Dividimos el trabajo en tres bloques: En el primer bloque, se han revisado las técnicas de escalado que utilizan una media simple, el método laplaciano simple, el laplaciano con piel y el escalado con mallado no uniforme y se han evaluado en un ejercicio tridimensional de escalado de la conductividad hidráulica. El campo usado como referencia es una realización condicional a escala fina de la conductividad hidráulica del experimento de macrodispersión realizado en la base de la fuerza aérea estadounidense de Columbus en Misuri (MADE en su acrónimo inglés). El objetivo de esta sección es doble, primero, comparar la efectividad de diferentes técnicas de escalado para producir modelos capaces de reproducir el comportamiento observado del movimiento del penacho de tritio, y segundo, demostrar y analizar las condiciones bajo las cuales el escalado puede proporcionar un modelo a una escala gruesa en el que el flujo y el transporte puedan predecirse con al ecuación de advección-dispersión en condiciones aparentemente no fickianas. En otros casos, se observa que la discrepancia en la predicción del transporte entre las dos escalas persiste, y la ecuación de advección-dispersión no es suficiente para explicar el transporte en la escala gruesa. Por esta razón, se ha desarrollado una metodología para el escalado del transporte en formaciones muy heterogéneas en tres dimensiones. El método propuesto se basa en un escalado de la conductividad hidráulica por el método laplaciano con piel y centrado en los interbloques, seguido de un escalado de los parámetros de transporte que requiere la inclusión de un proceso de transporte con transferencia de masa multitasa para compensar la pérdida de heterogeneidad inherente al cambio de escala. El método propuesto no sólo reproduce el flujo y el transporte en la escala gruesa, sino que reproduce también la incertidumbre asociada con las predicciones según puede observarse analizando la variabilidad del conjunto de curvas de llegada. / Li ., L. (2011). Upscaling and Inverse Modeling of Groundwater Flow and Mass Transport in Heterogeneous Aquifers [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/12268 / Palancia

In this dissertation we discuss some upscaling methods for flow and transport in heterogeneous reservoirs. We studied realization-based multi-phase flow and transport upscaling and ensemble-level flow upscaling. Multi-phase upscaling is more accurate than single-phase upscaling and is often required for high level of coarsening. In multi-phase upscaling, the upscaled transport parameters are time-dependent functions and are challenging to compute. Due to the hyperbolic feature of the saturation equation, the nonlocal effects evolve in both space and time. Standard local two-phase upscaling gives significantly biased results with reference to fine-scale solutions. In this work, we proposed two types of multi-phase upscaling methods, TOF (time-offlight)- based two-phase upscaling and local-global two-phase upscaling. These two methods incorporate global flow information into local two-phase upscaling calculations. A linear function of time and time-of-flight and a global coarse-scale two-phase solution (time-dependent) are used respectively in these two approaches. The local boundary condition therefore captures the global flow effects both spatially and temporally. These two methods are applied to permeability distributions with various correlation lengths. Numerical results show that they consistently improve existing two-phase upscaling methods and provide accurate coarse-scale solutions for both flow and transport. We also studied ensemble level flow upscaling. Ensemble level upscaling is up scaling for multiple geological realizations and often required for uncertainty quantification. Solving the flow problem for all the realizations is time-consuming. In recent years, some stochastic procedures are combined with upscaling methods to efficiently compute the upscaled coefficients for a large set of realization. We proposed a fast perturbation approach in the ensemble level upscaling. By Karhunen-Lo`eve expansion (KLE), we proposed a correction scheme to fast compute the upscaled permeability for each realization. Then the sparse grid collocation and adaptive clustering are coupled with the correction scheme. When we solve the local problem, the solution can be represented by a product of Green's function and source term. Using collocation and clusering technique, one can avoid the computation of Green's function for all the realizations. We compute Green's function at the interpolation nodes, then for any realization, the Green's function can be obtained by interpolation. The above techniques allow us to compute the upscaled permeability rapidly for all realizations in stochastic space.

