Éditeur(s) : HAL CCSD Springer Verlag (Germany) Springer Verlag
Résumé : Direct numerical simulations of flow through two millimeter-scale rock samples of limestone and sandstone are performed using three diverse fluid dynamic simulators. The resulting steady-state velocity fields are compared in terms of the associated empirical probability density functions (PDFs) and key statistics of the velocity fields. The pore space geometry of each sample is imaged at 5.06−μm voxel size resolution using X-ray microtomography. The samples offer contrasting characteristics in terms of total connected porosity (about 0.31 for the limestone and 0.07 for the sandstone) and are typical of several applications in hydrogeology and petroleum engineering. The three-dimensional fluid velocity fields within the explicit pore spaces are simulated using ANSYS® FLUENT® ANSYS Inc. (2009), EULAG Prusa et al. (Comput. Fluids 37, 1193–1207 2008), and SSTOKES Sarkar et al. (2002). These computational approaches are highly disperse in terms of algorithmic complexity, differ in terms of their governing equations, the adopted numerical methodologies, the enforcement of internal no-slip boundary conditions at the fluid-solid interface, and the computational mesh structure. As metrics of comparison to probe in a statistical sense the internal similarities/differences across sample populations of velocities obtained through the computational systems, we consider (i) integral quantities, such as the Darcy flux and (ii) main statistical moments of local velocity distributions including local correlations between velocity fields. Comparison of simulation results indicates that mutually consistent estimates of the state of flow are obtained in the analyzed samples of natural pore spaces despite the considerable differences associated with the three computational approaches. We note that in the higher porosity limestone sample, the structures of the velocity fields obtained using ANSYS FLUENT and EULAG are more alike than either compared against the results obtained using SSTOKES. In the low-porosity sample, the structures of the velocity fields obtained by EULAG and SSTOKES are more similar than either is to the fields obtained using ANSYS FLUENT. With respect to macroscopic quantities, ANSYS FLUENT and SSTOKES provide similar results in terms of the average vertical velocity for both of the complex microscale geometries considered, while EULAG tends to render the largest velocity values. The influence of the pore space structure on fluid velocity field characteristics is also discussed.
ISSN: 1420-0597

hal-01174152
https://hal.archives-ouvertes.fr/hal-01174152
DOI : 10.1007/s10596-015-9486-7

Résumé : Cette thèse à pour objet l'étude théorique et numérique de solutions dans les équations aux dérivées partielles non linéaires de la physique, en particulier en dynamique des fluides. La présence de discontinuités dans les solutions de ces équations complique la compréhension mathématique des phénomènes mis enjeu et leur traitement numérique, notamment en vue de simulations informatiques . Nous étudions ces équations par une méthode de régularisation dans un espace fonctionnel approprié. Lorsque des schémas numériques construits par des méthodes différentes conduisent à des résultats identiques, ceci jusque dans leurs moindres détails, il semble alors naturel de s'interroger dans quelle mesure ces suites de solutions numériques constituent une approximation d'une solution des équations étudiées. Nous construisons des suites de solutions approchées à partir d'un schéma numérique original,stable et suffisamment simple pour démontrer que ses suites constituent une méthode asymptotique de Maslov au sens des distributions en dimension trois d'espèce. La technique de régularisation employée consiste à étendre les variables réelles du problème ne des variables complexes, ce qui nous permet de construire des familles de solutions particulières que l'on ramène au cas réel en faisant tendre un petit paramètre vers O. Les solutions physiques recherchées apparaissent alors comme valeurs au bord de fonction holomorphes. Nous illustrons les résultats obtenus par des applications en cosmologie dans les cadres Newtoniens et relativistes pour des systèmes sans pression, puis avec pression et auto-gravitation, ainsi que pour le système des gaz parfaits.
This thesis is devoted to the theoretical and numerical study of singular solutions appearing in nonlinear partial differential complicates the mathematical understanding of the phenomena under concem as well as their numerical treatment, in particular in view of computation. These equations are studied by a regularization method in an appropriate functional space. When completely different numerical methods give the same results up to the smallest details one can reasonably expect that these numerical results suggest the existence of a mathematical solution of theses equations. We construct sequences of approximate solutions from an original numerical scheme, which is stable and simple enough to prove that these sequences constitute a Maslov asymptotic method in three space dimension. The regularization technique in use consits in extending the real variables of the problem into complex ones, which perrnits to construct families of particular equations that we bring back to the real case by letting a small paramater tend to zero. The expected physical solutions appear as boundary values of holomorphie functions . Illustrations are given by applications to cosmology in the Newtorian and re1ativistic settings for pressure1ess fluid dynamics, then in presence of self-gravitation and pressure as weil as for the systemof ideal gases

