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Results for “Journal of Fluid Mechanics”

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USGS2009

Thermal conductivity of hydrate-bearing sediments

A thorough understanding of the thermal conductivity of hydrate-bearing sediments is necessary for evaluating phase transformation processes that would accompany energy production from gas hydrate deposits and for estimating regional heat flow based on the observed depth to the base of the gas hydrate stability zone. The coexistence of multiple phases (gas hydrate, liquid and gas pore fill, and solid sediment grains) and their complex spatial arrangement hinder the a priori prediction of the thermal conductivity of hydrate-bearing sediments. Previous studies have been unable to capture the full parameter space covered by variations in grain size, specific surface, degree of saturation, nature of pore filling material, and effective stress for hydrate-bearing samples. Here we report on systematic measurements of the thermal conductivity of air dry, water- and tetrohydrofuran (THF)-saturated, and THF hydrate–saturated sand and clay samples at vertical effective stress of 0.05 to 1 MPa (corresponding to depths as great as 100 m below seafloor). Results reveal that the bulk thermal conductivity of the samples in every case reflects a complex interplay among particle size, effective stress, porosity, and fluid-versus-hydrate filled pore spaces. The thermal conductivity of THF hydrate–bearing soils increases upon hydrate formation although the thermal conductivities of THF solution and THF hydrate are almost the same. Several mechanisms can contribute to this effect including cryogenic suction during hydrate crystal growth and the ensuing porosity reduction in the surrounding sediment, increased mean effective stress due to hydrate formation under zero lateral strain conditions, and decreased interface thermal impedance as grain-liquid interfaces are transformed into grain-hydrate interfaces.

Journal of Geophysical Research B: Solid Earth↗

USGS1996

Granular-flow rheology: Role of shear-rate number in transition regime

This paper examines the rationale behind the semiempirical formulation of a generalized viscoplastic fluid (GVF) model in the light of the Reiner-Rivlin constitutive theory and the viscoplastic theory, thereby identifying the parameters that control the rheology of granular flow. The shear-rate number ( N ) proves to be among the most significant parameters identified from the GVF model. As N → 0 and N →∞, the GVF model can reduce asymptotically to the theoretical stress versus shear-rate relations in the macroviscous and grain-inertia regimes, respectively, where the grain concentration ( C ) also plays a major role in the rheology of granular flow. Using available data obtained from the rotating-cylinder experiments of neutrally buoyant solid spheres dispersing in an interstitial fluid, the shear stress for granular flow in transition between the two regimes proves dependent on N and C in addition to some material constants, such as the coefficient of restitution. The insufficiency of data on rotating-cylinder experiments cannot presently allow the GVF model to predict how a granular flow may behave in the entire range of N ; however, the analyzed data provide an insight on the interrelation among the relevant dimensionless parameters.

Journal of Engineering Mechanics↗

USGS1999

P wave crustal velocity structure in the greater Mount Rainier area from local earthquake tomography

We present results from a local earthquake tomographic imaging experiment in the greater Mount Rainier area. We inverted P wave arrival times from local earthquakes recorded at permanent and temporary Pacific Northwest Seismograph Network seismographs between 1980 and 1996. We used a method similar to that described by Lees and Crosson [1989], modified to incorporate the parameter separation method for decoupling the hypocenter and velocity problems. In the upper 7 km of the resulting model there is good correlation between velocity anomalies and surface geology. Many focal mechanisms within the St. Helens seismic zone have nodal planes parallel to the epicentral trend as well as to a north-south trending low-velocity trough, leading us to speculate that the trough represents a zone of structural weakness in which a moderate ( M 6.5–7.0) earthquake could occur. In contrast, the western Rainier seismic zone does not correlate in any simple way with anomaly patterns or focal mechanism fault planes, leading us to infer that it is less likely to experience a moderate earthquake. A ∼10 km-wide low-velocity anomaly occurs 5 to 18 km beneath the summit of Mount Rainier, which we interpret to be a signal of a region composed of hot, fractured rock with possible small amounts of melt or fluid. No systematic velocity pattern is observed in association with the southern Washington Cascades conductor. A midcrustal anomaly parallels the Olympic-Wallowa lineament as well as several other geophysical trends, indicating that it may play an important role in regional tectonics.

