Geological/flow properties computed from a heterogeneous rock sample represent the properties of the entire medium if the size of the sample is larger than the size of the representative elementary volume (REV) of the rock. Among these properties, relative permeability is believed to have the most influence on multiphase-flow behavior. Therefore, much care must be taken to ensure that relative permeability has been computed beyond the REV size. However, in the literature, experimental and numerical evaluations of relative permeability are mostly performed without such care, and the saturation functions are calculated at different flow rates while the length of the sample remains the same.
In this work, a series of numerical simulations of waterflooding are performed in a model made of alternating parallel layers of two rock types. Upscaled relative permeabilities are computed on samples at different lengths, changing from millimeter to kilometer scale. Flow behavior for different samples is analyzed according to capillary, viscous, and gravity effects, which are monitored during the simulation.
Although the REV size for some properties such as porosity seems to be the smallest replica block (unit block), our results show that the REV for relative permeability follows a power-law trend and changes with flow rate and scale. More importantly, for the first time, it is shown that the REV size is not necessarily identical for different phases. It is also demonstrated that especially at small scales, breakthrough can occur at layers where it was not expected. This study identifies the range of the length scale for which either experimental or numerical determination of relative permeability is valid.