A dynamic model of two-phase flow for simulating gas kick and facilitating model-based control in drilling operations

Abstract

A low-order two-phase dynamic flow model for drilling operations with gas kick is developed. The purpose is to enable fast and robust simulation of the behavior and propagation of influx gas in the bore hole, and the effects it has on the total flow dynamics. The model handles both open and closed wells, as well as the full range of pump rates and gas influx rates that are likely to occur in drilling operations. It incorporates equations for gas bubbles into a low-order liquid model in a new way. Some aspects of the gas are described in a mechanistic way, but with a new “dual-shape” bubble representation approach. Momentum is treated for the mixture as a whole, while conservation of mass is handled individually for each of the two phases. The result is a model consisting of a set of ordinary differential equations on explicit form, which makes it possible to couple it with control system- and estimation theory. A comparison with published data from four different sources shows that the model is able to qualitatively reproduce both steady state and transient responses in a handful quite different flow situations. In particular, we verified that the dominating effects that the gas has on compressibility, friction loss and hydrostatic pressure of the total mixture are satisfactory reproduced.