- Water resources, Method of Characteristics, Applied Mathematics, Transport Phenomena in Porous Media, Fluid flow in porous media, Reactive transport modeling, and 7 moreMagmatic Dynamics, Poroelasticity, Adsorption and wastewater treatment, Earthquakes, Planetesimals, Core formation, and Two phase flow, melt migration within upper mantleedit
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... more
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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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... more
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 mineral−liquid 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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The segregation of dense core-forming melts by porous flow is a natural mechanism for core formation in early planetesimals. However, experimental observations show that texturally equili-brated metallic melt does not wet the silicate... more
The segregation of dense core-forming melts by porous flow is a natural mechanism for core formation in early planetesimals. However, experimental observations show that texturally equili-brated metallic melt does not wet the silicate grain boundaries and tends to reside in isolated pockets that prevent percola-tion. Here we use pore-scale simulations to determine the minimum melt fraction required to induce porous flow, the perco-lation threshold. The composition of terrestrial planets suggests that typical planetesimals contain enough metal to overcome this threshold. Nevertheless, it is currently thought that melt segregation is prevented by a pinch-off at melt fractions slightly below the percolation threshold. In contrast to previous work, our simulations on irregular grain geometries reveal that a texturally equilibrated melt network remains connected down to melt fractions of only 1 to 2%. This hysteresis in melt connectivity allows percolative core formation in planetesimals that contain enough metal to exceed the percolation threshold. Evidence for the per-colation of metallic melt is provided by X-ray microtomography of primitive achondrite Northwest Africa (NWA) 2993. Microstruc-tural analysis shows that the metal–silicate interface has characteristics expected for a texturally equilibrated pore network with a dihedral angle of ∼85 •. The melt network therefore remained close to textural equilibrium despite a complex history. This suggests that the hysteresis in melt connectivity is a viable process for percolative core formation in the parent bodies of primitive achondrites.
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Keywords: solitary wave chromatography trace element melt migration magma dynamics fluid migration Porosity waves arise naturally from the equations describing fluid migration in ductile rocks. Here, we show that higher-dimensional... more
Keywords: solitary wave chromatography trace element melt migration magma dynamics fluid migration 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.
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Geological carbon storage has the potential to reduce anthropogenic carbon dioxide emissions, if large volumes can be injected and securely retained. Storage capacity is limited by regional pressure buildup in the subsurface. However,... more
Geological carbon storage has the potential to reduce anthropogenic carbon dioxide emissions, if large volumes can be injected and securely retained. Storage capacity is limited by regional pressure buildup in the subsurface. However, natural CO2 reservoirs in the United States are commonly underpressured, suggesting that natural processes reduce the pressure buildup over time and increase storage security. To identify these processes, we studied Bravo Dome natural CO2 reservoir (New Mexico, USA), where the gas pressure is up to 6.4 MPa below the hydrostatic pressure, i.e., less than 30% of the expected pressure. Here, we show that the dissolution of CO2 into the brine reduces the pressure by 1.02 ± 0.08 MPa, because Bravo Dome is isolated from the ambient hydrologic system. This challenges the assumption that the successful long-term storage of CO 2 is limited to open geological formations. We also show that the formation containing the reservoir was already 2.85 ± 2.02 MPa underpressured before CO2 emplacement. This is likely due to the overlying evaporite layer, which prevents recharge. Similar underpressured formations below regional evaporites are widespread in the midcontinent of the United States. This suggests the existence of significant storage capacities with properties similar to Bravo Dome, which has contained large volumes of CO2 over millennial time scales.
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Please cite this article in press as: Huerta, N.J., et al., Reactive transport of CO2-saturated water in a cement fracture: Application to wellbore leakage during geologic CO2 storage. Time dependence of fluid flux up a leaky well has... more
Please cite this article in press as: Huerta, N.J., et al., Reactive transport of CO2-saturated water in a cement fracture: Application to wellbore leakage during geologic CO2 storage. Time dependence of fluid flux up a leaky well has significant implications for the feasibility of geologic CO2 storage. We present laboratory experiments that study various boundary conditions, fluid fluxes, and residence times to understand the range of behavior in fractured cement cores. Carbonic acid progressively reacts with cement by dissolving phases which neutralize the acid and liberate calcium ions. This dissolution does not increase the aperture of the fracture, due to the formation of an amorphous silicate residue. Where aqueous calcium concentration and pH are sufficiently high calcium carbonates become insoluble and precipitate in the open fracture. When the driving force for fluid flux is a constant pressure differential precipitation leads to a progressive reduction in fluid flux and the development of self-limiting behavior. With sufficient residence time precipitation leads to sealing of the leaky well.
