Multiscale descriptions of density-driven flow instabilities in porous media

Les instabilités engendrées par des gradients de densité interviennent dans une variété d'écoulements. Un exemple est celui de la séquestration géologique du dioxyde de carbone en milieux poreux. Ce gaz est injecté à haute pression dans des aquifères salines et profondes. La différence de densité entre la saumure saturée en CO2 dissous et la saumure environnante induit des courants favorables qui le transportent vers les couches géologiques profondes. Les gradients de densité peuvent aussi être la cause du transport indésirable de matières toxiques, ce qui peut éventuellement conduire à la pollution des sols et des eaux. La gamme d'échelles intervenant dans ce type de phénomènes est très large. Elle s'étend de l'échelle poreuse où les phénomènes de croissance des instabilités s'opèrent, jusqu'à l'échelle des aquifères à laquelle interviennent les phénomènes à temps long. Une reproduction fiable de la physique par la simulation numérique demeure donc un défi en raison du caractère multi-échelles aussi bien au niveau spatial et temporel de ces phénomènes. Il requiert donc le développement d'algorithmes performants et l'utilisation d'outils de calculs modernes. En conjugaison avec les méthodes de résolution itératives, les méthodes multi-échelles permettent de résoudre les grands systèmes d'équations algébriques de manière efficace. Ces méthodes ont été introduites comme méthodes d'upscaling et de downscaling pour la simulation d'écoulements en milieux poreux afin de traiter de fortes hétérogénéités du champ de perméabilité. Le principe repose sur l'utilisation parallèle de deux maillages, le premier est choisi en fonction de la résolution du champ de perméabilité (grille fine), alors que le second (grille grossière) est utilisé pour approximer le problème fin à moindre coût. La qualité de la solution multi-échelles peut être améliorée de manière itérative pour empêcher des erreurs trop importantes si le champ de perméabilité est complexe. Les méthodes adaptatives qui restreignent les procédures de mise à jour aux régions à forts gradients permettent de limiter les coûts de calculs additionnels. Dans le cas d'instabilités induites par des gradients de densité, l'échelle des phénomènes varie au cours du temps. En conséquence, des méthodes multi-échelles adaptatives sont requises pour tenir compte de cette dynamique. L'objectif de cette thèse est de développer des algorithmes multi-échelles adaptatifs et efficaces pour la simulation des instabilités induites par des gradients de densité. Pour cela, nous nous basons sur la méthode des volumes finis multi-échelles (MsFV) qui offre l'avantage de résoudre les phénomènes de transport tout en conservant la masse de manière exacte. Dans la première partie, nous pouvons démontrer que les approximations de la méthode MsFV engendrent des phénomènes de digitation non-physiques dont la suppression requiert des opérations de correction itératives. Les coûts de calculs additionnels de ces opérations peuvent toutefois être compensés par des méthodes adaptatives. Nous proposons aussi l'utilisation de la méthode MsFV comme méthode de downscaling: la grille grossière étant utilisée dans les zones où l'écoulement est relativement homogène alors que la grille plus fine est utilisée pour résoudre les forts gradients. Dans la seconde partie, la méthode multi-échelle est étendue à un nombre arbitraire de niveaux. Nous prouvons que la méthode généralisée est performante pour la résolution de grands systèmes d'équations algébriques. Dans la dernière partie, nous focalisons notre étude sur les échelles qui déterminent l'évolution des instabilités engendrées par des gradients de densité. L'identification de la structure locale ainsi que globale de l'écoulement permet de procéder à un upscaling des instabilités à temps long alors que les structures à petite échelle sont conservées lors du déclenchement de l'instabilité. Les résultats présentés dans ce travail permettent d'étendre les connaissances des méthodes MsFV et offrent des formulations multi-échelles efficaces pour la simulation des instabilités engendrées par des gradients de densité. - Density-driven instabilities in porous media are of interest for a wide range of applications, for instance, for geological sequestration of CO2, during which CO2 is injected at high pressure into deep saline aquifers. Due to the density difference between the C02-saturated brine and the surrounding brine, a downward migration of CO2 into deeper regions, where the risk of leakage is reduced, takes place. Similarly, undesired spontaneous mobilization of potentially hazardous substances that might endanger groundwater quality can be triggered by density differences. Over the last years, these effects have been investigated with the help of numerical groundwater models. Major challenges in simulating density-driven instabilities arise from the different scales of interest involved, i.e., the scale at which instabilities are triggered and the aquifer scale over which long-term processes take place. An accurate numerical reproduction is possible, only if the finest scale is captured. For large aquifers, this leads to problems with a large number of unknowns. Advanced numerical methods are required to efficiently solve these problems with today's available computational resources. Beside efficient iterative solvers, multiscale methods are available to solve large numerical