http://www.theses.fr/2011AGUY0478/document

Éditeur(s) : HAL CCSD
Résumé : International audience
The purpose of our study is to model a geothermal reservoir. When geothermal reservoir are assumed to be composed of pure water, the transfer of mass and energy is classically described by two balance equations: mass balance equation and the energy balance equation. In addition to those equations, fluid velocity ist classically given by the Darcy law while thermodynamic properties, inferred from theoretical or empirical equations of state, are used to close the mathematical system. Once this system is closed, there exist different solutions. The first one is to solve for pressure and temperature with a variable switch to saturation in the two-phase region (e.g. TOUGH2). The second one is to solve for pressure and enthalpy to increase stability of phase transition between single and two-phase states (e.g. Hydrotherm). We adopted the second option and chose te use a splitting method to get rid of the complexity of coupling equations and a finite volume method for the spatial discretization. Selecting object-oriented languages, we developed a multi-language framework, combining Python, Fortran and a C++ implementation of IAPWS (from the freesteam project) including the supercritical equations, in porous media velocity is given by Darcy law and to close the system physical properties are determined by the IAPWS-IF97 thermodynamic formulation. We resolve the equations in pressure and enthalpy instead of pressure and temperature in order to increase stability and to handle easier the passage from a single-phase to a two-phase system. We solve the system by using a splitting method - to get rid of the complexity of coupling equations - and a finite volume method. We offer some freedom to users thanks to the implementation of several methods like explicit or implicit Euler, Runge-Kutta or BDF2 for time solvers or GMRES and BICGSTAB for the linear solver. We can handle several boundary conditions like no-flow - describing a boundary which can not exchange matter with the exterior - or like a mixed-therm condition - a Dirichlet condition to the pressure and a Dirichlet or an outflow condition to the temperature in order to describe a recharge or a discharge zone - ... We're developing a multi-language framework, combining Python, Fortran and the C++ implementation of IAPWS (from the freesteam project). All these languages are object-oriented. We've applied this simulation model to the dogger in Paris, France, to several one-dimensional systems and a two-dimensional one made by Coumou with the CSMP++ platform. The dogger is a reservoir exploited to produce heat by pumping water at 70 and reinjecting it in the reservoir at 40. In the one-dimensional systems we wanted to observe the process of heat transfer from a higher temperature boundary to a smaller one in a high-energy domain. The last simulation shows the natural convection of water in a fault. For every simulation we compared the solutions we found with an other code (TOUGH2 or CSMP++) and they agreed. The next step will be to model the geothermal plant in Guadeloupe, West Indies. It's the only place in France - and in the West Indies so far - producing electricity with the earth power. The temperature can reach up to 1000 and the pressure range is around a few hundreds MPa. In some surface zones we can see two-phase water at atmospheric pressure. In the 1980s Bouillante was a laboratory for France. Since 1995 Bouillante has given 30GWh electricity a year to the Guadeloupeans.
PROCEEDINGS, Thirty-Ninth Workshop on Geothermal Reservoir Engineering
Stanford, United States

Droits : info:eu-repo/semantics/OpenAccess
hal-00944133
https://hal-brgm.archives-ouvertes.fr/hal-00944133
https://hal-brgm.archives-ouvertes.fr/hal-00944133/document
https://hal-brgm.archives-ouvertes.fr/hal-00944133/file/Copol.pdf

Éditeur(s) : HAL CCSD European Geosciences Union
Résumé : We designed a thermo-mechanical numerical model for fast-spreading mid-ocean ridge with variable viscosity, hydrothermal cooling, latent heat release, sheeted dyke layer, and variable melt intrusion possibilities. The model allows for modulating several accretion possibilities such as the "gabbro glacier" (G), the "sheeted sills" (S) or the "mixed shallow and MTZ lenses" (M). These three crustal accretion modes have been explored assuming viscosity contrasts of 2 to 3 orders of magnitude between strong and weak phases and various hydrothermal cooling conditions depending on the cracking temperatures value. Mass conservation (stream-function), momentum (vorticity) and temperature equations are solved in 2-D cartesian geometry using 2-D, alternate direction, implicit and semi-implicit finite-difference scheme. In a first step, an Eulerian approach is used solving iteratively the motion and temperature equations until reaching steady states. With this procedure, the temperature patterns and motions that are obtained for the various crustal intrusion modes and hydrothermal cooling hypotheses display significant differences near the mid-ocean ridge axis. In a second step, a Lagrangian approach is used, recording the thermal histories and cooling rates of tracers travelling from the ridge axis to their final emplacements in the crust far from the mid-ocean ridge axis. The results show that the tracer's thermal histories are depending on the temperature patterns and the crustal accretion modes near the mid-ocean ridge axis. The instantaneous cooling rates obtained from these thermal histories betray these discrepancies and might therefore be used to characterize the crustal accretion mode at the ridge axis. These deciphering effects are even more pronounced if we consider the average cooling rates occurring over a prescribed temperature range. Two situations were tested at 1275-1125 °C and 1050-850 °C. The first temperature range covers mainly the crystallization range that is characteristic of the high temperature areas in the model (i.e. the near-mid-oceanic-ridge axis). The second temperature range corresponds to areas in the model where the motion is mainly laminar and the vertical temperature profiles are closer to conductive. Thus, this situation results in less discriminating efficiency among the crustal accretion modes since the thermal and dynamic properties that are described are common to all the crustal accretion modes far from the ridge axis. The results show that numerical modeling of thermo-mechanical properties of the lower crusts may bring useful information to characterize the ridge accretion structure, hydrothermal cooling and thermal state at the fast-spreading ridges and may open discussions with petrological cooling rate results.
ISSN: 1991-959X

hal-00907012
https://hal.archives-ouvertes.fr/hal-00907012
DOI : 10.5194/gmd-6-1659-2013