Acceleration of Streamline Simulation Using Adaptive Mesh Refinement AlongStreamlines (2007)

Acceleration of Streamline Simulation Using Adaptive Mesh Refinement Along Streamlines Nikolay Andrianov; Nikolay Andrianov Schlumberger R&D Inc. Search for other works by this author on: This Site Google Scholar Kyrre Bratvedt Kyrre Bratvedt Schlumberger Search for other works by this author on: This Site Google Scholar Paper presented at the SPE Reservoir Simulation Symposium, Houston, Texas, U.S.A., February 2007. Paper Number: SPE-106181-MS https://doi.org/10.2118/106181-MS Published: February 26 2007 Cite View This Citation Add to Citation Manager Share Icon Share Twitter LinkedIn Get Permissions Search Site Citation Andrianov, Nikolay, and Kyrre Bratvedt. "Acceleration of Streamline Simulation Using Adaptive Mesh Refinement Along Streamlines." Paper presented at the SPE Reservoir Simulation Symposium, Houston, Texas, U.S.A., February 2007. doi: https://doi.org/10.2118/106181-MS Download citation file: Ris (Zotero) Reference Manager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex Search Dropdown Menu nav search search input Search input auto suggest search filter All ContentAll ProceedingsSociety of Petroleum Engineers (SPE)SPE Reservoir Simulation Conference Search Advanced Search AbstractStreamline methods have become an efficient technology for reservoir simulation. The key assumption of the method is that the pressure field can be updated relatively less frequently, and the saturations can be transported along the streamlines defined by the velocity field. The efficiency of the solution method along the streamlines is very important for the overall efficiency of the method.In this work, the acceleration of the saturation transport using adaptive mesh refinement (AMR) along streamlines is investigated. The refinement strategy is based on the multi-scale wavelet techniques. The one-dimensional solution is decomposed into a set of coarse-grid cell values and a set of solution details, which indicate the smoothness of the solution. This decomposition is recursively applied to the resulting representation until the coarsest mesh level is reached. From this multi-resolution representation of the solution an adaptive grid is constructed by thresholding of negligible details. Then, a second-order finite volume method is used on the obtained adaptive grid.The performance of the resulting multi-resolution scheme on a synthetic and a real reservoir model is studied, using two-phase incompressible and three-phase black oil compressible data. It is shown that the use of the AMR technique for realistic test cases can provide up to a five-fold acceleration compared to the solution of the same numerical method on a uniform grid. The proposed technique is implemented in a commercial reservoir simulator.IntroductionThis paper encompasses fast and accurate numerical simulation of large geological models. The requirement is to to simulate multimillion cell geological models on a standard computer within hours or less. Such requirements are dictated by, e.g., uncertainty analysis applications, where an engineer wishes to test as many variations of a geological model as possible.A proven numerical method for simulation of large geological models is the streamline method [1–10]. The method employs the traditional pressure-saturation formulation of the flow in porous media [11]. Traditionally, the governing equations are solved in a sequential manner: one solves the pressure equation, finds the corresponding Darcy's velocity, estimates the time step from the CFL condition, and performs the saturation transport step over this time step. The streamline method takes advantages of the knowledge that usually, the pressure field may be updated much less frequently than the CFL limitation requires for the transport equation. One specifies at which time instants the pressure equation should be solved; between the pressure updates, saturations are transported using a frozen velocity field. As the name of the method suggests, the 3D transport equations for saturations are transformed into a set of 1D equations along streamlines. Note that there are two time scales in the streamline simulation process: the one determined by the frequency of pressure updates (pressure time step), and the one dictated by the solution of the saturation transport along streamlines (saturation time step).It is apparent that the streamline simulation can be much faster than a conventional sequental method (e.g. IMPES [11]). The goal is to use the least possible number of pressure updates in order to maintain the required accuracy. Also, there is no global restriction on the saturation time step, since the latter may vary from one streamline to another.For some complex processes, much of the computational effort during streamline simulation is spent on the solution of the 1D transport equations [12]. Therefore, a fast numerical method for the saturation transport is crucial for the overall simulation process. One very successful numerical approach for the solution of 1D equations is the front-tracking method [3]. The idea is to employ analytical solutions to Riemann problems, and to track the discontinuities explicitly. However, for complex flow models (e.g. those with realistic relative permeabilities), the solution to the Riemann problem becomes complex. Also, an extension of the front-tracking method to compressible flows is not obvious. Keywords: streamline simulation, uniform streamline grid, Computation, threshold parameter, flow in porous media, Fluid Dynamics, adaptive mesh refinement, relative error, reservoir simulation, numerical relative error Subjects: Reservoir Fluid Dynamics, Reservoir Simulation, Flow in porous media, Streamline simulation This content is only available via PDF. 2007. Society of Petroleum Engineers You can access this article if you purchase or spend a download.