Journal of Geophysical Research B: Solid Earth↗

USGS2008

Swarms of similar long-period earthquakes in the mantle beneath Mauna Loa Volcano

We present analyses of two swarms of long-period (LP) earthquakes at > 30 km depth that accompanied the geodetically observed 2002–2005 Mauna Loa intrusion. The first LP earthquake swarm in 2002 consisted of 31 events that were precursory and preceded the start of Mauna Loa inflation; the second LP swarm of two thousand events occurred from 2004–2005. The rate of LP earthquakes slowed significantly coincident with the occurrence of the December 26, 2004 M w 9.3 Sumatra earthquake, suggesting that the seismic waves from this great earthquake may have had a dynamic triggering effect on the behavior of Mauna Loa's deep magma system. Using waveform cross correlation and double difference relocation, we find that a large number of earthquakes in each swarm are weakly similar and can be classified into two families. The relocated hypocenters for each family collapse to compact point source regions almost directly beneath the Mauna Loa intrusion. We suggest that the observed waveform characteristics are compatible with each family being associated with the resonance of a single fluid filled vertical crack of fixed geometry, with differences in waveforms between events being produced by slight variations in the trigger mechanism. If these LP earthquakes are part of the primary magma system that fed the 2002–2005 intrusion, as indicated by the spatial and temporal associations between mantle seismicity and surface deformation, then our results raise the possibility that this magma system may be quite focused at these depths as opposed to being a diffuse network. It is likely that only a few locations of Mauna Loa's deep magma system met the geometric and fluid dynamic conditions for generating LP earthquakes that were large enough to be recorded at the surface, and that much of the deep magma transfer associated with the 2002–2005 intrusion occurred aseismically.

Journal of Volcanology and Geothermal Research↗

USGS2012

Excitation of a buried magmatic pipe: A seismic source model for volcanic tremor

Recent observations of seismic events at various volcanoes suggest that harmonic tremor results from the sustained occurrence of so-called long-period or low-frequency events. Accordingly, we can view the long-period volcanic event as the elementary process of tremor and interpret it as the impulse response of the tremor-generating system. We present a seismic model in which the source of tremor is the acoustic resonance of a fluid-filled volcanic pipe triggered by excess gas pressure. The model consists of three elements, namely, a triggering mechanism, a resonator, and a radiator. For simplicity, we assume a hemispherical trigger, cylindrial resonator, and circular radiator set in a vertical configuration with the trigger capping the top of the pipe and the disk-shaped radiator shutting off its bottom. Considering the simple case of a source buried in a homogeneous half space, we then apply the discrete wave number method to obtain a complete representation of the ground motion response at near and intermediate distances. The results demonstrate that the displacement attributed to the pipe dominates the near-field motion, while that due to the disk is representative of the intermediate and far fields. The trigger itself has a smaller contribution, mainly limited to the field in the proximity of the source. The characteristics displayed by the free surface response evolve from a strong impulsive signature in the immediate vicinity of the epicenter to a well-developed harmonic wave train dominated by Rayleigh waves at larger distances. No clear shear arrival can be detected in the synthetic seismograms. The displacement spectrum reflects the organ-pipe modes of the conduit, and the bandwidth associated with the dominant spectral peak of motion is controlled by the combined losses due to viscous attenuation in the fluid and elastic radiation into the solid. In the case of the cylindrical magma column considered, the radiation loss is proportional to the square of the pipe radius, while the loss related to viscous damping is inversely proportional to the same factor, indicating that the relative importance of the two loss mechanisms is critically dependent on the geometry of the magma reservoir. The relative importance of the pipe and disk elements, likewise, is a function of the conduit cross section. This suggests the possibility of determining the geometry of the source as well as the radiation loss and in situ magma viscosity from a comparison of near- and far-field observations.

