Effective transmissivity of two-dimensional fracture networks

Zimmerman, Robert W.; Bodvarsson, G.S.

doi:10.2172/87080

Cited by 15 publications

(17 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The equivalent aperture for each fracture population is calculated using the generalized f ‐mean function given by

{\overset{true¯}{b}}_{h}^{3} = f^{- 1} ((), \sum_{i = 1}^{n} w_{i} f (b_{normalh i}^{3}))

where n is the total number of fractures, w i = l i / l tot is the length‐based weight of the i th fracture, b h i is the hydraulic aperture of the i th fracture, and f = x , 1/ x , or ln( x ) corresponds to arithmetic, harmonic, or geometric mean, respectively. Arithmetic mean treats fractures as connected in parallel and tends to give an upper bound, while harmonic mean assumes fractures as connected in series and tends to provide a lower bound [ de Marsily , ; Zimmerman and Bodvarsson , ; Ronayne and Gorelick , ; Leung and Zimmerman , ]. Permeability of 2D heterogeneous media is more likely to be governed by the geometric mean of local fracture permeability that follows a lognormal or power law distribution [ de Marsily , ; de Dreuzy et al ., ].…”

Section: Multiscale Growth Network With Stress‐ and Scale‐dependent mentioning

confidence: 99%

A new approach to upscaling fracture network models while preserving geostatistical and geomechanical characteristics

et al. 2015

View full text Add to dashboard Cite

A new approach to upscaling two-dimensional fracture network models is proposed for preserving geostatistical and geomechanical characteristics of a smaller-scale "source" fracture pattern. First, the scaling properties of an outcrop system are examined in terms of spatial organization, lengths, connectivity, and normal/shear displacements using fractal geometry and power law relations. The fracture pattern is observed to be nonfractal with the fractal dimension D ≈ 2, while its length distribution tends to follow a power law with the exponent 2 < a < 3. To introduce a realistic distribution of fracture aperture and shear displacement, a geomechanical model using the combined finite-discrete element method captures the response of a fractured rock sample with a domain size L = 2 m under in situ stresses. Next, a novel scheme accommodating discrete-time random walks in recursive self-referencing lattices is developed to nucleate and propagate fractures together with their stress-and scale-dependent attributes into larger domains of up to 54 m × 54 m. The advantages of this approach include preserving the nonplanarity of natural cracks, capturing the existence of long fractures, retaining the realism of variable apertures, and respecting the stress dependency of displacement-length correlations. Hydraulic behavior of multiscale growth realizations is modeled by single-phase flow simulation, where distinct permeability scaling trends are observed for different geomechanical scenarios. A transition zone is identified where flow structure shifts from extremely channeled to distributed as the network scale increases. The results of this paper have implications for upscaling network characteristics for reservoir simulation.

show abstract

“…The equivalent aperture for each fracture population is calculated using the generalized f ‐mean function given by

{\overset{true¯}{b}}_{h}^{3} = f^{- 1} ((), \sum_{i = 1}^{n} w_{i} f (b_{normalh i}^{3}))

Section: Multiscale Growth Network With Stress‐ and Scale‐dependent mentioning

confidence: 99%

A new approach to upscaling fracture network models while preserving geostatistical and geomechanical characteristics

et al. 2015

View full text Add to dashboard Cite

show abstract

“…The lattice models views the porous medium as a series of capillary networks superimposed on each other with different radius and density [16][17][18]. Discrete fracture networks also provide a solution to represent the effective conductivity of fractured rock at a grid-block scale [19]. Porous medium models which include some form of heterogeneity associated with a number of intrinsic characteristics (permeability, porosity) also seems to provide a solution to explain such behaviour [20].…”

