Reservoir forecasting based on statistical functional analysis of data and prediction variables [electronic resource]
Keywords: Energy Resources Engineering.

In the contemporary petroleum industry, decisions involving large allocations of resources need to be made in the presence of considerable uncertainty. Forecasting problems are often formulated to predict the outcome (or the distribution on a set of outcomes) of a possible decision-alternative before the actual decision is made and the actual outcome is observed. Traditionally, such forecasting problems are addressed using data inversion problems as an often iterative Bayesian-predictive-inference. Data inversion problems estimate the subsurface model parameters given observations in the dynamic data. Any forecasts are evaluated as responses of the subsurface models obtained as a solution of the inversion problem. This forecasting paradigm shifts the focus from the forecast needed for making a good decision to the parameters of the model subsurface being estimated. Over the years, in some cases, this change in focus has caused a progress-trap situation where more detailed subsurface models with a more detailed uncertainty description are sought without considering whether the increased detail is informative to the eventual decision maker. Furthermore, this increased detail often needs more time for analysis and computation that may delay the forecast for the decision maker and even lead to missed opportunities. This dissertation seeks to take a step towards a forecasting paradigm that focuses on the forecast variables that directly inform the agent that is making the decision. The forecasting problem is formulated with all the three variables: the observable historical data, the prediction needed for decision-making and the subsurface model properties. Rather than perceiving the historical-data and prediction variables entirely as physical responses of the subsurface model, as is the practice in the contemporary forecasting paradigm, the subsurface model is perceived as a parameter that establishes causality in the relationship between the historical-data and prediction variables. Statistical techniques to examine this data-prediction relationship in low dimensions using non-linear principal component analysis (NLPCA) have recently been introduced in the hydrogeology literature. However, non-linear techniques are not scalable to the large problems as encountered in the petroleum industry. An algorithm that utilizes statistical techniques that rely in linear operations such as functional component analysis (FCA) and canonical correlation analysis (CCA) by trading off linearity against low-dimensionality has been introduced for examining the data-prediction relationship. This provides a linear model of the data-prediction relationship that can be inferred using linear regression techniques to provide a usable estimate of the forecast uncertainty needed for many applications. Bootstrap techniques that test the reliability of such a forecast with a predictivity metric for the specific problem have also been introduced. This algorithm is validated using a hydrogeological forecasting problem involving the analog of a spatially uncertain German aquifer and its efficacy demonstrated using a reservoir engineering problem involving the analog of a structurally uncertain Libyan oil reservoir. In practice, the model-prediction relationship is defined using a forward-model flow simulator that models the prediction as a physical response of the subsurface. Global sensitivity techniques have been introduced in literature to examine the relationships between the prediction and the individual geological parameters of the subsurface model. Since these relationships are complex, some geological parameters that are insensitive for the prediction often interact with other geological parameters in significant ways to determine the response. In a forecasting paradigm that focuses on the prediction variable, effort spent on modeling uncertainty of aspects of the model that are insensitive for the prediction can be avoided. This dissertation introduces an algorithm that allows for reducing the uncertainty in a geological parameter that is insensitive for the prediction in a way that preserves the overall prediction uncertainty based on the interactions of the geological parameter. This algorithm is validated using an uncertainty modeling problem on the analog of a structurally uncertain Libyan oil reservoir. Together, the sensitivity and predictivity metrics serve as a statistical tool-kit that serves to examine the relationships of the prediction variable with the data and model variables respectively. This tool-kit can be applied to any forecasting problem in an application-specific workflow that constricts the Bayesian-predictive-inference. Only the most predictive aspects of the data and the most sensitive aspects of the model, that is, only the variables that are the most consequential to the forecast needed to inform the decision at hand need to be used in a data inversion problem. The efficacy of one such workflow has been demonstrated using a reservoir forecasting problem involving an analog of a structurally uncertain Libyan oil reservoir.