Journal of Geophysical Research Solid Earth↗

USGS1988

Generalized viscoplastic modeling of debris flow

Various concepts have been proposed or used in the development of Theological models for debris flow. The earliest model developed by Bagnold was based on the concept of the “dispersive” pressure generated by grain collisions. Bagnold's concept appears to be theoretically sound, but his empirical model has been found to be inconsistent with most theoretical models developed from non‐Newtonian fluid mechanics. Although the generality of Bagnold's model is still at issue, debris‐flow modelers in Japan have generally accepted Takahashi's formulas derived from Bagnold's model. Some efforts have recently been made by theoreticians in non‐Newtonian fluid mechanics to modify or improve Bagnold's concept or model. A viable rheological model should consist both of a rate‐independent part and a ratedependent part. A generalized viscoplastic fluid (GVF) model that has both parts as well as two major rheological properties (i.e., the normal stress effect and soil yield criterion) is shown to be sufficiently accurate, yet practical, for general use in debris‐flow modeling. In fact, Bagnold's model is found to be only a particular case of the GVF model. Analytical solutions for (steady) uniform debris flows in wide channels are obtained from the GVF model based on Bagnold's simplified assumption of constant grain concentration.

Journal of Hydraulic Engineering↗

USGS2009

Numerical models of caldera deformation: Effects of multiphase and multicomponent hydrothermal fluid flow

Ground surface displacement (GSD) in large calderas is often interpreted as resulting from magma intrusion at depth. Recent advances in geodetic measurements of GSD, notably interferometric synthetic aperture radar, reveal complex and multifaceted deformation patterns that often require complex source models to explain the observed GSD. Although hydrothermal fluids have been discussed as a possible deformation agent, very few quantitative studies addressing the effects of multiphase flow on crustal mechanics have been attempted. Recent increases in the power and availability of computing resources allow robust quantitative assessment of the complex time-variant thermal interplay between aqueous fluid flow and crustal deformation. We carry out numerical simulations of multiphase (liquid-gas), multicomponent (H 2O-CO2) hydrothermal fluid flow and poroelastic deformation using a range of realistic physical parameters and processes. Hydrothermal fluid injection, circulation, and gas formation can generate complex, temporally and spatially varying patterns of GSD, with deformation rates, magnitudes, and geometries (including subsidence) similar to those observed in several large calderas. The potential for both rapid and gradual deformation resulting from magma-derived fluids suggests that hydrothermal fluid circulation may help explain deformation episodes at calderas that have not culminated in magmatic eruption.

Journal of Geophysical Research B: Solid Earth↗

USGS1989

Salinity variations in submarine hydrothermal systems by layered double-diffusive convection

Various mechanisms have been proposed to explain the salinity variations in vent fluids of seafloor geothermal systems. New experiments reacting diabase and evolved seawater were carried out to reproduce earlier published observations of Cl depletions attributed to formation of an ephemeral Cl-bearing mineral. The absence of any Cl depletions in the present study suggests that the formation of Cl-bearing minerals is not sufficiently widespread to account for the observed salinity variations in the vent fluids. A re-evaluation of both field and laboratory evidence has led to a new model for subseafloor circulation that accounts for salinity variations as well as other chemical and mineralogic observations. In place of a simple single-pass convection system, we propose that the seafloor systems consist of two vertically nested convection cells in which a brine layer at depth heats and drives an overlying seawater cell. Such layering of salinities, a process known in fluid mechanics as double-diffusive convection, is an expected result when convection is induced in saline fluids. The process provides for stable high-temperature heat transfer upward from the cracking front adjacent to the magma, and for limited chemical exchange of the brine with the overlying seawater to explain salinity variations and high metal contents in the vent fluids. The brine also provides an effective medium to produce the secondary mineral assemblages observed in rocks from the mid-ocean ridges and ophiolites unsuccessfully produced in laboratory studies using seawater. The brine originates from the two-phase separation of seawater during magmatic/tectonic events and accumulates and remains relatively stable in the region immediately above the magma chamber.

