A semianalytical solution for one-dimensional transient wave propagation in a saturated single-layer porous medium with a fluid surface layer

One-dimensional transient wave propagation in a saturated single-layer porous medium with a fluid surface layer is studied in this paper. An analytical solution for a special case with a dynamic permeability coefficient k_f → ∞ and a semianalytical solution for a general case with an arbitrary dynamic permeability coefficient are presented. The eigenfunction expansion and precise time step integration methods are employed. The solution is presented in series form, and thus, the long-term dynamic responses of saturated porous media with small permeability coefficients can be easily computed. We first transform the nonhomogeneous boundary conditions into homogeneous boundary conditions, and then we obtain the eigenvalues and orthogonal eigenfunctions of the fluid–solid system. Finally, the solutions in the time domain are developed. As the model is one dimensional, geometric attenuation is absent, and only the attenuation in the saturated porous medium is considered. We can apply this model to analyse the influences of different seabed types on the propagation of acoustic waves in the fluid layer, which is very important in ocean acoustics and ocean seismic. This solution can also be employed to validate the accuracies of various numerical methods.     

Numerical simulation of fully saturated porous materials

Fully coupled, porous solid–fluid formulation, implementation and related modeling and simulation issues are presented in this work. To this end, coupled dynamic field equations with u?p?U formulation are used to simulate pore fluid and soil skeleton (elastic–plastic porous solid) responses. Present formulation allows, among other features, for water accelerations to be taken into account. This proves to be useful in modeling dynamic interaction of media of different stiffnesses (as in soil–foundation–structure interaction). Fluid compressibility is also explicitly taken into account, thus allowing excursions into modeling of limited cases of non‐saturated porous media. In addition to these features, present formulation and implementation models in a realistic way the physical damping, which dissipates energy. In particular, the velocity proportional damping is appropriately modeled and simulated by taking into account the interaction of pore fluid and solid skeleton. Similarly, the displacement proportional damping is physically modeled through elastic–plastic processes in soil skeleton. An advanced material model for sand is used in present work and is discussed at some length. Also explored in this paper are the verification and validation issues related to fully coupled modeling and simulations of porous media. Illustrative examples describing the dynamical behavior of porous media (saturated soils) are presented. The verified and validated methods and material models are used to predict the behavior of level and sloping grounds subjected to seismic shaking. Copyright © 2008 John Wiley & Sons, Ltd.     

XFEM-based cohesive zone approach for modeling near-wellbore hydraulic fracture complexity

Near-wellbore fracture tortuosity has important impacts on the productivity of fractured oil and gas wells and the injectivity of CO₂ or solids disposal injectors. Previous models for simulating near-wellbore fracture tortuosity usually assume fracture growth in linear-elastic media, without considering the effects of porous features of the rock. In this paper, a 2D fully coupled model is developed to simulate near-wellbore fracturing using the XFEM-based cohesive segment method. The model takes into account a variety of crucial physical aspects, including fracture extension and turning, fluid flow in the fracture, fluid leak-off through wellbore wall and fracture surfaces, pore fluid flow, and rock deformation. The proposed model was verified against two sets of published experimental results. Numerical examples were carried out to investigate the effects of various parameters on near-wellbore fracture trajectory, injection pressure, and fracture width. Results show that near-wellbore fracture behaviors are not only dependent on rock elastic properties and field stresses, but also greatly influenced by porous properties of the rock, such as permeability and leak-off coefficient. Some field implications were provided based on the simulation results. By overcoming some limitations of the previous models, the proposed model predicts more realistic fracture evolution in the near-wellbore region and provides an attractive tool for design and evaluation of many field operations, for which near-wellbore fracture behaviors play an important role on their successes.

