Boundary Control and Estimation for Underbalanced Drilling With Uncertain Reservoir Parameters

Abstract

In underbalanced drilling (UBD), the bottom hole pressure is kept below pore pressure, causing pressure-dependent influx of reservoir gas into the wellbore that makes the system unstable at low drawdowns. In this article, we propose a feedback controller which stabilizes the system, represented by the “reduced drift flux model (DFM),” around an arbitrary pressure setpoint, while using only topside measurement and assuming unknown reservoir parameters. A particular challenge with this problem is the distributed and highly nonlinear nature of the system dynamics, where the “reduced DFM” models gas–liquid flow as a nonlinear transport equation with a nonlocal integral source term. An observer e..