18 resultados para open-boundary-conditions
em Université de Lausanne, Switzerland
Resumo:
There is increasing evidence to suggest that the presence of mesoscopic heterogeneities constitutes the predominant attenuation mechanism at seismic frequencies. As a consequence, centimeter-scale perturbations of the subsurface physical properties should be taken into account for seismic modeling whenever detailed and accurate responses of the target structures are desired. This is, however, computationally prohibitive since extremely small grid spacings would be necessary. A convenient way to circumvent this problem is to use an upscaling procedure to replace the heterogeneous porous media by equivalent visco-elastic solids. In this work, we solve Biot's equations of motion to perform numerical simulations of seismic wave propagation through porous media containing mesoscopic heterogeneities. We then use an upscaling procedure to replace the heterogeneous poro-elastic regions by homogeneous equivalent visco-elastic solids and repeat the simulations using visco-elastic equations of motion. We find that, despite the equivalent attenuation behavior of the heterogeneous poro-elastic medium and the equivalent visco-elastic solid, the seismograms may differ due to diverging boundary conditions at fluid-solid interfaces, where there exist additional options for the poro-elastic case. In particular, we observe that the seismograms agree for closed-pore boundary conditions, but differ significantly for open-pore boundary conditions. This is an interesting result, which has potentially important implications for wave-equation-based algorithms in exploration geophysics involving fluid-solid interfaces, such as, for example, wave field decomposition.
Resumo:
14C dating models are limited when considering recent groundwater for which the carbon isotopic signature of the total dissolved inorganic carbon (TDIC) is mainly acquired in the unsaturated zone. Reducing the uncertainties of dating thus implies a better identification of the processes controlling the carbon isotopic composition of the TDIC during groundwater recharge. Geochemical interactions between gas, water and carbonates in the unsaturated zone were investigated for two aquifers (the carbonate-free Fontainebleau sands and carbonate-bearing Astian sands, France) in order to identify the respective roles of CO2 and carbonates on the carbon isotopic signatures of the TDIC; this analysis is usually approached using open or closed system terms. Under fully open system conditions, the seasonality of the 13C values in the soil CO2 can lead to important uncertainties regarding the so-called "initial 14C activity" used in 14C correction models. In a carbonate-bearing unsaturated zone such as in the Astian aquifer, we show that an approach based on fully open or closed system conditions is not appropriate. Although the chemical saturation between water and calcite occurs rapidly within the first metre of the unsaturated zone, the carbon isotopic contents (δ13C) of the CO2 and the TDIC evolve downward, impacted by the dissolution-precipitation of the carbonates. In this study, we propose a numerical approach to describe this evolution. The δ13C and the A 14C (radiocarbon activity) of the TDIC at the base of the carbonate-hearing unsaturated zone depends on (i) the δ13C and the A 14C of the TDIC in the soil determined by the soil CO2, (ii) the water's residence time in the unsaturated zone and (iii) the carbonate precipitation-dissolution fluxes. In this type of situation, the carbonate δ13C-A 14C evolutions indicate the presence of secondary calcite and permit the calculation of its accretion flux, equal to ~ 4.5 ± 0.5 x 10-9 mol grock-1 yr-1. More generally, for other sites under temperate climate and with similar properties to the Astian sands site, this approach allows for a reliable determination of the carbon isotopic composition at the base of the unsaturated zone as the indispensable "input function" data of the carbon cycle into the aquifer.
Resumo:
There is increasing evidence to suggest that the presence of mesoscopic heterogeneities constitutes an important seismic attenuation mechanism in porous rocks. As a consequence, centimetre-scale perturbations of the rock physical properties should be taken into account for seismic modelling whenever detailed and accurate responses of specific target structures are desired, which is, however, computationally prohibitive. A convenient way to circumvent this problem is to use an upscaling procedure to replace each of the heterogeneous porous media composing the geological model by corresponding equivalent visco-elastic solids and to solve the visco-elastic equations of motion for the inferred equivalent model. While the overall qualitative validity of this procedure is well established, there are as of yet no quantitative analyses regarding the equivalence of the seismograms resulting from the original poro-elastic and the corresponding upscaled visco-elastic models. To address this issue, we compare poro-elastic and visco-elastic solutions for a range of marine-type models of increasing complexity. We found that despite the identical dispersion and attenuation behaviour of the heterogeneous poro-elastic and the equivalent visco-elastic media, the seismograms may differ substantially due to diverging boundary conditions, where there exist additional options for the poro-elastic case. In particular, we observe that at the fluid/porous-solid interface, the poro- and visco-elastic seismograms agree for closed-pore boundary conditions, but differ significantly for open-pore boundary conditions. This is an important result which has potentially far-reaching implications for wave-equation-based algorithms in exploration geophysics involving fluid/porous-solid interfaces, such as, for example, wavefield decomposition.
