quartz aggregates. The objectives were to determine (1) the extent and rate of fluid penetration; (2) the effect of varying both P-T conditions and microstructure; and (3) the fluid penetration pathways. Experiments on CO₂ penetration into dunite annealed in the absence of MgO indicate rapid and pervasive fluid transport on a grain-dimension scale, but a limited penetration distance ( 1 mm). Additional experiments on dunite annealed in the presence of MgO (either dispersed or present at both ends), however, resulted in CO₂ penetration that was both pervasive on the scale of individual grains and almost always completely through the 5 mm long samples. The abundance of fine (10 μm) grains in the MgO-free dunite, in contrast to the much larger grain sizes of the samples annealed with MgO present, suggests the difference in fluid penetration behavior may arise because the strength variation in dunite scales with the grain size. Effects arising from changes in olivine point defect chemistry, however, are an additional possibility. The response of synthetic quartzite to CO₂ overpressure is distinct from that of dunite: Quartzite experiences rapid and complete penetration of CO₂, via a macroscopically visible system of transgranular fractures, over the range of P-T conditions investigated.The small amount of porosity ( 2–3%) present in most rock samples fabricated for this study, lacks three-dimensional connectivity, thus precluding any enhanced fluid penetration via porous flow. Pores could possibly enhance fluid penetration as the result of a small reduction in resistance to fracture, but the probable abundance of strength-controlling flaws in natural rocks is likely to produce similar behavior.The results of our experiments on olivine and olivine + MgO suggest that the transport of pressurized CO₂ in very olivine-rich mantle environments will be pervasive on the scale of individual grains and its extent may be dependent on rock microstructure and/or crystal chemical effects. Such pervasive fluid transport, perhaps associated with magma decarbonation, may have interesting implications for both magma transport and local LREE enrichment of adjacent mantle wall-rock. The ease with which quartzite is penetrated by CO₂ at the conditions of our experiments underscores the possible role of decarbonation reactions in crustal permeability-enhancement processes.     

Assessment of the prediction error in a large-scale application of a dynamic soil acidification model

 The prediction error of a relatively simple soil acidification model (SMART2) was assessed before and after calibration, focussing on the Al and NO₃ concentrations on a block scale. Although SMART2 is especially developed for application on a national to European scale, it still runs at a point support. A 5×5 km² grid was used for application on the European scale. Block characteristic values were obtained simply by taking the median value of the point support values within the corresponding grid cell. In order to increase confidence in model predictions on large spatial scales, the model was calibrated and validated for the Netherlands, using a resolution that is feasible for Europe as a whole. Because observations are available only at the point support, it was necessary to transfer them to the block support of the model results. For this purpose, about 250 point observations of soil solution concentrations in forest soils were upscaled to a 5×5 km² grid map, using multiple linear regression analysis combined with block kriging. The resulting map with upscaled observations was used for both validation and calibration. A comparison of the map with model predictions using nominal parameter values and the map with the upscaled observations showed that the model overestimated the predicted Al and NO₃ concentrations. The nominal model results were still in the 95% confidence interval of the upscaled observations, but calibration improved the model predictions and strongly reduced the model error. However, the model error after calibration remains rather large.     

Density-dependent dispersion in heterogeneous porous media Part II: Comparison with nonlinear models

The results of a series of high-resolution numerical experiments are used to test and compare three nonlinear models for high-concentration-gradient dispersion. Gravity stable miscible displacement is considered. The first model, introduced by Hassanizadeh, is a modification of Fick’s law which involves a second-order term in the dispersive flux equation and an additional dispersion parameter β. The numerical experiments confirm the dependency of β on the flow rate. In addition, a dependency on travelled distance is observed. The model can successfully be applied to nearly homogeneous media (σ² = 0.1), but additional fitting is required for more heterogeneous media.The second and third models are based on homogenization of the local scale equations describing density-dependent transport. Egorov considers media that are heterogeneous on the Darcy scale, whereas Demidov starts at the pore-scale level. Both approaches result in a macroscopic balance equation in which the dispersion coefficient is a function of the dimensionless density gradient. In addition, an expression for the concentration variance is derived. For small σ², Egorov’s model predictions are in satisfactory agreement with the numerical experiments without the introduction of any new parameters. Demidov’s model involves an additional fitting parameter, but can be applied to more heterogeneous media as well.     

