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Now showing items 1 - 16 of 2984

  • Theory of dissolution and precipitation waves-redux

    Zefreh, Masoud Ghaderi   Doster, Florian   Hesse, Marc A.  

    We present a local equilibrium theory for the reactive transport of two salts that share an anion in an ideal solution. We revisit this classic problem using the theory of hyperbolic partial differential equations accounting for the volume of precipitates. We construct analytical solutions for the 2 x 2 system of conservation laws in the absence of hydrodynamic dispersion. The character of the system depends on the saturation of the salts, that is, whether the fluid is saturated with both, either of the two or none of the salts. We provide a comprehensive analysis of the system and its solution. Each primitive variable, the amount of precipitate and the concentration of ions, remains constant along one class of waves that propagate in the system. The analysis of the system allows identification of seven bifurcations with respect to the intermediate state.
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  • Chromatographic analysis of the acidity-salinity transport system

    McNeece, Colin J.   Luetzenkirchen, Johannes   Hesse, Marc A.  

    The effects of acidity and salinity on solute transport in porous media are important to a diverse range of fields from seawater intrusion to nuclear waste storage. Recent transport experiments in quartz sand show the difficulty in capturing the coupling of acidity and salinity under acidic conditions for this system. Here we study the ability of different surface complexation models to capture this coupling, through an analysis of the reactive transport equations in the limit of no diffusion. This chromatographic analysis leads to a graphical representation of the full set of solutions in the phase plane, thus allowing a comprehensive comparison of the transport behavior arising from different SCMs. The analysis shows that the predicted coupling is improved by including amphoteric behavior of the quartz surface. The inclusion of a secondary proton sorption reaction increases the magnitude of surface charge under acidic conditions strengthening the acidity-salinity coupling. This suggests that even though the overall surface is negative above the point of zero charge, positively charged sites play an important role in the reactive transport of acidity and salinity.
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  • On mass transport in porosity waves

    Jordan, Jacob S.   Hesse, Marc A.   Rudge, John F.  

    Porosity waves arise naturally from the equations describing fluid migration in ductile rocks. Here, we show that higher-dimensional porosity waves can transport mass and therefore preserve geochemical signatures, at least partially. Fluid focusing into these high porosity waves leads to recirculation in their center. This recirculating fluid is separated from the background flow field by a circular dividing streamline and transported with the phase velocity of the porosity wave. Unlike models for one-dimensional chromatography in geological porous media, tracer transport in higher-dimensional porosity waves does not produce chromatographic separations between relatively incompatible elements due to the circular flow pattern. This may allow melt that originated from the partial melting of fertile heterogeneities or fluid produced during metamorphism to retain distinct geochemical signatures as they rise buoyantly towards the surface. (C) 2017 Elsevier B.V. All rights reserved.
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  • Effect of Dispersion on Solutal Convection in Porous Media

    Liang, Yu   Wen, Baole   Hesse, Marc A.   DiCarlo, David  

    Solutal convection in porous media is thought to be controlled by the molecular Rayleigh number, Ra-m, the ratio of the buoyant driving force over diffusive dissipation. The mass flux should increase linearly with Ra-m and the finger spacing should decrease as Ra-m(-1/2). Instead, our experiments find that flux levels off at large Ra-m and finger spacing increases with Ra-m. Here we show that the convective pattern is controlled by a dispersive Rayleigh number, Ra-d, balancing buoyancy and dispersion. Increasing the bead size of the porous medium increases Ra-m but decreases Ra-d and hence coarsens the pattern. While the flux is predominantly controlled by Ra-m, the anisotropy of mechanical dispersion leads to an asymmetry in the pattern that limits the flux at large bead sizes. Plain Language Summary Pattern formation in simple physical systems is intriguing, and convection in porous media is an example that was thought to be well understood. Convection is controlled by the balance between buoyant driving forces and dissipative mechanisms such as diffusion that smear out the concentration and hence density differences. Here we use simple laboratory experiments to show that the convective pattern is controlled by a different process than previously thought. A Rayleigh number based on mechanical dispersion, which is independent of fluid properties, predicts the flow pattern of solutal convection in bead packs.
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  • Theory of dissolution and precipitation waves - redux

    Ghaderi Zefreh, Masoud   Doster, Florian   Hesse, Marc A.  

