Domain Decomposition Methods in Reservoir Simulation Coupling Well and Full Field Models

In industrial reservoir simulators wells are usually with just a few large discrete cells and simplified source terms. The complex flow mechanisms that arise around wells are thus not accurately represented. This can have serious consequences on results. A natural idea to obviate these defects would be to use a finer grid mesh around the wells. But such local grid refinements intoduces mesh irregularities with an excessive contrast in the mesh sizes between the grids. Conventional numerical schemes and conventional solvers to handle such irregularities are often inadequate and considerbly degrade the computational performance of codes. This papers considers an other approach by decomposing the above problem over two overlapping or non overlapping subdomains: reservoir and wells. For each time step, we solve the differential equations in separate mesh resolutions and iterate between subdomains until convergence is reached at the internal boundary. The boundary conditions are provided by results of the adjacent domain (pressures, saturations and fluxes). We present some techniques of decomposed modelling applied to model equations of diphasic immiscible flows. We use overlapping subdomains or alternately non overlapping domains with relaxation of interface conditions to achieve convergence. These algorithms have been developped for a threedimensional Dead-Oil model with slight compressibility, under “fully implicit” formulation. We compare different strategies related to imposed boundary conditions on the interface of subdomains (Dirichlet/Neumann) and their influence on number of global iterations.