Journal of Geology↗

USGS2025

Review: The hydrogeology of critical mineral resources relevant to the energy transition

Attaining the goals of the international treaty on climate change (the Paris Agreement) will greatly increase the demand for the critical minerals required to implement clean-energy technologies. This poses both challenges and opportunities to the hydrogeologic community from several perspectives. Here, important insights that the hydrogeological sciences have to offer for mineral exploration, mineral production, and addressing environmental issues related to mining and mine decommissioning are summarized. This study focuses on copper, cobalt, lithium, and rare earths to represent the broad spectrum of critical minerals and illustrate their relevance by referring to projected demands and production rates. The current understanding of the hydrogeologic processes that form major deposits of these minerals are then summarized. Ore is defined as the naturally occurring material from which minerals of economic value can be extracted, where most ore deposits are the products of complex hydrogeologic couplings between fluid flow, heat transport, solute transport, chemical reactions, and mechanical deformation. Exploration models for the discovery of deeper, hidden deposits are potentially informed by hydrogeologic theory and hydrogeochemical processes. Hydrogeologic understanding and methods are also essential to production and recovery. Longstanding challenges are mine dewatering and (conversely) mine water supply, as well as mineral-extraction practices such as spoil heap leaching and in situ mining. New challenges arise from element extraction from subsurface brines. Finally, the quantity of water use and potential environmental impacts of mining on water quality are at the core of ‘social license’: the approval and acceptance of society to mining activities.

Hydrogeology Journal↗

USGS2003

Hydrological response to earthquakes in the Haibara well, central Japan - II. Possible mechanism inferred from time-varying hydraulic properties

28 coseismic groundwater level decreases have been observed at the Haibara well, Shizuoka prefecture, central Japan, from 1981 to 1997. These groundwater level changes cannot be explained as the poroelastic response to coseismic static strain. We use the atmospheric pressure and tidal responses of the well, rock properties measured on core samples from the same formation and pumping test results to characterize the hydraulic and mechanical properties of the aquifer. The responses of the Haibara well to the M2 Earth tide constituent and to atmospheric pressure have varied over time. In particular, increasing amplitude and decreasing phase lags were observed after the 1993 pumping test, as well as after earthquakes that caused coseismic water level changes. The tidal response, together with the surface load efficiency derived from the atmospheric pressure response, is used to estimate the mechanical properties of the aquifer. The largest amplitude of the M2 constituent, 2.2 mm, is small enough to imply that pore fluid in this system is approximately twice as compressible as water, possibly due to the presence of a small amount of exsolved gas. Diffusion of a coseismic pressure drop near the well could account for the observed time histories of the water level changes. The time histories of the water level drops are well matched by the decay of a coseismic pressure drop at least 80 m away from the well. Removal of a small amount of gas from the formation in that location might in turn explain the coseismic pressure drops.

Geophysical Journal International↗

USGS2017

Magnetotelluric imaging of lower crustal melt and lithospheric hydration in the Rocky Mountain Front transition zone, Colorado, USA

We present an electrical resistivity model of the crust and upper mantle from two‐dimensional (2‐D) anisotropic inversion of magnetotelluric data collected along a 450 km transect of the Rio Grande rift, southern Rocky Mountains, and High Plains in Colorado, USA. Our model provides a window into the modern‐day lithosphere beneath the Rocky Mountain Front to depths in excess of 150 km. Two key features of the 2‐D resistivity model are (1) a broad zone (~200 km wide) of enhanced electrical conductivity (<20 Ωm) in the midcrust to lower crust that is centered beneath the highest elevations of the southern Rocky Mountains and (2) hydrated lithospheric mantle beneath the Great Plains with water content in excess of 100 ppm. We interpret the high conductivity region of the lower crust as a zone of partially molten basalt and associated deep‐crustal fluids that is the result of recent (less than 10 Ma) tectonic activity in the region. The recent supply of volatiles and/or heat to the base of the crust in the late Cenozoic implies that modern‐day tectonic activity in the western United States extends to at least the western margin of the Great Plains. The transition from conductive to resistive upper mantle is caused by a gradient in lithospheric modification, likely including hydration of nominally anhydrous minerals, with maximum hydration occurring beneath the Rocky Mountain Front. This lithospheric “hydration front” has implications for the tectonic evolution of the continental interior and the mechanisms by which water infiltrates the lithosphere.

