Single- and Two-Phase Flow Models for Concentric Casing Underbalanced Drilling

Underbalanced Drilling process (UBD) is applied to oil fields where the original pressure has been depleted as a consequence of an intensive exploitation. In such technique, due to the incorporation of nitrogen into the Drilling Fluid (DF), the downhole pressure is close to the reservoir pressure. This work presents a single-phase, one-dimensional and transient mathematical model for the flow of: (1) nitrogen in an annulus, and (2) DF in a drill pipe. It is also presented a one-dimensional, transient, mathematical drift-flux model for the DF-gas two-phase flow in an annulus. The mathematical models are based on the mass, momentum and energy conservation equations, which are solved numerically using the finite difference technique in an implicit scheme. The models allow predicting pressure, velocity and temperature profiles. The predictions are in agreement with experimental and field data reported in the literature.