Resumo:
We present a novel numerical algorithm for the simulation of seismic wave propagation in porous media, which is particularly suitable for the accurate modelling of surface wave-type phenomena. The differential equations of motion are based on Biot's theory of poro-elasticity and solved with a pseudospectral approach using Fourier and Chebyshev methods to compute the spatial derivatives along the horizontal and vertical directions, respectively. The time solver is a splitting algorithm that accounts for the stiffness of the differential equations. Due to the Chebyshev operator the grid spacing in the vertical direction is non-uniform and characterized by a denser spatial sampling in the vicinity of interfaces, which allows for a numerically stable and accurate evaluation of higher order surface wave modes. We stretch the grid in the vertical direction to increase the minimum grid spacing and reduce the computational cost. The free-surface boundary conditions are implemented with a characteristics approach, where the characteristic variables are evaluated at zero viscosity. The same procedure is used to model seismic wave propagation at the interface between a fluid and porous medium. In this case, each medium is represented by a different grid and the two grids are combined through a domain-decomposition method. This wavefield decomposition method accounts for the discontinuity of variables and is crucial for an accurate interface treatment. We simulate seismic wave propagation with open-pore and sealed-pore boundary conditions and verify the validity and accuracy of the algorithm by comparing the numerical simulations to analytical solutions based on zero viscosity obtained with the Cagniard-de Hoop method. Finally, we illustrate the suitability of our algorithm for more complex models of porous media involving viscous pore fluids and strongly heterogeneous distributions of the elastic and hydraulic material properties.
Resumo:
Coronary magnetic resonance angiography (MRA) is a technique aimed at establishing a noninvasive test for the assessment of significant coronary stenoses. There are certain boundary conditions that have hampered the clinical success of coronary MRA and coronary vessel wall imaging. Recent advances in hardware and software allow for consistent visualization of the proximal and mid portions of the native coronary arteries. Current research focuses on the use of intravascular MR contrast agents and black blood coronary angiography. One common goal is to create a noninvasive test which might allow for screening for major proximal and mid coronary artery disease. These novel approaches will represent a major step forward in diagnostic cardiology.
Resumo:
The multiscale finite volume (MsFV) method has been developed to efficiently solve large heterogeneous problems (elliptic or parabolic); it is usually employed for pressure equations and delivers conservative flux fields to be used in transport problems. The method essentially relies on the hypothesis that the (fine-scale) problem can be reasonably described by a set of local solutions coupled by a conservative global (coarse-scale) problem. In most cases, the boundary conditions assigned for the local problems are satisfactory and the approximate conservative fluxes provided by the method are accurate. In numerically challenging cases, however, a more accurate localization is required to obtain a good approximation of the fine-scale solution. In this paper we develop a procedure to iteratively improve the boundary conditions of the local problems. The algorithm relies on the data structure of the MsFV method and employs a Krylov-subspace projection method to obtain an unconditionally stable scheme and accelerate convergence. Two variants are considered: in the first, only the MsFV operator is used; in the second, the MsFV operator is combined in a two-step method with an operator derived from the problem solved to construct the conservative flux field. The resulting iterative MsFV algorithms allow arbitrary reduction of the solution error without compromising the construction of a conservative flux field, which is guaranteed at any iteration. Since it converges to the exact solution, the method can be regarded as a linear solver. In this context, the schemes proposed here can be viewed as preconditioned versions of the Generalized Minimal Residual method (GMRES), with a very peculiar characteristic that the residual on the coarse grid is zero at any iteration (thus conservative fluxes can be obtained).