Colorado↗

USGS2005

Magmatic unrest beneath Mammoth Mountain, California

Mammoth Mountain, which stands on the southwest rim of Long Valley caldera in eastern California, last erupted ∼57,000 years BP. Episodic volcanic unrest detected beneath the mountain since late 1979, however, emphasizes that the underlying volcanic system is still active and capable of producing future volcanic eruptions. The unrest symptoms include swarms of small ( M ≤ 3) earthquakes, spasmodic bursts (rapid-fire sequences of brittle-failure earthquakes with overlapping coda), long-period (LP) and very-long-period (VLP) volcanic earthquakes, ground deformation, diffuse emission of magmatic CO 2 , and fumarole gases with elevated 3 He/ 4 He ratios. Spatial-temporal relations defined by the multi-parameter monitoring data together with earthquake source mechanisms suggest that this Mammoth Mountain unrest is driven by the episodic release of a volume of CO 2 -rich hydrous magmatic fluid derived from the upper reaches of a plexus of basaltic dikes and sills at mid-crustal depths (10–20 km). As the mobilized fluid ascends through the brittle–plastic transition zone and into overlying brittle crust, it triggers earthquake swarm activity and, in the case of the prolonged, 11-month-long earthquake swarm of 1989, crustal deformation and the onset of diffuse CO 2 emissions. Future volcanic activity from this system would most likely involve steam explosions or small-volume, basaltic, strombolian or Hawaiian style eruptions. The impact of such an event would depend critically on vent location and season.

California↗

USGS2014

A review of environmental impacts of salts from produced waters on aquatic resources

Salts are frequently a major constituent of waste waters produced during oil and gas production. These produced waters or brines must be treated and/or disposed and provide a daily challenge for operators and resource managers. Some elements of salts are regulated with water quality criteria established for the protection of aquatic wildlife, e.g. chloride (Cl − ), which has an acute standard of 860 mg/L and a chronic standard of 230 mg/L. However, data for establishing such standards has only recently been studied for other components of produced water, such as bicarbonate (HCO 3 − ), which has acute median lethal concentrations (LC50s) ranging from 699 to > 8000 mg/L and effects on chronic toxicity from 430 to 657 mg/L. While Cl− is an ion of considerable importance in multiple geographical regions, knowledge about the effects of hardness (calcium and magnesium) on its toxicity and about mechanisms of toxicity is not well understood. A multiple-approach design that combines studies of both individuals and populations, conducted both in the laboratory and the field, was used to study toxic effects of bicarbonate (as NaHCO 3 ). This approach allowed interpretations about mechanisms related to growth effects at the individual level that could affect populations in the wild. However, additional mechanistic data for HCO 3 − , related to the interactions of calcium (Ca 2 + ) precipitation at the microenvironment of the gill would dramatically increase the scientific knowledge base about how NaHCO 3 might affect aquatic life. Studies of the effects of mixtures of multiple salts present in produced waters and more chronic effect studies would give a better picture of the overall potential toxicity of these ions. Organic constituents in hydraulic fracturing fluids, flowback waters, etc. are a concern because of their carcinogenic properties and this paper is not meant to minimize the importance of maintaining vigilance with respect to potential organic contamination.