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Geologic carbon storage in deep saline aquifers is a promising technology for reducing anthro-pogenic emissions into the atmosphere. Dissolution of injected CO2 into resident brines is one of the primary trapping mechanisms generally... more
Geologic carbon storage in deep saline aquifers is a promising technology for reducing anthro-pogenic emissions into the atmosphere. Dissolution of injected CO2 into resident brines is one of the primary trapping mechanisms generally considered necessary to provide long-term storage security. Given that diffusion of CO2 in brine is woefully slow, convective dissolution, driven by a small increase in brine density with CO2 saturation, is considered to be the primary mechanism of dissolution trapping. Previous studies of convective dissolution have typically only considered the convective process in the single-phase region below the capillary transition zone and have either ignored the overlying two-phase region where dissolution actually takes place or replaced it with a virtual region with reduced or enhanced constant per-meability. Our objective is to improve estimates of the long-term dissolution flux of CO2 into brine by including the capillary transition zone in two-phase model simulations. In the fully two-phase model, there is a capillary transition zone above the brine-saturated region over which the brine saturation decreases with increasing elevation. Our two-phase simulations show that the dissolution flux obtained by assuming a brine-saturated, single-phase porous region with a closed upper boundary is recovered in the limit of vanishing entry pressure and capillary transition zone. For typical finite entry pressures and capillary transition zone, however, convection currents penetrate into the two-phase region. This removes the mass transfer limitation of the diffusive boundary layer and enhances the convective dissolution flux of CO2 more than 3 times above the rate assuming single-phase conditions.
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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... more
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 p H 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.
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The geologic sequestration of carbon dioxide (CO 2) in structural and stratigraphic traps is a viable option to reduce anthropogenic emissions. While dissolution of the CO 2 stored in these traps reduces the long-term leakage risk, the... more
The geologic sequestration of carbon dioxide (CO 2) in structural and stratigraphic traps is a viable option to reduce anthropogenic emissions. While dissolution of the CO 2 stored in these traps reduces the long-term leakage risk, the dissolution process remains poorly understood in systems that reflect the appropriate subsurface geometry. Here, we study dissolution in a porous layer that exhibits a feature relevant for CO 2 storage in structural and stratigraphic traps: a finite CO 2 source along the top boundary that extends only part way into the layer. This feature represents the finite extent of the interface between free-phase CO 2 pooled in a trap and the underlying brine. Using theory and simulations, we describe the dissolution mechanisms in this system for a wide range of times and Rayleigh numbers, and classify the behaviour into seven regimes. For each regime, we quantify the dissolution flux numerically and model it analytically, with the goal of providing simple expressions to estimate the dissolution rate in real systems. We find that, at late times, the dissolution flux decreases relative to early times as the flow of unsaturated water to the CO 2 source becomes constrained by a lateral exchange flow though the reservoir. Application of the models to several representative reservoirs indicates that dissolution is strongly affected by the reservoir properties; however, we find that reservoirs with high permeabilities (k 1 Darcy) that are tens of metres thick and several kilometres wide could potentially dissolve hundreds of megatons of CO 2 in tens of years.
