Kathleen M. Dyer

Bayesian Inference and Markov Chain Monte Carlo Sampling to Reconstruct a Contaminant Source on a Continental Scale

Abstract A methodology combining Bayesian inference with Markov chain Monte Carlo (MCMC) sampling is applied to a real accidental radioactive release that occurred on a continental scale at the end of May 1998 near Algeciras, Spain. The source parameters (i.e., source location and strength) are reconstructed from a limited set of measurements of the release. Annealing and adaptive procedures are implemented to ensure a robust and effective parameter-space exploration. The simulation setup is similar to an emergency response scenario, with the simplifying assumptions that the source geometry and release time are known. The Bayesian stochastic algorithm provides likely source locations within 100 km from the true source, after exploring a domain covering an area of approximately 1800 km × 3600 km. The source strength is reconstructed with a distribution of values of the same order of magnitude as the upper end of the range reported by the Spanish Nuclear Security Agency. By running the Bayesian MCMC algorit...

Sequential Monte-Carlo Framework for Dynamic Data-Driven Event Reconstruction for Atmospheric Release

The release of hazardous materials into the atmosphere can have a tremendous impact on dense populations. We propose an atmospheric event reconstruction framework that couples observed data and predictive computer-intensive dispersion models via Bayesian methodology. Due to the complexity of the model framework, a sampling-based approach is taken for posterior inference that combines Markov chain Monte Carlo (MCMC) and sequential Monte Carlo (SMC) strategies.

Model verification: synthetic single pattern simulations using seismic reflection data

During Phase 1 of the Weyburn Project (2000-2004), 4D reflection seismic data were used to map CO2 migration within the Midale reservoir, while an extensive fluid sampling program documented the geochemical evolution triggered by CO2-brine-oilmineral interactions. The aim of this task (3b.11) is to exploit these existing seismic and geochemical data sets, augmented by CO2/H2O injection and HC/H2O production data toward optimizing the reservoir model and thereby improving site characterization and dependent predictions of long-term CO2 storage in the Weyburn-Midale reservoir. Our current project activities have concentrated on completing and testing a stochastic inversion method that will identify reservoir models that optimize agreement between the observed and predicted seismic response. This report describes the results of a validation test that uses synthetic seismic data to identify optimal porosity/permeability distributions within the reservoir. The report partially fulfills deliverable D3: “Model verification: synthetic single pattern simulations” in the project’s statement of work. A future deliverable will describe verification activities related to the geochemical inversion algorithm. This work has been performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. Introduction When completed, our completed stochastic inversion tool will explicitly integrate reactive transport modeling, facies-based geostatistical methods, and a novel stochastic inversion technique to optimize agreement between observed and predicted storage performance. Such optimization will be accomplished through stepwise refinement of: 1) the reservoir model—principally its permeability magnitude and heterogeneity—and 2) geochemical parameters—primarily key mineral volume fractions and kinetic data. We anticipate that these refinements will facilitate significantly improved history matching and forward modeling of CO2 storage. Our tool uses the Markov Chain Monte Carlo (MCMC) methodology. Deliverable D1, previously submitted as a report titled “Development of a Stochastic Inversion Tool To Optimize Agreement Between The Observed And Predicted Seismic Response To CO2 Injection/Migration in the Weyburn-Midale Project” (Ramirez et al., 2009), described the stochastic inversion approach that will identify reservoir models that optimize agreement between the observed and predicted seismic response. The software that implements this approach has been completed and requires that its performance be verified. This document contains deliverable D3, a report that summarizes verification activities that evaluate the performance of the software and its ability to recover reservoir model permeabilities that optimize agreement between measured and predicted seismic reflection data. A future deliverable will describe verification activities that ensure recovery of geochemical parameters (mineral volume fraction, kinetic parameters) that optimize agreement between measured and predicted aqueous chemistry data.