Upscaling and Discretization Errors in Reservoir Simulation

Reservoir simulation models are used as an everyday tool for reservoir management. The number of grid blocks in a simulation model is generally much smaller than the number of the grid blocks in the geological model. The geological model is therefore regularly upscaled for building reasonably sized simulation models. Any upscaling causes a loss in detail and introduces errors. Understanding the nature of the errors that occur due to the upscaling step is important because it can provide a handle on the kind of upscaling to be performed and the optimum level of upscaling. Furthermore, understanding interaction of gridding and upscaling errors is essential for building reliable simulation models. In this paper we analyze errors introduced due to the upscaling step. Firstly, the generality of the purely local single phase upscaling is considered and the errors introduced due to its use in complex multiphase flows are investigated. Three kinds of errors, namely total upscaling errors, discretization errors, and errors due to the loss of heterogeneity are defined and their behavior as a function of the level of upscaling is studied for different types of permeability distributions. The reasons for apparently low total upscaling errors at high levels of upscaling are investigated. The efficacy of the geostatistical tools (variograms, QQ plots) for understanding the geological structure of the upscaled models as compared to the reference model is tested for different cases. Secondly, the uncertainty introduced in the flow results due to the upscaling errors is studied in conjunction with the uncertainty incorporated through the introduction of geological variability in the ensemble of geological models. The behavior of upscaling errors and geological variability as a function of level of upscaling is studied, and its possible impact on important reservoir management decisions, is analyzed. It is shown that the uncertainty models of cumulative oil profiles, obtained from flow results of highly upscaled models can contain significant uncertainties. These uncertainties are a result of upscaling errors and therefore cannot be considered to represent only geological uncertainty, which is captured by the introduction of geological variability in the ensemble of the geological models.