systems. Originally, multiscale methods have been developed as upscaling-downscaling techniques to resolve strong permeability contrasts. In this case, two static grids are used: one is chosen with respect to the resolution of the permeability field (fine grid); the other (coarse grid) is used to approximate the fine-scale problem at low computational costs. The quality of the multiscale solution can be iteratively improved to avoid large errors in case of complex permeability structures. Adaptive formulations, which restrict the iterative update to domains with large gradients, enable limiting the additional computational costs of the iterations. In case of density-driven instabilities, additional spatial scales appear which change with time. Flexible adaptive methods are required to account for these emerging dynamic scales. The objective of this work is to develop an adaptive multiscale formulation for the efficient and accurate simulation of density-driven instabilities. We consider the Multiscale Finite-Volume (MsFV) method, which is well suited for simulations including the solution of transport problems as it guarantees a conservative velocity field. In the first part of this thesis, we investigate the applicability of the standard MsFV method to density- driven flow problems. We demonstrate that approximations in MsFV may trigger unphysical fingers and iterative corrections are necessary. Adaptive formulations (e.g., limiting a refined solution to domains with large concentration gradients where fingers form) can be used to balance the extra costs. We also propose to use the MsFV method as downscaling technique: the coarse discretization is used in areas without significant change in the flow field whereas the problem is refined in the zones of interest. This enables accounting for the dynamic change in scales of density-driven instabilities. In the second part of the thesis the MsFV algorithm, which originally employs one coarse level, is extended to an arbitrary number of coarse levels. We prove that this keeps the MsFV method efficient for problems with a large number of unknowns. In the last part of this thesis, we focus on the scales that control the evolution of density fingers. The identification of local and global flow patterns allows a coarse description at late times while conserving fine-scale details during onset stage. Results presented in this work advance the understanding of the Multiscale Finite-Volume method and offer efficient dynamic multiscale formulations to simulate density-driven instabilities. - Les nappes phréatiques caractérisées par des structures poreuses et des fractures très perméables représentent un intérêt particulier pour les hydrogéologues et ingénieurs environnementaux. Dans ces milieux, une large variété d'écoulements peut être observée. Les plus communs sont le transport de contaminants par les eaux souterraines, le transport réactif ou l'écoulement simultané de plusieurs phases non miscibles, comme le pétrole et l'eau. L'échelle qui caractérise ces écoulements est définie par l'interaction de l'hétérogénéité géologique et des processus physiques. Un fluide au repos dans l'espace interstitiel d'un milieu poreux peut être déstabilisé par des gradients de densité. Ils peuvent être induits par des changements locaux de température ou par dissolution d'un composé chimique. Les instabilités engendrées par des gradients de densité revêtent un intérêt particulier puisque qu'elles peuvent éventuellement compromettre la qualité des eaux. Un exemple frappant est la salinisation de l'eau douce dans les nappes phréatiques par pénétration d'eau salée plus dense dans les régions profondes. Dans le cas des écoulements gouvernés par les gradients de densité, les échelles caractéristiques de l'écoulement s'étendent de l'échelle poreuse où les phénomènes de croissance des instabilités s'opèrent, jusqu'à l'échelle des aquifères sur laquelle interviennent les phénomènes à temps long. Etant donné que les investigations in-situ sont pratiquement impossibles, les modèles numériques sont utilisés pour prédire et évaluer les risques liés aux instabilités engendrées par les gradients de densité. Une description correcte de ces phénomènes repose sur la description de toutes les échelles de l'écoulement dont la gamme peut s'étendre sur huit à dix ordres de grandeur dans le cas de grands aquifères. Il en résulte des problèmes numériques de grande taille qui sont très couteux à résoudre. Des schémas numériques sophistiqués sont donc nécessaires pour effectuer des simulations précises d'instabilités hydro-dynamiques à grande échelle. Dans ce travail, nous présentons différentes méthodes numériques qui permettent de simuler efficacement et avec précision les instabilités dues aux gradients de densité. Ces nouvelles méthodes sont basées sur les volumes finis multi-échelles. L'idée est de projeter le problème original à une échelle plus grande où il est moins coûteux à résoudre puis de relever la solution grossière vers l'échelle de départ. Cette technique est particulièrement adaptée pour résoudre des problèmes où une large gamme d'échelle intervient et évolue de manière spatio-temporelle. Ceci permet de réduire les coûts de calculs en limitant la description détaillée du problème aux régions qui contiennent un front de concentration mobile. Les aboutissements sont illustrés par la simulation de phénomènes tels que l'intrusion d'eau salée ou la séquestration de dioxyde de carbone.

