Decline curve analysis is widely used in industry to perform production forecasting and to estimate reserves volumes. A useful technique in verifying the validity of a decline model is to estimate the Arps decline parameters, the loss ratio and the b-factor, with respect to time. This is used to check the model fit and to determine the flow regimes under which the reservoir produces. Existing methods to estimate the b-factor are heavily impacted by noise in production data. In this work, we introduce a new method to estimate the Arps decline parameters.
We treat the loss ratio and the b-factor over time as parameters to be estimated in a Bayesian framework. We include prior information on the parameters in the model. This serves to regularize the solution and prevent noise in the data from being amplified. We then fit the parameters to the model using Markov chain Monte Carlo methods to obtain probability distributions of the parameters. These distributions characterize the uncertainty in the parameters being estimated. We then compare our method with existing methods using simulated and field data.
We show that our method produces smooth loss ratio and b-factor estimates over time. Estimates using the three-point derivative method are not matched with data, and results in biased estimates of the Arps parameters. This can lead to misleading fits in decline curve analysis and unreliable estimates of reserves. We show that our technique helps in identification of end of linear flow and start of boundary dominated flow. We use our method on simulated data, with and without noise. Finally, we demonstrate the validity of our method on field cases.
Fitting a decline curve using the loss ratio and b-factor plots is a powerful technique that can highlight important features in the data and the possible points of failure of a model. Calculating these plots using the Bourdet three-point derivative induces bias and magnifies noise. Our analysis ensures that this estimation is robust and repeatable by adding prior information on the parameters to the model and by calibrating the estimates to the data.