State-of-the-Art of the Windowing Technique

Abstract The windowing technique was first introduced by Heinemann and Deimbacher(1) in 1993. 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 is the near wellbore area, for the purpose of resolving near wellbore effects. By applying the 3D (k-)PEBI gridding(2) method, grids for arbitrary trajectories ofadvanced wells that resolve the near wellbore area and the wellbore itself can be generated. To handle detailed grids in full scale models, the timestep length must be drastically reduced. Therefore, these grids can only be used efficiently if the solution of the equations for the full, coarse model and the refined area is separated. This can be done based on a special kind of domain decomposition, which forms the theoretical basis of the windowing technique. Besides well modelling, the windowing technique has many other applications. Keeping overall CPU time consumption in the order of magnitude of a conventional model, the windowing technique is not only a potential approach to replace the analytical Peaceman model(3) in full field reservoir simulation, but also can be used for efficient well test simulation or dynamic flow based gridding. This paper presents the state-of-the-art of current window gridding techniques and their solution methodologies. Several examples to demonstrate the advantages of this tool for detailed and full field reservoir simulation are included. Introduction Special treatment and high resolution of regions of interest, both in time and space, have always been important issues in reservoir simulation. Several techniques have been developed in the past in attempting to solve the CPU efficiency problem in the application of local grid refinement, including patch refinement, true refinement, or multigrid methods(4–8). None of these techniques could fully satisfy the requirements of local grid replacement by flexible and irregular grids and its time dependent incorporation in full field reservoir simulation. The concept of the windowing and local timestepping technique was first introduced by Heinemann and Deimbacher in 1993(9–11). Application and further developments of the windowing technique proved it to be a multi-purpose numerical tool for a wide range of applications for simulation problems, including ell modelling in full field reservoir simulation and flow based gridding. Since its first publication, the technique has undergone several modifications. The purpose of this paper is to present the methodology in its current form and to give a coherent picture of the state-of-the-art of its application. Therefore, we first summarize the window solution methodology as it is implemented to date. Then the technique is validated using a small coning example. Finally, the state-of-the-art of its application, both from a gridding and simulation perspective, including well modelling, well test simulation, and flow based gridding, will be presented.