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  • Transient solute transport with sorption in Poiseuille flow

    Zhang, Li   Hesse, Marc A.   Wang, Moran  

    Previous work on solute transport with sorption in Poiseuille flow has reached contradictory conclusions. Some have concluded that sorption increases mean solute transport velocity and decreases dispersion relative to a tracer, while others have concluded the opposite. Here we resolve this contradiction by deriving a series solution for the transient evolution that recovers previous results in the appropriate limits. This solution shows a transition in solute transport behaviour from early to late time that is captured by the first- and zeroth-order terms. Mean solute transport velocity is increased at early times and reduced at late times, while solute dispersion is initially reduced, but shows a complex dependence on the partition coefficient k at late times. In the equilibrium sorption model, the time scale of the early regime and the duration of the transition to the late regime both increase with ln k for large k. The early regime is pronounced in strongly sorbing systems (k >> 1). The kinetic sorption model shows a similar transition from the early to the late transport regime and recovers the equilibrium results when adsorption and desorption rates are large. As the reaction rates slow down, the duration of the early regime increases, but the changes in transport velocity and dispersion relative to a tracer diminish. In general, if the partition coefficient k is large, the early regime is well developed and the behaviour is well characterized by the analysis of the limiting case without desorption.
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  • Challenges in Coupling Acidity and Salinity Transport in Porous Media

    McNeece, Colin J.   Hesse, Marc A.  

    Salinity is an increasingly prescient issue in reactive transport, from low salinity water flooding to fracking brine leakage. Of primary concern is the effect of salinity on surface chemistry. Transport and batch experiments show a strong coupling of salinity and acidity through chemical interactions at the mineralliquid interface. This coupling is ascribed to the combined effects of ionic strength on electrostatic behavior of the interface and competitive sorption between protons and other cations for binding sites on the surface. The effect of these mechanisms is well studied in batch settings and readily describes observed behavior. In contrast, the transport literature is sparse, primarily applied to synthetic materials, and offers only qualitative agreement with observations. To address, this gap in knowledge, we conduct a suite of column flood experiments through silica sand, systematically varying salinity and acidity conditions. Experiments are compared to a reactive transport model incorporating the proposed coupling mechanisms. The results highlight the difficulty in applying such models to realistic media under both basic and acidic conditions with a single set of parameters. The analysis and experimental results show the observed error is the result of electrostatic assumptions within the surface chemistry model and provide a strong constraint on further model development.
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  • Reactive transport of aqueous protons in porous media

    McNeece, Colin J.   Hesse, Marc A.  

    The sorption of protons determines the surface charge of natural media and is therefore a first-order control on contaminant transport. Significant effort has been extended to develop chemical models that quantify the sorption of protons at the mineral surface. To compare these models' effect on predicted proton transport, we present analytic solutions for column experiments through silica sand. Reaction front morphology is controlled by the functional relationship between the total sorbed and total aqueous proton concentrations. An inflection point in this function near neutral pH leads to a reversal in the classic front formation mechanism under basic conditions, such that proton desorption leads to a self-sharpening front, while adsorption leads to a spreading front. A composite reaction front comprising both a spreading and self-sharpening segment can occur when the injected and initial concentrations straddle the inflection point. This behavior is unique in single component reactive transport and arises due to the auto-ionization of water rather than electrostatic interactions at the mineral surface. We derive a regime diagram illustrating conditions under which different fronts occur, highlighting areas where model predictions diverge. Chemical models are then compared and validated against a systematic set of column experiments. (C) 2016 Published by Elsevier Ltd.
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  • Conditions for the Long‐Term Preservation of a Deep Brine Reservoir in Ceres

    Castillo‐Rogez, Julie C.   Hesse, Marc A.   Formisano, M.   Sizemore, H.   Bland, M.   Ermakov, A. I.   Fu, R. R.  

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  • Reactive transport in a partially molten system with binary solid solution

    Jordan, Jacob S.   Hesse, Marc A.  

