Gas well deliverability: backpressure, Forchheimer, and numerical models

Abstract

The Forchheimer and backpressure models are commonly employed to describe gas well deliverability and interpret multipoint well tests. While the Forchheimer model is regarded as more robust, the backpressure equation remains widely used. However, both models’ have unaddressed limitations, and it is unclear when their predictions diverge. This study investigates both models’ validity against numerical solutions of the diffusivity equation. Results show that the models’ accuracy depends on two dimensionless groups: the turbulence intensity ratio and the highest drawdown tested in a multipoint test. Only the Forchheimer model consistently yields flow rate errors below 10% when 25% of the reservoir pressure is tested, following industry guidelines, while the backpressure equation exhibits an average error of 30%. The backpressure equation is accurate under laminar or highly turbulent conditions but deteriorates in the transition between the two, diverging from the Forchheimer model. To mitigate the inadequacy of the backpressure model, testing pressure drawdowns as high as 40% of reservoir pressure is recommended.