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Two approaches are traditionally used to build numerical models for facies distributions within a reservoir. Pixel-based techniques aim at generating simulated realizations that honor the well data values, and reproduce a given variogram which models two-point spatial correlation. However, because the variogram cannot look at spatial continuity between more than two locations at a time, pixel-based algorithms give poor representations of the actual facies geometries. In contrast, object-based techniques allow reproducing crisp geometries, but the conditioning on well data requires iterative ``trial-anderror'' corrections, which can be time-consuming, particularly when the data are dense with regard to the average object size. This paper presents a new approach that combines the easy conditioning of pixel-based algorithms with the ability to reproduce ``shapes'' of object-based techniques, without being too time and memory demanding. In this new approach, the complex geological structures expected to be present in the reservoir are characterized by multiple-point statistics, which express joint variability at many more than two locations at a time. Such multiple-point statistics cannot be inferred from typically sparse well data but could be read from training images depicting the expected subsurface heterogeneities. A training image need not carry any locally accurate information on the reservoir; it need only reflect a prior stationary geological/structural concept. Thus training images can be generated by object-based algorithms freed of the constraint of data conditioning. The multiple-point statistics inferred from the training image(s) are then exported to the reservoir model, where they are anchored to the well data using a pixel-based sequential simulation algorithm. * Now with Chevron Petroleum Technology Co. This algorithm is tested for the simulation of a turbidite system where flow is controlled by meandering channels with cross-bedding. The training image reflecting the channel patterns is an unconditional realization generated by an objectbased algorithm. The final simulated numerical models reproduce these channel patterns, and honor exactly all well data values at their locations. The methodology proposed appears to be practical, general, and fast.

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Abstract. Geological uncertainty quantification is critical to subsurface modeling and prediction, such as groundwater, oil or gas, and geothermal resources, and needs to be continuously updated with new data. We provide an automated method for uncertainty quantification and the updating of geological models using borehole data for subsurface developments within a Bayesian framework. Our methodologies are developed with the Bayesian evidential learning protocol for uncertainty quantification. Under such a framework, newly acquired borehole data directly and jointly update geological models (structure, lithology, petrophysics, and fluids), globally and spatially, without time-consuming model rebuilding. To address the above matters, an ensemble of prior geological models is first constructed by Monte Carlo simulation from prior distribution. Once the prior model is tested by means of a falsification process, a sequential direct forecasting is designed to perform the joint uncertainty quantification. The direct forecasting is a statistical learning method that learns from a series of bijective operations to establish “Bayes–linear-Gauss” statistical relationships between model and data variables. Such statistical relationships, once conditioned to actual borehole measurements, allow for fast-computation posterior geological models. The proposed framework is completely automated in an open-source project. We demonstrate its application by applying it to a generic gas reservoir dataset. The posterior results show significant uncertainty reduction in both spatial geological model and gas volume prediction and cannot be falsified by new borehole observations. Furthermore, our automated framework completes the entire uncertainty quantification process efficiently for such large models.

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A new geostatistical approach, known as multiple-point statistics (MPS) simulation, recently has been proposed to generate 3D depositional facies models that integrate both large-scale information derived from seismic data and fine-scale information derived from well logs, cores, and analog studies. In this paper, the practicality, flexibility, and CPU advantage of this new approach are demonstrated through the modeling of an actual deepwater turbidite reservoir. First, based on well-log interpretation and a global geological understanding of the reservoir architecture, a training image depicting sinuous sand bodies is generated using a nonconditional object-based simulation algorithm. Then, disconnected sand bodies are interpreted from seismic amplitude data using a principal component cluster analysis technique, while a sand probability cube is generated using a principal component proximity transform of the same seismic. Multiple-point geostatistics allows simulating multiple realizations of channel bodies similar to the training image, constrained to the local sand probabilities, partially interpreted sand bodies, and well-log data. As illustrated in this paper, to account for uncertainty about the geometry of the sand bodies, different training images associated with alternative conceptual models proposed by the geologists can be considered.

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