This paper describes real space renormalization schemes for determining effective flow properties of heterogeneous reservoirs, focusing on effective permeabilities. Effective properties are calculated in a hierarchical fashion by dividing the system up into cells, consisting of a number of grid-blocks, and calculating the effective properties of each of these cells. Each cell is then treated as a single grid-block in a larger cell and so on. This paper discusses two types of scheme: small-cell methods, which are very simple to implement and computationally very efficient, and large-cell methods, which provide the greater accuracy required to deal with strongly anisotropic systems. The large-cell method has advantages in determining the effective per meability of cross-sectional models, where discontinuous impermeable shales often cause difficulties for small-cell schemes with the locally imposed cell boundary conditions. Each of the large cells contains many grid-blocks and the effective permeability is calculated by replacing each cell by its equivalent resistor network. In 2D these resistor networks can be reduced to single equivalent resistors by a systematic sequence of exact resistor transformations mirroring the ‘differential real space renormalization’ technique developed in statistical physics. This large cell method appears more attractive for anisotropic systems with a finite fraction of impermeable material and can be extended to allow for mesh refinement. A test problem using outcrop data illustrates the capabilities of the method.


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