     

Multi‐species diffusion analysis in porous media under various dry density and temperature conditions: molecular dynamics simulation,homogenization analysis,and finite element method

In porous media, chemical species that dissolve in pore water can be transported via diffusion mechanisms or advective fluxes, close to or far away from where precipitation occurs. In the case of a high‐level radioactive waste disposal system, compacted bentonite is used in a buffer material in an engineering barrier system to minimize the amount of specific nuclides that breach into the surrounding host rock. To minimize breaching, it is very important to understand the transport mechanism of multiple chemical species in porous media. In the following research, we introduced FEM analysis methods using the results of the molecular dynamics simulation and homogenization analysis (MD/HA) method. First, the diffusion coefficients of ions (Cl^?, I^?, and Na⁺) in different water layers of Na‐beidellite were calculated using the MD/HA procedure under various dry density (1.2, 1.6, and 2.0 Mg/m³) and temperature (293, 323, and 363 K) conditions. Next, using FEM analysis that used the MD/HA results as input parameters, the diffusion behaviors of ions in porous media were calculated. The results indicate that the diffusion coefficients of the interlayer water in Na‐beidellite are different from the diffusion coefficients under dry density conditions. Further, the concentration profiles (C_t/C₀) of iodine and chloride are proportional to temperature but inversely proportional to dry density. Copyright © 2014 John Wiley & Sons, Ltd.     

Numerical analysis of thermal fracturing in subsurface cold water injection by finite element methods

Integration of poromechanics and fracture mechanics plays an important role in understanding a series of thermal fracturing phenomena in subsurface porous media such as cold water flooding for enhanced oil recovery, produced‐water reinjection for waste disposal, cold water injection for geothermal energy extraction, and CO₂ injection for geosequestration. Thermal fracturing modeling is important to prevent the potential risks when fractures propagate into undesired zones, and it involves the coupling of heat transfer, mass transport, and stress change as well as the fracture propagation. Analytical method, finite element method, and finite difference method as well as boundary element method have been used to perform the thermal fracturing modeling considering different degrees and combinations of coupling. In this paper, extended finite element method is employed for the thermal fracturing modeling in a fully coupled fashion with remeshing avoided, and the stabilized finite element method is employed to account for the convection‐dominated heat transfer in the fracturing process with numerical oscillation circumvented. With the thermal fracturing model, a hypothetical numerical experiment on cold water injection into a deep warm aquifer is conducted. Results show that parameters such as injection rate, injection temperature, aquifer stiffness, and permeability can affect the fracture development in different ways and extended finite element method and stabilized finite element method provide effective tools for thermal fracturing simulation. Copyright © 2012 John Wiley & Sons, Ltd.     

Impact of CO<Subscript>2</Subscript> injection rate on heat extraction at the HDR geothermal field of Zhacanggou,China

CO₂ is now considered as a novel heat transmission fluid to extract geothermal energy. It can achieve the goal of energy exploitation and CO₂ geological sequestration. Taking Zhacanggou as research area, a “Three-spot” well pattern (one injection with two production), “wellbore–reservoir” coupled model is built, and a constant injection rate is set up. A fully coupled wellbore–reservoir simulator—T2Well—is introduced to study the flow mechanism of CO₂ working as heat transmission fluid, the variance pattern of each physical field, the influence of CO₂ injection rate on heat extraction and the potential and sustainability of heat resource in Guide region. The density profile variance resulting from temperature differences of two wells can help the system achieve “self-circulation” by siphon phenomenon, which is more significant in higher injection rate cases. The density of CO₂ is under the effect of both pressure and temperature; moreover, it has a counter effect on temperature and pressure. The feedback makes the flow process in wellbore more complex. In low injection rate scenarios, the temperature has a dominating impact on the fluid density, while in high rate scenario, pressure plays a more important role. In most scenarios, it basically keeps stable during 30-year operation. The decline of production temperature is <5 °C. However, for some high injection rate cases (75 and 100 kg/s), due to the heat depletion in reservoir, there is a dramatic decline for production temperature and heat extraction rate. Therefore, a 50-kg/s CO₂ injection rate is more suitable for “Three-spot” well pattern in Guide region.     

