Fluid flow partitioning between fractures and a permeable rock matrix

Abstract

Field data‐based finite‐element simulations of flow partitioning between fractures and a permeable rock matrix reveal critical fracture aperture values that mark the transition from matrix to fracture dominated flow. For matrix permeabilities of 0.00 1–1 D, the matrix either dominates or contributes significantly to the total flow. The percentage of the flow‐normal cross‐section that is occupied by fractures, Af, strongly influences the fracture‐matrix permeability ratio, above which fractures will dominate flow. This ratio is 102–104 for Af = 10−4–10−3 (mean = 5 × 10−3), but also depends on the proportion of fractures which fully penetrate the representative elementary volume. Fluid‐velocity spectra for the fractured rock have three important characteristics: (1) Darcy velocity is only poorly correlated with permeability, (2) flow velocities have characteristic values, even if fracture‐length frequency relations are self similar, and (3) fracture and matrix velocities overlap.

The impact of different aperture distribution models and critical stress criteria on equivalent permeability in fractured rocks

“…The transition between the latter two regimes is not analyzed in our study, but we do identify when fractures contribute significantly to permeability (Figures 9a and 9b). Our studied pavements are significantly larger than the 44 m 2 pavement model studied in Matthäi and Belayneh [2004]. We find the lowest ratios for the aperture-frequency and Barton-Bandis methods with a matrix permeability of 100 mD to 1 darcy, with a k f /k m ratio between 10 2 and 10 3 .…”

“…These models fall in the third category as defined by Matthäi and Belayneh [2004]. The ratio for power law aperture-frequency scaling does not correspond to the predicted flow domains, as the contribution of these apertures to permeability is low, irrespective of matrix permeability.…”

“…In all models, increasing matrix permeability decreases the relative contribution of fractures, although the matrix-fracture contrast depends on the used aperture method. Matthäi and Belayneh [2004] used a similar approach to identify three characteristic flow regimes, defined by the ratio between intrinsic fracture permeability k f and matrix permeability k m , based on a 44 m 2 pavement model with two sets of natural fractures, each with a constant but different aperture, and fracture porosities similar to the values in this study. For a k f /k m ratio smaller than 10 2 they found that fractures have a negligible impact on permeability.…”

“…Fracture aperture is less commonly analyzed, resulting in large uncertainties in fluid flow modeling, as small variations in aperture have large implications on rock flow [de Dreuzy et al, 2001[de Dreuzy et al, , 2002[de Dreuzy et al, , 2012Matthäi and Belayneh, 2004;Klimczak et al, 2010;Schultz et al, 2013] and transport properties [Nick et al, 2011]. Borehole imaging tools provide an estimate of aperture [Luthi and Souhaite, 1990], although with some uncertainty, especially in the absence of accurate calibration [Makel, 2007;Ponziani et al, 2015].…”

“…The aim of this study is to compare the different aperture models and their impact on equivalent permeability in naturally fractured reservoirs, using equivalent permeability models [e.g., Matthäi and Belayneh, 2004]. We consider different critical stress criteria to predict which fractures will contribute to fluid flow under in situ stress conditions.…”