Resumo:
Oxidative metabolism of isolated toad skin epithelium (Bufo viridis) was investigated in vitro under open-circuit conditions using the spectrophotometric oxyhemoglobin micromethod. This highly sensitive technique has been adapted for studying several epithelia in parallel and for detecting possible regional variations of oxygen uptake in individual epithelium. Changes in the proportion of mitochondria-rich cells (MRC) by ionic acclimation affected oxidative metabolism under nontransporting condition. After acclimation of animals to either NaNO3 or NaCl solutions (100 mmol/l, for greater than 2 wk), the number of MRC per square millimeter in epithelia from nonacclimated and NaNO3- and NaCl-acclimated animals was 350 +/- 113, 460 +/- 196, and 107 +/- 52, respectively. O2 uptake of nonacclimated and NaNO3-acclimated epithelia was significantly higher than that of NaCl-acclimated epithelia (i.e., 0.89 and 0.90 vs. 0.57 nmol O2.h-1.mm-2, respectively). The correlation established between O2 uptake and number of MRC allowed evaluation of the respiration rate of one single MRC, i.e., approximately 1 pmol O2/h. The lowest mitochondrial oxidative activity was found in the epithelia from NaCl-acclimated toads where the uncoupler 2,4-dinitrophenol (50 mumols/l) had the highest relative stimulatory effect (+114%). Acetazolamide (50 mumols/l), a potent inhibitor of carbonic anhydrase mainly present in the MRC, reduced selectively by 31% O2 uptake of the MRC-rich epithelia (NaNO3 acclimated). O2 uptake increased significantly by approximately 80% when basolateral pH increased from 5.8 to 7.8, but did not depend on apical pH. These findings indicate that under nontransporting (open-circuit) conditions, aerobic metabolism of the isolated toad skin epithelium is related to the density and/or characteristics of the MRC.(ABSTRACT TRUNCATED AT 250 WORDS)
Resumo:
We implemented Biot-type porous wave equations in a pseudo-spectral numerical modeling algorithm for the simulation of Stoneley waves in porous media. Fourier and Chebyshev methods are used to compute the spatial derivatives along the horizontal and vertical directions, respectively. To prevent from overly short time steps due to the small grid spacing at the top and bottom of the model as a consequence of the Chebyshev operator, the mesh is stretched in the vertical direction. As a large benefit, the Chebyshev operator allows for an explicit treatment of interfaces. Boundary conditions can be implemented with a characteristics approach. The characteristic variables are evaluated at zero viscosity. We use this approach to model seismic wave propagation at the interface between a fluid and a porous medium. Each medium is represented by a different mesh and the two meshes are connected through the above described characteristics domain-decomposition method. We show an experiment for sealed pore boundary conditions, where we first compare the numerical solution to an analytical solution. We then show the influence of heterogeneity and viscosity of the pore fluid on the propagation of the Stoneley wave and surface waves in general.
Resumo:
We present a novel numerical approach for the comprehensive, flexible, and accurate simulation of poro-elastic wave propagation in 2D polar coordinates. An important application of this method and its extensions will be the modeling of complex seismic wave phenomena in fluid-filled boreholes, which represents a major, and as of yet largely unresolved, computational problem in exploration geophysics. In view of this, we consider a numerical mesh, which can be arbitrarily heterogeneous, consisting of two or more concentric rings representing the fluid in the center and the surrounding porous medium. The spatial discretization is based on a Chebyshev expansion in the radial direction and a Fourier expansion in the azimuthal direction and a Runge-Kutta integration scheme for the time evolution. A domain decomposition method is used to match the fluid-solid boundary conditions based on the method of characteristics. This multi-domain approach allows for significant reductions of the number of grid points in the azimuthal direction for the inner grid domain and thus for corresponding increases of the time step and enhancements of computational efficiency. The viability and accuracy of the proposed method has been rigorously tested and verified through comparisons with analytical solutions as well as with the results obtained with a corresponding, previously published, and independently bench-marked solution for 2D Cartesian coordinates. Finally, the proposed numerical solution also satisfies the reciprocity theorem, which indicates that the inherent singularity associated with the origin of the polar coordinate system is adequately handled.