Up-scaling application of microbial carbonate precipitation: optimization of urease production using response surface methodology and injection modification

In order to reduce the cost of the microbial-induced carbonate precipitation, mixotrophic growth of Sporosarcina pasteurii was carried out at different yeast extract/sodium acetate concentrations and constant chemical oxygen demand for optimal production of urease enzyme. Optimization of cultivation conditions was also investigated using a 3-level central composite design approach based on the response surface methodology. A good agreement between predicted values of enzyme activity and experimental results was observed (R ² value of 0.973). All three chosen independent variables had statistically great effects on the efficiency of urease activity. The maximum activity of 2.98 mM urea min^?1 was achieved at yeast extract concentration of 5 g L^?1, NH₄ concentration of 9.69 g L^?1, and incubation time of 60 h as the optimal conditions. Thereafter, a novel injection procedure as sequencing batch mode injection has been proposed for bacteria and cementation fluid injection at obtained optimal urease activity. After fourth injection of bacteria and cementation fluid, uniform CaCO₃ distribution with unconfined compression strength of 795 kPa was obtained even for poorly graded sand. The presented experimental approach for optimizing urease activity and strength production in porous media can be used to design the treatment protocol for practical engineering applications.     

Numerical modeling of the geomechanical behavior of Ghawar Arab-D carbonate petroleum reservoir undergoing CO<Subscript>2</Subscript> injection

Sedimentary porous rocks can be used for long-term subsurface containment of CO₂. Before injecting CO₂ to sedimentary reservoirs, it is necessary to perform stability analysis of the reservoir and to estimate the maximum sustainable pore fluid pressures. In order to avoid the reservoir damage during the CO₂ injection, the effective stresses in the reservoir should be evaluated. In this paper, numerical modeling techniques are used for the evaluation of stresses and deformations in a naturally fractured carbonate sedimentary reservoir. The developed numerical modeling scheme couples the behavior of the CO₂ injection and the change in the geomechanical behavior of the sedimentary carbonate reservoir for a case study from Saudi Arabia. The present investigation extends the previous studies by considering the sorption-based deformation during the injection of the compressed CO₂ fluid into the Arab-D naturally fractured carbonate reservoir. The change in permeability during the injection of CO₂ is evaluated. The adopted CO₂ injection scenario was shown to be within the safe maximum occupancy, and that the increase in the pore pressure does not result in the reservoir failure.     

Isotopic fronts in hydrothermally mineralized carbonate rocks

Advective-dispersive fluid flow through permeable and porous rock causes systematic alteration of the infiltrated rock. O and Sr isotopes can be used as tracers to monitor exchange processes between mineralizing hydrothermal solutions and carbonate host rocks. Fluid infiltration into rock of initially uniform isotopic composition leads to characteristic changes in ¹⁸O and ⁸⁷Sr in the rock, that depend on infiltration distance, fluid velocity, diffusivity and reaction kinetics. For fast fluid-solid equilibrium during advective flow, the shape of such alteration profiles can be described by the dimensionless Peclet number (P _e ), which expresses the fluid flux, infiltration distance and diffusivity. In the case of mineralization from low to moderate temperature solutions, isotope exchange is not instantaneous, but kinetically controlled, and a similar parameter, the Damköhler number (N _d ) expressing fluid flux, isotope exchange rate and infiltration distance, becomes more useful. N _d - and P _e -values have been estimated for various examples of carbonatehosted hydrothermal mineralization in the Eastern Alps (Austria) and the Benue Trough (Nigeria) by modelling O and Sr isotope data from ore (or gangue minerals) and host rock. The values obtained enable a rough differentiation between pervasive and channelled fluid flow as the prevailing transport mechanism to be made. Results indicate that both highly channelled fluid flow through fractures without significant interaction with the wall-rock, and pervasive fluid flow with infiltration distances into the percolated host rock of the order of 100 m, occur near mineral deposits. In the latter case, the extent of O and Sr isotopic alteration of the host rock can be used as an effective exploration tool.     

Numerical simulation of liquefaction in porous media using nonlinear fluid flow law

It is well known that for a sufficiently high seepage velocity, the governing flow law of porous media is nonlinear (J. Computers & Fluids 2010; 39 : 2069–2077). However, this fact has not been considered in the studies of soil‐pore fluid interaction and in conventional soil mechanics. In the present paper, a fully explicit dynamic finite element method is developed for nonlinear Darcy law. The governing equations are expressed for saturated porous media based on the extension of the Biot (J. Appl. Phys. 1941; 12 : 155–164) formulation. The elastoplastic behavior of soil under earthquake loading is simulated using a generalized plasticity theory that is composed of a yield surface along with non‐associated flow rule. Numerical simulations of porous media subjected to horizontal and vertical components of ground motion excitations with different permeability coefficients are carried out; while computed maximum pore water pressure is specially taken into consideration to make the difference between Darcy and non‐Darcy flow regimes tangible. Finally, the effect of non‐Darcy flow on the evaluated liquefaction potential of sand in comparison to conventional Darcy law is examined. Copyright © 2014 John Wiley & Sons, Ltd.     

