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Modified Reinshaw and Pollard Criteria for a Non-Orthogonal Cohesive Natural Interface Intersected by an Induced Fracture

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Abstract

Hydraulic fracturing is a widely used stimulation method to enhance the productivity of unconventional resources. The hydraulic fracturing operation in naturally fractured reservoirs or when it is expected to intersect a natural interface, such as an interbed is subjected to complexity. The induced fracture may cross, get arrested by or open the fracture plane upon its arrival at the natural interface. Besides other parameters, this depends on the natural interface mechanical properties, including the cohesion and friction angle of the interface. Several analytical criteria have been developed to predict the interaction mechanism of induced and natural fracture. While these analytical solutions have been developed based on some simplified assumptions, they can provide a good understanding of the effect of different parameters. The first part of this paper summarizes the available criteria for interaction of hydraulic and natural fractures. Important factors will be mentioned and illustrations will be given to present the limitations of each criterion. The second part discusses the development and validation of an extension to Renshaw and Pollard criterion in the form a single analytical formula for non-orthogonal cohesive fracture. This includes the contribution of the strength of the in-fill material to the bonding of the two sides of a fracture, hence its effect on the interaction mechanism. The proposed criterion was validated using published laboratory data. Finally, a methodology is proposed to help the design of interaction experiments in the laboratory, which can also be used for prediction of interaction mode in numerical simulations.

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Abbreviations

σ v :

Vertical in situ stress

σ HMax :

Maximum horizontal stress

σ hMin :

Minimum horizontal stress

θ :

Angle of approach

τ :

Shear stress acting on the plane of the natural interface

σ n :

Normal stress acting on the plane of the natural interface as a result of in situ stresses

T o :

Rock tensile strength

σ T :

Sum of stress acting parallel to the natural fracture as a result of in situ stresses

b :

Coefficient that can be calculated from Eq. 3

c :

Length of slippage zone

l :

Half-length of open section of the fracture

μ f :

Friction coefficient

x 0 :

Location of the point at which re-initiation will occur

v(x 0):

Coefficient that can be calculated from Eq. 5

P n :

Overpressure or net pressure

W&T:

Warpinski and Teufel

τ 0 :

Shear strength of the natural fracture plane

R&P:

Renshaw and Pollard

σ τ′ :

Total shear stress applied on the plane of the natural interface

σ H′ :

Total normal stress applied on the plane of the natural interface

μ f′ :

Apparent friction coefficient

μ f″ :

Total friction coefficient

K IC :

Mode I rock fracture toughness

r c (±π/2):

Critical distance from the intersection point where the stresses on the orthogonal (θ = ±π/2) natural interface is maximized

α :

A coefficient that was described in Eq. 26

P resis :

Re-initiation resistance pressure

P fluid :

Fracturing fluid pressure

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Acknowledgments

V.R. acknowledges the financial support from the Australian research Council linkage project LP 120200797, Australian Worldwide Exploration (AWE) limited and Norwest Energy NL Companies. The authors appreciate the valuable technical input from Dr. Rob Jeffrey.

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  1. Department of Petroleum Engineering, Curtin University, 26 Dick Perry Ave., Kensington, WA, 6151, Australia

    M. Sarmadivaleh & V. Rasouli

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  1. M. Sarmadivaleh
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  2. V. Rasouli
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Correspondence to M. Sarmadivaleh.

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Sarmadivaleh, M., Rasouli, V. Modified Reinshaw and Pollard Criteria for a Non-Orthogonal Cohesive Natural Interface Intersected by an Induced Fracture. Rock Mech Rock Eng 47, 2107–2115 (2014). https://doi.org/10.1007/s00603-013-0509-1

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