International audience3D geological models commonly built to manage natural resources are much affected by uncertainty because most of the subsurface is inaccessible to direct observation. Appropriate ways to intuitively visualize uncertainties are therefore critical to draw appropriate decisions. However, empirical assessments of uncertainty visualization for decision making are currently limited to two-dimensional map data, while most geological entities are either surfaces embedded in a 3D space or volumes. This paper first reviews a typical example of decision making under uncertainty, where uncertainty visualization methods can actually make a difference. This issue is illustrated on a real Middle East oil and gas reservoir, looking for the optimal location of a new appraisal well. In a second step, we propose a user study that goes beyond traditional 2D map data, using 2.5D pressure data for the purposes of well design. Our experiments study the quality of adjacent versus coincident representations of spatial uncertainty as compared to the presentation of data without uncertainty; the representations quality is assessed in terms of decision accuracy. Our study was conducted within a group of 123 graduate students specialized in geology
Effective workflows for translating Earth models into simulation models require grids that preserve geologic accuracy, offer flexible resolution control, integrate tightly with upscaling, and can be generated easily. Corner-point grids and pillar-based unstructured grids fail to satisfy these objectives; hence, a truly 3D unstructured approach is required. This paper describes unstructured cutcell gridding tools that address these needs and improve the integration of our overall reservoir-modeling workflows.The construction of simulation grids begins with the geologic model: a numerical representation of the reservoir structure, stratigraphy, and properties. Our gridding uses a geochronological (GeoChron) map from physical coordinates to an unfaulted and unfolded depositional coordinate system. The mapping is represented implicitly on a tetrahedral mesh that conforms to faults, and it facilitates accurate geostatistical modeling of static depositional properties. In the simplest use case, we create an explicit representation of the geologic model as an unstructured polyhedral grid. Away from faults and other discontinuities, the cells are hexahedral, highly orthogonal, and arranged in a structured manner. Geometric cutting operations create general polyhedra adjacent to faults and explicit contact polygons across faults. The conversion of implicit models to explicit grids is conceptually straightforward, but the implementation is nontrivial because of the limitations of finite precision arithmetic and the need to remove small cells formed in the cutting process.In practice, simulation grids are often constructed at coarser resolutions than Earth models. Our implementation of local grid coarsening and refinement exploits the flexibility of unstructured grids to minimize upscaling errors and to preserve critical geologic features. Because the simulation grid and the geologic model are constructed by use of the same mapping, fine cells can be nested exactly inside coarse cells. Therefore, flow-based upscaling can be applied efficiently without resampling onto temporary local grids. This paper describes algorithms and data structures for constructing, storing, and simulating cut-cell grids. Examples illustrate the accurate modeling of normal faults, y-faults, overturned layers, and complex stratigraphy. Flow results, including a fieldsector model, show the suitability of cut-cell grids for simulation.
Historically it has been a challenge to rapidly produce a geomodel that can honor the detailed form of complex faulting and folding, while enabling sensible property modeling and that is tailored to fluid flow simulations. In structurally complex areas, the construction of accurate 3D geological models is often impeded by the complexity of the fault framework, the resulting layer segmentation, "multi-z" horizons in compressive settings and steeply dipping to overturned layers. In particular, standard geocellular models, such as pillar grids, may fail to honor complex structural features. To address those issues, methodologies using a mapping between the geological space and a 3D parametric space — often referred to as depositional space — have been described in the literature for geological grid construction and property population. Using case examples of structurally complex settings, we illustrate a depositional unstructured grid construction workflow. Compared to known methodologies, the depositional space is computed using a geomechanically-based approach. We illustrate that the methodology allows for complex structural configurations to be effectively modeled and transformed into a geocellular model honoring the full structural complexity. Our depositional unstructured model can then be populated with properties and used directly for flow simulations.