A geochemical clogging model with carbonate precipitation rates under hydrothermal conditions

A step-wise numerical calculation method was developed to provide predictions of when and where carbonate deposits might be found through reservoirs during CO₂ sequestration. Flow experiments through porous media using a supersaturated carbonate fluid were also performed in order to observe flow rates. In order to evaluate precipitation rates and permeability change in the formation, calculated flow rates based on the proposed geochemical clogging model were compared with the experimentally observed data. Both high and low temperature cases were studied to understand how hydrothermal conditions can affect precipitation rates of carbonate. According to chemical kinetics, growth rates of minerals are generally proportional to the saturation index (S.I.) that depends on temperature. Thus, a supersaturated fluid has the advantage of improving the filtration and the amount of C fixation (σ). However, when the ratio of filtration coefficient (λ) to pore fluid velocity (u) increases, the permeability around the injection point tends to be significantly reduced by carbonate accumulation, and thus, this might result in insufficient injection of CO₂. Therefore, it is essential to understand how to control both λ and u so that the precipitation of carbonate can be located as far away from the inlet as possible.     

Exact solutions for one‐dimensional transient response of fluid‐saturated porous media

Based on the Biot theory, the exact solutions for one‐dimensional transient response of single layer of fluid‐saturated porous media and semi‐infinite media are developed, in which the fluid and solid particles are assumed to be compressible and the inertial, viscous and mechanical couplings are taken into account. First, the control equations in terms of the solid displacement u and a relative displacement w are expressed in matrix form. For problems of single layer under homogeneous boundary conditions, the eigen‐values and the eigen‐functions are obtained by means of the variable separation method, and the displacement vector u is put forward using the searching method. In the case of nonhomogeneous boundary conditions, the boundary conditions are first homogenized, and the displacement field is constructed basing upon the eigen‐functions. Making use of the orthogonality of eigen‐functions, a series of ordinary differential equations with respect to dimensionless time and their corresponding initial conditions are obtained. Those differential equations are solved by the state‐space method, and the series solutions for three typical nonhomogeneous boundary conditions are developed. For semi‐infinite media, the exact solutions in integral form for two kinds of nonhomogeneous boundary conditions are presented by applying the cosine and sine transforms to the basic equations. Finally, three examples are studied to illustrate the validity of the solutions, and to assess the influence of the dynamic permeability coefficient and the fluid inertia to the transient response of porous media. Copyright © 2010 John Wiley & Sons, Ltd.     

Fluid infiltration and regional metamorphism of the Waits River Formation, north-east Vermont, USA

