Multi-scale approach to invasion percolation of rock fracture networks

Abstract

A multi-scale scheme for the invasion percolation of rock fracture networks with heterogeneous fracture aperture fields is proposed. Inside fractures, fluid transport is calculated on the finest scale and found to be localized in channels as a consequence of the aperture field. The channel network is characterized and reduced to a vectorized artificial channel network (ACN). Different realizations of ACNs are used to systematically calculate efficient apertures for fluid transport inside differently sized fractures as well as fracture intersection and entry properties. Typical situations in fracture networks are parameterized by fracture inclination, flow path length along the fracture and intersection lengths in the entrance and outlet zones of fractures. Using these scaling relations obtained from the finer scales, we simulate the invasion process of immiscible fluids into saturated discrete fracture networks, which were studied in previous works.

Multiscale fracture network characterization and impact on flow: A case study on the Latemar carbonate platform

“…Fracture to matrix flow ratios ( q f / q m ) [ Matthäi and Nick , ] averaged over the domain are 141 in x and 268 in y direction for the well‐connected DetflowC_DWC model and are 9.7 and 14.3 for the less connected DetflowC_DLC . The matrix contribution is less than 1% for the well‐connected representation (DWC), and a similar result could probably be reached with a hydraulic channel network including artificial channels for flow through the matrix between dead‐ending fractures [ Ebrahimi et al ., ]. However, q f / q m in the less‐connected representation (DLC) reach ratios below 10 (>10% matrix contribution) for the eastern portion of the domain, where despite a well‐spaced series of E‐W fractures, no cross connectivity is achieved (Figures c and ).…”

“…The effect on permeability for differences in connectivity between the DWC and DLC networks does signify the degree to which flow channelizes into the matrix at a disconnected fracture tip and over what distance before reaching an adjacent well‐oriented fracture. Such matrix channels between disconnected fractures [ Ebrahimi et al ., ] strongly reduce the effective permeability particularly in the direction of the disconnected fracture set (i.e., roughly aligning to the x axis). The denoted topological differences between the domains (Figure ) stem from nuanced differences in fracture network development under influence of causative stress field and mechanical properties across the platform.…”

“…Variations in fracture aperture, including their morphology, asperities, and cementation, certainly have a relevant effect on fracture permeability. Models that account for nonparallel fracture walls show in 3‐D how flow is localized due to local heterogeneities in aperture and fracture intersection streaks and controlled by mechanical closure [ Brown , ; Dijk et al ., ; Nick et al ., ; de Dreuzy et al ., ; Ebrahimi et al ., ]. At the field scale, parallel‐plate fracture apertures may be assigned as function of length [ Bonnet et al ., ; Ortega et al ., ], which may still represent the average volumetric flow through a rough‐walled fracture reasonably well [ Dijk et al ., ; Nick et al ., ].…”

“…As coupling of aperture to in situ stresses falls beyond scope of this study, we chose for uniform apertures to illustrate most clearly the role of natural fracture network geometry at a 10 1 –10 3 m devoid of other relevant factors. Such mesoscale network estimates of the effective permeability can change up to 1 order of magnitude because of aperture heterogeneities alone [ Matthäi and Belayneh , ; de Dreuzy et al ., ; Ebrahimi et al ., ], although the impact of different fracture apertures should be addressed in future research.…”

Investigation of multi-scale gas transport behavior in organic-rich shale

“…It has been demonstrated that gas slippage or Knudsen diffusion is critical for investigating gas flow in matrix shale, no matter for correcting laboratory permeability or analyzing field data (Javadpour et al, 2007;Freeman, 2010;Schepers et al, 2009;Wang et al, 2009). However, the study of non-linear flow theory is still in the start stage, which is mostly based on theoretical researches (Dreuzy et al, 2012;Wang et al, 2013;Ebrahimi et al, 2014). The most important theory in the early age is the Klinkenberg model (Klinkenberg, 1941).…”