Publications

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In this study we developed an efficient Bayesian inversion framework for interpreting marine seismic Amplitude Versus Angle and Controlled-Source Electromagnetic data for marine reservoir characterization. The framework uses a multi-chain Markov-chain Monte Carlo sampler, which is a hybrid of DiffeRential Evolution Adaptive Metropolis and Adaptive Metropolis samplers. The inversion framework is tested by estimating reservoir-fluid saturations and porosity based on marine seismic and Controlled-Source Electromagnetic data. The multi-chain Markov-chain Monte Carlo is scalable in terms of the number of chains, and is useful for computationally demanding Bayesian model calibration in scientific and engineering problems. As a demonstration, the approach is used to efficiently and accurately estimate the porosity and saturations in a representative layered synthetic reservoir. The results indicate that the seismic Amplitude Versus Angle and Controlled-Source Electromagnetic joint inversion provides better estimation of reservoir saturations than the seismic Amplitude Versus Angle only inversion, especially for the parameters in deep layers. The performance of the inversion approach for various levels of noise in observational data was evaluated — reasonable estimates can be obtained with noise levels up to 25%. Sampling efficiency due to the use of multiple chains was also checked and was found to have almost linear scalability.

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We present the development of a parallel Markov Chain Monte Carlo (MCMC) method called SAChES, Scalable Adaptive Chain-Ensemble Sampling. This capability is targed to Bayesian calibration of com- putationally expensive simulation models. SAChES involves a hybrid of two methods: Differential Evo- lution Monte Carlo followed by Adaptive Metropolis. Both methods involve parallel chains. Differential evolution allows one to explore high-dimensional parameter spaces using loosely coupled (i.e., largely asynchronous) chains. Loose coupling allows the use of large chain ensembles, with far more chains than the number of parameters to explore. This reduces per-chain sampling burden, enables high-dimensional inversions and the use of computationally expensive forward models. The large number of chains can also ameliorate the impact of silent-errors, which may affect only a few chains. The chain ensemble can also be sampled to provide an initial condition when an aberrant chain is re-spawned. Adaptive Metropolis takes the best points from the differential evolution and efficiently hones in on the poste- rior density. The multitude of chains in SAChES is leveraged to (1) enable efficient exploration of the parameter space; and (2) ensure robustness to silent errors which may be unavoidable in extreme-scale computational platforms of the future. This report outlines SAChES, describes four papers that are the result of the project, and discusses some additional results.

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Compressible jet-in-crossflow interactions are poorly simulated using Reynolds-Averaged Navier Stokes (RANS) equations. This is due to model-form errors (physical approximations) in RANS as well as the use of parameter values simply picked from literature (hence- forth, the nominal values of the parameters). Previous work on the Bayesian calibration of RANS models has yielded joint probability densities of C = (Cµ;Cϵ2;Cϵ1), the most influential parameters of the RANS equations. The calibrated values were far more predictive than the nominal parameter values and the advantage held across a range of freestream Mach numbers and jet strengths. In this work we perform Bayesian calibration across a range of Mach numbers and jet strengths and compare the joint densities, with a view of determining whether compressible jet-in-crossflow could be simulated with either a single joint probability density or a point estimate for C. We find that probability densities for ;Cϵ2 agree and also indicate that the range typically used in aerodynamic simulations should be extended. The densities for ;Cϵ1 agree, approximately, with the nominal value. The densities for ;Cµ do not show any clear trend, indicating that they are not strongly constrained by the calibration observables, and in turn, do not affect them much. We also compare the calibrated results to a recently developed analytical model of a jet-in-cross flow interaction. We find that the values of C estimated by the analytical model delivers prediction accuracies comparable to the calibrated joint densities of the parameters across a range of Mach numbers and jet strengths.

The k-ε turbulence model has been described as perhaps “the most widely used complete turbulence model.” This family of heuristic Reynolds Averaged Navier-Stokes (RANS) turbulence closures is supported by a suite of model parameters that have been estimated by demanding the satisfaction of well-established canonical flows such as homogeneous shear flow, log-law behavior, etc. While this procedure does yield a set of so-called nominal parameters, it is abundantly clear that they do not provide a universally satisfactory turbulence model that is capable of simulating complex flows. Recent work on the Bayesian calibration of the k-ε model using jet-in-crossflow wind tunnel data has yielded parameter estimates that are far more predictive than nominal parameter values. Here we develop a self-similar asymptotic solution for axisymmetric jet-in-crossflow interactions and derive analytical estimates of the parameters that were inferred using Bayesian calibration. The self-similar method utilizes a near field approach to estimate the turbulence model parameters while retaining the classical far-field scaling to model flow field quantities. Our parameter values are seen to be far more predictive than the nominal values, as checked using RANS simulations and experimental measurements. They are also closer to the Bayesian estimates than the nominal parameters. A traditional simplified jet trajectory model is explicitly related to the turbulence model parameters and is shown to yield good agreement with measurement when utilizing the analytical derived turbulence model coefficients. The close agreement between the turbulence model coefficients obtained via Bayesian calibration and the analytically estimated coefficients derived in this paper is consistent with the contention that the Bayesian calibration approach is firmly rooted in the underlying physical description.

Compressible jet-in-crossflow interactions are poorly simulated using Reynolds-Averaged Navier Stokes (RANS) equations. This is due to model-form errors (physical approximations) in RANS as well as the use of parameter values simply picked from literature (hence- forth, the nominal values of the parameters). Previous work on the Bayesian calibration of RANS models has yielded joint probability densities of C = (Cµ;Cϵ2;Cϵ1), the most influential parameters of the RANS equations. The calibrated values were far more predictive than the nominal parameter values and the advantage held across a range of freestream Mach numbers and jet strengths. In this work we perform Bayesian calibration across a range of Mach numbers and jet strengths and compare the joint densities, with a view of determining whether compressible jet-in-crossflow could be simulated with either a single joint probability density or a point estimate for C. We find that probability densities for ;Cϵ2 agree and also indicate that the range typically used in aerodynamic simulations should be extended. The densities for ;Cϵ1 agree, approximately, with the nominal value. The densities for ;Cµ do not show any clear trend, indicating that they are not strongly constrained by the calibration observables, and in turn, do not affect them much. We also compare the calibrated results to a recently developed analytical model of a jet-in-cross flow interaction. We find that the values of C estimated by the analytical model delivers prediction accuracies comparable to the calibrated joint densities of the parameters across a range of Mach numbers and jet strengths.

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