CO2 utilization in the perspective of industrial ecology, an overview

Carbon dioxide emissions from anthropic activities have accumulated in the atmosphere in excess of 800 Gigatons since preindustrial times, and are continuously increasing. Among other strategies, CO2 capture and storage is one option to mitigate the emissions from large point sources. In addition, carbon dioxide extraction from ambient air is assessed to reduce the atmospheric concentration of CO2. Both direct and indirect (through photosynthesis) pathways are possible. Geological sequestration has significant disadvantages (high cost, low public acceptance, long term uncertainty) whereas carbon dioxide recycling (or utilization) is more consistent with the basic principle of industrial ecology, almost closing material cycles. In this article, a series of technologies for CO2 capture and valorization is described as integrated and optimized pathways. This integration increases the environmental and economic benefits of each technology. Depending on the source of carbon dioxide, appropriate capture and valorization processes are evaluated based on material and energy constraints.

Technical and economic factors in applying the enhanced coalbed methane recovery process

Geological sequestration of CO2 is a technically feasible and potentially economic option for significantly and safely reducing greenhouse gas emissions, with CO2 injection already practiced in Canada and the USA to enhance crude oil production. The Enhanced Coalbed Methane (ECBM) process is seen as the next most economical sequestration options. The authors estimate an incremental methane recovery factor from 20% to 50%, depending on coal rank and seam depth. Others have estimated the potential to increase worldwide CBM production, utilising ECBM, by 18 Trillion cubic meters, while simultaneously sequestering 345 Giga tonnes of CO2. This paper presents technical and economic factors to consider for developing a commercial ECBM project. Technical factors include: geostructural and hydrogeological issues, geochemical reactions, stressed and competitive sorption, counter-diffusion, effective and relative 4-D coal permeability and methane recovery levels. Key economic factors are injectant acquisition price, sale price of methane and the level of carbon credits.

Table 2. Performance summary of K-based sorbents capturing CO2

This article reviews the progress made in CO2 capture, storage, and utilization in Chinese Academy of Sciences (CAS). New concepts such as adsorption using dry regenerable solid sorbents as well as functional ionic liquids (ILs) for CO2 capture are thoroughly discussed. Carbon sequestration, such as geological sequestration, mineral carbonation and ocean storage are also covered. The utilization of CO2 as a raw material in the synthesis of chemicals and liquid energy carriers which offers a way to mitigate the increasing CO2 buildup is introduced.

