Probabilistic collocation and lagrangian sampling for advective tracer transport in randomly heterogeneous porous media

The Karhunen-Loeve (KL) decomposition and the polynomial chaos (PC) expansion are elegant and efficient tools for uncertainty propagation in porous media. Over recent years, KL/PC-based frameworks have successfully been applied in several contributions for the flow problem in the subsurface context. It was also shown, however, that the accurate solution of the transport problem with KL/PC techniques is more challenging. We propose a framework that utilizes KL/PC in combination with sparse Smolyak quadrature for the flow problem only. In a subsequent step, a Lagrangian sampling technique is used for transport. The flow field samples are calculated based on a PC expansion derived from the solutions at relatively few quadrature points. To increase the computational efficiency of the PC-based flow field sampling, a new reduction method is applied. For advection dominated transport scenarios, where a Lagrangian approach is applicable, the proposed PC/Monte Carlo method (PCMCM) is very efficient and avoids accuracy problems that arise when applying KL/PC techniques to both flow and transport. The applicability of PCMCM is demonstrated for transport simulations in multivariate Gaussian log-conductivity fields that are unconditional and conditional on conductivity measurements.     

Calcium isotope fractionation in calcite and aragonite

Calcium isotope fractionation was measured on skeletal aragonite and calcite from different marine biota and on inorganic calcite. Precipitation temperatures ranged from 0 to 28°C. Calcium isotope fractionation shows a temperature dependence in accordance with previous observations: 1000 · ln(α_cc) = −1.4 + 0.021 · T (°C) for calcite and 1000 · ln(α_ar) = −1.9 + 0.017 · T (°C) for aragonite. Within uncertainty the temperature slopes are identical for the two polymorphs. However, at all temperatures calcium isotopes are more fractionated in aragonite than in calcite. The offset in δ^44/40Ca is about 0.6‰. The underlying mechanism for this offset may be related to the different coordination numbers and bond strengths of the calcium ions in calcite and aragonite crystals, or to different Ca reaction behavior at the solid-liquid interface. Recently, the observed temperature dependence of the Ca isotope fractionation was explained quantitatively by the temperature control on precipitation rates of calcium carbonates in an experimental setting (Lemarchand et al., 2004). We show that this mechanism can in principle also be applied to CaCO₃ precipitation in natural environments in normal marine settings. Following this model, Ca isotope fractionation in marine Ca carbonates is primarily controlled by precipitation rates. On the other hand the larger Ca isotope fractionation of aragonite compared to calcite can not be explained by different precipitation rates. The rate control model of Ca isotope fractionation predicts a strong dependence of the Ca isotopic composition of carbonates on ambient CO₃²⁻ concentration. While this model is in general accordance with our observations in marine carbonates, cultured specimens of the planktic foraminifer Orbulina universa show no dependence of Ca-isotope fractionation on the ambient CO₃²⁻ concentration. The latter observation implies that the carbonate chemistry in the calcifying vesicles of the foraminifer is independent from the ambient carbonate ion concentration of the surrounding water.     

Quantification of organic pollutant degradation in contaminated aquifers using compound specific stable isotope analysis - Review of recent developments

Compound specific stable isotope analysis (CSIA) has been established as a viable tool for proving, characterizing and assessing degradation of organic pollutants within contaminated aquifers. The fractionation of stable isotopes during contaminant degradation leads to observable shifts in stable isotope ratios which can serve as an indicator for in situ pollutant degradation and allow for a quantitative assessment by means of the so-called Rayleigh (distillation) equation.This review highlights the recent developments of the Rayleigh equation approach for quantifying in situ degradation of organic pollutants in contaminated aquifers. The advantages and limitations of the Rayleigh equation approach are discussed and suggestions for improvements are given. Concepts are provided to estimate the uncertainty due to errors or variability of input parameters and how to deal with such uncertainty. Moreover, the applicability of the Rayleigh equation approach is evaluated regarding the heterogeneity and complexity of groundwater systems. For such systems, the review discusses the relevance of non-destructive processes, which affect the concentration (e.g., dispersive mixing) and potentially also the stable isotope ratio of contaminants (e.g., sorption, volatilization), and the resulting implications for the Rayleigh equation approach.     

