On the Interchangeability between the Forchheimer and the Backpressure Models for Gas Well Deliverability

Summary The prediction of sandface deliverability is crucial for designing production equipment and surface facilities for gas wells. The backpressure and the Forchheimer models are the most popular deliverability models for gas wells. However, despite describing the same phenomenon, their different mathematical natures result in the divergence of their predictions. With this study, we aim to explain and address this divergence by interrelating the two models in a fully analytical framework. The theoretical basis of the Forchheimer equation was successfully extended to the backpressure equation using two dimensionless groups—the turbulence intensity ratio and the highest tested drawdown. The backpressure equation was corrected using the developed theoretical framework to be as accurate as the Forchheimer equation, yielding a median absolute open flow (AOF) error of 8% compared with an uncorrected accuracy of 25%. The framework was also used to interpret isochronal tests using the backpressure equation without stabilized flow data, and the prediction error was within 5%. The outcomes of this study are crucial for the accurate prediction of gas well deliverability, which is the cornerstone of production engineering and reservoir planning. Through this study, we explain and address the limitations of the backpressure model, proposing improvements to make it as robust as the Forchheimer model.