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Textural equilibrium controls the distribution of the liquid phase in many naturally occurring porous materials such as partially molten rocks and alloys, salt–brine and ice– water systems. In these materials, pore geometry evolves to... more
Textural equilibrium controls the distribution of the liquid phase in many naturally occurring porous materials such as partially molten rocks and alloys, salt–brine and ice– water systems. In these materials, pore geometry evolves to minimize the solid–liquid interfacial energy while maintaining a constant dihedral angle, θ , at solid–liquid contact lines. We present a level set method to compute an implicit representation of the liquid– solid interface in textural equilibrium with space-filling tessellations of multiple solid grains in three dimensions. Each grain is represented by a separate level set function and interfacial energy minimization is achieved by evolving the solid–liquid interface under surface diffusion to constant mean curvature surface. The liquid volume and dihedral angle constraints are added to the formulation using virtual convective and normal velocity terms. This results in an initial value problem for a system of non-linear coupled PDEs governing the evolution of the level sets for each grain, using the implicit representation of the solid grains as initial condition. A domain decomposition scheme is devised to restrict the computational domain of each grain to few grid points around the grain. The coupling between the interfaces is achieved in a higher level on the original computational domain. The spatial resolution of the discretization is improved through high-order spatial differentiation schemes and localization of computations through domain composition. Examples of three-dimensional solutions are also obtained for different grain distributions networks that illustrate the geometric flexibility of the method.
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Keywords: noble gases shale gas two-phase flow migration–fractionation geochemical tracers geological carbon storage Environmental monitoring of shale gas production and geological carbon dioxide (CO 2) storage requires identification of... more
Keywords: noble gases shale gas two-phase flow migration–fractionation geochemical tracers geological carbon storage Environmental monitoring of shale gas production and geological carbon dioxide (CO 2) storage requires identification of subsurface gas sources. Noble gases provide a powerful tool to distinguish different sources if the modifications of the gas composition during transport can be accounted for. Despite the recognition of compositional changes due to gas migration in the subsurface, the interpretation of geochemical data relies largely on zero-dimensional mixing and fractionation models. Here we present two-phase flow column experiments that demonstrate these changes. Water containing a dissolved noble gas is displaced by gas comprised of CO 2 and argon. We observe a characteristic pattern of initial co-enrichment of noble gases from both phases in banks at the gas front, followed by a depletion of the dissolved noble gas. The enrichment of the co-injected noble gas is due to the dissolution of the more soluble major gas component, while the enrichment of the dissolved noble gas is due to stripping from the groundwater. These processes amount to chromatographic separations that occur during two-phase flow and can be predicted by the theory of gas injection. This theory provides a mechanistic basis for noble gas fractionation during gas migration and improves our ability to identify subsurface gas sources after post-genetic modification. Finally, we show that compositional changes due to two-phase flow can qualitatively explain the spatial compositional trends observed within the Bravo Dome natural CO 2 reservoir and some regional compositional trends observed in drinking water wells overlying the Marcellus and Barnett shale regions. In both cases, only the migration of a gas with constant source composition is required, rather than multi-stage mixing and fractionation models previously proposed.
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We present a set of reactive transport experiments in cement fractures. The experiments simulate coupling between flow and reaction when acidic, CO 2-rich fluids flow along a leaky wellbore. An analog dilute acid with a pH between 2.0 and... more
We present a set of reactive transport experiments in cement fractures. The experiments simulate coupling between flow and reaction when acidic, CO 2-rich fluids flow along a leaky wellbore. An analog dilute acid with a pH between 2.0 and 3.15 was injected at constant rate between 0.3 and 9.4 cm/s into a fractured cement core. Pressure differential across the core and effluent pH were measured to track flow path evolution, which was analyzed with electron microscopy after injection. In many experiments reaction was restricted within relatively narrow, tortuous channels along the fracture surface. The observations are consistent with coupling between flow and dissolution/precipitation. Injected acid reacts along the fracture surface to leach calcium from cement phases. Ahead of the reaction front, high pH pore fluid mixes with calcium-rich water and induces mineral precipitation. Increases in the pressure differential for most experiments indicate that precipitation can be sufficient to restrict flow. Experimental data from this study combined with published field evidence for mineral precipitation along cemented annuli suggests that leakage of CO 2-rich fluids along a wellbore may seal the leakage pathway if the initial aperture is small and residence time allows mobilization and precipitation of minerals along the fracture.
