Numerical Reservoir Calculation On PEBI Grids And Implementation

Recently, China is the second largest oil consumption nation in the world. As the rapid development of national economic, the requirement of oil is continuously rising, this results in that the oil import dependency is about 50%. While After years of production, many old oil fields in our country already entered middle or later period. Fine development is necessary to keep the stable production in old oil fields.One of fine development's contents is to retrieve the connectivity of sand bodies, the macro-pores and the distribution of remaining oil by various dynamic monitor technologies. Over a long period of injection-production and increases of infilling wells in old oil fields, the consistency of well network is compact and the transformation of oil-water distribution becomes very complicated, so the target of production has been shifted to the remaining oil which highly disperses but relatively concentrates in certain spot. And this puts new demands on the interpretation, evaluation and simulation of testing data. Because the analytical method is difficult to solve problems with heterogeneous reservoir, reservoir with complicated boundaries or multi-phase flow, numerical method is necessary to be developed. The regular grids are not effective to describe complicated boundaries, so the development of unstructured grids is obligatory. The numerical calculation should be able to accurately simulate the transient pressure to fulfill the demands of explanation of pressure data.Therefore, this paper researches on the numerical calculation model of multi-layer, multi-phase, heterogeneous reservoir on PEBI grid. The model contain the below parts.1. Meshing. After comparing the Cartesian grid, corner grid, curvilinear grid, the mid-point grid, radial grid and PEBI grid, PEBI grid are chosen to discrete the space of the reservoir. Restricted edge algorithm is proposed to generate PEBI grids in the reservoir. By classifying vertical wells, fractural wells, horizontal wells, faults and boundaries, the algorithm split the reservoir into point modules, line modules, circle module, rounded rectangular modules and flat modules. By considering the interferences between the modules, restricted edges of each module are obtained. After generating grid points within restricted edges of every module, grid points of the reservoir are obtained. After making Delaunay triangulation to the mesh points, the Voronoi graph of the grid points is generated. Then the 2-D or 3-D PEBI grid of the reservoir can be obtained. This algorithm can generate correct PEBI grids of reservoir which involves complicated boundaries, faults, interferences between wells, interferences between wells and fault.2. Reservoir model. The numerical model is based on black-oil model, and it discretizes the equations on PEBI grid. The single-phase and multi-phase discretized equations are derived in detail. The non-linear item of the equations is linearized. In the single-phase equation, explicit method or iterating implicit method can be used to linearize the non-linear item. The non-linear item of the multi-phase equation can be divided into weak non-linear item and strong non-linear item. The processing method of the weak non-linear item is similar to the single-phase. The half explicit method or full explicit method can be use to linearize the strong non-linear item.3. Well models. The existing models are introduced, such as source-sink model, van Pollen model and Peaceman model. Internal boundary model is proposed for vertical well, vertical fractural well and horizontal well. Correspondingly, the mesh methods are analyzed, and the well index is derived from Darcy law. Because horizontal well usually need to be discretized into separate grids, the flow equation has been derived from infinite conduction model and average flow model.4. Numerical well testing software is developed based on the above research. The software can generate correct PEBI mesh of complicated quickly, and can calculate single-phase, two-phase and three-phase flow. After compared to foreign softwares, this software is proved to be correct and stable, and can be applied in oil fields.