Representative-Elementary-Volume Analysis of Two-Phase Flow in Layered Rocks

Abstract

Summary 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.

How pore structure non‐stationarity compromises flow properties representativity (REV) for soil samples: Pore‐scale modelling and stationarity analysis

“…Addressing the issue at hand, it does not matter if REV can be found or not, we still can perform the homogenization step using structural information and known boundary conditions even for non‐stationary pore structures; elucidating what this means for upscaling (Jang, Narsilio, & Santamarina, 2011; Sedaghat & Azizmohammadi, 2019; Sedaghat, Gerke, Azizmohammadi, & Matthai, 2016) will require considerable additional research.…”

Does the symmetry of absolute permeability influence relative permeability tensors in naturally fractured rocks?

“…As it is shown, although forcing symmetricity for the absolute permeability tensor does not affect the diagonal terms and the eigenvalues, k r yx , in significantly influenced for both phases. Here, forcing the 2.37 × 10 −3 2 × 10 −5 -0.0829 0 0 Linear Set 4 3.33 × 10 −11 -8.33 × 10 −4 1.28 × 10 −4 2 × 10 −5 -0.010 0 0 Linear Here, although a more intense counter-current imbibition could be concluded (Sedaghat 2017) if the symmetricity is not applied, the general interpretation of the two-phase flow behaviour does not seem to be hugely affected by the change in the methodology. For the Hornelen model, forcing the symmetricity not only changes all the relative permeability tensor components, it also makes the eigenvalues, the principal values at which the lateral flows get negligible, not match with the diagonal components (Fig.…”