A phase-field method for the direct simulation of two-phase flows in pore-scale media using a non-equilibrium wetting boundary condition

Advances in pore-scale imaging (e.g., μ-CT scanning), increasing availability of computational resources, and recent developments in numerical algorithms have started rendering direct pore-scale numerical simulations of multi-phase flow on pore structures feasible. Quasi-static methods, where the viscous and the capillary limit are iterated sequentially, fall short in rigorously capturing crucial flow phenomena at the pore scale. Direct simulation techniques are needed that account for the full coupling between capillary and viscous flow phenomena. Consequently, there is a strong demand for robust and effective numerical methods that can deliver high-accuracy, high-resolution solutions of pore-scale flow in a computationally efficient manner. Direct simulations of pore-scale flow on imaged volumes can yield important insights about physical phenomena taking place during multi-phase, multi-component displacements. Such simulations can be utilized for optimizing various enhanced oil recovery (EOR) schemes and permit the computation of effective properties for Darcy-scale multi-phase flows.We implement a phase-field model for the direct pore-scale simulation of incompressible flow of two immiscible fluids. The model naturally lends itself to the transport of fluids with large density and viscosity ratios. In the phase-field approach, the fluid-phase interfaces are expressed in terms of thin transition regions, the so-called diffuse interfaces, for increased computational efficiency. The conservation law of mass for binary mixtures leads to the advective Cahn–Hilliard equation and the condition that the velocity field is divergence free. Momentum balance, on the other hand, leads to the Navier–Stokes equations for Newtonian fluids modified for two-phase flow and coupled to the advective Cahn–Hilliard equation. Unlike the volume of fluid (VoF) and level-set methods, which rely on regularization techniques to describe the phase interfaces, the phase-field method facilitates a thermodynamic treatment of the phase interfaces, rendering it more physically consistent for the direct simulations of two-phase pore-scale flow. A novel geometric wetting (wall) boundary condition is implemented as part of the phase-field method for the simulation of two-fluid flows with moving contact lines. The geometric boundary condition accurately replicates the prescribed equilibrium contact angle and is extended to account for dynamic (non-equilibrium) effects. The coupled advective Cahn–Hilliard and modified Navier–Stokes (phase-field) system is solved by using a robust and accurate semi-implicit finite volume method. An extension of the momentum balance equations is also implemented for Herschel–Bulkley (non-Newtonian) fluids. Non-equilibrium-induced two-phase flow problems and dynamic two-phase flows in simple two-dimensional (2-D) and three-dimensional (3-D) geometries are investigated to validate the model and its numerical implementation. Quantitative comparisons are made for cases with analytical solutions. Two-phase flow in an idealized 2-D pore-scale conduit is simulated to demonstrate the viability of the proposed direct numerical simulation approach.     

Sources of fluids and gases expelled at cold seeps offshore Georgia, eastern Black Sea

Four seep sites located within an ∼20 km² area offshore Georgia (Batumi seep area, Pechori Mound, Iberia Mound, and Colkheti Seep) show characteristic differences with respect to element concentrations, and oxygen, hydrogen, strontium, and chlorine isotope signatures in pore waters, as well as impregnation of sediments with petroleum and hydrocarbon potential. All seep sites have active gas seepage, near surface authigenic carbonates and gas hydrates. Cokheti Seep, Iberia Mound, and Pechori Mound are characterized by oil-stained sediments and gas seepage decoupled from deep fluid advection and bottom water intrusion induced by gas bubble release. Pechori Mound is further characterized by deep fluid advection of lower salinity pore fluids. The Pechori Mound pore fluids are altered by mineral/water reactions at elevated temperatures (between 60 and 110 °C) indicated by heavier oxygen and lighter chlorine isotope values, distinct Li and B enrichment, and K depletion. Strontium isotope ratios indicate that fluids originate from late Oligocene strata. This finding is supported by the occurrence of hydrocarbon impregnations within the sediments. Furthermore, light hydrocarbons and high molecular weight impregnates indicate a predominant thermogenic origin for the gas and oil at Pechori Mound, Iberia Mound, and Colkheti Seep. C₁₅₊ hydrocarbons at the oil seeps are allochtonous, whereas those at the Batumi seep area are autochthonous. The presence of oleanane, an angiosperm biomarker, suggests that the hydrocarbon source rocks belong to the Maikopian Formation. In summary, all investigated seep sites show a high hydrocarbon potential and hydrocarbons of Iberia Mound, Colkheti Seep, and Pechori Mound are predominantly of thermogenic origin. However, only at the latter seep site advection of deep pore fluids is indicated.     

