Sequential Implicit Newton Method for Coupled Multi-Segment Wells

Abstract Accurate and robust well modeling is essential for performing reservoir simulations of practical interest. The Multi-Segment well (MSWell) model is able to describe the well topology and accurately represent the multiphase multicomponent flow and transport behavior in the wellbore. The fully coupled method (FC) has been developed and widely applied on coupled reservoir and MSWell modeling due to its unconditional stability and consistent implementation. A local well solver can be applied to provide a better nonlinear precondition for MSWell variables in order to accelerate the nonlinear convergence of the FC method. However, solving the coupled MSWell and reservoir model in a fully implicit scheme can still present limitations on some practical applications. First, the well or surface facility solver can be separate from the existing reservoir simulator, making it challenging to employ the fully implicit method. Second, complex linear and nonlinear solvers need to be designed to pair the specific wells and reservoir models. These solvers have to account for the different flow characteristics and discretization domains between reservoir and MSWell. A sequential coupling scheme can become preferable in such situations. Sequential fully Implicit method (SFI) splits the fully coupled reservoir and MSWell equations into two parts and solves them sequentially. In spite of accomplishing an implicit coupling in a sequential scheme, SFI suffers the slow outer loop convergence rate especially when reservoir is strongly coupled with the wells, which is very often the case. The slow convergence is caused by the linear convergence rate of the fix point iteration used in the SFI. Here, we developed a sequential implicit Newton's method (SIN) for coupled MSWells. SIN incorporates a Newton update at the end of each sequential step to achieve a quadratic convergence of outer iterations, while require a limited extra computational cost. Numerical results show that SIN attains comparable nonlinear Newton iterations with the FC in the coupled heterogeneous reservoir and complex MSWell problems.