One of the most challenging tasks in reservoir engineering is to homogenize data from a fine to a coarser model in a systematic and robust manner. This chapter reviews a variety of such upscaling methods. Simple averaging is sufficient for additive properties but only correct in special cases for nonadditive properties like permeability. The correct effective permeability depends on the applied flow field. In flow-based upscaling, one solves local flow problems with various types of boundary conditions to determine effective permeabilities or transmissibilities. We outline the most common methods, and discuss methods that reduce the influence of the prescribed boundary conditions by computing flow solutions on larger domains. Computations are achieved by imposing boundary conditions derived from a global flow solution. A number of cases compare the accuracy of different upscaling methods, and we discuss how flow diagnostics can be used for quality control. The last example summarizes major parts of the book by going all the way from geological horizons via flow simulation to upscaled models with flow diagnostics quality control.

The chapter starts by explaining how petroleum reservoirs are formed and gives a brief introduction to various concepts from geology to non-geologists. Next, we discuss the continuum hypothesis and how flow through subsurface porous media is modeled on different spatial scales. An essential part is to develop a description of petrophysical properties like porosity and permeability. We explain how this is achieved in MRST, and outline a few examples of models that give realistic representations of reservoir rocks. This includes the popular SPE10 benchmark and a model of a shallow-marine formation.