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[1] Carbon capture and storage is currently the only technology that may allow significant reductions in CO 2 emissions from large point sources. Seismic images of geological CO 2 storage show the rise of CO 2 is influenced by horizontal... more
[1] Carbon capture and storage is currently the only technology that may allow significant reductions in CO 2 emissions from large point sources. Seismic images of geological CO 2 storage show the rise of CO 2 is influenced by horizontal shales. The buoyant CO 2 spreads beneath impermeable barriers until a gap allows its upward migration. The large number and small scale of these barriers makes the prediction of the CO 2 migration path and hence the magnitude of CO 2 trapping very challenging. We show that steady buoyancy dominated flows in complex geometries can be modeled as a cascade of flux partitioning events. This approach allows the analysis of two-dimensional plume dispersal from a horizontal injection well. We show that the plume spreads laterally with height y above the source according to (y/h) 1/2 L, where L is the width of the shales and h is their vertical separation. The fluid volume below successive shale layers, and therefore the magnitude of trapped CO 2 , increase as (y/h) 5/4 above the source, so that every additional layer of barriers traps more CO 2 than the one below. Upscaling small scale flow barriers by reducing the vertical permeability, common in numerical simulations of CO 2 storage, does not capture the dispersion and trapping of the CO 2 plume by the flow barriers.
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We present a linear stability analysis of density-driven miscible flow in porous media in the context of carbon dioxide sequestration in saline aquifers. Carbon dioxide dissolution into the underlying brine leads to a local density... more
We present a linear stability analysis of density-driven miscible flow in porous media in the context of carbon dioxide sequestration in saline aquifers. Carbon dioxide dissolution into the underlying brine leads to a local density increase that results in a gravitational instability. The physical phenomenon is analogous to the thermal convective instability in a semi-infinite domain, owing to a step change in temperature at the boundary. The critical time for the onset of convection in such problems has not been determined accurately by previous studies. We present a solution, based on the dominant mode of the self-similar diffusion operator, which can accurately predict the critical time and the associated unstable wavenumber. This approach is used to explain the instability mechanisms of the critical time and the long-wave cutoff in a semi-infinite domain. The dominant mode solution, however, is valid only for a small parameter range. We extend the analysis by employing the quasi-steady-state approximation (QSSA) which provides accurate solutions in the self-similar coordinate system. For large times, both the maximum growth rate and the most dangerous mode decay as t 1/4. The long-wave and the shortwave cutoff modes scale as t 1/5 and t 4/5 , respectively. The instability problem is also analysed in the nonlinear regime by high-accuracy direct numerical simulations. The nonlinear simulations at short times show good agreement with the linear stability predictions. At later times, macroscopic fingers display intense nonlinear interactions that significantly influence both the front propagation speed and the overall mixing rate. A dimensional analysis for typical aquifers shows that for a permeability variation of 1 −3000 mD, the critical time can vary from 2000 yrs to about 10 days while the critical wavelength can be between 200 m and 0.3 m.
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Budgets of 4-He and 40-Ar provide constraints on the chemical evolution of the solid Earth and atmosphere. Although continental crust accounts for the majority of 4-He and 40-Ar degassed from the Earth, degassing mechanisms are subject to... more
Budgets of 4-He and 40-Ar provide constraints on the chemical evolution of the solid Earth and atmosphere. Although continental crust accounts for the majority of 4-He and 40-Ar degassed from the Earth, degassing mechanisms are subject to scholarly debate. Here we provide a constraint on crustal degassing by comparing the noble gases accumulated in the Bravo Dome natural CO 2 reservoir, New Mexico USA, with the radiogenic production in the underlying crust. A detailed geological model of the reservoir is used to provide absolute abundances and geostatistical uncertainty of 4-He, 40-Ar, 21-Ne, 20-Ne, 36-Ar, and 84-Kr. The present-day production rate of crustal radiogenic 4 He and 40 Ar, henceforth referred to as 4-He * and 40-Ar * , is estimated using the basement composition, surface and mantle heat flow, and seismic estimates of crustal density. After subtracting mantle and atmospheric contributions, the reservoir contains less than 0.02% of the radiogenic production in the underlying crust. This shows unequivocally that radiogenic noble gases are effectively retained in cratonic continental crust over millennial timescales. This also requires that approximately 1.5 Gt of mantle derived CO 2 migrated through the crust without mobilizing the crustally accumulated gases. This observation suggests transport along a localized fracture network. Therefore, the retention of noble gases in stable crystalline continental crust allows shallow accumulations of radiogenic gases to record tectonic history. At Bravo Dome, the crustal 4-He */40-Ar * ratio is one fifth of the expected crustal production ratio, recording the preferential release of 4-He during the Ancestral Rocky Mountain orogeny, 300 Ma.