Abstract The Siluro-Devonian Waits River Formation of north-east Vermont was deformed, intruded by plutons and regionally metamorphosed during the Devonian Acadian Orogeny. Five metamorphic zones were mapped based on the mineralogy of carbonate rocks. From low to high grade, these are: (1) ankerite-albite, (2) ankerite-oligoclase, (3) biotite, (4) amphibole and (5) diopside zones. Pressure was near 4.5kbar and temperature varied from c. 450° C in the ankerite-albite zone to c. 525° C in the diopside zone. Fluid composition for all metamorphic zones was estimated from mineral equilibria. Average calculated χ_co2[= CO₂/(CO₂+ H₂O)] of fluid in equilibrium with the marls increases with increasing grade from 0.05 in the ankerite-oligoclase zone, to 0.25 in the biotite zone and to 0.44 in the amphibole zone. In the diopside zone, χ_CO2 decreases to 0.06. Model prograde metamorphic reactions were derived from measured modes, mineral chemistry, and whole-rock chemistry. Prograde reactions involved decarbonation with an evolved volatile mixture of χ_CO2 > 0.50. The χ_CO2 of fluid in equilibrium with rocks from all zones, however, was generally <0.40. This difference attests to the infiltration of a reactive H₂O-rich fluid during metamorphism. Metamorphosed carbonate rocks from the formation suggests that both heat flow and pervasive infiltration of a reactive H₂O-rich fluid drove mineral reactions during metamorphism. Average time-integrated volume fluxes (cm³ fluid/cm² rock), calculated from the standard equation for coupled fluid flow and reaction in porous media, are (1) ankerite-oligoclase zone: c. 1 × 10⁴; (2) biotite zone: c. 3 × 10⁴; (3) amphibole zone: c. 10 × 10⁴; and diopside zone: c. 60 × 10⁴. The increase in calculated flux with increasing grade is at least in part the result of internal production of volatiles from prograde reactions in pelitic schists and metacarbonate rocks within the Waits River Formation. The mapped pattern of time-integrated fluxes indicates that the Strafford-Willoughby Arch and the numerous igneous intrusions in the field area focused fluid flow during metamorphism. Many rock specimens in the diopside zone experienced extreme alkali depletion and also record low χ_CO2. Metamorphic fluids in equilibrium with diopside zone rocks may therefore represent a mixture of acid, H₂O-rich fluids given off by the crystallizing magmas, and CO₂-H₂O fluids produced by devolatilization reactions in the host marls. Higher fluxes and different fluid compositions recorded near the plutons suggest that pluton-driven hydrothermal cells were local highs in the larger regional metamorphic hydrothermal system.     

Remediation of colloid-facilitated contaminant transport in saturated porous media treated by nanoparticles

Facilitation of contaminant transport in porous media due to the effect of indigenous colloidal fine materials has been widely observed in laboratory and field studies. It has been explained by the increase in the apparent solubility of low soluble contaminants as a result of their adsorption on the surface of fine particles. Attachment of colloidal fine particles onto the rock surface could be a promising remedy for this challenge. In this experimental study, the effect of five types of metal oxide nanoparticles, γ-Al₂O₃, ZnO, CuO, MgO, and SiO_2, on suspension transport was investigated. In several core flooding tests, different nanofluids were used to saturate the synthetic porous media. Subsequently, after sufficient soaking time, the suspension was injected into the treated porous media. Analysis of the effluent samples’ concentration by Turbidimeter apparatus demonstrated that the presence of nanoparticles on the rock surface resulted in a significant reduction in fine concentrations in the effluent samples compared with non-treated media; ZnO and γ-Al₂O₃ demonstrated the best scenarios among the tests performed in this study. In order to characterize the surface properties of the treated porous media, the zeta potential of the surface was measured. Results showed that the treated porous media acts as a strong adsorbent of fine particles, which are the main carrier of contaminants in porous media. These findings were quantitatively confirmed by calculation of the total energy of interaction between the fine particles and rock surface using the Derjaguin–Landau–Verwey–Overbeek theory.     

Transport of stable isotopes: I: Development of a kinetic continuum theory for stable isotope transport

