Petroleum decline analysis using time series

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As the world's oil resources dwindle, the petroleum engineer is repeatedly confronted with the need to predict the remaining production capacity for producing oil reservoirs. The common procedure used to make such predictions, the extrapolation of a least squares fit of exponential or hyperbolic form, is reviewed and its problems and disadvantages discussed. An alternative, time series analysis, is then proposed and compared with the current procedure. Oil reserves from fields in North Dakota are predicted using time series models and standard hyperbolic or exponential decline curves and the time series methods were found to be more accurate and to indicate a forecast function of exponential form. A method of efficiently estimating the parameters in the forecast function is presented. This method does not use the forecast function in a regression fit. Instead, the time series model is fitted and a relationship between the time series model parameters and the forecast function parameters is derived.