Resumo:
We present a novel numerical approach for the comprehensive, flexible, and accurate simulation of poro-elastic wave propagation in cylindrical coordinates. An important application of this method is the modeling of complex seismic wave phenomena in fluid-filled boreholes, which represents a major, and as of yet largely unresolved, computational problem in exploration geophysics. In view of this, we consider a numerical mesh consisting of three concentric domains representing the borehole fluid in the center, the borehole casing and the surrounding porous formation. The spatial discretization is based on a Chebyshev expansion in the radial direction, Fourier expansions in the other directions, and a Runge-Kutta integration scheme for the time evolution. A domain decomposition method based on the method of characteristics is used to match the boundary conditions at the fluid/porous-solid and porous-solid/porous-solid interfaces. The viability and accuracy of the proposed method has been tested and verified in 2D polar coordinates through comparisons with analytical solutions as well as with the results obtained with a corresponding, previously published, and independently benchmarked solution for 2D Cartesian coordinates. The proposed numerical solution also satisfies the reciprocity theorem, which indicates that the inherent singularity associated with the origin of the polar coordinate system is handled adequately.
Resumo:
The multiscale finite-volume (MSFV) method is designed to reduce the computational cost of elliptic and parabolic problems with highly heterogeneous anisotropic coefficients. The reduction is achieved by splitting the original global problem into a set of local problems (with approximate local boundary conditions) coupled by a coarse global problem. It has been shown recently that the numerical errors in MSFV results can be reduced systematically with an iterative procedure that provides a conservative velocity field after any iteration step. The iterative MSFV (i-MSFV) method can be obtained with an improved (smoothed) multiscale solution to enhance the localization conditions, with a Krylov subspace method [e.g., the generalized-minimal-residual (GMRES) algorithm] preconditioned by the MSFV system, or with a combination of both. In a multiphase-flow system, a balance between accuracy and computational efficiency should be achieved by finding a minimum number of i-MSFV iterations (on pressure), which is necessary to achieve the desired accuracy in the saturation solution. In this work, we extend the i-MSFV method to sequential implicit simulation of time-dependent problems. To control the error of the coupled saturation/pressure system, we analyze the transport error caused by an approximate velocity field. We then propose an error-control strategy on the basis of the residual of the pressure equation. At the beginning of simulation, the pressure solution is iterated until a specified accuracy is achieved. To minimize the number of iterations in a multiphase-flow problem, the solution at the previous timestep is used to improve the localization assumption at the current timestep. Additional iterations are used only when the residual becomes larger than a specified threshold value. Numerical results show that only a few iterations on average are necessary to improve the MSFV results significantly, even for very challenging problems. Therefore, the proposed adaptive strategy yields efficient and accurate simulation of multiphase flow in heterogeneous porous media.
Resumo:
The efficacy of inoculation of single pure bacterial cultures into complex microbiomes, for example, in order to achieve increased pollutant degradation rates in contaminated material (that is, bioaugmentation), has been frustrated by insufficient knowledge on the behaviour of the inoculated bacteria under the specific abiotic and biotic boundary conditions. Here we present a comprehensive analysis of genome-wide gene expression of the bacterium Sphingomonas wittichii RW1 in contaminated non-sterile sand, compared with regular suspended batch growth in liquid culture. RW1 is a well-known bacterium capable of mineralizing dibenzodioxins and dibenzofurans. We tested the reactions of the cells both during the immediate transition phase from liquid culture to sand with or without dibenzofuran, as well as during growth and stationary phase in sand. Cells during transition show stationary phase characteristics, evidence for stress and for nutrient scavenging, and adjust their primary metabolism if they were not precultured on the same contaminant as found in the soil. Cells growing and surviving in sand degrade dibenzofuran but display a very different transcriptome signature as in liquid or in liquid culture exposed to chemicals inducing drought stress, and we obtain evidence for numerous 'soil-specific' expressed genes. Studies focusing on inoculation efficacy should test behaviour under conditions as closely as possible mimicking the intended microbiome conditions.