Calcium isotope fractionation in modern scleractinian corals

The ⁴⁴Ca/⁴⁰Ca ratios of cultured (Acropora sp.) and open ocean (Pavona clavus, Porites sp.) tropical reef corals are positively correlated with growth temperature. The slope of the temperature-fractionation relation is similar to inorganic aragonite precipitates. However, δ^44/40Ca of the coral aragonite is offset from inorganic and sclerosponge aragonite by about +0.5‰. This offset can neither be explained by the very fast, biologically controlled calcification of scleractinian corals, nor as a consequence of calcification from a partly closed volume of fluid. As corals actively transport calcium through several cell layers to the site of calcification, the most likely explanation for the offset is a biologically induced fractionation. Our results indicate a limited use of Ca isotopes in scleractinian corals as temperature proxy.     

A data based mechanistic approach to nonlinear flood routing and adaptive flood level forecasting

Operational flood forecasting requires accurate forecasts with a suitable lead time, in order to be able to issue appropriate warnings and take appropriate emergency actions. Recent improvements in both flood plain characterization and computational capabilities have made the use of distributed flood inundation models more common. However, problems remain with the application of such models. There are still uncertainties associated with the identifiability of parameters; with the computational burden of calculating distributed estimates of predictive uncertainty; and with the adaptive use of such models for operational, real-time flood inundation forecasting. Moreover, the application of distributed models is complex, costly and requires high degrees of skill. This paper presents an alternative to distributed inundation models for real-time flood forecasting that provides fast and accurate, medium to short-term forecasts. The Data Based Mechanistic (DBM) methodology exploits a State Dependent Parameter (SDP) modelling approach to derive a nonlinear dependence between the water levels measured at gauging stations along the river. The transformation of water levels depends on the relative geometry of the channel cross-sections, without the need to apply rating curve transformations to the discharge. The relationship obtained is used to transform water levels as an input to a linear, on-line, real-time and adaptive stochastic DBM model. The approach provides an estimate of the prediction uncertainties, including allowing for heterescadasticity of the multi-step-ahead forecasting errors. The approach is illustrated using an 80 km reach of the River Severn, in the UK.     

Calcium isotope record of Phanerozoic oceans: Implications for chemical evolution of seawater and its causative mechanisms

A total of 280 brachiopods of Ordovician to Cretaceous age, complemented by published data from belemnites and planktonic foraminifera, are used to reconstruct the evolution of calcium isotope composition of seawater (δ^44/40Ca_SW) over the Phanerozoic. The compiled δ^44/40Ca_SW record shows a general increase from ∼1.3‰ (NIST SRM 915a) at the beginning of the Ordovician to ∼2‰ at present. Superimposed on this trend is a major long-term positive excursion from the Early Carboniferous to Early Permian as well as several short-term, mostly negative, oscillations.A numerical model of the global cycles of calcium, carbon, magnesium and strontium was used to estimate whether the recorded δ^44/40Ca_SW variations can be explained by varying magnitudes of input and output fluxes of calcium to the oceans. The model uses the record of marine ⁸⁷Sr/⁸⁶Sr ratios as proxy for seafloor spreading rates, a record of oceanic Mg/Ca ratios to estimate rates of dolomite formation, and reconstructed atmospheric CO₂, discharge and erosion rates to estimate continental weathering fluxes.The model results indicate that varying magnitudes of the calcium input and output fluxes cannot explain the observed δ^44/40Ca_SW trends, suggesting that the isotope signatures of these fluxes must also have changed. As a possible mechanism we suggest variable isotope fractionation in the sedimentary output flux controlled by the dominant mineralogy in marine carbonate deposits, i.e. the oscillating ‘calcite-aragonite seas’. The ultimate control of the calcium isotope budget of the Phanerozoic oceans appears to have been tectonic processes, specifically variable rates of oceanic crust production that modulated the hydrothermal calcium flux and the oceanic Mg/Ca ratio, which in turn controlled the dominant mineralogy of marine carbonates, hence the δ^44/40Ca_SW. As to the causes of the short-term oscillations recorded in the secular δ^44/40Ca_SW trend, we tentatively propose that these are related to variable rates of dolomite formation and/or to changing chemical composition of the riverine flux, in particular and ratios, induced by variable proportions of silicate vs. carbonate weathering rates on the continents.