Unified modeling of flow liquefaction and cyclic mobility

Flow liquefaction and cyclic mobility are two different phenomena that are encountered during strong earthquakes. Flow liquefaction is associated with the contractive behavior of loose granular materials and cyclic mobility is associated with the dilative response of both loose and dense granular materials at low confining stresses. These two types of response pertain to the same material and therefore should be modeled in a consistent manner. Whether a soil in a given state exhibits contractive or dilative behavior is dependent on its dilatancy, d=d_v^p/d_q^p. A form of the dilatancy d=d(η,ψ,C) is proposed, where η=q/p is the stress ratio, and ψ and C denote the internal state variables and the intrinsic properties, respectively. It has been shown that such a state-dependent dilatancy is effective in describing both the contractive and dilative behavior. This allows the soil behavior associated with flow liquefaction and cyclic mobility during earthquakes to be modeled in a unified way.     

Recherche d''une politique de gestion des stocks d''eau de barrages-réservoirs en vue de soutenir les étiages : 2. Utilisation d''un modèle alterné annuel apports-déficits pour la recherche des conditions de gestion

In the upper catchment of the River Loire, France, the construction of five reservoir dams has been planned to sustain the low flows in the Loire valley. The management of these reservoirs, to be built successively, must be approached from partial or complete points of view in order to establish the daily draft decisions at every stage of the project.A hydrological criteria concerning the low flows at a station in the valley (namely the “objective point”) is used to judge the results. It is possible to determine the optimal carry-over storage for this criterion with the use of a long series of simulated inflows to reservoirs and annual deficits, when the future conditions are presumed to be known. The statistical analysis of the results helps in the formulation of the objectives for long-term Q₁ assuring the carry-over storage for a predetermined risk of failure.This objective for long-term Q₁ will not hold good if the low flow is severe. Thus some deterministic and statistical hypotheses have been used to formulate an objective for the mean term of flow Q₂ (t_j) which is calculated each day t_j and adjusted to the hydrological conditions of the year. The target draft C_b at the objective point is the minimum of the pair [(Q₁, Q₂ (t_j)].Water is discharged each day to meet this target flow, while maintaining all the constraints of the flows downstream to the reservoirs. It takes into account the time needed for transfer of water and permits a good prediction of either the flow propagation in the upper watershed or the evolution of the inflows from downstream catchments.A modular model is used to calculate the daily flow. The results obtained from simulation were satisfactory.

Résumé

La construction de cinq barrages réservoirs est envisagée sur le haut-bassin de la Loire, en vue de soutenir les débits d'étiage dans la basse vallée. Une gestion en temps réel s'exprime par une formulation journalière des débits à lacher aux ouvrages de retenue. Cette formulation résulte d'une optimisation de la gestion des volumes d'apports, compte tenu d'une contrainte de défaillance liée à un état vide des réserves en cours d'étiage.La recherche de la gestion optimale des reports interannuels est faite au moyen d'un critère purement hydrologique: la distribution de probabilité des débits d'étiage en une station de la vallée, appelée point objectif. Une longue série simulée d'apports annuels aux réservoirs et de déficits au point objectif permet de déterminer les reports interannuels optimaux vis-à-vis de ce critère dans le cas d'un avenir certain. L'analyse statistique des reports effectués dans ces conditions permet de dégager la formulation d'un objectif à long terme assurant un report interannuel pour un risque déterminé de défaillance. Cet objectif défini en début de saison d'étiage et optimisant le report envisagé est appelé l'objectif à long terme Q₁. En cas de réserves assez faibles en début de saison, et d'étiage plus sévère que prévu, le maintien “ne varietur” de cet objectif peut conduire à la vidange totale des réservoirs en cours d'étiage. Une contrainte journalière a été ajoutée pour limiter ce risque. La répartition de la totalité des réserves disponibles sur la période probable d'étiage restant à courir, définit un objectif à moyen terme Q₂ (t_j). Sa réactualisation chaque jour évite toute défaillance brusque de la gestion. Le débit que l'on cherche à maintenir au point objectif ou débit cible est défini chaque jour par le minimum du couple [Q₁, Q₂ (t_j)].La réalisation pratique de ce débit cible à partir des délestages effectués aux différents barrages tient compte de la propagation des débits lachés et des prévisions d'apports des bassins intermédiaires. Un modèle modulaire de bassin a été conçu qui permet le calcul des lachures journalières réalisant un débit cible défini.La simulation de la méthode proposée sur les séries historiques disponibles fournit des résultats très satisfaisants.     

