Predicting the Representative Elementary Volume by Determining the Evolution Law of the Convergence Cone

In order to characterise a rock formation prior to subsurface operations, it is required to find a microscale rock volume for which the homogenised property does not fluctuate when the size of the sample is increased; the Representative Elementary Volume (REV). Its determination usually comes at the cost of a large number of simulations, making it overall a computationally expensive process. Therefore, many scientific studies have been dedicated to optimising the process of finding REV. Using statistical numerical methods, it is shown that the fluctuation of the effective property corresponds overall to a cone-like shape convergence. We suggest determining the generic evolution law of the cone of convergence, which can be used to predict the size of the REV and the effective physical property. This study is based on simulations of Stokes flow through idealised microstructures from which the permeability is upscaled. By tracing and plotting the convergence of permeability for multiple samples, the full cone of convergence appears. The cone shows exponential growth and decay, converging towards the effective permeability of the microstructure. By fitting a log-normal distribution on the collected data points, we show that the generic evolution law of the cone of convergence can always be described with two parameters, independently of the porosity. We show that the determined law of the cone also applies to real microstructures, despite the presence of natural heterogeneities. The new method allows us to reduce the computational costs of finding all characteristics related to REV by simulating several subsamples rather than the full-sized sample, unlocking thereby high-resolution samples which are often too computationally expensive. The use of a statistical model provides quantification of the precision level we can obtain on the REV determination.