Decline curve analysis in unconventional resource plays using logistic growth models



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Current models used to forecast production in unconventional oil and gas formations are often not producing valid results. When traditional decline curve analysis models are used in shale formations, Arps b-values greater than 1 are commonly obtained, and these values yield infinite cumulative production, which is non-physical.. Additional methods have been developed to prevent the unrealistic values produced, like truncating hyperbolic declines with exponential declines when a minimum production rate is reached. Truncating a hyperbolic decline with an exponential decline solves some of the problems associated with decline curve analysis, but it is not an ideal solution. The exponential decline rate used is arbitrary, and the value picked greatly effects the results of the forecast. A new empirical model has been developed and used as an alternative to traditional decline curve analysis with the Arps equation. The new model is based on the concept of logistic growth models. Logistic growth models were originally developed in the 1830s by Belgian mathematician, Pierre Verhulst, to model population growth. The new logistic model for production forecasting in ultra-tight reservoirs uses the concept of a carrying capacity. The carrying capacity provides the maximum recoverable oil or gas from a single well, and it causes all forecasts produced with this model to be within a reasonable range of known volumetrically available oil. Additionally the carrying capacity causes the production rate forecast to eventually terminate as the cumulative production approaches the carrying capacity. The new model provides a more realistic method for forecasting reserves in unconventional formations than the traditional Arps model. The typical problems encountered when using conventional decline curve analysis are not present when using the logistic model.
Predictions of the future are always difficult and often subject to factors such as operating conditions, which can never be predicted. The logistic growth model is well established, robust, and flexible. It provides a method to forecast reserves, which has been shown to accurately trend to existing production data and provide a realistic forecast based on known hydrocarbon volumes.