Geological Characterisation of Depleted Oil and Gas Reservoirs for Carbon Sequestration Potentials in a Field in the Niger Delta, Nigeria

The injectivity, containment and storage capacity of sandstone reservoirs in a field in the Coastal Swamp depobelt of the onshore eastern Niger Delta were evaluated using wireline logs and seismic data to assess their potentials for carbon dioxide storage and geosequestration. The reservoir formation consists of multilayered alternating beds of sandstone and shale cap rocks. Active seismicity and fracturing intensity are low and growth faults provide the reservoir sealing mechanisms. Three reservoirs were delineated at depths between 3319 m and 3539 m which will keep injected CO2 in a supercritical state. The reservoir depth of at least 800 m, porosity and permeability of more than 10 percent and 20 mD, and a caprock thickness of at least 10 m, in addition to geothermal gradients of 13.46 to 33.66 ºC /km are the ideal conditions for the efficacy of storage. Comparison of the derived reservoir and seal properties such as porosity, permeability, thickness and depth with the minimum recommended site selection criteria shows that the reservoirs are potential candidates for carbon geosequestration with a total theoretical storage capacity of 147MM tons.

Probabilistic electrical resistivity tomography of a CO2 sequestration analog

Electrical resistivity tomography (ERT) is a well-established method for geophysical characterization and has shown potential for monitoring geologic CO2 sequestration, due to its sensitivity to electrical resistivity contrasts generated by liquid/gas saturation variability. In contrast to deterministic inversion approaches, probabilistic inversion provides the full posterior probability density function of the saturation field and accounts for the uncertainties inherent in the petrophysical parameters relating the resistivity to saturation. In this study, the data are from benchtop ERT experiments conducted during gas injection into a quasi-2D brine-saturated sand chamber with a packing that mimics a simple anticlinal geological reservoir. The saturation fields are estimated by Markov chain Monte Carlo inversion of the measured data and compared to independent saturation measurements from light transmission through the chamber. Different model parameterizations are evaluated in terms of the recovered saturation and petrophysical parameter values. The saturation field is parameterized (1) in Cartesian coordinates, (2) by means of its discrete cosine transform coefficients, and (3) by fixed saturation values in structural elements whose shape and location is assumed known or represented by an arbitrary Gaussian Bell structure. Results show that the estimated saturation fields are in overall agreement with saturations measured by light transmission, but differ strongly in terms of parameter estimates, parameter uncertainties and computational intensity. Discretization in the frequency domain (as in the discrete cosine transform parameterization) provides more accurate models at a lower computational cost compared to spatially discretized (Cartesian) models. A priori knowledge about the expected geologic structures allows for non-discretized model descriptions with markedly reduced degrees of freedom. Constraining the solutions to the known injected gas volume improved estimates of saturation and parameter values of the petrophysical relationship. (C) 2014 Elsevier B.V. All rights reserved.

In-situ infrared spectroscopy as a non-invasive technique to study carbon sequestration at high pressure and high temperature

We would like to thank EPSRC for a Doctoral Training Grant (G.A.M) and the Erasmus programme for supporting the study visit to Turin (R.W). We would also like to thank Dr. Federico Cesano for SEM/EDX measurements and for fruitful discussion. Dr. Jo Duncan is thanked for his tremendous insight during XRD interpretation.

Carbon sequestration in agricultural soils in the Cerrado region of the Brazilian Amazon

The introduction of crop management practices after conversion of Amazon Cerrado into cropland influences soil C stocks and has direct and indirect consequences on greenhouse gases (GHG) emissions. The aim of this study was to quantify soil C sequestration, through the evaluation of the changes in C stocks, as well as the GHG fluxes (N(2)O and CH(4)) during the process of conversion of Cerrado into agricultural land in the southwestern Amazon region, comparing no-tillage (NT) and conventional tillage (CT) systems. We collected samples from soils and made gas flux measurements in July 2004 (the dry season) and in January 2005 (the wet season) at six areas: Cerrado, CT cultivated with rice for 1 year (1CT) and 2 years (2CT), and NT cultivated with soybean for 1 year (1NT), 2 years (2NT) and 3 years (3NT), in each case after a 2-year period of rice under CT. Soil samples were analyzed in both seasons for total organic C and bulk density. The soil C stocks, corrected for a mass of soil equivalent to the 0-30-cm layer under Cerrado, indicated that soils under NT had generally higher C storage compared to native Cerrado and CT soils. The annual C accumulation rate in the conversion of rice under CT into soybean under NT was 0.38 Mg ha(-1) year(-1). Although CO(2) emissions were not used in the C sequestration estimates to avoid double counting, we did include the fluxes of this gas in our discussion. In the wet season, CO(2) emissions were twice as high as in the dry season and the highest N(2)O emissions occurred under the NT system. There were no CH(4) emissions to the atmosphere (negative fluxes) and there were no significant seasonal variations. When N(2)O and CH(4) emissions in C-equivalent were subtracted (assuming that the measurements made on 4 days were representative of the whole year), the soil C sequestration rate of the conversion of rice under CT into soybean under NT was 0.23 Mg ha(-1) year(-1). Although there were positive soil C sequestration rates, our results do not present data regarding the full C balance in soil management changes in the Amazon Cerrado. (C) 2008 Elsevier B.V. All rights reserved.

