Abstract
In a fully integrated reservoir and surface facility simulator, an overlapping multiplicative Schwarz method was chosen to solve the coupled system, using perforated grid blocks as the overlapping layer. But in many cases it was found that this overlapping approach did not improve global linear solver performance, and the matrix for the extended surface network, which included the perforated grid-blocks, was much larger and denser and lost its original tree structure, which taxed the linear solver for the network. Furthermore, the pressure solver for the reservoir domain was totally decoupled from the network domain. The loose coupling in the pressure solution led to the disappointing performance. In most cases, the accuracy of the pressure solution across the reservoir and surface network directly determines the performance of the global linear solver, so it is crucial to define an appropriate global pressure matrix to represent the flow exchange between these two domains.
Taking advantage of a new formulation for a generalized network model of wells and facilities in which node-based variables, pressure and component compositions, are chosen as the primary variables, instead of mixed node and connection- based variables, algebraic methods are designed to reduce the full system matrix, involving pressure and component masses for the reservoir domain and pressure and component compositions for the network domain, to a pressure-only matrix. This global pressure matrix works as the first stage preconditioning matrix in a two-stage solution method. For the reservoir domain, a widely-used IMPES-like reduction method was implemented. This paper focuses on methods to construct the pressure matrix for the network domain and coupling matrices between the domains. Performance comparisons between different approaches are presented.