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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... more
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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Motivated by geological carbon dioxide (CO2) storage, we present a vertical-equilibrium sharp-interface model for the migration of immiscible gravity currents with constant residual trapping in a two-dimensional confined aquifer. The... more
Motivated by geological carbon dioxide (CO2) storage, we present a vertical-equilibrium sharp-interface model for the migration of immiscible gravity currents with constant residual trapping in a two-dimensional confined aquifer. The residual acts as a loss term that reduces the current volume continuously. In the limit of a horizontal aquifer, the interface shape is self-similar at early and at late times. The spreading of the current and the decay of its volume are governed by power-laws. At early times the exponent of the scaling law is independent of the residual, but at late times it decreases with increasing loss. Owing to the self-similar nature of the current the volume does not become zero, and the current continues to spread. In the hyperbolic limit, the leading edge of the current is given by a rarefaction and the trailing edge by a shock. In the presence of residual trapping, the current volume is reduced to zero in finite time. Expressions for the up-dip migration distance and the final migration time are obtained. Comparison with numerical results shows that the hyperbolic limit is a good approximation for currents with large mobility ratios even far from the hyperbolic limit. In gently sloping aquifers, the current evolution is divided into an initial near-parabolic stage, with power-law decrease of volume, and a later near-hyperbolic stage, characterized by a rapid decay of the plume volume. Our results suggest that the efficient residual trapping in dipping aquifers may allow CO2 storage in aquifers lacking structural closure, if CO2 is injected far enough from the outcrop of the aquifer.
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Deep geological storage sites for nuclear waste are commonly located in rock salt to ensure hydrological isolation from groundwater. The low permeability of static rock salt is due to a percolation threshold. However, deformation may be... more
Deep geological storage sites for nuclear waste are commonly located in rock salt to ensure hydrological isolation from groundwater. The low permeability of static rock salt is due to a percolation threshold. However, deformation may be able to overcome this threshold and allow fluid flow. We confirm the percolation threshold in static experiments on synthetic salt samples with x-ray microtomography. We then analyze wells penetrating salt deposits in the Gulf of Mexico. The observed hydrocarbon distributions in rock salt require that percolation occurred at porosities considerably below the static threshold due to deformation-assisted percolation. Therefore, the design of nuclear waste repositories in salt should guard against deformation-driven fluid percolation. In general, static percolation thresholds may not always limit fluid flow in deforming environments.
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Highly variable distributions of yttrium and rare earth elements (Y+REEs) are documented in pelitic garnet from the Picuris Mountains, New Mexico, and from Passo del Sole, Switzerland, and in mafic garnet from the Franciscan Complex,... more
Highly variable distributions of yttrium and rare earth elements (Y+REEs) are documented in pelitic garnet from the Picuris Mountains, New Mexico, and from Passo del Sole, Switzerland, and in mafic garnet from the Franciscan Complex, California. The wide variety of these Y+REE zoning patterns, and those described previously in other occurrences, imply diverse origins linked to differing degrees of mobility of these elements through the intergranular medium during garnet growth. In the Picuris Mountains, large, early-nucleating crystals have radial profiles of Y+REE dominated by central peaks and annular maxima, in patterns that vary systematically with atomic number. Superimposed on these features are narrow spikes in HREEs and MREEs, located progressively rimward with decreasing atomic number. In contrast, profiles in small, late-nucleating crystals contain only broad central maxima for all Y+REEs. In garnet from Passo del Sole, Y+REE zoning varies radically from sample to sample: in some rocks, crystals of all sizes display only central peaks for all Y+REEs; in others, profiles exhibit irregular fluctuations in Y+REE contents that match up with small-scale patchy zon-ing in Y and Ca X-ray maps. In the Franciscan Complex, Y+REE in garnet cores fluctuate unsystem-atically, but mantles and rims display concentric oscillatory zoning for both major elements and Y+REEs. Our interpretation of the complexity of Y+REE distributions in metamorphic garnet centres on the concept that these distributions vary primarily in response to the length scales over which these elements can equilibrate during garnet growth. Very short length scales of equilibration, due to low intergranular mobility, produce overprint zoning characterized by small-scale irregularities. Higher but still restricted mobility yields diffusion-controlled uptake, characterized by patterns of central peaks and annular maxima that vary with atomic number and are strongly influenced by T–t paths during garnet growth. Still greater mobility permits progressively greater, potentially rock-wide, equilibration with major-and accessory-phase assemblages, leading to mineralogical controls: an unchanging mineral assemblage during garnet growth produces bell-shaped profiles resembling those produced by Rayleigh fractionation, whereas changes in major-and/or accessory-phase assemblages produce profiles with distinct annuli and sharp discontinuities in concentration. The very high mobility associated with influxes of Y+REE-bearing fluids can cause these element distributions to be dominated by factors external to the rock, yielding profiles characterized by abrupt shifts or oscillations that are not correlated to changes in mineral assemblages.
