Streamline-based methods can be used as effective post-processing tools for assessing flow patterns and well allocation factors in reservoir simulation. This type of diagnostic information can be useful for a number of applications, including visualization, model ranking, upscaling validation, and optimization of well placement or injection allocation. In this paper, we investigate finite-volume methods as an alternative to streamlines for obtaining flow diagnostic information. Given a computed flux field, we solve the stationary transport equations for tracer and time of flight by use of either single-point upstream (SPU) weighting or a truly multidimensional upstream (MDU) weighting scheme. We use tracer solutions to partition the reservoir into volumes associated with injector/producer pairs and to calculate fluxes (well allocation factors) associated with each volume. The heterogeneity of the reservoir is assessed with time of flight to construct flowcapacity/storage-capacity (F-vs.-U) diagrams that can be used to estimate sweep efficiency. We compare the results of our approach with streamline-based calculations for several numerical examples, and we demonstrate that finite-volume methods are a viable alternative. The primary advantages of finite-volume methods are the applicability to unstructured grids and the ease of implementation for general-purpose simulation formulations. The main disadvantage is numerical diffusion, but we show that a MDU weighting scheme is able to reduce these errors.

International audienceThis work presents a new subdivision method to upscale absolute permeability fields. This process, called two-step method, consists in (i) solving micro-scale equations on subdomains obtained from the full domain regular decomposition and (ii) solve a second upscaling with Darcy’s law on the permeability fields obtained in the first step. The micro-scale equations used depend on the case studied. The two-step upscaling process is validated on randomly generated Darcy-scale permeability fields by measuring the numerical error induced by upscaling. The method is then applied to real domains obtained from sandstone micro-tomographic images. The method specificities due to pore-space structure are discussed. The main advantage of the two-step upscaling method resides in the drastic reduction of computational costs (CPU time and memory usage) while maintaining a numerical error similar to that of other upscaling procedures. This new upscaling method may improve permeability predictions by the use of finer meshes or larger sample volumes

Ideally, probabilistic forecasts improve the decision quality, capture upsides and mitigate downsides. Unfortunately, one of the risks associated with probabilistic forecasts is the possible creation of a large number of models with similar properties or responses. Methods to identify representative models from an ensemble of models are thus necessary. In this paper, we extend the use of distance-based methods, developed at Stanford Center for Reservoir Forecasting, and Kernel clustering techniques to the selection of models for economic decision-making. Using mathematical tools, the large set of models in a high-dimensional space is mapped to a low-dimensional space and a distance function based on several prediction-related quantities is used to quantify the similarities and dissimilarities among an ensemble of history-matched models. We then construct a small portfolio of models with a diverse range of prediction performances for less cost-intensive probabilistic forecasts. The approach is applied to an offshore gas condensate field in the Asia-Pacific region. Two possible development plans were competing: continue to produce from existing geological structures, or extend the development to accumulations connected through a saddle in the carbonate reservoir. The decision was impacted by the uncertainty on remaining volumes in place and connectivity between structures. Based on the uncertainty management plans, 925 history-matched models are generated with genetic algorithms. Within the context of distance-based modeling, an application-tailored distance function between models is designed, balancing static (scenario independent) and dynamic (scenario dependent) properties of the models. Then, eight diverse and representative models are selected among the 925 models. We show that the eight selected models, while offering an equally good history-match, cover well the uncertainty ranges of the static and dynamic properties considered. The selected models can be used to evaluate different possible development scenarios for final business decision making.

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This paper describes the combined use of streamline and geostatistical sequential simulation to a Middle Eastern reservoir with a long production history and a significant number of wells. In the algorithm presented, streamlines are used to delineate drainage regions for producers that are to be history matched. The time-of-flight of the streamlines is used to establish the relationship between historical rate mismatch and permeability of the drainage region. Rather than correcting permeability directly, we use the corrections supplied by the streamlines to constrain the geostatistical algorithms and thereby ensure a consistent geological scenario at every iteration in the process. Before applying the methodology to a real field case, we use a simple synthetic example to explain the main points. Finally, we show the application of the history-matched model for evaluating an infill well prospect and how streamline simulation and finite-difference simulation are used as complementary tools to increase the predictive power of the numerical model of the reservoir. Introduction Calibration of reservoir properties, such as permeability, to production history is an ill-posed inverse problem. The large number of model parameters and the complex nature of the constraints calls for adapted optimization techniques. Most research on history matching consists of finding suitable optimization techniques to handle such large inverse problems and provide a satisfactory solution for engineering purposes. A novel technique is proposed here, based on streamline simulation and geostatistics. It is validated on a synthetic field, and applied successfully to a carbonate reservoir in the Middle-East. The use of streamline-based techniques as a complement to finite-difference simulators arose when commercial streamline simulators proved their capacity to perform fast field simulations1,2. Advantages and general drawbacks of streamlines have been discussed extensively3, and CPU speed is often cited as the most important advantage over finite-difference simulators. Because the practical resolution of inverse problems requires numerous forward function evaluations, having a fast simulation technique was a promising breakthrough for traditional trial-error history-matching methods. A number of streamline-based history-matching techniques have thus been developed and successfully investigated. Mappings between streamlines and water-cut errors were developed on 2D fivespot patterns4,5. Multiple well scenarios and assisted historymatching techniques were also elaborated6. Field situations soon followed; case studies showed the advantages of streamlines over finite-difference techniques on a field example7,8. New techniques evolved from this tool9,10,11. The methods developed set the stage for an efficient use of streamline simulation not only for their ability to run large simulations in a short time, but also to indicate regions within a reservoir that potentially cause mismatch between simulation and historical field data. Localization of error in space-time, initially a side product of streamline simulation, was in fact a major improvement for history-matching methods.