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- Resumen es exacto "Reservoir simulation is an essential tool for the study of subsurface flow and transport phenomena in the context of energy and environmental applications. To create a first model of the petrophysical properties of the reservoir, data from geophysical surveys are used. This is a discrete model (called a static model or fine grid), defined with a support scale Delta, which may vary according to the spatial direction. In general, simulate the flow in the reservoir directly on the fine grid is too expensive. Therefore, an upscaling procedure is usually performed, that allows transferring the petrophysical properties of the reservoir from the fine grid to a coarser simulation grid (or dynamic model), with a characteristic spatial scale (or aggregation scale) lambda > Δ, on which it is more feasible to perform the simulations. In particular, this thesis focuses on the transformation of the hydraulic conductivity of the fine grid (k(r), r is the position vector on the fine grid), into an equivalent one (Keq), defined on the coarse grid, since this magnitude is critical for the flow structure in the reservoir. On the other hand, we use a stochastic approach, in which, instead of assessing a deterministic value of Keq from a single image or map of the reservoir, we consider an ensemble of realizations that can represent it, and then analyze the distribution of Keq values (Keq probability density function, or PDF) associated with that ensemble. This allows us to consider not only the ensemble average or mean value of Keq, but also the higher order (Gaussian) moments of the PDF, such as variance and skewness. In this thesis, different local and global upscaling methods (or formulations) are compared, including a new one based on viscous energy dissipation, and a local method is retained for the rest of the work. The way in which the components of higher hydraulic conductivity in the reservoir are spatially organized (especially, the way they are connected), has a major impact on Keq. In the second part of the thesis, the interrelationship between connectivity, the aggregation scale λ, and Keq is addressed, working on two types of model reservoirs (or media) widely used as reference in the literature: multigaussian ones, which have a lognormal distribution of conductivities frequently observed in nature, for example for sandstone rocks, and binary ones, which are a simplified representation of reservoirs composed of multiple facies or flow units, domains or zones with different well-contrasted characteristic conductivities. For example, a domain dominated by sandstones (high conductivity) and another dominated by pelites or shales (low conductivity). In both types, we analyzed a wide range of connectivity scenarios, considering different “connectivity structures”, in which the high conductivity facies have an increased or decreased connectivity with respect to an intermediate case, given by the multigaussian media (truncated for the binary case). In the case of multigaussian reservoirs, different degrees of heterogeneity are further modeled by varying the variance of the distribution of the fine grid conductivities, and the texture of heterogeneity by varying the covariance function (or variogram) and its correlation length (which gives the “grain size” of the heterogeneity). In this regard, one of the main results of the thesis shows how previous theoretical and numerical predictions by other authors, for the variation of Keq with λ in multigaussian media, are extended to a broader connectivity scenarios. For the case of binary media, we focus on the percolation of the high conductivity component of the reservoir, which has presented a challenge for upscaling since it involves the divergence of the REV (Representative Elemental Volume) and the lack of characteristic spatial scales. Different textures of heterogeneity are sampled by varying the proportion of the high conductivity component. The interrelationship between percolation, connectivity and Keq is studied in 2D and 3D reservoirs. It is concluded in this case that any influence of connectivity on Keq can be explained simply by a shift of the percolation threshold. The results presented in this thesis show that including explicit connectivity information is important in the calculation of Keq."
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