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Compaction–dissolution waves in porosity and melt pressure form spontaneously in numerical simulations of melt migration in an upwelling, viscously compacting, porous column in a solubility gradient. The melt fraction is assumed to be... more
Compaction–dissolution waves in porosity and melt pressure form spontaneously in numerical simulations of melt migration in an upwelling, viscously compacting, porous column in a solubility gradient. The melt fraction is assumed to be small and the solid comprises olivine and orthopyroxene. The solubility of orthopyroxene in the melt is assumed to increase linearly with height and induces a gradient reaction, assumed to be at local equilibrium. Approximations for the vertical, 1-D, steady-state solutions are derived assuming negligible resistance to compaction. The linear stability of the steady-state solutions is characterized by complex eigenvalues and an oscillatory instability with strong wavenumber selection. This instability leads to the formation of checkerboard compaction–dissolution waves observed in the non-linear numerical simulations. The phase velocity of these waves is larger than the solid velocity but smaller than the melt velocity. The oscillatory instability is realized over a range of parameters and the variation in wave properties is explored. A power-law bulk-viscosity formulation, ξ = η/φ m f , is shown to decrease growth rates linearly in the exponent, m. For small perturbations, the growth rates and phase velocities measured from high-resolution numerical simulations are predicted by the linear theory as well as the dominant wavenumber in the non-linear regime. We present a regime diagram for reaction infiltration instabilities in viscously compacting porous media and show that compaction–dissolution waves are favored by increasing solid upwelling and small solubility gradients relative to high-porosity channels. The regime diagram suggests that the formation of compaction–dissolution waves is a feasible new physical mechanism for melt transport beneath mid-ocean ridges.
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As a fluid carries solutes through a porous material, species that sorb onto the surface of the material travel more slowly than the fluid. Stronger adsorption results in slower solute migration, or increased solute retardation. The... more
As a fluid carries solutes through a porous material, species that sorb onto the surface of the material travel more slowly than the fluid. Stronger adsorption results in slower solute migration, or increased solute retardation. The adsorption of strontium (Sr 2+) onto iron-oxides is strongly pH-dependent and becomes significant at high pH. Radioactive Sr 2+ isotopes are, therefore, commonly stored in alkaline solutions to maximize their retardation. Field observations and numerical simulations of the leakage of such solutions into low-pH soils, however, show that even Sr 2+ stored in alkaline solutions can migrate without retardation. Migration occurs because hydrodynamic dispersion allows mixing of Sr 2+ with the low-pH fluid forming an acidic Sr 2+-rich plume which can travel without retardation. Here we report the first experimental observations confirming this dispersion-induced fast Sr 2+ transport. We report column-flood experiments where a high-pH solution containing Sr 2+ was injected into a low-pH porous medium of iron-oxide-coated beads. We observe both a strongly retarded Sr 2+ front and an isolated fast pulse of Sr 2+ traveling at the average fluid velocity. This dispersion-induced fast pulse of strontium must be taken into account when considering the safety of radionuclide storage in alkaline solutions.
