Sub-volume analysis of pore-network simulations: Determining the asymptotic longitudinal dispersion coefficient

Abstract

This work introduces a new method called sub-volume analysis (SVA) to calculate macroscopic model parameters with their uncertainties from pore-scale simulations. We apply the SVA to calculate the longitudinal dispersion coefficient of the advection–dispersion model (ADM) from continuous tracer injection problems simulated with pore-network models. The SVA application presented here allows for verifying if a given network has enough length to reach an asymptotic dispersion regime where ADM applies. We tested the method using statistically constructed pore networks and pore networks built by joining several network units extracted from Berea sandstone images. There is complete agreement within the error margins for the asymptotic longitudinal dispersion coefficients obtained with the SVA and those obtained from breakthrough curve fitting. We also showed that the SVA gives more accurate results than those from the breakthrough curve fitting and much more accurate results than those from the method of spatial moments. Unlike the other methods, the SVA estimates the parameter uncertainty using a single pore-network realization.