Functional Approach to Data Mining, Forecasting, and Uncertainty Quantification in Unconventional Reservoirs

Abstract

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 for shale systems. However, the most current applications of these techniques often ignore the systematic time variations in production decline rates. Traditional decline curve modeling techniques fall short in predicting actual physical parameters and are highly dependent on the assumed physical model.In this paper, we propose a non-parametric statistical approach, more specifically, using a modern technique termed functional data analysis (FDA). In FDA production data is modeled as a time series composed of a sum of weighted smooth analytical basis functions. Instead of assuming a model, this technique allows us to learn the model from the data by jointly fitting all production profiles in the field. Principal component analysis can be applied to the functional data, termed (fPCA). Applying fPCA to declining rates from many wells, transforms time varying data into lower-dimensional score data. We found that in the real field data studied, 2-3 such functional principal components were sufficient to describe the entire production in a shale play. Low dimensional score data is also very valuable for data mining and sensitivities studies that enable better understanding of production drivers. Finally, building regressional relationships between geological and completions parameters and functional principal component scores enables forecasting production at new well locations with new sets of geological and completion parameters.Proposed methodology is demonstrated on a real reservoir case study with 172 horizontal and hydraulically fractured wells. Wells originate from one of the most prolific shale plays in North America, and have been in production for at least 500 days. Case study was focused on oil production rates, and obtained forecasting error over multiple test sets (100) was 21% (on average).

Universal Kriging of functional data: Trace-variography vs cross-variography? Application to gas forecasting in unconventional shales

“…Part of such technical innovation lies in understanding the impact of the geological and hydraulic fracturing factors on production, which drives the spatial variability of production in wells. Due to the complexity involved, statistical approaches based on data are preferred over physical modeling approaches (Mohaghegh, 2011(Mohaghegh, , 2013Kormaksson et al, 2015;Grujic et al, 2015). Production rates in wells start from an initial peak in production right after hydraulic fracturing followed by a long multi-month decline.…”