Effect of grassland management on soil carbon sequestration in Rondonia and Mato Grosso states, Brazil

Grassland management affects soil organic carbon (SOC) content and a variety of management options have been proposed to sequester carbon. However, studies conducted in Brazilian pastures have shown divergent responses for the SOC depending on management practices. Our objective was to evaluate the effects of management on SOC stocks in grasslands of the Brazilian states of Rondonia and Mato Grosso, and to derive region-specific factors for soil C stock change associated with different management conditions. Compared to SOC stocks in native vegetation, degraded grassland management decreased SOC by a factor of 0.91 +/- 0.14, nominal grassland management reduced SOC stock for Oxisols by a relatively small factor of 0.99 +/- 0.08, whereas, SOC storage increased by a factor of 1.24 +/- 0.07 with nominal management for other soil types. Improved grassland management on Oxisols increased SOC storage by 1.19 +/- 0.07, relative to native stocks, but there were insufficient data to evaluate the impact of improved grassland management for other soil types. Using these results, we also evaluated the potential for grassland management to sequester or emit C to the atmosphere, and found that degraded grassland management decreased stocks by about 0.27-0.28 Mg C ha(-1) yr(-1); nominal management on Oxisols decreased C at a rate of 0.03 Mg C ha(-1) yr(-1), while nominal management on others soil types and improved management on Oxisols increased stocks by 0.72 Mg C ha(-1) yr(-1) and 0.61 Mg C ha(-1) yr(-1), respectively. Therefore, when well managed or improved, grasslands in Rondonia and Mato Grosso states have the potential to sequester C. (c) 2008 Elsevier B.V. All rights reserved.

Coexistence of forest and savanna in an Amazonian area from a geological perspective

Question: How can the coexistence of savanna and forest in Amazonian areas with relatively uniform climates be explained? Location: Eastern Marajo Island, northeast Amazonia, Brazil. Methods: The study integrated floristic analysis, terrain morphology, sedimentology and delta(13)C of soil organic matter. Floristic analysis involved rapid ecological assessment of 33 sites, determination of occurrence, specific richness, hierarchical distribution and matrix of floristic similarity between paired vegetation types. Terrain characterization was based on analysis of Landsat images using 4(R), 5(G) and 7(B) composition and digital elevation model (DEM). Sedimentology involved field descriptions of surface and core sediments. Finally, radiocarbon dating and analysis of delta(13)C of soil profile organic matter and natural ecotone forest-savanna was undertaken. Results: Slight tectonic subsidence in eastern Marajo Island favours seasonal flooding, making it unsuitable for forest growth. However, this area displays slightly convex-up, sinuous morphologies related to paleochannels, covered by forest. Terra-firme lowland forests are expanding from west to east, preferentially occupying paleochannels and replacing savanna. Slack, running water during channel abandonment leads to disappearance of varzea/gallery forest at channel margins. Long-abandoned channels sustain continuous terra-firme forests, because of longer times for more species to establish. Recently abandoned channels have had less time to become sites for widespread tree development, and are either not vegetated or covered by savanna. Conclusion: Landforms in eastern Marajo Island reflect changes in the physical environment due to reactivation of tectonic faults during the latest Quaternary. This promoted a dynamic history of channel abandonment, which controlled a set of interrelated parameters (soil type, topography, hydrology) that determined species location. Inclusion of a geological perspective for paleoenvironmental reconstruction can increase understanding of plant distribution in Amazonia.

