Pore Space Connectivity and the Transport Properties of Rocks

Abstract

-Pore connectivity is likely one of the most important factors affecting the permeability of reservoir rocks. Furthermore, connectivity effects are not restricted to materials approaching a percolation transition but can continuously and gradually occur in rocks undergoing geological processes such as mechanical and chemical diagenesis. In this study, we compiled sets of published measurements of porosity, permeability and formation factor, performed in samples of unconsolidated granular aggregates, in which connectivity does not change, and in two other materials, sintered glass beads and Fontainebleau sandstone, in which connectivity does change. We compared these data to the predictions of a Kozeny-Carman model of permeability, which does not account for variations in connectivity, and to those of Bernabé et al. (2010Bernabé et al. ( , 2011 ]. Both models agreed equally well with experimental data obtained in unconsolidated granular media. But, in the other materials, especially in the low porosity samples that had undergone the greatest amount of sintering or diagenesis, only Bernabé et al. model matched the experimental data satisfactorily. In comparison, predictions of the Kozeny-Carman model differed by orders of magnitude. The advantage of the Bernabé et al. model was its ability to account for a continuous, gradual reduction in pore connectivity during sintering or diagenesis. Although we can only speculate at this juncture about the mechanisms responsible for the connectivity reduction, we propose two possible mechanisms, likely to be active at different stages of sintering and diagenesis, and thus allowing the gradual evolution observed experimentally.Résumé -Connectivité de l'espace poreux et propriétés de transport des roches -La connectivité porale est probablement l'un des plus importants facteurs affectant la perméabilité des roches réservoir. En outre, les effets de connectivité ne sont pas limités aux seuls matériaux approchant un seuil de percolation mais peuvent avoir lieu progressivement dans des roches soumises à des processus tels que la diagénèse mécanique ou chimique. Dans cette étude, nous avons compilé plusieurs jeux, préalablement publiés, de mesures de porosité, perméabilité et facteur de formation, obtenues sur des agrégats granulaires non-consolidés, pour lesquels la connectivité ne change pas, ainsi que dans deux autres matériaux, billes de verre frittées et grès de Fontainebleau, pour lesquels elle varie. Nous avons comparé ces données aux prédictions d'un modèle de perméabilité de type Kozeny-Carman, qui ne tient pas compte des variations de connectivité, et à celles du modèle de Bernabé et al. (2010Bernabé et al. ( , 2011

Percolation connectivity, pore size, and gas apparent permeability: Network simulations and comparison to experimental data

“…In the case of liquid permeability, the validity of this generalization was indeed confirmed by comparing the inferred model to experimental rock data [Bernabé et al, 2010[Bernabé et al, , 2011[Bernabé et al, , 2015a. This approach was also successfully applied to other transport properties Bernabé et al, 2015b;Li et al, 2015].…”

“…For example, we argued that the model and data in Figure correspond to two slightly different types of materials. We applied our model to unconsolidated glass beads, while Klinkenberg [] measured k app in consolidated granular media (fritted glass filters and sandstones), which certainly experienced substantial reductions in connectivity and augmentations of pore‐scale heterogeneity (see Bernabé et al [] for an analysis of fritted glass materials and Fontainebleau sandstone). Similarly, the underestimation of the slopes of the k app versus 1/< p > curves shown in Figure can be partially due to our using a slightly overestimated r H value corresponding to idealized pores with circular cross section, which may be a poor representation of the highly complex, cross‐sectional shapes of the pore‐throats in rocks.…”

“…Although pipe networks are not realistic representations of porous rocks, one may reasonably conjecture that universal relationships should be applicable to real porous rocks. In the case of liquid permeability, the validity of this generalization was indeed confirmed by comparing the inferred model to experimental rock data [ Bernabé et al , , , ]. This approach was also successfully applied to other transport properties [ Tang et al , ; Bernabé et al , ; Li et al , ].…”

Passive advection‐dispersion in networks of pipes: Effect of connectivity and relationship to permeability

“…Numerical approximations of the functions C k (σ) and β(σ) were determined by Bernabé et al [2010Bernabé et al [ , 2011 in pipe networks constructed using the same procedures as in the present study. It is worth noting that equation (5) was found to hold satisfactorily in relatively simple porous materials such as unconsolidated granular aggregates, sintered glass beads, and clay free sandstones [Bernabé et al, 2015]. In agreement with equation (5), the series of simulations described in section 4.3 (performed using variable R and fixed values of (z À z c ), σ and R/l) yielded d<(X i À <X i >) 2 >/ dt = 2D L ∝k m L = 2 (Figure 9) and d<(Y i À <Y i >) 2 >/dt ≈ d<(Z i À <Z i >) 2 >/dt = 2D T ∝k m T = 2 ¼ ffiffi ffi k p (Figure 10).…”

“…The realizations had equal linear dimensions in the three space directions (i.e., overall cubic shape). The SC and FCC networks contained 41,472 branches, while there were 46,656 in the BCC cells.The hydraulic radius, i.e., twice the ratio of the total volume to total surface area of the pipes in the network, is a convenient characteristic length scale controlling permeability (one important advantage is that the hydraulic radius is physically measurable in real porous media; for a more detailed discussion see Bernabé et al [, , ]). In most of the networks investigated here, we fixed the network hydraulic radius R to 40 · 10 −6 m, although values as low as 20 · 10 −6 m and as high as 120 · 10 −6 m were also considered.…”