Managed pressure drilling (MPD) is a drilling technique used to address the narrow density window under complex geological environments. It has widespread applications in the exploration and exploitation of oil and gas, both onshore and offshore. In this study, to achieve effective control of the downhole pressure to ensure safety, a gas-liquid two-phase flow model based on the drift flux model is developed to describe the characteristics of transient multiphase flow in the wellbore. The advection upwind splitting method (AUSM) numerical scheme is used to assist with calculation and analysis, and the monotonic upwind scheme for conservation laws (MUSCLs) technique with second-order precision is adopted in combination with the Van Leer slope limiter to improve precision. Relevant data sourced from prior literature are used to validate the suggested model, the results of which reveal an excellent statistical consistency. Further, the influences of various parameters in a field application, including backpressure, density, and mass flow, are analyzed. Over the course of later-stage drilling, a combination of wellhead backpressure and displacement is recommended to exercise control. Energies 2019, 12, 3930 2 of 21 MPD with the homogeneous flow model (HFM), two-fluid model (TFM), and drift flow model (DFM).The HFM is incapable of ensuring accuracy in reflecting the flow characteristics of each phase, and its calculation accuracy is less than satisfactory; thus, it is rarely applied nowadays. A four-dimensional hypercube has been suggested to describe gas-liquid two-phase flow, and a set of hyperbolic partial differential equations (PDEs) can be derived [10,11]. Of these, the most complicated is the high-fidelity model, which has the capability of describing how physical variables (momentum, mass, and energy) are transmitted and meet the requirements of the thermodynamic equilibrium equation [12][13][14][15]. Despite this, these models are highly complicated to solve, and it is possible that the calculation process does not converge enough to use high-order numerical schemes. Therefore, the simplified DFM was first suggested by Zuber and Findlay [16] and was subsequently improved by Ishii [17]. In the DFM, mass conservation of the gas-liquid two-phase is taken into consideration separately, and the interactions occurring between the two phases are discounted. Relative to the TFM, the DFM demonstrates various advantages such as having a simple form and less computation; thus, it has been commonly applied in the theoretical research process [18][19][20]. In order to enhance its accuracy, the majority of the following studies concentrated on the empirical parameters of this constitutive relationship. In fact, the calculation process remains complicated to some extent. In addition, there are many more simplified equations that have been derived for application under different scenarios, including early gas-kick detection and parameter estimation [21][22][23][24]. However, these models give no consideration to how the chara...