International Journal of Coal Geology↗

USGS2013

Chemical controls on fault behavior: weakening of serpentinite sheared against quartz-bearing rocks and its significance for fault creep in the San Andreas system

The serpentinized ultramafic rocks found in many plate-tectonic settings commonly are juxtaposed against crustal rocks along faults, and the chemical contrast between the rock types potentially could influence the mechanical behavior of such faults. To investigate this possibility, we conducted triaxial experiments under hydrothermal conditions (200-350°C), shearing serpentinite gouge between forcing blocks of granite or quartzite. In an ultramafic chemical environment, the coefficient of friction, µ, of lizardite and antigorite serpentinite is 0.5-0.6, and µ increases with increasing temperature over the tested range. However, when either lizardite or antigorite serpentinite is sheared against granite or quartzite, strength is reduced to µ ~ 0.3, with the greatest strength reductions at the highest temperatures (temperature weakening) and slowest shearing rates (velocity strengthening). The weakening is attributed to a solution-transfer process that is promoted by the enhanced solubility of serpentine in pore fluids whose chemistry has been modified by interaction with the quartzose wall rocks. The operation of this process will promote aseismic slip (creep) along serpentinite-bearing crustal faults at otherwise seismogenic depths. During short-term experiments serpentine minerals reprecipitate in low-stress areas, whereas in longer experiments new Mg-rich phyllosilicates crystallize in response to metasomatic exchanges across the serpentinite-crustal rock contact. Long-term shear of serpentinite against crustal rocks will cause the metasomatic mineral assemblages, which may include extremely weak minerals such as saponite or talc, to play an increasingly important role in the mechanical behavior of the fault. Our results may explain the distribution of creep on faults in the San Andreas system.

California↗

USGS2006

An effective medium inversion algorithm for gas hydrate quantification and its application to laboratory and borehole measurements of gas hydrate-bearing sediments

The presence of gas hydrate in marine sediments alters their physical properties. In some circumstances, gas hydrate may cement sediment grains together and dramatically increase the seismic P- and S-wave velocities of the composite medium. Hydrate may also form a load-bearing structure within the sediment microstructure, but with different seismic wave attenuation characteristics, changing the attenuation behaviour of the composite. Here we introduce an inversion algorithm based on effective medium modelling to infer hydrate saturations from velocity and attenuation measurements on hydrate-bearing sediments. The velocity increase is modelled as extra binding developed by gas hydrate that strengthens the sediment microstructure. The attenuation increase is modelled through a difference in fluid flow properties caused by different permeabilities in the sediment and hydrate microstructures. We relate velocity and attenuation increases in hydrate-bearing sediments to their hydrate content, using an effective medium inversion algorithm based on the self-consistent approximation (SCA), differential effective medium (DEM) theory, and Biot and squirt flow mechanisms of fluid flow. The inversion algorithm is able to convert observations in compressional and shear wave velocities and attenuations to hydrate saturation in the sediment pore space. We applied our algorithm to a data set from the Mallik 2L–38 well, Mackenzie delta, Canada, and to data from laboratory measurements on gas-rich and water-saturated sand samples. Predictions using our algorithm match the borehole data and water-saturated laboratory data if the proportion of hydrate contributing to the load-bearing structure increases with hydrate saturation. The predictions match the gas-rich laboratory data if that proportion decreases with hydrate saturation. We attribute this difference to differences in hydrate formation mechanisms between the two environments.

