There is growing interest in using advanced imaging techniques to describe the complex pore-space of natural rocks at resolutions that allow for quantitative assessment of the flow and transport behaviors in these complex media. Here, we focus on representations of the complex pore-space obtained from X-ray microtomography and the subsequent use of such 'pore-scale' representations to characterize the overall porosity and permeability of the rock sample. Specifically, we analyze the impact of sub-resolution porosity on the macroscopic (Darcy scale) flow properties of the rock. The pore structure of a rock sample is obtained using high-resolution X-ray microtomography (3.16 3 µm 3 /voxel). Image analysis of the Berea sandstone sample indicates that about 2 % of the connected porosity lies below the resolution of the instrument. We employ a Darcy-Brinkman approach, in which a Darcy model is used for the sub-resolution porosity, and the Stokes equation is used to describe the flow in the fully resolved pore-space. We compare the Darcy-Brinkman numerical simulations with core flooding experiments, and we show that proper interpretation of the sub-resolution porosity can be essential in characterizing the overall permeability of natural porous media.
A multi-scale synchrotron-based X-ray microtomographic dataset of residually trapped air after gravity-driven brine imbibition was acquired for three samples with differing pore topologies and morphologies;image volumes were reconstructed with voxel sizes from 4.44 µm down to 0.64 µm. Capillary pressure distributionsamong the population of trapped ganglia were investigated by calculating interfacial curvature in order to assess the potential for remobilization of residually-trapped non-wetting ganglia due to differences in capillary pressure presented by neighbor ganglia. For each sample, sintered glass beads, Boise sandstone and Fontainebleau sandstone, sub-volumes with different voxel sizes were analyzed to quantify air/brine interfaces and interfacial curvatures and investigate the effect of image resolution on both fluid phase identification and curvature estimates. Results show that the method developed for interfacial curvature estimation leads to reliable capillary pressure estimates for gas ganglia. Higher resolution images increase confidence in curvature calculations, especially for the sandstone samples that display smaller gas-brine interfaces which are then represented by a higher number of voxels when imaged with a micron or sub-micron voxels size. The analysis of subvolumes from the Boise and Fontainebleau dataset highlights the presence of a residuallytrapped gas phase consisting of ganglia located in one or few pores and presenting significantly different capillary pressures, especially in the case of Fontainebleau sandstone. As a result, Ostwald ripening could occur, leading to gas transfer from ganglia with higher capillary pressure to surrounding ganglia with lower capillary pressures. More generally, at the pore-scale, most gas ganglia do present similar capillary pressures and Ostwald ripening would then not represent a major mechanism for residually-trapped gas transfer and remobilization.
In a saturated solution with dispersed clusters of a second phase, the mechanism by which the larger clusters grow at the expense of the smaller ones is called Ostwald ripening. Although the mechanism is well understood in situations where multiple clusters of gas exist in a liquid solution, evolution is much more complicated to predict when the two phases interact with a solid matrix, since the solid plays a significant role in determining the shape of the interface. In this paper, we study capillary dominated regimes in porous media where the driving force is inter-cluster diffusion. By decomposing the Ostwald ripening mechanism into two processes that operate on different time scales – the diffusion of solute gas in the liquid and the readjustment of the shape of the gas–liquid interface to accommodate a change in mass – we develop a sequential algorithm to solve for the evolution of systems with multiple gas ganglia. In the absence of a solid matrix, thermodynamic equilibrium is reached when all of the gas phase aggregates to form one large bubble. In porous media on the other hand, we find that ripening can lead to equilibrium situations with multiple disconnected ganglia, and that evolution is highly dependent on initial conditions and the structure of the solid matrix. The fundamental difference between the two cases is in the relationship between mass and capillary pressure.
The dissolution of carbonate rocks usually leads to both porosity (φ) and permeability (k) increase. We present experimental evidences and physical-based models of positive and anti-correlated dynamics of k and φ observed during dissolution experiments of carbonate rocks. We study the way the rate of change of φ and k is controlled by the degree of undersaturation of the percolating solution for two different types of carbonate rocks. We document the occurrence of an anti-correlated k − φ trend when the flowing fluid (deionized water) has a weak capacity of dissolution. A positive correlation is found when CO 2 is added to the deionized water to increase the potential dissolution rate. Detailed analyses of the microstructures of the rock performed by X-ray microtomography reveal that low dissolution rate favors detachment of solid particles and their subsequent accumulation at the pore-throat inlet. Particles are detached from the rock matrix due to the differential dissolution rate of the indurated grains and the microporous cement. We then propose a simple phenomenological model to interpret the effect of the pore-throat clogging by the accumulation of partially dissolved carbonate particles. We conjecture that permeability is controlled by the decrease of the effective hydraulic radius and the increase of the tortuosity due to partial and localized obstruction of the pore network. Conversely, increasing the level of undersaturation of the flowing solution leads to an augmented potential of dissolving most of the transported particles before they reach the throats. In this case, both k and φ increase and display power-law correlations.
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