Exploring Decline Curve Residual Modeling using Kalman Filter

Abstract

In this paper we propose a new method to capture the fluctuations in decreasing of oil production that was not considered in the Arps model. The proposed method is called as the Decline Curve Residual (DCR) method. The DCR is defined as the difference between production data and the discretized Arps estimate for each corresponding time. The difference will then be modeled by time series model. The Kalman filter will be used to forecast the DCR using a state-space representation that is formed by an appropriate time series model. We also propose a scatter plot of Akaike’s Information Criterion (AIC) vs. Sum Square of Errors (SSE) value as a new tool to select the best model. Based on this scatter plot, the best model is selected from the point which gives the shortest distance from AIC and SSE value point to the origin. Based on our data, numerical study shows that the DCR is not stationary in variance. Therefore, we explore this DCR modeling using the autoregressive and moving average (ARMA) and generalized autoregressive conditional heteroscedasticity (GARCH) process. From the scatter plot of AIC vs. SSE value, the result shows that the best model is ARMA(2, 4)-GARCH(2, 1).