Performance prediction of reactive processes such as those associated with injection of chemicals that react with rock and fluids require accurate models of the processes. Frequently, these processes are studied at laboratory scale and modeling them at the field scale entails scale-up of laboratory observations taking into account the variability of parameters. Current practice of scale-up is to perform spatial averaging of attributes and account for residual variability by calibration and history matching. This results in poor predictions of future reservoir performance. In this paper we scale-up these reactive transport processes considering both the spatial and temporal characteristics of these processes.
The first part of the paper investigates spatiotemporal scale-up of dispersivity with field heterogeneity and reactivity of CO2 injection through numerical simulations. Transport processes in reservoir models at three different length scales are simulated using homogeneous and heterogeneous permeability models. The variation in dispersivity with spatiotemporal scale is plotted and various conclusions are deduced regarding the impact of the permeability and conservative/reactive transport. In the second part of the paper, a semi-analytical model for spatiotemporal covariance describing the reaction-dispersion process is used to derive the Representative Elementary Volume (REV) of concentration in combined space and time. This spatiotemporal covariance is used to compute the variance of mean concentration. The stabilization of this variance is indicative of the REV.
Key results of this work indicate that scaling characteristics of dispersivity distinctly differ for low permeability and high permeability media. Heterogeneous media exhibit scaling characteristics for both high and low permeability media. Another important result is that reactions affect scaling characteristics of dispersivity at only small and intermediate scales. The semi-analytical models for scale-up of reaction-dispersion processes indicate that purely spatial or temporal investigation does not produce accurate estimate of REV. However, when scaling is investigated in a spatiotemporal setting, then the REV can be defined fairly accurately.
These results can be important for designing laboratory experiments and to predict scaled-up field response. Additionally, results also demonstrate that spatiotemporal numerical discretization of recovery processes should be done appropriately after finding the combined spatiotemporal REV scale of the process.