Private valuation of carbon sequestration in forest plantations

Approval of the Clean Development Mechanism, provided for in the Kyoto Protocol, enables countries with afforested land to trade in carbon emissions reduction certificates related to carbon dioxide equivalent quantities (CO(2-e)) stored within a certain forest area. Potential CO(2-e) above base line sequestration was determined for two forest sites on commercial eucalyptus plantations in northern Brazil (Bahia). Compensation values for silvicultural regimes involving rotation lengths greater than economically optimal were computed using the Faustmann formula. Mean values obtained were US$8.16 (MgCO(2-e))(-1) and US $7.19 (MgCO(2-e))(-1) for average and high site indexes, respectively. Results show that carbon supply is more cost-efficient in highly productive sites. Annuities of US$18.8 Mg C(-1) and US$35.1 Mg C(-1) and yearly payments of US$4.4 m(-3) and US$8.2 m(-3) due for each marginal cubic meter produced were computed for high and average sites, respectively. The estimated value of the tonne of carbon defines minimum values to be paid to forest owners, in order to induce a change in silvicultural management regimes. A reduction of carbon supply could be expected as a result of an increase in wood prices, although it would not respond in a regular manner. For both sites, price elasticity of supply was found to be inelastic and increased as rotation length moved further away from economically optimal: 0.24 and 0.27 for age 11 years in average- and high-productivity sites, respectively. This would be due to biomass production potential as a limiting factor; beyond a certain threshold value. an increase in price does not sustain a proportional change in carbon storage supply. The environmental service valuation model proposed might be adequate for assessing potential supply in plantation forestry, from a private landowner perspective, with an economic opportunity cost. The model is not applicable to low commercial value forest plantations. (C) 2009 Elsevier B.V. All rights reserved.

Effects of geological inhomogeneity on high Rayleigh number steady state heat and mass transfer in fluid-saturated porous media heated from below

A parametric study is carried out to investigate how geological inhomogeneity affects the pore-fluid convective flow field, the temperature distribution, and the mass concentration distribution in a fluid-saturated porous medium. The related numerical results have demonstrated that (1) the effects of both medium permeability inhomogeneity and medium thermal conductivity inhomogeneity are significant on the pore-fluid convective flow and the species concentration distribution in the porous medium; (2) the effect of medium thermal conductivity inhomogeneity is dramatic on the temperature distribution in the porous medium, but the effect of medium permeability inhomogeneity on the temperature distribution may be considerable, depending on the Rayleigh number involved in the analysis; (3) if the coupling effect between pore-fluid flow and mass transport is weak, the effect of the Lewis number is negligible on the pore-fluid convective flow and temperature distribution, hut it is significant on the species concentration distribution in the medium.

Finite element analysis of flow patterns near geological lenses in hydrodynamic and hydrothermal systems

We use theoretical and numerical methods to investigate the general pore-fluid flow patterns near geological lenses in hydrodynamic and hydrothermal systems respectively. Analytical solutions have been rigorously derived for the pore-fluid velocity, stream function and excess pore-fluid pressure near a circular lens in a hydrodynamic system. These analytical solutions provide not only a better understanding of the physics behind the problem, but also a valuable benchmark solution for validating any numerical method. Since a geological lens is surrounded by a medium of large extent in nature and the finite element method is efficient at modelling only media of finite size, the determination of the size of the computational domain of a finite element model, which is often overlooked by numerical analysts, is very important in order to ensure both the efficiency of the method and the accuracy of the numerical solution obtained. To highlight this issue, we use the derived analytical solutions to deduce a rigorous mathematical formula for designing the computational domain size of a finite element model. The proposed mathematical formula has indicated that, no matter how fine the mesh or how high the order of elements, the desired accuracy of a finite element solution for pore-fluid flow near a geological lens cannot be achieved unless the size of the finite element model is determined appropriately. Once the finite element computational model has been appropriately designed and validated in a hydrodynamic system, it is used to examine general pore-fluid flow patterns near geological lenses in hydrothermal systems. Some interesting conclusions on the behaviour of geological lenses in hydrodynamic and hydrothermal systems have been reached through the analytical and numerical analyses carried out in this paper.