Relative permeability upscaling for heterogeneous reservoir models

Abstract

Detailed geological models usually contain multi-million grid cells, which makes the running of reservoir simulation difficult and time consuming. Therefore, reducing the number of grid cells, and in turn averaging reservoir properties within them, is desirable in order to make running simulations more feasible. Averaging reservoir properties within the coarse cells is usually referred to as upscaling, which can be achieved using different methods. Many upscaling techniques have been introduced in the literature. However, developing a practical and robust upscaling method has been a research topic for a long time. In this thesis, some of the upscaling methods, their application and limitations are presented. Special attention is given to two phase upscaling methods as they are within the scope of this project. Afterwards, a new two phase upscaling method, called Transmissibility Weighted Relative permeabilities (TWR), is proposed to upscale relative permeability curves in heterogeneous reservoirs. Also, a new method to generate well pseudos is introduced as a means of adjusting well results. The TWR method and the well pseudos were tested using synthetic 2D and 3D water flood models for different conditions in order to check the method’s performance. The results showed that the upscaled relative permeability curves (pseudo functions) succeeded in compensating for sub-grid heterogeneity and numerical dispersion so that the coarse models reproduced the fine models results. In order to make the use of the pseudo functions feasible in practice, a new method to group them, based on curve fitting of Chierici (1984) functional models, was introduced. Calculations of the TWR pseudos and the well pseudos were performed by writing C++ codes to do so. The grouping of the pseudos was accomplished using a non-linear regression solver.