Accounting for Serial Autocorrelation in Decline Curve Analysis of Marcellus Shale Gas Wells

Abstract

Current decline models fail to capture all of the behavior in shale gas production histories. That is, upon fitting one of these models, one often sees significant and sustained deviation of the flow rate data points from the decline trend. One way to measure this "lost signal" is to look at the autocorrelation in the residuals about the fitted decline model. Indeed, with many shale gas wells we see significant amounts of autocorrelation, especially when comparing the flow rate at one time to the next (lag one). Theoretically, this serially autocorrelated error can impact decline curve analysis in two ways: 1) inefficient estimation of decline curve parameters, and 2) lost signal in the data. Borrowing from time series statistics, there are two conventional ways of dealing with these potential problems: 1) estimate the decline curve parameters with generalized least squares or generalized nonlinear least squares, and 2) fitting an ARMA model to the residuals and adding it to the fitted decline curve. This paper investigates the practical implications of these two procedures by exercising them over decline curves fit to 8,527 Marcellus shale gas wells (all wells from that play with viable data for the analysis). The study explores the effect that generalized regression methods and ARMA-modeled residuals have on six different decline curves, and performance is measured in terms of sum of squared residuals (a metric for goodness-of-fit, calculated on the training data (first 24 months of each record)) and mean absolute percent error (a standard metric for forecasting accuracy, calculated on the testing data (all production rates after 24 months)). We find that inclusion of the ARMA-modeled residuals largely improves the goodness-of-fit for any decline curve, and improves the forecasting accuracy for the Hyperbolic decline curve and Duong's model. The use of generalized least squares or generalized nonlinear least squares has little benefit in fitting the decline curves, except for the Logistic Growth model, where it improves both fit and forecasting accuracy.