Mixing of miscible gas with oil in a reservoir decreases the effective strength of the gas, which can adversely affect miscibility and recovery efficiency. The mixing that occurs in a reservoir, however, is widely debated and often ignored in reservoir simulation, where very large grid blocks are used. Large grid blocks create artificially large mixing that can cause errors in predicted oil recovery. Reservoir mixing, or dispersion, is caused by diffusion of particles across streamlines of varying velocities. Mixing is enhanced by any mechanism that increases the area of contact between the gas and the oil, thereby allowing the effects of diffusion to be magnified. This is, in essence, the cause of scale-dependent dispersion. The contact area grows primarily because of variations in streamlines and their velocities around grains and through layers of various permeabilities (heterogeneity). Mixing can also be enhanced by crossflow, such as that caused by gravity and by the effects of other neighboring wells. This dissertation focuses on estimation of the level of effective local mixing at the field scale and its impact on oil recovery from miscible gas floods. Pore-level simulation was performed using the Navier-Stokes and convection-diffusion equations to examine the origin of scale dependent dispersion. We then estimated dispersivity at the macro scale as a function of key scaling groups in heterogeneous reservoirs. Lastly, we upscaled grid blocks to match the level of mixing at the pattern scale. Once the contact area ceases to grow with distance traveled, dispersion has reached its asymptotic limit. This generally occurs when the fluids are well mixed in transverse direction. We investigated a variety of pore-scale models to understand the nature of scale dependency. From the pore-scale study, we found that reservoir mixing or dispersion is caused by diffusion of particles across streamlines. Diffusion can be significantly enhanced if the surface area of contact between the reservoir and injected fluid are increased as fluids propagate through the reservoir. Echo and transmission dispersivities are scale dependent. They may or may not reach an asymptotic limit depending on the scale of heterogeneities encountered. The scale dependence results from an increase in the contact area between solute (gas) and resident fluid (oil) as heterogeneities are encountered, either at the pore or pattern-scale. The key scaling groups for first-contact miscible (FCM) flow are derived and their impact on mixing is analyzed. We examine only local mixing, not apparent mixing caused by variations in streamline path lengths (convective spreading). Local mixing is important because it affects the strength of the injected fluid, and can cause an otherwise multicontact miscible (MCM) flood to become immiscible. We then showed how to upscale miscible floods considering reservoir mixing. The sum of numerical dispersion and physical dispersion associated with the reservoir heterogeneities, geometry and fluid properties must be equal at both the fine- and large-scales. The maximum grid-block size allowed in both the x- and z-directions is determined from the scaling groups. Small grid-blocks must be used for reservoirs with uncorrelated permeabilities, while larger grid blocks can be used for more layered reservoirs. The predicted level of mixing for first-contact miscible floods can be extended with good accuracy to multicontact miscible (MCM) gas floods. / text

Pore-scale network modeling has become an effective method for accurate prediction and upscaling of macroscopic properties, such as permeability. Networks are either mapped directly from real media or stochastic methods are used that simulate their heterogeneous pore structure. Flow is then modeled by enforcing conservation of mass in each pore and approximations to the momentum equations are solved in the connecting throats. In many cases network modeling compares favorably to experimental measurements of permeability. However, computational and imaging restrictions generally limit the network size to the order of 1 mm3 (few thousand pores). For extremely heterogeneous media these models are not large enough in capturing the petrophysical properties of the entire heterogeneous media and inaccurate results can be obtained when upscaling to the continuum scale. Moreover, the boundary conditions imposed are artificial; a pressure gradient is imposed in one dimension so the influence of flow behavior in the surrounding media is not included. In this work we upscale permeability in large, heterogeneous media using physically-representative pore-scale network models (domain ~106 pores). High-performance computing is used to obtain accurate results in these models, but a more efficient, novel domain decomposition method is introduced for upscaling the permeability of pore-scale models. The medium is decomposed into hundreds of smaller networks (sub-domains) and then coupled with the surrounding models to determine accurate boundary conditions. Finite element mortars are used as a mathematical tool to ensure interfacial pressures and fluxes are matched at the interfaces of the networks boundaries. The results compare favorably to the more computationally intensive (and impractical) approach of upscaling the media as a single model. Moreover, the results are much more accurate than traditional hierarchal upscaling methods. This upscaling technique has important implications for using pore-scale models directly in reservoir simulators in a multiscale setting. The upscaling techniques introduced here on single phase flow can also be easily extended to other flow phenomena, such as multiphase and non-Newtonian behavior. / text