Composite titanomagnetite-ferrian ilmenite grains and correlative magnetic components in a dacite with self-reversed TRM

Electron microprobe and reflected light microscopic examinations confirm the presence of composite grains of ferrian ilmenite with X_ilm = 0.53 and titanomagnetite with X_usp = 0.13 in a dacite with self-reversed TRM. A parallel TRM component associated with titanomagnetite and a reversed component associated with self-reversing ferrian ilmenite are the principal NRM components. A subordinate, parallel component is associated with ferrian ilmenite which is not magnetically coupled to an “χ-phase”. The natural self-reversing properties are mainly a consequence of the dacite's high quenching temperature, calculated at 862–864°C using the Fe—Ti oxide geothermometer, and are most consistent with the self-reversal mechanism proposed by Lawson et al. [9].The conduction of thermal demagnetization and TRM induction tests in air had a much greater effect on the Fe—Ti oxides than did natural cooling, and resulted in significant oxidation with the consequent modification of some magnetic properties and the formation of another reversed TRM component. The subdivision of titanomagnetite grains by oxidation along fractures decreased its effective grain size and caused an apparent increase in its magnetic intensity, in addition to a slight increase in its resistance to alternating field demagnetization. The χ-phase associated with the reversed NRM component, with 0.42 > X_ilm 0.31, became Fe-enriched during the earlier stages of heat treatment. It is suggested that after heating at 600°C for two hours or more, this χ-phase exsolves as titanohematite with X_ilm < 0.33. The ferrian ilmenite host is consequently enriched in Ti, and another χ-phase much closer in composition to the host generates a reversed TRM component with T_b < 200°C.     

Hydrogeochemistry of the Simav geothermal field, western Anatolia, Turkey

Thermal waters hosted by Menderes metamorphic rocks emerge along fault lineaments in the Simav geothermal area. Thermal springs and drilled wells are located in the Eynal, Çitgöl and Na a locations, which are part of the Simav geothermal field. Studies were carried out to obtain the main chemical and physical characteristics of thermal waters. These waters are used for heating of residences and greenhouses and for balneological purposes. Bottom temperatures of the drilled wells reach 163°C with total dissolved solids around 2225 mg/kg. Surface temperatures of thermal springs vary between 51°C and 90°C. All the thermal waters belong to Na–HCO₃–SO₄ facies. The cold groundwaters are Ca–Mg–HCO₃ type. Dissolution of host rock and ion-exchange reactions in the reservoir of the geothermal system shift the Ca–Mg–HCO₃ type cold groundwaters to the Na–HCO₃–SO₄ type thermal waters. Thermal waters are oversaturated at discharge temperatures for aragonite, calcite, quartz, chalcedony, magnesite and dolomite minerals giving rise to a carbonate-rich scale. Gypsum and anhydrite minerals are undersaturated with all of the thermal waters. Boiling during ascent of the thermal fluids produces steam and liquid waters resulting in an increase of the concentrations of the constituents in discharge waters. Steam fraction, y, of the thermal waters of which temperatures are above 100°C is between 0.075 and 0.119. Reservoir pH is much lower than pH measured in the liquid phase separated at atmospheric conditions, since the latter experienced heavy loss of acid gases, mainly CO₂. Assessment of the various empirical chemical geothermometers and geochemical modelling suggest that reservoir temperatures vary between 175°C and 200°C.