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Brittleness Index: From Conventional to Hydraulic Fracturing Energy Model

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Abstract

The success of a hydraulic fracturing (HF) operation is strongly dependent on brittleness of the formation. Several models based on mechanical testing, mineral composition, and sonic log data have been proposed to quantify the brittleness of formations known as brittleness index (BI). The limitations of these conventional BI models, in particular, the consistency and applicability at field scale with the complex in situ conditions are poorly understood. We therefore developed a novel BI model based on the hydraulic fracture propagation energy (HFPE) criterion. A set of hydraulic fracturing (HF) experiments was conducted on samples with different mineralogy at true tri-axial stress conditions for model definition, i.e., the scaling law was employed to ensure that hydraulic fracture propagation resembles the field conditions. To assess the performance of the proposed BI model in predicting the rock fracability, the obtained results of the model on different samples were compared with conventional models. It was shown that the predictions of the conventional BI models are predominantly related to the failure characteristics of the rock rather than its fracability. We showed that such BI models cannot assess the hydraulic fracturing feasibility where complex failure mechanisms (i.e., splitting, shear, friction, etc.), geological condition (i.e., in situ stress) and operational factors (i.e., injection rate, fluid viscosity, etc.) are involved. The new proposed BI model, however, successfully predicted the fracability of different rock types.

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Abbreviations

BI:

Brittleness index

BIs:

Brittleness indices

HF:

Hydraulic fracturing

TTSC :

True tri-axial stress cell

UCS :

Uniaxial compressive strength

TCS :

Tri-axial compressive strength

BTT :

Brazilian tensile test

SCB :

Semi-circular bend

S1–4 :

Type of sample (1–4)

BHP:

Bottom hole pressure

HFPE:

Hydraulic fracture propagation energy

E :

Young’s modulus

v :

Poisson’s ratio

Ф :

Internal friction angle

σ T :

Tensile strength

K IC :

Fracture toughness

ε elastic :

Elastic strain

ε total :

Total strain

σ v :

Vertical stress

σ H :

Maximum horizontal stress

σ h :

Minimum horizontal stress

\(\emptyset\) :

Porosity

μ :

Viscosity

T :

Temperature

U s :

Elastic potential energy

U y :

Surface energy

U p :

Plastic deformation energy

E I :

Injection energy

ΔW :

Change of elastic potential energy

E HF :

The energy required for hydraulic fracture propagation

E G :

The energy required to create new fracture faces

E d :

Aseismic deformation energy according to fracture opening

E d (Ductile) :

Aseismic deformation energy according to fracture opening in ideally ductile rock

E d (Semi) :

Aseismic deformation energy according to fracture opening in semi-brittle rock

I :

Additional energy loss

I v :

Viscous dissipation energy

I l :

Fluid leak-off energy

E AES :

Seismic dissipated energy

E f :

Dissipated energy caused by friction of microshear plane

E H :

Dissipated energy caused by new surface creation of microshear failure

E R :

Dissipated energy through ultrasonic waves

Q(t):

Fluid injection rate

P b :

Breakdown pressure

P e :

BHP pressure when hydraulic fracture reaches the boundary

P(t):

Variable BHP with time during fracture propagation

t b :

Time of breakdown

t f :

Time at end of hydraulic fracture propagation

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Authors and Affiliations

  1. School of WASM: Minerals, Energy and Chemical Engineering, Curtin University, 26 Dick Perry Ave, Kensington, WA, 6151, Australia

    Runhua Feng, Ali Rezagholilou & Mohammad Sarmadivaleh

  2. The Lyell Centre, Heriot-Watt University, Edinburgh, EH14 4AS, Scotland, UK

    Yihuai Zhang

  3. School of Minerals and Energy Resources Engineering, UNSW Australia, Kensington, Sydney, 2052, Australia

    Hamid Roshan

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  1. Runhua Feng
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  2. Yihuai Zhang
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  5. Mohammad Sarmadivaleh
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Correspondence to Runhua Feng.

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Feng, R., Zhang, Y., Rezagholilou, A. et al. Brittleness Index: From Conventional to Hydraulic Fracturing Energy Model. Rock Mech Rock Eng 53, 739–753 (2020). https://doi.org/10.1007/s00603-019-01942-1

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