The Influx Management Envelope (IME) Culen et al. (2016), is a decision making tool for how to deal with a influx during managed pressure drilling (MPD) operations that offers a substantial improvement over the traditional MPD Well Control Matrix (WCM). However, in the case study by Gabaldon et al. (2017), it has been found that the simplified analytical solution introduced by Culen et al. (2016) makes the IME inaccurate for many real-world applications. This paper extends the original IME that considers the gas migration in the annulus as a single bubble, without making the simplifying assumptions that are required to make the equations explicit and analytically solvable. The underlying equations that are required to develop the IME is derived from first principles and it is shown that using realistic equations of state (EOS) for gas, and a single-bubble type model, the equations for the IME can be numerically solved yielding less conservative limits. The proposed approach is significantly faster than constructing the IME through high-fidelity simulations. The proposed method allows the calculation of peak circulating pressure at the surface and the maximum weak point pressure for a given kick size and initial shut-in pressure, as well as a kick envelope with respect to formation limits. This makes the contributions of this paper relevant for traditional well control decision making as well. The effect of considering various simplifying assumptions on the resulting IME is studied and different scenarios that compare the results of the proposed approach with that of the original single bubble equation for the IME by Culen et al. (2016) is presented.

The Influx Management Envelope (IME) is a tool for operational decision making when managing influxes in Managed Pressure Drilling (MPD) operations. There have been numerous developments to the IME in recent years, and it is gaining traction over the MPD Operating Matrix (MOM). Calculation of the IME can be done in different ways. The original approach of calculating an IME described in (Culen et al. 2016), give less acceptable influx sizes than using multiphase simulations. Some of this can be attributed to the used Equation of State (EOS), and some to the distribution of gas in the wellbore. There is ongoing work for creating purpose-built tools for generating IME's that consider the gas as a single bubble, but with a real gas EOS, as well as considering gas distribution. In this work, the sensitivity to the model used when creating an IME is studied. This is done through comparing the single-bubble real-gas IME by (Berg et al. 2019) with IME's generated using Drillbench Dynamic Well Control as well as the commercial multiphase flow simulator Ledaflow for synthetic test wells. Discrepancies between the results are discussed and the differences in the underlying model and calculation procedure with respect to the end IME is elaborated.