MCMC algorithm, integrated 4D seismic reservoir characterization and uncertainty analysis in a Bayesian framework

One of the important goals in petroleum exploration and production is to make quantitative estimates of a reservoir’s properties from all available but indirectly related surface data, which constitutes an inverse problem. Due to the inherent non-uniqueness of most inverse procedures, a deterministic solution may be impossible, and it makes more sense to formulate the inverse problem in a statistical Bayesian framework and to fully solve it by constructing the Posterior Probability Density (PPD) function using Markov Chain Monte Carlo (MCMC) algorithms. The derived PPD is the complete solution of an inverse problem and describes all the consistent models for the given data. Therefore, the estimated PPD not only leads to the most likely model or solution but also provides a theoretically correct way to quantify corresponding uncertainty. However, for many realistic applications, MCMC can be computationally expensive due to the strong nonlinearity and high dimensionality of the problem. In this research, to address the fundamental issues of efficiency and accuracy in parameter estimation and uncertainty quantification, I have incorporated some new developments and designed a new multiscale MCMC algorithm. The new algorithm is justified using an analytical example, and its performance is evaluated using a nonlinear pre-stack seismic waveform inversion application. I also find that the new technique of multi-scaling is particularly attractive in addressing model parameterization issues especially for the seismic waveform inversion. To derive an accurate reservoir model and therefore to obtain a reliable reservoir performance prediction with as little uncertainty as possible, I propose a workflow to integrate 4D seismic and well production data in a Bayesian framework. This challenging 4D seismic history matching problem is solved using the new multi-scale MCMC algorithm for reasonably accurate reservoir characterization and uncertainty analysis within an acceptable time period. To take advantage of the benefits from both the fine scale and the coarse scale, a 3D reservoir model is parameterized into two different scales. It is demonstrated that the coarse-scale model works like a regularization operator to make the derived fine-scale reservoir model smooth and more realistic. The derived best-fitting static petrophysical model is further used to image the evolution of a reservoir’s dynamic features such as pore pressure and fluid saturation, which provide a direct indication of the internal dynamic fluid flow.