Effective workflows for translating earth models into simulation models require grids that preserve geologic accuracy, offer flexible resolution control, integrate tightly with upscaling, and can be generated easily. Corner-point grids and pillar-based unstructured grids fail to satisfy these objectives; hence, a truly 3D unstructured approach is required. This paper describes unstructured cut-cell gridding tools that address these needs and improve the integration of our overall reservoir modeling workflows. The construction of simulation grids begins with the geologic model: a numerical representation of the reservoir structure, stratigraphy, and properties. Our gridding utilizes a geochronological (GeoChron) map from physical coordinates to an unfaulted and unfolded depositional coordinate system. The mapping is represented implicitly on a tetrahedral mesh that conforms to faults, and it facilitates accurate geostatistical modeling of static depositional properties. In the simplest use case, we create an explicit representation of the geologic model as an unstructured polyhedral grid. Away from faults and other discontinuities, the cells are hexahedral, highly orthogonal, and arranged in a structured manner. Geometric cutting operations create general polyhedra adjacent to faults and explicit contact polygons across faults. The conversion of implicit models to explicit grids is conceptually straightforward, but the implementation is nontrivial due to the limitations of finite precision arithmetic and the need to remove small cells formed in the cutting process. In practice, simulation grids are often constructed at coarser resolutions than earth models. Our implementation of local grid coarsening and refinement exploits the flexibility of unstructured grids to minimize upscaling errors and preserve critical geologic features. Because the simulation grid and the geologic model are constructed using the same mapping, fine cells can be nested exactly inside coarse cells. Therefore, flow-based upscaling can be applied efficiently without resampling onto temporary local grids. This paper describes algorithms and data structures for constructing, storing, and simulating cut-cell grids. Examples illustrate accurate modeling of normal faults, y-faults, overturned layers, and complex stratigraphy. Flow results, including a field sector model, show the suitability of cut-cell grids for simulation.
This reference is for an abstract only. A full paper was not submitted for this conference. Abstract 1 Introduction 3D visualization of flow simulation results is valuable in addressing field development issues such as appropriate placement of infill wells. However, integration of static and dynamic uncertainty in reservoir management decisions often lacks proper visualization methods - typically, alternative reservoir models are considered one after another, or, at best, local averages and "uncertainty maps" of hydrocarbon indicators or productivity indexes are viewed successively. Whereas uncertainty can dramatically impact reservoir performance, it is therefore often disregarded or misestimated during the decision making process. In this paper, we propose new ways of visualizing both the reservoir parameter values and associated local uncertainty, by exploiting the latest capacities of modern graphics cards (GPUs). Such visualization provides clear advantage over conventional techniques when analyzing and communicating reservoir modeling and flow simulation results. A case study illustrates that the resulting images of reservoir pressures and fluid saturations of multiple dynamic models are very intuitive and easily visually interpretable. Applications to reservoir management are numerous, for instance: well targeting to reduce geological uncertainty while maximizing encountered net-to-gross; risks associated to hydraulic fracturing and fault seal integrity; pore pressure uncertainty. 2 Methodology Typically, reservoir uncertainty is sampled by a perturbation of the unknown geological features which significantly contribute to reservoir uncertainty, e.g. fault transmissibility, local oil saturation and net-to-gross ratio, etc. Massonnat, 2000, Corre et al., 2000, Charles et al., 2001. These perturbed features are then used as input data of flow simulators, resulting in possibly radically different oil recovery scenarii. We approximate the local probability density function (pdf) of the flow simulation results with their discrete distribution Qureshi and Dimitrakopoulos, 2004, Thore et al., 2002. The local pdf can be simplified in uncertainty metrics such as variation coefficient or interquartile range. A challenge is then to provide intuitive ways of visualizing such local uncertainty in real time. Several uncertainty visualization methods are described in the literature Pang et al., 1997, Johnson and Sanderson, 2003, Griethe and Schumann, 2006, but few apply to reservoir issues as uncertainty display can obscure interesting reservoir features. Our approaches are inspired from annotation-based methods, which typically avoid such interferences as only little data are hidden by the uncertainty annotations Cedilnik and Rheingans, 2000. We map local reservoir uncertainty to either texture or blur intensity (figure 1), in a similar fashion as Rhodes et al. 2003 and Kosara et al. 2001. Both methods benefit from GPU hardware acceleration, making extensive use of shaders (parallel GPU computation) and framebuffer objects (off-screen rendering) for maximal efficiency. Nevertheless, both can be run on consumer graphics hardware. 