Scale-up of reactive processes in heterogeneous media
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Physical and chemical heterogeneities cause the porous media transport parameters to vary with scale, and between these two types of heterogeneities geological heterogeneity is considered to be the most important source of scale-dependence of transport parameters. Subsurface processes associated with chemical alterations result in changing reservoir properties with interlinked spatial and temporal scale, and there is uncertainty in the evolution of those properties and the chemical processes. This dissertation provides a framework and procedures to quantify the spatiotemporal scaling characteristics of reservoir attributes and transport processes in heterogeneous media accounting for chemical alterations in the reservoir. Conventional flow scaling groups were used to assess their applicability in scaling of recovery and Mixing Zone Length (MZL) in presence of chemical reactivity and permeability heterogeneity through numerical simulations of CO₂ injection. It was found out that these scaling groups are not adequate enough to capture the scaling of recovery and transport parameters in the combined presence of chemical reactivity and physical heterogeneity. In this illustrative example, MZL was investigated as a function of spatial scale, temporal scale, multi-scale heterogeneity, and chemical reactivity; key conclusions are that 1) the scaling characteristics of MZL distinctly differ for low permeability and high permeability media, 2) heterogeneous media with spatial arrangements of both high and low permeability regions exhibit scaling characteristics of both high and low permeability media, 3) reactions affect scaling characteristics of MZL in heterogeneous media, 4) a simple rescaling can combine various MZL curves by merging them into a single MZL curve irrespective of the correlation length of heterogeneity, and 5) estimates of MZL (and consequently predictions of oil recovery) will fluctuate corresponding to displacements in a permeable medium whose lateral length is smaller than the correlation length of geological formation. We illustrate and extend the procedure of estimating Representative Elementary Volume (REV) to include temporal scale by coupling it with spatial scale. The current practice 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. The proposed semi-analytical technique to scale-up in both space and time provides guidance for selection of spatial and temporal discretizations that takes into account the uncertainties due to sub-processes. Finally, a probabilistic particle tracking (PT) approach is proposed to scale-up flow and transport of diffusion-reaction (DR) processes while addressing multi-scale and multi-physics nature of DR mechanisms and also maintaining consistent reservoir heterogeneity at different levels of scales. This multi-scale modeling uses a hierarchical approach which is based on passing the macroscopic subsurface heterogeneity down to the finer scales and then returning more accurate reactive flow response. This PT method can quantify the impact of reservoir heterogeneity and its uncertainties on statistical properties such as reaction surface area and MZL, at various scales.