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Made available in DSpace on 2014-06-12T17:38:19Z (GMT). No. of bitstreams: 2 arquivo3892_1.pdf: 4418824 bytes, checksum: 2615d6af86dc68c334dbfb9f8b2a2b92 (MD5) license.txt: 1748 bytes, checksum: 8a4605be74aa9ea9d79846c1fba20a33 (MD5) Previous issue date: 2009 / Instituto Brasileiro de Geografia e Estatística / A transferência para uma escala maior ( upscaling ), tem sido um método muito utilizado no tratamento de informações associadas a uma grande quantidade de dados, tornando-se uma opção ainda mais relevante quando o excesso destes dados representa uma dificuldade na sua manipulação, levando à outras conseqüências tais como longo tempo de processamento, sobrecarga do sistema ou até mesmo inviabilização da simulação em alguns casos extremos. Desta forma, a transferência para uma escala maior tem como desafio a busca pela manutenção da representatividade da informação, utilizando uma menor quantidade de dados. A permeabilidade absoluta e a porosidade de campos de petróleo podem representar uma grande quantidade de dados nas simulações e, em casos realistas, com reservatórios altamente heterogêneos, a utilização de modelos com malhas muito refinadas se torna eventualmente inviável ou requer um longo tempo computacional para simulação. Isto motivou o estudo de duas metodologias clássicas de transferência para uma escala maior ( upscaling ) para dados referentes à permeabilidade, através do uso de médias pitagóricas (aritmética, geométrica, harmônica) e do uso do chamado Flow Based e para os dados referentes à porosidade, através do uso de média aritmética volumétrica. Foi desenvolvido um sistema chamado de Transfer , escrito em linguagem C, que atua como um gerenciador do processo de transferência de escala, além de possuir ferramentas para pré-processamento que auxiliam na conversão de dados entre o simulador IMEX e o sistema Transfer , assim como, entre o Transfer e o software ELMER e no pós-processamento, ferramentas para fazer o procedimento inverso. Ainda foram agregadas diversas ferramentas adicionais para auxilio no uso do sistema. Em relação aos aplicativos adotados, no caso específico da metodologia Flow Based , foi utilizado o software de resolução de problemas multifísicos ELMER do Finish IT Center for Sciense (CSC - Finlândia) para o cálculo da permeabilidade equivalente de macro-células utilizando o método dos elementos finitos. Também como forma de acelerar o processamento da metodologia Flow Based , foi desenvolvida uma versão do sistema Transfer para trabalhar de modo distribuído, visando aumentar a velocidade de processamento em relação ao sistema trabalhando em modo seqüencial. Como formas de avaliar as ferramentas desenvolvidas ou utilizadas, foram feitas simulações baseadas no desafio lançado pela Society of Petroleum Engineers (SPE) através do Tenth SPE Comparative Solution Project: A Comparison of Upscaling Techniques - SPE66599 (Christie-2001) que trata de dois modelos, sendo o primeiro um caso simples em duas dimensões com 2.000 células e o segundo um caso tridimensional com 1.122.000 células. Para obtenção de resultados, foi utilizado o simulador comercial de reservatórios IMEX da Computer Modeling Group (CMG), conjuntamente com os aplicativos BUILDER e RESULTS GRAPH que fazem parte do mesmo pacote da empresa. O presente trabalho contribuiu para que fosse criada uma ferramenta para transferência para escala superior ( upscaling ) de dados, utilizando duas metodologias distintas, com aplicação de computação distribuída, podendo ser utilizada em diversos contextos, tais como: simulação de reservatórios de petróleo, estudo de aqüíferos e contaminantes, etc. Também serviu como trabalho inicial de uma nova linha de pesquisa para o grupo de pesquisa PADMEC da UFPE

The groundwater specialists and the reservoir engineers share the same interest in simulating multiphase flow in soil with heterogeneous intrinsic properties. They also both face the challenge of going from a well-modeled micrometer scale to the reservoir scale with a controlled loss of information. This upscaling process is indeed worthy to make simulation over an entire reservoir manageable and stochastically repeatable. Two upscaling steps can be defined: one from the micrometer scale to the Darcy scale, and another from the Darcy scale to the reservoir scale. In this thesis, a new second upscaling multiscale algorithm Finite Volume Mixed Hybrid Multiscale Methods (Fv-MHMM) is investigated. Extension to a two-phase flow system is done by weakly and sequentially coupling saturation and pressure via IMPES-like method.

