Functional Approach to Data Mining, Forecasting, and Uncertainty Quantification
Authors: Wilson Adam 
Published: January 2017

This article, written by Special Publications Editor Adam Wilson, contains highlights of paper SPE 174849, “Functional Approach to Data Mining, Forecasting, and Uncertainty Quantification in Unconventional Reservoirs,” by Ognjen Grujic, Stanford University; Carla Da Silva, Anadarko Petroleum; and Jef Caers, Stanford University, prepared for the 2015 SPE Annual Technical Conference and Exhibition, Houston, 28–30 September. The paper has not been peer reviewed.
The difficulty in applying traditional reservoir-simulation and -modeling techniques for unconventional-reservoir forecasting makes the use of statistical and modern machine-learning techniques a relevant proposition. However, the most current applications of these techniques often ignore the systematic time variations in production-decline rates. This paper proposes a nonparametric statistical approach, using a modern technique termed functional data analysis (FDA). In FDA, production data are modeled as a time series composed of a sum of weighted smooth analytical basis functions.
Introduction
Many companies have adopted a so-called “data-centric process” for understanding and forecasting in unconventional reservoirs. This datacentric process comes as a consequence of the shortcomings of conventional reservoir-data-analysis and -modeling approaches, which mostly belong to the preshale era. Either the huge quantity of data collected in shales cannot be used fully with conventional modeling techniques or the rapid nature of shale development simply does not allow for lengthy reservoir-modeling and -simulation studies.
Decision variables in shales are rates or volumes of produced hydrocarbons. Therefore, understanding shales and identifying value-creating practices by use of data-driven techniques require proper handling of production-time series. This is often challenging because production time series come as noisy, discrete observations of production rates over time. Conventional approaches to this problem rely on parameterizing the system with decline curves and work in the parameter space of the assumed decline model, or, even simpler, work with the raw data. This paper takes an alternative nonparametric approach wherein the data are used to find the most-appropriate smooth and continuous representation of declining production time series. The approach for this nonparametric form relies on the statistical discipline termed FDA.
FDA allows for the exploration of stochastic variation in functional data and construction of low-dimensional representations of time series. In the context of shale production, these low-dimensional representations will enable a better understanding of relationships between the wells and, in conjunction with a distance-based generalized sensitivity analysis (DGSA), identification of the most-influential completion and reservoir parameters. Additionally, FDA enables formulation of a forecasting framework with high-dimensional Kriging-based regression, to produce best-guess estimates of the entire production profiles for new well locations.