    Melt extraction from the Earth's mantle through high-porosity channels is required to explain the composition of the oceanic crust. Feedbacks from reactive melt transport are thought to localize melt into a network of high-porosity channels. Recent studies invoke lithological heterogeneities in the Earth's mantle to seed the localization of partial melts. Therefore, it is necessary to understand the reaction fronts that form as melt flows across the lithological interface between the heterogeneity and the ambient mantle. Here we present a chromatographic analysis of reactive melt transport across lithological boundaries, using the theory of hyperbolic conservation laws. This is an extension of linear trace element chromatography to the coupling of major elements and energy transport. Our analysis allows the prediction of the nonlinear feedbacks that arise in reactive melt transport due to changes in porosity. This study considers the special case of a partially molten porous medium with binary solid solution. As melt traverses a lithological contact, binary solid solution leads to the formation of a reacted zone between an advancing reaction front and the initial contact. The analysis also shows that the behavior of a fertile heterogeneity depends on its absolute concentration, in addition to compositional differences between itself and the refractory background. We present a regime diagram that predicts if melt emanating from a fertile heterogeneity localizes into high-porosity channels or develops a zero porosity shell. The theoretical framework presented here provides a useful tool for understanding nonlinear feedbacks in reactive melt transport, because it can be extended to more complex and realistic phase behaviors.
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  • Joint inversion in coupled quasi-static poroelasticity

    Hesse, Marc A.   Stadler, Georg  

    Geodetic surveys now provide detailed time series maps of anthropogenic land subsidence and uplift due to injection and withdrawal of pore fluids from the subsurface. A coupled poroelastic model allows the integration of geodetic and hydraulic data in a joint inversion and has therefore the potential to improve the characterization of the subsurface and our ability to monitor pore pressure evolution. We formulate a Bayesian inverse problem to infer the lateral permeability variation in an aquifer from geodetic and hydraulic data and from prior information. We compute the maximum a posteriori (MAP) estimate of the posterior permeability distribution and a Gaussian approximation of the posterior. Computing the MAP estimate requires the solution of a large-scale minimization problem subject to the poroelastic equations, for which we propose an efficient Newton-conjugate gradient optimization algorithm. The covariance matrix of the Gaussian approximation of the posterior is given by the inverse Hessian of the log posterior, which we construct by exploiting low-rank properties of the data misfit Hessian. First and second derivatives are computed using adjoints of the time-dependent poroelastic equations, allowing us to fully exploit transient data. Using three increasingly complex model problems, we find the following general properties of poroelastic inversions: Augmenting standard hydraulic well data by surface deformation data improves the aquifer characterization. Surface deformation contributes the most in shallow aquifers but provides useful information even for the characterization of aquifers down to 1 km. In general, it is more difficult to infer high-permeability regions, and their characterization requires frequent measurement to resolve the associated short-response timescales. In horizontal aquifers, the vertical component of the surface deformation provides a smoothed image of the pressure distribution in the aquifer. Provided that the mechanical properties are known, coupled poroelastic inversion is therefore a promising approach to detect flow barriers and to monitor pore pressure evolution.
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  • Plate tectonic cycling modulates Earth's He-3/Ne-22 ratio (vol 498,pg 309,2018)

    Dygert, Nick   Jackson, Colin R. M.   Hesse, Marc A.   Tremblay, Marissa M.   Shuster, David L.   Gu, Jesse T.  

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  • Two-phase gravity currents in porous media RID B-4914-2011

    Golding, Madeleine J.   Neufeld, Jerome A.   Hesse, Marc A.   Huppert, Herbert E.  

    We develop a model describing the buoyancy-driven propagation of two-phase gravity currents, motivated by problems in groundwater hydrology and geological storage of carbon dioxide (CO(2)). In these settings, fluid invades a porous medium saturated with an immiscible second fluid of different density and viscosity. The action of capillary forces in the porous medium results in spatial variations of the saturation of the two fluids. Here, we consider the propagation of fluid in a semi-infinite porous medium across a horizontal, impermeable boundary. In such systems, once the aspect ratio is large, fluid flow is mainly horizontal and the local saturation is determined by the vertical balance between capillary and gravitational forces. Gradients in the hydrostatic pressure along the current drive fluid flow in proportion to the saturation-dependent relative permeabilities, thus determining the shape and dynamics of two-phase currents. The resulting two-phase gravity current model is attractive because the formalism captures the essential macroscopic physics of multiphase flow in porous media. Residual trapping of CO(2) by capillary forces is one of the key mechanisms that can permanently immobilize CO(2) in the societally important example of geological CO(2) sequestration. The magnitude of residual trapping is set by the areal extent and saturation distribution within the current, both of which are predicted by the two-phase gravity current model. Hence the magnitude of residual trapping during the post-injection buoyant rise of CO(2) can be estimated quantitatively. We show that residual trapping increases in the presence of a capillary fringe, despite the decrease in average saturation.
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  • Anomalous Reactive Transport in the Framework of the Theory of Chromatography

    Prigiobbe, Valentina   Hesse, Marc A.   Bryant, Steven L.  