Resumo:
Les problèmes d'écoulements multiphasiques en média poreux sont d'un grand intérêt pour de nombreuses applications scientifiques et techniques ; comme la séquestration de C02, l'extraction de pétrole et la dépollution des aquifères. La complexité intrinsèque des systèmes multiphasiques et l'hétérogénéité des formations géologiques sur des échelles multiples représentent un challenge majeur pour comprendre et modéliser les déplacements immiscibles dans les milieux poreux. Les descriptions à l'échelle supérieure basées sur la généralisation de l'équation de Darcy sont largement utilisées, mais ces méthodes sont sujettes à limitations pour les écoulements présentant de l'hystérèse. Les avancées récentes en terme de performances computationnelles et le développement de méthodes précises pour caractériser l'espace interstitiel ainsi que la distribution des phases ont favorisé l'utilisation de modèles qui permettent une résolution fine à l'échelle du pore. Ces modèles offrent un aperçu des caractéristiques de l'écoulement qui ne peuvent pas être facilement observées en laboratoire et peuvent être utilisé pour expliquer la différence entre les processus physiques et les modèles à l'échelle macroscopique existants. L'objet premier de la thèse se porte sur la simulation numérique directe : les équations de Navier-Stokes sont résolues dans l'espace interstitiel et la méthode du volume de fluide (VOF) est employée pour suivre l'évolution de l'interface. Dans VOF, la distribution des phases est décrite par une fonction fluide pour l'ensemble du domaine et des conditions aux bords particulières permettent la prise en compte des propriétés de mouillage du milieu poreux. Dans la première partie de la thèse, nous simulons le drainage dans une cellule Hele-Shaw 2D avec des obstacles cylindriques. Nous montrons que l'approche proposée est applicable même pour des ratios de densité et de viscosité très importants et permet de modéliser la transition entre déplacement stable et digitation visqueuse. Nous intéressons ensuite à l'interprétation de la pression capillaire à l'échelle macroscopique. Nous montrons que les techniques basées sur la moyenne spatiale de la pression présentent plusieurs limitations et sont imprécises en présence d'effets visqueux et de piégeage. Au contraire, une définition basée sur l'énergie permet de séparer les contributions capillaires des effets visqueux. La seconde partie de la thèse est consacrée à l'investigation des effets d'inertie associés aux reconfigurations irréversibles du ménisque causé par l'interface des instabilités. Comme prototype pour ces phénomènes, nous étudions d'abord la dynamique d'un ménisque dans un pore angulaire. Nous montrons que, dans un réseau de pores cubiques, les sauts et reconfigurations sont si fréquents que les effets d'inertie mènent à différentes configurations des fluides. A cause de la non-linéarité du problème, la distribution des fluides influence le travail des forces de pression, qui, à son tour, provoque une chute de pression dans la loi de Darcy. Cela suggère que ces phénomènes devraient être pris en compte lorsque que l'on décrit l'écoulement multiphasique en média poreux à l'échelle macroscopique. La dernière partie de la thèse s'attache à démontrer la validité de notre approche par une comparaison avec des expériences en laboratoire : un drainage instable dans un milieu poreux quasi 2D (une cellule Hele-Shaw avec des obstacles cylindriques). Plusieurs simulations sont tournées sous différentes conditions aux bords et en utilisant différents modèles (modèle intégré 2D et modèle 3D) afin de comparer certaines quantités macroscopiques avec les observations au laboratoire correspondantes. Malgré le challenge de modéliser des déplacements instables, où, par définition, de petites perturbations peuvent grandir sans fin, notre approche numérique apporte de résultats satisfaisants pour tous les cas étudiés. - Problems involving multiphase flow in porous media are of great interest in many scientific and engineering applications including Carbon Capture and Storage, oil recovery and groundwater remediation. The intrinsic complexity of multiphase systems and the multi scale heterogeneity of geological formations represent the major challenges to understand and model immiscible displacement in porous media. Upscaled descriptions based on generalization of Darcy's law are widely used, but they are subject to several limitations for flow that exhibit hysteric and history- dependent behaviors. Recent advances in high performance computing and the development of accurate methods to characterize pore space and phase distribution have fostered the use of models that allow sub-pore resolution. These models provide an insight on flow characteristics that cannot be easily achieved by laboratory experiments and can be used to explain the gap between physical processes and existing macro-scale models. We focus on direct numerical simulations: we solve the Navier-Stokes equations for mass and momentum conservation in the pore space and employ the Volume Of Fluid (VOF) method to track the evolution of the interface. In the VOF the distribution of the phases is described by a fluid function (whole-domain formulation) and special boundary conditions account for