More difficulties are now expected in exploring economically valuable reservoirs because most reservoirs have been already developed since beginning seismic exploration of the subsurface. In order to efficiently analyze heterogeneous fine-scale properties in subsurface layers, one ongoing challenge is accurately upscaling fine-scale (high frequency) logging measurements to coarse-scale data, such as surface seismic images. In addition, numerically efficient modeling cannot use models defined on the scale of log data. At this point, we need an upscaling method replaces the small scale data with simple large scale models. However, numerous unavoidable uncertainties still exist in the upscaling process, and these problems have been an important emphasis in geophysics for years. Regarding upscaling problems, there are predictable or unpredictable uncertainties in upscaling processes; such as, an averaging method, an upscaling algorithm, analysis of results, and so forth. To minimize the uncertainties, a Bayesian framework could be a useful tool for providing the posterior information to give a better estimate for a chosen model with a conditional probability. In addition, the likelihood of a Bayesian framework plays an important role in quantifying misfits between the measured data and the calculated parameters. Therefore, Bayesian methodology can provide a good solution for quantification of uncertainties in upscaling. When analyzing many uncertainties in porosities, wave velocities, densities, and thicknesses of rocks through upscaling well log data, the Markov Chain Monte Carlo (MCMC) method is a potentially beneficial tool that uses randomly generated parameters with a Bayesian framework producing the posterior information. In addition, the method provides reliable model parameters to estimate economic values of hydrocarbon reservoirs, even though log data include numerous unknown factors due to geological heterogeneity. In this thesis, fine layered well log data from the North Sea were selected with a depth range of 1600m to 1740m for upscaling using an MCMC implementation. The results allow us to automatically identify important depths where interfaces should be located, along with quantitative estimates of uncertainty in data. Specifically, interfaces in the example are required near depths of 1,650m, 1,695m, 1,710m, and 1,725m. Therefore, the number and location of blocked layers can be effectively quantified in spite of uncertainties in upscaling log data.

This study utilized (a) actual measured agricultural water use along with (b) geostatistical techniques, (c) crop simulation models, and (d) general circulation models (GCMs) to assess irrigation demand and the uncertainty associated with demand projections at spatial scales relevant to water resources management. In the first part of the study, crop production systems in Southwest Georgia are characterized and the crop simulation model error that may be associated with aggregated model inputs is estimated for multiple spatial scales. In the second portion of this study, a methodology is presented for characterizing regional irrigation strategies in the Lower Flint River basin and estimating regional water demand. Regional irrigation strategies are shown to be well represented with the moisture stress threshold (MST) algorithm, metered annual agricultural water use, and crop management data. Crop coefficient approaches applied at the regional scale to estimate agricultural water demand are shown to lack the interannual variability observed with this novel approach. In the third portion of this study, projections of regional agricultural demand under climate change in the Lower Flint River basin are presented. GCMs indicate a range of possible futures that include the possibility of relatively small changes in irrigation demand in the Lower Flint River basin. However, most of the GCMs utilized in this work project significant increases in median water demand towards the end of this century. In particular, results suggest that peak agricultural water demands in July and August may increase significantly. Overall, crop simulation models are shown to be useful tools for representing the intra-annual and interannual variability of regional irrigation demand. The novel approach developed may be applied to other locations in the world as agricultural water metering programs become more common.

Existing techniques measure soil moisture either at a point or over a large area many kilometers across. To bridge these two scales, we used the mobile cosmic-ray probe, or cosmic-ray rover, an instrument similar to the recently developed COSMOS probe, but bigger and mobile. This study explores the challenges and opportunities for making maps of soil moisture over large areas using the cosmic-ray rover. In 2012, soil moisture was mapped 22 times in a 25 km x 40 km survey area of the Tucson Basin at 1 km² resolution, i.e., at a scale comparable to that of a pixel for the Soil Moisture and Ocean Salinity (SMOS) satellite mission. The soil moisture distribution is influenced mainly by climatic variations, notably by the North American monsoon, which resulted in a systematic change in the regional variance as a function of the mean soil moisture.