Equations are developed describing migration of stable isotopes via a fluid phase infiltrating porous media. The formalism of continuum fluid mechanics is used to deal with the problem of microscopic inhomogeneity. Provision is made explicitly for local equilibrium exchange of isotopes between minerals and fluids as well as for kinetic control of isotopic exchange. Changing characteristic parameters of transport systems such as porosity, permeability, and changes in modal proportions of minerals due to precipitation or dissolution are taken into account.The kinetic continuum theory (KCIT) is used to show how to deduce the dominant mechanism of mass transport in metasomatic rocks. Determination of the transport mechanism requires data on the spatial distribution of the reaction progress of exchange reactions between minerals and fluids involving at least two stable isotope systems such as ¹³C-¹²C and ¹⁸O-¹⁶O, for example. It is concluded that a combination of field and laboratory measurements of two or more stable isotope systems can be used to place constraints not only on the mechanism of transport but also on the magnitude of fluid fluxes, the identity of fluid sources, and the molecular species composition of fluids.Variables used C number of chemical components - D _i,j hydrodynamic dispersion tensor [m²/s] - D _i ^j diffusion coefficient matrix [m²/s] - D ^* apparent diffusion coefficient, includes sorption, dispersion, porosity and tortuosity [m²/s] - F number of degrees of freedom (variance) - f _i ^j mass or number of isotope j in fluid species i - g acceleration due to gravity [m/s²] - flow [m³/m² s] - j isotope species - j chemical element - k coefficient defined in Eq. 17 - K permeability of porous media [m²], [darcy] - L _ij phenomenological diffusion coefficient matrix [mol²/j m s] - m number of fluid species - n number of isotope exchange vectors - p number of phases - P pressure [Pa] - P ^* hydrological pressure potential [Pa] - R ^j ratio of concentration of rare to common isotope of element j - r number of restrictions imposed on system - s _i ^j mass or number of isotope j in one mole of mineral phase i - t time [s] - V volume [m³] - X _i number of moles of fluid species i in unit fluid volume - X _l number of moles of mineral l in unit volume - X _l ^j mole fraction of isotope j in one mole mineral l - X ^* mole fraction with respect to the whole system - z space coordinate [m] - z transformed space coordinate - z ^* location of an infiltration front [m] - _x–y ^j fractionation factor between two phases, x, y, for isotope j - porosity - fluid viscosity [Ns/m²] - fraction of porosity accessible to a specific mass transport mechanism - chemical potential [j/mole] - stoichiometric reaction coefficient - normalized reaction progress variable - mass, specific mass [gr/cm] - tortuosity - fluid velocity [m/s] - c common isotope - init initial - j isotope species - r rare isotope - tot sum of common and rare isotope - dif diffusive - disp dispersive - eq mineral composition in equilibrium with initial infiltration concentration of the fluid - f fluid - inf infiltrative - r rock, without fluid phase - samp sample - std standard - sys system - tot fluid and rock     

Mechanical and flow behaviours and their interactions in coalbed geosequestration of CO2

Studying gas transport mechanisms in coal seams is crucial in determining the suitability of coal formations for geosequestration and/or CO₂-enhanced coal bed methane recovery (ECBM), estimating CO₂ storage capacity and recoverable volume of methane, and predicting the long-term integrity of CO₂ storage and possible leakages. Due to the dual porosity nature of coal, CO₂ transport is a combination of viscous flow and Fickian diffusion. Moreover, CO₂ is adsorbed by the coal which leads to coal swelling which can change the porous structure of coal and consequently affects the gas flow properties of coal, i.e. its permeability. In addition, during CO₂ permeation, the coal seam undergoes a change in effective stress due to the pore pressure alteration and this can also change the permeability of the coal seam. In addition, depending on the in situ conditions of the coal seam and the plan of the injection scheme, carbon dioxide can be in a supercritical condition which increases the complexity of the problem. We provide an overview of the recent studies on porous structure of coal, CO₂ adsorption onto coal, mechanisms of CO₂ transport in coalbeds and their measurement, and hydro-mechanical response of coal to CO₂ injection and identify opportunities for future research.     

Three‐dimensional nonlinear finite element analysis of pile groups in saturated porous media using a new transmitting boundary

The dynamic behaviour of pile groups subjected to an earthquake base shaking is analysed. An analysis is formulated in the time domain and the effects of material nonlinearity of soil, pile–soil–pile kinematic interaction and the superstructure–foundation inertial interaction on seismic response are investigated. Prediction of response of pile group–soil system during a large earthquake requires consideration of various aspects such as the nonlinear and elasto‐plastic behaviour of soil, pore water pressure generation in soil, radiation of energy away from the pile, etc. A fully explicit dynamic finite element scheme is developed for saturated porous media, based on the extension of the original formulation by Biot having solid displacement (u) and relative fluid displacement (w) as primary variables (u–w formulation). All linear relative fluid acceleration terms are included in this formulation. A new three‐dimensional transmitting boundary that was developed in cartesian co‐ordinate system for dynamic response analysis of fluid‐saturated porous media is implemented to avoid wave reflections towards the structure. In contrast to traditional methods, this boundary is able to absorb surface waves as well as body waves. The pile–soil interaction problem is analysed and it is shown that the results from the fully coupled procedure, using the advanced transmitting boundary, compare reasonably well with centrifuge data. Copyright © 2007 John Wiley & Sons, Ltd.     