Section: Introductionmentioning

confidence: 99%

Modelling of localised gas preferential pathways in claystone

Gérard

Harrington

Charlier

et al. 2014

International Journal of Rock Mechanics and Mining Sciences

View full text Add to dashboard Cite

A long-term injection gas test on initially saturated claystone samples under isotropic confining pressure is modelled in a 2D hydro-mechanical framework, which includes the hydraulic anisotropy. Evidences of localised pathways through the sample have been observed experimentally, which are difficult to reconcile with standard 2 phase flow models.The presence of an embedded pre-existing fracture is included in a continuum finite element model. A hydro-mechanical coupling between the fracture aperture, permeability and the retention properties along the fracture is included in the model. Thanks to the increase in permeability and the decrease of the air entry pressure induced by the rise in fluid pressure at constant mean total stress, the model provides a good agreement with the experimental observations. The discussion offers additional insight into the fluid flow mechanisms into the sample and the processes involved in the development of localised gas pathways. This study allows conclusions to be drawn regarding the performance of the model and its practical limitations.

show abstract

“…Bourbiaux et al (1998) also used the actual 3-D fracture network and, by applying a pressure gradient in each direction, calculated the equivalent FNP from incompressible steady-state flow. In addition to these numerical ones, semi-analytical approaches were also introduced (Hestir and Long 1990;Zimmerman and Bodvarsson 1996). In highly fractured and complex reservoirs, due to the higher number of required numerical nodes for computations, numerical approaches might demand relatively heavy computational efforts.…”

Section: Introductionmentioning

confidence: 99%

Equivalent Fracture Network Permeability of Multilayer-Complex Naturally Fractured Reservoirs

Jafari

Babadagli

2011

Transp Porous Med

View full text Add to dashboard Cite

Modeling naturally fractured reservoirs (NFRs) requires an accurate representation of fracture network permeability (FNP). Conventionally, logs, cores, seismic, and pressure transient tests are used as a data base for this. Our previous attempts showed that a strong correlation exists between the fractal parameters of 2-D fracture networks and their permeability (Jafari and Babadagli, SPE 113618, Western Regional and Pacific Section AAPG joint meeting, 2008; Jafari and Babadagli, SPE Reserv Eval Eng 12(3): 455-469, 2009a). We also showed that 1-D well (cores-logs) and 3-D reservoir data (well test) may not be sufficient in FNP mapping and that 2-D (outcrop) characteristics are needed (Jafari and Babadagli, SPE 124077, SPE/EAGE reservoir characterization and simulation conference, 2009b). This paper is an extension of those studies, where only 2-D (single-layer, uniform fracture characteristics in z direction) representations were used. In this paper, we considered a more complex and realistic 3-D network system. Two-dimensional random fractures with known fractal and statistical characteristics were distributed in the x-and y directions. A variation of fracture network characteristics in the z direction was presented by a multilayer system representing three different facieses with different fracture properties. Wells were placed in different locations of the model to collect 1-D fracture density and pressure transient data. In addition, five different fractal and statistical properties of the network of each layer were measured. The equivalent FNP was calculated using a commercial software package as the base case. Using available 1-D, 2-D, and 3-D data, multivariable regression analyses were performed to obtain equivalent FNP correlations for many different fracture network realizations. The derived equations were validated against a new set of synthetic fracture networks, and the conditions at which 1-D, 2-D and 3-D data are sufficient to map FNP were determined. The importance of the inclusion of each data type, i.e., 1-D, 2-D and 3-D, in the correlations was discussed. It was shown that using only 3-D data are insufficient This article is the revised and improved version of SPE 132431 presented at 123 340 A. Jafari, T. Babadagli to predict the FNP due to wide spatial heterogeneity of the fracture properties in the reservoir, which cannot be captured from single-well tests. Incorporating all types of data (1-D, 2-D, and 3-D) would result in better prediction. Also, it is recommended that the 2-D data of the most conductive layer in reservoir, which has longer fractures with a higher density, should be incorporated in the correlations.

show abstract

Effective transmissivity of two-dimensional fracture networks

Cited by 15 publications

References 10 publications

A new approach to upscaling fracture network models while preserving geostatistical and geomechanical characteristics

A new approach to upscaling fracture network models while preserving geostatistical and geomechanical characteristics

Modelling of localised gas preferential pathways in claystone

Equivalent Fracture Network Permeability of Multilayer-Complex Naturally Fractured Reservoirs

Contact Info

Product

Resources

About