Reduced order modeling of transient two-phase flows and its application to upward two-phase flows in the under-balanced drilling

•Reduced order modeling of two-phase flows is performed using POD.•Equation-free/Galerkin-free POD assisted method is used for ROM.•ROM of transient two-phase flow in under balanced drilling is performed using equation-free-POD.•The POD can reduce computational time of two-phase flows.

In this paper, reduced order modeling (ROM) of transient two-phase flow equations is performed based on the four-equation two-fluid model, using an equation-free/Galerkin-free proper orthogonal decomposition (POD) method. The AUSMDV∗ method is used to provide the required snapshots for the construction of the reduced basis vectors. The singular value decomposition method is employed to obtain the POD basis functions. An equation-free projective integration method is used to compute the flow variables. To validate the results, two two-phase flow test cases are solved using the presented POD method including two-phase shock tube and water–air separation problems. ROM of the governing equation for upward transient two-phase flow in the annulus of the drilling well is also performed using the POD method. The results show that the presented methodology can reduce the computational costs of the standard two-phase flows problems up to 35%. The time saving for upward two-phase flow in the drilling well may vary between 36% and 62% depending on the initial and boundary conditions of the problem under study.