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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... more
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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The multiscale finite volume (MSFV) method is introduced for the efficient solution of elliptic problems with rough coefficients in the absence of scale separation. The coarse operator of the MSFV method is presented as a multipoint flux... more
The multiscale finite volume (MSFV) method is introduced for the efficient solution of elliptic problems with rough coefficients in the absence of scale separation. The coarse operator of the MSFV method is presented as a multipoint flux approximation (MPFA) with numerical evaluation of the transmissibilities. The monotonicity region of the original MSFV coarse operator has been determined for the homogeneous anisotropic case. For grid-aligned anisotropy the monotonicity of the coarse operator is very limited. A compact coarse operator for the MSFV method is presented that reduces to a 7-point stencil with optimal monotonicity properties in the homogeneous case. For heterogeneous cases the compact coarse operator improves the monotonicity of the MSFV method, especially for anisotropic problems. The compact operator also leads to a coarse linear system much closer to an M-matrix. Gradients in the direction of strong coupling vanish in highly anisotropic elliptic problems with homogeneous Neumann boundary data, a condition referred to as transverse equilibrium (TVE). To obtain a monotone coarse operator for heterogeneous problems the local elliptic problems used to determine the transmissibilities must be able to reach TVE as well. This can be achieved by solving two linear local problems with homogeneous Neumann boundary conditions and constructing a third bilinear local problem with Dirichlet boundary data taken from the linear local problems. Linear combination of these local problems gives the MSFV basis functions but with hybrid boundary conditions that cannot be enforced directly. The resulting compact multiscale finite volume (CMSFV) method with hybrid local boundary conditions is compared numerically to the original MSFV method. For isotropic problems both methods have comparable accuracy, but the CMSFV method is robust for highly anisotropic problems where the original MSFV method leads to unphysical oscillations in the coarse solution and recirculations in the reconstructed velocity field. 1. Introduction. Natural porous media are heterogeneous at all length scales, and current advances in data integration and subsurface description provide increasingly detailed descriptions of the subsurface. Numerical methods for incompressible flow in porous media therefore lead to elliptic problems with highly oscillatory coefficients. Full resolution of the fine-scale features of the coefficient in realistic problems is often too expensive. In the last 10 years several multiscale methods have been developed to reduce computational complexity by incorporating fine-scale features into a set of coarse grid equations. A characteristic of multiscale methods for flow in porous media is that they allow a reconstruction of an approximate fine-scale solution from the coarse solution. The fine reconstruction is necessary for the subsequent transport calculations, which are very difficult to upscale. Methods designed for transport in porous media include the multiscale finite element method [17], the mixed multi
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Carbon dioxide (CO2) storage in deep geological formations can lead to significant reductions in anthropogenic CO2 emissions if large amounts of CO2 can be stored. Estimates of the storage capacity are therefore essential to the... more
Carbon dioxide (CO2) storage in deep geological formations can lead to significant reductions in anthropogenic CO2 emissions if large amounts of CO2 can be stored. Estimates of the storage capacity are therefore essential to the evaluation of individual storage sites as well as the feasibility of the technology. One important limitation on the storage capacity is the radius of review, the lateral extent of the pressure perturbation, of the storage project. We show that pressure dissipation into ambient mudrocks retards lateral pressure propagation significantly and therefore increases the storage capacity. For a three-layer model of a reservoir surrounded by thick mudrocks, the far-field pressure is approximated well by a single-phase model. Through dimensional analysis and numerical simulations, we show that the lateral extent of the pressure front follows a power law that depends on a single dissipation parameter M / log 10 R k R S R 2 l À Á , where R k and R S are the ratios of mudrock to reservoir permeability and specific storage, and R l is the aspect ratio of the confined pressure plume. Both the coefficient and the exponent of the power law are sigmoid decreasing functions of M. The M values of typical storage sites are in the region where the power-law changes rapidly. The combination of large uncertainty in mudrock properties and the sigmoid shape leads to wide and strongly skewed probability distributions for the predicted radius of review and storage capacity. Therefore, if the lateral extent of the pressure front limits the storage capacity, the determination of the mudrock properties is an important component of site characterization.
