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.

This content is only available via PDF.