the wetting properties of the porous medium. In the first part of this thesis we simulate drainage in a 2-D Hele-Shaw cell filled with cylindrical obstacles. We show that the proposed approach can handle very large density and viscosity ratios and it is able to model the transition from stable displacement to viscous fingering. We then focus on the interpretation of the macroscopic capillary pressure showing that pressure average techniques are subject to several limitations and they are not accurate in presence of viscous effects and trapping. On the contrary an energy-based definition allows separating viscous and capillary contributions. In the second part of the thesis we investigate inertia effects associated with abrupt and irreversible reconfigurations of the menisci caused by interface instabilities. As a prototype of these phenomena we first consider the dynamics of a meniscus in an angular pore. We show that in a network of cubic pores, jumps and reconfigurations are so frequent that inertia effects lead to different fluid configurations. Due to the non-linearity of the problem, the distribution of the fluids influences the work done by pressure forces, which is in turn related to the pressure drop in Darcy's law. This suggests that these phenomena should be taken into account when upscaling multiphase flow in porous media. The last part of the thesis is devoted to proving the accuracy of the numerical approach by validation with experiments of unstable primary drainage in a quasi-2D porous medium (i.e., Hele-Shaw cell filled with cylindrical obstacles). We perform simulations under different boundary conditions and using different models (2-D integrated and full 3-D) and we compare several macroscopic quantities with the corresponding experiment. Despite the intrinsic challenges of modeling unstable displacement, where by definition small perturbations can grow without bounds, the numerical method gives satisfactory results for all the cases studied.
Resumo:
For the development and evaluation of cardiac magnetic resonance (MR) imaging sequences and methodologies, the availability of a periodically moving phantom to model respiratory and cardiac motion would be of substantial benefit. Given the specific physical boundary conditions in an MR environment, the choice of materials and power source of such phantoms is heavily restricted. Sophisticated commercial solutions are available; however, they are often relatively costly and user-specific modifications may not easily be implemented. We therefore sought to construct a low-cost MR-compatible motion phantom that could be easily reproduced and had design flexibility. A commercially available K'NEX construction set (Hyper Space Training Tower, K'NEX Industries, Inc., Hatfield, PA) was used to construct a periodically moving phantom head. The phantom head performs a translation with a superimposed rotation, driven by a motor over a 2-m rigid rod. To synchronize the MR data acquisition with phantom motion (without introducing radiofrequency-related image artifacts), a fiberoptic control unit generates periodic trigger pulses synchronized to the phantom motion. Total material costs of the phantom are US$ < 200.00, and a total of 80 man-hours were required to design and construct the original phantom. With schematics of the present solution, the phantom reproduction may be achieved in approximately 15 man-hours. The presented MR-compatible periodically moving phantom can easily be reproduced, and user-specific modifications may be implemented. Such an approach allows a detailed investigation of motion-related phenomena in MR images.
Resumo:
Numerous measurements by XRD of the Scherrer width at half-peak height (001 reflection of illite), coupled with analyses of clay-size assemblages, provide evidence for strong variations in the conditions of low temperature metamorphism in the Tethyan Himalaya metasediments between the Spiti river and the Tso Morari. Three sectors can be distinguished along the Spiti river-Tso Morari transect. In the SW, the Takling and Parang La area is characterised by a metamorphism around anchizone-epizone boundary conditions. Further north, in the Dutung area, the metamorphic grade abruptly decreases to weak diagenesis, with the presence of mixed-layered clay phases. At the end of the profile towards the NE, a progressive metamorphic increase up to greenschist facies is recorded, marked by the appearance of biotite and chloritoid. The combination of these data with the structural. observations permits to propose that a nappe stack has been crosscut by the younger Dutung-Thaktote extensional fault zone (DTFZ). The change in metamorphism across this zone helps to assess the displacements which occurred during synorogenic extension. In the SW and NE parts of the studied transect, a burial of 12 km has been estimated, assuming a geothermal gradient of 25 degrees C/km. In the SW part, this burial is due to the juxtaposition of the Shikar Beh and Mata nappes and in the NE part, solely to burial beneath the Mata nappe. In the central part of the profile, the effect of the DTFZ is to bring down diagenetic sediments in-between the two aforesaid metamorphic zones. The offset along the Dutung-Thaktote normal faults is estimated at 16 km.