A Bayesian approach to causal and evidential analysis for uncertainty quantification throughout the reservoir forecasting process [electronic resource]
Keywords: Energy Resources Engineering.

In the oil and gas industry, decisions with often large financial implications and risks depend on quantities subject to substantial uncertainty. This uncertainty can be attributed to the lack of knowledge of the subsurface, as estimating subsurface parameters from data measurements of the response of the system is an inverse problem. Traditionally, these problems are addressed through deterministic inversion approaches, in which a single realization of subsurface parameters are sought such that their generated responses match the measured data. The prediction is then made by forward physical simulation of these sets of inverted model parameters. Further complicating the problem are potential inadequacies of the physical model. However, such approaches are typically iterative, computationally expensive, and their deterministic nature precludes realistic quantification of uncertainty. In this dissertation, we propose two probabilistic approaches to UQ formulated with a Bayesian framework, for two common prediction problems faced during the reservoir forecasting process: velocity model estimation and history matching. We begin by presenting a causal analysis for quantifying seismic uncertainty in sub-salt imaging applications. This workflow can be seen as an addition to conventional inversion methodologies, that generates multiple posterior velocity models that match observed seismic data, thereby enabling UQ on the seismic image. We introduce a novel geostatistical randomization method based on the Perlin Noise algorithm that accounts for prior information such as initial velocity estimates, illumination studies, and salt tectonics. To generate samples from the posterior, we introduce a dimension reduction of the velocity model using active subspaces followed by Weighted Kernel Density Estimation. The resulting posterior velocity models are migrated to yield a set of posterior seismic images. We apply this methodology to the SEAM Phase I model as a case study. We next consider uncertainty quantification for reservoir engineering applications that are typically addressed by history matching. We recognize that in many such circumstances, the prediction variable is far simpler than the reservoir model. We therefore develop an alternative paradigm to causal analysis termed evidential analysis, based on using statistical learning to directly infer the relationship between the data and prediction variable. This relationship, along with the actual measured data is used to produce a probabilistic estimate of the prediction. Prior information is used to construct prior reservoir models that serve to generate a training set of data-prediction variables for statistical regression. Depending on the nature of the variables and their underlying relationship, a variety of dimension reduction and regression techniques may be required. Such an approach avoids the difficult task of explicit inversion, and allows for easier incorporation of prior information into the prediction. This algorithm is demonstrated on a case study of a large Libyan Oil Reservoir. Evidential analysis thereby transforms the inversion problem into a statistical modeling problem. It provides an estimate of the posterior prediction uncertainty, but it does not generate the subsurface model parameters that correspond to those predictions. While the model parameters themselves are not required for decision making, they are often desired for quality checking, and for simulating other physical processes. Therefore, in the third part of this dissertation, we introduce a methodology for recovering the model parameters corresponding to the evidential analysis predictions. We specifically apply Sequential Importance Resampling to emphasize sampling model parameters that are consistent with the posterior predictions. This approach can also be applied for data assimilation, and providing updated predictions and model parameters as additional observed data becomes available. We again demonstrate this methodology on the Libyan Oil Reservoir.