3 Application to the Cloudspin reservoir We demonstrate the usefulness of our visualization tools on a set of pressure flow simulation results, computed on the Cloudspin reservoir. Key uncertain parameters were: - the oil behavior, quantified by three PVT tables; - the local pore volume of the reservoir; - the permeability and transmissibility fields of the reservoir; - the connate water saturation. Other sources of uncertainty were considered negligible in this study. We combined the selected uncertain parameters when running flow simulation, ending up with 27 possible pressure maps. Each pressure map was captured at different time-steps of the reservoir development. For each time step, the local uncertainty was sampled using a variation coefficient metric on the local pdfs. Pressure uncertainty behaviour could thus be studied through time. 4 Results The uncertainty metrics computed at each time step were successively displayed using our texture-based uncertainty visualization method (figure 2). These displays reveal the displacement of an uncertainty front, starting from production well at initial time step and moving towards the limits of the reservoir. This uncertainty front can be interpreted as the way depletion propagates around producer well: the size of the depleted area increases as production time increases, but uncertainties affect how the pressure drop propagates in the reservoir. Such images could be extremely useful in field management, for reservoir pressure directly affects oil recovery at production wells. 5 Conclusion Integrated uncertainty visualization is valuable to understand uncertainty behaviour in reservoir exploitation. We have shown a typical example on pressure uncertainty; our tools revealed the displacement of an uncertainty front, which could then be interpreted as the propagation of the pressure drop around the production well through time, with uncertainty at the boundaries of the depleted area. Nevertheless, such tools can help in a wide range of other reservoir applications involving uncertainty, such as field development in the presence of uncertainty, or support to the evaluation of locations where new data should be acquired. Furthermore, they can be useful for communication purposes, for a single image with joint data and uncertainty conveys more information than traditional visualization methods and is much easier to interpret than the whole set of possible scenarii. References A. Cedilnik and P. Rheingans. Procedural annotation of uncertain information. Proceedings of the 11th IEEE Visualization 2000 Conference (VIS 2000), 2000. T. Charles, J. Gumn, B. Corre, G. Vincent, and O. Dubrule. Experience with the quantification of subsurface uncertainties. SPE 68703, 2001. B. Corre, P. Thore, V. de Feraudry, and G. Vincent. Integrated uncertainty assessment for project evaluation and risk analysis. SPE 65205, 2000. H. Griethe and H. Schumann. The visualization of uncertain data: Methods and problems. Proceedings of SimVis 2006, SCS Publishing House, pages 143–156, 2006. C. Johnson and A. Sanderson. A next step: Visualizing errors and uncertainty. Computer Graphics and Applications, IEEE, 23(5):6–10, 2003. R. Kosara, S. Miksch, and H. Hauser. Semantic depth of field. Proceedings of the IEEE symposium on Information Visualization, pages 97–104, 2001. G. Massonnat. Can we sample the complete geological uncertainty space in reservoir-modeling uncertainty estimates? SPE Journal, 5(1):46–59, 2000. A. Pang, C. Wittenbrink, and S. Lodha. Approaches to uncertainty visualization. The Visual Computer, 13(8): 370–390, 1997. S. E. Qureshi and R. Dimitrakopoulos. Comparison of stochastic simulation algorithms in mapping spaces of uncertainty of non-linear transfer functions. Geostatistics Banff 2004, 14:959–968, 2004. P. Rhodes, R. Laramee, R. Bergeron, and T. Sparr. Uncertainty visualization methods in isosurface rendering. EUROGRAPHICS 2003 Short Papers, pages 83–88, 2003. P. Thore, A. Shtuka, M. Lecour, T. Ait-Ettajer, and R. Cognot. Structural uncertainties: Determination, management and applications. Geophysics, 67(3):840–852, 2002.
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