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Streamline models are routinely used for waterflood optimization and management and are being extended to more complex processes (e.g., compositional simulation). Despite these new developments, no systematic study has examined the underlying numerical spatial and temporal discretization errors in streamline simulation and their convergence. Such studies are a prerequisite to determining the optimal density of streamlines during simulation and ensuring the resulting accuracy of the solution.In this paper, we first examine transverse spatial errors (e.g., errors resulting from the number or placement of streamlines). We provide an analytic proof and a numeric demonstration of the order of spatial convergence of the mass-balance discretization error. Both global and local calculations are performed, and they demonstrate the impact of stagnation regions on the order of convergence. A second transverse error arises for faulted grids, where lack of flux continuity at cell faces can lead to incorrect trajectories. These trajectory errors are of zeroth order and can be resolved only by introducing additional degrees of freedom into the streamline velocity model. Longitudinal spatial errors also arise and are associated with the inaccurate calculation of time of flight across cells.We show that the commonly used algorithm for corner-point cells leads to inaccurate time-of-flight calculations for stratigraphic grids, depending upon aspect ratio. We provide a simple and exact means of calculating the time of flight for arbitrary corner-point cells, or unstructured grids, in two or three dimensions, for either compressible or incompressible flow. Finally, using this new time-of-flight formulation, we analyze a series of cross-sectional finite-difference simulations to identify grid-orientation errors in the numerical calculation of flux and spatial error.

INTRODUCCIÓNCon anterioridad al crecimiento económico y tecnológico que se precipita en la segunda mitad del siglo XX, la agricultura española era reconocible por su diversidad productiva, el carácter extensivo de los aprovechamientos, la importancia de las cosechas cerealistas en secano o la distribución de los bienes a cortas distancias. En ese contexto, la olivicultura tradicional se basaba en principios de economía orgánica y se aplicaban estrategias como las siguientes: trabajo humano intensivo; empleo del ganado como pieza básica en tanto que fuerza de trabajo y producción de estiércol; utilización de variedades adecuadas a las condiciones ecológicas locales y manejo inteligente de los reducidos e irregulares aportes pluviométricos (disminución de escorrentías, limitación de la evaporación por capilaridad, eliminación de competencia vegetal, uso de amplios marcos de plantación, etc.). Era habitual y acusada, en todo caso, la alternancia de buenas y malas cosechas (por ser el olivo planta vecera), asumida como tributo inevitable de un sistema sostenido en el tiempo pero limitado desde el punto de vista productivo (Naredo Pérez, 1983). El sistema fue rentable hasta que los costes de recolección, el mayor gasto que afrontaban las

En 2009, la comunidad autónoma de Andalucía conmemoró el vigésimo aniversario de la aprobaciôn por el Parlamento andaluz, de la ley 2/89 que estableció el primer Catálogo de zonas naturales protegidas. Esta ley ha permitido la creación del actual RENPA (Red de Espacios Protegidos de Andalucía) que ha conseguido homogeneizar la gestion de mencionadas areas. En dicho catálogo, la categoria de Parque Natural juega un papel fundamental desde un punto de vista territorial y socioeconómico. Los Parques Naturales disponen de una serie de herramientas de planificación y gestion que, inicialmente, provocaron las reticencias de un sector de la población y del partido de la oposición. Los habitantes lamentaron las restricciones de los usos tradicionales agro-silvopastorales. La oposición politico argumentaba que dichas limitaciones de los usos tradicionales del territorio, acelerarían el cierre de empresas y el éxodo rural, ya iniciado, de la población local. La Consejeria andaluza de Medio Ambiente respondió rápidamente a estas criticas, lanzando una serie de ayudas publicas y de financiación con el objeto de conseguir el desarrollo económico de estos territorios. Igualmente, creó una marca de comercialización de todos los productos fabricados u obtenidos en los espacios naturales protegidos. Estas medidas calmaron las tensiones iniciales pero, tras veinte anos de la ley 2/89, un nuevo debate ha surgido : ciertos municipios localizados en los espacios naturales protegidos más frecuentados, han comenzado a protestor en contra de las herramientas de gestion, argumentando que reducen considerablemente sus perspectivas económicas en relación a los municipios situados fuera de las zonas protegidas. El caso paradigmático que ha conducido a una verdadera «revuelta de alcaldes» y que ha puesto en jaque la credibilidad de la Administración andaluza, ha sido la construcción de un gran hotel, El Algarrobico, en pleno parque natural de Cabo de Gata-Nijar. Las organizaciones ecologistas y ciudadanas han conseguido paralizar su abertura por via judicial. Este articulo tiene como objeto reflexionar sobre este nuevo episodio de tensión entre conservation y desarrollo en los espacios naturales protegidos de Andalucía.

Understanding and capturing the uncertainty of the reservoir are keys to predicting its performance and making operational decisions. Conventional industry practices with a single or three (high-mid-low case) models have little ability to describe the full complexity of subsurface uncertainty and often yield poor performance in forecasting. To improve our understanding of the effect of reservoir uncertainty in performance, we need to use an ensemble of models which spans the full space of the uncertain parameters. These parameters may range widely from global parameters, such as water-oil contact and fault transmissibility, to cell-based properties, such as heterogeneous permeability and porosity. While it is ideal to explore all the possible parameter combinations, doing so can easily result in millions of models and become impractical for history matching and forecasting purposes. In this work we present a two-step history matching workflow where the uncertainties in the local heterogeneity and global parameters are investigated sequentially and yet in a manageable manner. The workflow begins with a geological model built based upon available information. The local geological heterogeneity, which cannot be readily determined from the information such as seismic images or well logs, is examined in the first step of the workflow. We create an ensemble of 103 to 105 models which span the uncertainty space for properties like permeability, porosity and/or net-to-gross but all are constrained to geostatistical data such as ranges, standard deviations and variograms. To effectively reduce the ensemble size, we implement the dynamic fingerprinting technique, a method based on streamline information (time of flight or drainage time), to screen and cluster the models. The concept behind this methodology is that for each distinct property realization, a given production schedule will generate a flow pattern which, like a fingerprint, is unique to that realization. This method is highly efficient since the time required to obtain the characteristic flow pattern is significantly shorter than the time of interest (typically the whole production history). The fingerprints from individual realizations are collected and clustered according to their principal flow pattern through single value decomposition. Each cluster aggregates a set of model realizations that despite their apparent difference in the model space, all correspond to similar principal flow trends. A single representative is then chosen from each cluster. The second step of the workflow aims to examine the uncertainties of the global parameters. For each representative obtained from the first step, we implement the standard workflow for Design of Experiment and proxy modeling to construct response surfaces as functions of global parameters. Algorithms such as Markov Chain Monte Carlo are then implemented to perform vast sampling and condition the models to the history data. The end result is a small set of models that are based on realistic geology, preserve flow-relevant subsurface uncertainty, and are conditioned to production data. The proposed workflow, which can be referred to as the probability history matching (PHM) workflow, provides an efficient and effective way to select representatives and condition to historical data. The selected models can be used for making forecasts and support development planning under uncertainty. An application of this workflow is shown on a real-world field example.