    The anomalous reactive transport considered here is the migration of contaminants through strongly sorbing permeable media without significant retardation. It has been observed in the case of heavy metals, organic compounds, and radionuclides, and it has critical implications on the spreading of contaminant plumes and on the design of remediation strategies. Even in the absence of the well-known fast migration pathways, associated with fractures and colloids, anomalous reactive transport arises in numerical simulations of reactive flow. It is due to the presence of highly pH-dependent adsorption and the broadening of the concentration front by hydrodynamic dispersion. This leads to the emergence of an isolated pulse or wave of a contaminant traveling at the average flow velocity ahead of the retarded main contamination front. This wave is considered anomalous because it is not predicted by the classical theory of chromatography, unlike the retardation of the main contamination front. In this study, we use the theory of chromatography to study a simple pH-dependent surface complexation model to derive the mathematical framework for the anomalous transport. We analyze the particular case of strontium (Sr2+) transport and define the conditions under which the anomalous transport arises. We model incompressible one-dimensional (1D) flow through a reactive porous medium for a fluid containing four aqueous species: H+, Sr2+, Na+, and Cl-. The mathematical problem reduces to a strictly hyperbolic 2 x 2 system of conservation laws for effective anions and Sr2+, coupled through a competitive Langmuir isotherm. One characteristic field is linearly degenerate while the other is not genuinely nonlinear due to an inflection point in the pH-dependent isotherm. We present the complete set of analytical solutions to the Riemann problem, consisting of only three combinations of a slow wave comprising either a rarefaction, a shock, or a shock-rarefaction with fast wave comprising only a contact discontinuity. Highly resolved numerical solutions at large P,clet numbers show excellent agreement with the analytic solutions in the hyperbolic limit. In the Riemann problem, the anomalous wave forms only if: hydrodynamic dispersion is present, the slow wave crosses the inflection locus, and the effective anion concentration increases along the fast path.
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  • Convective dissolution of carbon dioxide in saline aquifers

    Neufeld, Jerome A.   Hesse, Marc A.   Riaz, Amir   Hallworth, Mark A.   Tchelepi, Hamdi A.   Huppert, Herbert E.  

    Geological carbon dioxide (CO(2)) storage is a means of reducing anthropogenic emissions. Dissolution of CO(2) into the brine, resulting in stable stratification, increases storage security. The dissolution rate is determined by convection in the brine driven by the increase of brine density with CO(2) saturation. We present a new analogue fluid system that reproduces the convective behaviour of CO(2)-enriched brine. Laboratory experiments and high-resolution numerical simulations show that the convective flux scales with the Rayleigh number to the 4/5 power, in contrast with a classical linear relationship. A scaling argument for the convective flux incorporating lateral diffusion from downwelling plumes explains this nonlinear relationship for the convective flux, provides a physical picture of high Rayleigh number convection in a porous medium, and predicts the CO(2) dissolution rates in CO(2) accumulations. These estimates of the dissolution rate show that convective dissolution can play an important role in enhancing storage security. Citation: Neufeld, J. A., M. A. Hesse, A. Riaz, M. A. Hallworth, H. A. Tchelepi, and H. E. Huppert (2010), Convective dissolution of carbon dioxide in saline aquifers, Geophys. Res. Lett., 37, L22404, doi: 10.1029/2010GL044728.
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  • Dispersion of charged solute in charged micro- and nanochannel with reversible sorption

    Zhang, Li   Hesse, Marc A.   Wang, Moran  

    We study dispersion of a charged solute in a charged micro- and nanochannel with reversible sorption and derive an analytical solution for mass fraction in the fluid, transport velocity and dispersion coefficient. Electrical double layer formed on the charged surface gives rise to a charge-dependent solute transport by modifying the transverse distribution of the solute. We discuss the effect of sorption and electrical double layer on solute transport and show that the coupling between sorption and electrical double layer gives rise to charge-dependent transport even for a thin double layer. However, in this case, it can be reduced to a simple non-charge-dependent case by introducing the intrinsic sorption equilibrium constant.
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