A Bayesian Sampling Framework With Seismic Priors for Data Assimilation and Uncertainty Quantification

Nejadi, Siavash (University of Calgary) | Kazemi, Nasser (University of Calgary) | Hubbard, Stephen M. (University of Calgary) | Gates, Ian D. (University of Calgary)


We present a novel sampling algorithm for characterization and uncertainty quantification of heterogeneous multiple facies reservoirs. The method implements a Bayesian inversion framework to estimate physically plausible porosity distributions. This inversion process incorporates data matching at the well locations and constrains the model space by adding a priori information about the sub-surface structure using a seismic impedance volume. The new framework improves predictive performance and the geological realism of the assimilated ensemble through an efficient parameter estimation. The new parameter estimation process enables conditioning data assimilation to characterize the main features of geological uncertainty such as structural, stratigraphic, facies, and petrophysical properties.

The proposed workflow uses an ensemble-based Markov Chain Monte Carlo approach combined with sampling probability distributions that are physically meaningful. Moreover, the method targets geostatistical modeling to specific zones in the reservoir. Accordingly, it improves fulfilling the inherent stationarity assumption in geostatistical simulation techniques. Parameter sampling and geostatistical simulations are calculated through an inversion process. In other words, the models fit the known porosity field at the well locations and are structurally consistent within main reservoir compartments, zones, and layers obtained from the seismic impedance volume. The new sampling algorithm ensures that the automated history matching algorithm maintains diversity among ensemble members avoiding underestimation of the uncertainty in the posterior probability distribution.

We evaluate the efficiency of the sampling methodology on a synthetic model of a waterflooding field. The predictive capability of the assimilated ensemble is assessed by using production data and dynamic measurements. Also, the qualities of the results are examined by comparing the geological realism of the assimilated ensemble with the reference probability distribution of the model parameters and computing the predicted dynamic data mismatch. Our numerical examples show that incorporating the seismically constrained models as prior information results in an efficient model update scheme and favorable history matching.