State-of-the-Art in the Windowing Technique

Abstract The windowing technique was introduced in 1993 by Heinemann and Deimbacher (Ref 9). This method allows a locally restricted and time-dependent replacement of grids and parameters during simulation runs. Windows can represent any area of special interest in a reservoir. In most cases this will be the near wellbore area, in order to resolve near wellbore effects and to honor the pattern of flow. Introducing a wellblock with exactly the same dimensions as the real wellbore and gridding the near wellbore area allows to model all sorts of well trajectories, by applying the 3D (k-)PEBI grid method. Introducing small block sizes requires a drastic reduction of the timestep length. Therefore the windowing technique can only be applied if the solution of the equations for the full model and the solution of the window area is decoupled. This can be done based on a special kind of Domain Decomposition. In a first step the fully implicit solution for the full-scale model will be calculated but the inner blocks of the windows are solved for the pressure only, without updating the saturations and mole fractions, providing the boundary influx for the windows, which are then solved for the same overall time step with up to 1000 small local steps. The windowing technique can find numerous applications. Keeping overall CPU time consumption in he order of magnitude of a conventional model, the windowing technique is a potential approach to replace the analytical Peaceman (Ref. 23) model in full field reservoir simulation, while increasing the quality of the results. A further application of this technique is the simulation of well tests in full field reservoir models. This paper presents the advances in the gridding and dynamic solution process. Several examples to demonstrate the advantages of this technique for detail - and full field reservoir simulation will be included. Introduction Special treatment and high resolution, both in time and space, of regions of interest, as for example the near wellbore area, has always been an important question in reservoir simulation. But using small timesteps and local grid refinement unavoidably lead to long and uneconomical CPU times. In the attempt to solve this problem several techniques have been developed in the reservoir simulation literature, such as patch refinement. true refinement or multigrid methods (Ref. 2–6), but none of these approaches could fully satisfy the requirements of local grid replacement by flexible and irregular grids and its time dependent incorporation in full field reservoir simulation. In 1986 Aziz and Pedrosa introduced the concept of "hybrid grids" in a Cartesian block system (Ref. 1), trying to overcome the insufficiencies of the Peaceman model. Gridding the near wellbore area by hybrid grids honors the radial nature of flow, small block sizes help handling large saturation changes caused by high production rates. The paper showed that the solution of the equations in the radially gridded well region can be decoupled from the solution of the equations of the conventional grid system by either applying an iterative or a direct solution method.