Well data reveal reservoir layering with relatively high vertical resolution but are areally sparse, whereas seismic data have low vertical resolution but are areally dense. Improved reservoir models can be constructed by integrating these data. The proposed method combines stochastic seismic inversion, finer-scale well data, and geologic continuity models to build ensembles of geomodels.

Stochastic seismic inversions operating at the mesoscale (≈10 m) generate rock property estimates that are consistent with regional rock physics and true-amplitude imaged seismic data. These can be used in a cascading workflow to generate ensembles of fine-scale reservoir models, wherein each realization from the Bayesian seismic inversion is treated as an exact constraint for an associated finer scale stochastic model. We use two-point statistical models for the fine-scale model, modeling thickness and porosity of multiple facies directly. The update of these fine-scale models by the seismic constraints yields highly correlated truncated Gaussian distributions. These generate potentially rich pinchout behavior and flexible spatial connectivities in the fine scale model.

The seismic constraints confine the fine-scale models to a posterior subspace corresponding to the constraint hypersur-face. A Markov Chain Monte Carlo samples the posterior distribution in this subspace using projection methods that exploit the reduced dimensionality that comes with the exact constraints.

These methods are demonstrated in three-dimensional flow simulations on a cornerpoint grid, illustrating the effects of stratigraphic variability on flow behavior.

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