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As a fluid carries solutes through a porous material, species that sorb onto the surface of the material travel more slowly than the fluid. Stronger adsorption results in slower solute migration, or increased solute retardation. The... more
As a fluid carries solutes through a porous material, species that sorb onto the surface of the material travel more slowly than the fluid. Stronger adsorption results in slower solute migration, or increased solute retardation. The adsorption of strontium (Sr 2+) onto iron-oxides is strongly pH-dependent and becomes significant at high pH. Radioactive Sr 2+ isotopes are, therefore, commonly stored in alkaline solutions to maximize their retardation. Field observations and numerical simulations of the leakage of such solutions into low-pH soils, however, show that even Sr 2+ stored in alkaline solutions can migrate without retardation. Migration occurs because hydrodynamic dispersion allows mixing of Sr 2+ with the low-pH fluid forming an acidic Sr 2+-rich plume which can travel without retardation. Here we report the first experimental observations confirming this dispersion-induced fast Sr 2+ transport. We report column-flood experiments where a high-pH solution containing Sr 2+ was injected into a low-pH porous medium of iron-oxide-coated beads. We observe both a strongly retarded Sr 2+ front and an isolated fast pulse of Sr 2+ traveling at the average fluid velocity. This dispersion-induced fast pulse of strontium must be taken into account when considering the safety of radionuclide storage in alkaline solutions.
Research Interests: Reactive transport modeling, Contaminant Transport, Adsorption, Strontium, Contamination Dispersion, and 4 moreEnvironmental chemistry , Trace metals speciation and adsorption of organic and inorganic contaminants in aqeuous system, Anomalous Transport, pH dependent reactive transport, and Hydrodynamic dispersion
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... more
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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In texturally equilibrated porous media the pore geometry evolves to minimize the energy of the liquid-solid interfaces, while maintaining the dihedral angle θ at solid-solid-liquid contact lines. We present computations of... more
In texturally equilibrated porous media the pore geometry evolves to minimize the energy of the liquid-solid interfaces, while maintaining the dihedral angle θ at solid-solid-liquid contact lines. We present computations of three-dimensional texturally equilibrated pore networks using a level-set method. Our results show that the grain boundaries with the smallest area can be fully wetted by the pore fluid even for θ > 0. This was previously not thought to be possible at textural equilibrium and reconciles the theory with experimental observations. Even small anisotropy in the fabric of the porous medium allows the wetting of these faces at very low porosities, ϕ < 3%. Percolation and orientation of the wetted faces relative to the anisotropy of the fabric are controlled by θ. The wetted grain boundaries are perpendicular to the direction of stretching for θ > 60° and the pores do not percolate for any investigated ϕ. For θ < 60°, in contrast, the grain boundaries parallel to the direction of stretching are wetted and a percolating pore network forms for all ϕ investigated. At low θ even small anisotropy in the fabric induces large anisotropy in the permeability, due to the concentration of liquid on the grain boundaries and faces.
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The injection of carbon dioxide (CO 2) captured at large point sources into deep saline aquifers can significantly reduce anthropo-genic CO 2 emissions from fossil fuels. Dissolution of the injected CO 2 into the formation brine is a... more
The injection of carbon dioxide (CO 2) captured at large point sources into deep saline aquifers can significantly reduce anthropo-genic CO 2 emissions from fossil fuels. Dissolution of the injected CO 2 into the formation brine is a trapping mechanism that helps to ensure the long-term security of geological CO 2 storage. We use thermochronology to estimate the timing of CO 2 emplacement at Bravo Dome, a large natural CO 2 field at a depth of 700 m in New Mexico. Together with estimates of the total mass loss from the field we present, to our knowledge, the first constraints on the magnitude, mechanisms, and rates of CO 2 dissolution on millennial timescales. Apatite (U-Th)/He thermochronology records heating of the Bravo Dome reservoir due to the emplacement of hot volcanic gases 1.2–1.5 Ma. The CO 2 accumulation is therefore significantly older than previous estimates of 10 ka, which demonstrates that safe long-term geological CO 2 storage is possible. Integrating geophysical and geochemical data, we estimate that 1.3 Gt CO 2 are currently stored at Bravo Dome, but that only 22% of the emplaced CO 2 has dissolved into the brine over 1.2 My. Roughly 40% of the dissolution occurred during the emplacement. The CO 2 dissolved after emplacement exceeds the amount expected from diffusion and provides field evidence for convective dissolution with a rate of 0.1 g/(m 2 y). The similarity between Bravo Dome and major US saline aquifers suggests that significant amounts of CO 2 are likely to dissolve during injection at US storage sites, but that convective dissolution is unlikely to trap all injected CO 2 on the 10-ky timescale typically considered for storage projects. geological carbon storage | thermochronology | noble gases | porous media convection | carbon sequestration