Higher-Order Derivatives of Production Rate and Convolutional Neural Network for Production Forecasts

In recent years, many machine-learning models have been developed to predict future production of oil in gas in "shales". Long-short term memory (LSTM), the most widely used model, relies on the longterm production history for a reasonably accurate production forecast. All analytical and machine learning models, including LSTM, fail miserably in the absence of long production history. Our goal is to present a novel method of production forecasting using only 24 months of production data. The first and secondorder derivatives of the distance traveled give speed and acceleration to describe the trajectory and dynamics of a moving vehicle. Similarly, higher-order derivatives of hydrocarbon/water production rate vs. time uncover hidden patterns and fluctuations in a well that act as differential markers of its future recovery factor (RF). In this paper, we couple production data and their higher-order derivatives with other known parameters for a well, i.e., well length and initial production. The time-series data are passed into a Convolutional Neural Network (CNN) with two hidden layers of 16 nodes each, and one output layer. The model is trained to predict recovery factor (RF) in the 10th year of production. We analyze the first 24 months of production data for the Barnett (1500), Marcellus (800), Haynesville (800), and Eagle Ford (1000) shale wells. All wells have a minimum pressure interference time of 34 months. The production rate vs. time and its first, second, and third-order derivatives are coupled with the well length and initial production rate, and the data are normalized with their respective maxima. For the Barnett wells, the CNN model predicts recovery factors in their 10th year of production with an average accuracy of 90%. For the Marcellus, Haynesville, and Eagle Ford wells, the prediction accuracy in the 8th year of production is 89%, 92%, and 91%, respectively. Further, we divide the wells into three groups (A, B, C) depending on the range of their recovery factor (A:RF=0-0.3, B:RF=0.3-0.6, and C:RF=0.6-0.9). We show that the clusters of wells grouped by their RFs strongly correlate with the distribution of the higher-order de rivatives of production from these wells. Thus, we posit that the detailed production history and its derivatives are the most important variables that define distributions of maximum recoverable hydrocarbon from a source rock. Our novel method uses only 24 months of production data to predict future recovery factor with an outstanding average accuracy of 90%. We show that the higher-order derivatives of high-resolution production data available from the operators could be an excellent tool for well screening and predicting future production with reasonable accuracy.