Geophysical Journal International↗

USGS2009

The source of infrasound associated with long-period events at mount St. Helens

During the early stages of the 2004-2008 Mount St. Helens eruption, the source process that produced a sustained sequence of repetitive long-period (LP) seismic events also produced impulsive broadband infrasonic signals in the atmosphere. To assess whether the signals could be generated simply by seismic-acoustic coupling from the shallow LP events, we perform finite difference simulation of the seismo-acoustic wavefield using a single numerical scheme for the elastic ground and atmosphere. The effects of topography, velocity structure, wind, and source configuration are considered. The simulations show that a shallow source buried in a homogeneous elastic solid produces a complex wave train in the atmosphere consisting of P/SV and Rayleigh wave energy converted locally along the propagation path, and acoustic energy originating from , the source epicenter. Although the horizontal acoustic velocity of the latter is consistent with our data, the modeled amplitude ratios of pressure to vertical seismic velocity are too low in comparison with observations, and the characteristic differences in seismic and acoustic waveforms and spectra cannot be reproduced from a common point source. The observations therefore require a more complex source process in which the infrasonic signals are a record of only the broadband pressure excitation mechanism of the seismic LP events. The observations and numerical results can be explained by a model involving the repeated rapid pressure loss from a hydrothermal crack by venting into a shallow layer of loosely consolidated, highly permeable material. Heating by magmatic activity causes pressure to rise, periodically reaching the pressure threshold for rupture of the "valve" sealing the crack. Sudden opening of the valve generates the broadband infrasonic signal and simultaneously triggers the collapse of the crack, initiating resonance of the remaining fluid. Subtle waveform and amplitude variability of the infrasonic signals as recorded at an array 13.4 km to the NW of the volcano are attributed primarily to atmospheric boundary layer propagation effects, superimposed upon amplitude changes at the source.

Washington↗

USGS2025

Impact of gas/liquid phase change of CO2 during injection for sequestration

CO 2 sequestration in deep saline formations is an effective and important process to control the rapid rise in CO 2 emissions. The process of injecting CO 2 requires reliable predictions of the stress in the formation and the fluid pressure distributions – particularly since monitoring of the CO 2 migration is difficult – to mitigate leakage, prevent induced seismicity, and analyze wellbore stability. A key aspect of CO 2 is the gas–liquid phase transition at the temperatures and pressures of relevance to leakage and sequestration, which has been recognized as being critical for accurate predictions but has been challenging to model without ad hoc empiricisms. This paper presents a robust multiphase thermodynamics-based poromechanics model to capture the complex phase transition behavior of CO 2 and predict the stress and pressure distribution under super- and sub- critical conditions during the injection process. A finite element implementation of the model is applied to analyze the behavior of a multiphase porous system with CO 2 as it displaces the fluid brine phase. We find that if CO 2 undergoes a phase transition in the geologic reservoir, the spatial variation of the density is significantly affected, and the migration mobility of CO 2 decreases in the reservoir. A key feature of our approach is that we do not a priori assume the location of the CO 2 gas/liquid interface – or even if it occurs at all – but rather, this is a prediction of the model, along with the spatial variation of the phase of CO 2 and the change of the saturation profile due to the phase change.

Journal of the Mechanics and Physics of Solids↗

USGS2001

An analytical solution for transient flow of Bingham viscoplastic materials in rock fractures

We present below an analytical solution to model the one-dimensional transient flow of a Bingham viscoplastic material in a fracture with parallel walls (smooth or rough) that is subjected to an applied pressure gradient. The solution models the acceleration and the deceleration of the material as the pressure gradient changes with time. Two cases are considered: A pressure gradient applied over a finite time interval and an applied pressure gradient that is constant over time. The solution is expressed in dimensionless form and can therefore be used for a wide range of Bingham viscoplastic materials. The solution is also capable of capturing the transition that takes place in a fracture between viscoplastic flow and rigid plug flow. Also, it shows the development of a rigid central layer in fractures, the extent of which depends on the fluid properties (viscosity and yield stress), the magnitude of the pressure gradient, and the fracture aperture and surface roughness. Finally, it is shown that when a pressure gradient is applied and kept constant, the solution for the fracture flow rate converges over time to a steady-state solution that can be defined as a modified cubic law. In this case, the fracture transmissivity is found to be a non-linear function of the head gradient. This solution provides a tool for a better understanding of the flow of Bingham materials in rock fractures, interfaces, and cracks. ?? 2001 Elsevier Science Ltd. All rights reserved.

International Journal of Rock Mechanics and Mining↗