A Quick Decline Method for Forecasting Multiple Wells Using Sparse Functional Principal Component Analysis

Abstract

Accurate production forecasting for multiple wells that have both sparse and irregular measurements concurrently is a challenging task. Type-well analysis is commonly employed to model the average decline behavior of a group of wells from empirical relationships. The modeled type-well represents the behavior of a typical well in the studied reservoir. However, modifying the type-well to forecast individual well data is difficult. In this study, sparse functional principal component analysis (FPCA) is utilized to accurately forecast production from multiple wells simultaneously from the systematic statistical trends inferred from the group of wells. Sparse FPCA analyzes an ensemble of irregularly-sampled timeseries to describe the underlying random process (RP) using the decomposed components. As such, one can sample from the estimated RP and generate a smooth and regularly-sampled timeseries. The sparse FPCA is primarily an interpolation method where the reconstructed timeseries could not reach beyond the horizon set by the ensemble length. However, with the proposed approach in this study, the decomposed components of FPCA are extrapolated using an autoregressive integrated moving average (ARIMA) model to generate the full probabilistic forecasts beyond the horizon. In this proposed method, the underlying RP is extrapolated first, and then the extended timeseries are generated simultaneously by sampling from the new RP. To validate the accuracy of the extrapolated data in the short-term, part of the timeseries with longer histories are excluded from the training process and only used for testing. The sparse FPCA was applied to analyze monthly gas production data from 200 multi-fractured horizontal wells (MFHWs) of a selected operator in the Montney Formation in Canada. The results indicate that the production data of all the wells could be easily condensed using only two principal components, describing more than 99% of the information content of the production timeseries. Additionally, the resulting decomposed components were convoluted, and the production profiles of the wells with short histories were extended from the information contents of the ensemble. Additionally, with the proposed stochastic ARIMA technique, the production profiles of all the wells were forecasted for 400 months beyond the ensemble limit. The results demonstrate that the extrapolation could accurately match the measured data used for testing, which provides confidence in the stochastic long-term forecast. This study demonstrates for the first time that sparse FPCA can be combined with the ARIMA model to quickly conduct the probabilistic production forecast for hundreds and even thousands of MFHWs simultaneously, which can significantly improve the current type-well modeling workflows.