Feasibility of CO<Subscript>2</Subscript> migration detection using pressure and CO<Subscript>2</Subscript> saturation monitoring above an imperfect primary seal of a geologic CO<Subscript>2</Subscript> storage formation: a numerical investigation

A numerical model was developed to investigate the potential to detect fluid migration in a (homogeneous, isotropic, with constant pressure lateral boundaries) porous and permeable interval overlying an imperfect primary seal of a geologic CO₂ storage formation. The seal imperfection was modeled as a single higher-permeability zone in an otherwise low-permeability seal, with the center of that zone offset from the CO₂ injection well by 1400 m. Pressure response resulting from fluid migration through the high-permeability zone was detectable up to 1650 m from the centroid of that zone at the base of the monitored interval after 30 years of CO₂ injection (detection limit = 0.1 MPa pressure increase); no pressure response was detectable at the top of the monitored interval at the same point in time. CO₂ saturation response could be up to 774 m from the center of the high-permeability zone at the bottom of the monitored interval, and 1103 m at the top (saturation detection limit = 0.01). More than 6% of the injected CO₂, by mass, migrated out of primary containment after 130 years of site performance (including 30 years of active injection) in the case where the zone of seal imperfection had a moderately high permeability (10^??17 m² or 0.01 mD). Free-phase CO₂ saturation monitoring at the top of the overlying interval provides favorable spatial coverage for detecting fluid migration across the primary seal. Improved sensitivity of detection for pressure perturbation will benefit time of detection above an imperfect seal.     

Phase equilibria for graphitic metapelite including solution of CO2 in melt and cordierite: implications for dehydration,partial melting and graphite precipitation

When graphite is present, carbon‐bearing species dissolve in the C‐O‐H fluid and lower the activity of water (). Accordingly, metamorphic reactions that involve water, namely dehydration and partial melting reactions, adjust their P–T positions to accommodate the change of . In this modelling study, pseudosections are calculated for graphite‐bearing systems that are either closed or that progressively lose fluid and/or melt. The diagrams incorporate a new model of CO₂ solubility in felsic melts that we derived to be compatible with a recently published melt model. As the result of the lowered in the carbon‐bearing systems, the temperature displacements of the solidus can be as large as 50 °C at low pressures in cordierite‐bearing zones (<4 kbar), but are smaller than 15 °C at mid‐pressure P–T conditions (4–9 kbar). In the supersolidus region, the phase relations among silicate minerals + melt are very close to those in carbon‐free systems. The fluid CO₂ content increases as temperature increases in the supersolidus assemblages. The CO₂‐rich fluid can be stable in granulite facies conditions in an oxidized system. In graphitic systems, melt and/or cordierite dominate the CO₂ budget of high‐grade rocks. During cooling, the fluid that exsolves from such crystalizing melt is CO₂‐rich. In addition to the phase relations, the pseudosections presented in this study enable researchers to quantitatively investigate the evolution of phase modes, including graphite, along specific metamorphic P–T paths. At low pressures in the cordierite stability field, graphite is predicted to precipitate as the pressure increases or temperature decreases in the subsolidus assemblages, or temperature increases in the region of melt + fluid coexistence. On the other hand, the graphite abundance remains nearly constant along the mid‐pressure P–T series, but the graphite mode in the supersolidus region may increase due to residual enrichment if the melt is extracted. The modelling results show that metamorphic processes in closed systems lead to only small changes in graphite mode (a few tenths of a per cent). This strongly suggests that open‐system behaviours are required for large amounts of graphite deposition, including fluid infiltration and mixing or residual enrichment processes in high‐grade rocks. In addition to P–T pseudosections, P/T–X_O diagrams (X_O = O/(H + O) in the fluid) illustrate the thermodynamic features of internal buffering from another perspective, and explore the dependence of phase relations on the externally imposed redox state. If the system is equilibrated with CO₂ or CH₄‐rich infiltrating fluid, the temperature displacements of metamorphic reactions can be larger than 50 °C, compared with carbon‐free systems.