Éditeur(s) : HAL CCSD Springer Verlag (Germany) Springer Verlag
Résumé : Direct numerical simulations of flow through two millimeter-scale rock samples of limestone and sandstone are performed using three diverse fluid dynamic simulators. The resulting steady-state velocity fields are compared in terms of the associated empirical probability density functions (PDFs) and key statistics of the velocity fields. The pore space geometry of each sample is imaged at 5.06−μm voxel size resolution using X-ray microtomography. The samples offer contrasting characteristics in terms of total connected porosity (about 0.31 for the limestone and 0.07 for the sandstone) and are typical of several applications in hydrogeology and petroleum engineering. The three-dimensional fluid velocity fields within the explicit pore spaces are simulated using ANSYS® FLUENT® ANSYS Inc. (2009), EULAG Prusa et al. (Comput. Fluids 37, 1193–1207 2008), and SSTOKES Sarkar et al. (2002). These computational approaches are highly disperse in terms of algorithmic complexity, differ in terms of their governing equations, the adopted numerical methodologies, the enforcement of internal no-slip boundary conditions at the fluid-solid interface, and the computational mesh structure. As metrics of comparison to probe in a statistical sense the internal similarities/differences across sample populations of velocities obtained through the computational systems, we consider (i) integral quantities, such as the Darcy flux and (ii) main statistical moments of local velocity distributions including local correlations between velocity fields. Comparison of simulation results indicates that mutually consistent estimates of the state of flow are obtained in the analyzed samples of natural pore spaces despite the considerable differences associated with the three computational approaches. We note that in the higher porosity limestone sample, the structures of the velocity fields obtained using ANSYS FLUENT and EULAG are more alike than either compared against the results obtained using SSTOKES. In the low-porosity sample, the structures of the velocity fields obtained by EULAG and SSTOKES are more similar than either is to the fields obtained using ANSYS FLUENT. With respect to macroscopic quantities, ANSYS FLUENT and SSTOKES provide similar results in terms of the average vertical velocity for both of the complex microscale geometries considered, while EULAG tends to render the largest velocity values. The influence of the pore space structure on fluid velocity field characteristics is also discussed.
ISSN: 1420-0597

hal-01174152
https://hal.archives-ouvertes.fr/hal-01174152
DOI : 10.1007/s10596-015-9486-7

Éditeur(s) : HAL CCSD Springer Verlag (Germany) Springer Verlag
Résumé : International audience
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 CO2 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.
ISSN: 0169-3913

hal-01174145
https://hal.archives-ouvertes.fr/hal-01174145
DOI : 10.1007/s11242-015-0456-2